Sample records for two-dimensional fourier-transforms show

  1. Two-dimensional fourier transform spectrometer

    Energy Technology Data Exchange (ETDEWEB)

    DeFlores, Lauren; Tokmakoff, Andrei


    The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

  2. Two-dimensional fourier transform spectrometer (United States)

    DeFlores, Lauren; Tokmakoff, Andrei


    The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

  3. Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (United States)

    van Agthoven, Maria A.; Barrow, Mark P.; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A.; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B.


    Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules.

  4. Two-dimensional Fourier transform ESR correlation spectroscopy (United States)

    Gorcester, Jeff; Freed, Jack H.


    We describe our pulsed two-dimensional Fourier transform ESR experiment and demonstrate its applicabilty for the double resonance of motionally narrowed nitroxides. Multiple pulse irradiation of the entire nitroxide spectrum enables the correlation of two precessional periods, allowing observation of cross correlations between hyperfine lines introduced by magnetization transfer in the case of a three-pulse experiment (2D ELDOR), or coherence transfer in the case of a two-pulse experiment (COSY). Cross correlations are revealed by the presence of cross peaks which connect the autocorrelation lines appearing along the diagonal ω1=ω2. The amplitudes of these cross peaks are determined by the rates of magnetization transfer in the 2D ELDOR experiment. The density operator theory for the experiment is outlined and applied to the determination of Heisenberg exchange (HE) rates in 2,2,6,6-tetramethyl-4-piperidone-N-oxyl-d15 (PD-tempone) dissolved in toluene-d8. The quantitative accuracy of this experiment is established by comparison with the HE rate measured from the dependence of the spin echo T2 on nitroxide concentration.

  5. Optimal Padding for the Two-Dimensional Fast Fourier Transform (United States)

    Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.


    One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that

  6. Optical imaging process based on two-dimensional Fourier transform for synthetic aperture imaging ladar (United States)

    Sun, Zhiwei; Zhi, Ya'nan; Liu, Liren; Sun, Jianfeng; Zhou, Yu; Hou, Peipei


    The synthetic aperture imaging ladar (SAIL) systems typically generate large amounts of data difficult to compress with digital method. This paper presents an optical SAIL processor based on compensation of quadratic phase of echo in azimuth direction and two dimensional Fourier transform. The optical processor mainly consists of one phase-only liquid crystal spatial modulator(LCSLM) to load the phase data of target echo and one cylindrical lens to compensate the quadratic phase and one spherical lens to fulfill the task of two dimensional Fourier transform. We show the imaging processing result of practical target echo obtained by a synthetic aperture imaging ladar demonstrator. The optical processor is compact and lightweight and could provide inherent parallel and the speed-of-light computing capability, it has a promising application future especially in onboard and satellite borne SAIL systems.

  7. Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance (United States)

    Liang, Zhichun; Crepeau, Richard H.; Freed, Jack H.


    Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

  8. Multifrequency Two-Dimensional Fourier Transform ESR: An X/Ku Band Spectrometer (United States)

    Borbat, Petr P.; Crepeau, Richard H.; Freed, Jack H.


    A two-dimensional Fourier Transform ESR (2D FT ESR) spectrometer operating at 9.25 and 17.35 GHz is described. The Ku-band bridge uses an efficient heterodyne technique wherein 9.25 GHz is the intermediate frequency. At Ku-band the sensitivity is increased by almost an order of magnitude. One may routinely collect a full 2D ELDOR spectrum in less than 20 min for a sample containing 0.5-5 nmol of nitroxide spin-probe in the slow-motional regime. Broad spectral coverage at Ku-band is obtained by use of a bridged loop-gap resonator (BLGR) and of a dielectric ring resonator (DR). It is shown that an even more uniform spectral excitation is obtained by using shorter microwave pulses of about 3 ns duration. The dead-time at Ku-band is just 30-40 ns, yielding an improved SNR in 2D ELDOR spectra of nitroxide spin-probes withT2as short as 20-30 ns. A comparison of 2D ELDOR spectra obtained at 9.25 and 17.35 GHz for spin-labeled phospholipid probes (16PC) in 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG) membrane vesicles showed that both spectra could be satisfactorily simulated using the same set of model parameters even though they are markedly different in appearance. The improved sensitivity and shorter dead-time at Ku-band made it possible to obtain orientation-dependent 2D ELDOR spectra of the Cholestane (CSL) spin-probe in macroscopically aligned lipid bilayers of egg yolk PC using samples containing only 1 mg of lipid and just 5 nmol of spin-probe.


    Energy Technology Data Exchange (ETDEWEB)

    Davis, Benjamin L.; Berrier, Joel C.; Shields, Douglas W.; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S.; Lacy, Claud H. S. [Arkansas Center for Space and Planetary Sciences, 202 Field House, University of Arkansas, Fayetteville, AR 72701 (United States); Puerari, Ivanio [Instituto Nacional de Astrofisica, Optica y Electronica, Calle Luis Enrique Erro 1, 72840 Santa Maria Tonantzintla, Puebla (Mexico)


    A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

  10. Fourier transform two-dimensional fluorescence excitation spectrometer by using tandem Fabry-Pérot interferometer. (United States)

    Anzai, Hiroshi; Joshi, Neeraj Kumar; Fuyuki, Masanori; Wada, Akihide


    A Fourier transform two-dimensional fluorescence excitation spectrometer (FT-2DFES) was developed based on the multiplex technique using a tandem Fabry-Pérot interferometer (tandem FPI). In addition to the advantage of the multiplex technique, the main advantage of the tandem FPI is applicable to the modulation of transition with a large absorption bandwidth (larger than 100 nm) and is thus applicable to the modulation of the excitation of molecules in the condensed phase. As a demonstration of the effectiveness of FT-2DFES, we succeeded in separately observing the fluorescence excitation peaks from a mixed methanol solution of laser dyes (coumarin 480, rhodamine 6G, DCM (4-dicyanomethylene-2-methyl-6-(p-(dimethylamino)styryl)-4H-pyran), and LDS750). Furthermore, the energy transfer from rhodamine 6G to LDS750 was observed.

  11. Measurement of Galactic Logarithmic Spiral Arm Pitch Angle Using Two-Dimensional Fast Fourier Transform Decomposition

    CERN Document Server

    Davis, Benjamin L; Shields, Douglas W; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S; Lacy, Claud H S; Puerari, Ivânio


    A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

  12. Coordinate axes, location of origin, and redundancy for the one and two-dimensional discrete Fourier transform (United States)

    Ioup, G. E.; Ioup, J. W.


    Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.

  13. Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

    National Research Council Canada - National Science Library

    van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O’Connor, Peter B


    ...) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated...

  14. Two-Dimensional Fourier Transform Electronic Spectroscopy of Peridinin and Peridinin Analogs (United States)

    Khosravi, Soroush; Bishop, Michael; Obaid, Razib; Whitelock, Hope; Carroll, Ann Marie; Lafountain, Amy; Frank, Harry; Beck, Warren; Gibson, George; Berrah, Nora


    The peridinin chlorophyll- a protein (PCP) is a light harvesting complex in dinoflagellates that exhibits a carotenoid-to-chlorophyll (Chl) a excitation energy transfer (EET) efficiency of 85-95%. Unlike most light harvesting complexes, where the number of carotenoids is less than Chl, each subunit of PCP contains eight tightly-packed peridinins surrounding two Chl a molecules. The unusual solvent polarity dependence of the lowest excited S1 state of peridinin suggests the presence of an intramolecular charge-transfer (ICT) state. The nature of the ICT state, its coupling to the S1 of peridinin, and whether it enables the high EET efficiency is still unclear. Two-dimensional electronic Fourier transform spectroscopy (2DES) is a powerful method capable of examining these issues. The present work examines the ICT state of peridinin and peridinin analogs that have diminished ICT character. 2DES data adding new insight into the spectral signatures and nature of the ICT state in peridinin will be presented. Funded by the DoE-BES, Grant No. DE-SC0012376.

  15. Determination of grain-size distribution function using two-dimensional Fourier transforms of tone-pulse-encoded images (United States)

    Generazio, E. R.


    Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain-size distribution function from which the mean grain shape, size, and orientation can be obtained.

  16. Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images (United States)

    Generazio, E. R.


    Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

  17. Two-dimensional Fourier transform ESR in the slow-motional and rigid limits: 2D-ELDOR (United States)

    Patyal, Baldev R.; Crepeau, Richard H.; Gamliel, Dan; Freed, Jack H.


    The two-dimensional Fourier transform ESP techniques of stimulated SECSY and 2D-ELDOR are shown to be powerful methods for the study of slow motions for nitroxides. Stimulated SECSY provides magnetization transfer rates, whereas 2D-ELDOR displays how the rotational motions spread the spins out from their initial spectral positions to new spectral positions, as a function of mixing time. The role of nuclear modulation in studies of structure and dynamics is also considered.

  18. Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules (United States)

    Ma, Q.; Boulet, C.; Tipping, R. H.


    The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

  19. Theory of two-dimensional Fourier transform electron spin resonance for ordered and viscous fluids (United States)

    Lee, Sanghyuk; Budil, David E.; Freed, Jack H.


    A comprehensive theory for interpreting two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) experiments that is based on the stochastic Liouville equation is presented. It encompasses the full range of motional rates from fast through very slow motions, and it also provides for microscopic as well as macroscopic molecular ordering. In these respects it is as sophisticated in its treatment of molecular dynamics as the theory currently employed for analyzing cw ESR spectra. The general properties of the pulse propagator superoperator, which describes the microwave pulses in Liouville space, are analyzed in terms of the coherence transfer pathways appropriate for COSY (correlation spectroscopy), SECSY (spin-echo correlation spectroscopy), and 2D-ELDOR (electron-electron double resonance) sequences wherein either the free-induction decay (FID) or echo decay is sampled. Important distinctions are made among the sources of inhomogeneous broadening, which include (a) incomplete spectral averaging in the slow-motional regime, (b) unresolved superhyperfine structure and related sources, and (c) microscopic molecular ordering but macroscopic disorder (MOMD). The differing effects these sources of inhomogeneous broadening have on the two mirror image coherence pathways observed in the dual quadrature 2D experiments, as well as on the auto vs crosspeaks of 2D-ELDOR, is described. The theory is applied to simulate experiments of nitroxide spin labels in complex fluids such as membrane vesicles, where the MOMD model applies and these distinctions are particularly relevant, in order to extract dynamic and ordering parameters. The recovery of homogeneous linewidths from FID-based COSY experiments on complex fluids with significant inhomogeneous broadening is also described. The theory is applied to the ultraslow motional regime, and a simple method is developed to determine rotational rates from the broadening of the autopeaks of the 2D-ELDOR spectra as a

  20. [Apply fourier transform infrared spectra coupled with two-dimensional correlation analysis to study the evolution of humic acids during composting]. (United States)

    Bu, Gui-jun; Yu, Jing; Di, Hui-hui; Luo, Shi-jia; Zhou, Da-zhai; Xiao, Qiang


    The composition and structure of humic acids formed during composting play an important influence on the quality and mature of compost. In order to explore the composition and evolution mechanism, municipal solid wastes were collected to compost and humic and fulvic acids were obtained from these composted municipal solid wastes. Furthermore, fourier transform infrared spectra and two-dimensional correlation analysis were applied to study the composition and transformation of humic and fulvic acids during composting. The results from fourier transform infrared spectra showed that, the composition of humic acids was complex, and several absorbance peaks were observed at 2917-2924, 2844-2852, 2549, 1662, 1622, 1566, 1454, 1398, 1351, 990-1063, 839 and 711 cm(-1). Compared to humic acids, the composition of fulvci acids was simple, and only three peaks were detected at 1725, 1637 and 990 cm(-1). The appearance of these peaks showed that both humic and fulvic acids comprised the benzene originated from lignin and the polysaccharide. In addition, humic acids comprised a large number of aliphatic and protein which were hardly detected in fulvic acids. Aliphatic, polysaccharide, protein and lignin all were degraded during composting, however, the order of degradation was different between humic and fulvci acids. The result from two-dimensional correlation analysis showed that, organic compounds in humic acids were degraded in the following sequence: aliphatic> protein> polysaccharide and lignin, while that in fulvic acids was as following: protein> polysaccharide and aliphatic. A large number of carboxyl, alcohols and ethers were formed during the degradation process, and the carboxyl was transformed into carbonates. It can be concluded that, fourier transform infrared spectra coupled with two-dimensional correlation analysis not only can analyze the function group composition of humic substances, but also can characterize effectively the degradation sequence of these

  1. Towards analytically useful two-dimensional Fourier transform ion cyclotron resonance mass spectrometry. (United States)

    van Agthoven, Maria A; Delsuc, Marc-André; Bodenhausen, Geoffrey; Rolando, Christian


    Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry (MS) achieves high resolution and mass accuracy, allowing the identification of the raw chemical formulae of ions in complex samples. Using ion isolation and fragmentation (MS/MS), we can obtain more structural information, but MS/MS is time- and sample-consuming because each ion must be isolated before fragmentation. In 1987, Pfändler et al. proposed an experiment for 2D FT-ICR MS in order to fragment ions without isolating them and to visualize the fragmentations of complex samples in a single 2D mass spectrum, like 2D NMR spectroscopy. Because of limitations of electronics and computers, few studies have been conducted with this technique. The improvement of modern computers and the use of digital electronics for FT-ICR hardware now make it possible to acquire 2D mass spectra over a broad mass range. The original experiments used in-cell collision-induced dissociation, which caused a loss of resolution. Gas-free fragmentation modes such as infrared multiphoton dissociation and electron capture dissociation allow one to measure high-resolution 2D mass spectra. Consequently, there is renewed interest to develop 2D FT-ICR MS into an efficient analytical method. Improvements introduced in 2D NMR spectroscopy can also be transposed to 2D FT-ICR MS. We describe the history of 2D FT-ICR MS, introduce recent improvements, and present analytical applications to map the fragmentation of peptides. Finally, we provide a glossary which defines a few keywords for the 2D FT-ICR MS field.

  2. Design and implementation in VHDL code of the two-dimensional fast Fourier transform for frequency filtering, convolution and correlation operations

    Energy Technology Data Exchange (ETDEWEB)

    Vilardy, Juan M; Giacometto, F; Torres, C O; Mattos, L, E-mail: [Laboratorio de Optica e Informatica, Universidad Popular del Cesar, Sede balneario Hurtado, Valledupar, Cesar (Colombia)


    The two-dimensional Fast Fourier Transform (FFT 2D) is an essential tool in the two-dimensional discrete signals analysis and processing, which allows developing a large number of applications. This article shows the description and synthesis in VHDL code of the FFT 2D with fixed point binary representation using the programming tool Simulink HDL Coder of Matlab; showing a quick and easy way to handle overflow, underflow and the creation registers, adders and multipliers of complex data in VHDL and as well as the generation of test bench for verification of the codes generated in the ModelSim tool. The main objective of development of the hardware architecture of the FFT 2D focuses on the subsequent completion of the following operations applied to images: frequency filtering, convolution and correlation. The description and synthesis of the hardware architecture uses the XC3S1200E family Spartan 3E FPGA from Xilinx Manufacturer.

  3. Distinction of three wood species by Fourier transform infrared spectroscopy and two-dimensional correlation IR spectroscopy (United States)

    Huang, Anmin; Zhou, Qun; Liu, Junliang; Fei, Benhua; Sun, Suqin


    Dalbergia odorifera T. Chen, Pterocarpus santalinus L.F. and Pterocarpus soyauxii are three kinds of the most valuable wood species, which are hard to distinguish. In this paper, differentiation of D. odorifera, P. santalinus and P. soyauxii was carried out by using Fourier transform infrared spectroscopy (FT-IR), second derivative IR spectra and two-dimensional correlation infrared (2D-IR) spectroscopy. The three woods have their characteristic peaks in conventional IR spectra. For example, D. odorifera has obvious absorption peaks at 1640 and 1612 cm -1; P. santalinus has only one peak at 1614 cm -1; and P. soyauxii has one peak at 1619 cm -1 and one shoulder peak at 1597 cm -1. To enhance spectrum resolution and amplify the differences between the IR spectra of different woods, the second derivative technology was adopted to examine the three wood samples. More differences could be observed in the region of 800-1700 cm -1. Then, the thermal perturbation is applied to distinguish different wood samples in an easier way, because of the spectral resolution being enhanced by the 2D correlation spectroscopy. In the region of 1300-1800 cm -1, D. odorifera has five auto-peaks at 1518, 1575, 1594, 1620 and 1667 cm -1; P. santalinus has four auto-peaks at 1469, 1518, 1627 and 1639 cm -1 and P. soyauxii has only two auto-peaks at 1627 and 1639 cm -1. It is proved that the 2D correlation IR spectroscopy can be a new method to distinguish D. odorifera, P. santalinus and P. soyauxii.

  4. Verification of Ganoderma (lingzhi) commercial products by Fourier Transform infrared spectroscopy and two-dimensional IR correlation spectroscopy (United States)

    Choong, Yew-Keong; Sun, Su-Qin; Zhou, Qun; Lan, Jin; Lee, Han-Lim; Chen, Xiang-Dong


    Ganoderma commercial products are typically based on two sources, raw material (powder form and/or spores) and extract (water and/or solvent). This study compared three types of Ganoderma commercial products using 1 Dimensional Fourier Transform infrared and second derivative spectroscopy. The analyzed spectra of Ganoderma raw material products were compared with spectra of cultivated Ganoderma raw material powder from different mushroom farms in Malaysia. The Ganoderma extract product was also compared with three types of cultivated Ganoderma extracts. Other medicinal Ganoderma contents in commercial extract product that included glucan and triterpenoid were analyzed by using FTIR and 2DIR. The results showed that water extract of cultivated Ganoderma possessed comparable spectra with that of Ganoderma product water extract. By comparing the content of Ganoderma commercial products using FTIR and 2DIR, product content profiles could be detected. In addition, the geographical origin of the Ganoderma products could be verified by comparing their spectra with Ganoderma products from known areas. This study demonstrated the possibility of developing verification tool to validate the purity of commercial medicinal herbal and mushroom products.

  5. Identification of authentic and adulterated Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation analysis (United States)

    Qu, Lei; Chen, Jian-bo; Zhou, Qun; Zhang, Gui-jun; Sun, Su-qin; Guo, Yi-zhen


    As a kind of expensive perfume and valuable herb, the commercial Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy and two-dimensional (2D) correlation analysis are employed to establish a simple and quick identification method for the authentic and adulterated ALR. In the conventional infrared spectra, the standard ALR has a strong peak at 1658 cm-1 referring to the conjugated carbonyl of resin, while this peak is absent in the adulterated samples. The position, intensity, and shape of the auto-peaks and cross-peaks of the authentic and adulterated ALR are much different in the synchronous 2D correlation spectra with thermal perturbation. In the range of 1700-1500 cm-1, the standard ALR has four obvious auto-peaks, while the strongest one is at 1659 cm-1. The adulterated sample w-1 has three obvious auto-peaks and the strongest one is at 1647 cm-1. The adulterated sample w-2 has three obvious auto-peaks and the strongest one is at 1519 cm-1. The adulterated sample w-3 has four obvious auto-peaks and the strongest one is at 1690 cm-1. The above auto-peaks confirm that the standard ALR contains a certain content of resin compounds, while the three counterfeits contain little or different resins. The results show the potential of FT-IR spectroscopy and 2D correlation analysis in the simple and quick identification of authentic and adulterated ALR.

  6. Depth profiling of SBS/PET layered materials using step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy and two-dimensional correlation analysis

    Institute of Scientific and Technical Information of China (English)


    This paper demonstrates the application of step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy(FTIR-PAS) in non-destructively depth profiling of styrene-butadiene-styrene block copolymer/polyethylene terephthalate(SBS/PET) layered materials.The surface thicknesses of three layered samples were determined to be 1.2,4.3 and 9.4μm by using phase difference analysis,overcoming the spatial detection limits of FTIR.Combined with generalized two-dimensional(G2D) FTIR correlation analysis,the spatial origins of peaks in the SBS/PET spectrum are identified with those having overlapping peaks between different layers are resolved.

  7. Single-lens Fourier-transform-based optical color image encryption using dual two-dimensional chaotic maps and the Fresnel transform. (United States)

    Su, Yonggang; Tang, Chen; Li, Biyuan; Chen, Xia; Xu, Wenjun; Cai, Yuanxue


    We propose an optical color image encryption system based on the single-lens Fourier transform, the Fresnel transform, and the chaotic random phase masks (CRPMs). The proposed encryption system contains only one optical lens, which makes it more efficient and concise to implement. The introduction of the Fresnel transform makes the first phase mask of the proposed system also act as the main secret key when the input image is a non-negative amplitude-only map. The two CRPMs generated by dual two-dimensional chaotic maps can provide more security to the proposed system. In the proposed system, the key management is more convenient and the transmission volume is reduced greatly. In addition, the secret keys can be updated conveniently in each encryption process to invalidate the chosen plaintext attack and the known plaintext attack. Numerical simulation results have demonstrated the feasibility and security of the proposed encryption system.

  8. Chemical profiling and adulteration screening of Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation infrared (2D-IR) spectroscopy. (United States)

    Qu, Lei; Chen, Jian-Bo; Zhang, Gui-Jun; Sun, Su-Qin; Zheng, Jing


    As a kind of expensive perfume and valuable herb, Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy is employed to establish a simple and quick method for the adulteration screening of ALR. First, the principal chemical constituents of ALR are characterized by FT-IR spectroscopy at room temperature and two-dimensional correlation infrared (2D-IR) spectroscopy with thermal perturbation. Besides the common cellulose and lignin compounds, a certain amount of resin is the characteristic constituent of ALR. Synchronous and asynchronous 2D-IR spectra indicate that the resin (an unstable secondary metabolite) is more sensitive than cellulose and lignin (stable structural constituents) to the thermal perturbation. Using a certified ALR sample as the reference, the infrared spectral correlation threshold is determined by 30 authentic samples and 6 adulterated samples. The spectral correlation coefficient of an authentic ALR sample to the standard reference should be not less than 0.9886 (p=0.01). Three commercial adulterated ALR samples are identified by the correlation threshold. Further interpretation of the infrared spectra of the adulterated samples indicates the common adulterating methods - counterfeiting with other kind of wood, adding ingredient such as sand to increase the weight, and adding the cheap resin such as rosin to increase the content of resin compounds. Results of this research prove that FT-IR spectroscopy can be used as a simple and accurate quality control method of ALR.

  9. Chemical profiling and adulteration screening of Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation infrared (2D-IR) spectroscopy (United States)

    Qu, Lei; Chen, Jian-bo; Zhang, Gui-Jun; Sun, Su-qin; Zheng, Jing


    As a kind of expensive perfume and valuable herb, Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy is employed to establish a simple and quick method for the adulteration screening of ALR. First, the principal chemical constituents of ALR are characterized by FT-IR spectroscopy at room temperature and two-dimensional correlation infrared (2D-IR) spectroscopy with thermal perturbation. Besides the common cellulose and lignin compounds, a certain amount of resin is the characteristic constituent of ALR. Synchronous and asynchronous 2D-IR spectra indicate that the resin (an unstable secondary metabolite) is more sensitive than cellulose and lignin (stable structural constituents) to the thermal perturbation. Using a certified ALR sample as the reference, the infrared spectral correlation threshold is determined by 30 authentic samples and 6 adulterated samples. The spectral correlation coefficient of an authentic ALR sample to the standard reference should be not less than 0.9886 (p = 0.01). Three commercial adulterated ALR samples are identified by the correlation threshold. Further interpretation of the infrared spectra of the adulterated samples indicates the common adulterating methods - counterfeiting with other kind of wood, adding ingredient such as sand to increase the weight, and adding the cheap resin such as rosin to increase the content of resin compounds. Results of this research prove that FT-IR spectroscopy can be used as a simple and accurate quality control method of ALR.

  10. Analysis of Chuanxiong Rhizoma and its active components by Fourier transform infrared spectroscopy combined with two-dimensional correlation infrared spectroscopy (United States)

    Guo, Yizhen; Lv, Beiran; Wang, Jingjuan; Liu, Yang; Sun, Suqin; Xiao, Yao; Lu, Lina; Xiang, Li; Yang, Yanfang; Qu, Lei; Meng, Qinghong


    As complicated mixture systems, active components of Chuanxiong Rhizoma are very difficult to identify and discriminate. In this paper, the macroscopic IR fingerprint method including Fourier transform infrared spectroscopy (FT-IR), the second derivative infrared spectroscopy (SD-IR) and two-dimensional correlation infrared spectroscopy (2DCOS-IR), was applied to study and identify Chuanxiong raw materials and its different segmented production of HPD-100 macroporous resin. Chuanxiong Rhizoma is rich in sucrose. In the FT-IR spectra, water eluate is more similar to sucrose than the powder and the decoction. Their second derivative spectra amplified the differences and revealed the potentially characteristic IR absorption bands and combined with the correlation coefficient, concluding that 50% ethanol eluate had more ligustilide than other eluates. Finally, it can be found from 2DCOS-IR spectra that proteins were extracted by ethanol from Chuanxiong decoction by HPD-100 macroporous resin. It was demonstrated that the above three-step infrared spectroscopy could be applicable for quick, non-destructive and effective analysis and identification of very complicated and similar mixture systems of traditional Chinese medicines.

  11. Derivatization technique to increase the spectral selectivity of two-dimensional Fourier transform infrared focal plane array imaging: analysis of binder composition in aged oil and tempera paint. (United States)

    Zumbühl, Stefan; Scherrer, Nadim C; Eggenberger, Urs


    The interpretation of standard Fourier transform infrared spectra (FT-IR) on oil-based paint samples often suffers from interfering bands of the different compounds, namely, binder, oxidative aging products, carboxylates formed during aging, and several pigments and fillers. The distinction of the aging products such as ketone and carboxylic acid functional groups pose the next problem, as these interfere with the triglyceride esters of the oil. A sample preparation and derivatization technique using gaseous sulfur tetrafluoride (SF4), was thus developed with the aim to discriminate overlapping signals and achieve a signal enhancement on superposed compounds. Of particular interest in this context is the signal elimination of the broad carboxylate bands of the typical reaction products developing during the aging processes in oil-based paints, as well as signal interference originating from several typical pigments in this spectral range. Furthermore, it is possible to distinguish the different carbonyl-containing functional groups upon selective alteration. The derivatization treatment can be applied to both microsamples and polished cross sections. It increases the selectivity of the infrared spectroscopy technique in a fundamental manner and permits the identification and two-dimensional (2D) localization of binder components in aged paint samples at the micrometer scale. The combination of SF4 derivatization with high-resolution 2D FT-IR focal plane array (FPA) imaging delivers considerable advances to the study of micro-morphological processes involving organic compounds.

  12. Discrimination of different genuine Danshen and their extracts by Fourier transform infrared spectroscopy combined with two-dimensional correlation infrared spectroscopy (United States)

    Liu, Xin-hu; Xu, Chang-hua; Sun, Su-qin; Huang, Jian; Zhang, Ke; Li, Guo-yu; Zhu, Yun; Zhou, Qun; Zhang, Zhi-cheng; Wang, Jin-hui


    In this study, six varieties of Danshen from different populations and genuine ("Daodi" in Chinese transliteration) regions were discriminated and identified by a three-step infrared spectroscopy method (Fourier transform-infrared spectroscopy (FT-IR) coupled with second derivative infrared spectroscopy (SD-IR) and two dimensional correlation infrared spectroscopy (2D-IR)). Though only small differences were found among the FT-IR spectra of the six Danshen samples, the positions and intensities of peaks at 3393, 3371, 1613, 1050, and 1036 cm-1 could be considered as the key factors to discriminate them. More significant differences were exhibited in their SD-IR, particularly for the peaks around 1080, 1144, 695, 665, 800, 1610, 1510, 1450, 1117 and 1077 cm-1. The visual 2D-IR spectra provided dynamic chemical structure information of the six Danshen samples with presenting different particular auto-peak clusters, respectively. Moreover, the contents of salvianolic acid B in all samples were measured quantitatively by a validated ultra performance liquid chromatography (UPLC), which was consistent with the FT-IR findings. This study provides a promising method for characteristics and quality control of the complicated and extremely similar herbal medicine like Danshen, which is more cost effective and time saving.

  13. Real Clifford Windowed Fourier Transform

    Institute of Scientific and Technical Information of China (English)

    Mawardi BAHRI; Sriwulan ADJI; Ji Man ZHAO


    We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation,reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.

  14. [Study on the identification of radix scutellariae and extract using Fourier transform infrared spectroscopy and two-dimensional IR correlation spectroscopy]. (United States)

    Zhang, Chun-hui; Zhang, Gui-jun; Sun, Su-qin; Tu, Ya


    2D-IR correlation spectroscopy was used to do the research on crude and prepared drug of radix scutellariae and the extracts of them. The results show that the holistic shape of peaks among them are similar in the FTIR spectra. In second derivative spectra, the two absorption peaks: 1,745 and 1,411 cm(-1) of processed products move to the bigger wavenumber direction, while 1,357 cm(-1) of processed products moves to the smaller wavenumber direction; There are conspicuous differences in Two-dimensional infrared correlation spectroscopy among them: Four characteristic peaks are shown between 1,300 and 1,800 cm(-1). The intensity of peak at 1,575 cm(-1) is the strongest. There are three main districts about the autopeaks of sliced scutellariae. Wine-fried scutellariae has two auto-peak districts, in which all the auto-peaks are positively correlated. The FTIR spectra of total glycoside extract of different samples present characteristic peaks at 1,615, 1,585, 1,450 cm(-1) (vibration of phenyl framework) and 1,658 cm(-1) (=C-O ) respectively, therefore, the authors speculated that their mutual component is the compound of phenolic glycoside. The two-dimensional infrared correlation spectra present five automatic peaks (vibration of phenyl framework) in 800-1,800 cm(-1) (1,366, 1,420, 1,508, 1,585, 1,669 cm(-1)). So the authors can conclude that a lot of information can be provided by macro-fingerprint technology of infrared spectroscopy which can evaluate overall quality of radix scutellariae accurately and be used to study the characteristics of relevance of crude and prepared scutellariae.

  15. Feasibility study, software design, layout and simulation of a two-dimensional Fast Fourier Transform machine for use in optical array interferometry (United States)

    Boriakoff, Valentin


    The goal of this project was the feasibility study of a particular architecture of a digital signal processing machine operating in real time which could do in a pipeline fashion the computation of the fast Fourier transform (FFT) of a time-domain sampled complex digital data stream. The particular architecture makes use of simple identical processors (called inner product processors) in a linear organization called a systolic array. Through computer simulation the new architecture to compute the FFT with systolic arrays was proved to be viable, and computed the FFT correctly and with the predicted particulars of operation. Integrated circuits to compute the operations expected of the vital node of the systolic architecture were proven feasible, and even with a 2 micron VLSI technology can execute the required operations in the required time. Actual construction of the integrated circuits was successful in one variant (fixed point) and unsuccessful in the other (floating point).

  16. Comprehensive two-dimensional liquid chromatography with on-line Fourier-transform-infrared-spectroscopy detection for the characterization of copolymers

    NARCIS (Netherlands)

    Kok, S.J.; Hankemeier, T.; Schoenmakers, P.J.


    The on-line coupling of comprehensive two-dimensional liquid chromatography (liquid chromatography × size-exclusion chromatography, LC × SEC) and infrared (IR) spectroscopy has been realized by means of an IR flow cell. The system has been assessed by the functional-group analysis of a series of

  17. Comprehensive two-dimensional liquid chromatography with on-line Fourier-transform-infrared-spectroscopy detection for the characterization of copolymers

    NARCIS (Netherlands)

    Kok, S.J.; Hankemeier, T.; Schoenmakers, P.J.


    The on-line coupling of comprehensive two-dimensional liquid chromatography (liquid chromatography × size-exclusion chromatography, LC × SEC) and infrared (IR) spectroscopy has been realized by means of an IR flow cell. The system has been assessed by the functional-group analysis of a series of sty

  18. Studies of spin relaxation and molecular dynamics in liquid crystals by two-dimensional Fourier transform electron spin resonance. II. Perdeuterated-tempone in butoxy benzylidene octylaniline and dynamic cage effects (United States)

    Sastry, V. S. S.; Polimeno, Antonino; Crepeau, Richard H.; Freed, Jack H.


    Two-dimensional Fourier transform (2D-FT)-electron spin resonance (ESR) studies on the small globular spin probe perdeuterated tempone (PDT) in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments, over the temperature range of 95 °C to 24 °C, cover the isotropic (I), nematic (N), smectic A (SA), smectic B (SB), and crystal (C) phases. The 2D-ELDOR (two-dimensional electron-electron double resonance) spectra confirm the anomalously rapid reorientation of PDT, especially in the lower temperature phases. The model of a slowly relaxing local structure (SRLS) leads to generally very good non-linear least squares (NLLS) global fits to the sets of 2D-ELDOR spectra obtained at each temperature. These fits are significantly better than those achieved by the standard model of Brownian reorientation in a macroscopic orienting potential. The SRLS model is able to account for anomalies first observed in an earlier 2D-ELDOR study on PDT in a different liquid crystal in its smectic phases. Although it is instructional to extract the various spectral densities from the COSY (correlation spectroscopy) and 2D-ELDOR spectra, the use of NLLS global fitting to a full set of 2D-ELDOR spectra is shown to be more reliable and convenient for obtaining optimum model parameters, especially in view of possible (incipient) slow motional effects from the SRLS or dynamic cage. The cage potential is found to remain fairly constant at about kBT over the various phases (with only a small drop in the SB phase), but its asymmetry increases with decreasing temperature T. This value is significantly larger than the weak macroscopic orienting potential which increases from 0.1 to 0.3kBT with decreasing T. The cage relaxation rate, given by Rc is about 3×107 s-1 in the I phase, but increases to about 108 s-1 in the SA, SB, and C phases. The rotational diffusion tensor for PDT shows only a small T-independent asymmetry, and its mean rotational diffusion

  19. Analysis of crystallized lactose in milk powder by Fourier-transform infrared spectroscopy combined with two-dimensional correlation infrared spectroscopy (United States)

    Lei, Yu; Zhou, Qun; Zhang, Yan-ling; Chen, Jian-bo; Sun, Su-qin; Noda, Isao


    Infrared (IR) spectroscopy is used in combination with two-dimensional (2D) correlation IR spectroscopy to conduct rapid non-destructive quantitative research in milk powder without additional separation steps. The experiments conducted in both FT-IR and 2D FT-IR spectra suggest that characteristic spectroscopic features of milk powder containing different carbohydrate can be detected, and then determine the type of carbohydrate. To predict the approximate content of lactose while the carbohydrate is lactose, different amount of crystallized lactose has been added to the reference milk powder. The correlation coefficient could be used to determine the content of crystallized lactose in milk powder. The method provides a rapid and convenient means for assessing the quality of milk powder.

  20. The methyl C-H blueshift in N,N-dimethylformamide-water mixtures probed by two-dimensional Fourier-transform infrared spectroscopy. (United States)

    Xu, Zheng; Li, Haoran; Wang, Congmin; Pan, Haihua; Han, Shijun


    Two-dimensional correlation spectroscopy was used to study the composition-dependent spectral variations of the CH-stretching bands of N,N-dimethylformamide (DMF)-water mixtures with X(DMF) ranging from 0.98 to 0.60. By a detailed correlation analysis of the spectral changes of the CH- and OH-stretching bands, it is found that the intensities of the CH and OH bands change in different ways when the water content is increased. It is also found that two different regions of the water content can be distinguished, in which the intensity changes have different signatures. A tentative explanation for how these phenomena might be related to structural changes in the mixture is proposed. The structural change of DMF induced by the water hydrogen bonded on the carbonyl group is supposed to be the possible origin of the methyl C-H blueshift instead of the direct C-H...O interactions before the hydrophobic hydration takes place.

  1. κ-deformed Fourier transform (United States)

    Scarfone, A. M.


    We present a new formulation of Fourier transform in the picture of the κ-algebra derived in the framework of the κ-generalized statistical mechanics. The κ-Fourier transform is obtained from a κ-Fourier series recently introduced by Scarfone (2013). The kernel of this transform, that reduces to the usual exponential phase in the κ → 0 limit, is composed by a κ-deformed phase and a damping factor that gives a wavelet-like behaviour. We show that the κ-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the κ-algebra. As a relevant application, we discuss the central limit theorem for the κ-sum of n-iterate statistically independent random variables.

  2. In situ orientation studies of a poly(3-hydroxybutyrate)/poly(epsilon-caprolactone) blend by rheo-optical fourier transform infrared spectroscopy and two-dimensional correlation spectroscopic analysis. (United States)

    Unger, Miriam; Siesler, Heinz W


    In the present study, the orientation of a poly(3-hydroxybutyrate) (PHB)/poly(epsilon-caprolactone) (PCL) blend was monitored during uniaxial elongation by rheo-optical Fourier transform infrared (FT-IR) spectroscopy and analyzed by generalized two-dimensional correlation spectroscopy (2D-COS). The dichroism of the delta(CH(2)) absorption bands of PHB and PCL was employed to determine the polymer chain orientation in the PHB/PCL blend during the elongation up to 267% strain. From the PHB and PCL specific orientation functions it was derived that the PCL chains orient into the drawing direction while the PHB chains orient predominantly perpendicular to the applied strain. To extract more detailed information about the polymer orientation during uniaxial elongation, 2D-COS analysis was employed for the dichroic difference of the polarization spectra recorded during the drawing process. In the corresponding synchronous and asynchronous 2D correlation plots, absorption bands characteristic of the crystalline and amorphous regions of PHB and PCL were separated. Furthermore, the 2D-COS analysis revealed that during the mechanical treatment the PCL domains orient before the PHB domains.

  3. Fourier transform mass spectrometry. (United States)

    Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander


    This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

  4. Fourier transformation for pedestrians

    CERN Document Server

    Butz, Tilman


    Meant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it.

  5. Studies of spin relaxation and molecular dynamics in liquid crystals by two-dimensional Fourier transform electron spin resonance. I. Cholestane in butoxy benzylidene-octylaniline and dynamic cage effects (United States)

    Sastry, V. S. S.; Polimeno, Antonino; Crepeau, Richard H.; Freed, Jack H.


    Two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) studies on the rigid rodlike cholestane (CSL) spin-label in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments were performed over a wide temperature range: 96 °C to 25 °C covering the isotropic (I), nematic (N), smectic A (SA), smectic B (SB), and crystal (C) phases. It is shown that 2D-FT-ESR, especially in the form of 2D-ELDOR (two-dimensional electron-electron double resonance) provides greatly enhanced sensitivity to rotational dynamics than previous cw-ESR studies on this and related systems. This sensitivity is enhanced by obtaining a series of 2D-ELDOR spectra as a function of mixing time, Tm, yielding essentially a three-dimensional experiment. Advantage is taken of this sensitivity to study the applicability of the model of a slowly relaxing local structure (SRLS). In this model, a dynamic cage of solvent molecules, which relaxes on a slower time scale than the CSL solute, provides a local orienting potential in addition to that of the macroscopic aligning potential in the liquid crystalline phase. The theory of Polimeno and Freed for SRLS in the ESR slow motional regime is extended by utilizing the theory of Lee et al. to include 2D-FT-ESR experiments, and it serves as the basis for the analysis of the 2D-ELDOR experiments. It is shown that the SRLS model leads to significantly improved non-linear least squares fits to experiment over those obtained with the standard model of Brownian reorientation in a macroscopic aligning potential. This is most evident for the SA phase, and the use of the SRLS model also removes the necessity of fitting with the unreasonably large CSL rotational asymmetries in the smectic phases that are required in both the cw-ESR and 2D-ELDOR fits with the standard model. The cage potential is found to vary from about kBT in the isotropic phase to greater than 2kBT in the N and SA phases, with an abrupt drop to

  6. Generalized Fourier transforms classes

    DEFF Research Database (Denmark)

    Berntsen, Svend; Møller, Steen


    The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...

  7. Fourier transformation for pedestrians

    CERN Document Server

    Butz, Tilman


    This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.

  8. Generic Quantum Fourier Transforms

    CERN Document Server

    Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander


    The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.

  9. Fourier transforms in spectroscopy

    CERN Document Server

    Kauppinen, Jyrki


    This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi

  10. Fast Fourier transform telescope (United States)

    Tegmark, Max; Zaldarriaga, Matias


    We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore’s law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog⁡2N rather than N2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

  11. Fourier Transform Spectrometer System (United States)

    Campbell, Joel F. (Inventor)


    A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.

  12. Rainbow Fourier Transform (United States)

    Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.


    We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

  13. Fourier transforms principles and applications

    CERN Document Server

    Hansen, Eric W


    Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

  14. Study onβ-carotene under Thermal Treatment by Two-Dimensional Correlation Fourier Transform Infrared Spectroscopy%温度对β-胡萝卜素二维相关红外光谱的影响

    Institute of Scientific and Technical Information of China (English)

    卢明倩; 黄桂媛; 王巧贞; 许超; 黄庶识


    Abtract:[Objective]The aim of this study is to analyze the interaction between the different groups ofβ-carotene in the heating process.[Methods]Two-dimensional correlation spectrosco-py was applied to study the dynamic spectral changes ofβ-carotene from 30℃ to 100℃.[Re-sults]The changes of absorption characteristic peaks ofβ-carotene were inconspicuous in the conventional FTIR spectra and second derivative FTIR spectra during 30℃ to 100℃,which in-dicated that they had no oxidation reation.Two-dimensional correlation analysis showed that the changes of absorption peaks at 968 cm-1 ,1 442 cm-1 ,2 9 6 6 cm-1 and 3 0 1 2 cm-1 were more sen-sitive to temperature.Meanwhile,the order of different groups changes induced by temperature were as follows:the spectral changes of methyl-ene were faster than methyl,the spectral changes of methyl C-H symmetric stretching vibration in low wavenumber were faster than methyl anti-symmetric stretching vibration in high wavenumber,and olefin hydrocarbon symmetric stretching vibration were prior to olefin hydrocarbon anti-symmetric stretching vibration.[Con-clusion]This provides experimental basis for the mechanism of the conformational change ofβ-carotene in heating process.%【目的】了解在升温过程中β-胡萝卜素分子内不同基团之间的相互影响。【方法】采用二维相关红外光谱分析技术,研究β-胡萝卜素在30~100℃变温微扰过程中的动态光谱变化。【结果】β-胡萝卜素分子的吸收特征峰在一维红外光谱和二阶导数谱上变化不明显,表明其没有发生氧化反应。二维相关分析表明,反式共轭烯烃C—H 面外弯曲振动的968 cm-1,烯烃C—H 基团反对称弯曲振动的1442cm-1,甲基C—H 反对称伸缩振动的2966 cm-1和烯烃C—H 的对称伸缩振动的3012 cm-1,这些吸收峰的光谱变化对温度比较敏感。同时在微扰过程中,不同基团变化的先后顺序:亚甲基热运动引起的光谱变化快于

  15. Synchrotron radiation Fourier-transform infrared and Raman microspectroscopy study showing an increased frequency of creatine inclusions in the rat hippocampal formation following pilocarpine-induced seizures


    Dulinska, J.; Setkowicz, Z.; Janeczko, K.; C. SANDT; Dumas, P.; Uram, L.; Gzielo-Jurek, K.; Chwiej, J.


    In the present work, synchrotron radiation Fourier-transform infrared (SRFTIR) and Raman microspectroscopies were used to evaluate a possible role of creatine in the pathogenesis and progress of pilocarpine-evoked seizures and seizure-induced neurodegenerative changes in the rat hippocampal tissue. The main goal of this study was to identify creatine deposits within the examined brain area, to analyze their frequency in epileptic animals and naive controls and to examine correlations between ...

  16. Wavelet-fractional Fourier transforms

    Institute of Scientific and Technical Information of China (English)

    Yuan Lin


    This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.

  17. Fast Numerical Nonlinear Fourier Transforms

    CERN Document Server

    Wahls, Sander


    The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...

  18. Static Fourier transform infrared spectrometer. (United States)

    Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W


    Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared.

  19. Image encryption techniques based on the fractional Fourier transform (United States)

    Hennelly, B. M.; Sheridan, J. T.


    The fractional Fourier transform, (FRT), is a generalisation of the Fourier transform which allows domains of mixed spatial frequency and spatial information to be examined. A number of method have recently been proposed in the literature for the encryption of two dimensional information using optical systems based on the FRT. Typically, these methods require random phase screen keys to decrypt the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. We have proposed a new technique based on a random shifting or Jigsaw transformation. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in various FRT domains. The new method has been compared numerically with existing methods and shows comparable or superior robustness to blind decryption. An optical implementation is also proposed and the sensitivity of the various encryption keys to blind decryption is quantified. We also present a second image encryption technique, which is based on a recently proposed method of optical phase retrieval using the optical FRT and one of its discrete counterparts. Numerical simulations of the new algorithm indicates that the sensitivity of the keys is much greater than any of the techniques currently available. In fact the sensitivity appears to be so high that optical implementation, based on existing optical signal processing technology, may be impossible. However, the technique has been shown to be a powerful method of 2-D image data encryption.

  20. How to tickle spins with a fourier transform NMR spectrometer. (United States)

    Segawa, Takuya F; Carnevale, Diego; Bodenhausen, Geoffrey


    In the long bygone days of continuous-wave nuclear magnetic resonance (NMR) spectroscopy, a selected transition within a multiplet of a high-resolution spectrum could be irradiated by a highly selective continuous-wave (CW) radio-frequency (rf) field with a very weak amplitude ω(2)/(2π)≤J. This causes splittings of connected transitions, allowing one to map the connectivities of all transitions within the energy-level diagram of the spin system. Such "tickling" experiments stimulated the invention of two-dimensional spectroscopy, but seem to have been forgotten for nearly 50 years. We show that tickling can readily be achieved in homonuclear systems with Fourier transform spectrometers by applying short pulses in the intervals between the sampling points. Extensions to heteronuclear systems are even more straightforward since they can be carried out using very weak CW rf fields.

  1. Robust Video Watermarking Based on Discrete Fractional Fourier Transform

    Institute of Scientific and Technical Information of China (English)

    NIU Xiamu; SUN Shenghe


    A video watermarking techniquebased on discrete fractional Fourier transform(DFRFT) is proposed. Each frame of an original videois first decomposed into two-dimensional (2-D) mul-tiresolution representations by 2-D discrete wavelettransforms (DWT) along the spatial axis. Then thewavelet coefficient frames in each group of pictures(GOP, each GOP has 16 frames) are transformed intoDFRFT coefficient frames by one-dimensional (1-D)DFRFT along the temporal axis. The watermark isembedded into each DFRFT coefficient frame in theGOP, and the angular parameter of the DFRFT canbe changed to adapt itself to the original video. Experimental results show that the proposed techniqueis robust enough against the attacks of frame dropping, averaging and lossy compression.

  2. A More Accurate Fourier Transform

    CERN Document Server

    Courtney, Elya


    Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...

  3. Fourier Analysis and Structure Determination: Part I: Fourier Transforms. (United States)

    Chesick, John P.


    Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

  4. [Using 2-DCOS to identify the molecular spectrum peaks for the isomer in the multi-component mixture gases Fourier transform infrared analysis]. (United States)

    Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua


    The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.

  5. Novel Micro Fourier Transform Spectrometers

    Institute of Scientific and Technical Information of China (English)

    KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun


    The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.

  6. Fourier-transform optical microsystems (United States)

    Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.


    The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.

  7. JPL Fourier transform ultraviolet spectrometer (United States)

    Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.


    The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.

  8. Fourier-Transform Infrared Spectrometer (United States)

    Schindler, R. A.


    Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.

  9. Fourier Transform Methods. Chapter 4 (United States)

    Kaplan, Simon G.; Quijada, Manuel A.


    This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..

  10. Fourier transform spectroscopy in the visible and ultraviolet range. (United States)

    Luc, P; Gerstenkorn, S


    In cases where the photon noise is the limiting factor, the multiplex gain is not always conserved; however the throughput (Jacquinot's advantage) is not affected. Therefore extension of Fourier transform spectroscopy to higher frequencies has great possibilities. Studies at high resolution, both in emission and in absorption, show that the performance achieved by Fourier transform spectroscopy in the visible and uv range is comparable with that reached in the ir.

  11. 10th International Conference on Progress in Fourier Transform Spectroscopy

    CERN Document Server

    Keresztury, Gábor; Kellner, Robert


    19 plenary lectures and 203 poster papers presented at the 10th International Conference of Fourier Transform Spectroscopy in Budapest 1995 give an overview on the state-of-the art of this technology and its wide range of applications. The reader will get information on any aspects of FTS including the latest instrumental developments, e.g. in diode array detection, time resolution FTS, microscopy and spectral mapping, double modulation and two-dimensional FTS.

  12. Quantum copying and simplification of the quantum Fourier transform (United States)

    Niu, Chi-Sheng

    Theoretical studies of quantum computation and quantum information theory are presented in this thesis. Three topics are considered: simplification of the quantum Fourier transform in Shor's algorithm, optimal eavesdropping in the BB84 quantum cryptographic protocol, and quantum copying of one qubit. The quantum Fourier transform preceding the final measurement in Shor's algorithm is simplified by replacing a network of quantum gates with one that has fewer and simpler gates controlled by classical signals. This simplification results from an analysis of the network using the consistent history approach to quantum mechanics. The optimal amount of information which an eavesdropper can gain, for a given level of noise in the communication channel, is worked out for the BB84 quantum cryptographic protocol. The optimal eavesdropping strategy is expressed in terms of various quantum networks. A consistent history analysis of these networks using two conjugate quantum bases shows how the information gain in one basis influences the noise level in the conjugate basis. The no-cloning property of quantum systems, which is the physics behind quantum cryptography, is studied by considering copying machines that generate two imperfect copies of one qubit. The best qualities these copies can have are worked out with the help of the Bloch sphere representation for one qubit, and a quantum network is worked out for an optimal copying machine. If the copying machine does not have additional ancillary qubits, the copying process can be viewed using a 2-dimensional subspace in a product space of two qubits. A special representation of such a two-dimensional subspace makes possible a complete characterization of this type of copying. This characterization in turn leads to simplified eavesdropping strategies in the BB84 and the B92 quantum cryptographic protocols.

  13. Wavelets for approximate Fourier transform and data compression (United States)

    Guo, Haitao

    This dissertation has two parts. In the first part, we develop a wavelet-based fast approximate Fourier transform algorithm. The second part is devoted to the developments of several wavelet-based data compression techniques for image and seismic data. We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The classical Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. The main advantage of our algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals, resulting in much less computation. Thus the new algorithm provides an efficient complexity versus accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability. For waveform and image compression, we propose a novel scheme using the recently developed Burrows-Wheeler transform (BWT). We show that the discrete wavelet transform (DWT) should be used before the Burrows-Wheeler transform to improve the compression performance for many natural signals and images. We demonstrate that the simple concatenation of the DWT and BWT coding performs comparably as the embedded zerotree wavelet (EZW) compression for images. Various techniques that significantly improve the performance of our compression scheme are also discussed. The phase information is crucial for seismic data processing. However, traditional compression schemes do not pay special attention to preserving the phase of the seismic data, resulting in the loss of critical information. We propose a lossy compression method that preserves the phase as much as possible. The method is based on the self-adjusting wavelet transform that adapts to the locations of the significant signal components

  14. Research progress of the fractional Fourier transform in signal processing

    Institute of Scientific and Technical Information of China (English)


    The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.

  15. The multiple-parameter fractional Fourier transform

    Institute of Scientific and Technical Information of China (English)

    LANG Jun; TAO Ran; RAN QiWen; WANG Yue


    The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in frac-tional operator. A new source for the multiplicity of the weight-type fractional Fou-rier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters MN,∈ZM. Therefore a generalized frac-tional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.

  16. Volumetric and two-dimensional image interpretation show different cognitive processes in learners

    NARCIS (Netherlands)

    van der Gijp, Anouk; Ravesloot, C.J.; van der Schaaf, Marieke F; van der Schaaf, Irene C; Huige, Josephine C B M; Vincken, Koen L; Ten Cate, Olle Th J; van Schaik, JPJ


    RATIONALE AND OBJECTIVES: In current practice, radiologists interpret digital images, including a substantial amount of volumetric images. We hypothesized that interpretation of a stack of a volumetric data set demands different skills than interpretation of two-dimensional (2D) cross-sectional imag

  17. Fully phase encrypted memory using cascaded extended fractional Fourier transform (United States)

    Nishchal, Naveen K.; Joseph, Joby; Singh, Kehar


    In this paper, we implement a fully phase encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The fully phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, conjugate of encrypted image. The decrypted phase image is converted into an amplitude image by using phase contrast technique. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the phase image, alleviating the need of alignment in the Fourier plane, thereby making the system rugged.

  18. Two modified discrete chirp Fourier transform schemes

    Institute of Scientific and Technical Information of China (English)

    樊平毅; 夏香根


    This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.

  19. The Fourier Transform on Quantum Euclidean Space

    Directory of Open Access Journals (Sweden)

    Kevin Coulembier


    Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.

  20. The Geostationary Fourier Transform Spectrometer (United States)

    Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung


    The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.

  1. FFTW: Fastest Fourier Transform in the West (United States)

    Frigo, Matteo; Johnson, Steven G.


    FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). Benchmarks performed on a variety of platforms show that FFTW's performance is typically superior to that of other publicly available FFT software, and is even competitive with vendor-tuned codes. In contrast to vendor-tuned codes, however, FFTW's performance is portable: the same program will perform well on most architectures without modification. The FFTW library is required by other codes such as StarCrash and Hammurabi.

  2. Rotation-invariant texture analysis using Radon and Fourier transforms

    Institute of Scientific and Technical Information of China (English)

    Songshan Xiao; Yongxing Wu


    @@ Texture analysis is a basic issue in image processing and computer vision, and how to attain the rotationinvariant texture characterization is a key problem. This paper proposes a rotation-invariant texture analysis technique using Radon and Fourier transforms. This method uses Radon transform to convert rotation to translation, then utilizes Fourier transform and takes the moduli of the Fourier transform of these functions to make the translation invariant. A k-nearest-neighbor rule is employed to classify texture images. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. Experiment results show the feasibility of the proposed method and its robustness to additive white noise.

  3. SAW chirp Fourier transform for MB-OFDM UWB receiver

    Institute of Scientific and Technical Information of China (English)

    HE Peng-fei; L(U) Ying-hua; ZHANG Hong-xin; WANG Ye-qiu; XU Yong


    In the conventional multiband orthogonal frequency division multiplexing ultra wideband (MB-OFDM UWB )receiver, the fast Fourier transform (FFT) algorithm is realized by the expensive and power-consuming digital signal processor (DSP) chips. In this article, the lower power, lower cost, and lower complexity real-time analog surface acoustic wave (SAW)chirp Fourier transform devices were used to replace the DSP part. A MB-OFDM UWB receiver based on the M-C-M SAW chirp Fourier transform was presented, and the step of signal transformation from input signals was also depicted. The simulation results show that the proposed receiver provides similar bit error performance compared to the fully digital receiver when used in the channel environments proposed by the IEEE 802.15SG3a.

  4. Fourier transforms in radar and signal processing

    CERN Document Server

    Brandwood, David


    Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit

  5. Multifractional Fourier Transform Method and Its Applications to Image Encryption

    Institute of Scientific and Technical Information of China (English)

    RANQiwen; WANGQi; MAJing; TANLiying


    The multiplicity of the fractional Fourier transform(FRFT),which is intrinsic in any fractional operator,has been claimed by several authors,but never across-the-board developed.Particularly,the weight-type FRFT(WFRFT) has not been investigated.Starting with defining the multifractional Fourier transform (MFRFT),we gained the generalization permutation matrix group (GPMG)representation and multiplicity of the MFRFT,and the relationships among the MFRFT the standard WFRFT and the standard CFRFT.Finally,as a application,a novel image encryption method hased on the MFRFT is propounded.Similation results show that this method is safe,practicable and impactful.

  6. Composite Cyclotomic Fourier Transforms with Reduced Complexities

    CERN Document Server

    Wu, Xuebin; Chen, Ning; Yan, Zhiyuan; Wang, Ying


    Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which has not been investigated thoroughly yet, and (2) they have very high additive complexities when directly implemented. In this paper, we address both issues. One of the main contributions of this paper is efficient bilinear 11-point cyclic convolution algorithms, which allow us to construct CFFTs over GF$(2^{11})$. The other main contribution of this paper is that we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths, and the imp...

  7. Electronically-Scanned Fourier-Transform Spectrometer (United States)

    Breckinridge, J. B.; Ocallaghan, F. G.


    Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.

  8. A new twist to fourier transforms

    CERN Document Server

    Meikle, Hamish D


    Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs


    Institute of Scientific and Technical Information of China (English)

    Zhou Chaoying; Yang Lihua; Huang Daren


    A space DF is constructed and some characterizations of space DF are given. Itis shown that the classical Fourier transform is extended to the distribution space D'F, whichcan be embedded into the Schwartz distribution space D' continuously. It is also shown thatD'F is the biggest embedded subspace of D' on which the extended Fourier transform, F, is ahomeomorphism of D'F onto itself.

  10. Shift sampling theory of Fourier transform computation

    Institute of Scientific and Technical Information of China (English)



    The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.

  11. Fractional Fourier transform of Lorentz beams

    Institute of Scientific and Technical Information of China (English)

    Zhou Guo-Quan


    This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.

  12. Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling. (United States)

    Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail


    We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

  13. From Complex Fractional Fourier Transform to Complex Fractional Radon Transform

    Institute of Scientific and Technical Information of China (English)

    FAN Hong-Yi; JIANG Nian-Quan


    We show that for n-dimensional complex fractional Fourier transform the corresponding complex fractional Radon transform can also be derived, however, it is different from the direct product of two n-dimensional real fractional Radon transforms. The complex fractional Radon transform of two-mode Wigner operator is calculated.

  14. Volumetric and two-dimensional image interpretation show different cognitive processes in learners. (United States)

    van der Gijp, Anouk; Ravesloot, Cécile J; van der Schaaf, Marieke F; van der Schaaf, Irene C; Huige, Josephine C B M; Vincken, Koen L; Ten Cate, Olle Th J; van Schaik, Jan P J


    In current practice, radiologists interpret digital images, including a substantial amount of volumetric images. We hypothesized that interpretation of a stack of a volumetric data set demands different skills than interpretation of two-dimensional (2D) cross-sectional images. This study aimed to investigate and compare knowledge and skills used for interpretation of volumetric versus 2D images. Twenty radiology clerks were asked to think out loud while reading four or five volumetric computed tomography (CT) images in stack mode and four or five 2D CT images. Cases were presented in a digital testing program allowing stack viewing of volumetric data sets and changing views and window settings. Thoughts verbalized by the participants were registered and coded by a framework of knowledge and skills concerning three components: perception, analysis, and synthesis. The components were subdivided into 16 discrete knowledge and skill elements. A within-subject analysis was performed to compare cognitive processes during volumetric image readings versus 2D cross-sectional image readings. Most utterances contained knowledge and skills concerning perception (46%). A smaller part involved synthesis (31%) and analysis (23%). More utterances regarded perception in volumetric image interpretation than in 2D image interpretation (Median 48% vs 35%; z = -3.9; P Cognitive processes in volumetric and 2D cross-sectional image interpretation differ substantially. Volumetric image interpretation draws predominantly on perceptual processes, whereas 2D image interpretation is mainly characterized by synthesis. The results encourage the use of volumetric images for teaching and testing perceptual skills. Copyright © 2015 AUR. Published by Elsevier Inc. All rights reserved.

  15. Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

    Energy Technology Data Exchange (ETDEWEB)

    Patino, A [Universidad Technologica de Bolivar, Cartagena de Indias (Colombia); Durand, P-E; Fogret, E; Pellat-Finet, P, E-mail: [Laboratoire de mathematiques et applications des mathematiques, Universite de Bretagne Sud, B P 92116, 56321 Lorient cedex (France)


    According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

  16. Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform. (United States)

    Glasser, L.


    This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

  17. Fourier transforms and convolutions for the experimentalist

    CERN Document Server

    Jennison, RC


    Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t

  18. Fast Fourier Transform algorithm design and tradeoffs (United States)

    Kamin, Ray A., III; Adams, George B., III


    The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

  19. Stepwise Iterative Fourier Transform: The SIFT (United States)

    Benignus, V. A.; Benignus, G.


    A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.

  20. Ultrafast Fourier-transform parallel processor

    Energy Technology Data Exchange (ETDEWEB)

    Greenberg, W.L.


    A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.

  1. On the Scaled Fractional Fourier Transformation Operator

    Institute of Scientific and Technical Information of China (English)

    FAN Hong-Yi; HU Li-Yun


    Based on our previous study [Chin.Phys.Lett.24(2007)2238]in which the Fresnel operator corresponding to classical Fresnel transform was introduced,we derive the fractional Fourier transformation operator,and the optical operator method is then enriched.

  2. Fourier transforms on an amalgam type space

    CERN Document Server

    Liflyand, E


    We introduce an amalgam type space, a subspace of $L^1(\\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.

  3. Clifford Fourier transform on vector fields. (United States)

    Ebling, Julia; Scheuermann, Gerik


    Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

  4. Fourier transform infrared spectrometery: an undergraduate experiment (United States)

    Lerner, L.


    Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory.

  5. SAR processing based on the exact two-dimensional transfer function (United States)

    Chang, C. Y.; Jin, M. Y.; Curlander, J. C.


    The two-dimensional transfer functions of several synthetic aperture radar (SAR) focusing algorithms are derived considering the spaceborne SAR environments. The formulation includes the factors of the earth rotation and the antenna squint angles. The resultant transfer functions are explicitly expressed in terms of Doppler centroid frequency and Doppler frequency rate, which can be accurately estimated from the SAR data. Point target simulation results show that the algorithm based on the two-dimensional Fourier transformation outperforms the one-dimensional one for processing data acquired from high squint angles. The two-dimensional Fourier transformation approach appears to be a viable and simple solution for the processor design of future spaceborne SAR systems.

  6. Implementation of quantum and classical discrete fractional Fourier transforms. (United States)

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander


    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.


    Institute of Scientific and Technical Information of China (English)

    Zhang Xichun; Li Yunjie; Zhang Jun; Wei Gang


    This letter proposes a new method for concurrent voiced speech separation. Firstly the Wrapped Discrete Fourier Transform (WDFT) is used to decompose the harmonic spectra of the mixed speeches. Then the individual speech is reconstructed by using the sinusoidal speech model. By taking advantage of the non-uniform frequency resolution of WDFT, harmonic spectra parameters can be estimated and separated accurately. Experimental results on mixed vowels separation show that the proposed method can recover the original speeches effectively.

  8. Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

    Institute of Scientific and Technical Information of China (English)

    HUANG Da-Zu; CHEN Zhi-Gang; GUO Ying


    A (n, n )-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform.In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert.Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant.Security analysis shows that our scheme is secure.Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.

  9. On the Fourier transform of the greatest common divisor

    CERN Document Server

    van der Kamp, Peter H


    The discrete Fourier transform of the greatest common divisor is a multiplicative function that generalises both the gcd-sum function and Euler's totient function. On the one hand it is the Dirichlet convolution of the identity with Ramanujan's sum, and on the other hand it can be written as a generalised convolution product of the identity with the totient function. We show that this arithmetic function of two integers (a,m) counts the number of elements in the set of ordered pairs (i,j) such that i*j is equivalent to a modulo m. Furthermore we generalise a dozen known identities for the totient function, to identities which involve the discrete Fourier transform of the greatest common divisor, including its partial sums, and its Lambert series.

  10. Image restoration based on the discrete fraction Fourier transform (United States)

    Yan, Peimin; Mo, Yu L.; Liu, Hong


    The fractional Fourier transform is the powerful tool for time-variant signal analysis. For space-variant degradation and non-stationary processes the filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain filtering. In this paper the concept of filtering in fractional Fourier domains is applied to the problem of estimating degraded images. Efficient digital implementation using discrete Hermite eigenvectors can provide similar results to match the continuous outputs. Expressions for the 2D optimal filter function in fractional domains will be given for transform domains characterized by the two rotation angle parameters of the 2D fractional Fourier transform. The proposed method is used to restore images that have several degradations in the experiments. The results show that the method presented in this paper is valid.

  11. Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform (United States)

    Lang, Jun


    In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

  12. Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates. (United States)

    Dovlo, Edem; Baddour, Natalie


    The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

  13. Quantum Fourier transform in computational basis (United States)

    Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.


    The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.

  14. Replica Fourier Transform: Properties and applications

    Directory of Open Access Journals (Sweden)

    A. Crisanti


    Full Text Available The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.

  15. High order generalized permutational fractional Fourier transforms

    Institute of Scientific and Technical Information of China (English)

    Ran Qi-Wen; Yuan Lin; Tan Li-Ying; Ma Jing; Wang Qi


    We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT),is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +∞,M = 4k (k is a natural number), and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.

  16. Fourier Transform Fabry-Perot Interferometer (United States)

    Snell, Hilary E.; Hays, Paul B.


    We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.

  17. Fourier Transform Infrared Spectroscopic Studies in Flotation

    Institute of Scientific and Technical Information of China (English)


    Fourier transform infrared (FTIR) spectroscopy has been extensively employed in flotation research.The work done by the author and co-workers has been reported.A comparison has been made among the different FTIR spectroscopic techniques,e.g.,transmission FTIR spectroscopy,diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy,and attenuated total reflectance (ATR) FTIR spectroscopy.FTIR spectroscopy has been used to study the mechanism of interaction between the collector and the surfaces of different minerals,the mechanism of action of the depressant in improving the selectivity of flotation,and the mechanism of adsorption of the polymeric modifying reagent on mineral surfaces.The interaction between particles in mineral suspension has also been studied by FTIR spectroscopy.

  18. Fourier-transform spectroscopy instrumentation engineering

    CERN Document Server

    Saptari, Vidi


    Many applications today require the Fourier-transform (FT) spectrometer to perform close to its limitations, such as taking many quantitative measurements in the visible and in the near infrared wavelength regions. In such cases, the instrument should not be considered as a perfect ""black box."" Knowing where the limitations of performance arise and which components must be improved are crucial to obtaining repeatable and accurate results. One of the objectives of this book is to help the user identify the instrument's bottleneck.

  19. 连续Fourier变换、逆变换的数值计算%Numerical computation for continuous Fourier transform and inverse Fourier transform

    Institute of Scientific and Technical Information of China (English)

    魏鑫宇; 冯立新; 张国艳


    Based on the trigonometric interpolation theory, a function is approximated by its trigonometric interpolation function. By the properties of Dirac distribution function, the analytic expressions of the Fourier transform and inverse Fourier transform for the trigonometric interpolation function are derived to approximate the Fourier transform and inverse Fourier transform for the original function. The numerical formulations for calculating the Fourier transforms and the inverse Fourier transforms of the functions with one variable and two variables are derived, respectively. Comparing with the algorithm using rectangular formula of numerical integration, the numerical examples show that the proposed method achieves higher accuracy.%基于三角插值理论,用函数的三角插值函数代替函数本身,并借助Dirac广义函数的性质写出三角插值函数的Fourier变换、逆变换的解析表达式,将之作为函数的Fourier变换、逆变换的近似.基于这种想法,分别推导一元函数、二元函数的Fourier变换和Fourier逆变换的计算公式.数值实验表明,这种方法比通常基于矩形求积公式计算连续Fourier变换、逆变换的精度要高.

  20. Matrix isolation studies with Fourier transform IR

    Energy Technology Data Exchange (ETDEWEB)

    Green, David W.; Reedy, Gerald T.


    The combination of Fourier transform infrared (FT-IR) spectroscopy with the matrix-isolation techniques has advantages compared with the use of more conventional grating spectroscopy. Furthermore, the recent commercial availability of Fourier transform spectrometers has made FT-IR a practical alternative. Some advantages of the FT-IR spectrometer over the grating spectrometer are the result of the computerized data system that is a necessary part of the FT-IR spectrometer; other advantages are a consequence of the difference in optical arrangements and these represent the inherent advantages of the FT-IR method. In most applications with the matrix-isolation technique, the use of FT-IR spectroscopy results in either an improved signal-to-noise ratio or a shorter time for data collection compared with grating infrared spectroscopy. Fourier transform infrared spectroscopy has been used in the laboratory to study several molecular species in low-temperature matrices. Some species have been produced by high-temperature vaporization from Knudsen cells and others by sputtering. By sputtering, Ar and Kr matrices have been prepared which contain U atoms, UO, UO/sub 2/, UO/sub 3/, PuO, PuO/sub 2/, UN, or UN/sub 2/, depending upon the composition of the gas used to sputter as well as the identity of the metallic cathode. Infrared spectra of matrices containing these compounds are presented and discussed. (JRD)

  1. Fourier-transform Ghost Imaging with Hard X-rays

    CERN Document Server

    Yu, Hong; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming


    Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by X-ray crystallography, however, it is only applied to crystalline structures. Imaging techniques based on X-ray coherent diffraction or zone plates are capable of resolving the internal structure of non-crystalline materials at nanoscales, but it is still a challenge to achieve atomic resolution. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudo-thermal hard X-rays by measuring the second-order intensity correlation function of the light. We show that high resolution Fourier-transform diffraction pattern of a complex structure can be achieved at Fresnel region, and the amplitude and phase distributions of a sample in spatial domain can be retrieved successfully. The method of lensless X-ray Fourier-transform ghost imaging extends X-ray...

  2. Electro-optic imaging Fourier transform spectrometer (United States)

    Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)


    An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

  3. Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups


    Krovi, Hari; Russell, Alexander


    Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups (denoted D(G), for a group G). Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over D(G); in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the ce...

  4. The Fourier transform of tubular densities

    KAUST Repository

    Prior, C B


    We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.

  5. JCE Online: Interactive Fourier Transform Activities (United States)

    Zielinski, Theresa Julia


    In our vigorous teaching of concepts and skills to students, we may cover (hide) more than we uncover, obscuring significant relationships between mathematical models and their associated chemical concepts with excessive mathematical derivations. To set the record straight, I find that mathematical treatments of physical phenomena are beautiful and elegant. Students should know from where the equations and simplifications leading to them arise. They should know the limits of the equations in order to use them properly. However, this can be the Siren's song. For example, the mathematical representation of the Fourier transform and its significance as presented in most texts are too brief to convey understanding to the typical undergraduate student. Furthermore, a few hand calculations would not permit deeper probing of the method and its intimate link to spectroscopy. The Fourier transform is a very good example of how symbolic equation software can help to uncover the science by making the mathematical manipulations easier and the mathematical concepts more accessible. The complete articles and Mathcad documents described in these abstracts are available from JCE Online at

  6. White-light optical implementation of the fractional fourier transform with adjustable order control. (United States)

    Tajahuerce, E; Saavedra, G; Furlan, W D; Sicre, E E; Andrés, P


    An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.

  7. Parallel image registration method for snapshot Fourier transform imaging spectroscopy (United States)

    Zhang, Yu; Zhu, Shuaishuai; Lin, Jie; Zhu, Feijia; Jin, Peng


    A fast and precise registration method for multi-image snapshot Fourier transform imaging spectroscopy is proposed. This method accomplishes registration of an image array using the positional relationship between homologous points in the subimages, which are obtained offline by preregistration. Through the preregistration process, the registration problem is converted to the problem of using a registration matrix to interpolate subimages. Therefore, the hardware interpolation of graphics processing unit (GPU) texture memory, which has speed advantages for its parallel computing, can be used to significantly enhance computational efficiency. Compared to a central processing unit, GPU performance showed ˜27 times acceleration in registration efficiency.

  8. Multi-band Image Registration Method Based on Fourier Transform

    Institute of Scientific and Technical Information of China (English)

    庹红娅; 刘允才


    This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.

  9. The Discrete Fourier Transform on hexagonal remote sensing image (United States)

    Li, Yalu; Ben, Jin; Wang, Rui; Du, Lingyu


    Global discrete grid system will subdivide the earth recursively to form a multi-resolution grid hierarchy with no Overlap and seamless which help build global uniform spatial reference datum and multi-source data processing mode which takes the position as the object and in the aspect of data structure supports the organization, process and analysis of the remote sensing big data. This paper adopts the base transform to realize the mutual transformation of square pixel and hexagonal pixel. This paper designs the corresponding discrete Fourier transform algorithm for any lattice. Finally, the paper show the result of the DFT of the remote sensing image of the hexagonal pixel.

  10. Ash melting behavior by Fourier transform infrared spectroscopy

    Institute of Scientific and Technical Information of China (English)

    LI Han-xu; QIU Xiao-sheng; TANG Yong-xin


    A Fourier Transform Infrared Spectroscopic (FTIR) method involving a Fe2O3 flux was used to learn how China's coal ash melts. The relationship between ash fusion temperature and chemical composition, as well as the effects of Fe2O3 flux on the ash fusion temperature were studied. The relationship between ash fusion temperature and chemical composition, mineralogical phases and functional groups was analyzed with the FTIR method. The results show that the ash fusion temperature is related to the location and transmittance of certain absorption peaks, which is of great significance for the study of ash behavior.

  11. Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions (United States)

    Morelli, Eugene A.


    A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

  12. Fourier transforms in generalized Fock spaces

    Directory of Open Access Journals (Sweden)

    John Schmeelk


    Full Text Available A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…,where ϕ0∈C and ϕq∈L2(R3q, q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.

  13. Laser Field Imaging Through Fourier Transform Heterodyne

    Energy Technology Data Exchange (ETDEWEB)

    Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.


    The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.

  14. Multicomplementary operators via finite Fourier transform

    Energy Technology Data Exchange (ETDEWEB)

    Klimov, Andrei B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, Luis L [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada); Guise, Hubert de [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada)


    A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.

  15. Fourier transform spectroscopy for future planetary missions (United States)

    Brasunas, John; Kolasinski, John; Kostiuk, Ted; Hewagama, Tilak


    Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system. Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, we have developed CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. We discuss the roadmap for making CIRS-lite a viable candidate for future planetary missions, including the recent increased emphasis on ocean worlds (Europa, Encelatus, Titan) and also on smaller payloads such as CubeSats and SmallSats.

  16. Applying Quaternion Fourier Transforms for Enhancing Color Images

    Directory of Open Access Journals (Sweden)

    M.I. Khalil


    Full Text Available The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.

  17. Quantum process tomography of the quantum Fourier transform. (United States)

    Weinstein, Yaakov S; Havel, Timothy F; Emerson, Joseph; Boulant, Nicolas; Saraceno, Marcos; Lloyd, Seth; Cory, David G


    The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive-although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors which occurred over the full quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cumulative effect of small errors in the single qubit gates.

  18. Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy (United States)

    Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks


    Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.

  19. [Fourier Transform Spectrometer Based on Rotating Parallel-Mirror-Pair]. (United States)

    Zhao, Bao-wei; Xiangli, Bin; Cai, Qi-sheng; Lü, Qun-bo; Zhou, Jin-song


    In the temporally-modulated Fourier transform spectroscopy, the translational moving mirror is difficult to drive accurately, causing tilt and shear problems. While, a rotational moving mirror can solve these problems. A rotary Fourier transform spectrometer is recommanded in this paper. Its principle is analyzed and the optical path difference is deduced. Also, the constrains for engineering realization are presented. This spectrometer consists of one beamsplitter, two fixed mirrors, one rotating parallel mirror pair, a collimating lens, a collecting lens, and one detector. From it's principle, this spectrometer show a simple structure, and it is assembled and adjustmented easily because the two split light are interfered with each other after reflected through the same plane mirror; By calculating the expression of it's optical path difference, the spectrometer is easy to realize large optical path difference, meaning high spectral resolution; Through analyzing it's engineering design constraints and computer simulation, it is known that the spectrometer should get the high resolution sample by high-speed spinning motor, so it is easy to achieve precise motion control, good stability, fast measurement speed.

  20. Fourier transform approach in modulation technique of experimental measurements. (United States)

    Khazimullin, M V; Lebedev, Yu A


    An application of Fourier transform approach in modulation technique of experimental studies is considered. This method has obvious advantages compared with traditional lock-in amplifiers technique--simple experimental setup, a quickly available information on all the required harmonics, high speed of data processing using fast Fourier transform algorithm. A computationally simple, fast and accurate Fourier coefficients interpolation (FCI) method has been implemented to obtain a useful information from harmonics of a multimode signal. Our analysis shows that in this case FCI method has a systematical error (bias) of a signal parameters estimation, which became essential for the short data sets. Hence, a new differential Fourier coefficients interpolation (DFCI) method has been suggested, which is less sensitive to a presence of several modes in a signal. The analysis has been confirmed by simulations and measurements of a quartz wedge birefringence by means of the photoelastic modulator. The obtained bias, noise level, and measuring speed are comparable and even better than in lock-in amplifier technique. Moreover, presented DFCI method is expected to be promised candidate for using in actively developing imaging systems based on the modulation technique requiring fast digital signal processing of large data sets.

  1. Fourier transform inequalities for phylogenetic trees. (United States)

    Matsen, Frederick A


    Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.

  2. Fully phase-encrypted memory using cascaded extended fractional Fourier transform (United States)

    Nishchal, Naveen Kumar; Joseph, Joby; Singh, Kehar


    In this paper, we implement a fully phase-encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The full phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the decrypted phase image, alleviating the need of alignment in the Fourier plane making the system rugged.

  3. Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram. (United States)

    Barnett, Patrick D; Strange, K Alicia; Angel, S Michael


    This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

  4. Integrability of the Fourier transform: functions of bounded variation

    CERN Document Server

    Liflyand, E


    Certain relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The widest subspaces of the space of functions of bounded variation are indicated in which the cosine and sine Fourier transforms are integrable.

  5. Geometric interpretations of the Discrete Fourier Transform (DFT) (United States)

    Campbell, C. W.


    One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

  6. Realization of quantum discrete Fourier transform with NMR

    Institute of Scientific and Technical Information of China (English)


    The pulse sequences of the logic operations used in quantum discrete Fourier transform are designed for the experiment of nuclear magnetic resonance(NMR), and 2-qubit discrete Fourier transforms are implemented experimentally with NMR. The experimental errors are examined and methods for reducing the errors are proposed.


    Institute of Scientific and Technical Information of China (English)

    Yue Bing; Zhao Yuexia; Xu Zhoujun; Fu Hongjuan; Ma Fengning


    A set of discrete points obtained from audit records on a behavior session is processed with Fourier transform. The criterion of selecting Fourier transform coefficients is introduced, and is used to find a unified value from the set of coefficients. This unified value is compared with a threshold to determine whether the session is abnormal. Finally simple test results are reported.

  8. Fiber Optic Fourier Transform White-Light Interferometry

    Institute of Scientific and Technical Information of China (English)

    Yi Jiang; Cai-Jie Tang


    Fiber optic Fourier transform white-light inter-fereometry is presented to interrogate the absolute optical path difference of an Mach-Zehnder inter-ferometer. The phase change of the interferometer caused by scanning wavelength can be calculated by a Fourier transform-based phase demodulation technique. A linear output is achieved.

  9. Research progress on discretization of fractional Fourier transform

    Institute of Scientific and Technical Information of China (English)

    TAO Ran; ZHANG Feng; WANG Yue


    As the fractional Fourier transform has attracted a considerable amount of atten-tion in the area of optics and signal processing,the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier trans-form.Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain,the discre-tization of the fractional Fourier transform has been investigated recently.A sum-mary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper.The discretizations include sampling in the fractional Fourier domain,discrete-time fractional Fourier transform,frac-tional Fourier series,discrete fractional Fourier transform (including 3 main types:linear combination-type;sampling-type;and eigen decomposition-type),and other discrete fractional signal transform.It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.

  10. Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram (United States)

    Hanley, Quentin S.


    Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

  11. Thermal stabilization of static single-mirror Fourier transform spectrometers (United States)

    Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.


    Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.

  12. Cryogenic Scan Mechanism for Fourier Transform Spectrometer (United States)

    Brasunas, John C.; Francis, John L.


    A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear

  13. Improved Spectral Representation for Birdcall Based on Fractional Fourier Transform

    Institute of Scientific and Technical Information of China (English)


    A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart, and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart, and the better performance can be achieved if adaptive orders are used.

  14. Numerical Analysis of Inhomogeneous Dielectric Waveguide Using Periodic Fourier Transform

    Directory of Open Access Journals (Sweden)

    M. Moradian


    Full Text Available A general method is introduced to obtain the propagation constants of the inhomogeneous dielectric waveguide. The periodic Fourier transform is applied to the normalized Maxwell's equations and makes the field components periodic. Then they are expanded in Fourier series. Finally, the trapezoidal rule is applied to approximate the convolution integral which leads to a set of coupled second-order differential equations that can be solved as an eigenvalue-eigenvector problem. The normalized propagation constant can be obtained as the square roots of the eigenvalues of the coefficient matrices. The proposed method is applied to the dielectric waveguide with a two-layered dielectric profile in the transverse direction, and the first four-confined TE modes are obtained. The propagation constants for the mentioned dielectric waveguide are also derived analytically and are then compared with those derived by the proposed method. Comparison of results shows the efficacy of the proposed method.

  15. Persian Sign Language Recognition Using Radial Distance and Fourier Transform

    Directory of Open Access Journals (Sweden)

    Bahare Jalilian


    Full Text Available This paper provides a novel hand gesture recognition method to recognize 32 static signs of the Persian Sign Language (PSL alphabets. Accurate hand segmentation is the first and important step in sign language recognition systems. Here, we propose a method for hand segmentation that helps to build a better vision based sign language recognition system. The proposed method is based on YCbCr color space, single Gaussian model and Bayes rule. It detects region of hand in complex background and non-uniform illumination. Hand gesture features are extracted by radial distance and Fourier transform. Finally, the Euclidean distanceis used to compute the similarity between the input signs and all training feature vectors in the database. The system is tested on 480 posture images of the PSL, 15 images for each 32 signs. Experimental results show that our approach is capable to recognize all 32 PSL alphabets with 95.62% recognition rate.

  16. A rheumatoid arthritis study by Fourier transform infrared spectroscopy (United States)

    Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro


    Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.

  17. Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) (United States)

    Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.


    The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.

  18. A Fourier transform Raman spectrometer with visible laser excitation

    CERN Document Server

    Dzsaber, S; Bernáth, B; Gyüre, B; Fehér, T; Kramberger, C; Pichler, T; Simon, F


    We present the development and performance of a Fourier transformation (FT) based Raman spectrometer working with visible laser (532 nm) excitation. It is generally thought that FT-Raman spectrometers are not viable in the visible range where shot-noise limits the detector performance and therein they are outperformed by grating based, dispersive ones. We show that contrary to this common belief, the recent advances of high-performance interference filters makes the FT-Raman design a valid alternative to dispersive Raman spectrometers for samples which do not luminesce. We critically compare the performance of our spectrometer to two dispersive ones: a home-built single channel and a state-of-the-art CCD based instruments. We demonstrate a similar or even better sensitivity than the CCD based dispersive spectrometer particularly when the laser power density is considered. The instrument possesses all the known advantages of the FT principle of spectral accuracy, high throughput, and economic design. We also d...

  19. [Influence of collimation system on static Fourier transform spectrometer]. (United States)

    Jiang, Cheng-Zhi; Liang, Jing-Qiu; Liang, Zhong-Zhu; Sun, Qiang; Wang, Wei-Biao


    Collimation system provides collimated light for the static Fourier-transform spectroscopy (SFTS). Its quality is crucial to the signal to noise ratio (SNR) of SFTS. In the present paper, the physical model of SFTS was established based on the Fresnel diffraction theory by means of numerical software. The influence of collimation system on the SFTS was discussed in detail focusing on the aberrations of collimation lens and the quality of extended source. The results of simulation show that the influences of different kinds of aberrations on SNR take on obvious regularity, and in particular, the influences of off-axis aberrations on SNR are closely related to the location of off-axis point source. Finally the extended source's maximum radius allowed was obtained by simulation, which equals to 0.65 mm. The discussion results will be used for the design of collimation system.

  20. Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition

    Directory of Open Access Journals (Sweden)

    Yufeng Lu


    Full Text Available A fractional fourier transform (FrFT based chirplet signal decomposition (FrFT-CSD algorithm is proposed to analyze ultrasonic signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in signal decomposition and parameter estimation. FrFT rotates the signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in signal detection, estimation, and pattern recognition.

  1. The Pegg-Barnett phase operator and the discrete Fourier transform (United States)

    Perez-Leija, Armando; Andrade-Morales, Luis A.; Soto-Eguibar, Francisco; Szameit, Alexander; Moya-Cessa, Héctor M.


    In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm gives rise to the Pegg-Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.

  2. Fractional Fourier transform of apertured paraboloid refracting system

    Institute of Scientific and Technical Information of China (English)

    Jiannong Chen; Jinliang Yan; Defa Wang; Yongjiang Yu


    The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.

  3. Four-quadrant spatial phase-shifting Fourier transform digital holography for recording of cosine transform coefficients

    Institute of Scientific and Technical Information of China (English)

    Chujun Zheng; Peng Han; Hongsen Chang


    @@ A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π,and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.

  4. Security of image encryption scheme based on multi-parameter fractional Fourier transform (United States)

    Zhao, Tieyu; Ran, Qiwen; Yuan, Lin; Chi, Yingying; Ma, Jing


    Recently, multi-parameter fractional Fourier transform (MPFRFT) has been widely applied in the optics cryptosystem, which has attracted more and more researchers' attention. However, in further study we find a serious security problem on the MPFRFT which is the multi-choice of decryption key corresponding to an encryption key. The existence of multi-decryption-key hinders the application of this algorithm. We present a new generalized fractional Fourier transform, which can overcome the problem and enlarge the key space. The simulation results show that the proposed algorithm has higher security and key sensitivity.

  5. Estimation of structural modal parameters by fourier transform with an optimal window

    Institute of Scientific and Technical Information of China (English)

    ZHU Hong-ping; WAN Xin-hua


    An adaptive Fourier Transform (FT) with an optimal window has been proposed for the time-frequency analysis of nonstationary time series. The method allows for a good estimation of both frequency and amplitude of the spectrum and can be easily applied to the general case of time-varying signals. The evaluation of the proposed approach has been performed on measured time-varying signals from a suspension bridge model and a steel frame model whose data have the typical non-stationary characteristics. The numerical results show that the proposed approach can overcome some of the difficulties encountered in the classic Fourier transform technique and can achieve higher computation accuracy.

  6. Simple surface structure determination from Fourier transforms of angle-resolved photoemission extended fine structure

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)


    The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.

  7. Imaging Analysis by Means of Fractional Fourier Transform

    Institute of Scientific and Technical Information of China (English)


    Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.

  8. Electro-Optic Imaging Fourier Transform Spectral Polarimeter Project (United States)

    National Aeronautics and Space Administration — Boulder Nonlinear Systems, Inc. (BNS) proposes to develop an Electro-Optic Imaging Fourier Transform Spectral Polarimeter (E-O IFTSP). The polarimetric system is...

  9. On the physical relevance of the discrete Fourier transform

    CSIR Research Space (South Africa)

    Greben, JM


    Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...

  10. Embolic Doppler ultrasound signal detection via fractional Fourier transform. (United States)

    Gençer, Merve; Bilgin, Gökhan; Aydın, Nizamettin


    Computerized analysis of Doppler ultrasound signals can aid early detection of asymptomatic circulating emboli. For analysis, physicians use informative features extracted from Doppler ultrasound signals. Time -frequency analysis methods are useful tools to exploit the transient like signals such as Embolic signals. Detection of discriminative features would be the first step toward automated analysis of embolic Doppler ultrasound signals. The most problematic part of setting up emboli detection system is to differentiate embolic signals from confusing similar wave-like patterns such as Doppler speckle and artifacts caused by tissue movement, probe tapping, speaking etc. In this study, discrete version of fractional Fourier transform is presented as a solution in the detection of emboli in digitized Doppler ultrasound signals. An accurate set of parameters are extracted using short time Fourier transform and fractional Fourier transform and the results are compared to reveal detection quality. Experimental results prove the efficiency of fractional Fourier transform in which discriminative features becomes more evident.

  11. Quantum Fourier Transform and Phase Estimation in Qudit System

    Institute of Scientific and Technical Information of China (English)

    CAO Ye; PENG Shi-Guo; ZHENG Chao; LONG Gui-Lu


    The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc.In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case.They can be seen as subroutines in a main program run in a qudit quantum computer, and the quantum circuits are given.

  12. Simple optical setup implementation for digital Fourier transform holography

    Energy Technology Data Exchange (ETDEWEB)

    De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)


    In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.

  13. A discrete Fourier transform for virtual memory machines (United States)

    Galant, David C.


    An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

  14. A Graphical Presentation to Teach the Concept of the Fourier Transform (United States)

    Besalu, E.


    A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.

  15. Fourier Transform Moire Deflectometry for Measuring the 3-D Temperature Field

    Institute of Scientific and Technical Information of China (English)

    MA Li; WANG Ming; LIU Song; QI Xiaopin


    Fourier transform evaluation of fringe phase is applied to Moire deflectometry. 3-D gas temperature distribution for a given layer is reconstructed by optical tomography. The results show that the high-precise and automatic measurement for the 3-D gas temperature field can be realized by this technique.

  16. Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform (United States)

    Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos


    We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

  17. Experimental determination of Hurst exponent of the self-affine fractal patterns with optical fractional Fourier transform

    Institute of Scientific and Technical Information of China (English)

    FENG; Shaotong; HAN; Dianrong; DING; Heping


    By means of experimental technique of optical fractional Fourier transform,we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.

  18. System identification of two-dimensional continuous-time systems using wavelets as modulating functions. (United States)

    Sadabadi, Mahdiye Sadat; Shafiee, Masoud; Karrari, Mehdi


    In this paper, parameter identification of two-dimensional continuous-time systems via two-dimensional modulating functions is proposed. In the proposed method, trigonometric functions and sine-cosine wavelets are used as modulating functions. By this, a partial differential equation on the finite-time intervals is converted into an algebraic equation linear in parameters. The parameters of the system can then be estimated using the least square algorithms. The underlying computations utilize a two-dimensional fast Fourier transform algorithm, without the need for estimating the unknown initial or boundary conditions, at the beginning of each finite-time interval. Numerical simulations are presented to show the effectiveness of the proposed algorithm.

  19. Dynamic measurement of deformation using Fourier transform digital holographic interferometry (United States)

    Gao, Xinya; Wu, Sijin; Yang, Lianxiang


    Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.

  20. Electro-Optical Imaging Fourier-Transform Spectrometer (United States)

    Chao, Tien-Hsin; Zhou, Hanying


    An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

  1. Utilização de filtro de transformada de fourier para a minimização de ruídos em sinais analíticos Utilization of fourier transform filter for noise minimization in analytical signals

    Directory of Open Access Journals (Sweden)

    Eduardo O. Cerqueira


    Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices

  2. [Analysis of cell arrangements in Biota orientalis using Fourier transformation]. (United States)

    Duo, Hua-Qiong; Wang, Xi-Ming


    Fourier transform image-processing technology is applied for determining the cross section cell arrangement of early-wood in Biota orientalis. In this method, the disc-convoluted dot map from each cell radius with 10 pixels is transformed by Fourier transform, generating the angle distribution function in the power spectral pattern. The maximum value is the arrangement of the cell. The results of Fourier transform image-processing technology indicated that the arrangements of the cell of Biota orientalis are 15 degrees in oblique direction, respectively. This method provides a new basis for the digitized identification of the wood, and also the new theoretical research direction for the digitized identification and examination of the wood species.

  3. Online Botnet Detection Based on Incremental Discrete Fourier Transform

    Directory of Open Access Journals (Sweden)

    Xiaocong Yu


    Full Text Available Botnet detection has attracted lots of attention since botnet attack is becoming one of the most serious threats on the Internet. But little work has considered the online detection. In this paper, we propose a novel approach that can monitor the botnet activities in an online way. We define the concept of “feature streams” to describe raw network traffic. If some feature streams show high similarities, the corresponding hosts will be regarded as suspected bots which will be added into the suspected bot hosts set. After activity analysis, bot hosts will be confirmed as soon as possible. We present a simple method by computing the average Euclidean distance for similarity measurement.  To avoid huge calculation among feature streams, classical Discrete Fourier Transform (DFT technique is adopted. Then an incremental calculation of DFT coefficients is introduced to obtain the optimal execution time. The experimental evaluations show that our approach can detect both centralized and distributed botnet activities successfully with high efficiency and low false positive rate.

  4. The Formalization of Discrete Fourier Transform in HOL

    Directory of Open Access Journals (Sweden)

    Zhiping Shi


    Full Text Available Traditionally, Discrete Fourier Transform (DFT is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT and cosine frequency shift.

  5. Fourier transform infrared spectra applications to chemical systems

    CERN Document Server

    Ferraro, John R


    The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry.Presenting current information from leading experts in the field, Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-Infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography - Fourier Transform Interferometry.Volume 4 especially benefits spectroscopists and physicists, as well as researchers

  6. Recording Fractional Fourier Transform Hologram Using Holographic Zone Plate

    Institute of Scientific and Technical Information of China (English)

    高峰; 曾阳素; 张怡霄; 杨静; 高福华; 郭永康


    FRTH(fractional Fourier transform hologram) is a new kind of hologram that differs from common Fresnel holograms and Fourier transform holograms. Due to the flexibility of zone plate. A method that uses the -1 order diffraction wave of zone plate as the object wave and the 0 order diffraction wave as the reference wave to record FRTH is presented. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH using holographic zone plate is presented and experimental results are given.

  7. Phase retrieval for attacking fractional Fourier transform encryption. (United States)

    Kong, Dezhao; Shen, Xueju; Cao, Liangcai; Jin, Guofan


    An advanced iterative phase retrieval algorithm is applied to perform a ciphertext-only attack on the fractional Fourier transform-based double random phase encryption system. With the given complex amplitude of ciphertext and definite support of the object image, the original object image can be recovered by estimating the energy of support area in the recovered image. The encryption system can be attacked by analyzing the sensibility of fractional Fourier transform order keys and evaluating the energy of the object image support area. The proposed algorithm can obtain encrypted fractional order and retrieve two random phase keys. Numerical results demonstrate the efficacy of the proposed attacking method.

  8. Fourier-transform and global contrast interferometer alignment methods (United States)

    Goldberg, Kenneth A.


    Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.

  9. Fourier transform infrared spectra applications to chemical systems

    CERN Document Server

    Ferraro, John R


    Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc

  10. Calibration of the Herschel SPIRE Fourier Transform Spectrometer

    CERN Document Server

    Swinyard, B M; Hopwood, R; Valtchanov, I; Lu, N; Fulton, T; Benielli, D; Imhof, P; Marchili, N; Baluteau, J -P; Bendo, G J; Ferlet, M; Griffin, M J; Lim, T L; Makiwa, G; Naylor, D A; Orton, G S; Papageorgiou, A; Pearson, C P; Schulz, B; Sidher, S D; Spencer, L D; van der Wiel, M H D; Wu, R


    The Herschel SPIRE instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of 450-1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a spatially extended source and uses the Herschel telescope as primary calibrator. Conversion from extended to point-source calibration is carried out using observations of the planet Uranus. The model of the telescope emission is shown to be accurate to within 6% and repeatable to better than 0.06% and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3%. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1%, if the effects of the satellite absolu...

  11. Transmission fourier transform Raman spectroscopy of pharmaceutical tablet cores. (United States)

    Pelletier, Michael J; Larkin, Peter; Santangelo, Matthew


    Transmission Fourier transform (FT) Raman spectroscopy of pharmaceutical tablet cores is demonstrated using traditional, unmodified commercial instrumentation. The benefits of improved precision over backscattering Raman spectroscopy due to increased sample volume are demonstrated. Self-absorption effects on analyte band ratios and sample probe volume are apparent, however. A survey of near-infrared (NIR) absorption spectra in the FT-Raman spectral range (approximately 0 to 3500 wavenumber shift from 1064 nm, or 1064 to 1700 nm) of molecules with a wide range of NIR-active functional groups shows that although absorption at the laser wavelength (1064 nm) is relatively small, some regions of the Raman spectrum coincide with NIR absorbances of 0.5 per cm or greater. Fortunately, the pharmaceutically important regions of the Raman shift spectrum from 0 to 600 cm(-1) and from 1400 to 1900 cm(-1) exhibit low self-absorption for most organic materials. A statistical analysis of transmission FT-Raman noise in spectra collected from different regions of a pharmaceutical tablet provides insight into both spectral distortion and reduced sampling volume caused by self-absorption.

  12. Spin Glass Field Theory with Replica Fourier Transforms (United States)

    Pimentel, Iveta R.; De Dominicis, Cirano

    We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas n and the number of replica symmetry breaking steps R generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any i-replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi's solution for the free-energy of an Ising spin glass.

  13. SAR-based vibrometry using the fractional Fourier transform (United States)

    Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.


    A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.

  14. Improved Fast Fourier Transform Based Method for Code Accuracy Quantification

    Energy Technology Data Exchange (ETDEWEB)

    Ha, Tae Wook; Jeong, Jae Jun [Pusan National University, Busan (Korea, Republic of); Choi, Ki Yong [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)


    The capability of the proposed method is discussed. In this study, the limitations of the FFTBM were analyzed. The FFTBM produces quantitatively different results due to its frequency dependence. Because the problem is intensified by including a lot of high frequency components, a new method using a reduced cut-off frequency was proposed. The results of the proposed method show that the shortcomings of FFTBM are considerably relieved. Among them, the fast Fourier transform based method (FFTBM) introduced in 1990 has been widely used to evaluate a code uncertainty or accuracy. Prosek et al., (2008) identified its drawbacks, the so-called 'edge effect'. To overcome the problems, an improved FFTBM by signal mirroring (FFTBM-SM) was proposed and it has been used up to now. In spite of the improvement, the FFTBM-SM yielded different accuracy depending on the frequency components of a parameter, such as pressure, temperature and mass flow rate. Therefore, it is necessary to reduce the frequency dependence of the FFTBMs. In this study, the deficiencies of the present FFTBMs are analyzed and a new method is proposed to mitigate its frequency dependence.

  15. SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design

    NARCIS (Netherlands)

    Dool, T.C. van den; Kruizinga, B.; Braam, B.C.; Hamelinck, R.F.M.M.; Loix, N.; Loon, D. van; Dams, J.


    TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme in 2022. JAXA leads the development o

  16. Optical correlation based on the fractional Fourier transform. (United States)

    Granieri, S; Arizaga, R; Sicre, E E


    Some properties of optical correlation based on the fractional Fourier transform are analyzed. For a particular set of fractional orders, a filter is obtained that becomes insensitive to scale variations of the object. An optical configuration is also proposed to carry out the fractional correlation in a flexible way, and some experimental results are shown.

  17. Coupling of column liquid chromatography and Fourier transform infrared spectrometry

    NARCIS (Netherlands)

    Somsen, G.W; Gooijer, C; Velthorst, N.H; Brinkman, U.A Th


    This paper provides an extensive overview of the literature on the coupling of column liquid chromatography (LC) and Fourier transform infrared spectrometry (FT-IR). Flow-cell-based FT-IR detection and early solvent-elimination interfaces for LC-FT-IR are discussed in brief. A comprehensive descript

  18. Quantum Discrete Fourier Transform in an Ion Trap System

    Institute of Scientific and Technical Information of China (English)

    ZHENG Shi-Biao


    We propose two schemes for the implementation of quantum discrete Fourier transform in the ion trap system. In each scheme we design a tunable two-qubit phase gate as the main ingredient. The experimental implementation of the schemes would be an important step toward complex quantum computation in the ion trap system.

  19. Imaginary angle fractional Fourier transform and its optical implementation

    Institute of Scientific and Technical Information of China (English)

    华建文; 刘立人; 李国强


    The concept of imaginary angle fractional Fourier transform is proposed. Its existence and additive operation are proved. With this concept, FRT is expanded to the optical transform of convex lens outside the range of double focal length and that of concave lens.

  20. Fourier transformation methods in the field of gamma spectrometry

    Indian Academy of Sciences (India)

    A Abdel-Hafiez


    The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.

  1. Quaternion Fourier transforms for signal and image processing

    CERN Document Server

    Ell, Todd A; Sangwine, Stephen J


    Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.


    Institute of Scientific and Technical Information of China (English)

    Wang Xinsong; Zheng Weixing


    In this paper, a better asymptotic order of Fourier transform on SL(2 ,R) is obtained by using classicalanalysis and Lie analysis comparing with that of [5]、 [6], and the Plancherel theorem on Cc2 (SL (2, R)) isalso obtained as an application.

  3. a First Cryptosystem for Security of Two-Dimensional Data (United States)

    Mishra, D. C.; Sharma, Himani; Sharma, R. K.; Kumar, Naveen

    In this paper, we present a novel technique for security of two-dimensional data with the help of cryptography and steganography. The presented approach provides multilayered security of two-dimensional data. First layer security was developed by cryptography and second layer by steganography. The advantage of steganography is that the intended secret message does not attract attention to itself as an object of scrutiny. This paper proposes a novel approach for encryption and decryption of information in the form of Word Data (.doc file), PDF document (.pdf file), Text document, Gray-scale images, and RGB images, etc. by using Vigenere Cipher (VC) associated with Discrete Fourier Transform (DFT) and then hiding the data behind the RGB image (i.e. steganography). Earlier developed techniques provide security of either PDF data, doc data, text data or image data, but not for all types of two-dimensional data and existing techniques used either cryptography or steganography for security. But proposed approach is suitable for all types of data and designed for security of information by cryptography and steganography. The experimental results for Word Data, PDF document, Text document, Gray-scale images and RGB images support the robustness and appropriateness for secure transmission of these data. The security analysis shows that the presented technique is immune from cryptanalytic. This technique further provides security while decryption as a check on behind which RGB color the information is hidden.

  4. A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp. (United States)

    Barlow, Euan; Mulholland, Anthony J


    The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.

  5. [Biological Process Oriented Online Fourier Transform Infrared Spectrometer]. (United States)

    Xie, Fei; Wu, Qiong-shui; Zeng, Li-bo


    An online Fourier Transform Infrared Spectrometer and an ATR (Attenuated Total Reflection) probe, specifically at the application of real time measurement of the reaction substrate concentration in biological processes, were designed. (1) The spectrometer combined the theories of double cube-corner reflectors and flat mirror, which created a kind of high performance interferometer system. The light path folding way was utilized to makes the interferometer compact structure. Adopting double cube-corner reflectors, greatly reduces the influence of factors in the process of moving mirror movement such as rotation, tilt, etc. The parallelogram oscillation flexible support device was utilized to support the moving mirror moves. It cancelled the friction and vibration during mirror moving, and ensures the smooth operation. The ZnSe splitter significantly improved the hardware reliability in high moisture environment. The method of 60° entrance to light splitter improves the luminous flux. (2) An ATR in situ measuring probe with simple structure, large-flux, economical and practical character was designed in this article. The transmission of incident light and the light output utilized the infrared pipe with large diameter and innerplanted-high plating membrane, which conducted for the infrared transmission media of ATR probe. It greatly reduced the energy loss of infrared light after multiple reflection on the inner wall of the light pipe. Therefore, the ATR probe obtained high flux, improved the signal strength, which make the signal detected easily. Finally, the high sensitivity of MCT (Mercury Cadmium Telluride) detector was utilized to realize infrared interference signal collection, and improved the data quality of detection. The test results showed that the system yields the advantages of perfect moisture-proof performance, luminous flux, online measurement, etc. The designed online Fourier infrared spectrometer can real-time measured common reactant substrates

  6. The Characterisation of Pluripotent and Multipotent Stem Cells Using Fourier Transform Infrared Microspectroscopy

    Directory of Open Access Journals (Sweden)

    Mark J. Tobin


    Full Text Available Fourier transform infrared (FTIR microspectroscopy shows potential as a benign, objective and rapid tool to screen pluripotent and multipotent stem cells for clinical use. It offers a new experimental approach that provides a holistic measurement of macromolecular composition such that a signature representing the internal cellular phenotype is obtained. The use of this technique therefore contributes information that is complementary to that acquired by conventional genetic and immunohistochemical methods.

  7. Simulation of vortex laser beams propagation in parabolic index media based on fractional Fourier transform (United States)

    Mossoulina, O. A.; Kirilenko, M. S.; Khonina, S. N.


    We use radial Fractional Fourier transform to model vortex laser beams propagation in optical waveguides with parabolic dependence of the refractive index. To overcome calculation difficulties at distances proportional to a quarter of the period we use varied calculation step. Numerical results for vortex modes superposition propagation in a parabolic optical fiber show that the transverse beam structure can be changed significantly during the propagation. To provide stable transverse distribution input scale modes should be in accordance with fiber parameters.

  8. Foliage Plant Retrieval using Polar Fourier Transform, Color Moments and Vein Features

    CERN Document Server

    Kadir, Abdul; Susanto, Adhi; Santosa, Paulus Insap


    This paper proposed a method that combines Polar Fourier Transform, color moments, and vein features to retrieve leaf images based on a leaf image. The method is very useful to help people in recognizing foliage plants. Foliage plants are plants that have various colors and unique patterns in the leaf. Therefore, the colors and its patterns are information that should be counted on in the processing of plant identification. To compare the performance of retrieving system to other result, the experiments used Flavia dataset, which is very popular in recognizing plants. The result shows that the method gave better performance than PNN, SVM, and Fourier Transform. The method was also tested using foliage plants with various colors. The accuracy was 90.80% for 50 kinds of plants.

  9. The Fractional Fourier Transform and Its Application to Energy Localization Problems

    Directory of Open Access Journals (Sweden)

    ter Morsche Hennie G


    Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

  10. Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain. (United States)

    Liansheng, Sui; Meiting, Xin; Ailing, Tian


    A multiple-image encryption scheme is proposed based on the phase retrieval process and phase mask multiplexing in the fractional Fourier transform domain. First, each original gray-scale image is encoded into a phase only function by using the proposed phase retrieval process. Second, all the obtained phase functions are modulated into an interim, which is encrypted into the final ciphertext by using the fractional Fourier transform. From a plaintext image, a group of phase masks is generated in the encryption process. The corresponding decrypted image can be recovered from the ciphertext only with the correct phase mask group in the decryption process. Simulation results show that the proposed phase retrieval process has high convergence speed, and the encryption algorithm can avoid cross-talk; in addition, its encrypted capacity is considerably enhanced.

  11. Silhouette-free image encryption using interference in the multiple-parameter fractional Fourier transform domain. (United States)

    Zhong, Zhi; Qin, Haitao; Liu, Lei; Zhang, Yabin; Shan, Mingguang


    A novel approach for silhouette-free image encryption based on interference is proposed using discrete multiple-parameter fractional Fourier transform (DMPFrFT), which generalizes from fractional Fourier transform. An original image is firstly applied by chaotic pixel scrambling (CPS) and then encoded into the real part of a complex signal. Using interference principle, the complex signal generates three phase-only masks in DMPFrFT domain. The silhouette of the original image cannot be extracted using one or two of the three phase-only masks. The parameters of both CPS and DMPFrFT can also serve as encryption keys to extend the key space, which further enhance the level of cryptosystem security. Numerical simulations are demonstrated to show the feasibility and validity of this approach.

  12. Rejection of Linear FM Interference in DSSS System Based on Fractional Fourier Transform

    Institute of Scientific and Technical Information of China (English)

    QI Lin; TAO Ran; ZHOU Si-yong


    A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and biterror-ratio (BER) are obtained.

  13. Detection Algorithm for LFM Echo of Underwater Moving Targets Based on Discrete Fractional Fourier Transform

    Institute of Scientific and Technical Information of China (English)


    The mismatch between echo and replica caused by underwater moving target(UMT)'s radial velocity degrades the detection performance of the matched filter(MF) for the linear frequency modulation(LFM) signal. By using the focusing property of fractional Fourier transform(FRFT) to that signal, a detection algorithm for UMT's LFM echo based on the discrete fractional Fourier transform(DFRFT) is proposed. This algorithm is less affected by the target's radial velocity compared with the other MF detection algorithm utilizing zero radial velocity replica(ZRVR), and the mathematical relation between the output peak positions of these two algorithms exists in the case of existence of target echo. The algorithm can also estimate the target distance by using this relation. The simulation and experiment show that this algorithm's detection performance is better than or equivalent to that of the other MF algorithm utilizing ZRVR for the LFM echo of UMT with unknown radial velocity under reverberation noise background.

  14. Fourier Transform Ultrasound Spectroscopy for the determination of wave propagation parameters. (United States)

    Pal, Barnana


    The reported results for ultrasonic wave attenuation constant (α) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a consequence of the inherent wave propagation characteristics in a bounded medium. In the present work Fourier Transform Ultrasound Spectroscopy (FTUS) is adopted to determine ultrasonic wave propagation parameters, the wave number (k) and attenuation constant (α) at 1MHz frequency in tri-distilled water at room temperature (25°C). Pulse-echo signals obtained under same experimental conditions regarding the exciting input signal and reflecting boundary wall of the water container for various lengths of water columns are captured. The Fast Fourier Transform (FFT) components of the echo signals are taken to compute k, α and r, the reflection constant at the boundary, using Oak Ridge and Oxford method. The results are compared with existing literature values.

  15. Label-free identification of individual bacteria using Fourier transform light scattering

    CERN Document Server

    Jo, YoungJu; Kim, Min-hyeok; Park, HyunJoo; Kang, Suk-Jo; Park, YongKeun


    Rapid identification of bacterial species is crucial in medicine and food hygiene. In order to achieve rapid and label-free identification of bacterial species at the single bacterium level, we propose and experimentally demonstrate an optical method based on Fourier transform light scattering (FTLS) measurements and statistical classification. For individual rod-shaped bacteria belonging to four bacterial species (Listeria monocytogenes, Escherichia coli, Lactobacillus casei, and Bacillus subtilis), two-dimensional angle-resolved light scattering maps are precisely measured using FTLS technique. The scattering maps are then systematically analyzed, employing statistical classification in order to extract the unique fingerprint patterns for each species, so that a new unidentified bacterium can be identified by a single light scattering measurement. The single-bacterial and label-free nature of our method suggests wide applicability for rapid point-of-care bacterial diagnosis.

  16. A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis (United States)

    Ioup, G. E.


    Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.

  17. Automated charge state determination of complex isotope-resolved mass spectra by peak-target Fourier transform. (United States)

    Chen, Li; Yap, Yee Leng


    This study describes a new algorithm for charge state determination of complex isotope-resolved mass spectra. This algorithm is based on peak-target Fourier transform (PTFT) of isotope packets. It is modified from the widely used Fourier transform method because Fourier transform may give ambiguous charge state assignment for low signal-to-noise ratio (S/N) or overlapping isotopic clusters. The PTFT algorithm applies a novel "folding" strategy to enhance peaks that are symmetrically spaced about the targeted peak before applying the FT. The "folding" strategy multiplies each point to the high-m/z side of the targeted peak by its counterpart on the low-m/z side. A Fourier transform of this "folded" spectrum is thus simplified, emphasizing the charge state of the "chosen" ion, whereas ions of other charge states contribute less to the transformed data. An intensity-dependent technique is also proposed for charge state determination from frequency signals. The performance of PTFT is demonstrated using experimental electrospray ionization Fourier transform ion cyclotron resonance mass spectra. The results show that PTFT is robust for charge state determination of low S/N and overlapping isotopic clusters, and also useful for manual verification of potential hidden isotopic clusters that may be missed by the current analysis algorithms, i.e., AID-MS or THRASH.

  18. Prediction of Tide Height Using the Discrete Fourier Transform

    Directory of Open Access Journals (Sweden)

    Md. Towhiduzzaman


    Full Text Available In this study, I have investigated some aspects of astronomical tide and predicted tide time and height by different methods. This thesis deals with the prediction of height and time for both high and low waters of the ports set up in several places by discrete Fourier transform. I computed the tide height using Discrete Fourier Transform (DFT. The results are found to be in an agreement with the predicted data of others. By this work, we can predict the tide height of overall stations if the sample observed data are available for any kind of stations. I think that my work could be helpful to predict the tides over all stations where the observed data are available.

  19. A simple scanning mirror mechanism for a Fourier transform spectrometer (United States)

    Brasunas, John C.; Cushman, G. Mark


    We present a simple scanning mirror mechanism for a Fourier transform spectrometer, consisting of a voice coil actuator, a ball-bearing slide, and a single cube corner mirror or retroreflector. The use of a single cube corner reduces significantly the sensitivity of the Fourier transform spectrometer to the tilt of its moving mirror, enabling the simple mechanism. With simple velocity feedback using a linear velocity transducer, we achieve a scan speed stability of 2%-5% (root-mean-square) for scan speeds from 40 to 440 μm/s for a travel of 2.2 cm, corresponding to a spectral resolution of 0.06 cm-1. Fringe amplitude stability is about 5%. This scan mechanism was operated at standard temperature and pressure, but the relatively minute amount of lubricant in the ball-bearing slide may indicate possible operation under vacuum and/or cryogenic conditions.

  20. Implementing quantum Fourier transform with integrated photonic devices (United States)

    Tabia, Gelo Noel


    Many quantum algorithms that exhibit exponential speedup over their classical counterparts employ the quantum Fourier transform, which is used to solve interesting problems such as prime factorization. Meanwhile, nonclassical interference of single photons achieved on integrated platforms holds the promise of achieving large-scale quantum computation with multiport devices. An optical multiport device can be built to realize any quantum circuit as a sequence of unitary operations performed by beam splitters and phase shifters on path-encoded qudits. In this talk, I will present a recursive scheme for implementing quantum Fourier transform with a multimode interference photonic integrated circuit. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.

  1. Fourier transform spectrometer based on Fabry-Perot interferometer. (United States)

    Al-Saeed, Tarek A; Khalil, Diaa A


    We analyze the Fourier transform spectrometer based on a symmetric/asymmetric Fabry-Perot interferometer. In this spectrometer, the interferogram is obtained by recording the intensity as a function of the interferometer length. Then, we recover the spectrum by applying the discrete Fourier transform (DFT) directly on the interferogram. This technique results in spectral harmonic overlap and fictitious wavenumber components outside the original spectral range. For this purpose, in this work, we propose a second method to recover the spectrum. This method is based on expanding the DFT of the interferogram and the spectrum by a Haar or box function. By this second method, we recovered the spectrum and got rid of the fictitious spectral components and spectral harmonic overlap.

  2. Perfect vortex beam: Fourier transformation of a Bessel beam. (United States)

    Vaity, Pravin; Rusch, Leslie


    We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber.

  3. Scalable Fourier transform system for instantly structured illumination in lithography. (United States)

    Ye, Yan; Xu, Fengchuan; Wei, Guojun; Xu, Yishen; Pu, Donglin; Chen, Linsen; Huang, Zhiwei


    We report the development of a unique scalable Fourier transform 4-f system for instantly structured illumination in lithography. In the 4-f system, coupled with a 1-D grating and a phase retarder, the ±1st order of diffracted light from the grating serve as coherent incident sources for creating interference patterns on the image plane. By adjusting the grating and the phase retarder, the interference fringes with consecutive frequencies, as well as their orientations and phase shifts, can be generated instantly within a constant interference area. We demonstrate that by adapting this scalable Fourier transform system into lithography, the pixelated nano-fringe arrays with arbitrary frequencies and orientations can be dynamically produced in the photoresist with high variation resolution, suggesting its promising application for large-area functional materials based on space-variant nanostructures in lithography.

  4. Methods of theme presentation "The Fourier transform of impulse functions"

    Directory of Open Access Journals (Sweden)

    Faniya Ahmetova


    Full Text Available The paper considers the Fourier transform of impulse functions, which is the mathematical basis of the tasks associated with the theory of reception and signal conversion in optoelectronic system. The method of calculating of two functions convolution, its Fourier image and the image of the Fourier-Bessel axisymmetric functions are demonstrated in details. A table, which summarizes the analytical expression for the shifted impulse functions and records their Fourier transforms, is provided. A wide range of examples of solving tasks, containing the graphic illustration, is analyzed. A structured approach to the presentation of the material, which combines basic theoretical information and analysis of typical tasks, will help second-year students of optoelectronic specialty in their independent work and homework.

  5. Matrix-Vector Based Fast Fourier Transformations on SDR Architectures

    Directory of Open Access Journals (Sweden)

    Y. He


    Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.

  6. Ultrafast ranging lidar based on real-time Fourier transformation. (United States)

    Xia, Haiyun; Zhang, Chunxi


    Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory.

  7. Discrete Fourier Transform Analysis in a Complex Vector Space (United States)

    Dean, Bruce H.


    Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

  8. Time-frequency representation measurement based on temporal Fourier transformation (United States)

    Suen, Yifan; Xiao, Shaoqiu; Hao, Sumin; Zhao, Xiaoxiang; Xiong, Yigao; Liu, Shenye


    We propose a new scheme to physically realize the short-time Fourier transform (STFT) of chirped optical pulse using time-lens array that enables us to get time-frequency representation without using FFT algorithm. The time-lens based upon the four-wave mixing is used to perform the process of temporal Fourier transformation. Pump pulse is used for both providing the quadratic phase and being the window function of STFT. The idea of STFT is physically realized in our scheme. Simulations have been done to investigate performance of the time-frequency representation scheme (TFRS) in comparison with STFT using FFT algorithm. Optimal measurement of resolution in time and frequency has been discussed.

  9. Magnetic suspension based Fourier Transform Infrared Spectrometer mechanism (FTIS) (United States)

    Köker, Ingo; Langenbach, Harald; Schmid, Manfred; Lautier, Jean-Michel


    In the frame of an ESTEC technology contract the development of a Magnetically Suspended Fourier Transform Spectrometer Mechanism (FTIS) was carried out. The aim of the development is to avoid the issues found in mechanically suspended systems and to provide an active alignment and disturbance rejection capability for spectrometer applications. In the frame of FTIS an actively controlled suspension system based on the use of magnetic bearings was defined, developed and built as a demonstration model.

  10. Homology of balanced complexes via the Fourier transform

    CERN Document Server

    Meshulam, Roy


    Let G_0,...,G_k be finite abelian groups and let G_0*...*G_k be the join of the 0-dimensional complexes G_i. We give a characterization of the integral k-coboundaries of subcomplexes of G_0*...*G_k in terms of the Fourier transform on the group G_0 \\times ... \\times G_k. This leads to an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.

  11. Application of fast Fourier transformation in thermoluminescence thermogram reconstruction (United States)

    Pla, C.; Podgorsak, E. B.


    A thermoluminescence (TL) thermogram reconstruction technique based on fast Fourier transformation (FFT) techniques is presented. Only the first few terms of the real and imaginary ``frequency arrays,'' representing the thermogram in the frequency domain, are used for thermogram reconstruction by an inverse transformation. A method to determine the optimum number of FFT terms is discussed and a reconstruction study performed on six commonly used TL materials.

  12. Scaled Fractional Fourier Transform for Partially Coherent Beams

    Institute of Scientific and Technical Information of China (English)

    蔡阳健; 林强


    The definition of scaled fractional Fourier transform (SFRT) is extended to partially coherent beams based directly on the cross-spectral density. Based on this formula, an equivalent tensor ABCD law for the SFRT of partially coherent twisted anisotropic Gaussian-Schell model beams is derived. The derived formulae provide a powerful tool for analysing and calculating the SFRT of partially coherent beams. An application example is provided.

  13. Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation

    Institute of Scientific and Technical Information of China (English)

    QIAN Xiao-Qing; SONG Tong-Qiang


    We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.

  14. A Student's Guide to Fourier Transforms - 2nd Edition (United States)

    James, J. F.


    Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout

  15. Mass spectral peak distortion due to Fourier transform signal processing. (United States)

    Rockwood, Alan L; Erve, John C L


    Distortions of peaks can occur when one uses the standard method of signal processing of data from the Orbitrap and other FT-based methods of mass spectrometry. These distortions arise because the standard method of signal processing is not a linear process. If one adds two or more functions, such as time-dependent signals from a Fourier transform mass spectrometer and performs a linear operation on the sum, the result is the same as if the operation was performed on separate functions and the results added. If this relationship is not valid, the operation is non-linear and can produce unexpected and/or distorted results. Although the Fourier transform itself is a linear operator, the standard algorithm for processing spectra in Fourier transform-based methods include non-linear mathematical operators such that spectra processed by the standard algorithm may become distorted. The most serious consequence is that apparent abundances of the peaks in the spectrum may be incorrect. In light of these considerations, we performed theoretical modeling studies to illustrate several distortion effects that can be observed, including abundance distortions. In addition, we discuss experimental systems where these effects may manifest, including suggested systems for study that should demonstrate these peak distortions. Finally, we point to several examples in the literature where peak distortions may be rationalized by the phenomena presented here.

  16. [A novel spatial modulation Fourier transform spectrometer with adjustable spectral resolution]. (United States)

    Lian, Yu-Sheng; Liao, Ning-Fang; Lü, Hang; Wu, Wen-Min; Dong, Zhi-Gang


    In the premise of fulfilling the application requirement, the adjustment of spectral resolution can improve efficiency of data acquisition, data processing and data saving. So, by adjusting the spectral resolution, the performance of spectrometer can be improved, and its application range can be extended. To avoid the problems of the fixed spectral resolution of classical Fourier transform spectrometer, a novel type of spatial modulation Fourier transform spectrometer with adjustable spectral resolution is proposed in this paper. The principle of the novel spectrometer and its interferometer is described. The general expressions of the optical path difference and the lateral shear are induced by a ray tracing procedure. The equivalent model of the novel interferometer is analyzed. Meanwhile, the principle of the adjustment of spectral resolution is analyzed. The result shows that the novel spectrometer has the merits of adjustable spectral resolution, high stability, easy assemblage and adjustment etc. This theoretical study will provide the theoretical basis for the design of the spectrometer with adjustable spectral resolution and expand the application range of Fourier transform spectrometer.

  17. Experimental demonstration of an OFDM receiver based on a silicon-nanophot onic discrete Fourier transform filter

    DEFF Research Database (Denmark)

    Da Ros, Francesco; Nolle, Markus; Meuer, C.


    We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit.......We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit....

  18. Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform and chaos permutation (United States)

    Lang, Jun


    In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by use of the fractional Fourier transform, but most of their encryptions are complex value and need digital hologram technique to record their encrypted information, which is inconvenience for digital transmission. In this paper, we first propose a novel reality-preserving multiple-parameter fractional Fourier transform which share real-valuedness outputs as well as most of the properties required for a fractional transform. Then we propose a new approach for image encryption based on the real-valuedness of the reality-preserving multiple-parameter fractional Fourier transform and the decorrelation property of chaotic maps in order to meet the requirements of the secure image transmission. In the proposed scheme, the image is encrypted by juxtaposition of sections of the image in the reality-preserving multiple-parameter fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

  19. Quasi- Chun- Ching Shih's Fractional Fourier Transform with Periodicity of 2,3 and M

    Institute of Scientific and Technical Information of China (English)

    FAN Xi-zhi


    Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.

  20. Broadband Mid-Infrared Comb-Resolved Fourier Transform Spectroscopy (United States)

    Lee, Kevin; Mills, Andrew; Mohr, Christian; Jiang, Jie; Fermann, Martin; Maslowski, Piotr


    We report on a comb-resolved, broadband, direct-comb spectroscopy system in the mid-IR and its application to the detection of trace gases and molecular line shape analysis. By coupling an optical parametric oscillator (OPO), a 100 m multipass cell, and a high-resolution Fourier transform spectrometer (FTS), sensitive, comb-resolved broadband spectroscopy of dilute gases is possible. The OPO has radiation output at 3.1-3.7 and 4.5-5.5 μm. The laser repetition rate is scanned to arbitrary values with 1 Hz accuracy around 417 MHz. The comb-resolved spectrum is produced with an absolute frequency axis depending only on the RF reference (in this case a GPS disciplined oscillator), stable to 1 part in 10^9. The minimum detectable absorption is 1.6x10-6 wn Hz-1/2. The operating range of the experimental setup enables access to strong fundamental transitions of numerous molecular species for applications based on trace gas detection such as environmental monitoring, industrial gas calibration or medical application of human breath analysis. In addition to these capabilities, we show the application for careful line shape analysis of argon-broadened CO band spectra around 4.7 μm. Fits of the obtained spectra clearly illustrate the discrepancy between the measured spectra and the Voigt profile (VP), indicating the need to include effects such as Dicke narrowing and the speed-dependence of the collisional width and shift in the line shape model, as was shown in previous cw-laser studies. In contrast to cw-laser based experiments, in this case the entire spectrum (˜ 250 wn) covering the whole P and R branches can be measured in 16 s with 417 MHz resolution, decreasing the acquisition time by orders of magnitude. The parallel acquisition allows collection of multiple lines simultaneously, removing the correlation of possible temperature and pressure drifts. While cw-systems are capable of measuring spectra with higher precision, this demonstration opens the door for fast

  1. A Pseudospectral Time-Domain Algorithm for Calculating the Band Structure of a Two-Dimensional Photonic Crystal

    Institute of Scientific and Technical Information of China (English)

    何江平; 沈林放; 张全; 何赛灵


    A pseudospectral time-domain (PSTD) method is developed for calculating the band structure of a two-dimensional photonic crystal. Maxwell's equations are rewritten in terms of period fields by using the Bloch theorem. Instead of spatial finite differences, the fast Fourier transform is used to calculate the spatial derivatives. To reach a similar accuracy, fewer sample points are required in the present PSTD method as compared to the conventional finite-difference time-domain methods. Our numerical simulation shows that the present PSTD method is an efficient and accurate method for calculating the band structure of a photonic crystal.

  2. Statistical study of approximations to two dimensional inviscid turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Glaz, H.M.


    A numerical technique is developed for studying the ergodic and mixing hypotheses for the dynamical systems arising from the truncated Fourier transformed two-dimensional inviscid Navier-Stokes equations. This method has the advantage of exactly conserving energy and entropy (i.e., total vorticity) in the inviscid case except for numerical error in solving the ordinary differential equations. The development of the mathematical model as an approximation to a real physical (turbulent) flow and the numerical results obtained are discussed.

  3. A VLSI architecture for simplified arithmetic Fourier transform algorithm (United States)

    Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.


    The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

  4. Directional short-time Fourier transform of distributions

    Directory of Open Access Journals (Sweden)

    Katerina Hadzi-Velkova Saneva


    Full Text Available Abstract In this paper we consider the directional short-time Fourier transform (DSTFT that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013. We analyze the DSTFT and its transpose on test function spaces S ( R n $\\mathcal {S}(\\mathbb {R}^{n}$ and S ( Y 2 n $\\mathcal {S}(\\mathbb {Y}^{2n}$ , respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.

  5. Fourier Transform Infrared Spectroscopic Analysis of Protein Secondary Structures

    Institute of Scientific and Technical Information of China (English)

    Jilie KONG; Shaoning YU


    Infrared spectroscopy is one of the oldest and well established experimental techniques for the analysis of secondary structure of polypeptides and proteins. It is convenient, non-destructive, requires less sample preparation, and can be used under a wide variety of conditions. This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies. The experimental skills, data analysis, and correlations between the FTIR spectroscopic bands and protein secondary structure components are discussed. The applications of FTIR to the secondary structure analysis, conformational changes, structural dynamics and stability studies of proteins are also discussed.


    Directory of Open Access Journals (Sweden)

    Agata Bezubik


    Full Text Available The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail. Many specific properties of this new class of special functions useful in applications are studied. Such are the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density, corresponding discrete and continuous Fourier transforms, and others. Rapidly increasing precision of the interpolation with increasing density of the 3D lattice is shown in an example.

  7. Hyperspectral imaging using the single-pixel Fourier transform technique (United States)

    Jin, Senlin; Hui, Wangwei; Wang, Yunlong; Huang, Kaicheng; Shi, Qiushuai; Ying, Cuifeng; Liu, Dongqi; Ye, Qing; Zhou, Wenyuan; Tian, Jianguo


    Hyperspectral imaging technology is playing an increasingly important role in the fields of food analysis, medicine and biotechnology. To improve the speed of operation and increase the light throughput in a compact equipment structure, a Fourier transform hyperspectral imaging system based on a single-pixel technique is proposed in this study. Compared with current imaging spectrometry approaches, the proposed system has a wider spectral range (400-1100 nm), a better spectral resolution (1 nm) and requires fewer measurement data (a sample rate of 6.25%). The performance of this system was verified by its application to the non-destructive testing of potatoes.

  8. Atomic transition probabilities of Ce I from Fourier transform spectra (United States)

    Lawler, J. E.; Chisholm, J.; Nitz, D. E.; Wood, M. P.; Sobeck, J.; Den Hartog, E. A.


    Atomic transition probabilities for 2874 lines of the first spectrum of cerium (Ce I) are reported. These data are from new branching fraction measurements on Fourier transform spectra normalized with previously reported radiative lifetimes from time-resolved laser-induced-fluorescence measurements (Den Hartog et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 085006). The wavelength range of the data set is from 360 to 1500 nm. Comparisons are made to previous investigations which are less extensive. Accurate Ce i transition probabilities are needed for lighting research and development on metal halide high-intensity discharge lamps.

  9. A high-resolution Fourier-transform infrared spectrometer. (United States)

    Johnson, H. L.; Forbes, F. F.; Thompson, R. I.; Steinmetz , D. L.; Harris, O.


    We have developed a Fourier-transform infrared spectrometer having a resolution of 0.5/cm over the range of wavelength from 1 to 5.5 microns. It has been used to observe the sun over this wavelength range from a Lear Jet flying at an altitude of 14 km, and to observe a number of stars from the ground, using the 229-cm telescope of the Steward Observatory and the 152-cm aluminum-mirror telescope at the Observatorio Astronomico Nacional in the Sierra de San Pedro Martir, Baja California, Mexico. The solar spectrum is given here, while the ground-based spectra are being published separately.

  10. Fourier-transform Raman spectroscopic study of human hair (United States)

    Akhtar, W.; Edwards, H. G. M.; Farwell, D. W.; Nutbrown, M.


    Fourier-transform Raman microscopic spectra of normal, untreated and bleached hair fibres are presented. Vibrational assignments are made and differences are ascribed to the production of cysteic acid from cysteine. Changes in conformation associated with the disulphide bond in the keratotic component are noted from the ν(CSSC) vibrational modes at wave numbers near 500 cm -1. Raman spectra of hair root ends have also been investigated with a diminution in cysteine content being observed. Application of the technique to the biomedical investigation of healthy and diseased hair is proposed.

  11. Beam profile for the Herschel-SPIRE Fourier transform spectrometer. (United States)

    Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D


    One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile.

  12. Double passing the Kitt Peak 1-m Fourier transform spectrometer (United States)

    Jennings, D. E.; Hubbard, R.; Brault, J. W.


    Attention is given to a simple technique for performing the conversion of the Kitt Peak 1-m Fourier transform spectrometer's dual input/output optical configuration to a double pass configuration that improves spectral resolution by a factor of 2. The modification is made by placing a flat mirror in the output beam from each cat's eye, retroreflecting the beams back through the cat's eyes to the first beam splitter. A single detector is placed at the second input port, which then becomes the instrument's output.

  13. Fourier transform light scattering angular spectroscopy using digital inline holography. (United States)

    Kim, Kyoohyun; Park, YongKeun


    A simple and practical method for measuring the angle-resolved light scattering (ARLS) from individual objects is reported. Employing the principle of inline holography and a Fourier transform light scattering technique, both the static and dynamic scattering patterns from individual micrometer-sized objects can be effectively and quantitatively obtained. First, the light scattering measurements were performed on individual polystyrene beads, from which the refractive index and diameter of each bead were retrieved. Also, the measurements of the static and dynamic light scattering from intact human red blood cells are demonstrated. Using the present method, an existing microscope can be directly transformed into a precise instrument for ARLS measurements.

  14. Particle field holography data reduction by Fourier transform analysis (United States)

    Hess, Cecil F.; Trolinger, James D.


    The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.

  15. From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

    Institute of Scientific and Technical Information of China (English)

    吕翠红; 范洪义; 李东韡


    By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hy-perbolic function, i.e., tanα→tanhα, sinα→sinhα, we find quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within ordered product of operators (IWOP) wederive the unitary operator responsible for the FrST, which is composite and is made of eiπa†a/2 and exp[ iα2 (a2+a†2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.

  16. Discrete Fourier Transform in a Complex Vector Space (United States)

    Dean, Bruce H. (Inventor)


    An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

  17. Twin image elimination in digital holography by combination of Fourier transformations

    CERN Document Server

    Choudhury, Debesh


    We present a new technique for removing twin image in in-line digital Fourier holography using a combination of Fourier transformations. Instead of recording only a Fourier transform hologram of the object, we propose to record a combined Fourier transform hologram by simultaneously recording the hologram of the Fourier transform and the inverse Fourier transform of the object with suitable weighting coefficients. Twin image is eliminated by appropriate inverse combined Fourier transformation and proper choice of the weighting coefficients. An optical configuration is presented for recording combined Fourier transform holograms. Simulations demonstrate the feasibility of twin image elimination. The hologram reconstruction is sensitive to phase aberrations of the object, thereby opening a way for holographic phase sensing.

  18. The influence of glycerol on structural changes in waxy maize starch as studied by Fourier transform infra-red spectroscopy

    NARCIS (Netherlands)

    Vliegenthart, J.F.G.; Soest, J.J.G. van; Wit, D. de; Tournois, H.


    The influence of glycerol on the retrogradation kinetics for waxy maize starch-water systems was monitored by Fourier transform infra-red spectroscopy. The spectra showed the C---C and C---O stretching region (1300-800 cm−1) to be sensitive to the retrogradation process. A multistage kinetic process

  19. Variable-temperature Fourier-transform infrared studies of poly(L-lactic acid) in different states of order: A 2DCOS and PCMW2D analysis (United States)

    Zhang, Pudun; Unger, Miriam; Pfeifer, Frank; Siesler, Heinz W.


    Variable-temperature Fourier-transform infrared (FT-IR) spectra of a predominantly amorphous and a semi-crystalline poly(L-lactic acid) (PLLA) film were measured between 30 °C and 170 °C in order to investigate their temperature-dependent structural changes as a function of the initial state of order. For an in-depth analysis of the spectral variations in the carbonyl stretching band region (1803-1722 cm-1) two-dimensional correlation spectroscopy (2DCOS) and perturbation-correlation moving-window two-dimensional (PCMW2D) analyses were applied. Significant spectral changes were observed during heating of the amorphous PLLA sample whereas the semi-crystalline specimen showed only slight band shifts as a function of the external perturbation. The PCMW2D results suggested that for efficient 2DCOS analyses the heating process should be split up in two temperature intervals. These analyses then provided information on the recrystallization of the amorphous regions, the presence of an intermediate state of order and a sequence scenario for the observed spectral changes.

  20. Novel fringe scanning/Fourier transform method of synthetic imaging

    Energy Technology Data Exchange (ETDEWEB)

    Crawford, T.M.; Albano, R.K.


    We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.

  1. High Etendue Imaging Fourier Transform Spectrometer: initial results (United States)

    Horton, Richard F.; Conger, Chris A.; Pelligrino, L. S.


    At the Denver meeting, last year, we presented the High Etendue Imaging Fourier Transform Spectrometer, (HEIFTS), theory and optical design. This device uses a new 'image plane interferometer' geometry to produce 'autocorrelation function modulation' in the image plane of a 2D imaging array, such that the phase offset of the modulation varies linearly across the image. As a 2D image is pushbroomed across the imaging, array, the record of an individual scene pixel is recorded for each autocorrelation phase offset. The 3D array of this data is processed to yield an 'autocorrelation function' data cube, which is Fourier transformed to yield a 'wavenumber' hyperspectral data curve. A phase I device has been demonstrated in the laboratory and initial results are presented. The significant increase in signal to noise ratio, which the HEIFTS optical design promises over conventional hyperspectral imaging schemes, has been simulated, and results will be discussed. A Phase II system is being prepared for initial field deployment, and will be described.

  2. Integrated optics in an electrically scanned imaging Fourier transform spectrometer (United States)

    Breckinridge, James B. (Inventor); Ocallaghan, Fred G. (Inventor)


    An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.

  3. Fourier-Transform Ghost Imaging with Hard X Rays (United States)

    Yu, Hong; Lu, Ronghua; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming


    Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.

  4. Predictive analog-to-digital converter for Fourier-transform spectrometers. (United States)

    Deschênes, Jean-Daniel; Potvin, Simon; Ash, Jean-Simon; Genest, Jérôme


    This paper proposes the use of predictive analog-to-digital converters (ADC) to handle dynamic range issues in Fourier-transform spectrometers. Several predictive approaches are proposed, and one is implemented experimentally to show that the technique works. A system was implemented with 16 bit (13 bits effective) ADCs and digital-to-analog converters (DACs) operated at 8 bits to provide a comparison basis. Measurements of a blackbody at 900 °C performed using the setup show a 13 bit effective performance, limited by the input noise of the data acquisition card.

  5. Identification of early biomarkers during acetaminophen-induced hepatotoxicity by fourier transform infrared microspectroscopy.

    Directory of Open Access Journals (Sweden)

    Rekha Gautam

    Full Text Available Acetaminophen is a widely prescribed drug used to relieve pain and fever; however, it is a leading cause of drug-induced liver injury and a burden on public healthcare. In this study, hepatotoxicity in mice post oral dosing of acetaminophen was investigated using liver and sera samples with Fourier Transform Infrared microspectroscopy. The infrared spectra of acetaminophen treated livers in BALB/c mice show decrease in glycogen, increase in amounts of cholesteryl esters and DNA respectively. Rescue experiments using L-methionine demonstrate that depletion in glycogen and increase in DNA are abrogated with pre-treatment, but not post-treatment, with L-methionine. This indicates that changes in glycogen and DNA are more sensitive to the rapid depletion of glutathione. Importantly, analysis of sera identified lowering of glycogen and increase in DNA and chlolesteryl esters earlier than increase in alanine aminotransferase, which is routinely used to diagnose liver damage. In addition, these changes are also observed in C57BL/6 and Nos2(-/- mice. There is no difference in the kinetics of expression of these three molecules in both strains of mice, the extent of damage is similar and corroborated with ALT and histological analysis. Quantification of cytokines in sera showed increase upon APAP treatment. Although the levels of Tnfα and Ifnγ in sera are not significantly affected, Nos2(-/- mice display lower Il6 but higher Il10 levels during this acute model of hepatotoxicity. Overall, this study reinforces the growing potential of Fourier Transform Infrared microspectroscopy as a fast, highly sensitive and label-free technique for non-invasive diagnosis of liver damage. The combination of Fourier Transform Infrared microspectroscopy and cytokine analysis is a powerful tool to identify multiple biomarkers, understand differential host responses and evaluate therapeutic regimens during liver damage and, possibly, other diseases.

  6. Nih-3T3 Fibroblast Studied by Fourier Transform Infrared Spectroscopy

    CERN Document Server

    Iovenitti, Marco


    In this work I present the study of the behaviour response of mouse fibroblasts NIH-3T3 under UVB radiation using Fourier transform infrared spectroscopy (FT-IR), the preferred method of infrared spectroscopy. FT-IR, in fact, it is convenient to study molecular cell processes because it has the potential to provide the identification of the vibrational modes of some of the major compounds (lipid, proteins and nucleic acids) without being invasive in the biomaterials. The results show that apoptotic process is induced by UVB radiation.

  7. Color pattern recognition based on the joint fractional Fourier transform correlator

    Institute of Scientific and Technical Information of China (English)

    Weimin Jin; Yupei Zhang


    A new system of multi-channel single-output joint fractional Fourier transform correlator (JFRTC) for color pattern recognition is proposed based on the conventional system of multi-channel single-output joint transform correlator (JTC). The theoretical analysis and optical experiments are performed. With this method, one can obtain three correlation peaks at the output plane which show a pair of desired cross-correlation peaks and one auto-correlation peak. In comparison, the conventional system leads to more correlation peaks playing a noise role in color pattern recognition.

  8. Universal and special keys based on phase-truncated Fourier transform (United States)

    Qin, Wan; Peng, Xiang; Meng, Xiangfeng; Gao, Bruce


    We propose a novel optical asymmetric cryptosystem based on a phase-truncated Fourier transform. Two decryption keys independent of each other are generated. They are referred to as universal key and special key, respectively. Each of them can be used for decryption independently in absence of the other. The universal key is applicable to decrypt any ciphertext encoded by the same encryption key, but with poor legibility. On the contrary, the special key is adequate for legible decryption, but only valid for one ciphertext corresponding to the specified plaintext. A set of simulation results show the interesting performance of two types of decryption keys.

  9. Mastering the discrete Fourier transform in one, two or several dimensions pitfalls and artifacts

    CERN Document Server

    Amidror, Isaac


    The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and

  10. [The principle and analysis of micro-Fourier transform spectrometer based on MEMS micro-mirror]. (United States)

    Chen, Jian-Jun; Zhu, Yong; Liu, Bo; Wei, Wei; Zhang, Jie; Wang, Ning


    The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wave-length accuracy is approximately 1 nm and the sampling period of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR.

  11. Simple atmospheric transmittance calculation based on a Fourier-transformed Voigt profile. (United States)

    Kobayashi, Hirokazu


    A method of line-by-line transmission calculation for a homogeneous atmospheric layer that uses the Fourier-transformed Voigt profile is presented. The method is based on a pure Voigt function with no approximation and an interference term that takes into account the line-mixing effect. One can use the method to calculate transmittance, considering each line shape as it is affected by temperature and pressure, with a line database with an arbitrary wave-number range and resolution. To show that the method is feasible for practical model development, we compared the calculated transmittance with that obtained with a conventional model, and good consistency was observed.

  12. Fractional Fourier transform of Cantor sets: further numerical study

    Institute of Scientific and Technical Information of China (English)

    Gao Qiong; Liao tian-He; Cui Yuan-Feng


    This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.

  13. Charge reversal Fourier transform ion cyclotron resonance mass spectrometry. (United States)

    Lobodin, Vladislav V; Savory, Joshua J; Kaiser, Nathan K; Dunk, Paul W; Marshall, Alan G


    We report the first charge reversal experiments performed by tandem-in-time rather than tandem-in-space MS/MS. Precursor odd-electron anions from fullerene C(60), and even-electron ions from 2,7-di-tert-butylfluorene-9-carboxylic acid and 3,3'-bicarbazole were converted into positive product ions ((-)CR(+)) inside the magnet of a Fourier transform ion cyclotron resonance mass spectrometer. Charge reversal was activated by irradiating precursor ions with high energy electrons or UV photons: the first reported use of those activation methods for charge reversal. We suggest that high energy electrons achieve charge reversal in one step as double electron transfer, whereas UV-activated (-)CR(+) takes place stepwise through two single electron transfers and formally corresponds to a neutralization-reionization ((-)NR(+)) experiment.

  14. Observing Extended Sources with the \\Herschel SPIRE Fourier Transform Spectrometer

    CERN Document Server

    Wu, Ronin; Etxaluze, Mireya; Makiwa, Gibion; Naylor, David A; Salji, Carl; Swinyard, Bruce M; Ferlet, Marc; van der Wiel, Matthijs H D; Smith, Anthony J; Fulton, Trevor; Griffin, Matt J; Baluteau, Jean-Paul; Benielli, Dominique; Glenn, Jason; Hopwood, Rosalind; Imhof, Peter; Lim, Tanya; Lu, Nanyao; Panuzzo, Pasquale; Pearson, Chris; Sidher, Sunil; Valtchanov, Ivan


    The Spectral and Photometric Imaging Receiver (SPIRE) on the European Space Agency's Herschel Space Observatory utilizes a pioneering design for its imaging spectrometer in the form of a Fourier Transform Spectrometer (FTS). The standard FTS data reduction and calibration schemes are aimed at objects with either a spatial extent much larger than the beam size or a source that can be approximated as a point source within the beam. However, when sources are of intermediate spatial extent, neither of these calibrations schemes is appropriate and both the spatial response of the instrument and the source's light profile must be taken into account and the coupling between them explicitly derived. To that end, we derive the necessary corrections using an observed spectrum of a fully extended source with the beam profile and the source's light profile taken into account. We apply the derived correction to several observations of planets and compare the corrected spectra with their spectral models to study the beam c...

  15. Mid-Infrared Frequency Comb Fourier Transform Spectrometer

    CERN Document Server

    Adler, Florian; Foltynowicz, Aleksandra; Cossel, Kevin C; Briles, Travis C; Hartl, Ingmar; Ye, Jun


    Optical frequency-comb-based-high-resolution spectrometers offer enormous potential for spectroscopic applications. Although various implementations have been demonstrated, the lack of suitable mid-infrared comb sources has impeded explorations of molecular fingerprinting. Here we present for the first time a frequency-comb Fourier transform spectrometer operating in the 2100-to-3700-cm-1 spectral region that allows fast and simultaneous acquisitions of broadband absorption spectra with up to 0.0056 cm-1 resolution. We demonstrate part-per-billion detection limits in 30 seconds of integration time for various important molecules including methane, ethane, isoprene, and nitrous oxide. Our system enables precise concentration measurements even in gas mixtures that exhibit continuous absorption bands, and it allows detection of molecules at levels below the noise floor via simultaneous analysis of multiple spectral features. This system represents a near real-time, high-resolution, high-bandwidth mid-infrared sp...

  16. Lamellar grating optimization for miniaturized fourier transform spectrometers. (United States)

    Ferhanoglu, Onur; Seren, Hüseyin R; Lüttjohann, Stephan; Urey, Hakan


    Microfabricated Lamellar grating interferometers (LGI) require fewer components compared to Michelson interferotemeters and offer compact and broadband Fourier transform spectrometers (FTS) with good spectral resolution, high speed and high efficiency. This study presents the fundamental equations that govern the performance and limitations of LGI based FTS systems. Simulations and experiments were conducted to demonstrate and explain the periodic nature of the interferogram envelope due to Talbot image formation. Simulations reveal that the grating period should be chosen large enough to avoid Talbot phase reversal at the expense of mixing of the diffraction orders at the detector. Optimal LGI grating period selection depends on a number of system parameters and requires compromises in spectral resolution and signal-to-bias ratio (SBR) of the interferogram within the spectral range of interest. New analytical equations are derived for spectral resolution and SBR of LGI based FTS systems.

  17. Spatially Resolved Fourier Transform Spectroscopy in the Extreme Ultraviolet

    CERN Document Server

    Jansen, G S M; Freisem, L; Eikema, K S E; Witte, S


    Coherent extreme ultraviolet (XUV) radiation produced by table-top high-harmonic generation (HHG) sources provides a wealth of possibilities in research areas ranging from attosecond physics to high resolution coherent imaging. However, it remains challenging to fully exploit the coherence of such sources for interferometry and Fourier transform spectroscopy (FTS). This is due to the need for a measurement system that is stable at the level of a wavelength fraction, yet allowing a controlled scanning of time delays. Here we demonstrate XUV interferometry and FTS in the 17-55 nm wavelength range using an ultrastable common-path interferometer suitable for high-intensity laser pulses that drive the HHG process. This approach enables the generation of fully coherent XUV pulse pairs with sub-attosecond timing variation, tunable time delay and a clean Gaussian spatial mode profile. We demonstrate the capabilities of our XUV interferometer by performing spatially resolved FTS on a thin film composed of titanium and...

  18. The RC Circuit: An Approach with Fourier Transforms

    Indian Academy of Sciences (India)


    In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms(FT). This very general technique gives us a lot of insight intosolving first order differential equations with source terms dependingon time. In itself, the RC circuit is by far the mostcommonplace entity in modern electronics. But the method ofFT is not the accepted custom for an electronic engineer, whois probably more comfortable working with complex impedancesand phasors while solving problems in network analysis.In fact, what is used much more extensively is the Laplacetransform. But a lot of things, (including the complex impedanceitself, and some insight into complex analysis) can be understoodbetter if we use the FT approach to solve the differentialequations that come up in network analysis. The use of FTcomes smoothly from first principles – precisely what we setout to demonstrate here.

  19. Initial Results from the USNO Dispersed Fourier Transform Spectrograph

    CERN Document Server

    Hajian, A R; Cenko, A T; Olling, R P; Mozurkewich, D; Armstrong, J T; Pohl, B; Petrossian, S; Knuth, K H; Hindsley, R B; Murison, M; Efroimsky, M; Dantowitz, R; Kozubal, M; Currie, D G; Nordgren, T E; Tycner, C; McMillan, R S; Hajian, Arsen R.; Behr, Bradford B.; Cenko, Andrew T.; Olling, Robert P.; Mozurkewich, David; Pohl, Brian; Petrossian, Sevan; Knuth, Kevin H.; Hindsley, Robert B.; Murison, Marc; Efroimsky, Michael; Dantowitz, Ronald; Kozubal, Marek; Currie, Douglas G.; Nordgren, Tyler E.; Tycner, Christopher; Millan, Robert S. Mc


    We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well-suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high accuracy stellar spectrometers. In this paper, we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband i...

  20. Wide-Field Detected Fourier Transform CARS Microscopy (United States)

    Duarte, Alex Soares; Schnedermann, Christoph; Kukura, Philipp


    We present a wide-field imaging implementation of Fourier transform coherent anti-Stokes Raman scattering (wide-field detected FT-CARS) microscopy capable of acquiring high-contrast label-free but chemically specific images over the full vibrational ‘fingerprint’ region, suitable for a large field of view. Rapid resonant mechanical scanning of the illumination beam coupled with highly sensitive, camera-based detection of the CARS signal allows for fast and direct hyperspectral wide-field image acquisition, while minimizing sample damage. Intrinsic to FT-CARS microscopy, the ability to control the range of time-delays between pump and probe pulses allows for fine tuning of spectral resolution, bandwidth and imaging speed while maintaining full duty cycle. We outline the basic principles of wide-field detected FT-CARS microscopy and demonstrate how it can be used as a sensitive optical probe for chemically specific Raman imaging.

  1. Microscope system with on axis programmable Fourier transform filtering (United States)

    Martínez, José Luis; García-Martínez, Pascuala; Moreno, Ignacio


    We propose an on-axis microscope optical system to implement programmable optical Fourier transform image processing operations, taking advantage of phase and polarization modulation of a liquid crystal on silicon (LCOS) display. We use a Hamamatsu spatial light modulator (SLM), free of flickering, which therefore can be tuned to fully eliminate the zero order component of the encoded diffractive filter. This allows the realization of filtering operation on axis (as opposed to other systems in the literature that require operating off axis), therefore making use of the full space bandwidth provided by the SLM. The system is first demonstrated by implementing different optical processing operations based on phase-only blazed gratings such as phase contrast, band-pass filtering, or additive and substractive imaging. Then, a simple Differential interference contrast (DIC) imaging is obtained changing to a polarization modulation scheme, achieved simply by selecting a different incident state of polarization on the incident beam.

  2. Motion saliency detection using a temporal fourier transform (United States)

    Chen, Zhe; Wang, Xin; Sun, Zhen; Wang, Zhijian


    Motion saliency detection aims at detecting the dynamic semantic regions in a video sequence. It is very important for many vision tasks. This paper proposes a new type of motion saliency detection method, Temporal Fourier Transform, for fast motion saliency detection. Different from conventional motion saliency detection methods that use complex mathematical models or features, variations in the phase spectrum of consecutive frames are identified and extracted as the key to obtaining the location of salient motion. As all the calculation is made on the temporal frequency spectrum, our model is independent of features, background models, or other forms of prior knowledge about scenes. The benefits of the proposed approach are evaluated for various videos where the number of moving objects, illumination, and background are all different. Compared with some the state of the art methods, our method achieves both good accuracy and fast computation.

  3. On the finite Fourier transforms of functions with infinite discontinuities

    Directory of Open Access Journals (Sweden)

    Branko Saric


    Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.

  4. High-Throughput Screening Using Fourier-Transform Infrared Imaging

    Directory of Open Access Journals (Sweden)

    Erdem Sasmaz


    Full Text Available Efficient parallel screening of combinatorial libraries is one of the most challenging aspects of the high-throughput (HT heterogeneous catalysis workflow. Today, a number of methods have been used in HT catalyst studies, including various optical, mass-spectrometry, and gas-chromatography techniques. Of these, rapid-scanning Fourier-transform infrared (FTIR imaging is one of the fastest and most versatile screening techniques. Here, the new design of the 16-channel HT reactor is presented and test results for its accuracy and reproducibility are shown. The performance of the system was evaluated through the oxidation of CO over commercial Pd/Al2O3 and cobalt oxide nanoparticles synthesized with different reducer-reductant molar ratios, surfactant types, metal and surfactant concentrations, synthesis temperatures, and ramp rates.

  5. Short-time Fourier transform laser Doppler holography

    CERN Document Server

    Atlan, Michael


    We report a demonstration of laser Doppler holography at a sustained acquisition rate of 250 Hz on a 1 Megapixel complementary metal-oxide-semiconductor (CMOS) sensor array and image display at 10 Hz frame rate. The holograms are optically acquired in off-axis configuration, with a frequency-shifted reference beam. Wide-field imaging of optical fluctuations in a 250 Hz frequency band is achieved by turning time-domain samplings to the dual domain via short-time temporal Fourier transformation. The measurement band can be positioned freely within the low radio-frequency spectrum by tuning the frequency of the reference beam in real-time. Video-rate image rendering is achieved by streamline image processing with commodity computer graphics hardware. This experimental scheme is validated by a non-contact vibrometry experiment.

  6. Instrument concept of the imaging Fourier transform spectrometer GLORIA

    Directory of Open Access Journals (Sweden)

    F. Friedl-Vallon


    Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.

  7. Optical design of the ATMOS Fourier transform spectrometer (United States)

    Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.


    The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.

  8. A direct digital synthesis chirped pulse Fourier transform microwave spectrometer. (United States)

    Finneran, Ian A; Holland, Daniel B; Carroll, P Brandon; Blake, Geoffrey A


    Chirped pulse Fourier transform microwave (CP-FTMW) spectrometers have become the instrument of choice for acquiring rotational spectra, due to their high sensitivity, fast acquisition rate, and large bandwidth. Here we present the design and capabilities of a recently constructed CP-FTMW spectrometer using direct digital synthesis (DDS) as a new method for chirped pulse generation, through both a suite of extensive microwave characterizations and deep averaging of the 10-14 GHz spectrum of jet-cooled acetone. The use of DDS is more suited for in situ applications of CP-FTMW spectroscopy, as it reduces the size, weight, and power consumption of the chirp generation segment of the spectrometer all by more than an order of magnitude, while matching the performance of traditional designs. The performance of the instrument was further improved by the use of a high speed digitizer with dedicated signal averaging electronics, which facilitates a data acquisition rate of 2.1 kHz.

  9. On-chip photonic Fourier transform with surface plasmon polaritons

    Institute of Scientific and Technical Information of China (English)

    Shan Shan Kou; Guanghui Yuan; Qian wang; Luping Du; Eugeniu Balaur; Daohua Zhang; Dingyuan Tang


    The Fourier transform (FT),a cornerstone of optical processing,enables rapid evaluation of fundamental mathematical operations,such as derivatives and integrals.Conventionally,a converging lens performs an optical FT in free space when light passes through it.The speed of the transformation is limited by the thickness and the focal length of the lens.By usingthe wave nature of surface plasmon polaritons (SPPs),here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 μm,resulting in an increase of speed by four to five orders of magnitude.The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components.The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.

  10. A high-resolution Fourier Transform Spectrometer for planetary spectroscopy (United States)

    Cruikshank, D. P.; Sinton, W. M.


    The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.

  11. A Matrix Formulation of Discrete Chirp Fourier Transform Algorithms

    Institute of Scientific and Technical Information of China (English)

    Juan Pablo Soto Quiros; Domingo Rodriguez


    This work presents a computational matrix framework in terms of tensor signal algebra for the formulation of discrete chirp Fourier transform algorithms. These algorithms are used in this work to estimate the point target functions (impulse response functions) of multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) systems. This estimation technique is being studied as an alternative to the estimation of point target functions using the discrete cross-ambiguity function for certain types of environmental surveillance applications. The tensor signal algebra is presented as a mathematics environment composed of signal spaces, finite dimensional linear operators, and special matrices where algebraic methods are used to generate these signal transforms as computational estimators. Also, the tensor signal algebra contributes to analysis, design, and implementation of parallel algorithms. An instantiation of the framework was performed by using the MATLAB Parallel Computing Toolbox, where all the algorithms presented in this paper were implemented.

  12. Indirect Fourier transform in the context of statistical inference. (United States)

    Muthig, Michael; Prévost, Sylvain; Orglmeister, Reinhold; Gradzielski, Michael


    Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.

  13. OCTAD-S: digital fast Fourier transform spectrometers by FPGA (United States)

    Iwai, Kazumasa; Kubo, Yûki; Ishibashi, Hiromitsu; Naoi, Takahiro; Harada, Kenichi; Ema, Kenji; Hayashi, Yoshinori; Chikahiro, Yuichi


    We have developed a digital fast Fourier transform spectrometer made of an analog-to-digital converter (ADC) and a field-programmable gate array (FPGA). The base instrument has independent ADC and FPGA modules, which allow us to implement different spectrometers in a relatively easy manner. Two types of spectrometers have been instrumented: one with 4.096 GS/s sampling speed and 2048 frequency channels and the other with 2.048 GS/s sampling speed and 32,768 frequency channels. The signal processing in these spectrometers has no dead time, and the accumulated spectra are recorded in external media every 8 ms. A direct sampling spectroscopy up to 8 GHz is achieved by a microwave track-and-hold circuit, which can reduce the analog receiver in front of the spectrometer. Highly stable spectroscopy with a wide dynamic range was demonstrated in a series of laboratory experiments and test observations of solar radio bursts.

  14. Radix-3 Algorithm for Realization of Discrete Fourier Transform

    Directory of Open Access Journals (Sweden)

    M.Narayan Murty


    Full Text Available In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT of length N = 3m (m = 1, 2, 3,... is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If the input signal has length N, direct calculation of DFT requires O (N 2 complex multiplications (4N 2 real multiplications and some additions. This radix-3 algorithm reduces the number of multiplications required for realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.

  15. Fourier transform for fermionic systems and the spectral tensor network. (United States)

    Ferris, Andrew J


    Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.

  16. Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses

    Directory of Open Access Journals (Sweden)

    Lucy Lim


    Full Text Available Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices.

  17. Adaptive Controller for Compact Fourier Transform Spectrometer with Space Applications (United States)

    Keymeulen, D.; Yiu, P.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.; Conroy, M.


    Here we present noise mitigation techniques developed as part of an adaptive controller for a very compact Compositional InfraRed Interferometric Spectrometer (CIRIS) implemented on a stand-alone field programmable gate array (FPGA) architecture with emphasis on space applications in high radiation environments such as Europa. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. The design eschews a monochromatic reference laser typically used for sampling clock generation and instead utilizes constant time-sampling via internally generated clocks. This allows for a compact and robust device, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 µm) on planetary exploration missions. The instrument's embedded microcontroller is implemented on a VIRTEX-5 FPGA and a PowerPC with the aim of sampling the instrument's detector and optical rotary encoder in order to construct interferograms. Subsequent onboard signal processing provides spectral immunity from the noise effects introduced by the compact design's removal of a reference laser and by the radiation encountered during space flight to destinations such as Europa. A variety of signal processing techniques including resampling, radiation peak removal, Fast Fourier Transform (FFT), spectral feature alignment, dispersion correction and calibration processes are applied to compose the sample spectrum in real-time with signal-to-noise-ratio (SNR) performance comparable to laser-based FTS designs in radiation-free environments. The instrument's FPGA controller is demonstrated with the FTS to characterize its noise mitigation techniques and highlight its suitability for implementation in space systems.

  18. [Continuum based fast Fourier transform processing of infrared spectrum]. (United States)

    Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai


    To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.

  19. Fast Fourier Transform Co-Processor (FFTC)- Towards Embedded GFLOPs (United States)

    Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Wite, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland


    Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co- Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment.In frame of the ESA activity “Fast Fourier Transform DSP Co-processor (FFTC)” (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following:Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP.The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance.The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT- based processing tasks.A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses.The presentation will give and overview on the project, including the results of the validation of the FFTC ASIC prototypes.

  20. Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs (United States)

    Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas


    Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.

  1. Potential-Field Forward Modeling and Inversion Using 3D Fast Fourier Transforms (United States)

    Phillips, J. D.; Caratori Tontini, F.; Cocchi, L.


    Although 1D and 2D fast Fourier transforms (FFTs) have long been used for the filtering, interpretation, and modeling of potential-field data, 3D FFTs have not enjoyed similar popularity. This may change with the recent discovery (Caratori Tontini et al., in press, JGR) that simple 3D FFT filters can be used to transform distributions of density (or magnetization) within a box-shaped 3D volume into gravity (or magnetic) fields within the same volume. For example, the continuous 3D Fourier transform of the vertical gravity anomaly Δgz(x,y,z) in a volume is related to the 3D Fourier transform of the density ρ(x,y,z) in the volume by ℑ[Δgz] = i4πG(kz/ | k | 2)ℑ[ρ]; | k | ≠0, (1) where G is the gravitational constant, kx, ky, kz are wavenumbers, and | k | 2 = kx2+ ky2+ kz2. (2) Translating (1) into a digital FFT filtering operation requires careful consideration of the periodicity of the density distribution and the gravity field. Nevertheless, (1) provides a highly efficient way to calculate the vertical gravity anomaly of a 3D density distribution within a few minutes. The calculated gravity anomaly can be sampled at random points or on an arbitrary surface using tri-linear interpolation. An equivalent space- domain calculation of the gravity field on an arbitrary surface can take many hours. The inverse relation to (1) does not appear to offer a practical approach for calculating a reliable density distribution from observed gravity data. This is because the data would have to cover a substantial portion of the model volume, and because the transformation is undefined on the plane kz = 0, where both the denominator of the filter kernel and the Fourier transform of the gravity field are identically zero. Numerical experiments show that the density distribution resulting from the power on the plane kz = 0 represents a classic Parker annihilator. This annihilator can be calculated from the density distribution but not from the gravity field, as would be

  2. Spectral ’Fingerprinting’ of Phytoplankton Populations by Two-Dimensional Fluorescence and Fourier-Transform-Based Pattern Recognition. (United States)


    Marine Research. IS. K3LXOROS (Centinue en reveree side it necessa.yad Identlfy by blek nmer) ’-"luorescence Malysis J) Chlorophyll Auorescencej Marine... chlorophylls , carotenoids, and phycobilins. Chlorophyll a provides the universal link between these three groups since it is the only pigment present in...accessory pigments ( chlorophylls b and c, carotenoids, and phycobilins) and channels it into the photosynthetic process. This allows photosynthesis to

  3. Radon-Fractional Fourier Transform and Its Application to Radar Maneuvering Target Detection (Preprint) (United States)


    Radon -Fractional Fourier Transform and Its Application to Radar Maneuvering Target Detection Xiaolong Chen*, Fuqing Cai, Yu Cong, Jian Guan...unit (ARU) and Doppler frequency migration (DFM) effects. In this paper, a novel transform called the Radon -fractional Fourier transform (RFRFT) is...are carried out and the performances of different methods including MTD, FRFT, and the Radon -Fourier transform (RFT) are compared, which demonstrate

  4. Development of Imaging Fourier-Transform Spectroscopy for the Characterization of Turbulent Jet Flames (United States)



  5. Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods. (United States)

    Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K


    In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

  6. Fourier transform infrared spectroscopy approach for measurements of photoluminescence and electroluminescence in mid-infrared (United States)

    Zhang, Y. G.; Gu, Y.; Wang, K.; Fang, X.; Li, A. Z.; Liu, K. H.


    An improved Fourier transform infrared spectroscopy approach adapting to photoluminescence and electroluminescence measurements in mid-infrared has been developed, in which diode-pumped solid-state excitation lasers were adopted for photoluminescence excitation. In this approach, three different Fourier transform infrared modes of rapid scan, double modulation, and step scan were software switchable without changing the hardware or connections. The advantages and limitations of each mode were analyzed in detail. Using this approach a group of III-V and II-VI samples from near-infrared extending to mid-infrared with photoluminescence intensities in a wider range have been characterized at room temperature to demonstrate the validity and overall performances of the system. The weaker electroluminescence of quantum cascade lasers in mid-infrared band was also surveyed at different resolutions. Results show that for samples with relatively strong photoluminescence or electroluminescence out off the background, rapid scan mode is the most preferable. For weaker photoluminescence or electroluminescence overlapped with background, double modulation is the most effective mode. To get a better signal noise ratio when weaker photoluminescence or electroluminescence signal has been observed in double modulation mode, switching to step scan mode should be an advisable option despite the long data acquiring time and limited resolution.

  7. Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform (United States)

    Aalipour, Rasoul


    When a part of an optical wave-front experiences a sharp change in its phase, Fresnel diffraction becomes appreciable. Sharp change in phase occurs as a wave-front strikes with a phase step. The intensity distributions of diffraction patterns of the phase step is formulated by applying Fresnel-Kirchhoff integral. For while the incident light on the step is coherent, the Fresnel-Kirchhoff integral can be solved by using familiar Fresnel integrals. But, when the incident light is partially coherent, one can not express the diffraction integral as the Fresnel integrals and the problem is summarized in solving some unusual integrals. In this report, we propose Fourier transform method for solving the Fresnel-Kirchhoff integral. In this regard we use discrete Fourier transform method and calculate Fresnel diffraction from the 1D phase step by FFT-based algorithms. This method does not have any restriction on the coherence and profile shape of the incident light. We show that the method have appropriate solutions for coherent and partially coherent lights. For the case of the coherent light illumination of the step, the obtained results are in good agreement with the calculated results by using the Fresnel integrals in reported literatures.

  8. Fourier transform infrared spectroscopy approach for measurements of photoluminescence and electroluminescence in mid-infrared. (United States)

    Zhang, Y G; Gu, Y; Wang, K; Fang, X; Li, A Z; Liu, K H


    An improved Fourier transform infrared spectroscopy approach adapting to photoluminescence and electroluminescence measurements in mid-infrared has been developed, in which diode-pumped solid-state excitation lasers were adopted for photoluminescence excitation. In this approach, three different Fourier transform infrared modes of rapid scan, double modulation, and step scan were software switchable without changing the hardware or connections. The advantages and limitations of each mode were analyzed in detail. Using this approach a group of III-V and II-VI samples from near-infrared extending to mid-infrared with photoluminescence intensities in a wider range have been characterized at room temperature to demonstrate the validity and overall performances of the system. The weaker electroluminescence of quantum cascade lasers in mid-infrared band was also surveyed at different resolutions. Results show that for samples with relatively strong photoluminescence or electroluminescence out off the background, rapid scan mode is the most preferable. For weaker photoluminescence or electroluminescence overlapped with background, double modulation is the most effective mode. To get a better signal noise ratio when weaker photoluminescence or electroluminescence signal has been observed in double modulation mode, switching to step scan mode should be an advisable option despite the long data acquiring time and limited resolution.

  9. Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform. (United States)

    Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai


    The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences.

  10. Quantitative assessment with improved fast Fourier transform based method by signal mirroring

    Energy Technology Data Exchange (ETDEWEB)

    Prosek, Andrej [Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia)], E-mail:; Leskovar, Matjaz; Mavko, Borut [Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia)


    The comparison of calculated results to experimental measurements is very important for thermal-hydraulic code qualification. Recently, it was observed that the fast Fourier transform based method (FFTBM) favors certain trends when an edge (difference) is present in the signal between the first and the last data point of the investigated time signal. Namely, the discrete Fourier transform used for the code accuracy calculation views the time domain signal as an infinite periodic signal. The purpose of the present study was therefore to improve the FFTBM regarding the unphysical edge impact. This was achieved by signal mirroring. In the demonstration it was shown how the improved FFTBM by signal mirroring works. Besides two case studies also the code accuracy of the LOFT L2-5 test calculations performed in the frame of the Best-Estimate Methods Uncertainty and Sensitivity Evaluation (BEMUSE) program was assessed. The results show that the improved FFTBM by signal mirroring judges the accuracy in a consistent and unbiased way.

  11. [A phase error correction method for the new Fourier transforms spectrometer]. (United States)

    Wang, Ning; Gong, Tian-Cheng; Chen, Jian-Jun; Li, Yang; Yang, Yi-Ning; Zhu, Yong; Zhang, Jie; Chen, Wei-Min


    To decrease the distortion of the recovered spectrum, improve the quantity of the recovered spectrum and decrease the influence of the phase error of the new spectrum detection system based on MEMS (micro-electro-mechanical systems) micro-mirrors, a new phase error correction method for this system is proposed in the present paper. The source of phase error of the spectrum detection system based on MEMS micro-mirrors is analyzed firstly. The analyzed result indicated that the phase error of the new spectral Fourier transform detection system is the zero drift of the optical path difference, and the phase error can be corrected by Zero-crossing sampling which is realized by improving the structure of the interferometer system and Mertz product The spectrum detection system is set up and the phase error correction method is verified by this system. The experiment result is show that the quantity of the recovered spectrum of the spectrum detection is improved obviously by using the improved interferometer system and Mertz product, and the recovered spectrum has no negative peaks and the side lobes is suppressed markedly. This correction method can reduce the influence caused by phase error to the system performance well and improve the spectral detection performance effectively. In this paper, the origin of the system phase error based on the new MEMS micromirror Fourier transform spectroscopy detection system is analyzed, and the phase error correction method is proposed. This method can improve the performance of the spectrum detection system.

  12. Viewing the effective k-space coverage of MR images: phantom experiments with fast Fourier transform. (United States)

    Menke, Jan; Helms, Gunther; Larsen, Jörg


    The purpose of this experimental study was to evaluate whether the effective k-space coverage of MR images can in principle be viewed after multidimensional Fourier transform back to k-space. A water-soaked sponge phantom providing homogeneous k-space pattern was imaged with different standard MR sequences, utilizing elliptic acquisitions, partial-Fourier acquisitions and elliptic filtering as imaging examples. The resulting MR images were Fourier-transformed to the spatial frequency domain (the k-space) to visualize their effective k-space coverage. These frequency domain images are named "backtransformed k-space images." For a quantitative assessment, the sponge phantom was imaged with three-dimensional partial-Fourier sequences while varying the partial acquisition parameters in slice and phase direction. By linear regression analysis, the k-space coverage as expected from the sequence menu parameters was compared to the effective k-space coverage as observed in the backtransformed k-space images. The k-space coverage of elliptic and partial-Fourier acquisitions became visible in the backtransformed k-space images, as well as the effect of elliptic filtering. The expected and the observed k-space coverage showed a highly significant correlation (r=.99, PFourier-transforming MR images of a sponge phantom back to k-space. This method could be used for several purposes including sequence parameter optimization, basic imaging research, and to enhance a visual understanding of k-space, especially in three-dimensional MR imaging.

  13. Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups

    Energy Technology Data Exchange (ETDEWEB)

    Guedes, Carlos; Oriti, Daniele [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); Raasakka, Matti [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); LIPN, Institut Galilée, Université Paris-Nord, 99, av. Clement, 93430 Villetaneuse (France)


    The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.

  14. Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform. (United States)

    Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan


    Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

  15. Cloud cover typing from environmental satellite imagery. Discriminating cloud structure with Fast Fourier Transforms (FFT) (United States)

    Logan, T. L.; Huning, J. R.; Glackin, D. L.


    The use of two dimensional Fast Fourier Transforms (FFTs) subjected to pattern recognition technology for the identification and classification of low altitude stratus cloud structure from Geostationary Operational Environmental Satellite (GOES) imagery was examined. The development of a scene independent pattern recognition methodology, unconstrained by conventional cloud morphological classifications was emphasized. A technique for extracting cloud shape, direction, and size attributes from GOES visual imagery was developed. These attributes were combined with two statistical attributes (cloud mean brightness, cloud standard deviation), and interrogated using unsupervised clustering amd maximum likelihood classification techniques. Results indicate that: (1) the key cloud discrimination attributes are mean brightness, direction, shape, and minimum size; (2) cloud structure can be differentiated at given pixel scales; (3) cloud type may be identifiable at coarser scales; (4) there are positive indications of scene independence which would permit development of a cloud signature bank; (5) edge enhancement of GOES imagery does not appreciably improve cloud classification over the use of raw data; and (6) the GOES imagery must be apodized before generation of FFTs.

  16. Comparative evaluation of bioactivity of crystalline trypsin for drying by Fourier-transformed infrared spectroscopy. (United States)

    Otsuka, Makoto; Fukui, Yuya; Ozaki, Yukihiro


    The purpose of this study was to evaluate the enzymatic stability of colloidal trypsin powder during heating in a solid-state by using Fourier transform infrared (FT-IR) spectra with chemoinformatics and generalized two-dimensional (2D) correlation spectroscopy. Colloidal crystalline trypsin powders were heated using differential scanning calorimetry. The enzymatic activity of trypsin was assayed by the kinetic degradation method. Spectra of 10 calibration sample sets were recorded three times with a FT-IR spectrometer. The maximum intensity at 1634cm(-1) of FT-IR spectra and enzymatic activity of trypsin decreased as the temperature increased. The FT-IR spectra of trypsin samples were analyzed by a principal component regression analysis (PCR). A plot of the calibration data obtained was made between the actual and predicted trypsin activity based on a two-component model with gamma(2)=0.962. On the other hand, a 2D method was applied to FT-IR spectra of heat-treated trypsin. The result was consistent with that of the chemoinformetrical method. The results for deactivation of colloidal trypsin powder by heat-treatment indicated that nano-structure of crystalline trypsin changed by heating reflecting that the beta-sheet was mainly transformed, since the peak at 1634cm(-1) decreased with dehydration. The FT-IR chemoinformetrical method allows for a solid-state quantitative analysis of the bioactivity of the bulk powder of trypsin during drying.

  17. Two Dimensional Organometal Halide Perovskite Nanorods with Tunable Optical Properties. (United States)

    Aharon, Sigalit; Etgar, Lioz


    Organo-metal halide perovskite is an efficient light harvester in photovoltaic solar cells. Organometal halide perovskite is used mainly in its "bulk" form in the solar cell. Confined perovskite nanostructures could be a promising candidate for efficient optoelectronic devices, taking advantage of the superior bulk properties of organo-metal halide perovskite, as well as the nanoscale properties. In this paper, we present facile low-temperature synthesis of two-dimensional (2D) lead halide perovskite nanorods (NRs). These NRs show a shift to higher energies in the absorbance and in the photoluminescence compared to the bulk material, which supports their 2D structure. X-ray diffraction (XRD) analysis of the NRs demonstrates their 2D nature combined with the tetragonal 3D perovskite structure. In addition, by alternating the halide composition, we were able to tune the optical properties of the NRs. Fast Fourier transform, and electron diffraction show the tetragonal structure of these NRs. By varying the ligands ratio (e.g., octylammonium to oleic acid) in the synthesis, we were able to provide the formation mechanism of these novel 2D perovskite NRs. The 2D perovskite NRs are promising candidates for a variety of optoelectronic applications, such as light-emitting diodes, lasing, solar cells, and sensors.

  18. Component analyses of urinary nanocrystallites of uric acid stone formers by combination of high-resolution transmission electron microscopy, fast Fourier transformation, energy dispersive X-ray spectroscopy, X-ray diffraction and Fourier transform infrared spectroscopy. (United States)

    Sun, Xin-Yuan; Xue, Jun-Fa; Xia, Zhi-Yue; Ouyang, Jian-Ming


    This study aimed to analyse the components of nanocrystallites in urines of patients with uric acid (UA) stones. X-ray diffraction (XRD), Fourier transform infrared spectroscopy, high-resolution transmission electron microscopy (HRTEM), fast Fourier transformation (FFT) of HRTEM, and energy dispersive X-ray spectroscopy (EDS) were performed to analyse the components of these nanocrystallites. XRD and FFT showed that the main component of urinary nanocrystallites was UA, which contains a small amount of calcium oxalate monohydrate and phosphates. EDS showed the characteristic absorption peaks of C, O, Ca and P. The formation of UA stones was closely related to a large number of UA nanocrystallites in urine. A combination of HRTEM, FFT, EDS and XRD analyses could be performed accurately to analyse the components of urinary nanocrystallites.

  19. Fourier transform infrared absorption spectroscopy of jet-cooled radicals (United States)

    Rohrs, Henry W.; Wickham-Jones, C. Tom; Ellison, G. Barney; Berry, David; Argrow, Brian M.


    We describe an experiment that couples a high-resolution Fourier transform spectrometer (FTS) to a supersonic jet of radicals. A 1-mm-i.d. cylindrical SiC nozzle is resistively heated to 1500 K in order to decompose organic precursors and generate expansions of jet-cooled radicals. We have used this apparatus to pyrolyze alkyl nitrites to make alkoxy and nitric oxide radicals. The residence time of radicals in this hot nozzle is roughly 20 μs RONO→ΔRO+NO. We use the FTS to detect the IR absorption of the product NO (ν0=1876.1 cm-1) at resolutions as fine as 0.005 cm-1 FWHM. We observe the product NO from the pyrolysis of CH3CH2ONO to be rotationally cooled to roughly 50 K. The IR spectra indicate that the optical path length is about 3/4 cm and that the nitrites pyrolyze to produce approximately 1014 NO radicals cm-3 some 9 mm downstream from the nozzle. Our spectrometer is capable of detecting an absorption signal of 0.1% over a bandwidth of 100 cm-1 at 0.005 cm-1 resolution. Depending on the infrared cross section of the radical, this implies that we are able to monitor diatomic radical densities of roughly 5×1012 cm-3 (quantum state)-1.

  20. External Second Gate-Fourier Transform Ion Mobility Spectrometry.

    Energy Technology Data Exchange (ETDEWEB)

    Tarver, Edward E., III


    Ion mobility spectrometry (IMS) is recognized as one of the most sensitive and versatile techniques for the detection of trace levels of organic vapors. IMS is widely used for detecting contraband narcotics, explosives, toxic industrial compounds and chemical warfare agents. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention treaty verification as well as humanitarian de-mining efforts has mandated that equal importance be placed on the analysis time as well as the quality of the analytical data. (1) IMS is unrivaled when both speed of response and sensitivity has to be considered. (2) With conventional (signal averaging) IMS systems the number of available ions contributing to the measured signal to less than 1%. Furthermore, the signal averaging process incorporates scan-to-scan variations decreasing resolution. With external second gate Fourier Transform ion mobility spectrometry (FT-IMS), the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters to increase the spectral resolution. The FT-IMS entrance gate operates with a 50% duty cycle and so affords a 7 to 10-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.

  1. The Non-uniform Fast Fourier Transform in Computed Tomography

    CERN Document Server

    Tang, Junqi


    This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the potential computational efficiency which the Fourier Slice Theorem and the Non-uniform Fast Fourier Transform (NUFFT) will bring forth. In this Masters report, the detailed design of the NUFFT based forward projector including a novel 3D (derivative of) Radon space resampling method will be given. Meanwhile the complexity of the NUFFT based forward projector is analysed and compared with the non-Fourier based CT projector, and the advantage of the NUFFT based forward projection in terms of the computational efficiency is demonstrated in this report. Base on the design of the forward algorithm, the NUFFT based 3D direct reconstruction algorithm will be derived. The experiments will be taken to test the performance of the forward algorithm and the backprojection algorithm to sh...

  2. Fourier transform Raman approach to structural correlation in hemoglobin derivatives. (United States)

    Venkatesh, B; Ramasamy, S; Mylrajan, M; Asokan, R; Manoharan, P T; Rifkind, J M


    In order to obtain information on the structural aspects of hemoglobin (Hb), Fourier transform Raman (FT-R) measurements on various ferrous, ferric derivatives and nickel reconstituted Hb (NiHb) has been made. FT-R spectra for these derivatives were obtained by laser excitation in the near infrared region (NIR) (1064 nm) whereby the wave-number region (600-1700 cm-1) related to both porphyrin ring modes and some globin modes were monitored. Comparison of various modes was made based on previous resonance Raman (RR) results. The wave-number shifts with respect to changes in oxidation state and spin state are very similar to those observed by RR. Additional bands at 1654, 1459, and 1003 cm-1 for deoxyHb and at 1656, 1454, and 1004 cm-1 for oxy Hb can be correlated to globin modes. The shift in the position of these bands for the binding of oxygen can be related to changes in conformation during the transformation. The presence of two distinct sites in NiHb could be monitored by the use of FT-R technique.

  3. Resource requirements for a fault-tolerant quantum Fourier transform (United States)

    Goto, Hayato; Nakamura, Satoshi; Kujiraoka, Mamiko; Ichimura, Kouichi


    The quantum Fourier transform (QFT) is a basic subroutine for most quantum algorithms providing an exponential speedup over classical ones. We investigate resource requirements for a fault-tolerant QFT. To implement single-qubit rotations for a QFT in a fault-tolerant manner, we examine three types of approaches: ancilla-free gate synthesis, ancilla-assisted gate synthesis, and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation enables to perform specific single-qubit rotations required for the QFT exactly. It is unknown, however, which approach is better for the QFT. We estimated the resource requirement for a QFT in each case, where the resource is measured by the total number of the π / 8 gates denoted by T, which is called the T count. Contrary to the initial expectation, the total T count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is the best for a fault-tolerant QFT so far.

  4. Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy

    Directory of Open Access Journals (Sweden)

    Mehrotra Ranjana


    Full Text Available Abstract Background Ovarian cancer is the second most common cancer among women and the leading cause of death among gynecologic malignancies. In recent years, infrared (IR spectroscopy has gained attention as a simple and inexpensive method for the biomedical study of several diseases. In the present study infrared spectra of normal and malignant ovarian tissues were recorded in the 650 cm-1 to 4000 cm-1 region. Methods Post surgical tissue samples were taken from the normal and tumor sections of the tissue. Fourier Transform Infrared (FTIR data on twelve cases of ovarian cancer with different grades of malignancy from patients of different age groups were analyzed. Results Significant spectral differences between the normal and the ovarian cancerous tissues were observed. In particular changes in frequency and intensity in the spectral region of protein, nucleic acid and lipid vibrational modes were observed. It was evident that the sample-to-sample or patient-to-patient variations were small and the spectral differences between normal and diseased tissues were reproducible. Conclusion The measured spectroscopic features, which are the spectroscopic fingerprints of the tissues, provided the important differentiating information about the malignant and normal tissues. The findings of this study demonstrate the possible use of infrared spectroscopy in differentiating normal and malignant ovarian tissues.

  5. Screening cervical lesions with Fourier transform infrared spectroscopy

    Institute of Scientific and Technical Information of China (English)


    The screening results were reported based on the Fourier transform infrared spectroscopy (FTIR) analysis of the samples of exfoliated cervical cells from 354 women. Their spectra can be sorted into two types based on the emerging or not of the absorption bands near 970 cm-1 and 1 170 cm-1: T1 (83.1%) type without emerging, and T2 (16.9%) type with obviously emerging. All of the samples assigned to T1 were cytologically diagnosed as normal or within normal limits (PapⅠ). 28.9% and 71.1% of samples exhibiting T2 profile, were cytologically evaluated as Pap Ⅰand abnormal respectively. 3 women in the abnormal group were diagnosed as to have cervical cells with changes associated with high grade of inflammation, cervical scar and cervical erosion. Furthermore, based on the progressive change of the relative intensities of the absorption bands, both T1 and T2 profiles can be categorized into 6 subtypes. The observed heterogeneous spectra and the progressive changes in the absorption frequencies and the relative intensities exhibit features suggestive of the progressive process of cervical lesion. The FTIR method has the potential to complement the cytological smear for large-volume screening of cervical lesions.

  6. Chiral Process Monitoring Using Fourier Transform Microwave Spectroscopy (United States)

    Neill, Justin L.; Muckle, Matt; Pate, Brooks


    We present the application of Fourier transform microwave (FTMW) spectroscopy in monitoring the chiral purity of components in a reaction mixture. This is of particular interest due to the increasing use of continuous pharmaceutical manufacturing processes, in which a number of attributes (including the chiral purity of the product) can change on short time scales. Therefore, new techniques that can accomplish this measurement rapidly are desired. The excellent specificity of FTMW spectroscopy, coupled with newly developed techniques for measuring enantiomeric excess in a mixture, have motivated this work. In collaboration with B. Frank Gupton (Virginia Commonwealth University), we are testing this application first with the synthesis of artemisinin. Artemisinin, a common drug for malaria treatment, is of high global health interest and subject to supply shortages, and therefore a strong candidate for continuous manufacturing. It also has moderately high molecular weight (282 amu) and seven chiral centers, making it a good candidate to test the capabilities of FTMW spectroscopy. Using a miniature cavity-enhanced FTMW spectrometer design, we aim to demonstrate selective component quantification in the reaction mixture. Future work that will be needed to fully realize this application will be discussed. R.D. Suenram, J.U. Grabow, A.Zuban, and I.Leonov, Rev. Sci. Instrum. 70, 2127 (1999).

  7. Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS) (United States)

    Sromovsky, L. A.


    This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).

  8. Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability (United States)

    Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.


    The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.

  9. Fourier transform infrared microspectroscopy and multivariate methods for radiobiological dosimetry. (United States)

    Meade, A D; Clarke, C; Byrne, H J; Lyng, F M


    The scientific literature contains an ever-growing number of reports of applications of vibrational spectroscopy as a multivariate non-invasive tool for analysis of biological effects at the molecular level. Recently, Fourier transform infrared microspectroscopy (FTIRM) has been demonstrated to be sensitive to molecular events occurring in cells and tissue after exposure to ionizing radiation. In this work the application of FTIRM in the examination of dose-dependent molecular effects occurring in skin cells after exposure to ionizing radiation with the use of partial least-squares regression (PLSR) and generalized regression neural networks (GRNN) was studied. The methodology is shown to be sensitive to molecular events occurring with radiation dose and time after exposure. The variation in molecular species with dose and time after irradiation is shown to be non-linear by virtue of the higher modeling efficiency yielded from the non-linear algorithms. Dose prediction efficiencies of approximately +/-10 mGy were achieved at 96 h after irradiation, highlighting the potential applications of the methodology in radiobiological dosimetry.

  10. Ordered fast fourier transforms on a massively parallel hypercube multiprocessor (United States)

    Tong, Charles; Swarztrauber, Paul N.


    Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.

  11. Fourier transform ion cyclotron resonance mass spectrometry: a primer. (United States)

    Marshall, A G; Hendrickson, C L; Jackson, G S


    This review offers an introduction to the principles and generic applications of FT-ICR mass spectrometry, directed to readers with no prior experience with the technique. We are able to explain the fundamental FT-ICR phenomena from a simplified theoretical treatment of ion behavior in idealized magnetic and electric fields. The effects of trapping voltage, trap size and shape, and other nonidealities are manifested mainly as perturbations that preserve the idealized ion behavior modified by appropriate numerical correction factors. Topics include: effect of ion mass, charge, magnetic field, and trapping voltage on ion cyclotron frequency; excitation and detection of ICR signals; mass calibration; mass resolving power and mass accuracy; upper mass limit(s); dynamic range; detection limit, strategies for mass and energy selection for MSn; ion axialization, cooling, and remeasurement; and means for guiding externally formed ions into the ion trap. The relation of FT-ICR MS to other types of Fourier transform spectroscopy and to the Paul (quadrupole) ion trap is described. The article concludes with selected applications, an appendix listing accurate fundamental constants needed for ultrahigh-precision analysis, and an annotated list of selected reviews and primary source publications that describe in further detail various FT-ICR MS techniques and applications.

  12. Single beam Fourier transform digital holographic quantitative phase microscopy

    Energy Technology Data Exchange (ETDEWEB)

    Anand, A., E-mail:; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)


    Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.

  13. High-resolution wide-band Fast Fourier Transform spectrometers

    CERN Document Server

    Klein, Bernd; Krämer, Ingo; Bell, Andreas; Meyer, Klaus; Güsten, Rolf


    We describe the performance of our latest generations of sensitive wide-band high-resolution digital Fast Fourier Transform Spectrometer (FFTS). Their design, optimized for a wide range of radio astronomical applications, is presented. Developed for operation with the GREAT far infrared heterodyne spectrometer on-board SOFIA, the eXtended bandwidth FFTS (XFFTS) offers a high instantaneous bandwidth of 2.5 GHz with 88.5 kHz spectral resolution and has been in routine operation during SOFIA's Basic Science since July 2011. We discuss the advanced field programmable gate array (FPGA) signal processing pipeline, with an optimized multi-tap polyphase filter bank algorithm that provides a nearly loss-less time-to-frequency data conversion with significantly reduced frequency scallop and fast sidelobe fall-off. Our digital spectrometers have been proven to be extremely reliable and robust, even under the harsh environmental conditions of an airborne observatory, with Allan-variance stability times of several 1000 se...

  14. Fourier transform optical profilometry using fiber optic Lloyd's mirrors. (United States)

    Kart, Türkay; Kösoğlu, Gülşen; Yüksel, Heba; İnci, Mehmet Naci


    A fiber optic Lloyd's mirror assembly is used to obtain various optical interference patterns for the detection of 3D rigid body shapes. Two types of fiber optic Lloyd's systems are used in this work. The first consists of a single-mode optical fiber and a highly reflecting flat mirror to produce bright and dark strips. The second is constructed by locating a single-mode optical fiber in a v-groove, which is formed by two orthogonal flat mirrors to allow the generation of square-type interference patterns for the desired applications. The structured light patterns formed by these two fiber Lloyd's techniques are projected onto 3D objects. Fringe patterns are deformed due to the object's surface topography, which are captured by a digital CCD camera and processed with a Fourier transform technique to accomplish 3D surface topography of the object. It is demonstrated that the fiber-optic Lloyd's technique proposed in this work is more compact, more stable, and easier to configure than other existing surface profilometry systems, since it does not include any high-cost optical tools such as aligners, couplers, or 3D stages. The fringe patterns are observed to be more robust against environmental disturbances such as ambient temperature and vibrations.

  15. Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis. (United States)

    Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami


    Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications.

  16. Tunable room temperature terahertz sources based on two dimensional plasma instability in GaN HEMTs (United States)

    El Fatimy, A.; Suemitsu, T.; Otsuji, T.; Dyakonova, N.; Knap, W.; Meziani, Y. M.; Vandenbrouk, S.; Madjour, K.; Théron, D.; Gaquiere, Ch; Prystawko, P.; Skierbiszewski, C.


    In this work, we report on room temperature terahertz radiation from sub-micron size GaN/AlGaN based high electron mobility transistors (HEMTs). They could successfully replace the standard Fourier Transform spectrometer source and were investigated with a standard Si-bolometer as a detector. The relatively broad (~1THz) emission line was observed. The maxima were found to be tunable by the gate voltage between 0.75 and 2.1 THz. The observed emission was interpreted as due to the current driven plasma waves instability in the two-dimensional electron gas. The emitted power from a single device reached 150 nW, showing possible application of these transistors as compact sources for terahertz spectroscopy and imaging.

  17. Tunable room temperature terahertz sources based on two dimensional plasma instability in GaN HEMTs

    Energy Technology Data Exchange (ETDEWEB)

    Fatimy, A El; Suemitsu, T; Otsuji, T; Knap, W [Research Institute of Electrical Communication (RIEC), Tohoku University, 2-1-1 Katahira, Aoba-Ku, 980-8577, Sendai (Japan); Dyakonova, N [Groupe d' Etude des Semiconducteurs, UMR CNRS 5650, Universite Montpellier 2, 34095 Montpellier (France); Meziani, Y M [Dpto. de Fisica Aplicada, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca (Spain); Vandenbrouk, S; Madjour, K; Theron, D; Gaquiere, Ch [Institut d' Electronique et de Microelectronique du Nord, UMR CNRS 8520, 59655 Villeneuve d' Acsq (France); Prystawko, P; Skierbiszewski, C, E-mail:, E-mail: [Institutes of High Pressure Physics, PAS, Unipress, Sokolowska 29/37, 01-142 Warsaw (Poland)


    In this work, we report on room temperature terahertz radiation from sub-micron size GaN/AlGaN based high electron mobility transistors (HEMTs). They could successfully replace the standard Fourier Transform spectrometer source and were investigated with a standard Si-bolometer as a detector. The relatively broad ({approx}1THz) emission line was observed. The maxima were found to be tunable by the gate voltage between 0.75 and 2.1 THz. The observed emission was interpreted as due to the current driven plasma waves instability in the two-dimensional electron gas. The emitted power from a single device reached 150 nW, showing possible application of these transistors as compact sources for terahertz spectroscopy and imaging.

  18. A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

    Institute of Scientific and Technical Information of China (English)

    Pang Chao-Yang; Hu Ben-Qiong


    The discrete Fourier transform(DFT)is the base of modern signal processing.1-dimensional fast Fourier transform (1D FFT)and 2D FFT have time complexity O(N log N)and O(N2 log N)respectively.Since 1965,there has been no more essential breakthrough for the design of fast DFT algorithm.DFT has two properties.One property is that DFT is energy conservation transform.The other property is that many DFT coefficients are close to zero.The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy.One-dimensional quantum DFT(1D QDFT)and two-dimensional quantum DFT(2D QDFT)are presented in this paper.The quantum algorithm for convolution estimation is also presented in this paper.Compared with FFT,1D and 2D QDFT have time complexity O(√N)and O(N)respectively.QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.

  19. Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform

    Directory of Open Access Journals (Sweden)

    Carmen Fernández


    Full Text Available Localization operators in the discrete setting are used to obtain information on a signal f from the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.

  20. A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms (United States)

    Debnath, Lokenath


    This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

  1. Precise and fast spatial-frequency analysis using the iterative local Fourier transform. (United States)

    Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook


    The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

  2. Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme. (United States)

    Ogawa, Takahiro; Haseyama, Miki


    A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

  3. Monitoring bacterial processes by Fourier transform infrared spectroscopy : Helicobacter pylori drug inactivation and plasmid bioproduction in recombinant Escherichia coli cultures


    Scholz, Teresa; Lopes, Vitor V.; Calado, Cecília R. C.


    Fourier transform infrared (FTIR) spectroscopy is evaluated as a tool to monitor two bacterial processes: strain discrimination and drug inactivation studies with the gastric pathogen Helicobacter pylori and the plasmid production process based on high-density cultures of recombinant Escherichia coli. Results show, that after evaluation of different incubation conditions of H.pylori with the drug model, the application of principal component analysis to the FTIR spectra assembles the samples ...

  4. On-line preferential solvation studies of polymers by coupled chromatographic-Fourier transform infrared spectroscopic flow-cell technique. (United States)

    Malanin, M; Eichhorn, K-J; Lederer, A; Treppe, P; Adam, G; Fischer, D; Voigt, D


    Qualitative and quantitative comparison between liquid chromatography (LC) and LC coupled with Fourier transform infrared spectroscopy (LC-FTIR) to evaluate preferential solvation phenomenon of polymers in a mixed solvent has been performed. These studies show that LC-FTIR technique leads to detailed structural information without the requirement for determination of additional parameters for quantitative analysis except calibration. Appropriate experimental conditions for preferential solvation study have been established by variation of polymer concentration, molar mass and eluent content.

  5. Fourier-Transformed Infrared Spectroscopy Applied for Studying Compatible Interaction in the Pathosystem Phytophtora infestans-Solanum tuberosum


    Abdelmoumen TAOUTAOU; Socaciu, Carmen; Doru PAMFIL; Florinela FETEA; Erika BALAZS; Constantin BOTEZ; Adina CHIS; Daniela BRICIU; Alexandru BRICIU


    In this study we used the Fourier-Transformed Infrared (FT-IR) technique to examine the compatible reaction of potato (Solanum tuberosum) to infection by the late blight agent Phytophthora infestans. Three virulent isolates have been used, different by their level of pathogenicity on R2 potato. The response was dependent on the pathogenicity of the isolate. The Infrared spectra in the middle infrared region (MIR) of infested versus healthy (control) leaves showed that controls absorb (intensi...

  6. [Evaluation of nutrient release profiles from polymer coated fertilizers using Fourier transform mid-infrared photoacoustic spectroscopy]. (United States)

    Shen, Ya-zhen; Du, Chang-wen; Zhou, Jian-min; Wang, Huo-yan; Chen, Xiao-qin


    The acrylate-like materials were used to develop the polymer coated controlled release fertilizer, the nutrients release profiles were determined, meanwhile the Fourier transform mid-infrared photoacoustic spectra of the coatings were recorded and characterized; GRNN model was used to predict the nutrients release profiles using the principal components of the mid-infrared photoacoustic spectra as input. Results showed that the GRNN model could fast and effectively predict the nutrient release profiles, and the predicted calibration coefficients were more than 0.93; on the whole, the prediction errors (RMSE) were influenced by the profiling depth of the spectra, the average prediction error was 10.28%, and the spectra from the surface depth resulted in a lowest prediction error with 7.14%. Therefore, coupled with GRNN modeling, Fourier transform mid-infrared photoacoustic spectroscopy can be used as an alternative new technique in the fast and accurate prediction of nutrient release from polymer coated fertilizer.

  7. A joint synchronization parameter estimation in fractional Fourier transform orthogonal frequency division multiplexing underwater acoustic communication system

    Directory of Open Access Journals (Sweden)

    Jia-chun Zheng


    Full Text Available In the conditions of Gaussian noise, symmetric alpha stable impulse noise, multipath propagation, Doppler effect, and so on, a joint synchronization algorithm is proposed for underwater acoustic communication system based on fractional Fourier transform orthogonal frequency division multiplexing. The algorithm realizes the orthogonal multicarrier underwater acoustic communication system synchronization based on that the symmetrical triangular linear frequency modulation signal has the energy convergence in the domain of fractional Fourier transform. In order to verify the effectiveness of the algorithm, hyperbolic frequency modulation signal and linear frequency modulation signal are used as the evaluation index, and the synchronization performance of bit error rate of them is compared by simulation and pool experiments. The simulation results show that the proposed algorithm in this article is resistant to Gaussian noise, symmetric alpha stable pulse noise, multipath propagation, and Doppler effect, compared with traditional synchronization algorithms; the synchronization error probability is low at the same signal-to-noise ratio.

  8. A Fourier transform infrared trace gas analyser for atmospheric applications

    Directory of Open Access Journals (Sweden)

    D. W. T. Griffith


    Full Text Available Concern in recent decades about human impacts on Earth's climate has led to the need for improved and expanded measurement capabilities for greenhouse gases in the atmosphere. In this paper we describe in detail an in situ trace gas analyser based on Fourier Transform Infrared (FTIR spectroscopy that is capable of simultaneous and continuous measurements of carbon dioxide (CO2, methane (CH4, carbon monoxide (CO, nitrous oxide (N2O and 13C in CO2 in air with high precision and accuracy. Stable water isotopes can also be measured in undried airstreams. The analyser is automated and allows unattended operation with minimal operator intervention. Precision and accuracy meet and exceed the compatibility targets set by the World Meteorological Organisation – Global Atmosphere Watch Programme for baseline measurements in the unpolluted troposphere for all species except 13C in CO2.

    The analyser is mobile and well suited to fixed sites, tower measurements, mobile platforms and campaign-based measurements. The isotopic specificity of the optically-based technique and analysis allows application of the analyser in isotopic tracer experiments, for example 13C in CO2 and 15N in N2O. We review a number of applications illustrating use of the analyser in clean air monitoring, micrometeorological flux and tower measurements, mobile measurements on a train, and soil flux chamber measurements.

  9. Fourier Transform Spectrometer measurements of Atmospheric Carbon Dioxide and Methane (United States)

    Kivi, Rigel; Heikkinen, Pauli; Chen, Huilin; Hatakka, Juha; Laurila, Tuomas


    Ground based remote sensing measurements of column CO2 and CH4 using Fourier Transform Spectrometers (FTS) within the Total Carbon Column Observing Network (TCCON) are known for high precision and accuracy. These measurements are performed at various locations globally and they have been widely used in carbon cycle studies and validation of space born measurements. The relevant satellite missions include the Orbiting Carbon Observatory-2 (OCO-2) by the National Aeronautics and Space Administration (NASA); the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) by the European Space Agency (ESA); the Greenhouse gases Observing SATellite (GOSAT) by the Japan Aerospace Exploration Agency (JAXA) and the upcoming Sentinel-5 Precursor mission, which is an ESA mission and scheduled for launch in 2016. Results of the column CO2 and CH4 measurements at Sodankylä in northern Finland (at 67.4° N, 26.6° E) are reported in this study. The measurements have been performed on regular basis since the beginning of the program in early 2009. We also present evaluation of the data quality of the ground based measurements and comparisons with the available satellite based retrievals. In case of comparisons between the GOSAT and ground based retrievals of CO2 and CH4 no significant biases were found. Sodankylä is one of the northernmost stations in the TCCON network. However, the data coverage has been relatively good thanks to the progress towards automation of the FTS measurement system. At Sodankylä the retrievals have been also compared with the balloon borne AirCore measurements at the site. AirCore sampling system is directly related to the World Meteorological Organization in situ trace gas measurement scales. The balloon platform allows sampling in both stratosphere and troposphere, which is a benefit, compared to the aircraft in situ measurements.

  10. Fractional Fourier Transform Applied to Digital Images Encryption (United States)

    Vilardy, Juan M.; Torres, Cesar O.; Mattos, Lorenzo


    In the present paper a digital algorithm was developed to make phase encryption of digital indexed images to color using the fractional Fourier transform (the images in RGB are converted to indexed before to encrypt). The indexed images are represented by a matrix of M×N pixels (where M defines the height and N is the Width of the image) and a color map (it's a matrix of C×3 elements, where C indicates the colors number of the image and the number 3 indicates the three columns associated with the color components: Red, Green and Blue of each pixel of the matrix of M×N) associated to the matrix of pixels to suitably represent the color information of the image. The indexed image (matrix of M×N pixels) to encrypt is placed as the phase of a complex exponential, then is transformed three times and multiplied in intermediate steps by two random phase masks statistically independent thus to obtain the encrypted image, for decrypt the coding image the encryption procedure is applied in the inverse sense to the conjugated complex of the encrypted image, then is taken the negative of the phase of the resulting function of the decryption process and the original image is obtained this way that had been encrypted; For the color map equal procedure is applied in the encryption/decryption process described previously for the matrix of M×N pixels. In the implemented cryptographic algorithm five keys are used, constituted by three fractional orders and two random phase masks, all these keys are necessary for a correct decryption providing a dependability to the transference of images by means of the communications nets.

  11. Continuously tunable optical multidimensional Fourier-transform spectrometer. (United States)

    Dey, P; Paul, J; Bylsma, J; Deminico, S; Karaiskaj, D


    A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization

  12. Accelerating the 2-point and 3-point galaxy correlation functions using Fourier transforms

    CERN Document Server

    Slepian, Zachary


    Though Fourier Transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight direction is not constant on the Cartesian grid. Here we show how FTs can be used to compute the multipole moments of the anisotropic 2PCF. We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein (2015). In both cases, these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density of objects in the survey. With the upcoming large datasets of DESI, Euclid, and LSST, FT techniques will therefore offer an important complement to simple pair or triplet counts.

  13. Speeding-up exchange-mediated saturation transfer experiments by Fourier transform

    Energy Technology Data Exchange (ETDEWEB)

    Carneiro, Marta G.; Reddy, Jithender G.; Griesinger, Christian; Lee, Donghan, E-mail: [Max-Planck Institute for Biophysical chemistry, Department of NMR-based Structural Biology (Germany)


    Protein motions over various time scales are crucial for protein function. NMR relaxation dispersion experiments play a key role in explaining these motions. However, the study of slow conformational changes with lowly populated states remained elusive. The recently developed exchange-mediated saturation transfer experiments allow the detection and characterization of such motions, but require extensive measurement time. Here we show that, by making use of Fourier transform, the total acquisition time required to measure an exchange-mediated saturation transfer profile can be reduced by twofold in case that one applies linear prediction. In addition, we demonstrate that the analytical solution for R{sub 1}ρ experiments can be used for fitting the exchange-mediated saturation transfer profile. Furthermore, we show that simultaneous analysis of exchange-mediated saturation transfer profiles with two different radio-frequency field strengths is required for accurate and precise characterization of the exchange process and the exchanging states.

  14. Denoise in the pseudopolar grid Fourier space using exact inverse pseudopolar Fourier transform

    CERN Document Server

    Wei, Fan Jun


    In this paper I show a matrix method to calculate the exact inverse pseudopolar grid Fourier transform, and use this transform to do noise removals in the k space of pseudopolar grids. I apply the Gaussian filter to this pseudopolar grid and find the advantages of the noise removals are very excellent by using pseudopolar grid, and finally I show the Cartesian grid denoise for comparisons. The results present the signal to noise ratio and the variance are much better when doing noise removals in the pseudopolar grid than the Cartesian grid. The noise removals of pseudopolar grid or Cartesian grid are both in the k space, and all these noises are added in the real space.

  15. GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography. (United States)

    Xu, Daguang; Huang, Yong; Kang, Jin U


    We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

  16. Simultaneous small-angle neutron scattering and Fourier transform infrared spectroscopic measurements on cocrystals of syndiotactic polystyrene with polyethylene glycol dimethyl ethers1 (United States)

    Kaneko, Fumitoshi; Seto, Naoki; Sato, Shuma; Radulescu, Aurel; Schiavone, Maria Maddalena; Allgaier, Jürgen; Ute, Koichi


    Syndiotactic polystyrene (sPS) is a crystalline polymer which has a unique property; it is able to form cocrystals with a wide range of chemical compounds, in which the guest molecules are confined in the vacancies of the host sPS crystalline region. Recently, it has been found that even polyethylene glycol oligomers with a molecular weight of more than several hundreds can be introduced into the sPS crystalline region. It is quite important to know how such a long-chain molecule is stored in the host sPS lattice. To tackle this issue, a new simultaneous measurement method combing small-angle neutron scattering and Fourier transform infrared spectroscopy (SANS/FTIR), which has been recently developed by the authors, was applied to an sPS cocrystal with polyethylene glycol dimethyl ether with a molecular weight of 500 (PEGDME500). The temperature-dependent changes of the SANS profile and FTIR spectrum were followed from room temperature up to 413 K for a one-dimensionally oriented SANS/PEGDME500 cocrystal sample. The intensity of the reflections due to the stacking of crystalline lamellae showed a significant temperature dependence. The two-dimensional pattern in the high Q region of SANS also changed depending on temperature. The combined information obtained by SANS and FTIR suggested that PEGDME500 molecules are distributed in both the crystalline and amorphous regions in the low-temperature region close to room temperature, but they are predominantly included in the amorphous region in the high-temperature region. It was also suggested by the two-dimensional SANS profile that PEGDME500 molecules in the crystalline region have an elongated structure along the thickness direction of the crystalline lamellae. PMID:27738412

  17. Quantum Color Image Encryption Algorithm Based on A Hyper-Chaotic System and Quantum Fourier Transform (United States)

    Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong


    To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.

  18. Herschel SPIRE Fourier Transform Spectrometer: Calibration of its Bright-source Mode

    CERN Document Server

    Lu, Nanyao; Swinyard, Bruce M; Benielli, Dominique; Fulton, Trevor; Hopwood, Rosalind; Imhof, Peter; Lim, Tanya; Marchili, Nicola; Naylor, David A; Schulz, Bernhard; Sidher, Sunil; Valtchanov, Ivan


    The Fourier Transform Spectrometer (FTS) of the Spectral and Photometric Imaging REceiver (SPIRE) on board the ESA Herschel Space Observatory has two detector setting modes: (a) a nominal mode, which is optimized for observing moderately bright to faint astronomical targets, and (b) a bright-source mode recommended for sources significantly brighter than 500 Jy, within the SPIRE FTS bandwidth of 446.7-1544 GHz (or 194-671 microns in wavelength), which employs a reduced detector responsivity and out-of-phase analog signal amplifier/demodulator. We address in detail the calibration issues unique to the bright-source mode, describe the integration of the bright-mode data processing into the existing pipeline for the nominal mode, and show that the flux calibration accuracy of the bright-source mode is generally within 2% of that of the nominal mode, and that the bright-source mode is 3 to 4 times less sensitive than the nominal mode.

  19. Fourier-transform infrared spectroscopy (FTIR) analysis of triclinic and hexagonal birnessites. (United States)

    Ling, Florence T; Post, Jeffrey E; Heaney, Peter J; Kubicki, James D; Santelli, Cara M


    The characterization of birnessite structures is particularly challenging for poorly crystalline materials of biogenic origin, and a determination of the relative concentrations of triclinic and hexagonal birnessite in a mixed assemblage has typically required synchrotron-based spectroscopy and diffraction approaches. In this study, Fourier-transform infrared spectroscopy (FTIR) is demonstrated to be capable of differentiating synthetic triclinic Na-birnessite and synthetic hexagonal H-birnessite. Furthermore, IR spectral deconvolution of peaks resulting from MnO lattice vibrations between 400 and 750cm(-1) yield results comparable to those obtained by linear combination fitting of synchrotron X-ray absorption fine structure (EXAFS) data when applied to known mixtures of triclinic and hexagonal birnessites. Density functional theory (DFT) calculations suggest that an infrared absorbance peak at ~1628cm(-1) may be related to OH vibrations near vacancy sites. The integrated intensity of this peak may show sensitivity to vacancy concentrations in the Mn octahedral sheet for different birnessites.

  20. Voice Activity Detection in Noisy Environments Based on Double-Combined Fourier Transform and Line Fitting

    Directory of Open Access Journals (Sweden)

    Jinsoo Park


    Full Text Available A new voice activity detector for noisy environments is proposed. In conventional algorithms, the endpoint of speech is found by applying an edge detection filter that finds the abrupt changing point in a feature domain. However, since the frame energy feature is unstable in noisy environments, it is difficult to accurately find the endpoint of speech. Therefore, a novel feature extraction algorithm based on the double-combined Fourier transform and envelope line fitting is proposed. It is combined with an edge detection filter for effective detection of endpoints. Effectiveness of the proposed algorithm is evaluated and compared to other VAD algorithms using two different databases, which are AURORA 2.0 database and SITEC database. Experimental results show that the proposed algorithm performs well under a variety of noisy conditions.

  1. Calculation of Computational Complexity for Radix-2 (p) Fast Fourier Transform Algorithms for Medical Signals. (United States)

    Amirfattahi, Rassoul


    Owing to its simplicity radix-2 is a popular algorithm to implement fast fourier transform. Radix-2(p) algorithms have the same order of computational complexity as higher radices algorithms, but still retain the simplicity of radix-2. By defining a new concept, twiddle factor template, in this paper, we propose a method for exact calculation of multiplicative complexity for radix-2(p) algorithms. The methodology is described for radix-2, radix-2 (2) and radix-2 (3) algorithms. Results show that radix-2 (2) and radix-2 (3) have significantly less computational complexity compared with radix-2. Another interesting result is that while the number of complex multiplications in radix-2 (3) algorithm is slightly more than radix-2 (2), the number of real multiplications for radix-2 (3) is less than radix-2 (2). This is because of the twiddle factors in the form of which need less number of real multiplications and are more frequent in radix-2 (3) algorithm.

  2. Time-Frequency Signal Processing Based on Fractional Fourier Transform in Passive Sonar Classification

    Directory of Open Access Journals (Sweden)

    Vahid Bagheri


    Full Text Available This paper introduce a new data SONAR classification method based on Short-Time Fractional Fourier Transform (STFrFT analysis. The passive SONAR system receives the acoustic signals radiated by vessels and attempts to categorize them as a function of the similarities between vessels of the same class.Here, a time-frequency processing and feature extraction method is developed in order to improve the performance of a feedforwardneural network, which is used to classify five classes of vessels.Processing of time-varying signals in fractional fourier domain allows us to estimate the signal with higher concentration than conventional fourier domain, making the technique robust against additive noise, maintaining same computational complexity. With the purpose of dimension reduction and classification improvement, we use Linear Discriminant Analysis (LDA technique. The feasibility of the proposed technique (STFrFTLDA has been tested experimentally using a real database. The experimental results show the superiority of the proposed method

  3. High-definition Fourier transform infrared spectroscopic imaging of prostate tissue (United States)

    Wrobel, Tomasz P.; Kwak, Jin Tae; Kadjacsy-Balla, Andre; Bhargava, Rohit


    Histopathology forms the gold standard for cancer diagnosis and therapy, and generally relies on manual examination of microscopic structural morphology within tissue. Fourier-Transform Infrared (FT-IR) imaging is an emerging vibrational spectroscopic imaging technique, especially in a High-Definition (HD) format, that provides the spatial specificity of microscopy at magnifications used in diagnostic surgical pathology. While it has been shown for standard imaging that IR absorption by tissue creates a strong signal where the spectrum at each pixel is a quantitative "fingerprint" of the molecular composition of the sample, here we show that this fingerprint also enables direct digital pathology without the need for stains or dyes for HD imaging. An assessment of the potential of HD imaging to improve diagnostic pathology accuracy is presented.

  4. Kinetic study of olive oil degradation monitored by fourier transform infrared spectrometry. Application to oil characterization. (United States)

    Román Falcó, Iván P; Grané Teruel, Nuria; Prats Moya, Soledad; Martín Carratalá, M Luisa


    A new approach for the determination of kinetic parameters of the cis/trans isomerization during the oxidation process of 24 virgin olive oils belonging to 8 different varieties is presented. The accelerated process of degradation at 100 °C was monitored by recording the Fourier transform infrared spectra. The parameters obtained confirm pseudo-first-order kinetics for the degradation of cis and the appearance of trans double bonds. The kinetic approach affords the induction time and the rate coefficient; these parameters are related to the fatty acid profile of the fresh olive oils. The data obtained were used to compare the oil stability of the samples with the help of multivariate statistical techniques. Fatty acid allowed a classification of the samples in five groups, one of them constituted by the cultivars with higher stability. Meanwhile, the kinetic parameters showed greater ability for the characterization of olive oils, allowing the classification in seven groups.

  5. Integrated phase unwrapping algorithm for the measurement of 3D shapes by Fourier transform profilometry

    Institute of Scientific and Technical Information of China (English)

    Shuang-qing WU; Yin ZHANG; San-yuan ZHANG; Xiu-zi YE


    An integrated and reliable phase unwrapping algorithm is proposed based on residues and blocking-lines detection,closed contour extraction and quality map ordering for the measurement of 3D shapes by Fourier-transform profilometry (FTP).The proposed algorithm first detects the residues on the wrapped phase image, applies wavelet analysis to generate the blockinglines that can just connect the residues of opposite polarity, then carries out the morphology operation to extract the closed contour of the shape, and finally uses the modulation intensity information and the Laplacian of Gaussian operation of the wrapped phase image as the quality map. The unwrapping process is completed from a region of high reliability to that of low reliability and the blocking-lines can prevent the phase error propagation effectively. Furthermore, by using the extracted closed contour to exclude the invalid areas from the phase unwrapping process, the algorithm becomes more efficient. The experiment shows the effectiveness of the new algorithm.

  6. Demonstration of a compressive-sensing Fourier-transform on-chip spectrometer. (United States)

    Podmore, Hugh; Scott, Alan; Cheben, Pavel; Velasco, Aitor V; Schmid, Jens H; Vachon, Martin; Lee, Regina


    We demonstrate compressive-sensing (CS) spectroscopy in a planar-waveguide Fourier-transform spectrometer (FTS) device. The spectrometer is implemented as an array of Mach-Zehnder interferometers (MZIs) integrated on a photonic chip. The signal from a set of MZIs is composed of an undersampled discrete Fourier interferogram, which we invert using l1-norm minimization to retrieve a sparse input spectrum. To implement this technique, we use a subwavelength-engineered spatial heterodyne FTS on a chip composed of 32 independent MZIs. We demonstrate the retrieval of three sparse input signals by collecting data from restricted sets (8 and 14) of MZIs and applying common CS reconstruction techniques to this data. We show that this retrieval maintains the full resolution and bandwidth of the original device, despite a sampling factor as low as one-fourth of a conventional (non-compressive) design.

  7. Detection of Left-Sided and Right-Sided Hearing Loss via Fractional Fourier Transform

    Directory of Open Access Journals (Sweden)

    Shuihua Wang


    Full Text Available In order to detect hearing loss more efficiently and accurately, this study proposed a new method based on fractional Fourier transform (FRFT. Three-dimensional volumetric magnetic resonance images were obtained from 15 patients with left-sided hearing loss (LHL, 20 healthy controls (HC, and 14 patients with right-sided hearing loss (RHL. Twenty-five FRFT spectrums were reduced by principal component analysis with thresholds of 90%, 95%, and 98%, respectively. The classifier is the single-hidden-layer feed-forward neural network (SFN trained by the Levenberg–Marquardt algorithm. The results showed that the accuracies of all three classes are higher than 95%. In all, our method is promising and may raise interest from other researchers.

  8. Predicting the thermal/structural performance of the atmospheric trace molecules spectroscopy /ATMOS/ Fourier transform spectrometer (United States)

    Miller, J. M.


    ATMOS is a Fourier transform spectrometer to measure atmospheric trace molecules over a spectral range of 2-16 microns. Assessment of the system performance of ATMOS includes evaluations of optical system errors induced by thermal and structural effects. In order to assess the optical system errors induced from thermal and structural effects, error budgets are assembled during system engineering tasks and line of sight and wavefront deformations predictions (using operational thermal and vibration environments and computer models) are subsequently compared to the error budgets. This paper discusses the thermal/structural error budgets, modelling and analysis methods used to predict thermal/structural induced errors and the comparisons that show that predictions are within the error budgets.

  9. Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform

    Institute of Scientific and Technical Information of China (English)

    QI Lin; TAO Ran; ZHOU Siyong; WANG Yue


    This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.

  10. An Archive of Spectra from the Mayall Fourier Transform Spectrometer at Kitt Peak

    CERN Document Server

    Pilachowski, C A; Young, M D; Dennis, H B; Gopu, A; Henschel, R; Hayashi, S


    We describe the SpArc science gateway for spectral data obtained during the period from 1975 through 1995 at the Kitt Peak National Observatory using the Fourier Transform Spectrometer (FTS) in operation at the Mayall 4-m telescope. SpArc is hosted by Indiana University Bloomington and is available for public access. The archive includes nearly 10,000 individual spectra of more than 800 different astronomical sources including stars, nebulae, galaxies, and Solar System objects. We briefly describe the FTS instrument itself, and summarize the conversion of the original interferograms into spectral data and the process for recovering the data into FITS files. The architecture of the archive is discussed, and the process for retrieving data from the archive is introduced. Sample use cases showing typical FTS spectra are presented.

  11. Calibration transfer based on maximum margin criterion for qualitative analysis using Fourier transform infrared spectroscopy. (United States)

    Hu, Yong; Peng, Silong; Bi, Yiming; Tang, Liang


    A traditional multivariate calibration transfer method such as piecewise direct standardization (PDS) is usually applied to quantitative analysis. To make the method apply to qualitative analysis of Fourier Transform Infrared spectroscopy (FTIR), we propose an improved calibration transfer method based on the maximum margin criterion (CTMMC). The new method not only considers the spectral changes under different conditions, but also takes into account the geometric characteristics of spectra from different classes, so the transformed spectra from different classes will be separated as far as possible, and this will improve the performance of the follow-up qualitative analysis. A comparative study is provided between the proposed method CTMMC and other traditional calibration transfer methods on two data sets. Experimental results show that the proposed method can achieve better performance than previous methods.

  12. An Archive of Spectra from the Mayall Fourier Transform Spectrometer at Kitt Peak (United States)

    Pilachowski, C. A.; Hinkle, K. H.; Young, M. D.; Dennis, H. B.; Gopu, A.; Henschel, R.; Hayashi, S.


    We describe the SpArc science gateway for spectral data obtained using the Fourier Transform Spectrometer (FTS) in operation at the Mayall 4-m telescope at the Kitt Peak National Observatory during the period from 1975 through 1995. SpArc is hosted by Indiana University Bloomington and is available for public access. The archive includes nearly 10,000 individual spectra of more than 800 different astronomical sources including stars, nebulae, galaxies, and solar system objects. We briefly describe the FTS instrument itself and summarize the conversion of the original interferograms into spectral data and the process for recovering the data into FITS files. The architecture of the archive is discussed and the process for retrieving data from the archive is introduced. Sample use cases showing typical FTS spectra are presented.

  13. Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform. (United States)

    Tang, Heng-He; Liu, Pu-Kun


    A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

  14. Preliminary study on diffuse axonal injury by Fourier transform infrared spectroscopy histopathology imaging. (United States)

    Yang, Tiantong; He, Guanglong; Zhang, Xiang; Chang, Lin; Zhang, Haidong; Ripple, Mary G; Fowler, David R; Li, Ling


    The objective of this study was to evaluate the application of Fourier transform infrared (FTIR) spectroscopy for detecting diffuse axonal injury (DAI) in a mouse model. Brain tissues from DAI mouse model were prepared with H&E, silver, and β-amyloid precursor protein (β-APP) immunohistochemistry stains and were also studied with FTIR. The infrared spectrum images showed high absorption of amide II in the subcortical white matter of the experimental mouse brain, while there was no obvious expression of amide II in the control mouse brain. The areas with high absorption of amide II were in the same distribution as the DAI region confirmed by the silver and β-APP studies. The result suggests that high absorption of amide II correlates with axonal injury. The use of FTIR imaging allows the biochemical changes associated with DAI pathologies to be detected in the tissues, thus providing an important adjunct method to the current conventional pathological diagnostic techniques.

  15. A quantitative and qualitative method to control chemotherapeutic preparations by Fourier transform infrared-ultraviolet spectrophotometry. (United States)

    Dziopa, Florian; Galy, Guillaume; Bauler, Stephanie; Vincent, Benoit; Crochon, Sarah; Tall, Mamadou Lamine; Pirot, Fabrice; Pivot, Christine


    Chemotherapy products in hospitals include a reconstitution step of manufactured drugs providing an adapted dosage to each patient. The administration of highly iatrogenic drugs raises the question of patients' safety and treatment efficiency. In order to reduce administration errors due to faulty preparations, we introduced a new qualitative and quantitative routine control based on Fourier Transform Infrared (FTIR) and UV-Visible spectrophotometry. This automated method enabled fast and specific control for 14 anticancer drugs. A 1.2 mL sample was used to assay and identify each preparation in less than 90 sec. Over a two-year period, 9370 controlled infusion bags showed a 1.49% nonconformity rate, under 15% tolerance from the theoretical concentration and 96% minimum identification matching factor. This study evaluated the reliability of the control process, as well as its accordance to chemotherapy deliverance requirements. Thus, corrective measures were defined to improve the control process.

  16. Propagation of a general-type beam through a truncated fractional Fourier transform optical system. (United States)

    Zhao, Chengliang; Cai, Yangjian


    Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

  17. Fast Fourier Transform Chlorine Nuclear Quadrupole Resonance Spectroscopy. (United States)

    D'Iorio, Marie

    A nuclear quadrupole resonance spectrometer operating in the frequency range 1-40 MHz was updated for fast Fourier transform spectroscopy and coupled to a Nicolet 1180 computer and data acquisition system. It was used with a low temperature cryostat for studies shown down to liquid helium temperature and with a high pressure/low temperature system for studies down to liquid nitrogen temperature and up to six kilobars. The study of the ('35)Cl NQR spectrum of K(,2)OsCl(,6) at 298 K and 77 K revealed the presence of a satellite associated with the nearest neighbour chlorines to H('+) ion impurities located at vacant octahedral sties. This result is in agreement with the predictions of a point charge model calculation. A residence time for the H('+) ion was deduced and is consistent with the result obtained from dielectric measurements. A detailed study of the ('35)Cl NQR frequency in K(,2)ReCl(,6) was performed in the temperature range 85 - 130K where two structural phase transitions occur, and at pressures from 1 to 2643 bars. A number of unusual features were revealed and discussed as the possible signature of incommensurate behavior. The primary effect of the pressure was to alter the temperatures at which the phase transitions occurred. Contrary to the behavior expected, the transition temperature for the antiferrorotative transition has a negative pressure coefficient. The spin-lattice and spin-spin relaxation times for the ('35)Cl and ('37)Cl isotopes of the one dimensional XY system, PrCl(,3), were measured at 4.2K. The spin-lattice relaxation is exponential and dominated by magnetic dipole -dipole interactions. The spin-spin relaxation is non-exponential and dominated by electric quadrupolar interactions arising from the coupling of the electric dipole moment at the praseodymium site and the quadrupole moment of the chlorine ion. The temperature dependence of the spin-spin relaxation time was investigated. At 17.4 K both magnetic dipolar and electric

  18. The Application of Fourier Transform Infrared Photoacoustics Spectroscopy (FTIR-PAS for Rapid Soil Quality Evaluation

    Directory of Open Access Journals (Sweden)

    Ichwana Ichwana


    The Application of Fourier Transform Infrared Photoacoustics Spectroscopy (FTIR-PAS for Rapid Soil Quality Evaluation Abstract. The major function of soil is to provide fundamental natural resources for survival of plants, animals, and the human race. Soil functions depend on the balances of its structure and composition, well as the chemical, biological, and physical properties. It is become one important key aspect and routine activity in crop management system. To monitor and determine soil quality properties, several methods were already widely used in which most of them are based on solvent extraction followed by other laboratory procedures. However, these methods often require laborious and complicated processing for samples. They are time consuming and destructive. In last few decades, the application of infrared spectroscopy as non-destructive technique in determining soil quality properties (C, N, P and K rapidly and simultaneously. Fourier transform infrared spectrum (FTIR were acquired in wavelength range from 1000 to 2500 nm with applying photo-acoustic spectroscopy (PAS. Least square-support vector machine regression (LS-SVM approach was then applied to predict soil quality properties. The results showed that C and N can be predicted accurately using FTIR-PAS whilst other parameters (P, K, Mg, Ca, S can be predicted with maximum RPD index is 1.9. Moreover, soil clay, moisture and soil microbes were feasible to be detected by using FTIR-PAS combining with discriminant analysis (LS-DA or cluster analysis (CA. It may conclude that FTIR-PAS technology can be used as a real time method  in monitoring soil quality and fertility properties.

  19. Monitoring of Methyldopa by Fast Fourier Transform Continuous Cyclic Voltammetry at Gold Microelectrode

    Institute of Scientific and Technical Information of China (English)

    NOROUZI,Parviz; GANJALI,Mohammad Reza; SHAHTAHERI,Sayed Jamaleddin; DINARVAND,Rasoul; HAMZEHPOOR,Ali


    A continuous cyclic voltammetric study of methyldopa at gold micro electrode was carried out.The drug in phosphate buffer (pH 2.0) is adsorpted at 400 mV,giving rise to change in the current of well-defined oxidation peak of gold in the flow injection system.The proposed detection method has some of advantages,the greatest one of which are as follows;first,it is no more necessary to remove oxygen from the analyte solution and second,this is a very fast and appropriate technique for determination of the drug compound in a wide variety of chromatographic analysis methods.Signal-to-noise ratio has significantly increased by application of discrete Fast Fourier transform (FFT) method,background subtraction and two-dimensional integration of the electrode response over a selected potential range and time window.Also in this work some parameters such as sweep rate,eluent pH,and accumulation time and potential were optimized.The linear concentration range was of 1.0×10-7-1.0×10-11 mol·L-1 (r=0.9975) with a limit of detection and quantitation 0.004 nmol·L-1 and 0.03 nmol·L-1,respectively.The method has the requisite accuracy,sensitivity,precision and selectivity to assay methyldopa in tablets.The influences of pH of eluent,accumulation potential,sweep rate,and accumulation time on the determination of the methyldopa were considered.

  20. Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform

    Directory of Open Access Journals (Sweden)

    Zohreh Moghareh Abed


    Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.

  1. Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR. (United States)

    Perkins, W. D.


    This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)

  2. Improved method of generating bit reversed numbers for calculating fast fourier transform

    Digital Repository Service at National Institute of Oceanography (India)

    Suresh, T.

    Fast Fourier Transform (FFT) is an important tool required for signal processing in defence applications. This paper reports an improved method for generating bit reversed numbers needed in calculating FFT using radix-2. The refined algorithm takes...

  3. Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy (United States)

    D'Astous, Y.; Blanchard, M.


    In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

  4. Research about vibration characteristics of timing chain system based on short-time Fourier transform (United States)

    Xi, Jiaxin; Liu, Ning


    Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.

  5. A High Resolution Fourier-Transform Spectrometer for the Measurement of Atmospheric Column Abundances (United States)

    Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.


    A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).

  6. The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction. (United States)

    King, Roy W.; Williams, Kathryn R.


    Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)

  7. Fourier transform of delayed fluorescence as an indicator of herbicide concentration. (United States)

    Guo, Ya; Tan, Jinglu


    It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method.

  8. Multi-channel sampling theorems for band-limited signals with fractional Fourier transform

    Institute of Scientific and Technical Information of China (English)


    Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.

  9. The Design of Lens Imaging System by Means of Fractional Fourier Transform

    Institute of Scientific and Technical Information of China (English)

    CHEN Jiannong; XU Qiang; D.R.Selviah


    The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing specific imaging system. The Gaussian imaging formula of single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system through an example.

  10. Optical Image Addition and Encryption by Multi-Exposure Based on Fractional Fourier Transform Hologram

    Institute of Scientific and Technical Information of China (English)

    CHEN Lin-Fei; ZHAO Dao-Mu


    @@ We propose a new method to add different images together by optical implementation that is realized by the multi-exposure based on fractional Fourier transform hologram. Partial image fusion is proposed and realized by this method. Multiple images encryption can also be implemented by the multi-exposure of the hologram based on fractional Fourier transform. Computer simulations prove that this method is valid.

  11. Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm (United States)

    Heisler, R.


    A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

  12. Compact imaging spectrometer combining Fourier transform spectroscopy with a Fabry-Perot interferometer. (United States)

    Pisani, Marco; Zucco, Massimo


    An imaging spectrometer based on a Fabry-Perot interferometer is presented. The Fabry-Perot interferometer scans the mirror distance up to contact and the intensity modulated light signal is transformed using a Fourier Transform based algorithm, as the Michelson based Fourier Transform Spectrometers does. The resulting instrument has the advantage of a compact, high numerical aperture, high luminosity hyperspectral imaging device. Theory of operation is described along with one experimental realization and preliminary results.

  13. OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation

    DEFF Research Database (Denmark)

    Palushani, Evarist; Richter, T.; Ludwig, R.


    We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....

  14. Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion

    DEFF Research Database (Denmark)

    Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael


    Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....

  15. Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts (United States)

    Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.


    By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

  16. Two-dimensional calculus

    CERN Document Server

    Osserman, Robert


    The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

  17. Two dimensional vernier (United States)

    Juday, Richard D. (Inventor)


    A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.

  18. Strongly interacting two-dimensional Dirac fermions

    NARCIS (Netherlands)

    Lim, L.K.; Lazarides, A.; Hemmerich, Andreas; de Morais Smith, C.


    We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature


    Institute of Scientific and Technical Information of China (English)

    FENG Xiang-bo; YAN Yi-xin; ZHANG Wei


    Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields,and spatial wave information could be obtained from the radar images.Two-dimensional Fourier Transform (2-D FT) is the common algorithm to derive the spectra of radar images.However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms.When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain.In this article, we introduce two-dimensional Wavelet Transform (2-D WT) to capture the non-homogeneity of wave fields from nearshore radar images.The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves.Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West (SSW) to West South West (WSW).To verify the results of2-D WT, wave shoaling in radar images is calculated based on dispersion relation.The theoretical calculation results agree with the results of 2-D WT on the whole.The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.

  20. Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots

    Energy Technology Data Exchange (ETDEWEB)

    Cundiff, Steven T. [Univ. of Colorado, Boulder, CO (United States)


    This final report describes the activities undertaken under grant "Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots". The goal of this program was to implement optical 2-dimensional Fourier transform spectroscopy and apply it to electronic excitations, including excitons, in semiconductors. Specifically of interest are quantum wells that exhibit disorder due to well width fluctuations and quantum dots. In both cases, 2-D spectroscopy will provide information regarding coupling among excitonic localization sites.

  1. The investigation on two-dimensional pilot-symbol-aided channel estimation method for OFDM system

    Institute of Scientific and Technical Information of China (English)

    Sun Juying; Zhang Yanhua


    Channel estimation for orthogonal frequency division multiplexing (OFDM) system has attracted widespread attention. In this paper, a novel efficient two-dimensional (2-D) channel estimation algorithm based on fast Fourier transform (FFT) is proposed for a time-variant, frequency-selective wideband wireless channel. Both theoretical analysis and simulation results are addressed in the paper. The simulation results prove that the proposed algorithm has simpler implementation, better performance and wider application than other traditional decision-directed algorithms.

  2. Simple Scheme for Realizing the General Conditional Phase Shift Gate and a Simulation of Quantum Fourier Transform in Circuit QED

    Institute of Scientific and Technical Information of China (English)

    吴春旺; 韩阳; 邓志姣; 李虹轶; 陈平形; 李承祖


    We propose a theoretical scheme for realizing the general conditional phase shift gate of charge qubits situated in a high-Q superconducting transmission line resonator. The phase shifting angle can be tuned from 0 to 27r by simply adjusting the qubit-resonator detuning and the interaction time. Based on this gate proposal, we give a detailed procedure to implement the three-qubit quantum Fourier transform with circuit quantum eleetrodynamics (QED). A careful analysis of the decoherence sources shows that the algorithm can be achieved with a high fidelity using current circuit QED techniques.

  3. Characterization of Campylobacter jejuni applying flaA short variable region sequencing, multilocus sequencing and Fourier transform infrared spectroscopy

    DEFF Research Database (Denmark)

    Josefsen, Mathilde Hartmann; Bonnichsen, Lise; Larsson, Jonas

    flaA short variable region sequencing and phenetic Fourier transform infrared (FTIR) spectroscopy was applied on a collection of 102 Campylobacter jejuni isolated from continuous sampling of organic, free range geese and chickens. FTIR has been shown to serve as a valuable tool in typing.......94 and 0.92, respectively. Dendrograms based on cluster analysis grouped the isolates in 6 clusters based on flaA sequences and 9 clusters based on the FTIR spectroscopy profiles. Furthermore, the cluster analysis of flaA sequences, MLST and FTIR spectroscopy profiles showed a surprisingly high degree...

  4. Evaluation of chondromalacia in the knee joint using three dimensional Fourier transformation constructive interference in steady state (CISS)

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, Sam Hyun; Ha, Doo Hoe; Kwak, Jin Young [College of Medicine, Pochon CHA University, Sungnam (Korea, Republic of); Lee, Young Soo [Pundang CHA General Hospital, College of Medicine, Pochon CHA University, Seoul (Korea, Republic of)


    To assess the usefulness of three-dimensional Fourier transformation constructive interference in steady state (CISS) for the evaluation of chondromalacia. In 110 knee joints which underwent both MR imaging and arthroscopy, the findings were retrospectively reviewed. MR imaging sequences included two-dimensional dual-echo turbo spin-echo imaging along the sagittal and coronal planes, two-dimensional fast low-angle shot (FLASH) with magnetization transfer along the axial plane, and three-dimensional CISS along the sagittal plane. After the cartilage surfaces of each joint were divided into eight areas (each medial and lateral area of patellar facets, trochlear surfaces, femoral condyles, and tibial plateaux), a total of 880 areas were assessed. Using both combined two-dimensional (2-D turbo spin-echo and FLASH) and CISS imaging during different sessions, each chondromalacia case was assigned one of five grades. Arthroscopy revealed the presence of chondromalacia in 162 areas. This was first grade in 77 areas, second grade in 38, third grade in 21, and fourth grade in 26. The sensitivity, specificity, and accuracy of 2-D and CISS imaging were 48.1%, 93.7% and 85.3%, and 45.7%, 95.3% and 86.1%, respectively. Agreement between MR and arthroscopic staging occurred in 81.48% of 2-D imaging procedures and 82.16% of CISS procedures. If a difference of one grade was accepted, these proportions rose to 84.32% and 85.22%, respectively, though this increase was statistically insignificant. Though CISS imaging was less sensitive than 2-D imaging in the grading of chondromalacia, additional CISS imaging can help improve the accuracy of this grading.

  5. Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments

    CERN Document Server

    Nemeth, Alexandra; Mancal, Tomas; Lukes, Vladimir; Hauer, Juergen; Kauffmann, Harald F; Sperling, Jaroslaw


    This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic techniques for studying a dye molecule in solution. Ultrafast laser pulse excitation of an electronic transition coupled to vibrational modes induces a propagating vibrational wave packet that manifests itself in oscillating signal intensities and line-shapes. For the two-dimensional electronic spectra we can attribute the observed modulations to periodic enhancement and decrement of the relative amplitudes of rephasing and non-rephasing contributions to the total response. Different metrics of the two-dimensional signals are shown to relate to the frequency-frequency correlation function which provides the connection between experimentally accessible observations and the underlying microscopic molecular dynamics. A detailed theory of the time-dependent two-dimensional spectral li...

  6. [Study on miniature static Fourier transform spectrometer used in laser warning receiver]. (United States)

    Tian, Er-Ming; Zhang, Ji-Long; Li, Xiao; Zhang, Yue; Wang, Zhi-Bin


    A miniature static Fourier transform spectrometer (MSFTS) as the component of coherent discriminating laser warning receiver (CDLWR) was designed in the present study by using a modified wedge interfering etalon (MWIE), a linear charge couple device (CCD) and a fast digital signal processor (DSP). The MSFTS possesses some advantages such as small volume, low cost, high speed, stable performance and good signal to noise ratio. MSFTS can detect the spectrum of HIPL, the short pulse width of laser is about 10 ns, and the spectrum scope is from 400 to 1 100 nm. The key element of MSFTS is MWIE which is composed of two triangle prisms, one of which is a right angle prism with two equal acute angles of 45 degrees, another prism has no right angle, one of the acute angles is 45 degrees, and another is slightly smaller than 45 degrees. The long sides of the two prisms were bonded by transparent glass glue, and the adhesive surface is plated with special material which serves as a beam splitter (BS). The incident laser will be split into two equal strength beams with continuously changing optical path difference, the two beams will interfere and form interferogram which will be focused by a cylinder as a line and transformed as s electronic signal by CCD. The electronic signal was processed by using a DSP, and finally we obtained the spectrum of the incident hostile laser by applying fast Fourier transform (FFT). We have established the experiment system of MSFTS, and used the system and the spectrometer Q8344A made by Advantest Company in Japan to measure the spectra of the seven lasers with different central wavelengths: 635, 650, 670, 780, 808, 850 and 980 nm. The measurement result shows that the worst wavelength resolution is 8. 845 nm at 1 100 nm, the best wavelength resolution is 1.170 nm at 400 nm, the relative average error of central wavelength is 0.269 nm, the absolute average error is 0.919 nm and signal-to-noise ratio of our experiment system is better than

  7. Fourier Transform Infrared Spectroscopy: A Potential Technique for Noninvasive Detection of Spermatogenesis (United States)

    Gilany, Kambiz; Pouracil, Roudabeh Sadat Moazeni; Sadeghi, Mohammad Reza


    Background The seminal plasma is an excellent source for noninvasive detection of spermatogenesis. The seminal plasma of normospermic and azoospermic men has been analyzed for detection of spermatogenesis. Methods Optical spectroscopy (Attenuated Total Reflectance-Infrared spectroscopy (ATR-IR) and Fourier Transform infrared spectroscopy (FT-IR) has been used to analyze the seminal plasma and the metabolome of seminal plasma for detection of spermatogenesis. Results The seminal plasma of normospermic and azoospermic men has been analyzed by ATR-IR. The results show that there is a pattern variation in the azoospermic men compared to normospermic men. However, the seminal plasma is too complex to show significant pattern variation. Therefore, the metabolome which is a subcomponent of the seminal plasma was analyzed. The seminal plasma metabolome of normospermic and azoospermic men has been analyzed by FT-IR. A significant pattern change was observed. The data combined with chemometrics analysis showed that significant changes are observed at metabolome level. Conclusion We suggest that FT-IR has the potential as a diagnostic tool instead of testicular biopsy. PMID:24523955

  8. Two-dimensional optical spectroscopy

    CERN Document Server

    Cho, Minhaeng


    Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.

  9. Discrete Fourier Transform Method for Discrimination of Digital Scintillation Pulses in Mixed Neutron-Gamma Fields

    CERN Document Server

    Safari, M J; Afarideh, H; Jamili, S; Bayat, E


    A Discrete Fourier Transform Method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain using the sine and cosine Fourier transforms in combination with the discrete Fourier transform. The method is largely benefited from considerable differences that usually is available between the zero-frequency components of sine and cosine and the norm of the amplitude of the DFT for neutrons and gamma-ray signals. Moreover, working in frequency domain naturally results in considerable suppression of the unwanted effects of various noise sources that is expected to be effective in time domain methods. The proposed method could also be assumed as a generalized nonlinear weighting method that could result in a new class of pulse shape discrimination methods, beyond definition of the DFT. A comparison to the traditional Charge Integration Method (CIM), as well as the Frequency G...

  10. Functional differential equations for the q-Fourier transform of q-Gaussians

    Energy Technology Data Exchange (ETDEWEB)

    Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)


    In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

  11. Fast Inverse Nonlinear Fourier Transforms for Fiber Bragg Grating Design and Related Problems

    CERN Document Server

    Wahls, Sander


    The problem of constructing a fiber Bragg grating profile numerically such that the reflection coefficient of the grating matches a given specification is considered. The well-known analytic solution to this problem is given by a suitable inverse nonlinear Fourier transform (also known as inverse scattering transform) of the specificed reflection coefficient. Many different algorithms have been proposed to compute this inverse nonlinear Fourier transform numerically. The most efficient ones require $\\mathcal{O}(D^{2})$ floating point operations (flops) to generate $D$ samples of the grating profile. In this paper, two new fast inverse nonlinear Fourier transform algorithms that require only $\\mathcal{O}(D\\log^{2}D)$ flops are proposed. The merits of our algorithms are demonstrated in numerical examples, in which they are compared to a conventional layer peeling method, the Toeplitz inner bordering method and integral layer peeling. One of our two algorithms also extends to the design problem for fiber-assiste...

  12. Inversion of Fourier Transforms by Means of Scale-Frequency Series

    Directory of Open Access Journals (Sweden)

    Nassar H. S. Haidar


    Full Text Available We report on inversion of the Fourier transform when the frequency variable can be scaled in a variety of different ways that improve the resolution of certain parts of the frequency domain. The corresponding inverse Fourier transform is shown to exist in the form of two dual scale-frequency series. Upon discretization of the continuous scale factor, this Fourier transform series inverse becomes a certain nonharmonic double series, a discretized scale-frequency (DSF series. The DSF series is also demonstrated, theoretically and practically, to be rate-optimizable with respect to its two free parameters, when it satisfies, as an entropy maximizer, a pertaining recursive nonlinear programming problem incorporating the entropy-based uncertainty principle.

  13. Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra (United States)

    Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.


    We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

  14. Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion (United States)

    Yükçü, Niyazi


    Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical properties of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.

  15. Continuous Fourier transform method and apparatus. [for the analysis of simultaneous analog signal components (United States)

    Munoz, R. M. (Inventor)


    An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.

  16. Fourier-transform spectroscopy: new methods and applications: introduction by the feature editors. (United States)

    Traub, W A; Winkel, R J; Goldman, A


    We are pleased to introduce this special issue of papers on Fourier-transform spectroscopy, which grew out of a recent topical meeting sponsored by the Optical Society of America. The topical meeting welcomed all researchers who practice the art of Fourier-transform spectroscopy in the laboratory, in the atmosphere, and in space. The power and the wide applicability of Fourier-transform spectroscopy unite these fields with a common mathematical and instrumental bond. The meeting probed each of these areas in depth, bringing out new ideas for instrumentation, analysis, and applications. There was a strong sentiment at the meeting that the quality of papers and posters was exceptionally high and that it would be important for future progress in the field to have the results of this meeting captured in print. This special issue is the fruit of that effort.

  17. Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors. (United States)

    Luo, David; Kudenov, Michael W


    Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing.

  18. Analysis of Resistant Starches in Rat Cecal Contents Using Fourier Transform Infrared Photoacoustic Spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Anderson, Timothy J. [Ames Laboratory; Ai, Yongfeng [Iowa State University; Jones, Roger W. [Ames Laboratory; Houk, Robert S. [Ames Laboratory; Jane, Jay-lin [Iowa State University; Zhao, Yinsheng [Iowa State University; Birt, Diane F. [Iowa State University; McClelland, John F. [Ames Laboratory


    Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) qualitatively and quantitatively measured resistant starch (RS) in rat cecal contents. Fisher 344 rats were fed diets of 55% (w/w, dry basis) starch for 8 weeks. Cecal contents were collected from sacrificed rats. A corn starch control was compared against three RS diets. The RS diets were high-amylose corn starch (HA7), HA7 chemically modified with octenyl succinic anhydride, and stearic-acid-complexed HA7 starch. To calibrate the FTIR-PAS analysis, samples from each diet were analyzed using an enzymatic assay. A partial least-squares cross-validation plot generated from the enzymatic assay and FTIR-PAS spectral results for starch fit the ideal curve with a R2 of 0.997. A principal component analysis plot of components 1 and 2 showed that spectra from diets clustered significantly from each other. This study clearly showed that FTIR-PAS can accurately quantify starch content and identify the form of starch in complex matrices.

  19. Attenuated total reflectance Fourier transform infrared spectroscopy method to differentiate between normal and cancerous breast cells. (United States)

    Lane, Randy; See, Seong S


    Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) is used to find the structural differences between cancerous breast cells (MCF-7 line) and normal breast cells (MCF-12F line). Gold nanoparticles were prepared and the hydrodynamic diameter of the gold nanoparticles found to be 38.45 nm. The Gold nanoparticles were exposed to both MCF-7 and MCF-12F cells from lower to higher concentrations. Spectroscopic studies founds nanoparticles were within the cells, and increasing the nanoparticles concentration inside the cells also resulted in sharper IR peaks as a result of localized surface Plasmon resonance. Asymmetric and symmetric stretching and bending vibrations between phosphate, COO-, CH2 groups were found to give negative shifts in wavenumbers and a decrease in peak intensities when going from noncancerous to cancerous cells. Cellular proteins produced peak assignments at the 1542 and 1644 cm(-1) wavenumbers which were attributed to the amide I and amide II bands of the polypeptide bond of proteins. Significant changes were found in the peak intensities between the cell lines in the spectrum range from 2854-2956 cm(-1). Results show that the concentration range of gold nanoparticles used in this research showed no significant changes in cell viability in either cell line. Therefore, we believe ATR-FTIR and gold nanotechnology can be at the forefront of cancer diagnosis for some time to come.

  20. Analysis of serum cortisol levels by Fourier Transform Infrared Spectroscopy for diagnosis of stress in athletes

    Directory of Open Access Journals (Sweden)

    Lia Campos Lemes

    Full Text Available Abstract Introduction Fourier-transform infrared (FT-IR spectroscopy is a technique with great potential for body fluids analyses. The aim of this study was to examine the impact of session training on cortisol concentrations in rugby players by means of infrared analysis of serum. Methods Blood collections were performed pre, post and 24 hours after of rugby training sessions. Serum cortisol was analyzed by FT-IR spectroscopy and chemiluminescent immunoassay. Results There was a significant difference between the integrated area, in the region of 1180-1102 cm-1, of the spectra for pre, post and post 24 h serums. The cortisol concentration obtained by chemiluminescent immunoassay showed no significant difference between pre, post and post 24 h. Positive correlations were obtained between the techniques (r = 0.75, post (r = 0.83 and post 24 h (r = 0.73. Conclusion The results showed no increase in cortisol levels of the players after the training sessions, as well as positive correlations indicating that FT-IR spectroscopy have produced promising results for the analysis of serum for diagnosis of stress.

  1. Identification of Contaminated Cells with Viruses, Bacteria, or Fungi by Fourier Transform Infrared Microspectroscopy

    Directory of Open Access Journals (Sweden)

    V. Erukhimovitch


    Full Text Available Fourier transform infrared microspectroscopy (FTIR-M can detect small molecular changes in cells and therefore was previously applied for the identification of different biological samples. In the present study, FTIR spectroscopy was used for the identification and discrimination of Vero cells infected with herpes viruses or contaminated with bacteria or fungi in cell culture. Vero cells in culture were infected herpes simplex virus type 1 (HSV-1 or contaminated with E. coli bacteria or Candida albicans fungi and analyzed by FTIR microscopy at 24 h postinfection/contamination. Specific different spectral changes were observed according to the infecting or contaminating agent. For instance, both pure fungi and cell culture contaminated with this fungi showed specific peaks at 1030 cm−1 and at 1373 cm−1 regions, while pure E. coli and cell culture contaminated with this bacteria showed a specific and unique peak at 1657 cm−1. These results support the potential of developing FTIR microspectroscopy as a simple, reagent free method for identification and discrimination between different tissue infection or contamination with various pathogens.

  2. Portable Gas Analyzer Based on Fourier Transform Infrared Spectrometer for Patrolling and Examining Gas Exhaust

    Directory of Open Access Journals (Sweden)

    Yuntao Liang


    Full Text Available Aimed at monitoring emission of organic gases such as CH4, C2H6, C3H8, iso-C4H10, n-C4H10, C2H4, C3H6, C2H2, CO, and CO2, from coal mines, petroleum refineries, and other plants, a Fourier Transform Infrared (FT-IR spectrometer was used to develop a portable gas analyzer for patrolling and examining gas exhaust. Firstly, structure of the instrument was introduced. Then, a spectral analysis approach was presented. Finally, instrument was tested with standard gases and with actual gases emitted from a petroleum refinery. For the latter test, a gas chromatograph (GC was used as a reference instrument. The test results showed that the detection limit of every component of analyte was less than 10 × 10−6. The maximum test error of every analyte was less than 15 × 10−6 when its practical concentration was no more than 500 × 10−6. A final comparison showed that the result curves of analytes obtained with FT-IR spectrometer almost overlapped with those obtained with GC, and their resulting noise was less than 6.4% when the practical gas concentration was above 100 × 10−6. As a result, our instrument was suitable to be used as a portable instrument for monitoring exhaust gases.

  3. Renal Graft Fibrosis and Inflammation Quantification by an Automated Fourier-Transform Infrared Imaging Technique. (United States)

    Vuiblet, Vincent; Fere, Michael; Gobinet, Cyril; Birembaut, Philippe; Piot, Olivier; Rieu, Philippe


    Renal interstitial fibrosis and interstitial active inflammation are the main histologic features of renal allograft biopsy specimens. Fibrosis is currently assessed by semiquantitative subjective analysis, and color image analysis has been developed to improve the reliability and repeatability of this evaluation. However, these techniques fail to distinguish fibrosis from constitutive collagen or active inflammation. We developed an automatic, reproducible Fourier-transform infrared (FTIR) imaging-based technique for simultaneous quantification of fibrosis and inflammation in renal allograft biopsy specimens. We generated and validated a classification model using 49 renal biopsy specimens and subsequently tested the robustness of this classification algorithm on 166 renal grafts. Finally, we explored the clinical relevance of fibrosis quantification using FTIR imaging by comparing results with renal function at 3 months after transplantation (M3) and the variation of renal function between M3 and M12. We showed excellent robustness for fibrosis and inflammation classification, with >90% of renal biopsy specimens adequately classified by FTIR imaging. Finally, fibrosis quantification by FTIR imaging correlated with renal function at M3, and the variation in fibrosis between M3 and M12 correlated well with the variation in renal function over the same period. This study shows that FTIR-based analysis of renal graft biopsy specimens is a reproducible and reliable label-free technique for quantifying fibrosis and active inflammation. This technique seems to be more relevant than digital image analysis and promising for both research studies and routine clinical practice.

  4. Fourier transform infrared spectroscopic imaging of cardiac tissue to detect collagen deposition after myocardial infarction (United States)

    Cheheltani, Rabee; Rosano, Jenna M.; Wang, Bin; Sabri, Abdel Karim; Pleshko, Nancy; Kiani, Mohammad F.


    Myocardial infarction often leads to an increase in deposition of fibrillar collagen. Detection and characterization of this cardiac fibrosis is of great interest to investigators and clinicians. Motivated by the significant limitations of conventional staining techniques to visualize collagen deposition in cardiac tissue sections, we have developed a Fourier transform infrared imaging spectroscopy (FT-IRIS) methodology for collagen assessment. The infrared absorbance band centered at 1338 cm-1, which arises from collagen amino acid side chain vibrations, was used to map collagen deposition across heart tissue sections of a rat model of myocardial infarction, and was compared to conventional staining techniques. Comparison of the size of the collagen scar in heart tissue sections as measured with this methodology and that of trichrome staining showed a strong correlation (R=0.93). A Pearson correlation model between local intensity values in FT-IRIS and immuno-histochemical staining of collagen type I also showed a strong correlation (R=0.86). We demonstrate that FT-IRIS methodology can be utilized to visualize cardiac collagen deposition. In addition, given that vibrational spectroscopic data on proteins reflect molecular features, it also has the potential to provide additional information about the molecular structure of cardiac extracellular matrix proteins and their alterations.

  5. A method to correct sampling ghosts in historic near-infrared Fourier Transform Spectrometer (FTS measurements

    Directory of Open Access Journals (Sweden)

    S. Dohe


    Full Text Available The Total Carbon Column Observing Network (TCCON has been established to provide ground-based remote sensing measurements of the column-average dry air mole fractions of key greenhouse gases. To ensure the network wide consistency, biases between Fourier Transform spectrometers at different sites have to be well controlled. In this study we investigate a fundamental correction scheme for errors in the sampling of the interferogram. This is a two-step procedure in which the laser sampling error (LSE is quantified using a subset of suitable interferograms and then used to resample all the interferograms in the timeseries. Timeseries of measurements acquired at the TCCON sites Izaña and Lauder are used to demonstrate the method. At both sites the sampling error histories show changes in LSE due to instrument interventions. Estimated LSE are in good agreement with sampling errors inferred from lamp measurements of the ghost to parent ratio (Lauder. The LSE introduce retrieval biases which are minimised when the interferograms are resampled. The original timeseries of Xair and XCO2 at both sites show discrepancies of 0.2–0.5% due to changes in the LSE associated with instrument interventions or changes in the measurement sample rate. After resampling discrepancies are reduced to 0.1% at Lauder and 0.2% at Izaña. In the latter case, coincident changes in interferometer alignment may also contribute to the residual difference.

  6. Application of Fractional Fourier Transform to Moving Target Indication via Along-Track Interferometry

    Directory of Open Access Journals (Sweden)

    Chiu Shen


    Full Text Available A relatively unknown yet powerful technique, the so-called fractional Fourier transform (FrFT, is applied to SAR along-track interferometry (SAR-ATI in order to estimate moving target parameters. By mapping a target's signal onto a fractional Fourier axis, the FrFT permits a constant-velocity target to be focused in the fractional Fourier domain thereby affording orders of magnitude improvement in SCR. Moving target velocity and position parameters are derived and expressed in terms of an optimum fractional angle and a measured fractional Fourier position , allowing a target to be accurately repositioned and its velocity components computed without actually forming an SAR image. The new estimation algorithm is compared with the matched filter bank approach, showing some of the advantages of the FrFT method. The proposed technique is applied to the data acquired by the two-aperture CV580 airborne radar system configured in its along-track mode. Results show that the method is effective in estimating target velocity and position parameters.

  7. All-optical WDM Regeneration of DPSK Signals using Optical Fourier Transformation and Phase Sensitive Amplification

    DEFF Research Database (Denmark)

    Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian;


    We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....

  8. Interferometric time delay correction for Fourier transform spectroscopy in the extreme ultraviolet (United States)

    Meng, Yijian; Zhang, Chunmei; Marceau, Claude; Naumov, A. Yu.; Corkum, P. B.; Villeneuve, D. M.


    We demonstrate a Fourier transform spectrometer in the extreme ultraviolet (XUV) spectrum using a high-harmonic source, with wavelengths as short as 32 nm. The femtosecond infrared laser source is divided into two separate foci in the same gas jet to create two synchronized XUV sources. An interferometric method to determine the relative delay between the two sources is shown to improve the accuracy of the delay time, with corrections of up to 200 asec required. By correcting the time base before the Fourier transform, the frequency resolution is improved by up to an order of magnitude.

  9. Three-dimensional radiative transfer using a Fourier-transform matrix-operator method (United States)

    Martonchik, J. V.; Diner, D. J.


    The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.

  10. Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

    Energy Technology Data Exchange (ETDEWEB)

    Aldea, N; Pintea, S; Rednic, V [National Institute for Research and Development of Isotopic and Molecular Technologies, 65-103 Donath, 400293 Cluj-Napoca (Romania); Matei, F [University of Agricultural Sciences and Veterinary Medicine, 3-5 Calea Manastur, 400372 Cluj-Napoca (Romania); Hu Tiandou; Xie Yaning, E-mail: nicolae.aldea@itim-cj.r [Beijing Synchrotron Radiation Facilities of Beijing Electron Positron Collider National Laboratory (China)


    The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe{sub 3}O{sub 4} core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.

  11. DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation

    DEFF Research Database (Denmark)

    Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael


    We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated.......We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated....

  12. 1.28 Tbaud Nyquist Signal Transmission using Time-Domain Optical Fourier Transformation based Receiver

    DEFF Research Database (Denmark)

    Hu, Hao; Kong, Deming; Palushani, Evarist


    We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries.......We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries....

  13. 16 channel WDM regeneration in a single phase-sensitive amplifier through optical Fourier transformation

    DEFF Research Database (Denmark)

    Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads


    We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude......We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...

  14. Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware

    DEFF Research Database (Denmark)

    Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard


    We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe the performa......We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe...

  15. First Signal on the Cryogenic Fourier-Transform Ion Cyclotron Resonance Mass Spectrometer (United States)

    Lin, Cheng; Mathur, Raman; Aizikov, Kostantin; O'Connor, Peter B.


    The construction and achievement of the first signal on a cryogenic Fourier-transform ion cyclotron resonance mass spectrometer (FT-ICR-MS) are reported here, demonstrating proof-of-concept of this new instrument design. Building the FTICR cell into the cold bore of a superconducting magnet provided advantages over conventional warm bore design. At 4.2 K, the vacuum system cryopumps itself, thus removing the requirement for a large bore to achieve the desired pumping speed for maintaining base pressure. Furthermore, because the bore diameter has been reduced, the amount of magnet wire needed to achieve high field and homogeneity was also reduced, greatly decreasing the cost/Tesla of the magnet. The current instrument implements an actively shielded 14-Tesla magnet of vertical design with an external matrix assisted laser desorption/ionization (MALDI) source. The first signal was obtained by detecting the laser desorbed/ionized (LDI) C60+• ions, with the magnet at 7 Tesla, unshimmed, and the preamplifier mounted outside of the vacuum chamber at room temperature. A subsequent experiment done with the magnet at 14 Tesla and properly shimmed produced a C60 spectrum showing ∼350,000 resolving power at m/z ∼720. Increased magnetic field strength improves many FTMS performance parameters simultaneously, particularly mass resolving power and accuracy. PMID:17931882

  16. Suspended trapping gas chromatography I fourier transform mass spectrometry for analysis of complex organic mixtures. (United States)

    Hogan, J D; Laude, D A


    The superior sensitivity , dynamic range, and mass measurement accuracy of suspended trapping pulse sequences for gas chromatography combined with Fourier transform mass spectrometry (GC/FTMS) separations of complex organic mixtures is demonstrated. By combining intense ionization conditions with a suspended trapping event prior to detection the working range of the trapped ion cell is increased by 10(3) . Improved detection limits are shown for the GC/FTMS separation of a peppermint oil, with the suspended trapping total ion chromatogram yielding 28 peaks, compared with 15 with a conventional trapping pulse sequence. A fivefold to fifteenfold improvement in signal-to-noise for suspended trapping measurements is also demonstrated with comparison spectra from separations of an unleaded gasoline sample. Suspended trapping spectra show little mass discrimination when an external ion reservoir is used, and chromatographic peak heights differ from conventional spectra by less than 30% if the initial ion population is within the space charge limit of the cell. Finally, average wide band mass measurement errors for components differing in concentration by several orders of magnitude are improved by a factor of 6 to 20 with suspended trapping compared with conventional trapping . For example, average errors of 8.7 ppm are obtained for a suspended trapping GC/FTMS separation of peppermint oil from a single calibration table in which the analysis is perfonned in the absence of calibrant.

  17. Identification of four Sedum plant medicines by Fourier transform infrared spectra

    Directory of Open Access Journals (Sweden)

    Ran Xu


    Full Text Available Background: Sedum sarmentosum bunge (SSB., S. lineare Thunb. (SLT, S. erythrostictum migo. (SEM, and S. aizoon L. (SAL were four widely used Chinese traditional drugs or ethnic drugs, which were easy to be confused with each other. Objective: This study aimed at developing a rapid and accurate method to identify the four Sedum plant medicines with very similar appearances and close relationships. Materials and Methods: The herbal medicines employed here were SSB, SLT, SEM, and SAL collected in different places and seasons. Through comparing the infrared (IR spectra of their 70% ethanol extracts, the results showed that the IR spectra of the four plant medicines possessed not only some common characteristics but also certain notable distinctions, such as shapes, numbers, positions, intensity, and ratios of the absorbing peaks. Results: By Fourier transform infrared (FT-IR spectroscopy, the four medicines could be effectively differed, their habitats could be judged preliminarily, and the genetic relationships of the original plants of the four medicines could also be estimated to some extent. Conclusion: The application of FT-IR spectroscopy in crude medicine authentication and quality evaluation deserved to be further emphasized.

  18. Discrimination of organic coffee via Fourier transform infrared-photoacoustic spectroscopy. (United States)

    Gordillo-Delgado, Fernando; Marín, Ernesto; Cortés-Hernández, Diego Mauricio; Mejía-Morales, Claudia; García-Salcedo, Angela Janet


    Procedures for the evaluation of the origin and quality of ground and roasted coffee are constantly needed for the associated industry due to complexity of the related market. Conventional Fourier transform infrared (FTIR) spectroscopy can be used for detecting changes in functional groups of compounds, such as coffee. However, dispersion, reflection and non-homogeneity of the sample matrix can cause problems resulting in low spectral quality. On the other hand, sample preparation frequently takes place in a destructive way. To overcome these difficulties, in this work a photoacoustic cell has been adapted as a detector in a FTIR spectrophotometer to perform a study of roasted and ground coffee from three varieties of Coffea arabica grown by organic and conventional methods. Comparison between spectra of coffee recorded by FTIR-photoacoustic spectrometry (PAS) and by FTIR spectrophotometry showed a better resolution of the former method, which, aided by principal components analysis, allowed the identification of some absorption bands that allow the discrimination between organic and conventional coffee. The results obtained provide information about the spectral behavior of coffee powder which can be useful for establishing discrimination criteria. It has been demonstrated that FTIR-PAS can be a useful experimental tool for the characterization of coffee. Copyright © 2012 Society of Chemical Industry.

  19. High-resolution subtyping of Staphylococcus aureus strains by means of Fourier-transform infrared spectroscopy. (United States)

    Johler, Sophia; Stephan, Roger; Althaus, Denise; Ehling-Schulz, Monika; Grunert, Tom


    Staphylococcus aureus causes a variety of serious illnesses in humans and animals. Subtyping of S. aureus isolates plays a crucial role in epidemiological investigations. Metabolic fingerprinting by Fourier-transform infrared (FTIR) spectroscopy is commonly used to identify microbes at species as well as subspecies level. In this study, we aimed to assess the suitability of FTIR spectroscopy as a tool for S. aureus subtyping. To this end, we compared the subtyping performance of FTIR spectroscopy to other subtyping methods such as pulsed field gel electrophoresis (PFGE) and spa typing in a blinded experimental setup and investigated the ability of FTIR spectroscopy for identifying S. aureus clonal complexes (CC). A total of 70 S. aureus strains from human, animal, and food sources were selected, for which clonal complexes and a unique virulence and resistance gene pattern had been determined by DNA microarray analysis. FTIR spectral analysis resulted in high discriminatory power similar as obtained by spa typing and PFGE. High directional concordance was found between FTIR spectroscopy based subtypes and capsular polysaccharide expression detected by FTIR spectroscopy and the cap specific locus, reflecting strain specific expression of capsular polysaccharides and/or other surface glycopolymers, such as wall teichoic acid, peptidoglycane, and lipoteichoic acid. Supervised chemometrics showed only limited possibilities for differentiation of S. aureus CC by FTIR spectroscopy with the exception of CC45 and CC705. In conclusion, FTIR spectroscopy represents a valuable tool for S. aureus subtyping, which complements current molecular and proteomic strain typing.

  20. A static Fourier transform spectrometer for atmospheric sounding: concept and experimental implementation. (United States)

    Lacan, Antoine; Bréon, François-Marie; Rosak, Alain; Brachet, Frank; Roucayrol, Lionel; Etcheto, Pierre; Casteras, Christophe; Salaün, Yves


    Spaceborne remote sensing can be used to retrieve the atmospheric composition and complement the surface or airborne measurement networks. In recent years, a lot of attention has been placed on the monitoring of carbon dioxide for an estimate of surface fluxes from the observed spatial and temporal gradients of its concentration. Although other techniques may be used to estimate atmospheric CO(2) concentration, the most promising for the near future is the absorption spectroscopy, focusing on the CO(2) absorption lines at 1.6 and/or 2.0 microns. For this objective, the French space agency (CNES) has developed a new spectrometer concept that is sufficiently compact to be placed onboard a microsatellite platform. The principle is that of a Fourier Transform Spectrometer (FTS), although the classical moving mirror is replaced by two sets of mirrors organized in steps. The interferogram is then imaged on a CCD matrix. The concept allows a very high resolving power, although limited to narrow spectral bands, which is well suited for the observation of a few CO(2) absorption lines. The laboratory model shows that a resolving power of about 65000 is achieved with a signal to noise on the spectra around 300. A modulating plate on the light path allows an easy of the path difference. Although this component adds some complexity to the instrument, it greatly improves the information content of the measurements.

  1. Fourier-transform far-infrared spectroscopic ellipsometry for standoff material identification

    Energy Technology Data Exchange (ETDEWEB)

    Ortolani, Michele, E-mail: michele.ortolani@ifn.cnr.i [Consiglio Nazionale delle Ricerche, Istituto di Fotonica e Nanotecnologie, Via Cineto Romano 42, I-00156 Rome (Italy); Schade, Ulrich [Helmholtz Zentrum Berlin fuer Materialen und Energie, Albert-Einstein-Strasse 15, D-12489 Berlin (Germany)


    The ellipsometry is an efficient method to determine the optical properties of matter. It has been largely employed with grating spectrometers in the visible, UV and near-infrared ranges for the characterization of thin films, surfaces and interfaces. In the mid- and far-infrared, where most substance-specific absorption lines are present, spectroscopic ellipsometry with Fourier-transform spectrometers is still not extended as a routine method. In particular, the lack of powerful sources in the far-infrared/terahertz range has prevented standoff application of this method. We will show that it is possible to measure the complex dielectric constant of a solid in the far-infrared and terahertz range by a reflection experiment with polarized light and ellipsometric analysis with a suitable calibration procedure. Extraction of terahertz synchrotron radiation from storage rings provides a suitable source for research-grade experiments. The optical constants determined by ellipsometry compare well with those obtained by Kramers-Kronig procedures, a method which, however, requires broader frequency range and absolute reflectance standard. We will present the case of remote spectroscopic identification of explosive materials, which is relevant for forthcoming security applications.

  2. Thermal stability of high concentration lysozyme across varying pH: A Fourier Transform Infrared study

    Directory of Open Access Journals (Sweden)

    Sathyadevi Venkataramani


    Full Text Available Aim: The current work is aimed at understanding the effect of pH on the thermal stability of hen egg white lysozyme (HEWL at high concentration (200 mg/mL. Materials and Methods: Fourier Transform Infrared (FTIR Spectroscopy with modified hardware and software to overcome some of the traditional challenges like water subtraction, sample evaporation, proper purging etc., are used in this study. Results: HEWL was subjected to thermal stress at pH 3.0-7.0 between 25°C and 95°C and monitored by FTIR spectroscopy. Calculated T m values showed that the enzyme exhibited maximum thermal stability at pH 5.0. Second derivative plots constructed in the amide I region suggested that at pH 5.0 the enzyme possessed higher amount of α-helix and lower amount of aggregates, when compared to other pHs. Conclusions: Considering the fact that HEWL has attractive applications in various industries and being processed under different experimental conditions including high temperatures, our work is able to reveal the reason behind the pH dependent thermal stability of HEWL at high concentration, when subjected to heat denaturation. In future, studies should aim at using various excipients that may help to increase the stability and activity of the enzyme at this high concentration.

  3. Fourier Transform Ion Cyclotron Resonance Mass Spectrometry at the Cyclotron Frequency (United States)

    Nagornov, Konstantin O.; Kozhinov, Anton N.; Tsybin, Yury O.


    The phenomenon of ion cyclotron resonance allows for determining mass-to-charge ratio, m/z, of an ensemble of ions by means of measurements of their cyclotron frequency, ω c . In Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), the ω c quantity is usually unavailable for direct measurements: the resonant state is located close to the reduced cyclotron frequency (ω+), whereas the ω c and the corresponding m/z values may be calculated via theoretical derivation from an experimental estimate of the ω+ quantity. Here, we describe an experimental observation of a new resonant state, which is located close to the ω c frequency and is established because of azimuthally-dependent trapping electric fields of the recently developed ICR cells with narrow aperture detection electrodes. We show that in mass spectra, peaks close to ω+ frequencies can be reduced to negligible levels relative to peaks close to ω c frequencies. Due to reduced errors with which the ω c quantity is obtained, the new resonance provides a means of cyclotron frequency measurements with precision greater than that achieved when ω+ frequency peaks are employed. The described phenomenon may be considered for a development into an FT-ICR MS technology with increased mass accuracy for applications in basic research, life, and environmental sciences.

  4. Identification of Plant-Pathogenic Fungi Using Fourier Transform Infrared Spectroscopy Combined with Chemometric Analyses

    Institute of Scientific and Technical Information of China (English)

    CHAI A-li; WANG Yi-kai; ZHU Fa-di; SHI Yan-xia; XIE Xue-wen; LI Bao-ju


    Identification of plant-pathogenic fungi is time-consuming due to cultivation and microscopic exami-nation and can be influenced by the interpretation of the micro-morphological characters observed.The present investigation aimed to create a simple but sophisticated method for the identification of plant-pathogenic fungi by Fourier transform infrared (FTIR)spectroscopy.In this study,FTIR-attenuated total reflectance (ATR) spectroscopy was used in combination with chemometric analysis for identification of important pathogenic fun-gi of horticultural plants.Mixtures of mycelia and spores from 27 fungal strains belonging to nine different families were collected from liquid PD or solid PDA media cultures and subj ected to FTIR-ATR spectroscopy measurements.The FTIR-ATR spectra ranging from 4 000 to 400 cm-1 were obtained.To classify the FTIR-ATR spectra,cluster analysis was compared with canonical vitiate analysis (CVA)in the spectral regions of 3 050~2 800 and 1 800~900 cm-1 .Results showed that the identification accuracies achieved 97.53% and 9 9.1 8% for the cluster analysis and CVA analysis,respectively,demonstrating the high potential of this tech-nique for fungal strain identification.

  5. Fourier-transform infrared spectroscopy for rapid screening and live-cell monitoring: application to nanotoxicology

    Energy Technology Data Exchange (ETDEWEB)

    Sundaram, S. K.; Sacksteder, Colette A.; Weber, T. J.; Riley, Brian J.; Addleman, Raymond S.; Harrer, Bruce J.; Peterman, John W.


    A significant challenge to realize the full potential of nanotechnology for therapeutic and diagnostic applications is to understand and evaluate how live-cells interact with an external stimulus, e.g., a nanosized particle (NSP), and the toxicity and broad risk associated with these stimuli. NSPs are increasingly used in medicine with largely undetermined hazards in complex cell dynamics and environments. It is difficult to capture the complexity and dynamics of these interactions by following an omics-based approach exclusively, which are expensive and time-consuming. Additionally, this approach needs destructive sampling methods. Live-cell attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectrometry is well suited to provide noninvasive approach to provide rapid screening of cellular responses to potentially toxic NSPs or any stimuli. Herein we review the technical basis of the approach, the instrument configuration and interface with the biological media, and various effects that impact the data, data analysis, and toxicity. Our preliminary results on live-cell monitoring show promise for rapid screening the NSPs.

  6. Fourier Transform Microwave Spectroscopic Studies of Dimethyl Ether and Ethylene Flames (United States)

    Obenchain, Daniel A.; Wullenkord, Julia; Kohse-Höinghaus, Katharina; Grabow, Jens-Uwe; Hansen, Nils


    Microwave spectroscopy has been a proven technique for the detection of short-lived molecules produced from a variety of molecular sources. With the goal of observing more reactive intermediates produced in combustion reactions, the products of a home-built flat flame burner were measured on a coaxially oriented beam resonator arrangement (COBRA) Fourier transform microwave spectrometer. The products are coupled into a molecular beam using a fast-mixing nozzle styled after the work of Gutowsky and co-workers. Probing the flame at various positions, the relative abundance of products can be observed as a function of flame depth. One dimensional intensity profiles are available for formaldehyde, ketene, acetaldehyde, and dimethyl ether, where either a dimethyl ether fuel or an ethylene fuel was burned in the presence of oxygen. The current arrangement allows only for stable species produced in the flame to be observed in the molecular beam. This combination of species source and detection shows promise for future work in observing new, short-lived, combustion intermediates. J.-U. Grabow, W. Stahl, H. Dreizler, Rev. Sci. Instrum. 67, 4072, 1996 T. Emilsson, T. D. Klots, R. S. Ruoff, H.S. Gutowsky, J. Chem. Phys. 93, 6971, 1990

  7. Analysis of Index Gases of Coal Spontaneous Combustion Using Fourier Transform Infrared Spectrometer

    Directory of Open Access Journals (Sweden)

    Xiaojun Tang


    Full Text Available Analysis of the index gases of coal for the prevention of spontaneous combustion is of great importance for the enhancement of coal mine safety. In this work, Fourier Transform Infrared Spectrometer (FTIRS is presented to be used to analyze the index gases of coal in real time to monitor spontaneous combustion conditions. Both the instrument parameters and the analysis method are introduced at first by combining characteristics of the absorption spectra of the target analyte with the analysis requirements. Next, more than ten sets of the gas mixture containing ten components (CH4, C2H6, C3H8, iso-C4H10, n-C4H10, C2H4, C3H6, C2H2, CO, and CO2 are included and analyzed with a Spectrum Two FTIRS made by Perkin Elmer. The testing results show that the detection limit of most analytes is less than 2×10-6. All the detection limits meet the monitoring requirements of coal spontaneous combustion in China, which means that FTIRS may be an ideal instrument and the analysis method used in this paper is sufficient for spontaneous combustion gas monitoring on-line and even in situ, since FTIRS has many advantages such as fast analysis, being maintenance-free, and good safety.

  8. Fourier-transform infrared anisotropy in cross and parallel sections of tendon and articular cartilage

    Directory of Open Access Journals (Sweden)

    Bidthanapally Aruna


    Full Text Available Abstract Background Fourier Transform Infrared Imaging (FTIRI is used to investigate the amide anisotropies at different surfaces of a three-dimensional cartilage or tendon block. With the change in the polarization state of the incident infrared light, the resulting anisotropic behavior of the tissue structure is described here. Methods Thin sections (6 μm thick were obtained from three different surfaces of the canine tissue blocks and imaged at 6.25 μm pixel resolution. For each section, infrared imaging experiments were repeated thirteen times with the identical parameters except a 15° increment of the analyzer's angle in the 0° – 180° angular space. The anisotropies of amide I and amide II components were studied in order to probe the orientation of the collagen fibrils at different tissue surfaces. Results For tendon, the anisotropy of amide I and amide II components in parallel sections is comparable to that of regular sections; and tendon's cross sections show distinct, but weak anisotropic behavior for both the amide components. For articular cartilage, parallel sections in the superficial zone have the expected infrared anisotropy that is consistent with that of regular sections. The parallel sections in the radial zone, however, have a nearly isotropic amide II absorption and a distinct amide I anisotropy. Conclusion From the inconsistency in amide anisotropy between superficial to radial zone in parallel section results, a schematic model is used to explain the origins of these amide anisotropies in cartilage and tendon.

  9. Rotor-System Log-Decrement Identification Using Short-Time Fourier-Transform Filter

    Directory of Open Access Journals (Sweden)

    Qihang Li


    Full Text Available With the increase of the centrifugal compressor capability, such as large scale LNG and CO2 reinjection, the stability margin evaluation is crucial to assure the compressor work in the designed operating conditions in field. Improving the precision of parameter identification of stability is essential and necessary as well. Based on the time-varying characteristics of response vibration during the sine-swept process, a short-time Fourier transform (STFT filter was introduced to increase the signal-noise ratio and improve the accuracy of the estimated stability parameters. A finite element model was established to simulate the sine-swept process, and the simulated vibration signals were used to study the filtering effect and demonstrate the feasibility to identify the stability parameters by using Multiple-Input and Multiple-Output system identification method that combines the prediction error method and instrumental variable method. Simulation results show that the identification method with STFT filter improves the estimated accuracy much well and makes the curves of frequency response function clearer. Experiment was carried out on a test rig as well, which indicates the identification method is feasible in stability identification, and the results of experiment indicate that STFT filter works very well.

  10. Characterization of Rainwater Dissolved Organic Matter by Ultrahigh Resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (United States)

    Mead, R. N.; Podgorski, D. C.; Mullaugh, K. M.; Avery, B.; Kieber, R. J.; Willey, J. D.; Cooper, W. T.


    Rainwater is a complex, heterogeneous mixture of dissolved organic matter (DOM) that remains largely uncharacterized at the molecular level. Rainwater with dissolved organic carbon values ranging from 3 to 450 μM was collected during 40 separate rain events from 2007-2011 that included coastal and terrestrial storms based upon 36 hour back trajectories. Individual rain samples were lypholized and solvent added in preparation for analysis by negative electrospray ionization and atmospheric pressure photoionization Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). This data set is unique in that each rain event was analyzed individually and not combined allowing for unprecedented insight into rainwater DOM at the molecular level on an episodic basis. Unique elemental compositions were assigned for compounds belonging to CHO, CHOS and CHON classes. Data visualization by van Krevelen diagrams showed clear differences in coastal and terrestrial storm events with a majority of coastal storms having high H/C (1.5-2.0) relative to terrestrial storms. Further inspection of the data revealed that rainwater has relatively high O/C (1.4) and low H/C (<0.5) which suggests rainwater DOM is compositionally different than fog water, water soluble organic carbon isolated from aerosols and surface waters.

  11. Fourier transform infrared spectroscopic imaging and multivariate regression for prediction of proteoglycan content of articular cartilage.

    Directory of Open Access Journals (Sweden)

    Lassi Rieppo

    Full Text Available Fourier Transform Infrared (FT-IR spectroscopic imaging has been earlier applied for the spatial estimation of the collagen and the proteoglycan (PG contents of articular cartilage (AC. However, earlier studies have been limited to the use of univariate analysis techniques. Current analysis methods lack the needed specificity for collagen and PGs. The aim of the present study was to evaluate the suitability of partial least squares regression (PLSR and principal component regression (PCR methods for the analysis of the PG content of AC. Multivariate regression models were compared with earlier used univariate methods and tested with a sample material consisting of healthy and enzymatically degraded steer AC. Chondroitinase ABC enzyme was used to increase the variation in PG content levels as compared to intact AC. Digital densitometric measurements of Safranin O-stained sections provided the reference for PG content. The results showed that multivariate regression models predict PG content of AC significantly better than earlier used absorbance spectrum (i.e. the area of carbohydrate region with or without amide I normalization or second derivative spectrum univariate parameters. Increased molecular specificity favours the use of multivariate regression models, but they require more knowledge of chemometric analysis and extended laboratory resources for gathering reference data for establishing the models. When true molecular specificity is required, the multivariate models should be used.

  12. Probing superstructure of chicken corneal stroma by Fourier transform second harmonic generation microscopy (United States)

    Lee, Sheng-Lin; Chen, Yang-Fang; Dong, Chen-Yuan


    The unique organization of the corneal stromal collagen is responsible for mechanical strength and optical clarity of the eye. However, factors and reasons on formation of the corneal stroma is still not fully understood. Second-harmonic generation (SHG) is a nonlinear second order optical process occurring in noncentrosymmetric systems with a large hyperpolarizability. Through the combination of the second harmonic generation (SHG) microcopy and optimized Fourier-transform analysis, mature chicken corneas are investigated to probe the depth-dependent collagen organization of the corneal stroma. Our results show that the anterior stroma behaves like a fan-like distribution of successively and counterclockwisely rotated fibrous lamellae for paired corneas from the same chicken. However, the posterior stroma maintains a non-rotating pattern while increasing in depth. Surprisingly, the thickness of the anterior stroma remains almost constant throughout the temporal-nasal direction, but the posterior stroma does not behave the same. Through quantitative analysis, the natural transition of the anterior and posterior stroma is also determined. These findings enhance our understanding of the collagen-rich tissue in the chicken cornea model. Moreover, the Fourier-transformbased modality, in combination with SHG microscopy, serves as a promising tool to determine collagen alignment in embryonic development, tissue engineering and corneal diseases.

  13. Automotive FMCW Radar-enhanced Range Estimation via a Local Resampling Fourier Transform

    Directory of Open Access Journals (Sweden)

    Cailing Wang


    Full Text Available In complex traffic scenarios, more accurate measurement and discrimination for an automotive frequency-modulated continuous-wave (FMCW radar is required for intelligent robots, driverless cars and driver-assistant systems. A more accurate range estimation method based on a local resampling Fourier transform (LRFT for a FMCW radar is developed in this paper. Radar signal correlation in the phase space sees a higher signal-noise-ratio (SNR to achieve more accurate ranging, and the LRFT - which acts on a local neighbour as a refinement step - can achieve a more accurate target range. The rough range is estimated through conditional pulse compression (PC and then, around the initial rough estimation, a refined estimation through the LRFT in the local region achieves greater precision. Furthermore, the LRFT algorithm is tested in numerous simulations and physical system experiments, which show that the LRFT algorithm achieves a more precise range estimation than traditional FFT-based algorithms, especially for lower bandwidth signals.

  14. Approaches towards Implementation of Multi-bit Digital Receiver using Fast Fourier Transform

    Directory of Open Access Journals (Sweden)

    Abhijit S. Kulkarni


    Full Text Available This paper compares different digital receiver signal processing schemes as applied to current ESM/RWR systems. The schemes include fast fourier transform (FFT-based, FIR filter-based and mixed architectures. Use of polyphase FFT and IIR filters is also discussed. The specifications and signal processing requirements of a modern digital electronic warfare (EW receiver are discussed. The design procedures and architectures for all the schemes are brought out. The tradeoffs involved in selection of different parameters for these schemes are also discussed. The digital receiver schemes are modeled and analyzed for different metrics such as, Parameter measurement accuracies, Pulse handling capability, Frequency separation capability, Number of multipliers required for implementation etc. The analysis is done for a 500 MHz BW digital receiver and assumes 8 bit ADC in the front end. The results obtained for the comparison are discussed in the paper. Limited simulations show that overlapped FFT scheme is a better approach for digital receiver processing.Defence Science Journal, 2013, 63(2, pp.198-203, DOI:

  15. Influence of external voltage on the reprotonated polyaniline films by Fourier Transform Infrared spectroscopy. (United States)

    Zhou, Tieli; Xing, Shuangxi; Zhang, Chuanzhou; Wu, Yan; Zhao, Chun


    In this paper, we reported the electrical fourier transform infrared (FT-IR) spectra measurements on the reprotonated polyaniline (PANI) thin films. Application of external voltage reduced the intensity in FT-IR spectra and resulted in the shift of band situation. The FT-IR spectra as a function of temperature were also conducted in order to investigate the effect of Joule heating. We found that the influence of CC of phenyl units and the CC of quinoid were quite different as a function of external voltage and temperature. The current-voltage (I-V) curves of the PANI film measured in the range of 0-175 V showed that the resistance kept constant at 0-75 V while it increased from 75 to 175 V. The I-V curves confirmed the presence of Joule heating effect during 75-175 V. According to the experiment results, we concluded that external voltage could produce large average hopping energy, which allowed the charge transfer by hopping between the conducting domains during 0-75 V. The deprotonation of PANI was caused by Joule heating effect, resulting in the decreasing conductivity from 75 to 175 V.

  16. Fourier transform infrared spectroscopy and theoretical study of dimethylamine dimer in the gas phase. (United States)

    Du, Lin; Kjaergaard, Henrik G


    Dimethylamine (DMA) has been studied by gas-phase Fourier transform infrared (FTIR) spectroscopy. We have identified a spectral transition that is assigned to the DMA dimer. The IR spectra of the dimer in the gas phase are obtained by spectral subtraction of spectra recorded at different pressures. The enthalpy of hydrogen bond formation was obtained for the DMA dimer by temperature-dependence measurements. We complement the experimental results with ab initio and anharmonic local mode model calculations of monomer and dimer. Compared to the monomer, our calculations show that in the dimer the N-H bond is elongated, and the NH-stretching fundamental shifts to a lower wavenumber. More importantly, the weak NH-stretching fundamental transition has a pronounced intensity increase upon complexation. However, the first NH-stretching overtone transition is not favored by the same intensity enhancement, and we do not observe the first NH-stretching overtone of the dimer. On the basis of the measured and calculated intensity of the NH-stretching transition of the dimer, the equilibrium constant for dimerization at room temperature was determined.

  17. Fourier transform based dynamic error modeling method for ultra-precision machine tool (United States)

    Chen, Guoda; Liang, Yingchun; Ehmann, Kornel F.; Sun, Yazhou; Bai, Qingshun


    In some industrial fields, the workpiece surface need to meet not only the demand of surface roughness, but the strict requirement of multi-scale frequency domain errors. Ultra-precision machine tool is the most important carrier for the ultra-precision machining of the parts, whose errors is the key factor to influence the multi-scale frequency domain errors of the machined surface. The volumetric error modeling is the important bridge to link the relationship between the machine error and machined surface error. However, the available error modeling method from the previous research is hard to use to analyze the relationship between the dynamic errors of the machine motion components and multi-scale frequency domain errors of the machined surface, which plays the important reference role in the design and accuracy improvement of the ultra-precision machine tool. In this paper, a fourier transform based dynamic error modeling method is presented, which is also on the theoretical basis of rigid body kinematics and homogeneous transformation matrix. A case study is carried out, which shows the proposed method can successfully realize the identical and regular numerical description of the machine dynamic errors and the volumetric errors. The proposed method has strong potential for the prediction of the frequency domain errors on the machined surface, extracting of the information of multi-scale frequency domain errors, and analysis of the relationship between the machine motion components and frequency domain errors of the machined surface.

  18. Fourier transform infrared spectroscopy and Raman spectroscopy as tools for identification of steryl ferulates. (United States)

    Mandak, Eszter; Zhu, Dan; Godany, Tamas A; Nyström, Laura


    Steryl ferulates are a mixture of minor bioactive compounds, possessing well-established health benefits. However, individual steryl ferulate species show structural differences, which seem to substantially influence their health-promoting potential. In this study, we tested Fourier transform infrared (FTIR) spectroscopy and Raman spectroscopy, as potential tools in the identification of steryl ferulates. On the basis of our spectral data obtained from various individual steryl ferulates and steryl ferulate mixtures extracted from rice (γ-oryzanol), corn bran, and wheat bran, we provide comprehensive peak assignment tables for both FTIR and Raman. With the help of FTIR spectroscopy, structural differences between individual steryl ferulates were possible to identify, such as the presence of the cyclopropane ring and additional differences in the side chain of the sterane skeleton. Data obtained with Raman spectroscopy provided us with a control for FTIR peak assignment and also with some additional information on the samples. However, detecting structural differences between steryl ferulates was not possible with this method. We consider that FTIR spectroscopy alone or combined with Raman provides detailed data on the structures of steryl ferulates. Moreover, thorough peak assignment tables presented in this study could prove to be helpful tools when identifying steryl ferulates, especially as a group, in future studies.


    Directory of Open Access Journals (Sweden)

    Ary Setyawan


    Full Text Available Dammar Asphalt (Daspal is expected to be used as a bio-asphalt renewable binder for road construction. It is made with a modification of the "Jabung", which is the dammar gum based material mixed with grounded red brick debris and low quality cooking oil at a certain ratio. Dammar gum is obtained from the Dipterocarpaceae family of trees in India and East Asia, most are produced by tapping trees. The gum varies in color from clear to pale yellow. Dammar gum is a triterpenoid resin, containing a large number of triterpenes and their oxidation products. Many of them are low molecular weight compounds. The objective of this research is to analyze the chemical properties of Daspal uses a Resonance Fourier Transform Infrared Spectroscopy (FTIR method to compare with conventional asphalt. The investigation using spectral data showed that all types of Daspal have similar functional groups of Saturate, Aromatic, Resins, and Asphalten as the 60/70 penetration conventional bitumen, so that based on its chemical properties Daspal can be considered as bioaspal.

  20. [Study on transmission efficiency of interference system in spatially modulated Fourier transform spectrometer]. (United States)

    Lü, Jin-Guang; Liang, Jing-Qiu; Liang, Zhong-Zhu; Qin, Yu-Xin; Tian, Chao


    The reflection of the optic system surface and the absorption of the infrared material could reduce the transmission of the incident light in spatially modulated Fourier transform infrared spectrometer. Through the calculation of the transmission function of the interference system and the simulation of the interferogram image and recovered spectrum affected by transmission function, it was indicated that the contrast of the interferogram image declined and the spectral line intensity weakened. The theoretical analysis shows that the contrast of the interferogram image was related to the intensity reflectance of the anti-reflection film, and the attenuation of the spectrum was determined by transmission efficiency concerned with intensity reflectance R1 of the anti-reflection film, intensity reflectance R2 of the beam splitter film, and the absorption coefficient. By means of the analysis and argumentation, the absorption of the material could be ignored in our investigative wave band. So the transmission efficiency was determined only by R1 and R2. Then taking the transmission efficiency as the design target, according to the transmission required by system, the tolerance of the R1 and R2 could be gained.

  1. Detecting change in biological rhythms: a multivariate permutation test approach to Fourier-transformed data. (United States)

    Blackford, Jennifer Urbano; Salomon, Ronald M; Waller, Niels G


    Treatment-related changes in neurobiological rhythms are of increasing interest to psychologists, psychiatrists, and biological rhythms researchers. New methods for analyzing change in rhythms are needed, as most common methods disregard the rich complexity of biological processes. Large time series data sets reflect the intricacies of underlying neurobiological processes, but can be difficult to analyze. We propose the use of Fourier methods with multivariate permutation test (MPT) methods for analyzing change in rhythms from time series data. To validate the use of MPT for Fourier-transformed data, we performed Monte Carlo simulations and compared statistical power and family-wise error for MPT to Bonferroni-corrected and uncorrected methods. Results show that MPT provides greater statistical power than Bonferroni-corrected tests, while appropriately controlling family-wise error. We applied this method to human, pre- and post-treatment, serially-sampled neurotransmitter data to confirm the utility of this method using real data. Together, Fourier with MPT methods provides a statistically powerful approach for detecting change in biological rhythms from time series data.

  2. A Novel Short-Time Fourier Transform-Based Fall Detection Algorithm Using 3-Axis Accelerations

    Directory of Open Access Journals (Sweden)

    Isu Shin


    Full Text Available The short-time Fourier transform- (STFT- based algorithm was suggested to distinguish falls from various activities of daily living (ADLs. Forty male subjects volunteered in the experiments including three types of falls and four types of ADLs. An inertia sensor unit attached to the middle of two anterior superior iliac spines was used to measure the 3-axis accelerations at 100 Hz. The measured accelerations were transformed to signal vector magnitude values to be analyzed using STFT. The powers of low frequency components were extracted, and the fall detection was defined as whether the normalized power was less than the threshold (50% of the normal power. Most power was observed at the frequency band lower than 5 Hz in all activities, but the dramatic changes in the power were found only in falls. The specificity of 1–3 Hz frequency components was the best (100%, but the sensitivity was much smaller compared with 4 Hz component. The 4 Hz component showed the best fall detection with 96.9% sensitivity and 97.1% specificity. We believe that the suggested algorithm based on STFT would be useful in the fall detection and the classification from ADLs as well.

  3. In-situ Investigation of BBr_3/benzene Solution by Fourier Transformation Infrared Spectroscopy

    Institute of Scientific and Technical Information of China (English)

    YU Li-li; GAI Li-gang; CUI De-Hang; WANG Qi-long


    By means of the in-situ Fourier transformation infrared spectroscopy(FTIR), the properties of BBr_3/ benzene solution, which is usually used as the reactant and solution to synthesize BN by benzene-thermal method, have been investigated. The results show that there are some side reactions between BBr_3 and benzene: (1) BBr_3 as an electron-deficient molecule reacts with benzene at room temperature; (2) below 100℃, substitution of Br atom for H atom of benzene(ring-H) dominates in BBr_3/benzene solution; (3) cracking of benzene ring occurs at a temperature above 100℃; (4) decomposition of benzene molecules and formation of long-chain aliphatic compounds feature the spectra of BBr_3/benzene solution collected at above 160℃. They are unfavor for BN to form when BBr_3 is excessive in the synthesis of BN by benzene-thermal route. On the basis of the experimental results, a coordination reaction mechanism via a η~2-C_6H_6 binding mode in BBr_3/benzene solution is suggested.

  4. Artifacts Induced by Selective Blanking of Time-Domain Data in Fourier Transform Mass Spectrometry (United States)

    Xian, Feng; Valeja, Santosh G.; Beu, Steve C.; Hendrickson, Christopher L.; Marshall, Alan G.


    Fourier transform mass spectrometry (FTMS) of the isolated isotopic distribution for a highly charged biomolecule produces time-domain signal containing large amplitude signal "beats" separated by extended periods of much lower signal magnitude. Signal-to-noise ratio for data sampled between beats is low because of destructive interference of the signals induced by members of the isotopic distribution. Selective blanking of the data between beats has been used to increase spectral signal-to-noise ratio. However, blanking also eliminates signal components and, thus, can potentially distort the resulting FT spectrum. Here, we simulate the time-domain signal from a truncated isotopic distribution for a single charge state of an antibody. Comparison of the FT spectra produced with or without blanking and with or without added noise clearly show that blanking does not improve mass accuracy and introduces spurious peaks at both ends of the isotopic distribution (thereby making it more difficult to identify posttranslational modifications and/or adducts). Although the artifacts are reduced by use of multiple Gaussian (rather than square wave) windowing, blanking appears to offer no advantages for identifying true peaks or for mass measurement.

  5. Reference Beam Pattern Design for Frequency Invariant Beamforming Based on Fast Fourier Transform. (United States)

    Zhang, Wang; Su, Tao


    In the field of fast Fourier transform (FFT)-based frequency invariant beamforming (FIB), there is still an unsolved problem. That is the selection of the reference beam to make the designed wideband pattern frequency invariant (FI) over a given frequency range. This problem is studied in this paper. The research shows that for a given array, the selection of the reference beam pattern is determined by the number of sensors and the ratio of the highest frequency to the lowest frequency of the signal (RHL). The length of the weight vector corresponding to a given reference beam pattern depends on the reference frequency. In addition, the upper bound of the weight length to ensure the FI property over the whole frequency band of interest is also given. When the constraints are added to the reference beam, it does not affect the FI property of the designed wideband beam as long as the symmetry of the reference beam is ensured. Based on this conclusion, a scheme for reference beam design is proposed.

  6. Metabolomic Prediction of Pregnancy Viability in Superovulated Cattle Embryos and Recipients with Fourier Transform Infrared Spectroscopy

    Directory of Open Access Journals (Sweden)

    Marta Muñoz


    Full Text Available We analyzed embryo culture medium (CM and recipient blood plasma using Fourier transform infrared spectroscopy (FTIR metabolomics to identify spectral models predictive of pregnancy outcome. Embryos collected on Day 6 from superovulated cows in 2 countries were individually cultured in synthetic oviduct fluid medium with BSA for 24 h before embryo transfer. Spent CM, blank controls, and plasma samples (Day 0 and Day 7 were evaluated using FTIR. The spectra obtained were analyzed. The discrimination capability of the classifiers was assessed for accuracy, sensitivity (pregnancy, specificity (nonpregnancy, and area under the ROC curve (AUC. Endpoints considered were Day 60 pregnancy and birth. High AUC was obtained for Day 60 pregnancy in CM within individual laboratories (France AUC=0.751±0.039, Spain AUC=0.718±0.024, while cumulative data decreased the AUC (AUC=0.604 ± 0.029. Predictions for CM at birth were lower than Day 60 pregnancy. Predictions with plasma at birth improved cumulative over individual results (Day 0: France AUC=0.690±0.044; Spain AUC<0.55; cumulative AUC=0.747±0.032. Plasma generally predicted pregnancy and birth better than CM. These first results show that FTIR metabolomics could allow the identification of embryos and recipients with improved pregnancy viability, which may contribute to increasing the efficiency of selection schemes based on ET.

  7. Quantitative analysis of biological tissues using Fourier transform-second-harmonic generation imaging (United States)

    Ambekar Ramachandra Rao, Raghu; Mehta, Monal R.; Toussaint, Kimani C., Jr.


    We demonstrate the use of Fourier transform-second-harmonic generation (FT-SHG) imaging of collagen fibers as a means of performing quantitative analysis of obtained images of selected spatial regions in porcine trachea, ear, and cornea. Two quantitative markers, preferred orientation and maximum spatial frequency are proposed for differentiating structural information between various spatial regions of interest in the specimens. The ear shows consistent maximum spatial frequency and orientation as also observed in its real-space image. However, there are observable changes in the orientation and minimum feature size of fibers in the trachea indicating a more random organization. Finally, the analysis is applied to a 3D image stack of the cornea. It is shown that the standard deviation of the orientation is sensitive to the randomness in fiber orientation. Regions with variations in the maximum spatial frequency, but with relatively constant orientation, suggest that maximum spatial frequency is useful as an independent quantitative marker. We emphasize that FT-SHG is a simple, yet powerful, tool for extracting information from images that is not obvious in real space. This technique can be used as a quantitative biomarker to assess the structure of collagen fibers that may change due to damage from disease or physical injury.

  8. Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics. (United States)

    Greene, Samuel M; Batista, Victor S


    We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S1/S2 interconversion dynamics of pyrazine after UV photoexcitation to the S2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

  9. Quantization-Based Digital Audio Watermarking in Discrete Fourier Transform Domain

    Directory of Open Access Journals (Sweden)

    Senbin Yang


    Full Text Available To explore the principle and performances of Quantization Index Modulation (QIM watermarking algorithm, the realization schemes of this algorithm in Discrete Fourier Transform (DFT domain are classified into three types according to the differences of quantizer parameters, and then the illustrative diagrams of these schemes are given, so the properties of transparency, robustness and capacity of each scheme are concluded. The scheme with best distortion-robustness trade-off is found on that basis. The more efficient embedding and extracting formulas of this scheme are given, and the performances are researched by theoretical analysis rather than computer simulation. The conclusions show that the transparency is in proportion to the square of quantization step and small DFT coefficient leads to poor transparency. The robustness to Additive White Gaussian Noise (AWGN only relates to the quantization step and the algorithm is susceptible to amplitude scale and resampling attacks. The possible capacity is Fo/2 bits per second, which can satisfy various watermarking applications. To improve the robustness, an adaptive quantization algorithm based on masking properties of the Human Auditory System (HAS is proposed at the end of this paper, and the algorithm is evaluated in the analog channel environment and its robustness is proved by the results.

  10. Radiometric Short-Term Fourier Transform analysis of photonic Doppler velocimetry recordings and detectivity limit (United States)

    Prudhomme, G.; Berthe, L.; Bénier, J.; Bozier, O.; Mercier, P.


    Photonic Doppler Velocimetry is a plug-and-play and versatile diagnostic used in dynamic physic experiments to measure velocities. When signals are analyzed using a Short-Time Fourier Transform, multiple velocities can be distinguished: for example, the velocities of moving particle-cloud appear on spectrograms. In order to estimate the back-scattering fluxes of target, we propose an original approach "PDV Radiometric analysis" resulting in an expression of time-velocity spectrograms coded in power units. Experiments involving micron-sized particles raise the issue of detection limit; particle-size limit is very difficult to evaluate. From the quantification of noise sources, we derive an estimation of the spectrogram noise leading to a detectivity limit, which may be compared to the fraction of the incoming power which has been back-scattered by the particle and then collected by the probe. This fraction increases with their size. At last, some results from laser-shock accelerated particles using two different PDV systems are compared: it shows the improvement of detectivity with respect to the Effective Number of Bits (ENOB) of the digitizer.

  11. Fourier Transform Ion Cyclotron Resonance Mass Spectrometry at the Cyclotron Frequency. (United States)

    Nagornov, Konstantin O; Kozhinov, Anton N; Tsybin, Yury O


    The phenomenon of ion cyclotron resonance allows for determining mass-to-charge ratio, m/z, of an ensemble of ions by means of measurements of their cyclotron frequency, ω c . In Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), the ω c quantity is usually unavailable for direct measurements: the resonant state is located close to the reduced cyclotron frequency (ω+), whereas the ω c and the corresponding m/z values may be calculated via theoretical derivation from an experimental estimate of the ω+ quantity. Here, we describe an experimental observation of a new resonant state, which is located close to the ω c frequency and is established because of azimuthally-dependent trapping electric fields of the recently developed ICR cells with narrow aperture detection electrodes. We show that in mass spectra, peaks close to ω+ frequencies can be reduced to negligible levels relative to peaks close to ω c frequencies. Due to reduced errors with which the ω c quantity is obtained, the new resonance provides a means of cyclotron frequency measurements with precision greater than that achieved when ω+ frequency peaks are employed. The described phenomenon may be considered for a development into an FT-ICR MS technology with increased mass accuracy for applications in basic research, life, and environmental sciences. Graphical Abstract ᅟ.

  12. Fourier-transform infrared spectroscopy (FTIR) analysis of triclinic and hexagonal birnessites

    Energy Technology Data Exchange (ETDEWEB)

    Ling, Florence T.; Post, Jeffrey E.; Heaney, Peter J.; Kubicki, James D.; Santelli, Cara M.


    The characterization of birnessite structures is particularly challenging for poorly crystalline materials of biogenic origin, and a determination of the relative concentrations of triclinic and hexagonal birnessite in a mixed assemblage has typically required synchrotron-based spectroscopy and diffraction approaches. In this study, Fourier-transform infrared spectroscopy (FTIR) is demonstrated to be capable of differentiating synthetic triclinic Na-birnessite and synthetic hexagonal H-birnessite. Furthermore, IR spectral deconvolution of peaks resulting from Mnsingle bondO lattice vibrations between 400 and 750 cm- 1 yield results comparable to those obtained by linear combination fitting of synchrotron X-ray absorption fine structure (EXAFS) data when applied to known mixtures of triclinic and hexagonal birnessites. Density functional theory (DFT) calculations suggest that an infrared absorbance peak at ~ 1628 cm- 1 may be related to OH vibrations near vacancy sites. The integrated intensity of this peak may show sensitivity to vacancy concentrations in the Mn octahedral sheet for different birnessites.

  13. Monitoring light-induced structural changes of Channelrhodopsin-2 by UV-visible and Fourier transform infrared spectroscopy. (United States)

    Ritter, Eglof; Stehfest, Katja; Berndt, Andre; Hegemann, Peter; Bartl, Franz J


    Channelrhodopsin-2 (ChR2) is a microbial type rhodopsin and a light-gated cation channel that controls phototaxis in Chlamydomonas. We expressed ChR2 in COS-cells, purified it, and subsequently investigated this unusual photoreceptor by flash photolysis and UV-visible and Fourier transform infrared difference spectroscopy. Several transient photoproducts of the wild type ChR2 were identified, and their kinetics and molecular properties were compared with those of the ChR2 mutant E90Q. Based on the spectroscopic data we developed a model of the photocycle comprising six distinguishable intermediates. This photocycle shows similarities to the photocycle of the ChR2-related Channelrhodopsin of Volvox but also displays significant differences. We show that molecular changes include retinal isomerization, changes in hydrogen bonding of carboxylic acids, and large alterations of the protein backbone structure. These alterations are stronger than those observed in the photocycle of other microbial rhodopsins like bacteriorhodopsin and are related to those occurring in animal rhodopsins. UV-visible and Fourier transform infrared difference spectroscopy revealed two late intermediates with different time constants of tau = 6 and 40 s that exist during the recovery of the dark state. The carboxylic side chain of Glu(90) is involved in the slow transition. The molecular changes during the ChR2 photocycle are discussed with respect to other members of the rhodopsin family.

  14. ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation

    Directory of Open Access Journals (Sweden)

    Sarunya Kanjanawattana


    Full Text Available Image classification plays a vital role in many areas of study, such as data mining and image processing; however, serious problems collectively referred to as the course of dimensionality have been encountered in previous studies as factors that reduce system performance. Furthermore, we also confront the problem of different graph characteristics even if graphs belong to same types. In this study, we propose a novel method of graph-type classification. Using our approach, we open up a new solution of high-dimensional images and address problems of different characteristics by converting graph images to one dimension with a discrete Fourier transformation and creating numeric datasets using wavelet and Hough transformations. Moreover, we introduce a new classifier, which is a combination between artificial neuron networks (ANNs and support vector machines (SVMs, which we call ANNSVM, to enhance accuracy. The objectives of our study are to propose an effective graph-type classification method that includes finding a new data representative used for classification instead of two-dimensional images and to investigate what features make our data separable. To evaluate the method of our study, we conducted five experiments with different methods and datasets. The input dataset we focused on was a numeric dataset containing wavelet coefficients and outputs of a Hough transformation. From our experimental results, we observed that the highest accuracy was provided using our method with Coiflet 1, which achieved a 0.91 accuracy.

  15. Application of Local Fourier Transform to Mathematical Simulation of Synchronous Machines with Valve Excitation Systems

    Directory of Open Access Journals (Sweden)

    Fedotov A.


    Full Text Available The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.

  16. Application of Local Fourier Transform to Mathematical Simulation of Synchronous Machines with Valve Excitation Systems (United States)

    Fedotov, A.; Fedotov, E.; Bahteev, K.


    The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.

  17. Digital watermarking for still image based on discrete fractional fourier transform

    Institute of Scientific and Technical Information of China (English)


    Presents a digital watermarking technique based on discrete fractional Fourier transform(DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed tech nique is robust to lossy compression attack.

  18. Cryogenic magnetic bearing scanning mechanism design for the SPICA/SAFARI Fourier Transform Spectrometer

    NARCIS (Netherlands)

    Dool, T.C. van den; Hamelinck, R.F.M.M.; Kruizinga, B.; Gielesen, W.L.M.; Braam, B.C.; Nijenhuis, J.R.; Loix, N.; Luyckx, S.; Loon, D. van; Kooijman, P.P.; Swinyard, B.M.


    TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted

  19. Digital image pattern recognition system using normalized Fourier transform and normalized analytical Fourier-Mellin transform (United States)

    Vélez-Rábago, Rodrigo; Solorza-Calderón, Selene; Jordan-Aramburo, Adina


    This work presents an image pattern recognition system invariant to translation, scale and rotation. The system uses the Fourier transform to achieve the invariance to translation and the analytical Forier-Mellin transform for the invariance to scale and rotation. According with the statistical theory of box-plots, the pattern recognition system has a confidence level at least of 95.4%.

  20. Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images

    NARCIS (Netherlands)

    Yamahata, C.; Sarajlic, Edin; Stranczl, M.; Krijnen, Gijsbertus J.M.; Gijs, M.A.M.


    We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope

  1. Specification of the Fast Fourier Transform algorithm as a term rewriting system

    NARCIS (Netherlands)

    Rodenburg, P.H.; Hoekzema, D.J.


    We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of sem

  2. Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images

    NARCIS (Netherlands)

    Yamahata, C.; Sarajlic, E.; Stranczl, M.; Krijnen, G.J.M.; Gijs, M.A.M.


    We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope

  3. Postdispersion system for astronomical observations with Fourier transform spectrometers in the thermal infrared (United States)

    Wiedermann, Guenter; Jennings, D. E.; Hanel, R. H.; Kunde, V. G.; Moseley, S. H.


    A postdispersion system for astronomical observations with Fourier transform spectrometers in the thermal infrared has been developed which improves the sensitivity of radiation noise limited observations by reducing the spectral range incident on the detector. Special attention is given to the first-generation blocked impurity band detector. Planetary, solar, and stellar observations are reported.

  4. Measurement of surface temperature and emissivity by a multitemperature method for Fourier-transform infrared spectrometers

    DEFF Research Database (Denmark)

    Clausen, Sønnik; Morgenstjerne, Axel; Rathmann, Ole


    Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single...

  5. Fourier Transform Ion Cyclotron Resonance Mass Spectrometry. Development of instrumentation, data aquisition software and processing methods

    NARCIS (Netherlands)

    Barbu, I.M.


    This thesis describes, the use of a Fourier Transform Ion Cyclotron (FTICR) mass spectrometer in the study of biological samples with, imaging mass spectrometry (MS). To achieve this goal experiments were performed on an in-house modified FTICR-MS instrument (for which special acquisition software w

  6. VUV Fourier-transform absorption study of the Lyman and Werner bands in D-2

    NARCIS (Netherlands)

    Lange, de A.; Dickenson, G.D.; Salumbides, E.J.; Ubachs, W.M.G.; Oliveira, de N.; Joyeux, D.; Nahon, L.


    An extensive survey of the D-2 absorption spectrum has been performed with the high-resolution VUV Fourier-transform spectrometer employing synchrotron radiation. The frequency range of 90 000-119 000 cm (1) covers the full depth of the potential wells of the B (1)Sigma(+)(u), B' 1 Sigma(+)(u), and

  7. Cryogenic magnetic bearing scanning mechanism design for the SPICA/SAFARI Fourier Transform Spectrometer

    NARCIS (Netherlands)

    Dool, T.C. van den; Hamelinck, R.F.M.M.; Kruizinga, B.; Gielesen, W.L.M.; Braam, B.C.; Nijenhuis, J.R.; Loix, N.; Luyckx, S.; Loon, D. van; Kooijman, P.P.; Swinyard, B.M.


    TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted o

  8. Fourier transform spectroscopy around 3 microns with a broad difference frequency comb

    CERN Document Server

    Meek, Samuel A; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie


    We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.

  9. 16 channel WDM regeneration in a single phase-sensitive amplifier through optical Fourier transformation

    DEFF Research Database (Denmark)

    Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads


    We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...

  10. The Fourier transform solution for the Green's function of monoenergetic neutron transport theory


    Ganapol, Barry D.


    Nearly 45 years ago, Ken Case published his seminal paper on the singular eigenfunction solution for the Green's function of the monoenergetic neutron transport equation with isotropic scattering. Previously, the solution had been obtained by Fourier transform. While it is apparent the two had to be equivalent, a convincing equivalence proof for general anisotropic scattering remained a challenge until now.

  11. The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry. (United States)

    Suslick, Kenneth S.; And Others


    Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)

  12. An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions. (United States)

    Eastman, M. P.; And Others


    Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

  13. Measurement of Microscopic Deformations Using Double-Exposure Holographic Interferometry and the Fourier Transform Method

    Directory of Open Access Journals (Sweden)

    Percival Almoro


    Full Text Available Microscopic deformations on the surface of a circular diaphragm were measured using double exposure holographic interferometry and Fourier transform method (FTM. The three-dimensional surface deformations were successfully visualized by applying FTM to holographic interferogram analysis. The minimum surface displacement measured was 0.317 µm. This was calibrated via the Michelson interferometry technique.

  14. Development of secondary cell wall in cotton fibers as examined with Fourier transform-infrared spectroscopy (United States)

    Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...

  15. Limitations and potential of spectral subtractions in fourier-transform infrared (FTIR) spectroscopy of soil samples (United States)

    Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...

  16. Study of cancer cell lines with Fourier transform infrared (FTIR)/vibrational absorption (VA) spectroscopy

    DEFF Research Database (Denmark)

    Uceda Otero, E. P.; Eliel, G. S. N.; Fonseca, E. J. S.


    In this work we have used Fourier transform infrared (FTIR) / vibrational absorption (VA) spectroscopy to study two cancer cell lines: the Henrietta Lacks (HeLa) human cervix carcinoma and 5637 human bladder carcinoma cell lines. Our goal is to experimentally investigate biochemical changes and d...

  17. Two-dimensional capillary origami

    Energy Technology Data Exchange (ETDEWEB)

    Brubaker, N.D., E-mail:; Lega, J., E-mail:


    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

  18. A new Fourier transform based CBIR scheme for mammographic mass classification: a preliminary invariance assessment (United States)

    Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin


    The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.

  19. Fourier transforms of spherical distributions on compact symmetric spaces


    Olafsson, Gestur; Schlichtkrull, Henrik


    In our previous articles "A local Paley-Wiener theorem for compact symmetric spaces", Adv. Math. 218 (2008), 202--215, and "Fourier series on compact symmetric spaces" (submitted) we studied Fourier series on a compact symmetric space M=U/K. In particular, we proved a Paley-Wiener type theorem for the smooth functions on M, which have sufficiently small support and are K-invariant, respectively K-finite. In this article we extend those results to K-invariant distributions on M. We show that t...

  20. Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms

    Directory of Open Access Journals (Sweden)

    Kokilashvili V


    Full Text Available As is well known, invariant operators with a shift can be bounded from into only if . We show that the case might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak type inequalities for the Hilbert transform when . The examples of couple of weights which guarantee the fulfillness of two-weighted strong (weak type inequalities for singular integrals are presented. The method of proof of the main results allows us to generalize the results of this paper to the singular integrals which are defined on homogeneous groups. The Fourier multiplier theorem is also proved.