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Sample records for linear ion-trap fourier-transform

  1. Utility of Higher Harmonics in Electrospray Ionization Fourier Transform Electrostatic Linear Ion Trap Mass Spectrometry.

    Dziekonski, Eric T; Johnson, Joshua T; McLuckey, Scott A

    2017-04-18

    Mass resolution (M/ΔM fwhm) is observed to linearly increase with harmonic order in a Fourier transform electrostatic linear ion trap (ELIT) mass spectrometer. This behavior was predicted by Grosshans and Marshall for frequency-multiple detection in a Fourier transform ion cyclotron resonance mass spectrometer only for situations when the prominent mechanism for signal decay is ion ejection from the trap. As the analyzer pressure in our ELIT chamber is relatively high, such that collisional scattering and collision-induced dissociation are expected to underlie much of the ion loss, we sought to explore the relationship between harmonic order and mass resolution. Mass resolutions of 36 900 (fundamental), 75 850 (2nd harmonic), and 108 200 (3rd harmonic) were obtained for GdO + (avg. m/z 173.919) with a transient length of 300 ms. To demonstrate that the mass resolution was truly increasing with harmonic order, the unresolved isotopes at the fundamental distribution of cytochrome c +8 (m/z ∼ 1549) were nearly baseline, resolved at the third harmonic (mass resolution ≈ 23 000) with a transient length of only 200 ms. This experiment demonstrates that, when the ion density is sufficiently low, ions with frequency differences of less than 4 Hz remain uncoalesced. Higher harmonics can be used to increase the effective mass resolution for a fixed transient length and thereby may enable the resolution of closely spaced masses, determination of a protein ion's charge state, and study of the onset of peak coalescence when the resolution at the fundamental frequency is insufficient.

  2. Electrostatic ion trap and Fourier transform measurements for high-resolution mass spectrometry

    Bhushan, K. G.; Gadkari, S. C.; Yakhmi, J. V.; Sahni, V. C.

    2007-01-01

    We report on the development of an electrostatic ion trap for high-resolution mass spectrometry. The trap works on purely electrostatic fields and hence trapping and storing of ions is not mass restrictive, unlike other techniques based on Penning, Paul, or radio frequency quadrupole ion traps. It allows simultaneous trapping and studying of multiple mass species over a large mass range. Mass spectra were recorded in ''dispersive'' and ''self-bunching'' modes of ions. Storage lifetimes of about 100 ms and mass resolving power of about 20 000 could be achieved from the fifth harmonic Fourier transform spectrum of Xe ions recorded in the self-bunching mode

  3. Microfabricated linear Paul-Straubel ion trap

    Mangan, Michael A [Albuquerque, NM; Blain, Matthew G [Albuquerque, NM; Tigges, Chris P [Albuquerque, NM; Linker, Kevin L [Albuquerque, NM

    2011-04-19

    An array of microfabricated linear Paul-Straubel ion traps can be used for mass spectrometric applications. Each ion trap comprises two parallel inner RF electrodes and two parallel outer DC control electrodes symmetric about a central trap axis and suspended over an opening in a substrate. Neighboring ion traps in the array can share a common outer DC control electrode. The ions confined transversely by an RF quadrupole electric field potential well on the ion trap axis. The array can trap a wide array of ions.

  4. Calibration and fluctuation of the secular frequency peak amplitude versus initial condition distribution of the ion cloud confined into a three-dimensional quadrupole ion trap using a fourier transform operating mode and a steady ion flow injection mode

    Janulyte, A.; Andre, J.; Carette, M.; Mercury, M.; Reynard, C; Zerega, Y.

    2009-01-01

    A specific Fourier transform operating mode is applied to a 3-dimensional quadrupolar ion trap for mass analysis (Fourier Transform Quadrupolar Ion Trap (FTQIT) Operating Mode or Mass Spectrometer). With this operating mode, an image signal, which is representative of the collective motion of simultaneously confined ions, is made up from a set of recorded time-of-flight histograms. In an ion trap, the secular frequency of ion motion depends on m/Z ratio of the ion. By Fourier transformation of the image signal, one observes the frequency peak of each confined ionic species. When only one ionic species is confined, the peak amplitude is proportional to the maximal amplitude of the image signal. The maximal amplitude of the image signal is expressed according to the operating parameters, the initial conditions of the ions and the number of ions. Simulation tools lead to fluctuation calculation of the maximal amplitude of the image signal. Two origins are explored: (1) the fluctuation of the numbers of ions according to the steady ion flow injection mode (SIFIM) used with this operating mode and (2) the distribution fluctuation of the initial positions and velocities. Initial confinement conditions, obtained with SIFIM injection mode, lead to optimal detection with small fluctuations of the peak amplitude for Fourier transform operating mode applied to an ion trap. (authors)

  5. Performance of the linear ion trap Orbitrap mass analyzer for qualitative and quantitative analysis of drugs of abuse and relevant metabolites in sewage water

    Bijlsma, L.; Emke, E.; Hernández, F.; de Voogt, P.

    2013-01-01

    This work illustrates the potential of liquid chromatography coupled to a hybrid linear ion trap Fourier Transform Orbitrap mass spectrometer for the simultaneous identification and quantification of 24 drugs of abuse and relevant metabolites in sewage water. The developed methodology consisted of

  6. A comb-sampling method for enhanced mass analysis in linear electrostatic ion traps

    Greenwood, J. B.; Kelly, O.; Calvert, C. R.; Duffy, M. J.; King, R. B.; Belshaw, L.; Graham, L.; Alexander, J. D.; Williams, I. D. [Centre for Plasma Physics, School of Mathematics and Physics, Queen' s University Belfast, Belfast BT7 1NN (United Kingdom); Bryan, W. A. [Department of Physics, Swansea University, Swansea SA2 8PP (United Kingdom); Turcu, I. C. E.; Cacho, C. M.; Springate, E. [Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot, Oxfordshire OX11 0QX (United Kingdom)

    2011-04-15

    In this paper an algorithm for extracting spectral information from signals containing a series of narrow periodic impulses is presented. Such signals can typically be acquired by pickup detectors from the image-charge of ion bunches oscillating in a linear electrostatic ion trap, where frequency analysis provides a scheme for high-resolution mass spectrometry. To provide an improved technique for such frequency analysis, we introduce the CHIMERA algorithm (Comb-sampling for High-resolution IMpulse-train frequency ExtRAaction). This algorithm utilizes a comb function to generate frequency coefficients, rather than using sinusoids via a Fourier transform, since the comb provides a superior match to the data. This new technique is developed theoretically, applied to synthetic data, and then used to perform high resolution mass spectrometry on real data from an ion trap. If the ions are generated at a localized point in time and space, and the data is simultaneously acquired with multiple pickup rings, the method is shown to be a significant improvement on Fourier analysis. The mass spectra generated typically have an order of magnitude higher resolution compared with that obtained from fundamental Fourier frequencies, and are absent of large contributions from harmonic frequency components.

  7. Linear Vlasov plasma oscillations in the Fourier transformed velocity space

    Sedláček, Zdeněk; Nocera, L.

    2002-01-01

    Roč. 296, - (2002), s. 117-124 ISSN 0375-9601 Institutional research plan: CEZ:AV0Z2043910 Keywords : linear Vlasov plasma Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.483, year: 2002

  8. Study on sampling of continuous linear system based on generalized Fourier transform

    Li, Huiguang

    2003-09-01

    In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

  9. Linear Ion Traps in Space: The Mars Organic Molecule Analyzer (MOMA) Instrument and Beyond

    Arevalo, Ricardo; Brinckerhoff, William; Mahaffy, Paul; van Amerom, Friso; Danell, Ryan; Pinnick, Veronica; Li, Xiang; Hovmand, Lars; Getty, Stephanie; Grubisic, Andrej; Goesmann, Fred; Cottin, Hervé

    2015-11-01

    Historically, quadrupole mass spectrometer (QMS) instruments have been used to explore a wide survey of planetary targets in our solar system, from Venus (Pioneer Venus) to Saturn (Cassini-Huygens). However, linear ion trap (LIT) mass spectrometers have found a niche as smaller, versatile alternatives to traditional quadrupole analyzers.The core astrobiological experiment of ESA’s ExoMars Program is the Mars Organic Molecule Analyzer (MOMA) onboard the ExoMars 2018 rover. The MOMA instrument is centered on a linear (or 2-D) ion trap mass spectrometer. As opposed to 3-D traps, LIT-based instruments accommodate two symmetrical ion injection pathways, enabling two complementary ion sources to be used. In the case of MOMA, these two analytical approaches are laser desorption mass spectrometry (LDMS) at Mars ambient pressures, and traditional gas chromatography mass spectrometry (GCMS). The LIT analyzer employed by MOMA also offers: higher ion capacity compared to a 3-D trap of the same volume; redundant detection subassemblies for extended lifetime; and, a link to heritage QMS designs and assembly logistics. The MOMA engineering test unit (ETU) has demonstrated the detection of organics in the presence of wt.%-levels of perchlorate, effective ion enhancement via stored waveform inverse Fourier transform (SWIFT), and derivation of structural information through tandem mass spectrometry (MS/MS).A more progressive linear ion trap mass spectrometer (LITMS), funded by the NASA ROSES MatISSE Program, is being developed at NASA GSFC and promises to augment the capabilities of the MOMA instrument by way of: an expanded mass range (i.e., 20 - 2000 Da); detection of both positive and negative ions; spatially resolved (<1 mm) characterization of individual rock core layers; and, evolved gas analysis and GCMS with pyrolysis up to 1300° C (enabling breakdown of refractory phases). The Advanced Resolution Organic Molecule Analyzer (AROMA) instrument, being developed through NASA

  10. Fractional finite Fourier transform.

    Khare, Kedar; George, Nicholas

    2004-07-01

    We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

  11. Fourier transform NMR

    Hallenga, K.

    1991-01-01

    This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs

  12. A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range

    Wei Wang

    2016-09-01

    Full Text Available A Fourier transform spectrometer (FTS that incorporates a closed-loop controlled, electrothermally actuated microelectromechanical systems (MEMS micromirror is proposed and experimentally verified. The scan range and the tilting angle of the mirror plate are the two critical parameters for MEMS-based FTS. In this work, the MEMS mirror with a footprint of 4.3 mm × 3.1 mm is based on a modified lateral-shift-free (LSF bimorph actuator design with large piston and reduced tilting. Combined with a position-sensitive device (PSD for tilt angle sensing, the feedback controlled MEMS mirror generates a 430 µm stable linear piston scan with the mirror plate tilting angle less than ±0.002°. The usable piston scan range is increased to 78% of the MEMS mirror’s full scan capability, and a spectral resolution of 0.55 nm at 531.9 nm wavelength, has been achieved. It is a significant improvement compared to the prior work.

  13. The JPL Hg(sup +) Extended Linear Ion Trap Frequency Standard: Status, Stability, and Accuracy Prospects

    Tjoelker, R. L.; Prestage, J. D.; Maleki, L.

    1996-01-01

    Microwave frequency standards based on room temperature (sup 199)Hg(sup +) ions in a Linear Ion Trap (LITS) presently achieve a Signal to Noise and line Q inferred short frequency stability. Long term stability has been measured for averaging intervals up to 5 months with apparent sensitivity to variations in ion number/temperature limiting the flicker floor.

  14. Applicability of hybrid linear ion trap-high resolution mass spectrometry and quadrupole-linear ion trap-mass spectrometry for mycotoxin analysis in baby food.

    Rubert, Josep; James, Kevin J; Mañes, Jordi; Soler, Carla

    2012-02-03

    Recent developments in mass spectrometers have created a paradoxical situation; different mass spectrometers are available, each of them with their specific strengths and drawbacks. Hybrid instruments try to unify several advantages in one instrument. In this study two of wide-used hybrid instruments were compared: hybrid quadrupole-linear ion trap-mass spectrometry (QTRAP®) and the hybrid linear ion trap-high resolution mass spectrometry (LTQ-Orbitrap®). Both instruments were applied to detect the presence of 18 selected mycotoxins in baby food. Analytical parameters were validated according to 2002/657/CE. Limits of quantification (LOQs) obtained by QTRAP® instrument ranged from 0.45 to 45 μg kg⁻¹ while lower limits of quantification (LLOQs) values were obtained by LTQ-Orbitrap®: 7-70 μg kg⁻¹. The correlation coefficients (r) in both cases were upper than 0.989. These values highlighted that both instruments were complementary for the analysis of mycotoxin in baby food; while QTRAP® reached best sensitivity and selectivity, LTQ-Orbitrap® allowed the identification of non-target and unknowns compounds. Copyright © 2011 Elsevier B.V. All rights reserved.

  15. Frequency-scanning MALDI linear ion trap mass spectrometer for large biomolecular ion detection.

    Lu, I-Chung; Lin, Jung Lee; Lai, Szu-Hsueh; Chen, Chung-Hsuan

    2011-11-01

    This study presents the first report on the development of a matrix-assisted laser desorption ionization (MALDI) linear ion trap mass spectrometer for large biomolecular ion detection by frequency scan. We designed, installed, and tested this radio frequency (RF) scan linear ion trap mass spectrometer and its associated electronics to dramatically extend the mass region to be detected. The RF circuit can be adjusted from 300 to 10 kHz with a set of operation amplifiers. To trap the ions produced by MALDI, a high pressure of helium buffer gas was employed to quench extra kinetic energy of the heavy ions produced by MALDI. The successful detection of the singly charged secretory immunoglobulin A ions indicates that the detectable mass-to-charge ratio (m/z) of this system can reach ~385 000 or beyond.

  16. A Linear Ion Trap with an Expanded Inscribed Diameter to Improve Optical Access for Fluorescence Spectroscopy

    Rajagopal, Vaishnavi; Stokes, Chris; Ferzoco, Alessandra

    2018-02-01

    We report a custom-geometry linear ion trap designed for fluorescence spectroscopy of gas-phase ions at ambient to cryogenic temperatures. Laser-induced fluorescence from trapped ions is collected from between the trapping rods, orthogonal to the excitation laser that runs along the axis of the linear ion trap. To increase optical access to the ion cloud, the diameter of the round trapping rods is 80% of the inscribed diameter, rather than the roughly 110% used to approximate purely quadrupolar electric fields. To encompass as much of the ion cloud as possible, the first collection optic has a 25.4 mm diameter and a numerical aperture of 0.6. The choice of geometry and collection optics yields 107 detected photons/s from trapped rhodamine 6G ions. The trap is coupled to a closed-cycle helium refrigerator, which in combination with two 50 Ohm heaters enables temperature control to below 25 K on the rod electrodes. The purpose of the instrument is to broaden the applicability of fluorescence spectroscopy of gas-phase ions to cases where photon emission is a minority relaxation pathway. Such studies are important to understand how the microenvironment of a chromophore influences excited state charge transfer processes.

  17. Application of linear discriminant analysis and Attenuated Total Reflectance Fourier Transform Infrared microspectroscopy for diagnosis of colon cancer.

    Khanmohammadi, Mohammadreza; Bagheri Garmarudi, Amir; Samani, Simin; Ghasemi, Keyvan; Ashuri, Ahmad

    2011-06-01

    Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) microspectroscopy was applied for detection of colon cancer according to the spectral features of colon tissues. Supervised classification models can be trained to identify the tissue type based on the spectroscopic fingerprint. A total of 78 colon tissues were used in spectroscopy studies. Major spectral differences were observed in 1,740-900 cm(-1) spectral region. Several chemometric methods such as analysis of variance (ANOVA), cluster analysis (CA) and linear discriminate analysis (LDA) were applied for classification of IR spectra. Utilizing the chemometric techniques, clear and reproducible differences were observed between the spectra of normal and cancer cases, suggesting that infrared microspectroscopy in conjunction with spectral data processing would be useful for diagnostic classification. Using LDA technique, the spectra were classified into cancer and normal tissue classes with an accuracy of 95.8%. The sensitivity and specificity was 100 and 93.1%, respectively.

  18. Performance of the linear ion trap Orbitrap mass analyzer for qualitative and quantitative analysis of drugs of abuse and relevant metabolites in sewage water.

    Bijlsma, Lubertus; Emke, Erik; Hernández, Félix; de Voogt, Pim

    2013-03-20

    This work illustrates the potential of liquid chromatography coupled to a hybrid linear ion trap Fourier Transform Orbitrap mass spectrometer for the simultaneous identification and quantification of 24 drugs of abuse and relevant metabolites in sewage water. The developed methodology consisted of automatic solid-phase extraction using Oasis HLB cartridges, chromatographic separation of the targeted drugs, full-scan accurate mass data acquisition under positive electrospray ionization mode over an m/z range of 50-600Da at a resolution of 30,000 FWHM and simultaneous MS(n) measurements to obtain information of fragment ions generated in the linear ion trap. Accurate mass of the protonated molecule, together with at least one nominal mass product ion and retention time allowed the confident identification of the compounds detected in these complex matrices. In addition to the highly reliable qualitative analysis, Orbitrap analyzer also proved to have satisfactory potential for quantification at sub-ppb analyte levels, a possibility that has been very little explored in the literature until now. The limits of quantification ranged from 4 to 68ngL(-1) in influent sewage water, and from 2 to 35ngL(-1) in effluent, with the exception of MDA, morphine and THC that presented higher values as a consequence of the high ionization suppression in this type of samples. Satisfactory recoveries (70-120%) and precision (abuse could be identified and quantified, mainly MDMA, benzoylecgonine, codeine, oxazepam and temazepam. Orbitrap also showed potential for retrospective investigation of ketamine metabolites in the samples without the need of additional analysis. Copyright © 2013 Elsevier B.V. All rights reserved.

  19. A linear radiofrequency ion trap for accumulation, bunching, and emittance improvement of radioactive ion beams

    Herfurth, F.; Dilling, J.; Kellerbauer, A.

    2000-05-01

    An ion beam cooler and buncher has been developed for the manipulation of radioactive ion beams. The gas-filled linear radiofrequency ion trap system is installed at the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. Its purpose is to accumulate the 60-keV continuous ISOLDE ion beam with high efficiency and to convert it into low-energy low-emittance ion pulses. The efficiency was found to exceed 10% in agreement with simulations. A more than 10-fold reduction of the ISOLDE beam emittance can be achieved. The system has been used successfully for first on-line experiments. Its principle, setup and performance will be discussed. (orig.)

  20. Design and Application of a High-Temperature Linear Ion Trap Reactor

    Jiang, Li-Xue; Liu, Qing-Yu; Li, Xiao-Na; He, Sheng-Gui

    2018-01-01

    A high-temperature linear ion trap reactor with hexapole design was homemade to study ion-molecule reactions at variable temperatures. The highest temperature for the trapped ions is up to 773 K, which is much higher than those in available reports. The reaction between V2O6 - cluster anions and CO at different temperatures was investigated to evaluate the performance of this reactor. The apparent activation energy was determined to be 0.10 ± 0.02 eV, which is consistent with the barrier of 0.12 eV calculated by density functional theory. This indicates that the current experimental apparatus is prospective to study ion-molecule reactions at variable temperatures, and more kinetic details can be obtained to have a better understanding of chemical reactions that have overall barriers. [Figure not available: see fulltext.

  1. Simulating the performance of a distance-3 surface code in a linear ion trap

    Trout, Colin J.; Li, Muyuan; Gutiérrez, Mauricio; Wu, Yukai; Wang, Sheng-Tao; Duan, Luming; Brown, Kenneth R.

    2018-04-01

    We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface code to the linear chain of ions. We develop a physically motivated Pauli error model that allows for fast simulation and captures the key sources of noise in an ion trap quantum computer including gate imperfections and ion heating. Our simulations showed a consistent requirement of a two-qubit gate fidelity of ≥99.9% for the logical memory to have a better fidelity than physical two-qubit operations. Finally, we perform an analysis of the error subsets from the importance sampling method used to bound the logical error rates to gain insight into which error sources are particularly detrimental to error correction.

  2. Precursor and Neutral Loss Scans in an RF Scanning Linear Quadrupole Ion Trap

    Snyder, Dalton T.; Szalwinski, Lucas J.; Schrader, Robert L.; Pirro, Valentina; Hilger, Ryan; Cooks, R. Graham

    2018-03-01

    Methodology for performing precursor and neutral loss scans in an RF scanning linear quadrupole ion trap is described and compared to the unconventional ac frequency scan technique. In the RF scanning variant, precursor ions are mass selectively excited by a fixed frequency resonance excitation signal at low Mathieu q while the RF amplitude is ramped linearly to pass ions through the point of excitation such that the excited ion's m/z varies linearly with time. Ironically, a nonlinear ac frequency scan is still required for ejection of the product ions since their frequencies vary nonlinearly with the linearly varying RF amplitude. In the case of the precursor scan, the ejection frequency must be scanned so that it is fixed on a product ion m/z throughout the RF scan, whereas in the neutral loss scan, it must be scanned to maintain a constant mass offset from the excited precursor ions. Both simultaneous and sequential permutation scans are possible; only the former are demonstrated here. The scans described are performed on a variety of samples using different ionization sources: protonated amphetamine ions generated by nanoelectrospray ionization (nESI), explosives ionized by low-temperature plasma (LTP), and chemical warfare agent simulants sampled from a surface and analyzed with swab touch spray (TS). We lastly conclude that the ac frequency scan variant of these MS/MS scans is preferred due to electronic simplicity. In an accompanying manuscript, we thus describe the implementation of orthogonal double resonance precursor and neutral loss scans on the Mini 12 using constant RF voltage. [Figure not available: see fulltext.

  3. Simultaneous and Sequential MS/MS Scan Combinations and Permutations in a Linear Quadrupole Ion Trap.

    Snyder, Dalton T; Szalwinski, Lucas J; Cooks, R Graham

    2017-10-17

    Methods of performing precursor ion scans as well as neutral loss scans in a single linear quadrupole ion trap have recently been described. In this paper we report methodology for performing permutations of MS/MS scan modes, that is, ordered combinations of precursor, product, and neutral loss scans following a single ion injection event. Only particular permutations are allowed; the sequences demonstrated here are (1) multiple precursor ion scans, (2) precursor ion scans followed by a single neutral loss scan, (3) precursor ion scans followed by product ion scans, and (4) segmented neutral loss scans. (5) The common product ion scan can be performed earlier in these sequences, under certain conditions. Simultaneous scans can also be performed. These include multiple precursor ion scans, precursor ion scans with an accompanying neutral loss scan, and multiple neutral loss scans. We argue that the new capability to perform complex simultaneous and sequential MS n operations on single ion populations represents a significant step in increasing the selectivity of mass spectrometry.

  4. MSM, an Efficient Workflow for Metabolite Identification Using Hybrid Linear Ion Trap Orbitrap Mass Spectrometer

    Cho, Robert; Huang, Yingying; Schwartz, Jae C.; Chen, Yan; Carlson, Timothy J.; Ma, Ji

    2012-05-01

    Identification of drug metabolites can often yield important information regarding clearance mechanism, pharmacologic activity, or toxicity for drug candidate molecules. Additionally, the identification of metabolites can provide beneficial structure-activity insight to help guide lead optimization efforts towards molecules with optimal metabolic profiles. There are challenges associated with detecting and identifying metabolites in the presence of complex biological matrices, and new LC-MS technologies have been developed to meet these challenges. In this report, we describe the development of an experimental approach that applies unique features of the hybrid linear ion trap Orbitrap mass spectrometer to streamline in vitro and in vivo metabolite identification experiments. The approach, referred to as MSM, utilizes multiple collision cells, dissociation methods, mass analyzers, and detectors. With multiple scan types and different dissociation modes built into one experimental method, along with flexible post-acquisition analysis options, the MSM workflow offers an attractive option to fast and reliable identification of metabolites in different kinds of in vitro and in vivo samples. The MSM workflow was successfully applied to metabolite identification analysis of verapamil in both in vitro rat hepatocyte incubations and in vivo rat bile samples.

  5. Linear ion-trap mass spectrometric characterization of human pituitary nitrotyrosine-containing proteins

    Zhan, Xianquan; Desiderio, Dominic M.

    2007-01-01

    The nitric oxide-mediated Tyr-nitration of endogenous proteins is associated with several pathological and physiological processes. In order to investigate the presence - and potential roles - of Tyr-nitration in the human pituitary, a large-format two-dimensional gel separation plus a Western blot against a specific anti-3-nitrotyrosine antibody were used to separate and detect nitroproteins from a human pituitary proteome. The nitroproteins were subjected to in-gel trypsin digestion, and high-sensitivity vacuum matrix-assisted laser desorption/ionization (vMALDI) linear ion-trap tandem mass spectrometry was used to analyze the tryptic peptides. Those MS/MS data were used to determine the amino acid sequence and the specific nitration site of each tryptic nitropeptide, and were matched to corresponding proteins with Bioworks TuboSEQUEST software. Compared to our previous study, 16 new nitrotyrosine-immunoreactive positive Western blot spots were found within the area pI 3.0-10 and Mr 10-100 kDa. Four new nitroproteins were discovered: the stanniocalcin 1 precursor--involved in calcium and phosphate metabolism; mitochondrial co-chaperone protein HscB, which might act as a co-chaperone in iron-sulfur cluster assembly in mitochrondria; progestin and adipoQ receptor family member III--a seven-transmembrane receptor; proteasome subunit alpha type 2--involved in an ATP/ubiquitin-dependent non-lysosomal proteolytic pathway. Those data demonstrate that nitric oxide-mediated Tyr-nitration might participate in various biochemical, metabolic, and pathological processes in the human pituitary.

  6. Development of a Linear Ion Trap Mass Spectrometer (LITMS) Investigation for Future Planetary Surface Missions

    Brinckerhoff, W.; Danell, R.; Van Ameron, F.; Pinnick, V.; Li, X.; Arevalo, R.; Glavin, D.; Getty, S.; Mahaffy, P.; Chu, P.; hide

    2014-01-01

    Future surface missions to Mars and other planetary bodies will benefit from continued advances in miniature sensor and sample handling technologies that enable high-performance chemical analyses of natural samples. Fine-scale (approx.1 mm and below) analyses of rock surfaces and interiors, such as exposed on a drill core, will permit (1) the detection of habitability markers including complex organics in association with their original depositional environment, and (2) the characterization of successive layers and gradients that can reveal the time-evolution of those environments. In particular, if broad-based and highly-sensitive mass spectrometry techniques could be brought to such scales, the resulting planetary science capability would be truly powerful. The Linear Ion Trap Mass Spectrometer (LITMS) investigation is designed to conduct fine-scale organic and inorganic analyses of short (approx.5-10 cm) rock cores such as could be acquired by a planetary lander or rover arm-based drill. LITMS combines both pyrolysis/gas chromatograph mass spectrometry (GCMS) of sub-sampled core fines, and laser desorption mass spectrometry (LDMS) of the intact core surface, using a common mass analyzer, enhanced from the design used in the Mars Organic Molecule Analyzer (MOMA) instrument on the 2018 ExoMars rover. LITMS additionally features developments based on the Sample Analysis at Mars (SAM) investigation on MSL and recent NASA-funded prototype efforts in laser mass spectrometry, pyrolysis, and precision subsampling. LITMS brings these combined capabilities to achieve its four measurement objectives: (1) Organics: Broad Survey Detect organic molecules over a wide range of molecular weight, volatility, electronegativity, concentration, and host mineralogy. (2) Organic: Molecular Structure Characterize internal molecular structure to identify individual compounds, and reveal functionalization and processing. (3) Inorganic Host Environment Assess the local chemical

  7. A compensated multi-pole linear ion trap mercury frequency standard for ultra-stable timekeeping.

    Burt, Eric A; Diener, William A; Tjoelker, Robert L

    2008-12-01

    The multi-pole linear ion trap frequency standard (LITS) being developed at the Jet Propulsion Laboratory (JPL) has demonstrated excellent short- and long-term stability. The technology has now demonstrated long-term field operation providing a new capability for timekeeping standards. Recently implemented enhancements have resulted in a record line Q of 5 x 10(12) for a room temperature microwave atomic transition and a short-term fractional frequency stability of 5 x 10(-14)/tau(1/2). A scheme for compensating the second order Doppler shift has led to a reduction of the combined sensitivity to the primary LITS systematic effects below 5 x 10(-17) fractional frequency. Initial comparisons to JPL's cesium fountain clock show a systematic floor of less than 2 x 10(-16). The compensated multi-pole LITS at JPL was operated continuously and unattended for a 9-mo period from October 2006 to July 2007. During that time it was used as the frequency reference for the JPL geodetic receiver known as JPLT, enabling comparisons to any clock used as a reference for an International GNSS Service (IGS) site. Comparisons with the laser-cooled primary frequency standards that reported to the Bureau International des Poids et Mesures (BIPM) over this period show a frequency deviation less than 2.7 x 10(-17)/day. In the capacity of a stand-alone ultra-stable flywheel, such a standard could be invaluable for long-term timekeeping applications in metrology labs while its methodology and robustness make it ideal for space applications as well.

  8. Determination of vanillin, ethyl vanillin, and coumarin in infant formula by liquid chromatography-quadrupole linear ion trap mass spectrometry.

    Shen, Yan; Han, Chao; Liu, Bin; Lin, Zhengfeng; Zhou, Xiujin; Wang, Chengjun; Zhu, Zhenou

    2014-02-01

    A simple, precise, accurate, and validated liquid chromatography-quadrupole linear ion trap mass spectrometry method was developed for the determination of vanillin, ethyl vanillin, and coumarin in infant formula samples. Following ultrasonic extraction with methanol/water (1:1, vol/vol), and clean-up on an HLB solid-phase extraction cartridge (Waters Corp., Milford, MA), samples were separated on a Waters XSelect HSS T3 column (150 × 2.1-mm i.d., 5-μm film thickness; Waters Corp.), with 0.1% formic acid solution-acetonitrile as mobile phase at a flow rate of 0.25 mL/min. Quantification of the target was performed by the internal standard approach, using isotopically labeled compounds for each chemical group, to correct matrix effects. Data acquisition was carried out in multiple reaction monitoring transitions mode, monitoring 2 multiple reaction monitoring transitions to ensure an accurate identification of target compounds in the samples. Additional identification and confirmation of target compounds were performed using the enhanced product ion modus of the linear ion trap. The novel liquid chromatography-quadrupole linear ion trap mass spectrometry platform offers the best sensitivity and specificity for characterization and quantitative determination of vanillin, ethyl vanillin, and coumarin in infant formula and fulfills the quality criteria for routine laboratory application. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

  9. The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

    Franzen, J.

    1994-01-01

    The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd

  10. Fourier Transform Mass Spectrometry

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

    2011-01-01

    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. PMID:21742802

  11. 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

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

    2014-01-01

    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.

  12. IDENTIFICATION OF MICROCYSTIN TOXINS FROM A STRAIN OF MICROCYSTIS AERUGINOSA BY LIQUID CHROMATOGRAPHY INTRODUCTION INTO A HYBRID LINEAR ION TRAP-FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTROMETER

    The cyclic heptapeptide microcystin toxins produced by a strain of Microcystis aeruginosa that has not been investigated previously were separated by liquid chromatography and identified by high-accuracy m/z measurements of their [M + H]+ ions and the fragment i...

  13. The fractional Fourier transform and applications

    Bailey, David H.; Swarztrauber, Paul N.

    1991-01-01

    This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

  14. UV Photodissociation Action Spectroscopy of Haloanilinium Ions in a Linear Quadrupole Ion Trap Mass Spectrometer

    Hansen, Christopher S.; Kirk, Benjamin B.; Blanksby, Stephen J.; O'Hair, Richard. A. J.; Trevitt, Adam J.

    2013-06-01

    UV-vis photodissociation action spectroscopy is becoming increasingly prevalent because of advances in, and commercial availability of, ion trapping technologies and tunable laser sources. This study outlines in detail an instrumental arrangement, combining a commercial ion-trap mass spectrometer and tunable nanosecond pulsed laser source, for performing fully automated photodissociation action spectroscopy on gas-phase ions. The components of the instrumentation are outlined, including the optical and electronic interfacing, in addition to the control software for automating the experiment and performing online analysis of the spectra. To demonstrate the utility of this ensemble, the photodissociation action spectra of 4-chloroanilinium, 4-bromoanilinium, and 4-iodoanilinium cations are presented and discussed. Multiple photoproducts are detected in each case and the photoproduct yields are followed as a function of laser wavelength. It is shown that the wavelength-dependent partitioning of the halide loss, H loss, and NH3 loss channels can be broadly rationalized in terms of the relative carbon-halide bond dissociation energies and processes of energy redistribution. The photodissociation action spectrum of (phenyl)Ag2 + is compared with a literature spectrum as a further benchmark.

  15. Fourier Transform Mass Spectrometry.

    Gross, Michael L.; Rempel, Don L.

    1984-01-01

    Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

  16. Generalized Fourier transforms classes

    Berntsen, Svend; Møller, Steen

    2002-01-01

    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...

  17. Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene.

    Sun, Lulu; Xue, Bing; Huang, Zhengxu; Cheng, Ping; Ma, Li; Ding, Li; Zhou, Zhen

    2018-07-01

    Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. Graphical Abstract ᅟ.

  18. Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene

    Sun, Lulu; Xue, Bing; Huang, Zhengxu; Cheng, Ping; Ma, Li; Ding, Li; Zhou, Zhen

    2018-04-01

    Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. [Figure not available: see fulltext.

  19. Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

    Axelrod, Jeremy

    2015-01-01

    The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

  20. Analysis of Disperse Dyes Using Liquid Chromatography/Linear Ion Trap Mass Spectrometry (LC/LIT-MSn) and Database Construction.

    Kato, Takao; Ikeue, Takahisa; Suzuki, Yasuhiro; Handa, Makoto

    2016-01-01

    Liquid chromatography/linear ion trap mass spectrometry (LC/LIT-MS(n)) was used to construct a database of disperse dyes. Fifty-three standard dyes were subjected to LC/LIT-MS(n) and characterized based on their mass spectra (MS, MS(2), and MS(3)), values of λmax (maximum absorption wavelength in the UV-visible spectrum), and retention times. The results demonstrate that it is possible to reliably identify coexisting dyes that cannot be separated by LC or detected by diode array detection due to their low molecular absorption coefficients. In addition, the by-products included in the standard dyes were found to provide important information for the identification and discrimination of dyestuffs synthesized using different processes. The confirmation of the effectiveness of LC/LIT-MS(n) analysis in detecting small amounts of disperse dyes in this study shows its potential for use in the discrimination of dyed fibers obtained at crime scenes.

  1. Food contaminant analysis at ultra-high mass resolution: application of hybrid linear ion trap - orbitrap mass spectrometry for the determination of the polyether toxins, azaspiracids, in shellfish.

    2010-10-30

    The biotoxins, azaspiracids (AZAs), from marine phytoplankton accumulate in shellfish and affect human health by causing severe gastrointestinal disturbance, diarrhea, nausea and vomiting. Specific and sensitive methods have been developed and validated for the determination of the most commonly occurring azaspiracid analogs. An LTQ Orbitrap mass spectrometer is a hybrid instrument that combines linear ion trap (LIT) mass spectrometry (MS) with high-resolution Fourier transform (FT) MS and this was exploited to perform simultaneous ultra-high-resolution full-scan MS analysis and collision-induced dissociation (CID) tandem mass spectrometry (MS\\/MS). Using the highest mass resolution setting (100,000 FWHM) in full-scan mode, the methodology was validated for the determination of six AZAs in mussel (Mytilus galloprovincialis) tissue extracts. Ultra-high mass resolution, together with a narrow mass tolerance window of ±2 mDa, dramatically improved detection sensitivity. In addition to employing chromatographic resolution to distinguish between the isomeric azaspiracid analogs, AZA1\\/AZA6 and AZA4\\/AZA5, higher energy collisionally induced dissociation (HCD) fragmentation on selected precursor ions were performed in parallel with full-scan FTMS. Using HCD MS\\/MS, most precursor and product ion masses were determined within 1 ppm of the theoretical m\\/z values throughout the mass spectral range and this enhanced the reliability of analyte identity.For the analysis of mussels (M. galloprovincialis), the method limit of quantitation (LOQ) was 0.010 µg\\/g using full-scan FTMS and this was comparable with the LOQ (0.007 µg\\/g) using CID MS\\/MS. The repeatability data were; intra-day RSD% (1.8-4.4%; n = 6) and inter-day RSD% (4.7-8.6%; n = 3). Application of these methods to the analysis of mussels (M. edulis) that were naturally contaminated with azaspiracids, using high-resolution full-scan Orbitrap MS and low-resolution CID MS\\/MS, produced

  2. Generalized Fourier transforms classes

    Berntsen, Svend; Møller, Steen

    2002-01-01

    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 foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....

  3. Ejection of Coulomb Crystals from a Linear Paul Ion Trap for Ion-Molecule Reaction Studies.

    Meyer, K A E; Pollum, L L; Petralia, L S; Tauschinsky, A; Rennick, C J; Softley, T P; Heazlewood, B R

    2015-12-17

    Coulomb crystals are being increasingly employed as a highly localized source of cold ions for the study of ion-molecule chemical reactions. To extend the scope of reactions that can be studied in Coulomb crystals-from simple reactions involving laser-cooled atomic ions, to more complex systems where molecular reactants give rise to multiple product channels-sensitive product detection methodologies are required. The use of a digital ion trap (DIT) and a new damped cosine trap (DCT) are described, which facilitate the ejection of Coulomb-crystallized ions onto an external detector for the recording of time-of-flight (TOF) mass spectra. This enables the examination of reaction dynamics and kinetics between Coulomb-crystallized ions and neutral molecules: ionic products are typically cotrapped, thus ejecting the crystal onto an external detector reveals the masses, identities, and quantities of all ionic species at a selected point in the reaction. Two reaction systems are examined: the reaction of Ca(+) with deuterated isotopologues of water, and the charge exchange between cotrapped Xe(+) with deuterated isotopologues of ammonia. These reactions are examples of two distinct types of experiment, the first involving direct reaction of the laser-cooled ions, and the second involving reaction of sympathetically-cooled heavy ions to form a mixture of light product ions. Extensive simulations are conducted to interpret experimental results and calculate optimal operating parameters, facilitating a comparison between the DIT and DCT approaches. The simulations also demonstrate a correlation between crystal shape and image shape on the detector, suggesting a possible means for determining crystal geometry for nonfluorescing ions.

  4. Ion Trap Quantum Computing

    2011-12-01

    variations of ion traps, including (1) the cylindrically symmetric 3D ring trap; (2) the linear trap with a combination of cavity QED; (#) the symmetric...concepts of quantum information. The major demonstration has been the test of a Bell inequality as demonstrated by Rowe et al. [50] and a decoherence...famous physics experiment [62]. Wolfgang Paul demonstrated a similar apparatus during his Nobel Prize speech [63]. This device is hyperbolic- parabolic

  5. Fourier transforms in spectroscopy

    Kauppinen, Jyrki

    2000-01-01

    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

  6. Fast Fourier transform telescope

    Tegmark, Max; Zaldarriaga, Matias

    2009-01-01

    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 2 N rather than N 2 ) 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.

  7. Fourier Transform Spectrometer System

    Campbell, Joel F. (Inventor)

    2014-01-01

    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.

  8. Rainbow Fourier Transform

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

    2012-01-01

    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).

  9. Screening and identification of steroidal saponins from Anemarrhena asphodeloides employing UPLC tandem triple quadrupole linear ion trap mass spectrometry.

    Xia, Yong-Gang; Guo, Xin-Dong; Liang, Jun; Yang, Bing-You; Kuang, Hai-Xue

    2017-09-01

    This study presents a practical and valid strategy for the screening and structural characterization of Anemarrhena asphodeloides Bge steroidal saponins (SSs) using ultra-high performance liquid chromatography coupled with triple quadrupole linear ion trap mass spectrometry. The whole analytical protocols integrate four-step procedures in the positive mode: (1) rational deduction of mass fragmentation pathways of A. asphodeloides SSs; (2) untargeted screening of potential A. asphodeloides SSs by multiple-ion monitoring-information-dependent-acquiring-enhanced product ion (MIM-IDA-EPI) scan through reverse phase liquid chromatography; (3) comprehensive construction of an ammoniated precursor ion database by combining untargeted MIM-IDA-EPI scans and data literature; and (4) structural interpretation of targeted A. asphodeloides SSs using MIM-IDA-EPI and multiple reaction monitoring (MRM)-IDA-EPI with an energy-resolved technique. The protocols were used to analyze SSs in A. asphodeloides; of the 87 detected SSs that were unambiguously characterized or tentatively identified, 19 compounds were the first to be reported from A. asphodeloides and 13 ones were characterized as potential new compounds. Accuracy of the analytical procedure was demonstrated by structural identification of three SSs by NMR spectroscopy. The proposed schemes hold an excellent promise in the structural prediction and interpretation of complex SSs from plant medicines by mass spectrometry. Copyright © 2017 Elsevier Inc. All rights reserved.

  10. Fourier transforms principles and applications

    Hansen, Eric W

    2014-01-01

    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.

  11. A linear radiofrequency quadrupole ion trap for the cooling and bunching of radioactive ion beams

    Kellerbauer, A G; Dilling, J; Henry, S; Herfurth, F; Kluge, H J; Lamour, E; Moore, R B; Scheidenberger, C; Schwarz, S; Sikler, G; Szerypo, J

    2002-01-01

    A linear radiofrequency quadrupole ion guide and beam buncher has been installed at the ISOLTRAP mass spectrometry experiment at the ISOLDE facility at CERN. The apparatus is being used as a beam cooling, accumulation, and bunching system. It operates with a buffer gas that cools the injected ions and converts the quasicontinuous 60- keV beam from the ISOLDE facility to 2.5-keV beam pulses with improved normalized transverse emittance. Recent measurements suggest a capture efficiency of the ion guide of up to 40% and a cooling and bunching efficiency of at least 12% which is expected to still be increased. The improved ISOLTRAP setup has so far been used very successfully in three on-line experiments. (12 refs).

  12. On fractional Fourier transform moments

    Alieva, T.; Bastiaans, M.J.

    2000-01-01

    Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

  13. Application of High-Performance Liquid Chromatography Coupled with Linear Ion Trap Quadrupole Orbitrap Mass Spectrometry for Qualitative and Quantitative Assessment of Shejin-Liyan Granule Supplements

    Jifeng Gu; Weijun Wu; Mengwei Huang; Fen Long; Xinhua Liu; Yizhun Zhu

    2018-01-01

    A method for high-performance liquid chromatography coupled with linear ion trap quadrupole Orbitrap high-resolution mass spectrometry (HPLC-LTQ-Orbitrap MS) was developed and validated for the qualitative and quantitative assessment of Shejin-liyan Granule. According to the fragmentation mechanism and high-resolution MS data, 54 compounds, including fourteen isoflavones, eleven ligands, eight flavonoids, six physalins, six organic acids, four triterpenoid saponins, two xanthones, two alkaloi...

  14. Screening of Carotenoids in Tomato Fruits by Using Liquid Chromatography with Diode Array-Linear Ion Trap Mass Spectrometry Detection.

    Gentili, Alessandra; Caretti, Fulvia; Ventura, Salvatore; Pérez-Fernández, Virginia; Venditti, Alessandro; Curini, Roberta

    2015-08-26

    This paper presents an analytical strategy for a large-scale screening of carotenoids in tomato fruits by exploiting the potentialities of the triple quadrupole-linear ion trap hybrid mass spectrometer (QqQLIT). The method involves separation on C30 reversed-phase column and identification by means of diode array detection (DAD) and atmospheric pressure chemical ionization-mass spectrometry (APCI-MS). The authentic standards of six model compounds were used to optimize the separative conditions and to predict the chromatographic behavior of untargeted carotenoids. An information dependent acquisition (IDA) was performed with (i) enhanced-mass scan (EMS) as the survey scan, (ii) enhanced-resolution (ER) scan to obtain the exact mass of the precursor ions (16-35 ppm), and (iii) enhanced product ion (EPI) scan as dependent scan to obtain structural information. LC-DAD-multiple reaction monitoring (MRM) chromatograms were also acquired for the identification of targeted carotenoids occurring at low concentrations; for the first time, the relative abundance between the MRM transitions (ion ratio) was used as an extra tool for the MS distinction of structural isomers and the related families of geometrical isomers. The whole analytical strategy was high-throughput, because a great number of experimental data could be acquired with few analytical steps, and cost-effective, because only few standards were used; when applied to characterize some tomato varieties ('Tangerine', 'Pachino', 'Datterino', and 'Camone') and passata of 'San Marzano' tomatoes, our method succeeded in identifying up to 44 carotenoids in the 'Tangerine'" variety.

  15. Quantitation of isobaric phosphatidylcholine species in human plasma using a hybrid quadrupole linear ion-trap mass spectrometer

    Žáček, Petr; Bukowski, M.; Rosenberger, T. A.; Picklo, M.

    2016-01-01

    Roč. 57, č. 12 (2016), s. 2225-2234 ISSN 0022-2275 Institutional support: RVO:61388963 Keywords : shotgun lipidomics * triple quadrupole/ion-trap * human blood plasma * phosphatidylcholines Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 4.810, year: 2016 http://www.jlr.org/content/57/12/2225.full

  16. MRM screening/biomarker discovery with linear ion trap MS: a library of human cancer-specific peptides

    Yang, Xu; Lazar, Iulia M

    2009-01-01

    The discovery of novel protein biomarkers is essential in the clinical setting to enable early disease diagnosis and increase survivability rates. To facilitate differential expression analysis and biomarker discovery, a variety of tandem mass spectrometry (MS/MS)-based protein profiling techniques have been developed. For achieving sensitive detection and accurate quantitation, targeted MS screening approaches, such as multiple reaction monitoring (MRM), have been implemented. MCF-7 breast cancer protein cellular extracts were analyzed by 2D-strong cation exchange (SCX)/reversed phase liquid chromatography (RPLC) separations interfaced to linear ion trap MS detection. MS data were interpreted with the Sequest-based Bioworks software (Thermo Electron). In-house developed Perl-scripts were used to calculate the spectral counts and the representative fragment ions for each peptide. In this work, we report on the generation of a library of 9,677 peptides (p < 0.001), representing ~1,572 proteins from human breast cancer cells, that can be used for MRM/MS-based biomarker screening studies. For each protein, the library provides the number and sequence of detectable peptides, the charge state, the spectral count, the molecular weight, the parameters that characterize the quality of the tandem mass spectrum (p-value, DeltaM, Xcorr, DeltaCn, Sp, no. of matching a, b, y ions in the spectrum), the retention time, and the top 10 most intense product ions that correspond to a given peptide. Only proteins identified by at least two spectral counts are listed. The experimental distribution of protein frequencies, as a function of molecular weight, closely matched the theoretical distribution of proteins in the human proteome, as provided in the SwissProt database. The amino acid sequence coverage of the identified proteins ranged from 0.04% to 98.3%. The highest-abundance proteins in the cellular extract had a molecular weight (MW)<50,000. Preliminary experiments have

  17. Fourier transformation for engineering and natural science

    Klingen, B.

    2001-01-01

    The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

  18. Application of high-performance liquid chromatography-tandem mass spectrometry with a quadrupole/linear ion trap instrument for the analysis of pesticide residues in olive oil.

    Hernando, M D; Ferrer, C; Ulaszewska, M; García-Reyes, J F; Molina-Díaz, A; Fernández-Alba, A R

    2007-11-01

    This article describes the development of an enhanced liquid chromatography-mass spectrometry (LC-MS) method for the analysis of pesticides in olive oil. One hundred pesticides belonging to different classes and that are currently used in agriculture have been included in this method. The LC-MS method was developed using a hybrid quadrupole/linear ion trap (QqQ(LIT)) analyzer. Key features of this technique are the rapid scan acquisition times, high specificity and high sensitivity it enables when the multiple reaction monitoring (MRM) mode or the linear ion-trap operational mode is employed. The application of 5 ms dwell times using a linearly accelerating (LINAC) high-pressure collision cell enabled the analysis of a high number of pesticides, with enough data points acquired for optimal peak definition in MRM operation mode and for satisfactory quantitative determinations to be made. The method quantifies over a linear dynamic range of LOQs (0.03-10 microg kg(-1)) up to 500 microg kg(-1). Matrix effects were evaluated by comparing the slopes of matrix-matched and solvent-based calibration curves. Weak suppression or enhancement of signals was observed (ion (EPI) and MS3 were developed.

  19. General Correlation Theorem for Trinion Fourier Transform

    Bahri, Mawardi

    2017-01-01

    - The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

  20. Rapid Quantification of Four Anthocyanins in Red Grape Wine by Hydrophilic Interaction Liquid Chromatography/Triple Quadrupole Linear Ion Trap Mass Spectrometry.

    Sun, Yongming; Xia, Biqi; Chen, Xiangzhun; Duanmu, Chuansong; Li, Denghao; Han, Chao

    2015-01-01

    The identification and quantification of four anthocyanins (cyanidin-3-O-glucoside, peonidin-3-O-glucoside, delphinidin-3-O-glucoside, and malvidin-3-O-glucoside) in red grape wine were carried out by hydrophilic interaction liquid chromatography/triple quadrupole linear ion trap MS (HILIC/QTrap-MS/MS). Samples were diluted directly and separated on a Merck ZIC HILIC column with 20 mM ammonium acetate solution-acetonitrile mobile phase. Quantitative data acquisition was carried out in the multiple reaction monitoring mode. Additional identification and confirmation of target compounds were performed using the enhanced product ion mode of the linear ion trap. The LOQs were in the range 0.05-1.0 ng/mL. The average recoveries were in the range 94.6 to 104.5%. The HILIC/QTrap-MS/MS platform offers the best sensitivity and specificity for characterization and quantitative determination of the four anthocyanins in red grape wines and fulfills the quality criteria for routine laboratory application.

  1. Fourier transform nuclear magnetic resonance

    Geick, R.

    1981-01-01

    This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)

  2. App. 1. Fourier series and Fourier transform

    Anon.

    1977-01-01

    Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

  3. Asymmetric ion trap

    Barlow, Stephan E.; Alexander, Michael L.; Follansbee, James C.

    1997-01-01

    An ion trap having two end cap electrodes disposed asymmetrically about a center of a ring electrode. The inner surface of the end cap electrodes are conformed to an asymmetric pair of equipotential lines of the harmonic formed by the application of voltages to the electrodes. The asymmetry of the end cap electrodes allows ejection of charged species through the closer of the two electrodes which in turn allows for simultaneously detecting anions and cations expelled from the ion trap through the use of two detectors charged with opposite polarity.

  4. Improved Fourier-transform profilometry

    Mao Xianfu; Chen Wenjing; Su Xianyu

    2007-01-01

    An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object

  5. Fourier-transform optical microsystems

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

    1999-01-01

    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.

  6. Fourier Transform Methods. Chapter 4

    Kaplan, Simon G.; Quijada, Manuel A.

    2015-01-01

    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..

  7. Investigation of glucosinolate profile and qualitative aspects in sprouts and roots of horseradish (Armoracia rusticana) using LC-ESI-hybrid linear ion trap with Fourier transform ion cyclotron resonance mass spectrometry and infrared multiphoton dissociation.

    Agneta, Rosa; Rivelli, Anna Rita; Ventrella, Emanuela; Lelario, Filomena; Sarli, Giulio; Bufo, Sabino Aurelio

    2012-08-01

    Within the family of Brassicaceae, an important source of glucosinolates (GLSs) is represented by horseradish ( Armoracia rusticana P. Gaertner, B. Meyer & Scherbius), cultivated for its roots, which are grated fresh or processed into a sauce and used as a condiment. The characteristic pungent flavor of the root depends on the abundance of the bioactive GLS molecules. In crude plant extracts (sprouts and roots) of an accession of horseradish largely diffused in the Basilicata region (southern Italy), which develops many sprouts and produces white, fiery, and sharp-flavored marketable roots, we characterized the GLS profile by LC-ESI-LTQ-FTICR-MS and IRMPD. In sprouts and roots we identified 16 and 11 GLSs, respectively. We confirmed the presence of sinigrin, 4-hydroxyglucobrassicin, glucobrassicin, gluconasturtin, and 4-methoxyglucobrassicin and identified glucoiberin, gluconapin, glucocochlearin, glucoconringianin, glucosativin, glucoibarin, 5-hydroxyglucobrassicin, glucocapparilinearisin or glucobrassicanapin, glucotropaeolin, and glucoarabishirsutain, not previously characterized in horseradish. Of particular note was the presence of the putative 2-methylsulfonyl-oxo-ethyl-GLS.

  8. [Screening and confirmation of 24 hormones in cosmetics by ultra high performance liquid chromatography-linear ion trap/orbitrap high resolution mass spectrometry].

    Li, Zhaoyong; Wang, Fengmei; Niu, Zengyuan; Luo, Xin; Zhang, Gang; Chen, Junhui

    2014-05-01

    A method of ultra high performance liquid chromatography-linear ion trap/orbitrap high resolution mass spectrometry (UPLC-LTQ/Orbitrap MS) was established to screen and confirm 24 hormones in cosmetics. Various cosmetic samples were extracted with methanol. The extract was loaded onto a Waters ACQUITY UPLC BEH C18 column (50 mm x 2.1 mm, 1.7 microm) using a gradient elution of acetonitrile/water containing 0.1% (v/v) formic acid for the separation. The accurate mass of quasi-molecular ion was acquired by full scanning of electrostatic field orbitrap. The rapid screening was carried out by the accurate mass of quasi-molecular ion. The confirmation analysis for targeted compounds was performed with the retention time and qualitative fragments obtained by data dependent scan mode. Under the optimal conditions, the 24 hormones were routinely detected with mass accuracy error below 3 x 10(-6) (3 ppm), and good linearities were obtained in their respective linear ranges with correlation coefficients higher than 0.99. The LODs (S/N = 3) of the 24 compounds were hormones in 50 cosmetic samples. The results demonstrate that the method is a useful tool for the rapid screening and identification of the hormones in cosmetics.

  9. Application of High-Performance Liquid Chromatography Coupled with Linear Ion Trap Quadrupole Orbitrap Mass Spectrometry for Qualitative and Quantitative Assessment of Shejin-Liyan Granule Supplements.

    Gu, Jifeng; Wu, Weijun; Huang, Mengwei; Long, Fen; Liu, Xinhua; Zhu, Yizhun

    2018-04-11

    A method for high-performance liquid chromatography coupled with linear ion trap quadrupole Orbitrap high-resolution mass spectrometry (HPLC-LTQ-Orbitrap MS) was developed and validated for the qualitative and quantitative assessment of Shejin-liyan Granule. According to the fragmentation mechanism and high-resolution MS data, 54 compounds, including fourteen isoflavones, eleven ligands, eight flavonoids, six physalins, six organic acids, four triterpenoid saponins, two xanthones, two alkaloids, and one licorice coumarin, were identified or tentatively characterized. In addition, ten of the representative compounds (matrine, galuteolin, tectoridin, iridin, arctiin, tectorigenin, glycyrrhizic acid, irigenin, arctigenin, and irisflorentin) were quantified using the validated HPLC-LTQ-Orbitrap MS method. The method validation showed a good linearity with coefficients of determination (r²) above 0.9914 for all analytes. The accuracy of the intra- and inter-day variation of the investigated compounds was 95.0-105.0%, and the precision values were less than 4.89%. The mean recoveries and reproducibilities of each analyte were 95.1-104.8%, with relative standard deviations below 4.91%. The method successfully quantified the ten compounds in Shejin-liyan Granule, and the results show that the method is accurate, sensitive, and reliable.

  10. Application of High-Performance Liquid Chromatography Coupled with Linear Ion Trap Quadrupole Orbitrap Mass Spectrometry for Qualitative and Quantitative Assessment of Shejin-Liyan Granule Supplements

    Jifeng Gu

    2018-04-01

    Full Text Available A method for high-performance liquid chromatography coupled with linear ion trap quadrupole Orbitrap high-resolution mass spectrometry (HPLC-LTQ-Orbitrap MS was developed and validated for the qualitative and quantitative assessment of Shejin-liyan Granule. According to the fragmentation mechanism and high-resolution MS data, 54 compounds, including fourteen isoflavones, eleven ligands, eight flavonoids, six physalins, six organic acids, four triterpenoid saponins, two xanthones, two alkaloids, and one licorice coumarin, were identified or tentatively characterized. In addition, ten of the representative compounds (matrine, galuteolin, tectoridin, iridin, arctiin, tectorigenin, glycyrrhizic acid, irigenin, arctigenin, and irisflorentin were quantified using the validated HPLC-LTQ-Orbitrap MS method. The method validation showed a good linearity with coefficients of determination (r2 above 0.9914 for all analytes. The accuracy of the intra- and inter-day variation of the investigated compounds was 95.0–105.0%, and the precision values were less than 4.89%. The mean recoveries and reproducibilities of each analyte were 95.1–104.8%, with relative standard deviations below 4.91%. The method successfully quantified the ten compounds in Shejin-liyan Granule, and the results show that the method is accurate, sensitive, and reliable.

  11. Tunable fractional-order Fourier transformer

    Malyutin, A A

    2006-01-01

    A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

  12. Practical aspects of trapped ion mass spectrometry, 5 applications of ion trapping devices

    March, Raymond E

    2009-01-01

    Examines ion/neutral and ion/ion reactions, ion spectroscopy, and the structural characterization of proteins and peptides using quadropole ion trap mass spectrometry, Fourier transform - ion cyclotron resonance (FT-ICR) mass spectrometry, and traveling wave ion mobility mass spectrometry.

  13. Performance of the Linear Ion Trap Mass Spectrometer for the Mars Organic Molecule Analyzer (MOMA) Investigation on the 2018 Exomars Rover

    Arevalo, Ricardo, Jr.; Brinckerhoff, William B.; Pinnick, Veronica T.; van Amerom, Friso H. W.; Danell, Ryan M.; Li, Xiang; Getty, Stephanie; Hovmand, Lars; Atanassova, Martina; Mahaffy, Paul R.; hide

    2014-01-01

    The 2018 ExoMars rover mission includes the Mars Organic Molecule Analyzer (MOMA) investigation. MOMA will examine the chemical composition of samples acquired from depths of up to two meters below the martian surface, where organics may be protected from degradation derived from cosmic radiation and/or oxidative chemical reactions. When combined with the complement of instruments in the rover's Pasteur Payload, MOMA has the potential to reveal the presence of a wide range of organics preserved in a variety of mineralogical environments, and to begin to understand the structural character and potential origin of those compounds. The MOMA investigation is led by the Max Planck Institute for Solar System Research (MPS) with the mass spectrometer subsystem provided by NASA GSFC. MOMA's linear ion trap mass spectrometer (ITMS) is designed to analyze molecular composition of: (i) gas evolved from pyrolyzed powder samples and separated in a gas chromatograph; and, (ii) ions directly desorbed from crushed solid samples at Mars ambient pressure, as enabled by a pulsed UV laser system, fast-actuating aperture valve and capillary ion inlet. Breadboard ITMS and associated electronics have been advanced to high end-to-end fidelity in preparation for flight hardware delivery to Germany in 2015.

  14. Trace analysis of pesticides in paddy field water by direct injection using liquid chromatography-quadrupole-linear ion trap-mass spectrometry.

    Pareja, Lucía; Martínez-Bueno, M J; Cesio, Verónica; Heinzen, Horacio; Fernández-Alba, A R

    2011-07-29

    A multiresidue method was developed for the quantification and confirmation of 70 pesticides in paddy field water. After its filtration, water was injected directly in a liquid chromatograph coupled to a hybrid triple quadrupole-linear ion trap-mass spectrometer (QqLIT). The list of target analytes included organophosphates, phenylureas, sulfonylureas, carbamates, conazoles, imidazolinones and others compounds widely used in different countries where rice is cropped. Detection and quantification limits achieved were in the range from 0.4 to 80 ng L(-1) and from 2 to 150 ng L(-1), respectively. Correlation coefficients for the calibration curves in the range 0.1-50 μg L(-1) were higher than 0.99 except for diazinon (0.1-25 μg L(-1)). Only 9 pesticides presented more than 20% of signal suppression/enhancement, no matrix effect was observed in the studied conditions for the rest of the target pesticides. The method developed was used to investigate the occurrence of pesticides in 59 water samples collected in paddy fields located in Spain and Uruguay. The study shows the presence of bensulfuron methyl, tricyclazole, carbendazim, imidacloprid, tebuconazole and quinclorac in a concentration range from 0.08 to 7.20 μg L(-1). Copyright © 2011 Elsevier B.V. All rights reserved.

  15. Metabolism of nitazoxanide in rats, pigs, and chickens: Application of liquid chromatography coupled to hybrid linear ion trap/Orbitrap mass spectrometer.

    Huang, Xianhui; Guo, Chunna; Chen, Zhangliu; Liu, Yahong; He, Limin; Zeng, Zhenling; Yan, Chaoqun; Pan, Guangfang; Li, Shuaipeng

    2015-09-01

    Nitazoxanide (NTZ) is a nitrothiazole benzamide compound with a broad activity spectrum against parasites, Gram-positive and Gram-negative anaerobic bacteria, and viruses. In this study, hybrid linear ion trap/Orbitrap mass spectrometer providing a high mass resolution and accuracy was used to investigate the metabolism of NTZ in rats, pigs, and chickens. The results revealed that acetylation and glucuronidation were the main metabolic pathways in rats and pigs, whereas acetylation and sulfation were the major metabolic pathways in chickens, which indicated interspecies variations in drug metabolism and elimination. With the accurate mass data and the characteristic MS(n) product ions, we identified six metabolites in which tizoxanide and hydroxylated tizoxanide were phase I metabolites and tizoxanide glucuronide, tizoxanide glucose, tizoxanide sulfate and hydroxyl tizoxanide sulfate were phase II metabolites. Hydroxylated tizoxanide and tizoxanide glucose were identified for the first time. All the comprehensive data were provided to make out the metabolism of NTZ in rats, pigs and chickens more clearly. Copyright © 2015 Elsevier B.V. All rights reserved.

  16. Application of ultra-high pressure liquid chromatography linear ion-trap orbitrap to qualitative and quantitative assessment of pesticide residues.

    Farré, M; Picó, Y; Barceló, D

    2014-02-07

    The analysis of pesticides residues using a last generation high resolution and high mass accuracy hybrid linear ion trap-Orbitrap mass spectrometer (LTQ-Orbitrap-MS) was explored. Pesticides were extracted from fruits, fish, bees and sediments by QuEChERS and from water by solid-phase with Oasis HLB cartridges. Ultra-high pressure liquid chromatography (UHPLC)-LTQ-Orbitrap mass spectrometer acquired full scan MS data for quantification, and data dependent (dd) MS(2) and MS(3) product ion spectra for identification and/or confirmation. The regression coefficients (r(2)) for the calibration curves (two order of magnitude up to the lowest calibration level) in the study were ≥0.99. The LODs for 54 validated compounds were ≤2ngmL(-1) (analytical standards). The relative standard deviation (RSD), which was used to estimate precision, was always lower than 22%. The recovery of extraction and matrix effects ranged from 58 to 120% and from -92 to 52%, respectively. Mass accuracy was always ≤4ppm, corresponding to a maximum mass error of 1.6millimass units (mmu). This procedure was then successfully applied to pesticide residues in a set of the above-mentioned food and environmental samples. In addition to target analytes, this method enables the simultaneous detection/identification of non-target pesticides, pharmaceuticals, drugs of abuse, mycotoxins, and their metabolites. Copyright © 2013 Elsevier B.V. All rights reserved.

  17. Determination of eight pesticides of varying polarity in surface waters using solid phase extraction with multiwalled carbon nanotubes and liquid chromatography-linear ion trap mass spectrometry

    Dahane, Soraya; Derdour, Aicha; García, María Dolores Gil; Moreno, Ana Uclés; Galera, María Martínez; Viciana, María del Mar Socías

    2015-01-01

    We describe a MWCNT-based method for the solid-phase extraction of eight pesticides from environmental water samples. The analytes are extracted from 100 mL samples at pH 5.0 (containing 5 mmol L −1 of KCl) by passing the solution through a column filled with 20 mg of multiwalled carbon nanotubes. Following elution, the pesticides were determined by LC and electrospray ionization hybrid quadrupole linear ion trap MS. Two selected reaction monitoring transitions were monitored per compound, the most intense one being used for quantification and the second one for confirmation. In addition, an information-dependent acquisition experiment was performed for unequivocal confirmation of positive findings. Matrix effect was not found in real waters and therefore the quantitation was carried out with calibration graphs built with solvent based standards. Except for cymoxanil, the detection and quantitation limits in surface waters are in the range from 0.3 to 9.5 ng L −1 and 1.6 to 45.2 ng L −1 , respectively. Recoveries from spiked ultrapure water are ∼100 %, except for the most polar pesticides methomyl and cymoxanil. The same behavior is found for real water samples (except for phosalone). The relative standard deviation is <10 % in all cases. (author)

  18. Fourier transform of momentum distribution in vanadium

    Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.

    1985-01-01

    Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)

  19. Ion trap device

    Ibrahim, Yehia M.; Smith, Richard D.

    2016-01-26

    An ion trap device is disclosed. The device includes a series of electrodes that define an ion flow path. A radio frequency (RF) field is applied to the series of electrodes such that each electrode is phase shifted approximately 180 degrees from an adjacent electrode. A DC voltage is superimposed with the RF field to create a DC gradient to drive ions in the direction of the gradient. A second RF field or DC voltage is applied to selectively trap and release the ions from the device. Further, the device may be gridless and utilized at high pressure.

  20. Fluorescence profiles and cooling dynamics of laser-cooled Mg+ ions in a linear rf ion trap

    Zhao Xianzhen; Ryjkov, Vladimir L.; Schuessler, Hans A.

    2006-01-01

    Fluorescence line profiles and their implications on the cooling dynamics of the Mg + ions stored in a linear rf trap are studied. The line profile is dictated by the temperature of the ion cloud at different laser detunings. The upper bound of the lowest temperature was estimated for different values of the rf trapping potential amplitude and the buffer gas pressure. A general trend of this ultimate temperature to increase with the rf trapping voltage and buffer gas pressure is expected, with an abrupt change at some critical value corresponding to the transition to and from a strongly correlated liquid or crystal state. While on the one hand this expectation was confirmed when the buffer gas pressure was varied; on the other hand the influence of the amplitude of the trapping voltage on the ultimate temperature shows an interesting new feature of first dipping down before the sharp increase occurs

  1. Quantum arithmetic with the Quantum Fourier Transform

    Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

    2014-01-01

    The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

  2. Properties of the distributional finite Fourier transform

    Carmichael, Richard D.

    2016-01-01

    The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

  3. On the inverse windowed Fourier transform

    Rebollo Neira, Laura; Fernández Rubio, Juan Antonio

    1999-01-01

    The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed

  4. Wigner distribution and fractional Fourier transform

    Alieva, T.; Bastiaans, M.J.; Boashash, B.

    2003-01-01

    We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

  5. Digital quantum simulation, Schrödinger cat state spectroscopy and setting up a linear ion trap

    Hempel, C.

    2014-01-01

    This PhD thesis reports on two experiments in the field of quantum information processing using trapped calcium ions. In addition, the text covers the setup and characterization of a new linear Paul trap accompanied by a novel implementation of single-ion addressing using an acousto-optic deflector. The first of the two experiments is concerned with the proof-of-principle implementation of digital quantum simulations using up to 6 ions and 100 gate operations. It investigates the scaling behavior of simulations of elementary models of magnetism in terms of the number of involved spins and the complexity of their mutual interactions. The second experiment introduces the application of a Schroedinger cat state in the indirect detection of photon scattering events on a broad electronic transition. The method is shown to have a sensitivity down to the single photon level in a proof-of-principle demonstration using a mixed-isotope crystal of 40Ca+ and 44Ca+. A brief outlook towards future experiments and extensions of the experimental setup concludes the manuscript.(author) [de

  6. Nonlinear Fourier transform for dual-polarization optical communication system

    Gaiarin, Simone

    communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...

  7. Applications of Fourier transforms to generalized functions

    Rahman, M

    2011-01-01

    This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...

  8. Simultaneous identification and quantification of tetrodotoxin in fresh pufferfish and pufferfish-based products using immunoaffinity columns and liquid chromatography/quadrupole-linear ion trap mass spectrometry

    Guo, Mengmeng; Wu, Haiyan; Jiang, Tao; Tan, Zhijun; Zhao, Chunxia; Zheng, Guanchao; Li, Zhaoxin; Zhai, Yuxiu

    2017-07-01

    In this study, we established a comprehensive method for simultaneous identification and quantification of tetrodotoxin (TTX) in fresh pufferfish tissues and pufferfish-based products using liquid chromatography/quadrupole-linear ion trap mass spectrometry (LC-QqLIT-MS). TTX was extracted by 1% acetic acid-methanol, and most of the lipids were then removed by freezing lipid precipitation, followed by purification and concentration using immunoaffinity columns (IACs). Matrix effects were substantially reduced due to the high specificity of the IACs, and thus, background interference was avoided. Quantitation analysis was therefore performed using an external calibration curve with standards prepared in mobile phase. The method was evaluated by fortifying samples at 1, 10, and 100 ng/g, respectively, and the recoveries ranged from 75.8%-107%, with a relative standard deviation of less than 15%. The TTX calibration curves were linear over the range of 1-1 000 μg/L, with a detection limit of 0.3 ng/g and a quantification limit of 1 ng/g. Using this method, samples can be further analyzed using an information-dependent acquisition (IDA) experiment, in the positive mode, from a single liquid chromatography-tandem mass spectrometry injection, which can provide an extra level of confirmation by matching the full product ion spectra acquired for a standard sample with those from an enhanced product ion (EPI) library. The scheduled multiple reaction monitoring method enabled TTX to be screened for, and TTX was positively identified using the IDA and EPI spectra. This method was successfully applied to analyze a total of 206 samples of fresh pufferfish tissues and pufferfish-based products. The results from this study show that the proposed method can be used to quantify and identify TTX in a single run with excellent sensitivity and reproducibility, and is suitable for the analysis of complex matrix pufferfish samples.

  9. The Geostationary Fourier Transform Spectrometer

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

    2012-01-01

    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.

  10. Determination of Oxidized Phosphatidylcholines by Hydrophilic Interaction Liquid Chromatography Coupled to Fourier Transform Mass Spectrometry

    Pia Sala

    2015-04-01

    Full Text Available A novel liquid chromatography-mass spectrometry (LC-MS approach for analysis of oxidized phosphatidylcholines by an Orbitrap Fourier Transform mass spectrometer in positive electrospray ionization (ESI coupled to hydrophilic interaction liquid chromatography (HILIC was developed. This method depends on three selectivity criteria for separation and identification: retention time, exact mass at a resolution of 100,000 and collision induced dissociation (CID fragment spectra in a linear ion trap. The process of chromatography development showed the best separation properties with a silica-based Kinetex column. This type of chromatography was able to separate all major lipid classes expected in mammalian samples, yielding increased sensitivity of oxidized phosphatidylcholines over reversed phase chromatography. Identification of molecular species was achieved by exact mass on intact molecular ions and CID tandem mass spectra containing characteristic fragments. Due to a lack of commercially available standards, method development was performed with copper induced oxidation products of palmitoyl-arachidonoyl-phosphatidylcholine, which resulted in a plethora of lipid species oxidized at the arachidonoyl moiety. Validation of the method was done with copper oxidized human low-density lipoprotein (LDL prepared by ultracentrifugation. In these LDL samples we could identify 46 oxidized molecular phosphatidylcholine species out of 99 possible candidates.

  11. 21 Tesla Fourier Transform Ion Cyclotron Resonance Mass Spectrometer Greatly Expands Mass Spectrometry Toolbox

    Shaw, Jared B.; Lin, Tzu-Yung; Leach, Franklin E.; Tolmachev, Aleksey V.; Tolić, Nikola; Robinson, Errol W.; Koppenaal, David W.; Paša-Tolić, Ljiljana

    2016-10-12

    We provide the initial performance evaluation of a 21 Tesla Fourier transform ion cyclotron resonance mass spectrometer operating at the Environmental Molecular Sciences Laboratory at Pacific Northwest National Laboratory. The spectrometer constructed for the 21T system employs a commercial dual linear ion trap mass spectrometer coupled to a FTICR spectrometer designed and built in-house. Performance gains from moving to higher magnetic field strength are exemplified by the measurement of peptide isotopic fine structure, complex natural organic matter mixtures, and large proteins. Accurate determination of isotopic fine structure was demonstrated for doubly charged substance P with minimal spectral averaging, and 8,158 molecular formulas assigned to Suwannee River Fulvic Acid standard with RMS error of 10 ppb. We also demonstrated superior performance for intact proteins; namely, broadband isotopic resolution of the entire charge state distribution of apotransferrin (78 kDa) and facile isotopic resolution of monoclonal antibody under a variety of acquisition parameters (e.g. 6 s time-domains with absorption mode processing yielded resolution of approximately 1M at m/z =2,700).

  12. Cryogenic surface ion traps

    Niedermayr, M.

    2015-01-01

    Microfabricated surface traps are a promising architecture to realize a scalable quantum computer based on trapped ions. In principle, hundreds or thousands of surface traps can be located on a single substrate in order to provide large arrays of interacting ions. To this end, trap designs and fabrication methods are required that provide scalable, stable and reproducible ion traps. This work presents a novel surface-trap design developed for cryogenic applications. Intrinsic silicon is used as the substrate material of the traps. The well-developed microfabrication and structuring methods of silicon are utilized to create simple and reproducible traps. The traps were tested and characterized in a cryogenic setup. Ions could be trapped and their life time and motional heating were investigated. Long ion lifetimes of several hours were observed and the measured heating rates were reproducibly low at around 1 phonon per second at a trap frequency of 1 MHz. (author) [de

  13. Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

    2017-08-01

    Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array

  14. Fourier transforms in radar and signal processing

    Brandwood, David

    2011-01-01

    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

  15. The finite Fourier transform of classical polynomials

    Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

    2014-01-01

    The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

  16. On the Scaled Fractional Fourier Transformation Operator

    Hong-Yi, Fan; Li-Yun, Hu

    2008-01-01

    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

  17. A new twist to fourier transforms

    Meikle, Hamish D

    2004-01-01

    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

  18. Simultaneous Determination of Bioactive Monoterpene Indole Alkaloids in Ethanolic Extract of Seven Rauvolfia Species using UHPLC with Hybrid Triple Quadrupole Linear Ion Trap Mass Spectrometry.

    Kumar, Sunil; Singh, Awantika; Bajpai, Vikas; Srivastava, Mukesh; Singh, Bhim Pratap; Ojha, Sanjeev; Kumar, Brijesh

    2016-09-01

    Rauvolfia serpentina is an endangered plant species due to its over-exploitation. It has highly commercial and economic importance due to the presence of bioactive monoterpene indole alkaloids (MIAs) such as ajmaline, yohimbine, ajmalicine, serpentine and reserpine. To develop a validated, rapid, sensitive and selective ultra-high-performance liquid chromatography coupled with hybrid triple quadrupole-linear ion trap mass spectrometry (UHPLC-QqQLIT -MS/MS) method in the multiple reaction monitoring (MRM) mode for simultaneous determination of bioactive MIAs in ethanolic extract of seven Rauvolfia species and herbal formulations. The separation of MIAs was achieved on an ACQUITY UPLC BEH™ C18 column (1.7 μm, 2.1 mm × 50 mm) using a gradient mobile phase (0.1% aqueous formic acid and acetonitrile) at flow rate 0.3 μL/min in 7 min. The validated method showed good linearity (r(2)  ≥ 0.9999), limit of detection (LOD) (0.06-0.15 ng/mL), limit of quantitation (LOQ) (0.18-0.44 ng/mL), precisions [intraday: relative standard deviation (RSD) ≤ 2.24%, interday: RSD ≤ 2.74%], stability (RSD ≤ 1.53%) and overall recovery (RSD ≤ 2.23%). The validated method was applied to quantitate MIAs. Root of Rauvolfia vomitoria showed a high content of ajmaline (48.43 mg/g), serpentine (87.77 mg/g) whereas high quantities of yohimbine (100.21 mg/g) and ajmalicine (120.51 mg/g) were detected in R. tetraphylla. High content of reserpine was detected in R. micrantha (35.18 mg/g) and R. serpentina (32.38 mg/g). The encouraging results of this study may lead to easy selection of suitable Rauvolfia species according to the abundance of MIAs. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

  19. Fourier transform resampling: Theory and application

    Hawkins, W.G.

    1996-01-01

    One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

  20. The morphing of geographical features by Fourier transformation.

    Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

    2018-01-01

    This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

  1. Cryogenic Scan Mechanism for Fourier Transform Spectrometer

    Brasunas, John C.; Francis, John L.

    2011-01-01

    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

  2. Group-invariant finite Fourier transforms

    Shenefelt, M.H.

    1988-01-01

    The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

  3. Replica Fourier Transform: Properties and applications

    Crisanti, A.; De Dominicis, C.

    2015-01-01

    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

  4. Fourier transforms and convolutions for the experimentalist

    Jennison, RC

    1961-01-01

    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

  5. An optical Fourier transform coprocessor with direct phase determination.

    Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

    2017-10-20

    The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

  6. Fourier transform based scalable image quality measure.

    Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien

    2012-08-01

    We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.

  7. Rapid and sensitive determination of major polyphenolic components in Euphoria longana Lam. seeds using matrix solid-phase dispersion extraction and UHPLC with hybrid linear ion trap triple quadrupole mass spectrometry.

    Rathore, Atul S; Sathiyanarayanan, L; Deshpande, Shreekant; Mahadik, Kakasaheb R

    2016-11-01

    A rapid and sensitive method for the extraction and determination of four major polyphenolic components in Euphoria longana Lam. seeds is presented for the first time based on matrix solid-phase dispersion extraction followed by ultra high performance liquid chromatography with hybrid triple quadrupole linear ion trap mass spectrometry. Matrix solid-phase dispersion method was designed for the extraction of Euphoria longana seed constituents and compared with microwave-assisted extraction and ultrasonic-assisted extraction methods. An Ultra high performance liquid chromatography with hybrid triple quadrupole linear ion-trap mass spectrometry method was developed for quantitative analysis in multiple-reaction monitoring mode in negative electrospray ionization. The chromatographic separation was accomplished using an ACQUITY UPLC BEH C 18 (2.1 mm × 50 mm, 1.7 μm) column with gradient elution of 0.1% aqueous formic acid and 0.1% formic acid in acetonitrile. The developed method was validated with acceptable linearity (r 2 > 0.999), precision (RSD ≤ 2.22%) and recovery (RSD ≤ 2.35%). The results indicated that matrix solid-phase dispersion produced comparable extraction efficiency compared with other methods nevertheless was more convenient and time-saving with reduced requirements on sample and solvent volumes. The proposed method is rapid and sensitive in providing a promising alternative for extraction and comprehensive determination of active components for quality control of Euphoria longana products. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. Pi, Fourier Transform and Ludolph van Ceulen

    Vajta, Miklos

    2000-01-01

    The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as

  9. Fourier transform infrared spectrometery: an undergraduate experiment

    Lerner, L

    2016-01-01

    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. (paper)

  10. Wigner distribution and fractional Fourier transform

    Alieva, T.; Bastiaans, M.J.

    2001-01-01

    The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution

  11. The Fourier transform of tubular densities

    Prior, C B; Goriely, A

    2012-01-01

    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

  12. Geometric Representations for Discrete Fourier Transforms

    Cambell, C. W.

    1986-01-01

    Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

  13. Clifford Fourier transform on vector fields.

    Ebling, Julia; Scheuermann, Gerik

    2005-01-01

    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.

  14. Fourier transforms on a semisimple symmetric space

    Ban, E.P. van den; Schlichtkrull, H.

    1994-01-01

    Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation

  15. Fourier transforms on a semisimple symmetric space

    Ban, E.P. van den; Carmona, J.; Delorme, P.

    1997-01-01

    Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation

  16. Mini ion trap mass spectrometer

    Dietrich, D.D.; Keville, R.F.

    1995-09-19

    An ion trap is described which operates in the regime between research ion traps which can detect ions with a mass resolution of better than 1:10{sup 9} and commercial mass spectrometers requiring 10{sup 4} ions with resolutions of a few hundred. The power consumption is kept to a minimum by the use of permanent magnets and a novel electron gun design. By Fourier analyzing the ion cyclotron resonance signals induced in the trap electrodes, a complete mass spectra in a single combined structure can be detected. An attribute of the ion trap mass spectrometer is that overall system size is drastically reduced due to combining a unique electron source and mass analyzer/detector in a single device. This enables portable low power mass spectrometers for the detection of environmental pollutants or illicit substances, as well as sensors for on board diagnostics to monitor engine performance or for active feedback in any process involving exhausting waste products. 10 figs.

  17. Implementation of quantum and classical discrete fractional Fourier transforms

    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

    2016-01-01

    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. PMID:27006089

  18. Implementation of quantum and classical discrete fractional Fourier transforms.

    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

    2016-03-23

    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.

  19. Predicting blood β-hydroxybutyrate using milk Fourier transform infrared spectrum, milk composition, and producer-reported variables with multiple linear regression, partial least squares regression, and artificial neural network.

    Pralle, R S; Weigel, K W; White, H M

    2018-05-01

    Prediction of postpartum hyperketonemia (HYK) using Fourier transform infrared (FTIR) spectrometry analysis could be a practical diagnostic option for farms because these data are now available from routine milk analysis during Dairy Herd Improvement testing. The objectives of this study were to (1) develop and evaluate blood β-hydroxybutyrate (BHB) prediction models using multivariate linear regression (MLR), partial least squares regression (PLS), and artificial neural network (ANN) methods and (2) evaluate whether milk FTIR spectrum (mFTIR)-based models are improved with the inclusion of test-day variables (mTest; milk composition and producer-reported data). Paired blood and milk samples were collected from multiparous cows 5 to 18 d postpartum at 3 Wisconsin farms (3,629 observations from 1,013 cows). Blood BHB concentration was determined by a Precision Xtra meter (Abbot Diabetes Care, Alameda, CA), and milk samples were analyzed by a privately owned laboratory (AgSource, Menomonie, WI) for components and FTIR spectrum absorbance. Producer-recorded variables were extracted from farm management software. A blood BHB ≥1.2 mmol/L was considered HYK. The data set was divided into a training set (n = 3,020) and an external testing set (n = 609). Model fitting was implemented with JMP 12 (SAS Institute, Cary, NC). A 5-fold cross-validation was performed on the training data set for the MLR, PLS, and ANN prediction methods, with square root of blood BHB as the dependent variable. Each method was fitted using 3 combinations of variables: mFTIR, mTest, or mTest + mFTIR variables. Models were evaluated based on coefficient of determination, root mean squared error, and area under the receiver operating characteristic curve. Four models (PLS-mTest + mFTIR, ANN-mFTIR, ANN-mTest, and ANN-mTest + mFTIR) were chosen for further evaluation in the testing set after fitting to the full training set. In the cross-validation analysis, model fit was greatest for ANN, followed

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

    庹红娅; 刘允才

    2004-01-01

    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.

  1. Multichannel Dynamic Fourier-Transform IR Spectrometer

    Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

    2017-09-01

    A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

  2. Discrete Fourier transform in nanostructures using scattering

    Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.

    2004-01-01

    In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed

  3. The PROSAIC Laplace and Fourier Transform

    Smith, G.A.

    1994-01-01

    Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting

  4. Quantum Fourier Transform Over Galois Rings

    Zhang, Yong

    2009-01-01

    Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...

  5. Fourier Transform Spectrometer Controller for Partitioned Architectures

    Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.

    2013-01-01

    The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....

  6. Scaling ion traps for quantum computing

    Uys, H

    2010-09-01

    Full Text Available The design, fabrication and preliminary testing of a chipscale, multi-zone, surface electrode ion trap is reported. The modular design and fabrication techniques used are anticipated to advance scalability of ion trap quantum computing architectures...

  7. Discrete Fourier Transform in a Complex Vector Space

    Dean, Bruce H. (Inventor)

    2015-01-01

    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.

  8. Non-target screening of Allura Red AC photodegradation products in a beverage through ultra high performance liquid chromatography coupled with hybrid triple quadrupole/linear ion trap mass spectrometry.

    Gosetti, Fabio; Chiuminatto, Ugo; Mazzucco, Eleonora; Calabrese, Giorgio; Gennaro, Maria Carla; Marengo, Emilio

    2013-01-15

    The study deals with the identification of the degradation products formed by simulated sunlight photoirradiation in a commercial beverage that contains Allura Red AC dye. An UHPLC-MS/MS method, that makes use of hybrid triple quadrupole/linear ion trap, was developed. In the identification step the software tool information dependent acquisition (IDA) was used to automatically obtain information about the species present and to build a multiple reaction monitoring (MRM) method with the MS/MS fragmentation pattern of the species considered. The results indicate that the identified degradation products are formed from side-reactions and/or interactions among the dye and other ingredients present in the beverage (ascorbic acid, citric acid, sucrose, aromas, strawberry juice, and extract of chamomile flowers). The presence of aromatic amine or amide functionalities in the chemical structures proposed for the degradation products might suggest potential hazards to consumer health. Copyright © 2012 Elsevier Ltd. All rights reserved.

  9. Analog fourier transform channelizer and OFDM receiver

    2007-01-01

    An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...

  10. Noise figure of amplified dispersive Fourier transformation

    Goda, Keisuke; Jalali, Bahram

    2010-01-01

    Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.

  11. Fourier transform infrared spectroscopy of peptides.

    Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell

    2014-01-01

    Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.

  12. Complex nonlinear Fourier transform and its inverse

    Saksida, Pavle

    2015-01-01

    We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)

  13. Functional Fourier transforms and the loop equation

    Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.

    1986-01-01

    The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables

  14. Fourier transform spectroscopy of six stars

    Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia

    1981-01-01

    This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.

  15. Generalized Fourier transforms Fk,a

    Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent

    2009-01-01

    We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....

  16. Electro-optic imaging Fourier transform spectrometer

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

    2009-01-01

    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.

  17. Fourier-transforming with quantum annealers

    Itay eHen

    2014-07-01

    Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.

  18. (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

    Klimyk, A U; Patera, J

    2007-01-01

    We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

  19. The Fourier transform of tubular densities

    Prior, C B

    2012-05-18

    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.

  20. Fourier transform ion cyclotron resonance mass spectrometry

    Marshall, Alan G.

    1998-06-01

    As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.

  1. The Fourier transform of tubular densities

    Prior, C B; Goriely, A

    2012-01-01

    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. (paper)

  2. Fourier transform zero field NMR and NQR

    Zax, D.B.

    1985-01-01

    In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI

  3. Fourier transform spectra of quantum dots

    Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.

    2010-05-01

    Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.

  4. The prosaic Laplace and Fourier transform

    Smith, G.A.

    1995-01-01

    Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics

  5. Scalable error correction in distributed ion trap computers

    Oi, Daniel K. L.; Devitt, Simon J.; Hollenberg, Lloyd C. L.

    2006-01-01

    A major challenge for quantum computation in ion trap systems is scalable integration of error correction and fault tolerance. We analyze a distributed architecture with rapid high-fidelity local control within nodes and entangled links between nodes alleviating long-distance transport. We demonstrate fault-tolerant operator measurements which are used for error correction and nonlocal gates. This scheme is readily applied to linear ion traps which cannot be scaled up beyond a few ions per individual trap but which have access to a probabilistic entanglement mechanism. A proof-of-concept system is presented which is within the reach of current experiment

  6. Vector Radix 2 × 2 Sliding Fast Fourier Transform

    Keun-Yung Byun

    2016-01-01

    Full Text Available The two-dimensional (2D discrete Fourier transform (DFT in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT algorithm based on the vector radix (VR 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

  7. Multicomplementary operators via finite Fourier transform

    Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de

    2005-01-01

    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

  8. Fractional Fourier transform for confluent hypergeometric beams

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-01-01

    Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

  9. Two-dimensional fourier transform spectrometer

    DeFlores, Lauren; Tokmakoff, Andrei

    2013-09-03

    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.

  10. Fourier transforms in NMR, optical, and mass spectrometry

    Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH

    1990-01-01

    This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs

  11. Fourier transform and its application to 1D and 2D NMR

    Canet, D.

    1988-01-01

    In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr

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

    Branko Saric

    2002-01-01

    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.

  13. Automatic Fourier transform and self-Fourier beams due to parabolic potential

    Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

    2015-12-15

    We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

  14. Fourier transform inequalities for phylogenetic trees.

    Matsen, Frederick A

    2009-01-01

    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.

  15. Realization of quantum Fourier transform over ZN

    Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao

    2014-01-01

    Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)

  16. Fourier transformations for difference analogs of the harmonic oscillator

    Askey, R.; Atakishiyev, N.M.

    1995-01-01

    The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs

  17. The Fourier Transform for Certain HyperKähler Fourfolds

    Shen, M.; Vial, C.

    2016-01-01

    Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle

  18. Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

    Hanley, Quentin S.

    2012-01-01

    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",…

  19. Fourier transform in multimode systems in the Bargmann representation

    Lei, C; Vourdas, A

    2007-01-01

    A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed

  20. Lithium adduct as precursor ion for sensitive and rapid quantification of 20 (S)-protopanaxadiol in rat plasma by liquid chromatography/quadrupole linear ion trap mass spectrometry and application to rat pharmacokinetic study.

    Bao, Yuanwu; Wang, Quanying; Tang, Pingming

    2013-03-01

    A novel, rapid and sensitive liquid chromatography/quadrupole linear ion trap mass spectrometry [LC-ESI-(QqLIT)MS/MS] method was developed and validated for the quantification of protopanaxadiol (PPD) in rat plasma. Oleanolic acid (OA) was used as internal standard (IS). A simple protein precipitation based on acetonitrile (ACN) was employed. Chromatographic separation was performed on a Sepax GP-C18 column (50 × 2.1 mm, 5 μM) with a mobile phase consisting of ACN-water and 1.5 μM formic acid and 25 mM lithium acetate (90 : 10, v/v) at a flow rate of 0.4 ml/min for 3.0 min. Multiple-reaction-monitoring mode was performed using lithium adduct ion as precursor ion of m/z 467.5/449.4 and 455.6/407.4 for the drug and IS, respectively. Calibration curve was recovered over a concentration range of 0.5-100 ng/ml with a correlation coefficient >0.99. The limit of detection was 0.2 ng/ml in rat plasma for PPD. The results of the intraday and interday precision and accuracy studies were well within the acceptable limits. The validated method was successfully applied to investigate the pharmacokinetic study of PPD after intravenous and gavage administration to rat. Copyright © 2013 John Wiley & Sons, Ltd.

  1. Dual-polarization nonlinear Fourier transform-based optical communication system

    Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

    2018-01-01

    communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

  2. The relationship between shock response spectrum and fast Fourier transform

    Zola, Maurizio

    2001-01-01

    In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)

  3. Improved sensitivity of ochratoxin A analysis in coffee using high-performance liquid chromatography with hybrid triple quadrupole-linear ion trap mass spectrometry (LC-QqQLIT-MS/MS).

    Kokina, Aija; Pugajeva, Iveta; Bartkevics, Vadims

    2016-01-01

    A novel and sensitive method utilising high-performance liquid chromatography coupled to triple quadrupole-linear ion trap mass spectrometry (LC-QqQLIT-MS/MS) was developed in order to analyse the content of ochratoxin A (OTA) in coffee samples. The introduction of the triple-stage MS scanning mode (MS(3)) has been shown to increase greatly sensitivity and selectivity by eliminating the high chromatographic baseline caused by interference of complex coffee matrices. The analysis included the sample preparation procedure involving extraction of OTA using a methanol-water mixture and clean-up by immunoaffinity columns and detection using the MS(3) scanning mode of LC-QqQLIT-MS/MS. The proposed method offered a good linear correlation (r(2) > 0.998), excellent precision (RSD coffee beans and espresso beverages was 0.010 and 0.003 µg kg(-1), respectively. The developed procedure was compared with traditional methods employing liquid chromatography coupled to fluorescent and tandem quadrupole detectors in conjunction with QuEChERS and solid-phase extraction. The proposed method was successfully applied to the determination of OTA in 15 samples of coffee beans and in 15 samples of espresso coffee beverages obtained from the Latvian market. OTA was found in 10 samples of coffee beans and in two samples of espresso in the ranges of 0.018-1.80 µg kg(-1) and 0.020-0.440 µg l(-1), respectively. No samples exceeded the maximum permitted level of OTA in the European Union (5.0 µg kg(-1)).

  4. From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

    Ganapol, B.D.

    2001-01-01

    A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

  5. The application and improvement of Fourier transform spectrometer experiment

    Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

    2017-08-01

    According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

  6. Image reconstruction from pairs of Fourier-transform magnitude

    Hunt, B.R.; Overman, T.L.; Gough, P.

    1998-01-01

    The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America

  7. A strategy for comprehensive identification of sequential constituents using ultra-high-performance liquid chromatography coupled with linear ion trap-Orbitrap mass spectrometer, application study on chlorogenic acids in Flos Lonicerae Japonicae.

    Zhang, Jia-yu; Wang, Zi-jian; Li, Yun; Liu, Ying; Cai, Wei; Li, Chen; Lu, Jian-qiu; Qiao, Yan-jiang

    2016-01-15

    The analytical methodologies for evaluation of multi-component system in traditional Chinese medicines (TCMs) have been inadequate or unacceptable. As a result, the unclarity of multi-component hinders the sufficient interpretation of their bioactivities. In this paper, an ultra-high-performance liquid chromatography coupled with linear ion trap-Orbitrap (UPLC-LTQ-Orbitrap)-based strategy focused on the comprehensive identification of TCM sequential constituents was developed. The strategy was characterized by molecular design, multiple ion monitoring (MIM), targeted database hits and mass spectral trees similarity filter (MTSF), and even more isomerism discrimination. It was successfully applied in the HRMS data-acquisition and processing of chlorogenic acids (CGAs) in Flos Lonicerae Japonicae (FLJ), and a total of 115 chromatographic peaks attributed to 18 categories were characterized, allowing a comprehensive revelation of CGAs in FLJ for the first time. This demonstrated that MIM based on molecular design could improve the efficiency to trigger MS/MS fragmentation reactions. Targeted database hits and MTSF searching greatly facilitated the processing of extremely large information data. Besides, the introduction of diagnostic product ions (DPIs) discrimination, ClogP analysis, and molecular simulation, raised the efficiency and accuracy to characterize sequential constituents especially position and geometric isomers. In conclusion, the results expanded our understanding on CGAs in FLJ, and the strategy could be exemplary for future research on the comprehensive identification of sequential constituents in TCMs. Meanwhile, it may propose a novel idea for analyzing sequential constituents, and is promising for quality control and evaluation of TCMs. Copyright © 2015 Elsevier B.V. All rights reserved.

  8. A generic approach for expanding homolog-targeted residue screening of sulfonamides using a fast matrix separation and class-specific fragmentation-dependent acquisition with a hybrid quadrupole-linear ion trap mass spectrometer

    Huang Chunlin; Guo Bin; Wang Xiaoying; Li Jie; Zhu Weitao; Chen Bo; Ouyang Shan; Yao Shouzhuo

    2012-01-01

    Highlights: ► Generic homolog-targeted screening approach for multi-residual sulfonamide analogs. ► Single-tube extraction/partitioning-multifunction adsorption cleanup for direct injection. ► Class-specific fragmentation for expanding coverage of N 4 -acetyl and N-OH metabolites. ► PreS–IDA–EPI in LC–QqLIT for simultaneous screening and confirmation of real samples. - Abstract: A generic and efficient homolog-targeted approach was used to expand screening and detection of target class of sulfonamides and structural analogs, based on a fast single-tube extraction/partitioning-multifunction adsorption cleanup (SEP/MAC) for class-specific fragmentation-dependent acquisition with a liquid chromatography–hybrid triple-quadrupole linear ion trap mass spectrometer (LC–QqLIT). By combining the two-stage process conducted in a single tube as one-pot protocol, the straightforward SEP/MAC procedure was optimized to offer clean extracts with reasonable recovery (71–109% with RSDs 4 -acetyl and hydroxylamine metabolites plus their possible dimers. Moreover, the PreS-triggered automatically enhanced product ion spectral acquisition enabled simultaneous screening, profiling and confirmation of an unlimited number of analytes belonging to the sulfonamide class within a single analysis. The validation and application results of the generic SEP/MAC-based LC–QqLIT strategy consistently demonstrated favorable performances with acceptable accuracy (67–116%), precision (RSDs −1 ) to meet the acceptance criteria for all the sulfonamide–tissue combinations. Thus, the integration of the matrix-independent SEP/MAC procedure and the multiparameter matching algorithm with the unit-resolution LC–QqLIT instrument can serve as a valuable semi-targeted discovery strategy for rapid screening and reliable quantitative/confirmatory analysis of real samples.

  9. q-Generalization of the inverse Fourier transform

    Jauregui, M.; Tsallis, C.

    2011-01-01

    A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.

  10. On the physical relevance of the discrete Fourier transform

    Greben, JM

    1991-11-01

    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...

  11. A fourier transform quality measure for iris images

    Makinana, S

    2014-08-01

    Full Text Available to ensure that good quality images are selected for feature extraction, in order to improve iris recognition system. In addition, this research proposes a measure of iris image quality using a Fourier Transform. The experimental results demonstrate...

  12. Surface Fourier-transform lens using a metasurface

    Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun

    2015-01-01

    We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)

  13. Simple optical setup implementation for digital Fourier transform holography

    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: pams@if.uff.br [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)

    2011-01-01

    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.

  14. A discrete Fourier transform for virtual memory machines

    Galant, David C.

    1992-01-01

    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.

  15. Fourier Transform Infrared and Resonance Raman Spectroscopic Studies of Bacteriorhodopsin.

    Earnest, Thomas Nixon

    Fourier transform infrared and resonance Raman spectroscopy were used to investigate the structure and function of the light-activated, transmembrane proton pump, bacteriorhodopsin, from the purple membrane of Halobacterium halobium. Bacteriorhodopsin (bR) is a 27,000 dalton integral membrane protein consisting of 248 amino acids with a retinylidene chromophore. Absorption of a photon leads to the translocation of one or two protons from the inside of the cell to the outside. Resonance Raman spectroscopy allows for the study of the configuration of retinal in bR and its photointermediates by the selective enhancement of vibrational modes of the chromophore. This technique was used to determine that the chromophore is attached to lysine-216 in both the bR _{570} and the M _{412} intermediates. In bR with tyrosine-64 selectively nitrated or aminated, the chromophore appears to have the same configuration in that bR _{570} (all- trans) and M _{412} (13- cis) states as it does in unmodified bR. Polarized Fourier transform infrared spectroscopy (FTIR) permits the study of the direction of transition dipole moments arising from molecular vibrations of the protein and the retinal chromophore. The orientation of alpha helical and beta sheet components was determined for bR with the average helical tilt found to lie mostly parallel to the membrane normal. The beta sheet structures also exhibit an IR linear dichroism for the amide I and amide II bands which suggest that the peptide backbone is mostly perpendicular to the membrane plane although it is difficult to determine whether the bands originate from sheet or turn components. The orientation of secondary structure components of the C-1 (residues 72-248) and C-2 (residues 1-71) fragments were also investigated to determine the structure of these putative membrane protein folding intermediates. Polarized, low temperature FTIR -difference spectroscopy was then used to investigate the structure of bR as it undergoes

  16. Second order oscillations of a Vlasov-Poisson plasma in the Fourier transformed space

    Sedlacek, Z.; Nocera, L.

    1991-05-01

    The Vlasov-Poisson system of equations in the Fourier-transformed velocity space is studied. At first some results of the linear theory are reformulated: in the new representation the Van Kampen eigenmodes and their adjoint are found to be ordinary functions with convenient piece-wise continuity properties. A transparent derivation is given of the free-streaming temporal echo in terms of the kinematics of wave packets in the Fourier-transformed velocity space. This analysis is further extended to include Coulomb interactions which allows to establish a connection between the echo theory, the second order oscillations of Best and the phenomenon of linear sidebands. The calculation of the time evolution of the global second order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. It is concluded that the phenomenon of linear sidebands may be properly explained in terms of the intrinsic features of the equilibrium distribution function. (author) 5 figs., 32 refs

  17. Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.

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

    2016-09-01

    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. © The Author(s) 2016.

  18. A generic approach for expanding homolog-targeted residue screening of sulfonamides using a fast matrix separation and class-specific fragmentation-dependent acquisition with a hybrid quadrupole-linear ion trap mass spectrometer

    Huang Chunlin [Department of Biochemistry and Molecular Biology, School of Pharmacy and Life Science, University of South China, Hengyang 421001 (China); Guo Bin, E-mail: binnguo@126.com [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China); Wang Xiaoying [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China); Li Jie [Department of Biochemistry and Molecular Biology, School of Pharmacy and Life Science, University of South China, Hengyang 421001 (China); Zhu Weitao; Chen Bo [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China); Ouyang Shan [Food Inspection and Quarantine Center, Shenzhen Entry-Exit Inspection and Quarantine Bureau of the People' s Republic of China, Shenzhen 518067 (China); Yao Shouzhuo [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China)

    2012-08-06

    Highlights: Black-Right-Pointing-Pointer Generic homolog-targeted screening approach for multi-residual sulfonamide analogs. Black-Right-Pointing-Pointer Single-tube extraction/partitioning-multifunction adsorption cleanup for direct injection. Black-Right-Pointing-Pointer Class-specific fragmentation for expanding coverage of N{sup 4}-acetyl and N-OH metabolites. Black-Right-Pointing-Pointer PreS-IDA-EPI in LC-QqLIT for simultaneous screening and confirmation of real samples. - Abstract: A generic and efficient homolog-targeted approach was used to expand screening and detection of target class of sulfonamides and structural analogs, based on a fast single-tube extraction/partitioning-multifunction adsorption cleanup (SEP/MAC) for class-specific fragmentation-dependent acquisition with a liquid chromatography-hybrid triple-quadrupole linear ion trap mass spectrometer (LC-QqLIT). By combining the two-stage process conducted in a single tube as one-pot protocol, the straightforward SEP/MAC procedure was optimized to offer clean extracts with reasonable recovery (71-109% with RSDs < 20%) and decreased matrix interferences (-9 to 19%) of multiresidual sulfonamide extraction from different tissue samples. The novel use of neutral loss scan of 66 Da (NLS) or precursor ion scanning of m/z 108 (PreS) in positive ion mode was found to achieve more comprehensive coverage of protonated molecular ions of a wide array of sulfonamides including N{sup 4}-acetyl and hydroxylamine metabolites plus their possible dimers. Moreover, the PreS-triggered automatically enhanced product ion spectral acquisition enabled simultaneous screening, profiling and confirmation of an unlimited number of analytes belonging to the sulfonamide class within a single analysis. The validation and application results of the generic SEP/MAC-based LC-QqLIT strategy consistently demonstrated favorable performances with acceptable accuracy (67-116%), precision (RSDs < 25%), and sensitivity (LOQs {<=} 7.5 ng

  19. Analysis of polar organic contaminants in surface water of the northern Adriatic Sea by solid-phase extraction followed by ultrahigh-pressure liquid chromatography-QTRAP® MS using a hybrid triple-quadrupole linear ion trap instrument.

    Loos, Robert; Tavazzi, Simona; Paracchini, Bruno; Canuti, Elisabetta; Weissteiner, Christof

    2013-07-01

    Water-soluble polar organic contaminants are discharged by rivers, cities, and ships into the oceans. Little is known on the fate, pollution effects, and thresholds of toxic chemical mixtures in the marine environment. A new trace analytical method was developed for the multi-compound analysis of polar organic chemical contaminants in marine waters. The method is based on automated solid-phase extraction (SPE) of one-liter water samples followed by ultrahigh-pressure liquid chromatography triple-quadrupole linear ion-trap mass spectrometry (UHPLC-QTRAP(®) MS). Marine water samples from the open Adriatic Sea taken 16 km offshore from Venice (Italy) were analyzed. Method limits of quantification (LOQs) in the low picogram per liter (pg/l) concentration range were achieved. Among the 67 target chemicals analyzed, 45 substances could be detected above the LOQ. The chemicals detected at the highest concentrations were caffeine (up to 367 ng/l), nitrophenol (36 ng/l), 2,4-dinitrophenol (34 ng/l), 5-methyl-1H-benzotriazole (18.5 ng/l), sucralose (11 ng/l), 1H-benzotriazole (9.2 ng/l), terbuthylazine (9 ng/l), alachlor (7.7 ng/l), atrazine-desisopropyl (6.6 ng/l), diethyltoluamide (DEET) (5.0 ng/l), terbuthylazine-desethyl (4.3 ng/l), metolachlor (2.8 ng/l), perfluorooctanoic acid (PFOA) (2.5 ng/l), perfluoropentanoic acid (PFPeA) (2.3 ng/l), linuron (2.3 ng/l), perfluorohexanoic acid (PFHxA) (2.2 ng/l), diuron (2.0 ng/l), perfluorohexane sulfonate (PFHxS) (1.6 ng/l), simazine (1.6 ng/l), atrazine (1.5 ng/l), and perfluorooctane sulfonate (PFOS) (1.3 ng/l). Higher concentrations were detected during summer due to increased levels of tourist activity during this period.

  20. Rapid, high performance method for the determination of vitamin K(1), menaquinone-4 and vitamin K(1) 2,3-epoxide in human serum and plasma using liquid chromatography-hybrid quadrupole linear ion trap mass spectrometry.

    Gentili, Alessandra; Cafolla, Arturo; Gasperi, Tecla; Bellante, Simona; Caretti, Fulvia; Curini, Roberta; Fernández, Virginia Pérez

    2014-04-18

    Unlike the other fat-soluble vitamins, vitamin K circulates in the human bloodstream at very low levels because of a low intake in the diet. Mammals have developed an efficient recycling system, known as vitamin K-epoxide cycle, which involve quinone, hydroquinone and epoxide forms of the vitamin. Phylloquinone (K(1)) is the main homologue, while menaquinone-4 (MK-4) is both a member of the vitamin K(2) family and metabolite of K(1) in extra-hepatic tissues. Notwithstanding the recent advances, many aspects of the complex vitamin K physiology still remain to be investigated. Therefore, there is a critical need to develop more reliable analytical methods for determining the vitamin K and its metabolites in biological fluids and tissues. Nevertheless, relatively low concentrations, unavailability of some authentic standards and occurrence of interfering lipids make this a challenging task. The method proposed in the present paper can directly and accurately estimate K(1), K(1) 2,3-epoxide (K(1)O), and MK-4 in human serum and plasma at concentrations in the ng/L-μg/L range, using labelled internal standards and a quadrupole linear ion trap instrument operated in multiple reaction monitoring (MRM) mode. High sensitivity was achieved by removing signal "endogenous suppressors" and making the composition of the non-aqueous mobile phase suitable to support the positive atmospheric pressure chemical ionization of the analytes. An excellent selectivity resulted from the combination of some factors: the MRM acquisition, the adoption of an identification point system, an extraction optimized to remove most of the lipids and a tandem-C18 column-system necessary to separate isobaric interferences from analytes. The method was validated according to the Food and Drug Administration (FDA) guidelines and its accuracy was assessed by analysing 9 samples from the Vitamin K External Quality Assessment Scheme (KEQAS). Its feasibility in evaluating vitamin K status in human serum was

  1. SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design

    van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan

    2012-09-01

    TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 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 Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).

  2. Electro-Optical Imaging Fourier-Transform Spectrometer

    Chao, Tien-Hsin; Zhou, Hanying

    2006-01-01

    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.

  3. Active stabilization of ion trap radiofrequency potentials

    Johnson, K. G.; Wong-Campos, J. D.; Restelli, A.; Landsman, K. A.; Neyenhuis, B.; Mizrahi, J.; Monroe, C. [Joint Quantum Institute and University of Maryland Department of Physics, College Park, Maryland 20742 (United States)

    2016-05-15

    We actively stabilize the harmonic oscillation frequency of a laser-cooled atomic ion confined in a radiofrequency (rf) Paul trap by sampling and rectifying the high voltage rf applied to the trap electrodes. We are able to stabilize the 1 MHz atomic oscillation frequency to be better than 10 Hz or 10 ppm. This represents a suppression of ambient noise on the rf circuit by 34 dB. This technique could impact the sensitivity of ion trap mass spectrometry and the fidelity of quantum operations in ion trap quantum information applications.

  4. Solution of 3-dimensional diffusion equation by finite Fourier transformation

    Krishnani, P.D.

    1978-01-01

    Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

  5. Structural characterization of phospholipids by matrix-assisted laser desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry.

    Marto, J A; White, F M; Seldomridge, S; Marshall, A G

    1995-11-01

    Matrix-assisted laser desorption/ionization (MALDI) Fourier transform ion cyclotron resonance mass spectrometry provides for structural analysis of the principal biological phospholipids: glycerophosphatidylcholine, -ethanolamine, -serine, and -inositol. Both positive and negative molecular or quasimolecular ions are generated in high abundance. Isolated molecular ions may be collisionally activated in the source side of a dual trap mass analyzer, yielding fragments serving to identify the polar head group (positive ion mode) and fatty acid side chains (negative ion mode). Azimuthal quadrupolar excitation following collisionally activated dissociation refocuses productions close to the solenoid axis; subsequent transfer of product ions to the analyzer ion trap allows for high-resolution mass analysis. Cyro-cooling of the sample probe with liquid nitrogen greatly reduces matrix adduction encountered in the negative ion mode.

  6. Fourier transform infrared spectra applications to chemical systems

    Ferraro, John R

    1985-01-01

    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

  7. Fourier transform infrared spectra applications to chemical systems

    Ferraro, John R

    1978-01-01

    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

  8. Decay of the Fourier transform analytic and geometric aspects

    Iosevich, Alex

    2014-01-01

    The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

  9. Method of local pointed function reduction of original shape in Fourier transformation

    Dosch, H.; Slavyanov, S.Yu.

    2002-01-01

    The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru

  10. Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

    Salman Ahmad

    2014-06-01

    Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

  11. Matrix-assisted laser desorption fourier transform mass spectrometry for biological compounds

    Hettich, R.; Buchanan, M.

    1990-01-01

    The recent development of matrix-assisted UV laser desorption (LD) mass spectrometry has made possible the ionization and detection of extremely large molecules (with molecular weights exceeding 100,000 Daltons). This technique has generated enormous interest in the biological community for the direct examination of large peptides and oligonucleotides. Although this matrix-assisted ionization method has been developed and used almost exclusively with time-of-flight (TOF) mass spectrometers, research is currently in progress to demonstrate this technique with trapped ion mass spectrometers, such as Fourier transform ion cyclotron resonance mass spectrometry (FTMS). The potential capabilities of FTMS for wide mass range, high resolution measurement, and ion trapping experiments suggest that this instrumental technique should be useful for the detailed structural characterization of large ions generated by the matrix-assisted technique. We have recently demonstrated that matrix-assisted ultraviolet laser desorption can be successfully used with FTMS for the ionization of small peptides. The objective of this report is to summarize the application and current limitations of matrix-assisted laser desorption FTMS for the characterization of peptides and oligonucleotides at the isomeric level. 4 refs., 3 figs., 2 tabs.

  12. Dual beam encoded extended fractional Fourier transform security ...

    This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...

  13. Application of Migration Velocity Using Fourier Transform Approach ...

    Application of velocity by Fourier transform to process 3-D unmigrated seismic sections has been carried out in Fabi Field, Niger Delta – Nigeria. Usually, all seismic events (sections) are characterized by spikes or noise (random or coherent), multiples and shear waves so that when a seismic bed is dipping, the apparent ...

  14. Properties of the Simpson discrete fourier transform | Singh ...

    The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...

  15. Fourier transformation methods in the field of gamma spectrometry

    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.

  16. Fourier transform infrared spectrophotometry and X-ray powder ...

    This study aimed at demonstrating complementary roles offered by both Fourier transform infrared (FTIR) spectrophotometry and x-ray powder diffraction (XRPD) techniques in characterizing clay size fraction of kaolins. The clay size fraction of kaolin samples obtained from Kgwakgwe, Makoro, Lobatse and Serule kaolin ...

  17. Fourier transform distribution function of relaxation times; application and limitations

    Boukamp, Bernard A.

    2015-01-01

    A simple Fourier transform (FT) method is presented for obtaining a Distribution Function of Relaxation Times (DFRT) for electrochemical impedance spectroscopy (EIS) data. By using a special data extension procedure the FT is performed over the range from -∞ ≤ lnω ≤ + ∞. The integration procedure is

  18. SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design

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

    2012-01-01

    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

  19. Quaternion Fourier transforms for signal and image processing

    Ell, Todd A; Sangwine, Stephen J

    2014-01-01

    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.

  20. The RC Circuit: An Approach with Fourier Transforms

    The RC Circuit: An Approach with Fourier Transforms. Classroom Volume 21 Issue 11 November 2016 pp 1029-1042 ... 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 ...

  1. Fourier transform infrared (FTIR) spectroscopy for identification of ...

    Fourier transform infrared (FTIR) spectroscopy was used in this study to identify and determine spectral features of Chlorella vulgaris Beijerinck 1890 and Scenedesmus obliquus (Turpin) Kützing 1833. Two cultures were grown in a chemically-defined media under photoautotrophic culture conditions isolated from eutrophic ...

  2. HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS

    Endah Purwanti

    2014-05-01

    Full Text Available Health problems with cardiovascular system disorder are still ranked high globally. One way to detect abnormalities in the cardiovascular system especially in the heart is through the electrocardiogram (ECG reading. However, reading ECG recording needs experience and expertise, software-based neural networks has designed to help identify any abnormalities ofthe heart through electrocardiogram digital image. This image is processed using image processing methods to obtain ordinate chart which representing the heart’s electrical potential. Feature extraction using Fourier transforms which are divided into several numbers of coefficients. As the software input, Fourier transforms coefficient have been normalized. Output of this software is divided into three classes, namely heart with atrial fibrillation, coronary heart disease and normal. Maximum accuracy rate ofthis software is 95.45%, with the distribution of the Fourier transform coefficients 1/8 and number of nodes 5, while minimum accuracy rate of this software at least 68.18% by distribution of the Fourier transform coefficients 1/32 and the number of nodes 32. Overall result accuracy rate of this software has an average of86.05% and standard deviation of7.82.

  3. Note: Ion source design for ion trap systems

    Noriega, J. R.; Quevedo, M.; Gnade, B.; Vasselli, J.

    2013-06-01

    A small plasma (glow discharge) based ion source and circuit are described in this work. The ion source works by producing a high voltage pulsed discharge between two electrodes in a pressure range of 50-100 mTorr. A third mesh electrode is used for ion extraction. The electrodes are small stainless steel screws mounted in a MACOR ionization chamber in a linear arrangement. The electrode arrangement is driven by a circuit, design for low power operation. This design is a proof of concept intended for applications on small cylindrical ion traps.

  4. Application of the fractional Fourier transform to image reconstruction in MRI.

    Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

    2012-07-01

    The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

  5. Seasonal variations in the profile of main phospholipids in Mytilus galloprovincialis mussels: A study by hydrophilic interaction liquid chromatography-electrospray ionization Fourier transform mass spectrometry.

    Facchini, Laura; Losito, Ilario; Cataldi, Tommaso R I; Palmisano, Francesco

    2018-01-01

    A systematic characterization of phosphatidylcholines and phosphatidylethanolamines in mussels of sp Mytilus galloprovincialis was performed by high-efficiency hydrophilic interaction liquid chromatography combined with electrospray ionization and Fourier transform mass spectrometry (FTMS), based on a quadrupole-Orbitrap hybrid spectrometer. The FTMS/MS experiments under high collisional energy dissociation conditions, complemented by low-energy collisionally induced dissociation MS n (n = 2,3) experiments, performed in a linear ion trap mass spectrometer, were exploited for structural elucidation purposes. The described approach led to an unprecedented characterization of the mussel phospholipidome, with 185 phosphatidylcholines and 131 phosphatidylethanolamines species recognized, distributed among diacylic, plasmanylic, and plasmenylic forms. This was the starting point for the evaluation of the effects of season (in particular, of sea temperature) on the profile of those phospholipids. To this aim, a set of mussel samples retrieved from commercial sources in different periods of the year was considered. Principal component analysis revealed a clear separation between samples collected in periods characterized by cold, intermediate, or warm sea temperatures, respectively. In particular, an enrichment in phospholipids containing unsaturated side chains was observed in mussels collected from cold seawaters (winter-early spring), thus confirming the general model previously elaborated to explain the adaptation of marine invertebrates, including some bivalve molluscs, to low temperatures. On the other hand, relevant levels of plasma(e)nylic and acylic phospholipids bearing either saturated or non-methylene-interrupted side chains were found in mussels collected in warm seawaters (typical of summer and early autumn, at Italian latitudes). This finding opened interesting perspectives towards the development of strategies able to prevent global warming-related mussel

  6. Designing of a Quadrupole Paul Ion Trap

    Kiyani, Abouzar; Abdollahzadeh, M.; Sadat Kiai, S. M.; Zirak, A. R.

    2011-08-01

    The ion motion equation in a Paul ion trap known as Mathieu differential equation has been solved for the first time by using Runge-Kutta methods with 4th, 6th, and 8th orders. The first stability regions in az - qz plane and the corresponding qmax values were determined and compared. Also, the first stability regions of , , , ions in the Vdc - Vac plane were drown, and the threshold voltages for the ion separation was investigated.

  7. Application of Fourier transforms for microwave radiometric inversions

    Holmes, J. J.; Balanis, C. A.; Truman, W. M.

    1975-01-01

    Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

  8. Discrete Fourier Transform Analysis in a Complex Vector Space

    Dean, Bruce H.

    2009-01-01

    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.

  9. Fourier transform digital holographic adaptive optics imaging system

    Liu, Changgeng; Yu, Xiao; Kim, Myung K.

    2013-01-01

    A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541

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

    Y. He

    2008-05-01

    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.

  11. Meso-optical Fourier transform microscope with double focusing

    Batusov, Yu.A.; Soroko, L.M.; Tereshchenko, V.V.

    1992-01-01

    The meso-optical Fourier transform microscope (MFTM) with double focusing for particle tracks of low ionization level in the nuclear emulsion is described. It is shown experimentally that this device enables one to get high concentration of information about the position of the particle track in the nuclear emulsion and thus to increase the signal-to-noise ratio. It is shown that spreading of the meso-optical image of the particle track in the sagittal section of the MFTM can be eliminated completely in the frame of the diffraction limit. The number of the additional degrees of freedom in this new MFTM system along depth coordinate is equal to 20 in comparison to single degree of freedom in the Fourier transform microscope of the direct observation. 10 refs.; 15 figs

  12. Limitations on continuous variable quantum algorithms with Fourier transforms

    Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C

    2009-01-01

    We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.

  13. The Fourier transform for certain hyperkähler fourfolds

    Shen, Mingmin

    2016-01-01

    Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

  14. 10th International Conference on Progress in Fourier Transform Spectroscopy

    Keresztury, Gábor; Kellner, Robert

    1997-01-01

    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.

  15. Symmetrized neutron transport equation and the fast Fourier transform method

    Sinh, N.Q.; Kisynski, J.; Mika, J.

    1978-01-01

    The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations

  16. An algorithm for the basis of the finite Fourier transform

    Santhanam, Thalanayar S.

    1995-01-01

    The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

  17. Fast Fourier transformation results from gamma-ray burst profiles

    Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.

    1992-01-01

    Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.

  18. Calibration of the Herschel SPIRE Fourier Transform Spectrometer

    Swinyard, Bruce; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.- P.; Bendo, G. J.; Ferlet, M.; Griffin, Matthew Jason; Lim, T. L.; Makiwa, G.

    2014-01-01

    The Herschel Spectral and Photometric REceiver (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 sp...

  19. An OTDM-To-WDM Converter Using Optical Fourier Transformation

    Khin Su Myat Min; Zaw Myo Lwin; Hla Myo Tun

    2015-01-01

    We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements ar...

  20. Solving singular convolution equations using the inverse fast Fourier transform

    Krajník, E.; Montesinos, V.; Zizler, P.; Zizler, Václav

    2012-01-01

    Roč. 57, č. 5 (2012), s. 543-550 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular convolution equations * fast Fourier transform * tempered distribution Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/m8437t3563214048/

  1. The short time Fourier transform and local signals

    Okumura, Shuhei

    In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

  2. Optimization and simulation of MEMS rectilinear ion trap

    Huang Gang

    2015-04-01

    Full Text Available In this paper, the design of a MEMS rectilinear ion trap was optimized under simulated conditions. The size range of the MEMS rectilinear ion trap’s electrodes studied in this paper is measured at micron scale. SIMION software was used to simulate the MEMS rectilinear ion trap with different sizes and different radio-frequency signals. The ion-trapping efficiencies of the ion trap under these different simulation conditions were obtained. The ion-trapping efficiencies were compared to determine the performance of the MEMS rectilinear ion trap in different conditions and to find the optimum conditions. The simulation results show that for the ion trap at micron scale or smaller, the optimized length–width ratio was 0.8, and a higher frequency of radio-frequency signal is necessary to obtain a higher ion-trapping efficiency. These results have a guiding role in the process of developing MEMS rectilinear ion traps, and great application prospects in the research fields of the MEMS rectilinear ion trap and the MEMS mass spectrometer.

  3. Microfabricated Microwave-Integrated Surface Ion Trap

    Revelle, Melissa C.; Blain, Matthew G.; Haltli, Raymond A.; Hollowell, Andrew E.; Nordquist, Christopher D.; Maunz, Peter

    2017-04-01

    Quantum information processing holds the key to solving computational problems that are intractable with classical computers. Trapped ions are a physical realization of a quantum information system in which qubits are encoded in hyperfine energy states. Coupling the qubit states to ion motion, as needed for two-qubit gates, is typically accomplished using Raman laser beams. Alternatively, this coupling can be achieved with strong microwave gradient fields. While microwave radiation is easier to control than a laser, it is challenging to precisely engineer the radiated microwave field. Taking advantage of Sandia's microfabrication techniques, we created a surface ion trap with integrated microwave electrodes with sub-wavelength dimensions. This multi-layered device permits co-location of the microwave antennae and the ion trap electrodes to create localized microwave gradient fields and necessary trapping fields. Here, we characterize the trap design and present simulated microwave performance with progress towards experimental results. This research was funded, in part, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA).

  4. Random sampling of evolution time space and Fourier transform processing

    Kazimierczuk, Krzysztof; Zawadzka, Anna; Kozminski, Wiktor; Zhukov, Igor

    2006-01-01

    Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and 15 N-edited NOESY-HSQC spectra of 13 C 15 N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time

  5. Hochauflösende Fourier-Transform-Emissionsspektroskopie

    Uibel, Christian

    2000-01-01

    Mittels hochauflösender Fourier-Transform-Infrarot-Emissionsspektroskopie wurden tiefliegende elektronische Anregungszustände der mittelschweren zweiatomigen Radikale As2, Sb2 und TeF untersucht. Dabei lag das Interesse vor allem bei den Emissionen nicht voll erlaubter Übergänge wie beispielsweise der 3Σ +u →  1Σ +g- bzw. (1u) →  (0+g)-Übergänge bei den Stickstoff-Homologen. Dieses besondere Interesse an der genauen Analyse der 3Σ +u-Zustände liegt in ihrem metastab...

  6. Alternating multivariate trigonometric functions and corresponding Fourier transforms

    Klimyk, A U; Patera, J

    2008-01-01

    We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel

  7. Optical Two Dimensional Fourier Transform Spectroscopy of Layered Metal Dichalcogenides

    Dey, P.; Paul, J.; Stevens, C. E.; Kovalyuk, Z. D.; Kudrynskyi, Z. R.; Romero, A. H.; Cantarero, A.; Hilton, D. J.; Shan, J.; Karaiskaj, D.; Z. D. Kovalyuk; Z. R. Kudrynskyi Collaboration; A. H. Romero Collaboration; A. Cantarero Collaboration; D. J. Hilton Collaboration; J. Shan Collaboration

    2015-03-01

    Nonlinear two-dimensional Fourier transform (2DFT) measurements were used to study the mechanism of excitonic dephasing and probe the electronic structure of the excitonic ground state in layered metal dichalcogenides. Temperature-dependent 2DFT measurements were performed to probe exciton-phonon interactions. Excitation density dependent 2DFT measurements reveal exciton-exciton and exciton-carrier scattering, and the lower limit for the homogeneous linewidth of excitons on positively and negatively doped samples. U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0012635.

  8. An OTDM-To-WDM Converter Using Optical Fourier Transformation

    Khin Su Myat Min

    2015-08-01

    Full Text Available We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements are expressed.

  9. Directional short-time Fourier transform of distributions

    Katerina Hadzi-Velkova Saneva

    2016-04-01

    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.

  10. Hyperspectral imaging using the single-pixel Fourier transform technique

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

    2017-03-01

    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.

  11. Fourier transform infrared studies in solid egg white lysozyme

    Rivzi, T.Z.

    1994-12-01

    Fourier Transform Infrared (FTIR) Spectroscopy is the most recent addition to the arsenal of bioanalytical techniques capable of providing information about the secondary structure of proteins in a variety of environments. FTIR spectra have been obtained in solid egg white lysozyme. The spectra display the usual amide I, II and III bands. Secondary structural information obtained from the spectra after applying resolution enhancement techniques to the amide I band has been found consistent with the x-ray crystallographic data of the protein and also to the spectroscopic data of the protein in aqueous solution. (author). 17 refs, 6 figs, 2 tabs

  12. Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

    Morelli, Eugene A.

    2013-01-01

    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.

  13. Capillary supercritical fluid chromatography - Fourier transform infrared spectrometry

    Olesik, S.V.; French, S.B.; Movotny, M.

    1984-01-01

    One of the most demanding tasks asked of an analytical chemist today is to separate and identify the components of a nonvolatile complex mixture. An efficient separation technique combined with a universal detector that provides structural information, therefore, would be a great asset to analytical chemists. Capillary supercritical fluid chromatography (SFC) - Fourier transform infrared spectrometry (FTIR) shows great potential for being such a technique. SFC-FTIR shows great potential as a very powerful technique for separation and identification of thermally labile and nonvolatile compounds. Research is continuing in these labs to further optimize the technique. 2 refs

  14. H∞ Robust Control of a Large-Piston MEMS Micromirror for Compact Fourier Transform Spectrometer Systems

    Huipeng Chen

    2018-02-01

    Full Text Available Incorporating linear-scanning micro-electro-mechanical systems (MEMS micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large-piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and proportional-integral-derivative (PID closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with a full width at half maximum (FWHM spectral linewidth of 96 cm−1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

  15. A fractional Fourier transform analysis of the scattering of ultrasonic waves

    Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

    2015-01-01

    Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

  16. H∞ Robust Control of a Large-Piston MEMS Micromirror for Compact Fourier Transform Spectrometer Systems.

    Chen, Huipeng; Li, Mengyuan; Zhang, Yi; Xie, Huikai; Chen, Chang; Peng, Zhangming; Su, Shaohui

    2018-02-08

    Incorporating linear-scanning micro-electro-mechanical systems (MEMS) micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS) possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large-piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and proportional-integral-derivative (PID) closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with a full width at half maximum (FWHM) spectral linewidth of 96 cm -1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

  17. Valuation of European Call Option via Inverse Fourier Transform

    Rubenis Oskars

    2017-12-01

    Full Text Available Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.

  18. The gridding method for image reconstruction by Fourier transformation

    Schomberg, H.; Timmer, J.

    1995-01-01

    This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f. The method involves a window function w and proceeds in three steps. First, the convolution g = w * f is computed numerically on a Cartesian grid, using the available samples of f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w * f is much less error prone than merely interpolating f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform

  19. Progress report of a static Fourier transform spectrometer breadboard

    Rosak, A.; Tintó, F.

    2017-11-01

    MOLI instrument -for MOtionLess Interferometer- takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors -integrated into that interference cube- thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.

  20. Ultrafast and versatile spectroscopy by temporal Fourier transform

    Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

    2014-06-01

    One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

  1. Fourier series, Fourier transform and their applications to mathematical physics

    Serov, Valery

    2017-01-01

    This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...

  2. Soft x-ray microscope using Fourier transform holography

    McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H.

    1989-01-01

    A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 x 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs

  3. Gas Measurement Using Static Fourier Transform Infrared Spectrometers.

    Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W

    2017-11-13

    Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.

  4. Quasi-conical centrifugal ion trap

    Golikov, Yu.K.; Solov'ev, K.V.; Grigor'ev, D.V.; Flegontova, E.Yu.

    1999-01-01

    This paper describes a new excellent ion trap that principally differs from the classic hyperbolic one by its action. The action is based on the axisymmetric electrostatic quasi-conical field with the following potential type: F=F 0 [ln r - r 2 /2+z 2 ], where r, z are cylindrical dimensionless coordinates. The radial potential run (f=ln r-r 2 /2), in this case, is exactly presented by the approximation function f a =ar 2 +b/r 2 +c. In addition, there are some ranges of r (for example, 0.6< r<0.35), in which the concurrence accuracy value is above 0.5%. The paper presents the theory of particles dynamics in the centrifugal trap. Basic correlation for resolution ratios and sensitivity values are developed. Recommendations on the centrifugal trap design implementation, including the recording system, are given

  5. Ion trap architectures and new directions

    Siverns, James D.; Quraishi, Qudsia

    2017-12-01

    Trapped ion technology has seen advances in performance, robustness and versatility over the last decade. With increasing numbers of trapped ion groups worldwide, a myriad of trap architectures are currently in use. Applications of trapped ions include: quantum simulation, computing and networking, time standards and fundamental studies in quantum dynamics. Design of such traps is driven by these various research aims, but some universally desirable properties have lead to the development of ion trap foundries. Additionally, the excellent control achievable with trapped ions and the ability to do photonic readout has allowed progress on quantum networking using entanglement between remotely situated ion-based nodes. Here, we present a selection of trap architectures currently in use by the community and present their most salient characteristics, identifying features particularly suited for quantum networking. We also discuss our own in-house research efforts aimed at long-distance trapped ion networking.

  6. Proposed LLNL electron beam ion trap

    Marrs, R.E.; Egan, P.O.; Proctor, I.; Levine, M.A.; Hansen, L.; Kajiyama, Y.; Wolgast, R.

    1985-01-01

    The interaction of energetic electrons with highly charged ions is of great importance to several research fields such as astrophysics, laser fusion and magnetic fusion. In spite of this importance there are almost no measurements of electron interaction cross sections for ions more than a few times ionized. To address this problem an electron beam ion trap (EBIT) is being developed at LLNL. The device is essentially an EBIS except that it is not intended as a source of extracted ions. Instead the (variable energy) electron beam interacting with the confined ions will be used to obtain measurements of ionization cross sections, dielectronic recombination cross sections, radiative recombination cross sections, energy levels and oscillator strengths. Charge-exchange recombinaion cross sections with neutral gasses could also be measured. The goal is to produce and study elements in many different charge states up to He-like xenon and Ne-like uranium. 5 refs., 2 figs

  7. Ion traps fabricated in a CMOS foundry

    Mehta, K. K.; Ram, R. J. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Eltony, A. M.; Chuang, I. L. [Center for Ultracold Atoms, Research Laboratory of Electronics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Bruzewicz, C. D.; Sage, J. M., E-mail: jsage@ll.mit.edu; Chiaverini, J., E-mail: john.chiaverini@ll.mit.edu [Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02420 (United States)

    2014-07-28

    We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the top metal layer of the process for the trap electrodes. The process includes doped active regions and metal interconnect layers, allowing for co-fabrication of standard CMOS circuitry as well as devices for optical control and measurement. With one of the interconnect layers defining a ground plane between the trap electrode layer and the p-type doped silicon substrate, ion loading is robust and trapping is stable. We measure a motional heating rate comparable to those seen in surface-electrode traps of similar size. This demonstration of scalable quantum computing hardware utilizing a commercial CMOS process opens the door to integration and co-fabrication of electronics and photonics for large-scale quantum processing in trapped-ion arrays.

  8. Highly charged ion trapping and cooling

    Beck, B. R.; Church, D. A.; Gruber, L.; Holder, J. P.; Schneider, D.; Steiger, J.

    1998-01-01

    In the past few years a cryogenic Penning trap (RETRAP) has been operational at the Electron Beam Ion Trap (EBIT) facility at Lawrence Livermore National Laboratory. The combination of RETRAP and EBIT provides a unique possibility of producing and re-trapping highly charged ions and cooling them to very low temperatures. Due to the high Coulomb potentials in such an ensemble of cold highly charged ions the Coulomb coupling parameter (the ratio of Coulomb potential to the thermal energy) can easily reach values of 172 and more. To study such systems is not only of interest in astrophysics to simulate White Dwarf star interiors but opens up new possibilities in a variety of areas (e.g. laser spectroscopy), cold highly charged ion beams

  9. Utilization of the ion traps by SPIRAL

    Le Brun, C.; Lienard, E.; Mauger, F.; Tamain, B.

    1997-01-01

    An ion trap is a device capable of confine particles, ions or atoms in a well-controlled environment isolated from any exterior perturbations. There are different traps. They are utilized to collect or stock ions, to cool them after in order to subject them to high precision measurement of masses, magnetic moments, hyperfine properties, beta decay properties, etc. Some dozen of traps are currently used all over the world to study stable or radioactive ions.. SPIRAL has been designed and built to produce radioactive ions starting from various heavy ion beams. SPIRAL has the advantage that the projectile parameters, the target and the energy can be chosen to optimize the production in various regions of the nuclear chart. Also, in SPIRAL it is possible to extract more rapidly the radioactive ions formed in the targets. In addition, in SPIRAL the multicharged ion production in a ECR source is possible. The utilization of multicharged ions is indeed very useful for fast mass measurements or for the study of the interaction between the nucleus and the electronic cloud. Finally, utilization of a ion trap on SPIRAL can be designed first at the level of production target by installing a low energy output line. Than, the trap system could be up-graded and brought to its full utilization behind of the recoil spectrometer. It must be capable of selecting and slowing down the ions produced in the reactions (fusion transfer, very inelastic collisions, etc.) induced by the radioactive ions accelerated in CIME. At present, the collaboration is debating on the most favored subject to study and the most suited experimental setups. The following subjects were selected: ion capture, purification and manipulation; isomers (separation and utilization); mass measurements; hyperfine interactions; lifetimes, nuclear electric cloud; β decays; study of the N = Z nuclei close to the proton drip line; physical and chemical properties of transuranium systems

  10. Post-processing of EPR spectrum from dosimetric substances through filtering of Discrete Fourier Transform

    Vieira, Fabio P.B.; Bevilacqua, Joyce S.

    2014-01-01

    The use of electron paramagnetic resonance spectrometers - EPR - in radiation dosimetry is known for more than four decades. It is an important tool in the retrospective determination of doses absorbed. To estimate the dose absorbed by the sample, it is necessary to know the amplitude of the peak to peak signature of the substance in its EPR spectrum. This information can be compromised by the presence of spurious information: noise - of random and low intensity nature; and the behavior of the baseline - coming from the coupling between the resonator tube and the sample analyzed. Due to the intrinsic characteristics of the three main components of the signal, i.e. signature, noise, and baseline - the analysis in the frequency domain allows, through post-processing techniques to filter spurious information. In this work, an algorithm that retrieves the signature of a substance has been implemented. The Discrete Fourier Transform is applied to the signal and without user intervention, the noise is filtered. From the filtered signal, recovers the signature by Inverse Discrete Fourier Transform. The peak to peak amplitude, and the absorbed dose is calculated with an error of less than 1% for signals wherein the base line is linearized. Some more general cases are under investigation and with little user intervention, you can get the same error

  11. Mass measurement errors of Fourier-transform mass spectrometry (FTMS): distribution, recalibration, and application.

    Zhang, Jiyang; Ma, Jie; Dou, Lei; Wu, Songfeng; Qian, Xiaohong; Xie, Hongwei; Zhu, Yunping; He, Fuchu

    2009-02-01

    The hybrid linear trap quadrupole Fourier-transform (LTQ-FT) ion cyclotron resonance mass spectrometer, an instrument with high accuracy and resolution, is widely used in the identification and quantification of peptides and proteins. However, time-dependent errors in the system may lead to deterioration of the accuracy of these instruments, negatively influencing the determination of the mass error tolerance (MET) in database searches. Here, a comprehensive discussion of LTQ/FT precursor ion mass error is provided. On the basis of an investigation of the mass error distribution, we propose an improved recalibration formula and introduce a new tool, FTDR (Fourier-transform data recalibration), that employs a graphic user interface (GUI) for automatic calibration. It was found that the calibration could adjust the mass error distribution to more closely approximate a normal distribution and reduce the standard deviation (SD). Consequently, we present a new strategy, LDSF (Large MET database search and small MET filtration), for database search MET specification and validation of database search results. As the name implies, a large-MET database search is conducted and the search results are then filtered using the statistical MET estimated from high-confidence results. By applying this strategy to a standard protein data set and a complex data set, we demonstrate the LDSF can significantly improve the sensitivity of the result validation procedure.

  12. A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

    Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

    2015-09-01

    A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

  13. A high-resolution Fourier Transform Spectrometer for planetary spectroscopy

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

    1973-01-01

    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.

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

    Erdem Sasmaz

    2015-06-01

    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.

  15. A Fourier transform with speed improvements for microprocessor applications

    Lokerson, D. C.; Rochelle, R.

    1980-01-01

    A fast Fourier transform algorithm for the RCA 1802microprocessor was developed for spacecraft instrument applications. The computations were tailored for the restrictions an eight bit machine imposes. The algorithm incorporates some aspects of Walsh function sequency to improve operational speed. This method uses a register to add a value proportional to the period of the band being processed before each computation is to be considered. If the result overflows into the DF register, the data sample is used in computation; otherwise computation is skipped. This operation is repeated for each of the 64 data samples. This technique is used for both sine and cosine portions of the computation. The processing uses eight bit data, but because of the many computations that can increase the size of the coefficient, floating point form is used. A method to reduce the alias problem in the lower bands is also described.

  16. Using the fast fourier transform in binding free energy calculations.

    Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L

    2018-04-30

    According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  17. Collision-induced dissociation with Fourier transform mass spectrometry

    Cody, R.B.; Burnier, R.C.; Freiser, B.S.

    1982-01-01

    Collision-induced dissociations (CID) is demonstrated on a number of primary and secondary ions using a Nicolet prototype Fourier transform mass spectrometer (FT-MS). Like the triple quadrupole technique, CID using FT-MS is a relatively low energy and efficient process. The ability to study a wide range of ion-molecule reaction products is exemplified by results on proton-bound dimers and transition metal containing ionic species. Variation of collision energy by varying the RF irradiation level can provide information about product distributions as a function of energy as well as yield ion structural information. Like the triple quadrupole technique, no slits are employed and virtually all of the fragment ions formed by the CID process may be detected. Unlike all previous mass spectrometric techniques for studying CID, a tandem instrument is not required, and different experiments are performed by making software modifications rather than hardware modifications

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

    Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David

    2016-01-01

    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. PMID:26784175

  19. A rheumatoid arthritis study by Fourier transform infrared spectroscopy

    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

    2012-01-01

    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.

  20. Quantum Fourier transform, Heisenberg groups and quasi-probability distributions

    Patra, Manas K; Braunstein, Samuel L

    2011-01-01

    This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.

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

    Lucy Lim

    2016-01-01

    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.

  2. Analysis of cigarette smoke by Fourier transform infrared spectrometry

    Maddox, W.L. (Oak Ridge National Lab., TN); Mamantov, G.

    1977-02-01

    The application of Fourier transform infrared spectrometry (FT-IR) to the quantitative determination of several components in the gas phase of whole, dilute tobacco smoke was demonstrated. The 18-cm absorption cell was part of a cigarette smoking system similar to the intermittent inhalation exposure devices used in smoking and health research with rodents. Concentrations were measured for carbon monoxide, carbon dioxide, methane, ethylene, and methanol in 7 to 22% smoke. The precision of a measurement in 22% smoke ranged from 3% for carbon dioxide to 34% for ethylene. Absorbances measured for isoprene and hydrogen cyanide followed expected concentrations in different cigarette smokes. It was shown that the concentrations of these components remain constant during a 30-s hold-up following each puff on the cigarettes.

  3. Fourier transform wavefront control with adaptive prediction of the atmosphere.

    Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

    2007-09-01

    Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

  4. Generation of Fourier-transform-limited heralded single photons

    U'Ren, Alfred B.; Jeronimo-Moreno, Yasser; Garcia-Gracia, Hipolito

    2007-01-01

    In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets

  5. Topography description of thin films by optical Fourier Transform

    Jaglarz, Janusz

    2008-01-01

    In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates

  6. Topography description of thin films by optical Fourier Transform

    Jaglarz, Janusz [Institute of Physics, Cracow University of Technology, ul. Podchoraz.ych 1, 30-084 Krakow (Poland)], E-mail: pujaglar@cyfronet.krakow.pl

    2008-09-30

    In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates.

  7. Surface analysis by Fourier-transform infrared (FTIR) spectroscopy

    Powell, G.L.; Smyrl, N.R.; Fuller, E.L.

    1981-01-01

    A diffuse-reflectance capability for the Fourier transform infrared spectrometer at the Y-12 Plant Laboratory has been implemented. A sample cell with a 25 to 400 0 C temperature-controlled sample stage and an ultrahigh-vacuum-to-atmospheric pressure gas-handling capability has been developed. Absorbance of light from the spectrometer beam, resulting from the beam being scattered from a powder sample, can be measured. This capability of detecting molecular species on and in powders is to be used to study chemisorption on actinide and rare-earth metals, alloys, and compounds. Cell design is described along with experiments demonstrating its performance in detecting moisture absorption on uranium oxide, moisture and carbon dioxide absorption on the lithium hydride/hydroxide system, and carbon dioxide absorption on potassium borohydride. 13 figures

  8. Quantum copying and simplification of the quantum Fourier transform

    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.

  9. [Continuum based fast Fourier transform processing of infrared spectrum].

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

    2009-12-01

    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.

  10. Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

    Kumar, Sanjay

    2018-01-01

    In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

  11. Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

    Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

    2012-04-20

    It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

  12. TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation

    Ardisasmita, M. Syamsa

    1996-01-01

    The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed

  13. The calculation of site-dependent earthquake motions -3. The method of fast fourier transform

    Simpson, I.C.

    1976-10-01

    The method of Fast Fourier transform (FFT) is applied to the problem of the determination of site-dependent earthquake motions, which takes account of local geological effects. A program, VELAY 1, which uses the FFT method has been written and is described in this report. The assumptions of horizontally stratified, homogeneous, isotropic, linearly viscoelastic layers and a normally incident plane seismic wave are made. Several examples are given, using VELAY 1, of modified surface acceleration-time histories obtained using a selected input acceleration-time history and a representative system of soil layers. There is a discussion concerning the soil properties that need to be measured in order to use VELAY 1 (and similar programs described in previous reports) and hence generate site-dependent ground motions suitable for aseismic design of a nuclear power plant at a given site. (author)

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

    Carneiro, Marta G.; Reddy, Jithender G.; Griesinger, Christian; Lee, Donghan

    2015-01-01

    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 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

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

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

    2015-11-15

    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.

  16. Mats and LaSpec: High-precision experiments using ion traps and lasers at Fair

    Rodriguez, D.; Lallena, A.M.; Blaum, K.; Bohm, C.; Cakirli, R.B.; Crespo Lopez-Urrutia, J.R.; Eliseev, S.; Ketelaer, J.; Kreim, M.S.; Kowalska, M.; Litvinov, Y.A.; Nagy, S.; Neidherr, D.; Repp, J.; Roux, C.; Schabinger, B.; Ullrich, J.; Nortershauser, W.; Eberhardt, K.; Geppert, C.; Kramer, J.; Krieger, A.; Sanchez, R.; Ahammed, M.; Das, P.; Ray, A.; Algora, A.; Rubio, B.; Tain, J.L.; Audi, G.; Lunney, D.; Naimi, S.; Aysto, J.; Jokinen, A.; Kolhinen, V.; Moore, I.; Beck, D.; Block, M.; Geissel, H.; Heinz, S.; Herfurth, F.; Litvinov, Y.A.; Minaya-Ramirez, E.; Plab, W.R.; Quint, W.; Scheidenberger, C.; Winkler, M.; Bender, M.; Billowes, J.; Campbell, P.; Flanagan, K.T.; Schwarz, S.; Bollen, G.; Ferrer, R.; George, S.; Kester, O.; Brodeur, M.; Brunner, T.; Delheij, P.; Dilling, J.; Ettenauer, S.; Lapierre, A.; Bushaw, B.A.; Cano-Ott, D.; Martinez, T.; Cortes, G.; Gomez-Hornillos, M.B.; Dax, A.; Herlert, A.; Yordanov, D.; De, A.; Dickel, T.; Geissel, H.; Jesch, C.; Kuhl, T.; Petrick, M.; PlaB, W.R.; Scheidenberger, C.; Garcia-Ramos, J.E.; Gartzke, E.; Habs, D.; Szerypo, J.; Thirolf, P.G.; Weber, C.; Gusev, Y.; Nesterenko, D.; Novikov, Y.N.; Popov, A.; Seliverstov, M.; Vasiliev, A.; Vorobjev, G.; Heenen, P.H.; Marx, G.; Schweikhard, L.; Ziegler, F.; Hobein, M.; Schuch, R.; Solders, A.; Suhonen, M.; Huber, G.; Wendt, K.; Huyse, M.; Koudriavtsev, I.; Neyens, G.; Van Duppen, P.; Le Blanc, F.; Matos, M.; Reinhard, P.G.; Schneider, D.

    2010-05-15

    Nuclear ground state properties including mass, charge radii, spins and moments can be determined by applying atomic physics techniques such as Penning-trap based mass spectrometry and laser spectroscopy. The MATS and LaSpec setups at the low-energy beamline at FAIR will allow us to extend the knowledge of these properties further into the region far from stability. With MATS (Precision Measurements of very short-lived nuclei using an Advanced Trapping System for highly-charged ions) at FAIR we aim to apply several techniques to very short-lived radionuclides: High-accuracy mass measurements, in-trap conversion electron and alpha spectroscopy, and trap-assisted spectroscopy. The experimental setup of MATS is a unique combination of an electron beam ion trap for charge breeding, ion traps for beam preparation, and a high-precision Penning trap system for mass measurements and decay studies. For the mass measurements, MATS offers both a high accuracy and a high sensitivity. A relative mass uncertainty of 10{sup -9} can be reached by employing highly-charged ions and a non-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. Decay studies in ion traps will become possible with MATS. Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The accuracy of laser-spectroscopic-determined nuclear properties is very high while requirements concerning production rates are moderate. This Technical Design Report describes a new Penning trap mass spectrometry setup as well as a number of complementary experimental devices for laser spectroscopy. Since MATS and LaSpec require high-quality low

  17. Mats and LaSpec: High-precision experiments using ion traps and lasers at Fair

    Rodriguez, D.; Lallena, A.M.; Blaum, K.; Bohm, C.; Cakirli, R.B.; Crespo Lopez-Urrutia, J.R.; Eliseev, S.; Ketelaer, J.; Kreim, M.S.; Kowalska, M.; Litvinov, Y.A.; Nagy, S.; Neidherr, D.; Repp, J.; Roux, C.; Schabinger, B.; Ullrich, J.; Nortershauser, W.; Eberhardt, K.; Geppert, C.; Kramer, J.; Krieger, A.; Sanchez, R.; Ahammed, M.; Das, P.; Ray, A.; Algora, A.; Rubio, B.; Tain, J.L.; Audi, G.; Lunney, D.; Naimi, S.; Aysto, J.; Jokinen, A.; Kolhinen, V.; Moore, I.; Beck, D.; Block, M.; Geissel, H.; Heinz, S.; Herfurth, F.; Litvinov, Y.A.; Minaya-Ramirez, E.; Plab, W.R.; Quint, W.; Scheidenberger, C.; Winkler, M.; Bender, M.; Billowes, J.; Campbell, P.; Flanagan, K.T.; Schwarz, S.; Bollen, G.; Ferrer, R.; George, S.; Kester, O.; Brodeur, M.; Brunner, T.; Delheij, P.; Dilling, J.; Ettenauer, S.; Lapierre, A.; Bushaw, B.A.; Cano-Ott, D.; Martinez, T.; Cortes, G.; Gomez-Hornillos, M.B.; Dax, A.; Herlert, A.; Yordanov, D.; De, A.; Dickel, T.; Geissel, H.; Jesch, C.; Kuhl, T.; Petrick, M.; PlaB, W.R.; Scheidenberger, C.; Garcia-Ramos, J.E.; Gartzke, E.; Habs, D.; Szerypo, J.; Thirolf, P.G.; Weber, C.; Gusev, Y.; Nesterenko, D.; Novikov, Y.N.; Popov, A.; Seliverstov, M.; Vasiliev, A.; Vorobjev, G.; Heenen, P.H.; Marx, G.; Schweikhard, L.; Ziegler, F.; Hobein, M.; Schuch, R.; Solders, A.; Suhonen, M.; Huber, G.; Wendt, K.; Huyse, M.; Koudriavtsev, I.; Neyens, G.; Van Duppen, P.; Le Blanc, F.; Matos, M.; Reinhard, P.G.; Schneider, D.

    2010-01-01

    Nuclear ground state properties including mass, charge radii, spins and moments can be determined by applying atomic physics techniques such as Penning-trap based mass spectrometry and laser spectroscopy. The MATS and LaSpec setups at the low-energy beamline at FAIR will allow us to extend the knowledge of these properties further into the region far from stability. With MATS (Precision Measurements of very short-lived nuclei using an Advanced Trapping System for highly-charged ions) at FAIR we aim to apply several techniques to very short-lived radionuclides: High-accuracy mass measurements, in-trap conversion electron and alpha spectroscopy, and trap-assisted spectroscopy. The experimental setup of MATS is a unique combination of an electron beam ion trap for charge breeding, ion traps for beam preparation, and a high-precision Penning trap system for mass measurements and decay studies. For the mass measurements, MATS offers both a high accuracy and a high sensitivity. A relative mass uncertainty of 10 -9 can be reached by employing highly-charged ions and a non-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. Decay studies in ion traps will become possible with MATS. Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The accuracy of laser-spectroscopic-determined nuclear properties is very high while requirements concerning production rates are moderate. This Technical Design Report describes a new Penning trap mass spectrometry setup as well as a number of complementary experimental devices for laser spectroscopy. Since MATS and LaSpec require high-quality low-energy beams

  18. X-ray Fourier-transform holographic microscope

    Haddad, W.S.; Cullen, D.; Solem, J.C.; Boyer, K.; Rhodes, C.K.

    1988-01-01

    The properties of an x-ray Fourier-transform holographic instrument suitable for imaging hydrated biological samples are described. Recent advances in coherent x-ray source technology are making diffraction-limited holograms of microscopic structures, with corresponding high spatial resolution, a reality. A high priority application of snapshot x-ray holography is the study of microscopic biological structures in the hydrated living state. X-rays offer both high resolution and high contrast for important structures within living organisms, thereby rendering unnecessary the staining of specimens, essential for optical and electron microscopy. If the wavelength is properly chosen. Furthermore, the snapshot feature, arising from picosecond or subpicosecond exposure times, eliminates blurring occurring from either thermal heating or normal biological activity of the sample. Finally, with sufficiently high photon fluxes, such as those available from x-ray lasers, the x-ray snapshot can be accomplished with a single pulse, thereby yielding complete three-dimensional information on a sample having normal biological integrity at the moment of exposure. 10 refs., 6 figs

  19. Non-rigid registration of tomographic images with Fourier transforms

    Osorio, Ar; Isoardi, Ra; Mato, G

    2007-01-01

    Spatial image registration of deformable body parts such as thorax and abdomen has important medical applications, but at the same time, it represents an important computational challenge. In this work we propose an automatic algorithm to perform non-rigid registration of tomographic images using a non-rigid model based on Fourier transforms. As a measure of similarity, we use the correlation coefficient, finding that the optimal order of the transformation is n = 3 (36 parameters). We apply this method to a digital phantom and to 7 pairs of patient images corresponding to clinical CT scans. The preliminary results indicate a fairly good agreement according to medical experts, with an average registration error of 2 mm for the case of clinical images. For 2D images (dimensions 512x512), the average running time for the algorithm is 15 seconds using a standard personal computer. Summarizing, we find that intra-modality registration of the abdomen can be achieved with acceptable accuracy for slight deformations and can be extended to 3D with a reasonable execution time

  20. Fourier Transform Infrared Imaging analysis of dental pulp inflammatory diseases.

    Giorgini, E; Sabbatini, S; Conti, C; Rubini, C; Rocchetti, R; Fioroni, M; Memè, L; Orilisi, G

    2017-05-01

    Fourier Transform Infrared microspectroscopy let characterize the macromolecular composition and distribution of tissues and cells, by studying the interaction between infrared radiation and matter. Therefore, we hypothesize to exploit this analytical tool in the analysis of inflamed pulps, to detect the different biochemical features related to various degrees of inflammation. IR maps of 13 irreversible and 12 hyperplastic pulpitis, together with 10 normal pulps, were acquired, compared with histological findings and submitted to multivariate (HCA, PCA, SIMCA) and statistical (one-way ANOVA) analysis. The fit of convoluted bands let calculate meaningful band area ratios (means ± s.d., P < 0.05). The infrared imaging analysis pin-pointed higher amounts of water and lower quantities of type I collagen in all inflamed pulps. Specific vibrational markers were defined for irreversible pulpitis (Lipids/Total Biomass, PhII/Total Biomass, CH 2 /CH 3 , and Ty/AII) and hyperplastic ones (OH/Total Biomass, Collagen/Total Biomass, and CH 3 Collagen/Total Biomass). The study confirmed that FTIR microspectroscopy let discriminate tissues' biological features. The infrared imaging analysis evidenced, in inflamed pulps, alterations in tissues' structure and composition. Changes in lipid metabolism, increasing amounts of tyrosine, and the occurrence of phosphorylative processes were highlighted in irreversible pulpitis, while high amounts of water and low quantities of type I collagen were detected in hyperplastic samples. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

  1. Relativistic elliptic matrix tops and finite Fourier transformations

    Zotov, A.

    2017-10-01

    We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.

  2. The Fourier transform method for infinite medium resonance absorption problems

    Menon, S.V.G.; Sahni, D.C.

    1978-01-01

    A new method, using Fourier transforms, is developed for solving the integral equation of slowing down of neutrons in the resonance region. The transformations replace the slowing down equation with a discontinuous kernel by an integral equation with a continuous kernel over the interval (-infinity, infinity). Further the Doppler broadened line shape functions have simple analytical representations in the transform variable. In the limit of zero temperature, the integral equation reduces to a second order differential equation. Accurate expressions for the zero temperature resonance integrals are derived, using the WKB method. In general, the integral equation is seen to be amenable to solution by Ganss-Hermite quadrature formule. Doppler coefficients of 238 U resonances are given and compared with Monte Carlo calculations. The method is extended to include the effect of interference between neighbouring resonances of an absorber. For the case of two interfering resonances the slowing down equation is transformed to the coupled integral equations that are amenable to solution by methods indicated earlier. Numerical results presented for the low lying thorium-232 doublet show that the Doppler coefficients of the resonances are reduced considerably because of the overlap between them. (author)

  3. Fourier transform infrared spectroscopy in physics laboratory courses

    Möllmann, K-P; Vollmer, M

    2013-01-01

    Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes. (paper)

  4. Fourier transform nuclear magnetic resonance studies of 199Hg

    Krueger, H.; Lutz, O.; Nolle, A.; Schwenk, A.

    1975-01-01

    199 Hg Fourier Transform NMR studies of various solutions of diverse mercury salts in H 2 O and D 2 O or in the appropriate protonated and deuterated acids are reported for both Hg 2 ++ and Hg ++ . In the different solutions investigated the 199 Hg line positions depend on the concentration of the solution, on the solvents and their isotopic composition and on the temperature of the sample. A ratio of the Larmor frequency of 199 Hg and of 2 H in a Hg(NO 3 ) 2 solution in dilute DNO 3 is given. Using this ratio and the measured chemical shifts, a ratio of the Larmor frequencies of 199 Hg for infinite dilution relative to 2 H in pure D 2 O is given. From this a g 1 -factor for 199 Hg is derived and compared with the g 1 -factor of an optical pumping experiment. The resulting shielding constant is sigma (hydrated 199 Hg ++ versus 199 Hg atom) = -24.32(5) x 10 -4 . This yields an atomic reference scale for all measured NMR line shifts of mercury. (orig.) [de

  5. Convergence and summability of Fourier transforms and Hardy spaces

    Weisz, Ferenc

    2017-01-01

    This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations.  Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.

  6. Toward a soft x-ray Fourier-transform spectrometer

    Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T.; Moeller, D.

    1993-01-01

    The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range ±1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330

  7. Sparse-matrix factorizations for fast symmetric Fourier transforms

    Sequel, J.

    1987-01-01

    This work proposes new fast algorithms computing the discrete Fourier transform of certain families of symmetric sequences. Sequences commonly found in problems of structure determination by x-ray crystallography and in numerical solutions of boundary-value problems in partial differential equations are dealt with. In the algorithms presented, the redundancies in the input and output data, due to the presence of symmetries in the input data sequence, were eliminated. Using ring-theoretical methods a matrix representation is obtained for the remaining calculations; which factors as the product of a complex block-diagonal matrix times as integral matrix. A basic two-step algorithm scheme arises from this factorization with a first step consisting of pre-additions and a second step containing the calculations involved in computing with the blocks in the block-diagonal factor. These blocks are structured as block-Hankel matrices, and two sparse-matrix factoring formulas are developed in order to diminish their arithmetic complexity

  8. Closed contour fractal dimension estimation by the Fourier transform

    Florindo, J.B.; Bruno, O.M.

    2011-01-01

    Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.

  9. Large Molecule Structures by Broadband Fourier Transform Molecular Rotational Spectroscopy

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

    2016-06-01

    Fourier transform molecular rotational resonance spectroscopy (FT-MRR) using pulsed jet molecular beam sources is a high-resolution spectroscopy technique that can be used for chiral analysis of molecules with multiple chiral centers. The sensitivity of the molecular rotational spectrum pattern to small changes in the three dimensional structure makes it possible to identify diastereomers without prior chemical separation. For larger molecules, there is the additional challenge that different conformations of each diastereomer may be present and these need to be differentiated from the diastereomers in the spectral analysis. Broadband rotational spectra of several larger molecules have been measured using a chirped-pulse FT-MRR spectrometer. Measurements of nootkatone (C15H22O), cedrol (C15H26O), ambroxide (C16H28O) and sclareolide (C16H26O2) are presented. These spectra are measured with high sensitivity (signal-to-noise ratio near 1,000:1) and permit structure determination of the most populated isomers using isotopic analysis of the 13C and 18O isotopologues in natural abundance. The accuracy of quantum chemistry calculations to identify diastereomers and conformers and to predict the dipole moment properties needed for three wave mixing measurements is examined.

  10. Single beam Fourier transform digital holographic quantitative phase microscopy

    Anand, A., E-mail: arun-nair-in@yahoo.com; 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)

    2014-03-10

    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.

  11. The linear canonical transformation : definition and properties

    Bastiaans, Martin J.; Alieva, Tatiana; Healy, J.J.; Kutay, M.A.; Ozaktas, H.M.; Sheridan, J.T.

    2016-01-01

    In this chapter we introduce the class of linear canonical transformations, which includes as particular cases the Fourier transformation (and its generalization: the fractional Fourier transformation), the Fresnel transformation, and magnifier, rotation and shearing operations. The basic properties

  12. Modular Universal Scalable Ion-trap Quantum Computer

    2016-06-02

    SECURITY CLASSIFICATION OF: The main goal of the original MUSIQC proposal was to construct and demonstrate a modular and universally- expandable ion...Distribution Unlimited UU UU UU UU 02-06-2016 1-Aug-2010 31-Jan-2016 Final Report: Modular Universal Scalable Ion-trap Quantum Computer The views...P.O. Box 12211 Research Triangle Park, NC 27709-2211 Ion trap quantum computation, scalable modular architectures REPORT DOCUMENTATION PAGE 11

  13. Application of finite Fourier transformation for the solution of the diffusion equation

    Kobayashi, Keisuke

    1991-01-01

    The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

  14. Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

    Fan Hongyi; Hao Ren; Lu Hailiang

    2008-01-01

    Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible

  15. On the moments of the Wigner distribution and the fractional Fourier transform

    Alieva, T.; Bastiaans, M.J.; Veen, J.P.

    2000-01-01

    A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when

  16. The RC Circuit: An Approach with Fourier Transforms In this article ...

    CLASSROOM. Mitrajyoti Ghosh. 83, Mitrapara 2nd Lane, Harinavi,. Kolkata 700148, West Bengal,. India. Email: mijospeakingnow@gmail.com. The RC Circuit: An Approach with Fourier Transforms. In this article we shall mathematically analyse the Resistor-. Capacitor (RC) circuit with the help of Fourier transforms. (FT).

  17. On the windowed Fourier transform as an interpolation of the Gabor transform

    Bastiaans, M.J.; Prochßzka, A.; Uhlør, J.; Sovka, P.

    1997-01-01

    The windowed Fourier transform and its sampled version - the Gabor transform - are introduced. With the help of Gabor's signal expansion, an interpolation function is derived with which the windowed Fourier transform can be constructed from the Gabor transform. Using the Zak transform, it is shown

  18. Fast inverse nonlinear Fourier transformation using exponential one-step methods : Darboux transformation

    Vaibhav, V.K.

    2017-01-01

    This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the

  19. A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

    Debnath, Lokenath

    2012-01-01

    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…

  20. Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

    Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

    2014-10-07

    The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

  1. Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

    Ogawa, Takahiro; Haseyama, Miki

    2013-03-01

    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.

  2. Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

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

    2016-09-19

    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.

  3. The quantum state vector in phase space and Gabor's windowed Fourier transform

    Bracken, A J; Watson, P

    2010-01-01

    Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

  4. Fourier transform infrared spectroscopy for Kona coffee authentication.

    Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X

    2009-06-01

    Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations.

  5. Advanced multivariate data evaluation for Fourier transform infrared spectroscopy

    Diewok, J.

    2002-12-01

    The objective of the presented dissertation was the evaluation, application and further development of advanced multivariate data evaluation methods for qualitative and quantitative Fourier transform infrared (FT-IR) measurements, especially of aqueous samples. The focus was set on 'evolving systems'; i.e. chemical systems that change gradually with a master variable, such as pH, reaction time, elution time, etc. and that are increasingly encountered in analytical chemistry. FT-IR measurements on such systems yield 2-way and 3-way data sets, i.e. data matrices and cubes. The chemometric methods used were soft-modeling techniques, like multivariate curve resolution - alternating least squares (MCR-ALS) or principal component analysis (PCA), hard modeling of equilibrium systems and two-dimensional correlation spectroscopy (2D-CoS). The research results are presented in six publications and comprise: A new combination of FT-IR flow titrations and second-order calibration by MCR-ALS for the quantitative analysis of mixture samples of organic acids and sugars. A novel combination of MCR-ALS with a hard-modeled equilibrium constraint for second-order quantitation in pH-modulated samples where analytes and interferences show very similar acid-base behavior. A detailed study in which MCR-ALS and 2D-CoS are directly compared for the first time. From the analysis of simulated and experimental acid-base equilibrium systems, the performance and interpretability of the two methods is evaluated. Investigation of the binding process of vancomycin, an important antibiotic, to a cell wall analogue tripeptide by time-resolved FT-IR spectroscopy and detailed chemometric evaluation. Determination of red wine constituents by liquid chromatography with FT-IR detection and MCR-ALS for resolution of overlapped peaks. Classification of red wine cultivars from FT-IR spectroscopy of phenolic wine extracts with hierarchical clustering and soft independent modeling of class analogy (SIMCA

  6. Fourier transform Raman spectroscopy of synthetic and biological calcium phosphates.

    Sauer, G R; Zunic, W B; Durig, J R; Wuthier, R E

    1994-05-01

    Fourier-transform (FT) Raman spectroscopy was used to characterize the organic and mineral components of biological and synthetic calcium phosphate minerals. Raman spectroscopy provides information on biological minerals that is complimentary to more widely used infrared methodologies as some infrared-inactive vibrational modes are Raman-active. The application of FT-Raman technology has, for the first time, enabled the problems of high sample fluorescence and low signal-to-noise that are inherent in calcified tissues to be overcome. Raman spectra of calcium phosphates are dominated by a very strong band near 960 cm-1 that arises from the symmetric stretching mode (v1) of the phosphate group. Other Raman-active phosphate vibrational bands are seen at approximately 1075 (v3), 590 (v4), and 435 cm-1 (v2). Minerals containing acidic phosphate groups show additional vibrational modes. The different calcium phosphate mineral phases can be distinguished from one another by the relative positions and shapes of these bands in the Raman spectra. FT-Raman spectra of nascent, nonmineralized matrix vesicles (MV) show a distinct absence of the phosphate v1 band even though these structures are rich in calcium and phosphate. Similar results were seen with milk casein and synthetic Ca-phosphatidyl-serine-PO4 complexes. Hence, the phosphate and/or acidic phosphate ions in these noncrystalline biological calcium phosphates is in a molecular environment that differs from that in synthetic amorphous calcium phosphate. In MV, the first distinct mineral phase to form contained acidic phosphate bands similar to those seen in octacalcium phosphate. The mineral phase present in fully mineralized MV was much more apatitic, resembling that found in bones and teeth.(ABSTRACT TRUNCATED AT 250 WORDS)

  7. Novel control modes to improve the performance of rectilinear ion trap mass spectrometer with dual pressure chambers

    Huo, Xinming; Tang, Fei; Zhang, Xiaohua; Chen, Jin; Zhang, Yan; Guo, Cheng'an; Wang, Xiaohao

    2016-10-01

    The rectilinear ion trap (RIT) has gradually become one of the preferred mass analyzers for portable mass spectrometers because of its simple configuration. In order to enhance the performance, including sensitivity, quantitation capability, throughput, and resolution, a novel RIT mass spectrometer with dual pressure chambers was designed and characterized. The studied system constituted a quadrupole linear ion trap (QLIT) in the first chamber and a RIT in the second chamber. Two control modes are hereby proposed: Storage Quadrupole Linear Ion Trap-Rectilinear Ion Trap (SQLIT-RIT) mode, in which the QLIT was used at high pressure for ion storage and isolation, and the RIT was used for analysis; and Analysis Quadrupole Linear Ion Trap-Rectilinear Ion Trap (AQLIT-RIT) mode, in which the QLIT was used for ion storage and cooling. Subsequently, synchronous scanning and analysis were carried out by QLIT and RIT. In SQLIT-RIT mode, signal intensity was improved by a factor of 30; the limit of quantitation was reduced more than tenfold to 50 ng mL-1, and an optimal duty cycle of 96.4% was achieved. In AQLIT-RIT mode, the number of ions coexisting in the RIT was reduced, which weakened the space-charge effect and reduced the mass shift. Furthermore, the mass resolution was enhanced by a factor of 3. The results indicate that the novel control modes achieve satisfactory performance without adding any system complexity, which provides a viable pathway to guarantee good analytical performance in miniaturization of the mass spectrometer.

  8. The profiling of the metabolites of hirsutine in rat by ultra-high performance liquid chromatography coupled with linear ion trap Orbitrap mass spectrometry: An improved strategy for the systematic screening and identification of metabolites in multi-samples in vivo.

    Wang, Jianwei; Qi, Peng; Hou, Jinjun; Shen, Yao; Yang, Min; Bi, Qirui; Deng, Yanping; Shi, Xiaojian; Feng, Ruihong; Feng, Zijin; Wu, Wanying; Guo, Dean

    2017-02-05

    Drug metabolites identification and construction of metabolic profile are meaningful work for the drug discovery and development. The great challenge during this process is the work of the structural clarification of possible metabolites in the complicated biological matrix, which often resulting in a huge amount data sets, especially in multi-samples in vivo. Analyzing these complex data manually is time-consuming and laborious. The object of this study was to develop a practical strategy for screening and identifying of metabolites from multiple biological samples efficiently. Using hirsutine (HTI), an active components of Uncaria rhynchophylla (Gouteng in Chinese) as a model and its plasma, urine, bile, feces and various tissues were analyzed with data processing software (Metwork), data mining tool (Progenesis QI), and HR-MS n data by ultra-high performance liquid chromatography/linear ion trap-Orbitrap mass spectrometry (U-HPLC/LTQ-Orbitrap-MS). A total of 67 metabolites of HTI in rat biological samples were tentatively identified with established library, and to our knowledge most of which were reported for the first time. The possible metabolic pathways were subsequently proposed, hydroxylation, dehydrogenation, oxidation, N-oxidation, hydrolysis, reduction and glucuronide conjugation were mainly involved according to metabolic profile. The result proved application of this improved strategy was efficient, rapid, and reliable for metabolic profiling of components in multiple biological samples and could significantly expand our understanding of metabolic situation of TCM in vivo. Copyright © 2016 Elsevier B.V. All rights reserved.

  9. Ion Motion Stability in Asymmetric Surface Electrode Ion Traps

    Shaikh, Fayaz; Ozakin, Arkadas

    2010-03-01

    Many recently developed designs of the surface electrode ion traps for quantum information processing have asymmetry built into their geometries. The asymmetry helps rotate the trap axes to angles with respect to electrode surface that facilitate laser cooling of ions but introduces a relative angle between the RF and DC fields and invalidates the classical stability analysis of the symmetric case for which the equations of motion are decoupled. For asymmetric case the classical motion of a single ion is given by a coupled, multi-dimensional version of Mathieu's equation. In this poster we discuss the stability diagram of asymmetric surface traps by performing an approximate multiple scale perturbation analysis of the coupled Mathieu equations, and validate the results with numerical simulations. After obtaining the stability diagram for the linear fields, we simulate the motion of an ion in a given asymmetric surface trap, utilizing a method-of-moments calculation of the electrode fields. We obtain the stability diagram and compare it with the ideal case to find the region of validity. Finally, we compare the results of our stability analysis to experiments conducted on a microfabricated asymmetric surface trap.

  10. Quantitative determination of multi markers in five varieties of Withania somnifera using ultra-high performance liquid chromatography with hybrid triple quadrupole linear ion trap mass spectrometer combined with multivariate analysis: Application to pharmaceutical dosage forms.

    Chandra, Preeti; Kannujia, Rekha; Saxena, Ankita; Srivastava, Mukesh; Bahadur, Lal; Pal, Mahesh; Singh, Bhim Pratap; Kumar Ojha, Sanjeev; Kumar, Brijesh

    2016-09-10

    An ultra-high performance liquid chromatography electrospray ionization tandem mass spectrometry method has been developed and validated for simultaneous quantification of six major bioactive compounds in five varieties of Withania somnifera in various plant parts (leaf, stem and root). The analysis was accomplished on Waters ACQUITY UPLC BEH C18 column with linear gradient elution of water/formic acid (0.1%) and acetonitrile at a flow rate of 0.3mLmin(-1). The proposed method was validated with acceptable linearity (r(2), 0.9989-0.9998), precision (RSD, 0.16-2.01%), stability (RSD, 1.04-1.62%) and recovery (RSD ≤2.45%), under optimum conditions. The method was also successfully applied for the simultaneous determination of six marker compounds in twenty-six marketed formulations. Hierarchical cluster analysis and principal component analysis were applied to discriminate these twenty-six batches based on characteristics of the bioactive compounds. The results indicated that this method is advance, rapid, sensitive and suitable to reveal the quality of Withania somnifera and also capable of performing quality evaluation of polyherbal formulations having similar markers/raw herbs. Copyright © 2016 Elsevier B.V. All rights reserved.

  11. Analysis of the physical simulation on Fourier transform infrared spectrometer

    Yue, Peng-yuan; Wan, Yu-xi; Zhao, Zhen

    2017-10-01

    A kind of oscillating arm type Fourier Transform Infrared Spectrometer (FTS) which based on the corner cube retroreflector is presented, and its principle and properties are studied. It consists of a pair of corner cube retroreflector, beam splitter and compensator. The optical path difference(OPD) is created by oscillating reciprocating motion of the moving corner cube pair, and the OPD value is four times the physical shift value of the moving corner cube pair. Due to the basic property of corner cube retroreflector, the oscillating arm type FTS has no tilt problems. It is almost ideal for very high resolution infrared spectrometer. However, there are some factors to reduce the FTS capability. First, wavefront aberration due to the figures of these surfaces will reduce modulation of FTS system; second, corner cube retroreflector consist of three plane mirror, and orthogonal to each other. When there is a deviation from right angle, it will reduced the modulation of system; third, the apexes of corner cube retroreflector are symmetric about the surface of beam splitter, if one or both of the corner cube retroreflector is displaced laterally from its nominal position, phase of off-axis rays returning from the two arms were difference, this also contributes to loss of modulation of system. In order to solve these problems, this paper sets up a non-sequential interference model, and a small amount of oscillating arm rotation is set to realize the dynamic simulation process, the dynamic interference energy data were acquired at different times, and calculated the modulation of the FTS system. In the simulation, the influence of wedge error of beam splitter, compensator or between them were discussed; effects of oscillating arm shaft deviation from the coplanar of beam splitter was analyzed; and compensation effect of corner cube retroreflector alignment on beam splitter, oscillating arm rotary shaft alignment error is analyzed. In addition, the adjustment procedure

  12. Optimal Padding for the Two-Dimensional Fast Fourier Transform

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

    2011-01-01

    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

  13. Thyroid lesions diagnosis by Fourier transformed infrared absorption spectroscopy (FTIR)

    Albero, Felipe Guimaraes

    2009-01-01

    Thyroid nodules are a common disorder, with 4-7% of incidence in the Brazilian population. Although the fine needle aspiration (FNA) is an accurate method for thyroid tumors diagnosis, the discrimination between benign and malignant neoplasm is currently not possible in some cases with high incidence of false negative diagnosis, leading to a surgical intervention due to the risk of carcinomas. The aim of this study was to verify if the Fourier Transform infrared spectroscopy (FTIR) can contribute to the diagnosis of thyroid carcinomas and goiters, using samples of tissue and aspirates. Samples of FNA, homogenates and tissues of thyroid nodules with histopathological diagnosis were obtained and prepared for FTIR spectroscopy analysis. The FNA and homogenates samples were measured by μ-FTIR (between 950 . 1750 cm -1 ), at a nominal resolution of 4 cm -1 and 120 scans). Tissue samples were analyzed directly by ATR-FTIR technique, at a resolution 2 cm -1 , with 60 scans in the same region. All spectra were corrected by the baseline and normalized by amides area (1550-1640 cm -1 ) in order to minimize variations of sample homogeneity. Then, spectra were converted into second derivatives using the Savitzk-Golay algorithm with a 13 points window. The Ward's minimum variance algorithm and Euclidean distances among the points were used for cluster analysis. Some FNA samples showed complex spectral pattern. All samples showed some cell pellets and large amount of hormone, represented by the bands of 1545 and 1655 cm -1 . Bands in 1409, 1412, 1414, 1578 and 1579 cm -1 were also found, indicating possible presence of sugar, DNA, citric acid or metabolic products. In this study, it was obtained an excellent separation between goiter and malign lesion for the samples of tissues, with 100% of specificity in specific cluster and 67% sensibility and 50 of specificity. In homogenate and FNA samples this sensibility and specificity were lower, because among these samples, it were

  14. Intelligent Controller for a Compact Wide-Band Compositional Infrared Fourier Transform Spectrometer

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

    2013-12-01

    This paper presents the design and integration of an intelligent controller for CIRIS (Compositional InfraRed Interferometric Spectrometer) on a stand-alone field programmable gate array (FPGA) architecture. 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. This design eliminates the need for periodically accelerating/decelerating mirrors inherent to canonical Michelson designs and allows for a compact and robust device that is intrinsically radiation-hard, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 μm) on planetary exploration missions. A traditional Michelson FTS passes a monochromatic light source (incident light from the sample) through a system of refractors/mirrors followed by a mirror moving linearly in the plane of the incident light. This process selectively blocks certain wavelengths and permits measurement of the sample's absorption rates as a function of the wavelengths blocked to produce an 'inteferogram.' This is subsequently processed using a Fourier transform to obtain the sample's spectrum and ascertain the sample's composition. With our prototype CIRIS instrument in development at Design and Prototype Inc. and NASA-JPL, we propose the use of a rotating refractor spinning at a constant velocity to variably phase shift incident light to the detector as an alternative to a linearly moving mirror. This design eliminates sensitivity to vibrations, minimizing path length and non-linear errors due to minor perturbations to the system, in addition to facilitating compact design critical to meeting the strict volume requirements of spacecraft. Further, this is done without sacrificing spectral resolution or throughput when compared to Michelson or diffractive designs. While Michelson designs

  15. Quantitative evaluation of temporal partial coherence using 3D Fourier transforms of through-focus TEM images

    Kimoto, Koji; Sawada, Hidetaka; Sasaki, Takeo; Sato, Yuta; Nagai, Takuro; Ohwada, Megumi; Suenaga, Kazu; Ishizuka, Kazuo

    2013-01-01

    We evaluate the temporal partial coherence of transmission electron microscopy (TEM) using the three-dimensional (3D) Fourier transform (FT) of through-focus images. Young's fringe method often indicates the unexpected high-frequency information due to non-linear imaging terms. We have already used the 3D FT of axial (non-tilted) through-focus images to reduce the effect of non-linear terms on the linear imaging term, and demonstrated the improvement of monochromated lower-voltage TEM performance [Kimoto et al., Ultramicroscopy 121 (2012) 31–39]. Here we apply the 3D FT method with intentionally tilted incidence to normalize various factors associated with a TEM specimen and an imaging device. The temporal partial coherence of two microscopes operated at 30, 60 and 80 kV is evaluated. Our method is applicable to such cases where the non-linear terms become more significant in lower acceleration voltage or aberration-corrected high spatial resolution TEM. - Highlights: • We assess the temporal partial coherence of TEM using a 3-dimensional (3D) Fourier transform (FT) of through-focus images. • We apply the 3D FT method with intentionally tilted incidence to normalize various factors associated with a TEM specimen and an imaging device. • The spatial frequency at which information transfer decreases to 1/e 2 (13.5%) is determined for two lower-voltage TEM systems

  16. A low noise single-transistor transimpedance preamplifier for Fourier-transform mass spectrometry using a T feedback network.

    Lin, Tzu-Yung; Green, Roger J; O'Connor, Peter B

    2012-09-01

    A novel single-transistor transimpedance preamplifier has been introduced for improving performance in Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometry. A low noise junction field-effect transistor (JFET), BF862, is used as the main amplification stage of this trans-impedance preamplifier, and a T-shaped feedback network is introduced as both the feedback and the gate biasing solutions. The T feedback network has been studied using an operational amplifier (Op Amp), AD8099. Such a feedback system allows ~100-fold less feedback resistance at a given transimpedance, hence preserving bandwidth, which is beneficial to applications demanding high gain. The single-transistor preamplifier yields a tested transimpedance of ~10(4) Ω (80 dBΩ) in the frequency range between 1 kHz and 1 MHz (mass-to-charge ratio, m/z, of around 180-180k for a 12-T FT-ICR system), with a low power consumption of ~6 mW, which implies that this preamplifier is well suited to a 12-T FT-ICR mass spectrometer. In trading noise performance for higher trans-impedance, an alternative preamplifier design, an AD8099 preamplifier with the T feedback network, has also been studied with a capability of ~10(6) Ω (120 dBΩ) transimpedance in the same frequency range. The resistive components in the T feedback network reported here can be replaced by complex impedances, which allows adaptation of this feedback system to other frequency, transimpedance, and noise characteristics for applications not only in other mass spectrometers, such as Orbitrap, time-of-flight (TOF), and ion trap systems, but also in other charge/current detecting systems such as spectroscopy systems, microscopy systems, optical communication systems, or charge-coupled devices (CCDs).

  17. Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

    D'Astous, Y.; Blanchard, M.

    1982-05-01

    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)

  18. QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

    Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

  19. How to use the Fast Fourier Transform in Large Finite Fields

    Petersen, Petur Birgir

    2011-01-01

    The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.

  20. On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

    Atakishiyeva, M K; Atakishiyev, N M

    2015-01-01

    We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

  1. ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.

    Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...

  2. Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform

    Zohreh Moghareh Abed

    2010-01-01

    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.

  3. Engineering Model Panchromatic Fourier Transform Spectrometer (PanFTS) Instrument for the GEO-CAPE Mission

    National Aeronautics and Space Administration — The Panchromatic Fourier Transform Spectrometer (PanFTS) is an imaging spectrometer that can measure pollutants, greenhouse gases, and aerosols as called for in the...

  4. Improved method of generating bit reversed numbers for calculating fast fourier transform

    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...

  5. Fourier transform and mean quadratic variation of Bernoulli convolution on homogeneous Cantor set

    Yu Zuguo E-mail: yuzg@hotmail.comz.yu

    2004-07-01

    For the Bernoulli convolution on homogeneous Cantor set, under some condition, it is proved that the mean quadratic variation and the average of Fourier transform of this measure are bounded above and below.

  6. Atmospheric pressure chemical ionization Fourier transform ion cyclotron resonance mass spectrometry for complex thiophenic mixture analysis

    Hourani, Nadim; Andersson, Jan T.; Mö ller, Isabelle; Amad, Maan H.; Witt, Matthí as; Sarathy, Mani

    2013-01-01

    oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same

  7. Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

    Guo, Ya; Tan, Jinglu

    2014-12-21

    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. Copyright © 2014 Elsevier Ltd. All rights reserved.

  8. Experimental demonstrations of the properties of Fourier transforms using diffraction phenomena

    Bazin, M.J.; Lucie, P.H.; Oliveira, S.M.M. de.

    1984-01-01

    The standard mathematical properties of Fourier transforms and the experimental characteristics of diffraction phenomena are systematically brought together. An experimental realization of a particular case of the convolution theorem is displayed in details. (Author) [pt

  9. Atomic and nuclear physics with stored particles in ion traps

    Kluge, H J; Herfurth, F; Quint, W

    2002-01-01

    Trapping and cooling techniques play an increasingly important role in many areas of science. This review concentrates on recent applications of ion traps installed at accelerator facilities to atomic and nuclear physics such as mass spectrometry of radioactive isotopes, weak interaction studies, symmetry tests, determination of fundamental constants, laser spectroscopy, and spectroscopy of highly-charged ions. In addition, ion traps are proven to be extremely efficient devices for (radioactive) ion beam manipulation as, for example, retardation, accumulation, cooling, beam cleaning, charge-breeding, and bunching.

  10. Pulse shaping using the optical Fourier transform technique - for ultra-high-speed signal processing

    Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

    2009-01-01

    This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment.......This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment....

  11. Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

    Park, J. H.

    1984-01-01

    An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

  12. Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

    Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

    2017-08-01

    Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

  13. OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation

    Palushani, Evarist; Richter, T.; Ludwig, R.

    2012-01-01

    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

    Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

    2011-01-01

    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. On integral and finite Fourier transforms of continuous q-Hermite polynomials

    Atakishiyeva, M. K.; Atakishiyev, N. M.

    2009-01-01

    We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

  16. A New Green Method for the Quantitative Analysis of Enrofloxacin by Fourier-Transform Infrared Spectroscopy.

    Rebouças, Camila Tavares; Kogawa, Ana Carolina; Salgado, Hérida Regina Nunes

    2018-05-18

    Background: A green analytical chemistry method was developed for quantification of enrofloxacin in tablets. The drug, a second-generation fluoroquinolone, was first introduced in veterinary medicine for the treatment of various bacterial species. Objective: This study proposed to develop, validate, and apply a reliable, low-cost, fast, and simple IR spectroscopy method for quantitative routine determination of enrofloxacin in tablets. Methods: The method was completely validated according to the International Conference on Harmonisation guidelines, showing accuracy, precision, selectivity, robustness, and linearity. Results: It was linear over the concentration range of 1.0-3.0 mg with correlation coefficients >0.9999 and LOD and LOQ of 0.12 and 0.36 mg, respectively. Conclusions: Now that this IR method has met performance qualifications, it can be adopted and applied for the analysis of enrofloxacin tablets for production process control. The validated method can also be utilized to quantify enrofloxacin in tablets and thus is an environmentally friendly alternative for the routine analysis of enrofloxacin in quality control. Highlights: A new green method for the quantitative analysis of enrofloxacin by Fourier-Transform Infrared spectroscopy was validated. It is a fast, clean and low-cost alternative for the evaluation of enrofloxacin tablets.

  17. A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

    Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com [Universidade Federal de São Paulo, Depto. Ciências Exatas e da Terra, Rua Prof. Arthur Riedel, 275, Jd. Eldorado, CEP 09972-270 Diadema, SP (Brazil)

    2014-12-10

    Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

  18. Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

    Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

    2012-01-01

    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.

  19. High-fidelity operations in microfabricated surface ion traps

    Maunz, Peter

    2017-04-01

    Trapped ion systems can be used to implement quantum computation as well as quantum simulation. To scale these systems to the number of qubits required to solve interesting problems in quantum chemistry or solid state physics, the use of large multi-zone ion traps has been proposed. Microfabrication enables the realization of surface electrode ion traps with complex electrode structures. While these traps may enable the scaling of trapped ion quantum information processing (QIP), microfabricated ion traps also pose several technical challenges. Here, we present Sandia's trap fabrication capabilities and characterize trap properties and shuttling operations in our most recent high optical access trap (HOA-2). To demonstrate the viability of Sandia's microfabricated ion traps for QIP we realize robust single and two-qubit gates and characterize them using gate set tomography (GST). In this way we are able to demonstrate the first single qubit gates with a diamond norm of less than 1 . 7 ×10-4 , below a rigorous fault tolerance threshold for general noise of 6 . 7 ×10-4. Furthermore, we realize Mølmer-Sørensen two qubit gates with a process fidelity of 99 . 58(6) % also characterized by GST. These results demonstrate the viability of microfabricated surface traps for state of the art quantum information processing demonstrations. This research was funded, in part, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA).

  20. Study of heliumlike neon using an electron beam ion trap

    Wargelin, B.J.; Kahn, S.M.; Beiersdorfer, P.

    1992-01-01

    The 2-to-1 spectra of several astrophysically abundant He-like ions are being studied using the Electron Beam Ion Trap (EBIT) at Lawrence Livermore National Laboratory. Spectra are recorded for a broad range of plasma parameters, including electron density, energy, and ionization balance. We describe the experimental equipment and procedure and present some typical data

  1. Atomic physics measurements in an electron Beam Ion Trap

    Marrs, R.E.; Beiersdorfer, P.; Bennett, C.

    1989-01-01

    An electron Beam Ion Trap at Lawrence Livermore National Laboratory is being used to produce and trap very-highly-charged ions (q ≤ 70/+/) for x-ray spectroscopy measurements. Recent measurements of transition energies and electron excitation cross sections for x-ray line emission are summarized. 13 refs., 10 figs

  2. Dielectronic recombination measurements using the Electron Beam Ion Trap

    Knapp, D.A.

    1991-01-01

    We have used the Electron Beam Ion Trap at LLNL to study dielectronic recombination in highly charged ions. Our technique is unique because we observe the x-rays from dielectronic recombination at the same time we see x-rays from all other electron-ion interactions. We have recently taken high-resolution, state-selective data that resolves individual resonances

  3. Authentication of edible vegetable oils adulterated with used frying oil by Fourier Transform Infrared Spectroscopy.

    Zhang, Qing; Liu, Cheng; Sun, Zhijian; Hu, Xiaosong; Shen, Qun; Wu, Jihong

    2012-06-01

    The application of Fourier Transform Infrared (FTIR) Spectroscopy to authenticate edible vegetable oils (corn, peanut, rapeseed and soybean oil) adulterated with used frying oil was introduced in this paper. The FTIR spectrum of oil was divided into 22 regions which corresponded to the constituents and molecular structures of vegetable oils. Samples of calibration set were classified into four categories for corn and peanut oils and five categories for rapeseed and soybean oils by cluster analysis. Qualitative analysis of validation set was obtained by discriminant analysis. Area ratio between absorption band 19 and 20 and wavenumber shift of band 19 were treated by linear regression for quantitative analysis. For four adulteration types, LODs of area ratio were 6.6%, 7.2%, 5.5%, 3.6% and wavenumber shift were 8.1%, 9.0%, 6.9%, 5.6%, respectively. The proposed methodology is a useful tool to authenticate the edible vegetable oils adulterated with used frying oil. Copyright © 2011 Elsevier Ltd. All rights reserved.

  4. Adaptive ISAR Imaging of Maneuvering Targets Based on a Modified Fourier Transform.

    Wang, Binbin; Xu, Shiyou; Wu, Wenzhen; Hu, Pengjiang; Chen, Zengping

    2018-04-27

    Focusing on the inverse synthetic aperture radar (ISAR) imaging of maneuvering targets, this paper presents a new imaging method which works well when the target's maneuvering is not too severe. After translational motion compensation, we describe the equivalent rotation of maneuvering targets by two variables-the relative chirp rate of the linear frequency modulated (LFM) signal and the Doppler focus shift. The first variable indicates the target's motion status, and the second one represents the possible residual error of the translational motion compensation. With them, a modified Fourier transform matrix is constructed and then used for cross-range compression. Consequently, the imaging of maneuvering is converted into a two-dimensional parameter optimization problem in which a stable and clear ISAR image is guaranteed. A gradient descent optimization scheme is employed to obtain the accurate relative chirp rate and Doppler focus shift. Moreover, we designed an efficient and robust initialization process for the gradient descent method, thus, the well-focused ISAR images of maneuvering targets can be achieved adaptively. Human intervention is not needed, and it is quite convenient for practical ISAR imaging systems. Compared to precedent imaging methods, the new method achieves better imaging quality under reasonable computational cost. Simulation results are provided to validate the effectiveness and advantages of the proposed method.

  5. A high-speed computerized tomography image reconstruction using direct two-dimensional Fourier transform method

    Niki, Noboru; Mizutani, Toshio; Takahashi, Yoshizo; Inouye, Tamon.

    1983-01-01

    The nescessity for developing real-time computerized tomography (CT) aiming at the dynamic observation of organs such as hearts has lately been advocated. It is necessary for its realization to reconstruct the images which are markedly faster than present CTs. Although various reconstructing methods have been proposed so far, the method practically employed at present is the filtered backprojection (FBP) method only, which can give high quality image reconstruction, but takes much computing time. In the past, the two-dimensional Fourier transform (TFT) method was regarded as unsuitable to practical use because the quality of images obtained was not good, in spite of the promising method for high speed reconstruction because of its less computing time. However, since it was revealed that the image quality by TFT method depended greatly on interpolation accuracy in two-dimensional Fourier space, the authors have developed a high-speed calculation algorithm that can obtain high quality images by pursuing the relationship between the image quality and the interpolation method. In this case, radial data sampling points in Fourier space are increased to β-th power of 2 times, and the linear or spline interpolation is used. Comparison of this method with the present FBP method resulted in the conclusion that the image quality is almost the same in practical image matrix, the computational time by TFT method becomes about 1/10 of FBP method, and the memory capacity also reduces by about 20 %. (Wakatsuki, Y.)

  6. Economical Appraisal of Total Aflatoxin Level in the Poultry Feeds by Fourier Transform Infrared Spectroscopy

    Sherazai, S.T.H.; Shar, Z.; Iqbal, M.; Sumbal, G.A.

    2013-01-01

    Single-bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopy has been used for the quantitative determination of total aflatoxins in the broiler poultry feed. An FTIR calibration spanning the range 1-70 micro g/L aflatoxin standards in (70:30, v/v) methanol-water solvent system based on partial least square (PLS) model, developed by relating mid IR region between 3755-950 cm/ sub -1/. The excellent coefficient of various (using 0.998) was achieved with 1.49 relative mean square error of calibration (RMSEC). Aflatoxins from each of eight poultry feeds was extracted and the determined by the widely used commercially available Enzyme-linked Immunosorbent Assay (ELISA) procedure and the SB-ATR/FTIR method. The SB-ATR/FTIR aflatoxins predictions were related to those determined by the ELISA method by linear regression, producing an R value of 0.989 and a SD of +- 2.80 micro g/L. The result of the study clearly indicated that FT-IR spectroscopy due to its rapidity and simplicity along with data manipulation by advance computer software could be effectively used for routine determination of aflatoxins present in the poultry feeds at very low level. (author)

  7. Detection of Life Threatening Ventricular Arrhythmia Using Digital Taylor Fourier Transform.

    Tripathy, Rajesh K; Zamora-Mendez, Alejandro; de la O Serna, José A; Paternina, Mario R Arrieta; Arrieta, Juan G; Naik, Ganesh R

    2018-01-01

    Accurate detection and classification of life-threatening ventricular arrhythmia episodes such as ventricular fibrillation (VF) and rapid ventricular tachycardia (VT) from electrocardiogram (ECG) is a challenging problem for patient monitoring and defibrillation therapy. This paper introduces a novel method for detection and classification of life-threatening ventricular arrhythmia episodes. The ECG signal is decomposed into various oscillatory modes using digital Taylor-Fourier transform (DTFT). The magnitude feature and a novel phase feature namely the phase difference (PD) are evaluated from the mode Taylor-Fourier coefficients of ECG signal. The least square support vector machine (LS-SVM) classifier with linear and radial basis function (RBF) kernels is employed for detection and classification of VT vs. VF, non-shock vs. shock and VF vs. non-VF arrhythmia episodes. The accuracy, sensitivity, and specificity values obtained using the proposed method are 89.81, 86.38, and 93.97%, respectively for the classification of Non-VF and VF episodes. Comparison with the performance of the state-of-the-art features demonstrate the advantages of the proposition.

  8. Attenuated total internal reflection Fourier transform infrared spectroscopy: a quantitative approach for kidney stone analysis.

    Gulley-Stahl, Heather J; Haas, Jennifer A; Schmidt, Katherine A; Evan, Andrew P; Sommer, André J

    2009-07-01

    The impact of kidney stone disease is significant worldwide, yet methods for quantifying stone components remain limited. A new approach requiring minimal sample preparation for the quantitative analysis of kidney stone components has been investigated utilizing attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FT-IR). Calcium oxalate monohydrate (COM) and hydroxylapatite (HAP), two of the most common constituents of urinary stones, were used for quantitative analysis. Calibration curves were constructed using integrated band intensities of four infrared absorptions versus concentration (weight %). The correlation coefficients of the calibration curves range from 0.997 to 0.93. The limits of detection range from 0.07 +/- 0.02% COM/HAP where COM is the analyte and HAP is the matrix, to 0.26 +/- 0.07% HAP/COM where HAP is the analyte and COM is the matrix. This study shows that linear calibration curves can be generated for the quantitative analysis of stone mixtures provided the system is well understood especially with respect to particle size.

  9. Automated Gain Control and Internal Calibration With External Ion Accumulation Capillary liquid chromatography-electrospray ionization-fourier transform ion cyclotron resonance.

    Belov, Mikhail E.(VISITORS); Zhang, Rui (BATTELLE (PACIFIC NW LAB)); Strittmatter, Eric F.(BATTELLE (PACIFIC NW LAB)); Prior, David C.(BATTELLE (PACIFIC NW LAB)); Tang, Keqi (BATTELLE (PACIFIC NW LAB)); Smith, Richard D.(BATTELLE (PACIFIC NW LAB))

    2003-08-15

    When combined with capillary LC separations, Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (ESI-FTICR MS) has increasingly been applied for advanced characterization of proteolytic digests. Incorporation of external (to the ICR cell) ion accumulation multipoles with FTICR for ion pre selection and accumulation has enhanced the dynamic range, sensitivity and duty cycle of measurements. However, the highly variable ion production rate from an LC separation can result in overfilling of the external trap, resulting in m/z discrimination and fragmentation of peptide ions. An excessive space charge trapped in the ICR cell causes significant shifts in the detected ion cyclotron frequencies, reducing the achievable mass measurement accuracy (MMA) for protein identification. To eliminate m/z discrimination in the external ion trap, further increase the duty cycle and improve MMA, we developed a capability for data-dependent adjustment of ion accumulation times in the course of an LC separation, referred to as Automated Gain Control (AGC), in combination with low kinetic energy gated ion trapping and internal calibration using a dual-channel electrodynamic ion funnel. The system was initially evaluated in the analysis of a 0.5 mg/mL tryptic digest of bovine serum albumin. The implementation of LC/ESI/AGC/FTICR with internal calibration gave rise to a {approx} 10-fold increase in the number of identified tryptic peptides within mass measurement accuracy of 2 ppm as compared to that detected during the conventional LC/FTICR run with a fixed ion accumulation time and external calibration.

  10. Reconstruction of on-axis lensless Fourier transform digital hologram with the screen division method

    Jiang, Hongzhen; Liu, Xu; Liu, Yong; Li, Dong; Chen, Zhu; Zheng, Fanglan; Yu, Deqiang

    2017-10-01

    An effective approach for reconstructing on-axis lensless Fourier Transform digital hologram by using the screen division method is proposed. Firstly, the on-axis Fourier Transform digital hologram is divided into sub-holograms. Then the reconstruction result of every sub-hologram is obtained according to the position of corresponding sub-hologram in the hologram reconstruction plane with Fourier transform operation. Finally, the reconstruction image of on-axis Fourier Transform digital hologram can be acquired by the superposition of the reconstruction result of sub-holograms. Compared with the traditional reconstruction method with the phase shifting technology, in which multiple digital holograms are required to record for obtaining the reconstruction image, this method can obtain the reconstruction image with only one digital hologram and therefore greatly simplify the recording and reconstruction process of on-axis lensless Fourier Transform digital holography. The effectiveness of the proposed method is well proved with the experimental results and it will have potential application foreground in the holographic measurement and display field.

  11. Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

    Kobayashi, Keisuke

    1975-01-01

    The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

  12. Correlation between Onset Oxidation Temperature (OOT) and Fourier Transform Infrared Spectroscopy (FTIR) for monitoring the restabilization of Recycled Low-density Polyethylene (LDPE)

    Ruvolo-Filho, Adhemar; Pelozzi, Tadeu Luiz Alonso, E-mail: adhemar@power.ufscar.br [Universidade Federal de Sao Carlos (UFSCar), SP (Brazil). Departamento de Quimica

    2013-07-01

    In this work a new method was developed for monitoring the oxidative stability of restabilized and non-restabilized low-density polyethylene (LDPE) during multiple extrusion cycles. The method is based on correlations between Fourier Transform Infrared Spectroscopy (FTIR) and Onset Oxidation Temperature (OOT). Non-linear calibration curves correlating the concentration of primary or secondary antioxidants and the OOT values were obtained. (author)

  13. Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap

    Schulz, Stephan A; Poschinger, Ulrich; Ziesel, Frank; Schmidt-Kaler, Ferdinand [Universitaet Ulm, Institut fuer Quanteninformationsverarbeitung, Albert-Einstein-Allee 11, D-89069 Ulm (Germany)], E-mail: stephan.schulz@uni-ulm.de

    2008-04-15

    Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap into different storage and processing zones. The individual position control of many ions-each of them carrying qubit information in its long-lived electronic levels-by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms. We present a novel scalable microchip multi-segmented ion trap with two different adjacent zones, one for the storage and another dedicated to the processing of quantum information using single ions and linear ion crystals. A pair of radio-frequency-driven electrodes and 62 independently controlled dc electrodes allows shuttling of single ions or linear ion crystals with numerically designed axial potentials at axial and radial trap frequencies of a few megahertz. We characterize and optimize the microtrap using sideband spectroscopy on the narrow S{sub 1/2}{r_reversible}D{sub 5/2} qubit transition of the {sup 40}Ca{sup +} ion, and demonstrate coherent single-qubit Rabi rotations and optical cooling methods. We determine the heating rate using sideband cooling measurements to the vibrational ground state, which is necessary for subsequent two-qubit quantum logic operations. The applicability for scalable quantum information processing is proved.

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

    Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

    2011-01-01

    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.

  15. Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

    Holmes, J. J.; Balanis, C. A.

    1974-01-01

    Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

  16. Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

    Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

    2014-01-01

    A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

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

    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

    2015-12-01

    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. Graphical Abstract ᅟ.

  18. Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

    Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net [NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)

    2017-04-10

    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.

  19. Functional differential equations for the q-Fourier transform of q-Gaussians

    Umarov, S; Queiros, S M Duarte

    2010-01-01

    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.

  20. Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

    Huang, Lin; Lenells, Jonatan

    2018-03-01

    Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.

  1. Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

    Dovlo, Edem; Baddour, Natalie

    2015-01-01

    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.

  2. Functional differential equations for the q-Fourier transform of q-Gaussians

    Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

    2010-02-05

    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.

  3. Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

    Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

    2017-01-01

    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.

  4. Algorithm for three dimension reconstruction of magnetic resonance tomographs and X-ray images based on Fast Fourier Transform

    Bueno, Josiane M.; Traina, Agma Juci M.; Cruvinel, Paulo E.

    1995-01-01

    This work presents an algorithm for three-dimensional digital image reconstruction. Such algorithms based on the combination of both a Fast Fourier Transform method with Hamming Window and the use of a tri-linear interpolation function. The algorithm allows not only the generation of three-dimensional spatial spin distribution maps for Magnetic Resonance Tomography data but also X and Y-rays linear attenuation coefficient maps for CT scanners. Results demonstrates the usefulness of the algorithm in three-dimensional image reconstruction by doing first two-dimensional reconstruction and rather after interpolation. The algorithm was developed in C++ language, and there are two available versions: one under the DOS environment, and the other under the UNIX/Sun environment. (author)

  5. Ion trapping in the high-energy storage ring HESR

    Hinterberger, Frank [Bonn Univ. (Germany). Helmholtz-Institut fuer Strahlen- und Kernphysik

    2011-10-15

    The problem of ion trapping in the high-energy storage ring HESR is studied in the present report. Positive ions are trapped in the negative potential well of the antiproton beam. The ions are produced by the interaction between the antiproton beam and the residual gas. The adverse effects of ion trapping like tune shifts, tune spreads and coherent instabilities are reviewed. The ion production rate by ionization of the residual gas molecules is estimated. The negative potential well and the corresponding electric fields of the antiproton beam are evaluated in order to study the transverse and longitudinal motion of the ions and the accumulation in trapping pockets. The removal of ions can be achieved using clearing electrodes and under certain conditions resonant transverse beam shaking. Diagnostic tools and measurements of trapped ion effects are sketched. (orig.)

  6. Single Ion Trapping for the Enriched Xenon Observatory

    Waldman, Samuel J.; /Stanford U., Phys. Dept. /SLAC

    2006-03-28

    In the last decade, a variety of neutrino oscillation experiments have established that there is a mass difference between neutrino flavors, without determining the absolute neutrino mass scale. The Enriched Xenon Observatory for neutrinoless double beta decay (EXO) will search for the rare decays of xenon to determine the absolute value of the neutrino mass. The experiment uses a novel technique to minimize backgrounds, identifying the decay daughter product in real time using single ion spectroscopy. Here, we describe single ion trapping and spectroscopy compatible with the EXO detector. We extend the technique of single ion trapping in ultrahigh vacuum to trapping in xenon gas. With this technique, EXO will achieve a neutrino mass sensitivity of {approx_equal} .010 eV.

  7. Advanced ion trap structures with integrated tools for qubit manipulation

    Sterk, J. D.; Benito, F.; Clark, C. R.; Haltli, R.; Highstrete, C.; Nordquist, C. D.; Scott, S.; Stevens, J. E.; Tabakov, B. P.; Tigges, C. P.; Moehring, D. L.; Stick, D.; Blain, M. G.

    2012-06-01

    We survey the ion trap fabrication technologies available at Sandia National Laboratories. These include four metal layers, precision backside etching, and low profile wirebonds. We demonstrate loading of ions in a variety of ion traps that utilize these technologies. Additionally, we present progress towards integration of on-board filtering with trench capacitors, photon collection via an optical cavity, and integrated microwave electrodes for localized hyperfine qubit control and magnetic field gradient quantum gates. [4pt] This work was supported by Sandia's Laboratory Directed Research and Development (LDRD) Program and the Intelligence Advanced Research Projects Activity (IARPA). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  8. Overview of the Livermore electron beam ion trap project

    Beiersdorfer, P.; Behar, E.; Boyce, K.R.; Brown, G.V.; Chen, H.; Gendreau, K.C.; Graf, A.; Gu, M.-F.; Harris, C.L.; Kahn, S.M.; Kelley, R.L.; Lepson, J.K.; May, M.J.; Neill, P.A.; Pinnington, E.H.; Porter, F.S.; Smith, A.J.; Stahle, C.K.; Szymkowiak, A.E.; Tillotson, A.; Thorn, D.B.; Traebert, E.; Wargelin, B.J.

    2003-01-01

    The Livermore electron beam ion trap facility has recently been moved to a new location within LLNL, and new instrumentation was added, including a 32-pixel microcalorimeter. The move was accompanied by a shift of focus toward in situ measurements of highly charged ions, which continue with increased vigor. Overviews of the facility, which includes EBIT-I and SuperEBIT, and the research projects are given, including results from optical spectroscopy, QED, and X-ray line excitation measurements

  9. Paul Ion Trap as a Diagnostic for Plasma Focus

    Sadat Kiai, S. M.; Adlparvar, S.; Zirak, A.; Alhooie, Samira; Elahi, M.; Sheibani, S.; Safarien, A.; Farhangi, S.; Dabirzadeh, A. A.; Khalaj, M. M.; Mahlooji, M. S.; KaKaei, S.; Talaei, A.; Kashani, A.; Tajik Ahmadi, H.; Zahedi, F.

    2010-02-01

    The plasma discharge contamination by high and low Z Impurities affect the rate of nuclear fusion reaction products, specially when light particles have to be confined. These impurities should be analyzed and can be fairly controlled. This paper reports on the development of a Paul ion trap with ion sources by impact electron ionization as a diagnostic for the 10 kJ Iranian sunshine plasma focus device. Preliminary results of the residual gas are analyzed and presented.

  10. Space-charge effects in Penning ion traps

    Porobic, T.; Beck, M.; Breitenfeldt, M.; Couratin, C.; Finlay, P.; Knecht, A.; Fabian, X.; Friedag, P.; Flechard, X.; Lienard, E.; Ban, G.; Zákoucký, Dalibor; Soti, G.; Van Gorp, S.; Weinheimer, C.; Wursten, E.; Severijns, N.

    2015-01-01

    Roč. 785, JUN (2015), s. 153-162 ISSN 0168-9002 R&D Projects: GA MŠk LA08015; GA MŠk(CZ) LG13031 Institutional support: RVO:61389005 Keywords : Penning trap * space-charge * magnetron motion * ion trapping * buffer gas cooling * ion cyclotron resonance Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.200, year: 2015

  11. Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

    Kobayashi, Keisuke; Ishibashi, Hideo

    1978-01-01

    A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

  12. Simple example of track finding by Fourier transform and possibilities for vector or optical processors

    Underwood, D.

    1986-01-01

    Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs

  13. The Fourier transform as a signature for chaos in nuclear energy levels

    Bybee, C.R.; Mitchell, G.E.; Shriner, J.F. Jr.

    1996-01-01

    The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)

  14. OTDM-WDM Conversion Based on Time-Domain Optical Fourier Transformation with Spectral Compression

    Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

    2011-01-01

    We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown.......We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown....

  15. Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

    Aerts, Diederik; Czachor, Marek; Kuna, Maciej

    2016-01-01

    Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

  16. Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

    Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

    2009-05-01

    Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

  17. Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

    Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning

    2009-01-01

    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 3 O 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.

  18. Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

    Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

    2018-05-01

    In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

  19. Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

    Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

    2009-06-01

    Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

  20. Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

    Darian M. Onchiș

    2011-09-01

    Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

  1. Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

    Kobayashi, Keisuke

    1975-01-01

    A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

  2. Physiological response of Arundo donax to cadmium stress by Fourier transform infrared spectroscopy.

    Yu, Shunhui; Sheng, Li; Zhang, Chunyan; Deng, Hongping

    2018-06-05

    The present paper deals with the physiological response of the changes in chemical contents of the root, stem and leaf of Arundo donax seedlings stressed by excess cadmium using Fourier transform infrared spectroscopy technique, cadmium accumulation in plant by atomic absorption spectroscopy were tested after different concentrations cadmium stress. The results showed that low cadmium concentrations (Fourier transform infrared spectroscopy technique for the non-invasive and rapid monitoring of the plants stressed with heavy metals, Arundo donax is suitable for phytoremediation of cadmium -contaminated wetland. Copyright © 2018 Elsevier B.V. All rights reserved.

  3. Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware

    Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard

    2008-01-01

    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...

  4. DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation

    Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael

    2011-01-01

    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....

  5. All-optical WDM Regeneration of DPSK Signals using Optical Fourier Transformation and Phase Sensitive Amplification

    Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian

    2015-01-01

    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....

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

    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)

    1995-02-01

    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. The Fourier transform as a signature for chaos in nuclear energy levels

    Bybee, C.R. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Mitchell, G.E. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Shriner, J.F. Jr. [Tennessee Technological Univ., Cookeville (United States)

    1996-08-01

    The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)

  8. Systems and Methods for Ejection of Ions from an Ion Trap

    Cooks, Robert Graham (Inventor); Snyder, Dalton (Inventor)

    2018-01-01

    The invention generally relates to systems and methods for ejection of ions from an ion trap. In certain embodiments, systems and methods of the invention sum two different frequency signals into a single summed signal that is applied to an ion trap. In other embodiments, an amplitude of a single frequency signal is modulated as the single frequency signal is being applied to the ion trap. In other embodiments, a first alternating current (AC) signal is applied to an ion trap that varies as a function of time, while a constant radio frequency (RF) signal is applied to the ion trap.

  9. The Performance and Scientific Rationale for an Infrared Imaging Fourier Transform Spectrograph on a Large Space Telescope

    Graham, James R; Abrams, Mark; Bennett, C; Carr, J; Cook, K; Dey, A; Najita, J; Wishnow, E

    1998-01-01

    .... We consider the relationship between pixel size, spectral resolution, and diameter of the beam splitter for imaging and nonimaging Fourier transform spectrographs and give the condition required...

  10. Slow Light Based On-Chip High Resolution Fourier Transform Spectrometer For Geostationary Imaging of Atmospheric Greenhouse Gases, Phase I

    National Aeronautics and Space Administration — Fourier transform spectroscopy (FTS) in infrared wavelength range is an effective measure for global greenhouse gas monitoring. However, conventional FTS instruments...

  11. Determining Energies and Cross Sections of Individual Ions Using Higher-Order Harmonics in Fourier Transform Charge Detection Mass Spectrometry (FT-CDMS).

    Harper, Conner C; Elliott, Andrew G; Lin, Haw-Wei; Williams, Evan R

    2018-06-02

    A general method for in situ measurements of the energy of individual ions trapped and weighed using charge detection mass spectrometry (CDMS) is described. Highly charged (> 300 e), individual polyethylene glycol (PEG) ions are trapped and oscillate within an electrostatic trap, producing a time domain signal. A segmented Fourier transform (FT) of this signal yields the temporal evolution of the fundamental and harmonic frequencies of ion motion throughout the 500-ms trap time. The ratio of the fundamental frequency and second harmonic (HAR) depends on the ion energy, which is an essential parameter for measuring ion mass in CDMS. This relationship is calibrated using simulated ion signals, and the calibration is compared to the HAR values measured for PEG ion signals where the ion energy was also determined using an independent method that requires that the ions be highly charged (> 300 e). The mean error of 0.6% between the two measurements indicates that the HAR method is an accurate means of ion energy determination that does not depend on ion size or charge. The HAR is determined dynamically over the entire trapping period, making it possible to observe the change in ion energy that takes place as solvent evaporates from the ion and collisions with background gas occur. This method makes it possible to measure mass changes, either from solvent evaporation or from molecular fragmentation (MS n ), as well as the cross sections of ions measured using CDMS. Graphical Abstract.

  12. Does the entorhinal cortex use the Fourier transform?

    Orchard, Jeff; Yang, Hao; Ji, Xiang

    2013-01-01

    Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415

  13. Vibrational analysis of Fourier transform spectrum of the B u )–X g ...

    improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and r-centroid values. Keywords. Fourier transform spectroscopy; electronic spectrum of selenium dimer; vibrational analysis; Franck–Condon factor; r-centroid values.

  14. Vibrational analysis of Fourier transform spectrum of the B 3− u (0

    ... microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and -centroid values.

  15. PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

    Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...

  16. Fourier-transform ghost imaging with pure far-field correlated thermal light

    Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming

    2007-01-01

    Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed

  17. Direct fourier method reconstruction based on unequally spaced fast fourier transform

    Wu Xiaofeng; Zhao Ming; Liu Li

    2003-01-01

    First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)

  18. Ion-cyclotron-resonance- and Fourier-transform-ion-cyclotron-resonance spectroscopy: technology and application

    Luederwald, I.

    1977-01-01

    Instrumentation and technology of Ion-Cyclotron-Resonance and Fourier-Transform-Ion-Cyclotron-Resonance Spectroscopy are described. The method can be applied to studies of ion/molecule reactions in gas phase, to obtain thermodynamic data as gas phase acidity or basicity, proton and electron affinity, and to establish reaction mechanisms and ion structures. (orig.) [de

  19. Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

    Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

    1977-01-01

    An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

  20. Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix

    Antoon, M. K.; Starkey, K. M.; Koenig, J. L.

    1979-01-01

    The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.

  1. The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.

    Suslick, Kenneth S.; And Others

    1987-01-01

    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)

  2. Application of Local Fourier Transform to Mathematical Simulation of Synchronous Machines with Valve Excitation Systems

    Fedotov A.

    2017-02-01

    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.

  3. Flexibility of three differential constitutive models evaluated by large amplitude oscillatory shear and Fourier transform rheology

    Pivokonský, Radek; Filip, Petr; Zelenková, Jana

    2016-01-01

    Roč. 104, č. 8 (2016), s. 171-178 ISSN 0032-3861 Institutional support: RVO:67985874 Keywords : LAOS * fourier transform rheology * Giesekus model * PTT model * modified XPP model * poly(ethylene oxide) Subject RIV: BK - Fluid Dynamics Impact factor: 3.684, year: 2016

  4. Fourier transform infrared emission spectra of atomic rubidium: g- and h-states

    Civiš, Svatopluk; Ferus, Martin; Kubelík, Petr; Chernov, Vladislav E.; Zanozina, Ekaterina M.

    2012-01-01

    Roč. 45, č. 17 (2012), s. 175002 ISSN 0953-4075 R&D Projects: GA AV ČR IAAX00100903 Institutional support: RVO:61388955 Keywords : Fourier transform infrared emission spectra * atomic rubidium * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.031, year: 2012

  5. Reduction and coding of synthetic aperture radar data with Fourier transforms

    Tilley, David G.

    1995-01-01

    Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

  6. Development of secondary cell wall in cotton fibers as examined with Fourier transform-infrared spectroscopy

    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-...

  7. Limitations and potential of spectral subtractions in fourier-transform infrared (FTIR) spectroscopy of soil samples

    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...

  8. Description of the electron-hydrogen collision by the Coulomb Fourier transform method

    Levin, S.B.

    2005-01-01

    A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals

  9. On the Elliptic Nonabelian Fourier Transform for Unipotent Representations of p-Adic Groups

    Ciubotaru, D.; Opdam, E.; Cogdell, J.; Kim, J.-L.; Zhu, C.-B.

    2017-01-01

    In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these

  10. Fourier transform and the Verlinde formula for the quantum double of a finite group

    Koornwinder, T.H.; Schroers, B.J.; Slingerland, J.K.; Bais, F.A.

    1999-01-01

    We define a Fourier transform $S$ for the quantum double $D(G)$ of a finite group $G$. Acting on characters of $D(G)$, $S$ and the central ribbon element of $D(G)$ generate a unitary matrix representation of the group $SL(2,Z)$. The characters form a ring over the integers under both the algebra

  11. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam

    Nicolas, F.; Coëtmellec, S.; Brunel, M.; Allano, D.; Lebrun, D.; Janssen, A.J.E.M.

    2005-01-01

    The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by

  12. On the oxidation mechanism of microcrystalline silicon thin films studied by Fourier transform infrared spectroscopy

    Bronneberg, A. C.; Smets, A. H. M.; Creatore, M.; M. C. M. van de Sanden,

    2011-01-01

    Insight into the oxidation mechanism of microcrystalline silicon thin films has been obtained by means of Fourier transform infrared spectroscopy. The films were deposited by using the expanding thermal plasma and their oxidation upon air exposure was followed in time. Transmission spectra were

  13. 16 channel WDM regeneration in a single phase-sensitive amplifier through optical Fourier transformation

    Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads

    2016-01-01

    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. Superexponentially damped Vlasov plasma oscillations in the Fourier transformed velocity space

    Sedlacek, Z.; Nocera, L.

    2002-01-01

    The Landau (exponentially) damped solutions of the Vlasov-Poisson equation Fourier transformed with respect to velocity are genuine eigenmodes corresponding to complex eigenvalues. In addition there exist solutions decaying faster than exponentially which exhibit no oscillatory behaviour. A new characterization is given of the initial conditions that give rise to these solutions together with a numerical demonstration

  15. Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

    Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

    2018-02-01

    Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

  16. Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

    Lin, Sian-Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.; Chung, Wei-Ho

    2016-01-01

    In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h

  17. Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

    Dong Ping; Yang Ming; Cao Zhuoliang

    2008-01-01

    In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

  18. Specification of the Fast Fourier Transform algorithm as a term rewriting system

    Rodenburg, P.H.; Hoekzema, D.J.

    1987-01-01

    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

  19. From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation

    Bastiaans, M.J.; Leest, van A.J.

    1998-01-01

    Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function,

  20. Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

    Bastiaans, M.J.; Leest, van A.J.

    1998-01-01

    Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays

  1. Rotation-type input-output relationships for Wigner distribution moments in fractional Fourier transform systems

    Bastiaans, M.J.; Alieva, T.

    2002-01-01

    It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. This general input-output relationship is then broken down into a

  2. Orthonormal mode sets for the two-dimensional fractional Fourier transformation

    Alieva, T.; Bastiaans, M.J.

    2007-01-01

    A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

  3. A fast Fourier transform program for the deconvolution of IN10 data

    Howells, W.S.

    1981-04-01

    A deconvolution program based on the Fast Fourier Transform technique is described and some examples are presented to help users run the programs and interpret the results. Instructions are given for running the program on the RAL IBM 360/195 computer. (author)

  4. 3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

    Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl

    2013-01-01

    We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...

  5. On the measurement of Wigner distribution moments in the fractional Fourier transform domain

    Bastiaans, M.J.; Alieva, T.

    2002-01-01

    It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed

  6. Fourier-transform imaging of cotton and botanical and field trash mixtures

    Botanical and field cotton trash comingled with cotton lint can greatly reduce the marketability and quality of cotton. Trash can be found comingled with cotton lint during harvesting, ginning, and processing, thus this study is of interest. Attenuated Total Reflectance-Fourier Transform Infrared (A...

  7. Study of cancer cell lines with Fourier transform infrared (FTIR)/vibrational absorption (VA) spectroscopy

    Uceda Otero, E. P.; Eliel, G. S. N.; Fonseca, E. J. S.

    2013-01-01

    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...

  8. Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

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

    2010-01-01

    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…

  9. Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

    Miao, J.; Sayre, D.; Chapman, H.N.

    1998-01-01

    It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2x in each dimension (i.e., oversampling by 4x for 2D and 8x for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. copyright 1998 Optical Society of America

  10. Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

    Freedman, Michael H.; Wang, Zhenghan

    2007-01-01

    Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks

  11. 1.28 Tbaud Nyquist Signal Transmission using Time-Domain Optical Fourier Transformation based Receiver

    Hu, Hao; Kong, Deming; Palushani, Evarist

    2013-01-01

    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....

  12. Imaging properties of the mesooptical Fourier transform microscope for nuclear research emulsion

    Bencze, Gy.L.; Soroko, L.M.

    1987-01-01

    The optical signal transformation in the Mesooptical Fourier Transform Microscope (MFTM) for nuclear emulsion is treated in terms of Fourier Optics. A continuous conversion of the traditional optical microscope into the MFTM is followed. The images of dot-like and straight line objects given by the MFTM are discussed

  13. High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation

    Watanabe, A.; Furukawa, H.

    2018-04-01

    The resolution of multichannel Fourier transform (McFT) spectroscopy is insufficient for many applications despite its extreme advantage of high throughput. We propose an improved configuration to realise both performance using a two-dimensional area sensor. For the spectral resolution, we obtained the interferogram of a larger optical path difference by shifting the area sensor without altering any optical components. The non-linear phase error of the interferometer was successfully corrected using a phase-compensation calculation. Warping compensation was also applied to realise a higher throughput to accumulate the signal between vertical pixels. Our approach significantly improved the resolution and signal-to-noise ratio by factors of 1.7 and 34, respectively. This high-resolution and high-sensitivity McFT spectrometer will be useful for detecting weak light signals such as those in non-invasive diagnosis.

  14. Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

    Ermilov, A. S.; Zobov, V. E.

    2007-12-01

    To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.

  15. All-optical signal processing of OTDM and OFDM signals based on time-domain optical fourier transformation

    Galili, Michael; Guan, Pengyu; Lillieholm, Mads

    2017-01-01

    In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed.......In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed....

  16. On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity

    Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.

    2008-01-01

    It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

  17. q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity

    Atakishiyeva, M.K.; Atakishiyev, N.M.; Koornwinder, T.H.

    2009-01-01

    It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

  18. All-optical signal processing of OTDM and OFDM signals based on time-domain Optical Fourier Transformation

    Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen

    2014-01-01

    All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....

  19. Space-charge effects in Penning ion traps

    Porobić, T.; Beck, M.; Breitenfeldt, M.; Couratin, C.; Finlay, P.; Knecht, A.; Fabian, X.; Friedag, P.; Fléchard, X.; Liénard, E.; Ban, G.; Zákoucký, D.; Soti, G.; Van Gorp, S.; Weinheimer, Ch.; Wursten, E.; Severijns, N.

    2015-06-01

    The influence of space-charge on ion cyclotron resonances and magnetron eigenfrequency in a gas-filled Penning ion trap has been investigated. Off-line measurements with K39+ using the cooling trap of the WITCH retardation spectrometer-based setup at ISOLDE/CERN were performed. Experimental ion cyclotron resonances were compared with ab initio Coulomb simulations and found to be in agreement. As an important systematic effect of the WITCH experiment, the magnetron eigenfrequency of the ion cloud was studied under increasing space-charge conditions. Finally, the helium buffer gas pressure in the Penning trap was determined by comparing experimental cooling rates with simulations.

  20. Applying Kitaev's algorithm in an ion trap quantum computer

    Travaglione, B.; Milburn, G.J.

    2000-01-01

    Full text: Kitaev's algorithm is a method of estimating eigenvalues associated with an operator. Shor's factoring algorithm, which enables a quantum computer to crack RSA encryption codes, is a specific example of Kitaev's algorithm. It has been proposed that the algorithm can also be used to generate eigenstates. We extend this proposal for small quantum systems, identifying the conditions under which the algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate a simple example, in which the algorithm effectively generates eigenstates

  1. First experiments with the Greifswald electron-beam ion trap

    Schabinger, B.; Biedermann, C.; Gierke, S.; Marx, G.; Radtke, R.; Schweikhard, L.

    2013-09-01

    The former Berlin electron-beam ion trap (EBIT) was moved to Greifswald. In addition to x-ray studies the setup will be used for the investigation of interaction processes between highly charged ions and atomic clusters such as charge exchange and fragmentation. The EBIT setup has now been reassembled and highly charged ions have been produced from Xe-Ar gas mixtures to study the ‘sawtooth effect’. In addition, the layout of the extraction beamline, the interaction region and product analysis for interaction studies with highly charged ions are presented.

  2. Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

    Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

    2015-10-20

    In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

  3. Using Fourier transform infrared spectroscopy to evaluate biological effects induced by photodynamic therapy.

    Lima, Cassio A; Goulart, Viviane P; Correa, Luciana; Zezell, Denise M

    2016-07-01

    Vibrational spectroscopic methods associated with multivariate statistical techniques have been succeeded in discriminating skin lesions from normal tissues. However, there is no study exploring the potential of these techniques to assess the alterations promoted by photodynamic effect in tissue. The present study aims to demonstrate the ability of Fourier Transform Infrared (FTIR) spectroscopy on Attenuated total reflection (ATR) sampling mode associated with principal component-linear discriminant analysis (PC-LDA) to evaluate the biochemical changes caused by photodynamic therapy (PDT) in skin neoplastic tissue. Cutaneous neoplastic lesions, precursors of squamous cell carcinoma (SCC), were chemically induced in Swiss mice and submitted to a single session of 5-aminolevulinic acid (ALA)-mediated PDT. Tissue sections with 5 μm thickness were obtained from formalin-fixed paraffin-embedded (FFPE) and processed prior to the histopathological analysis and spectroscopic measurements. Spectra were collected in mid-infrared region using a FTIR spectrometer on ATR sampling mode. Principal Component-Linear Discriminant Analysis (PC-LDA) was applied on preprocessed second derivatives spectra. Biochemical changes were assessed using PCA-loadings and accuracy of classification was obtained from PC-LDA . Sub-bands of Amide I (1,624 and 1,650 cm(-1) ) and Amide II (1,517 cm(-1) ) indicated a protein overexpression in non-treated and post-PDT neoplastic tissue compared with healthy skin, as well as a decrease in collagen fibers (1,204, 1,236, 1,282, and 1,338 cm(-1) ) and glycogen (1,028, 1,082, and 1,151 cm(-1) ) content. Photosensitized neoplastic tissue revealed shifted peak position and decreased β-sheet secondary structure of proteins (1,624 cm(-1) ) amount in comparison to non-treated neoplastic lesions. PC-LDA score plots discriminated non-treated neoplastic skin spectra from post-PDT cutaneous lesions with accuracy of 92.8%, whereas non-treated neoplastic

  4. Sympathetic cooling of ions in a hybrid atom ion trap

    Hoeltkemeier, Bastian

    2016-10-27

    In this thesis the dynamics of a trapped ion immersed in a spatially localized buffer gas is investigated. For a homogeneous buffer gas, the ion's energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination and/or a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer gas atoms, the ion's energy distribution is numerically determined for arbitrary buffer gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion's equilibrium energy distribution are found. One of these is a novel regime at large atom-to-ion mass ratios where the final ion temperature can tuned by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling). The second part of the thesis presents a hybrid atom ion trap designed for sympathetic cooling of hydroxide anions. In this hybrid trap the anions are immersed in a cloud of laser cooled rubidium atoms. The translational and rovibrational temperatures of the anions is probed by photodetachment tomography and spectroscopy which shows the first ever indication of sympathetic cooling of anions by laser cooled atoms.

  5. Ball-grid array architecture for microfabricated ion traps

    Guise, Nicholas D.; Fallek, Spencer D.; Stevens, Kelly E.; Brown, K. R.; Volin, Curtis; Harter, Alexa W.; Amini, Jason M.; Higashi, Robert E.; Lu, Son Thai; Chanhvongsak, Helen M.; Nguyen, Thi A.; Marcus, Matthew S.; Ohnstein, Thomas R.; Youngner, Daniel W.

    2015-05-01

    State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with 40Ca+ ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with 171Yb+ ions in a second BGA trap.

  6. Ball-grid array architecture for microfabricated ion traps

    Guise, Nicholas D.; Fallek, Spencer D.; Stevens, Kelly E.; Brown, K. R.; Volin, Curtis; Harter, Alexa W.; Amini, Jason M.; Higashi, Robert E.; Lu, Son Thai; Chanhvongsak, Helen M.; Nguyen, Thi A.; Marcus, Matthew S.; Ohnstein, Thomas R.; Youngner, Daniel W.

    2015-01-01

    State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with 40 Ca + ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with 171 Yb + ions in a second BGA trap

  7. MOMA and other next-generation ion trap mass spectrometers for planetary exploration

    Arevalo, R. D., Jr.; Brinckerhoff, W. B.; Getty, S.; Mahaffy, P. R.; van Amerom, F. H. W.; Danell, R.; Pinnick, V. T.; Li, X.; Grubisic, A.; Southard, A. E.; Hovmand, L.; Cottin, H.; Makarov, A.

    2016-12-01

    Since the 1970's, quadrupole mass spectrometer (QMS) systems have served as low-risk, cost-efficient means to explore the inner and outer reaches of the solar system. These legacy instruments have interrogated the compositions of the lunar exosphere (LADEE), surface materials on Mars (MSL), and the atmospheres of Venus (Pioneer Venus), Mars (MAVEN) and outer planets (Galileo and Cassini-Huygens). However, the in situ detection of organic compounds on Mars and Titan, coupled with ground-based measurements of amino acids in meteorites and a variety of organics in comets, has underlined the importance of molecular disambiguation in the characterization of high-priority planetary environments. The Mars Organic Molecule Analyzer (MOMA) flight instrument, centered on a linear ion trap, enables the in situ detection of volatile and non-volatile organics, but also the characterization of molecular structures through SWIFT ion isolation/excitation and tandem mass spectrometry (MSn). Like the SAM instrument on MSL, the MOMA investigation also includes a gas chromatograph (GC), thereby enabling the chemical separation of potential isobaric interferences based on retention times. The Linear Ion Trap Mass Spectrometer (LITMS; PI: William Brinckerhoff), developed to TRL 6 via the ROSES MatISSE Program, augments the core MOMA design and adds: expanded mass range (from 20 - 2000 Da); high-temperature evolved gas analysis (up to 1300°C); and, dual polarity detector assemblies (supporting the measurement of negative ions). The LITMS instrument will be tested in the field in 2017 through the Atacama Rover Astrobiology Drilling Studies (ARADS; PI: Brian Glass) ROSES PSTAR award. Following on these advancements, the Advanced Resolution Organic Molecule Analyzer (AROMA; PI: Ricardo Arevalo Jr.), supported through the ROSES PICASSO Program, combines a highly capable MOMA/LITMS-like linear ion trap and the ultrahigh resolution CosmOrbitrap mass analyzer developed by a consortium of five

  8. MATS and LaSpec: High-precision experiments using ion traps and lasers at FAIR

    Rodríguez, D.; Blaum, K.; Nörtershäuser, W.; Ahammed, M.; Algora, A.; Audi, G.; Äystö, J.; Beck, D.; Bender, M.; Billowes, J.; Block, M.; Böhm, C.; Bollen, G.; Brodeur, M.; Brunner, T.; Bushaw, B. A.; Cakirli, R. B.; Campbell, P.; Cano-Ott, D.; Cortés, G.; Crespo López-Urrutia, J. R.; Das, P.; Dax, A.; de, A.; Delheij, P.; Dickel, T.; Dilling, J.; Eberhardt, K.; Eliseev, S.; Ettenauer, S.; Flanagan, K. T.; Ferrer, R.; García-Ramos, J.-E.; Gartzke, E.; Geissel, H.; George, S.; Geppert, C.; Gómez-Hornillos, M. B.; Gusev, Y.; Habs, D.; Heenen, P.-H.; Heinz, S.; Herfurth, F.; Herlert, A.; Hobein, M.; Huber, G.; Huyse, M.; Jesch, C.; Jokinen, A.; Kester, O.; Ketelaer, J.; Kolhinen, V.; Koudriavtsev, I.; Kowalska, M.; Krämer, J.; Kreim, S.; Krieger, A.; Kühl, T.; Lallena, A. M.; Lapierre, A.; Le Blanc, F.; Litvinov, Y. A.; Lunney, D.; Martínez, T.; Marx, G.; Matos, M.; Minaya-Ramirez, E.; Moore, I.; Nagy, S.; Naimi, S.; Neidherr, D.; Nesterenko, D.; Neyens, G.; Novikov, Y. N.; Petrick, M.; Plaß, W. R.; Popov, A.; Quint, W.; Ray, A.; Reinhard, P.-G.; Repp, J.; Roux, C.; Rubio, B.; Sánchez, R.; Schabinger, B.; Scheidenberger, C.; Schneider, D.; Schuch, R.; Schwarz, S.; Schweikhard, L.; Seliverstov, M.; Solders, A.; Suhonen, M.; Szerypo, J.; Taín, J. L.; Thirolf, P. G.; Ullrich, J.; van Duppen, P.; Vasiliev, A.; Vorobjev, G.; Weber, C.; Wendt, K.; Winkler, M.; Yordanov, D.; Ziegler, F.

    2010-05-01

    -destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. This accuracy limit is important for fundamental interaction tests, but also allows for the study of the fine structure of the nuclear mass surface with unprecedented accuracy, whenever required. The use of the FT-ICR technique provides true single ion sensitivity. This is essential to access isotopes that are produced with minimum rates which are very often the most interesting ones. Instead of pushing for highest accuracy, the high charge state of the ions can also be used to reduce the storage time of the ions, hence making measurements on even shorter-lived isotopes possible. Decay studies in ion traps will become possible with MATS. Novel spectroscopic tools for in-trap high-resolution conversion-electron and charged-particle spectroscopy from carrier-free sources will be developed, aiming e.g. at the measurements of quadrupole moments and E0 strengths. With the possibility of both high-accuracy mass measurements of the shortest-lived isotopes and decay studies, the high sensitivity and accuracy potential of MATS is ideally suited for the study of very exotic nuclides that will only be produced at the FAIR facility.Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The dependencies of the hyperfine splitting and isotope shift on the nuclear moments and mean square nuclear charge radii are well known and the theoretical framework for the extraction of nuclear parameters is well established. These extracted parameters provide fundamental information on the structure of nuclei at the limits of stability. Vital information on both bulk and valence

  9. Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

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

    2017-06-01

    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.

  10. Limited-angle three-dimensional reconstructions using Fourier transform iterations and Radon transform iterations

    Tam, K.C.; Perez-Mendez, V.

    1981-01-01

    The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time

  11. Flat-top pulse generation by the optical Fourier transform technique for ultrahigh speed signal processing

    Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

    2009-01-01

    This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super-Gaussian sp......This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super...

  12. The Pegg–Barnett phase operator and the discrete Fourier transform

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

    2016-01-01

    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. (invited comment)

  13. Advances in hyperspectral remote sensing I: The visible Fourier transform hyperspectral imager

    J. Bruce Rafert

    2015-05-01

    Full Text Available We discuss early hyperspectral research and development activities during the 1990s that led to the deployment of aircraft and satellite payloads whose heritage was based on the use of visible, spatially modulated, imaging Fourier transform spectrometers, beginning with early experiments at the Florida Institute of Technology, through successful launch and deployment of the Visible Fourier Transform Hyperspectral Imager on MightySat II.1 on 19 July 2000. In addition to a brief chronological overview, we also discuss several of the most interesting optical engineering challenges that were addressed over this timeframe, present some as-yet un-exploited features of field-widened (slit-less SMIFTS instruments, and present some images from ground-based, aircraft-based and satellite-based instruments that helped provide the impetus for the proliferation and development of entire new families of instruments and countless new applications for hyperspectral imaging.

  14. Suppression law of quantum states in a 3D photonic fast Fourier transform chip

    Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio

    2016-01-01

    The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135

  15. Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms

    Prakash, A; Lebensohn, R A

    2009-01-01

    In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations. Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version

  16. High-resolution magnetic-domain imaging by Fourier transform holography at 21 nm wavelength

    Schaffert, Stefan; Pfau, Bastian; Günther, Christian M; Schneider, Michael; Korff Schmising, Clemens von; Eisebitt, Stefan; Geilhufe, Jan

    2013-01-01

    Exploiting x-ray magnetic circular dichroism at the L-edges of 3d transition metals, Fourier transform holography has become a standard technique to investigate magnetic samples with sub-100 nm spatial resolution. Here, magnetic imaging in the 21 nm wavelength regime using M-edge circular dichroism is demonstrated. Ultrafast pulses in this wavelength regime are increasingly available from both laser- and accelerator-driven soft x-ray sources. We explain the adaptations concerning sample preparation and data evaluation compared to conventional holography in the 1 nm wavelength range. We find the correction of the Fourier transform hologram to in-plane Fourier components to be critical for high-quality reconstruction and demonstrate 70 nm spatial resolution in magnetization imaging with this approach. (paper)

  17. Effect of ion clouds micromotion on measured signal in Fourier transform ion cyclotron resonance: Computer simulation.

    Vladimirov, Gleb; Kostyukevich, Yury; Kharybin, Oleg; Nikolaev, Eugene

    2017-08-01

    Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.

  18. Fourier transform infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

    Sheng, Ming; Gorzsás, András; Tuck, Simon

    2016-01-01

    Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.

  19. High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

    Chan, Kenny K. H.; Tang, Shuo

    2010-01-01

    The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

  20. High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

    Morelli, Eugene A.

    1997-01-01

    Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

  1. Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer

    Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

    1993-10-01

    We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

  2. S-duality as Fourier transform for arbitrary ϵ1, ϵ2

    N Nemkov

    2014-01-01

    The Alday–Gaiotto–Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ −ϵ 1 /ϵ 2 = 1. Here I extend this conjecture to general values of ϵ 1 , ϵ 2 . Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ϵ 1 , ϵ 2 . The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g 2 ≡ −ϵ 1 ϵ 2 and hypermultiplet masses. (paper)

  3. Valence band structures of InAs/GaAs quantum rings using the Fourier transform method

    Jia Boyong; Yu Zhongyuan; Liu Yumin

    2009-01-01

    The valence band structures of strained InAs/GaAs quantum rings are calculated, with the four-band k · p model, in the framework of effective-mass envelope function theory. When determining the Hamiltonian matrix elements, we develop the Fourier transform method instead of the widely used analytical integral method. Using Fourier transform, we have investigated the energy levels as functions of the geometrical parameters of the rings and compared our results with those obtained by the analytical integral method. The results show that the energy levels in the quantum rings change dramatically with the inner radius, outer radius, average radius, width, height of the ring and the distance between two adjacent rings. Our method can be adopted in low-dimensional structures with arbitrary shape. Our results are consistent with those in the literature and should be helpful for studying and fabricating optoelectronic devices

  4. Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

    Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

    2017-10-01

    Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

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

    ter Morsche Hennie G

    2003-01-01

    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.

  6. Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

    Singh, Iqbal

    2008-01-01

    To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

  7. Stress wave calculations in composite plates using the fast Fourier transform.

    Moon, F. C.

    1973-01-01

    The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

  8. Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations

    Tam, K.C.; Perez-Mendez, V.

    1979-12-01

    The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables

  9. Mix ratio measurements of pozzolanic blends by Fourier transform infrared-attenuated total reflectance method

    Rebagay, T.V.; Dodd, D.A.

    1992-07-01

    The disposal of low-level radioactive liquid wastes at the Hanford Site near Richland, Washington, involves mixing the wastes with pozzolanic grout-forming solid blends. Checking the quality of each blend component and its mix ratio will ensure processibility of the blend and the long-term performance of the resulting waste grout. In earlier work at Hanford laboratories, Fourier transform infrared-transmission method (FTIR-TR) using KBr pellet was applied successfully in the analysis of blends consisting of cement, fly ash, and clays. This method involves time-consuming sample preparation resulting in slow turnaround for repetitive sampling. Because reflection methods do not require elaborate sample preparation, they have the potential to reduce turnaround analysis time. Neat samples may be examined making these methods attractive for quality control. This study investigates the capability of Fourier transform infrared-attenuated total reflectance method (FTIR-ATR) to analyze pozzolanic blends

  10. Tabletop single-shot extreme ultraviolet Fourier transform holography of an extended object.

    Malm, Erik B; Monserud, Nils C; Brown, Christopher G; Wachulak, Przemyslaw W; Xu, Huiwen; Balakrishnan, Ganesh; Chao, Weilun; Anderson, Erik; Marconi, Mario C

    2013-04-22

    We demonstrate single and multi-shot Fourier transform holography with the use of a tabletop extreme ultraviolet laser. The reference wave was produced by a Fresnel zone plate with a central opening that allowed the incident beam to illuminate the sample directly. The high reference wave intensity allows for larger objects to be imaged compared to mask-based lensless Fourier transform holography techniques. We obtain a spatial resolution of 169 nm from a single laser pulse and a resolution of 128 nm from an accumulation of 20 laser pulses for an object ~11x11μm(2) in size. This experiment utilized a tabletop extreme ultraviolet laser that produces a highly coherent ~1.2 ns laser pulse at 46.9 nm wavelength.

  11. Simple spectral method for solving propagation problems in cylindrical geometry with fast Fourier transforms

    Feit, M.D.; Fleck, J.A. Jr.

    1989-01-01

    We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage

  12. Techniques for Handling and Removal of Spectral Channels in Fourier Transform Synchrotron-Based Spectra

    Ibrahim, Amr; Predoi-Cross, Adriana; Teillet, Philippe M.

    2010-01-01

    Channel spectra are a big problem for those attempting to use synchrotron-based Fourier transform spectra for spectral lineshape studies. Due to the layout of the optical system at the CLS far-infrared beamline, the synchrotron beam undergoes unavoidable multiple reflections on the steering mirrors, beam splitter, several sets of windows, and filters. We present a method for eliminating channel spectra and compare the results of our technique with other methods available in the literature.

  13. Direct application of the fast Fourier transform to open resonator calculations

    Johnson, M.M.

    1974-01-01

    It is shown that the integral equations for resonators can be written in the form of convolution integrals. A graph is given of the ratio of the time required to compute resonator eigenmodes using the fast Fourier transform (FFT) to the time required to evaluate the resonator convolution equation directly as a function of the number of mirror grid points. Computational savings made by using the FFT are discussed

  14. Discrete fourier transform (DFT) analysis for applications using iterative transform methods

    Dean, Bruce H. (Inventor)

    2012-01-01

    According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

  15. Gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance mass spectrometry

    Joergensen, S.I.

    1985-01-01

    The subject of this thesis is gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry (chapter 2 contains a short description of this method). Three chapters are mainly concerned with mechanistic aspects of gas phase ion/molecule reactions. An equally important aspect of the thesis is the stability and reactivity of α-thio carbanions, dipole stabilized carbanions and homoenolate anions, dealt with in the other four chapters. (Auth.)

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

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

    2012-01-01

    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 quanti...

  17. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam.

    Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M

    2005-11-01

    The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.

  18. Fourier Transform Infrared Spectroscopy as a Tool in Analysis of Proteus mirabilis Endotoxins.

    Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

    2017-01-01

    Fourier transform infrared spectroscopy (FT-IR) was used to scan whole bacterial cells as well as lipopolysaccharides (LPSs, endotoxins) isolated from them. Proteus mirabilis cells, with chemically defined LPSs, served as a model for the ATR FT-IR method. The paper focuses on three steps of infrared spectroscopy: (1) sample preparation, (2) IR scanning, and (3) multivariate analysis of IR data (principal component analysis, PCA).

  19. Bell’s measure and implementing quantum Fourier transform with orbital angular momentum of classical light

    Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong

    2015-01-01

    We perform Bell’s measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell’s inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally. PMID:26369424

  20. Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

    Takeshi, Y.; Keisuke, K.

    1983-01-01

    The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method

  1. Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.

    Lange, K

    1982-03-01

    In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.

  2. Characterization of ceramic matrix composite degradation using Fourier transform infrared spectroscopy

    Henry, Christine; Criner, Amanda Keck; Imel, Megan; King, Derek

    2018-04-01

    Data collected with a handheld Fourier Transform Infrared (FTIR) device is analyzed and considered as a useful method for detecting and quantifying oxidation on the surface of ceramic matrix composite (CMC) materials. Experiments examine silicon carbide (SiC) coupons, looking for changes in chemical composition before and after thermal exposure. Using mathematical, physical and statistical models for FTIR reflectance data, this research seeks to quantify any detected spectral changes as an indicator of surface oxidation on the CMC coupon.

  3. Fourier Transform and Photoacoustic Absorption Spectra of Ethylene within 6035 6210 cm-1: Comparative Measurements

    Kapitanov, V.A.; Solodov, A.M.; Petrova, T.M.; Ponomarev, Y.N.

    2010-01-01

    Measurements of ethylene absorption spectra with Fourier Transform (FT) and Photoacoustic (PA) spectrometers within 6035-6210 cm -1 are described. The methodology used for building the frequency scale for both spectrometers is presented. The methane absorption spectrum, included into the HITRAN database, was used in both cases to calibrate the frequency scale. Ethylene absorption spectra were obtained with the two recording methods; a coincidence of the measured line center positions was obtained with an accuracy of 0.0005 cm -1

  4. Multivariate Calibration and Model Integrity for Wood Chemistry Using Fourier Transform Infrared Spectroscopy

    Zhou, Chengfeng; Jiang, Wei; Cheng, Qingzheng; Via, Brian K.

    2015-01-01

    This research addressed a rapid method to monitor hardwood chemical composition by applying Fourier transform infrared (FT-IR) spectroscopy, with particular interest in model performance for interpretation and prediction. Partial least squares (PLS) and principal components regression (PCR) were chosen as the primary models for comparison. Standard laboratory chemistry methods were employed on a mixed genus/species hardwood sample set to collect the original data. PLS was found to provide bet...

  5. Rotor-System Log-Decrement Identification Using Short-Time Fourier-Transform Filter

    Li, Qihang; Wang, Weimin; Chen, Lifang; Sun, Dan

    2015-01-01

    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 ...

  6. On Analog of Fourier Transform in Interior of the Light Cone

    Tatyana Shtepina

    2014-01-01

    Full Text Available We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.

  7. Spectrogram analysis of selected tremor signals using short-time Fourier transform and continuous wavelet transform

    Bartosch, T. [Erlanger-Nuernberg Univ., Erlanger (Germany). Lehrstul fuer Nachrichtentechnik I; Seidl, D. [Seismologisches Zentralobservatorium Graefenberg, Erlanegen (Greece). Bundesanstalt fuer Geiwissenschaften und Rohstoffe

    1999-06-01

    Among a variety of spectrogram methods short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were selected to analyse transients in non-stationary signals. Depending on the properties of the tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli (Italy).

  8. Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

    Mori, N.; Kobayashi, K.

    1996-01-01

    A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

  9. An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations

    Golubov, B I

    1998-01-01

    Let f-hat c be the Fourier cosine transform of f. Then, as proved for functions of class L p (R + ) in Titchmarsh's book 'Introduction to the theory of Fourier integrals' (1937), the Hardy operator and the Hardy-Littlewood operator can be defined. In the present paper similar equalities are proved for functions of class L p (R + ), 1< p≤2, and the Walsh-Fourier transformation

  10. Fourier transform infrared spectroscopic study of intact cells of the nitrogen-fixing bacterium Azospirillum brasilense

    Kamnev, A. A.; Ristić, M.; Antonyuk, L. P.; Chernyshev, A. V.; Ignatov, V. V.

    1997-06-01

    The data of Fourier transform infrared (FTIR) spectroscopic measurements performed on intact cells of the soil nitrogen-fixing bacterium Azospirillum brasilense grown in a standard medium and under the conditions of an increased metal uptake are compared and discussed. The structural FTIR information obtained is considered together with atomic absorption spectrometry (AAS) data on the content of metal cations in the bacterial cells. Some methodological aspects concerning preparation of bacterial cell samples for FTIR measurements are also discussed.

  11. Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy*

    Liu, Yan-de; Ying, Yi-bin; Fu, Xia-ping

    2005-01-01

    To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji appl...

  12. Solubilization of spider silk proteins and its structural analysis using Fourier transform infrared spectroscopy

    Osbin, K.; Jayan, Manuel; Bhadrakumari, S.; Predeep, P.

    2017-06-01

    This study investigates the presence of various amide bands present in different spider silk species, which provides extraordinary physical properties. Three different spider silks were collected from Western Ghats region. The collected spider silks samples belonging to the spider Heteropoda venatoria (species 1), Hersilia savignyi (species 2) and Pholcus phalangioides (species 3). Fourier transform infrared (FTIR) spectra reveals the protein peaks in the amide I, II, and III regions in all the three types of spider silk species.

  13. Physiological response of Arundo donax to cadmium stress by Fourier transform infrared spectroscopy

    Yu, Shunhui; Sheng, Li; Zhang, Chunyan; Deng, Hongping

    2018-06-01

    The present paper deals with the physiological response of the changes in chemical contents of the root, stem and leaf of Arundo donax seedlings stressed by excess cadmium using Fourier transform infrared spectroscopy technique, cadmium accumulation in plant by atomic absorption spectroscopy were tested after different concentrations cadmium stress. The results showed that low cadmium concentrations (spectroscopy technique for the non-invasive and rapid monitoring of the plants stressed with heavy metals, Arundo donax is suitable for phytoremediation of cadmium -contaminated wetland.

  14. Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

    Jelle, Bjørn Petter; Hovde, Per Jostein

    2012-01-01

    Material characterization may be carried out by the attenuated total reflectance (ATR) Fourier transform infrared (FTIR) radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for exa...

  15. Fourier transform infrared spectroscopy of dental unit water line biofilm bacteria

    Liaqat, Iram

    2009-01-01

    Fourier transform-infrared (FT-IR) spectroscopy has become an important tool for rapid analysis of complex biological samples. The infrared absorbance spectrum could be regarded as a “fingerprint” which is a feature of biochemical substances. The FT-IR spectra of fresh and stored dried samples of six bacterial isolates (Klebsiella sp., Bacillus cereus, Bacillus subtilis, Pseudomonas aeruginosa, Achromobacter xylosoxidans and Achromobacter sp.) were observed by variation in sample preparation....

  16. Fourier Transform Microwave Spectroscopy of Multiconformational Molecules and Van Der Waals Complexes.

    Hight Walker, Angela Renee

    1995-01-01

    With the use of a Fourier transform microwave (FTM) spectrometer, structural determinations of two types of species; multiconformational molecules and van der Waals complexes, have been performed. Presented in this thesis are three sections summarizing this research effort. The first section contains a detailed explanation of the FTM instrument. In Section II, the study of three multiconformational molecules is presented as two chapters. Finally, three chapters in Section III outline the work still in progress on many van der Waals complexes. Section I was written to be a "manual" for the FTM spectrometer and to aid new additions to the group in their understanding of the instrument. An instruction guide is necessary for home-built instruments such as this one due to their unique design and application. Vital techniques and theories are discussed and machine operation is outlined. A brief explanation of general microwave spectroscopy as performed on an FTM spectrometer is also given. Section II is composed of two chapters pertaining to multiconformational molecules. In Chapter 2, a complete structural analysis of dipropyl ether is reported. The only conformer assigned had C_{rm s} symmetry. Many transitions are yet unassigned. Chapter 3 summarizes an investigation of two nitrosamines; methyl ethyl and methyl propyl nitrosamine. Only one conformer was observed for methyl ethyl nitrosamine, but two were assigned to methyl propyl nitrosamine. Nuclear hyperfine structure and internal methyl rotation complicated the spectra. The final section, Section III, contains the ongoing progress on weakly bound van der Waals complexes. The analysis of the OCS--HBr complex identified the structure as quasi-linear with large amplitude bending motions. Five separate isotopomers were assigned. Transitions originating from the HBr--DBr complex were measured and presented in Chapter 5. Although early in the analysis, the structure was determined to be bent and deuterium bonded. The

  17. Radiometric and spectral calibrations of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) using principle component analysis

    Tian, Jialin; Smith, William L.; Gazarik, Michael J.

    2008-10-01

    The ultimate remote sensing benefits of the high resolution Infrared radiance spectrometers will be realized with their geostationary satellite implementation in the form of imaging spectrometers. This will enable dynamic features of the atmosphere's thermodynamic fields and pollutant and greenhouse gas constituents to be observed for revolutionary improvements in weather forecasts and more accurate air quality and climate predictions. As an important step toward realizing this application objective, the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) Engineering Demonstration Unit (EDU) was successfully developed under the NASA New Millennium Program, 2000-2006. The GIFTS-EDU instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw GIFTS interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. The radiometric calibration is achieved using internal blackbody calibration references at ambient (260 K) and hot (286 K) temperatures. The absolute radiometric performance of the instrument is affected by several factors including the FPA off-axis effect, detector/readout electronics induced nonlinearity distortions, and fore-optics offsets. The GIFTS-EDU, being the very first imaging spectrometer to use ultra-high speed electronics to readout its large area format focal plane array detectors, operating at wavelengths as large as 15 microns, possessed non-linearity's not easily removable in the initial calibration process. In this paper, we introduce a refined calibration technique that utilizes Principle Component (PC) analysis to compensate for instrument distortions and artifacts remaining after the initial radiometric calibration process, thus, further enhance the absolute calibration accuracy. This method is

  18. FREQUENCY COMPONENT EXTRACTION OF HEARTBEAT CUES WITH SHORT TIME FOURIER TRANSFORM (STFT

    Sumarna Sumarna

    2017-01-01

      Electro-acoustic human heartbeat detector have been made with the main parts : (a stetoscope (piece chest, (b mic condenser, (c transistor amplifier, and (d cues analysis program with MATLAB. The frequency components that contained in heartbeat. cues have also been extracted with Short Time Fourier Transform (STFT from 9 volunteers. The results of the analysis showed that heart rate appeared in every cue frequency spectrum with their harmony. The steps of the research were including detector instrument design, test and instrument repair, cues heartbeat recording with Sound Forge 10 program and stored in wav file ; cues breaking at the start and the end, and extraction/cues analysis using MATLAB. The MATLAB program included filter (bandpass filter with bandwidth between 0.01 – 110 Hz, cues breaking with hamming window and every part was calculated using Fourier Transform (STFT mechanism and the result were shown in frequency spectrum graph.   Keywords: frequency components extraction, heartbeat cues, Short Time Fourier Transform

  19. Principle and analysis of a rotational motion Fourier transform infrared spectrometer

    Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

    2017-09-01

    Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

  20. Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

    Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

    2016-10-01

    The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.