Neutron Fourier Diffractometer FSD for Internal Stress Analysis First Results
Aksenov, V L; Bokuchava, G D; Zhuravlev, V V; Kuzmin, E S; Bulkin, A P; Kudryashov, V A; Trounov, V A
2001-01-01
At the IBR-2 pulsed reactor (FLNP, JINR) a specialised instrument - neutron Fourier diffractometer FSD - intended for internal stress measurements in bulk materials is under construction. Internal stress studies by neutron diffraction has been successfully developed last years in leading neutron centres, including Dubna and Gatchina, due to several important advantages of this method in comparison with other techniques. In current work the operation principles and construction of the diffractometer, basic parameters and outcomes of test experiments are presented.
Kuzmin, E S; Bokuchava, G D; Zhuk, V V; Kudryashov, V A; Buklin, A P; Trounov, V A
2001-01-01
At the IBR-2 pulsed reactor (FLNP, JINR, Dubna), a specialized time-of-flight instrument Fourier-Stress-Diffractometer (FSD) intended for the measurement of internal steresses in bulk samples by using high-resolution neutron diffraction is under construction. One of the main components of the diffractometer is a new-type detector with combined electronic - geometrical focusing uniting a large solid angle and a small geometry contribution to the instrumental resolution. The first two modules of the detector, based on scintillation screen ZnS(Ag)/^{6}LiF with wavelength shifting fibers readout have been developed and tested. The design of the detector and associated electronics are described. The method of time focusing surface approximation, using the screen flexibility is proposed. Characteristics of tested modules in comparison with a detector of previous generation are presented and advantages of new detector design for high-resolution diffractometry are discussed.
Neutron Diffraction Measurements using the Cairo Fourier Diffractometer facility
International Nuclear Information System (INIS)
Maayof, R.M.A.; Elkady, A.S.
1999-01-01
The paper presents neutron diffraction investigations of different polycrystalline materials, performed at room temperature, using the Cairo Fourier Diffractometer Facility (CFDF),recently installed at one of the ET-RR-1 reactor horizontal channels. The neutron diffraction patterns were measured using the CFDF while its Fourier chopper was rotating with modulation frequency 136 KHz ;leading to-7us for the FWHM of the time resolution function. The diffraction patterns were analysed by a special program (MRIA), adapted especially to the CFDF conditions. The reliability of the C DF results was confirmed from comparison of the measured diffraction patterns with similar ones obtained from neutron and x-ray measurements
Research studies performed using the Cairo Fourier Diffractometer Facility
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Ridikas, D.
2009-12-01
This report represents the results of the research studies performed using the Cairo Fourier Diffractometer Facility (CFDF), within 10 years after it was installed and put into operation at the beginning of 1996. The main components of the CFDF were supplied by the IAEA according to the technical assistance project EGY/1/022 'Upgrading of Research Reactor Utilization'. The present report is the second published INDC report, while the first one, published at the beginning of 1997, was about the performance of the CFDF and its main characteristic parameters. Plenty of measurements were performed since then, yielding several publications both in local and international scientific periodicals and resulting in 8 M.Sc. and Ph.D. degrees from Egyptian Universities. In addition, a new approach for the analysis of the neutron spectra was implemented using the CFDF. Specially designed interface card with proper software program was applied instead of the reverse time of flight (RTOF) and Finnish made analyzer originally attached to the facility. It has been verified that the new approach can successfully replace the RTOF analyzer, significantly decreasing the time of measurement and saving the reactor's operation time. Besides, a special fault diagnostic system program was developed and tested for caring and handling the possible failures of the CFDF. Moreover, measurements were carried out for the diffraction spectra emitted at different points of one of the samples. The latter was scanned across the neutron beam of the CFDF, for studying the stress after welding; used in industrial applications. (author)
Maayouf, R M A
2002-01-01
The present work introduces a new design to replace the (Finnish make) reverse time of flight (RTOF) analyzer used for the Fourier diffractometer facilities. The new design applies a data acquisition system, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between signals received from the chopper-decoder and detector. It has been found from test measurements performed with the Cairo Fourier diffractometer facility (CFDF) and the similar high resolution one at JINR (Dubna-Russia) that the new design can successfully replace the Finnish make RTOF analyzer.
A New approach for the data acquisition system of the cairo fourier diffractometer
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Khalil, M.I.
2000-01-01
The present work deals with a new approach for the reverse time of flight (RTOF) analysis of the diffraction spectra. The approach is based on the same RTOF concept used for the design of a separate RTOF analyzer and applies, for data acquisition, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between the three signals received from the chopper decoder, detector and the pulsed neutron source respectively. The new approach have been realized for use with a Fourier diffractometer facility based on the RTOF concept. It has been found from test measurements performed with the high resolution Fourier diffractometer (HRFD) at the IBR-2 reactor (JINR, Dubna) that the new approach can successfully replace the RTOF analyzer
Multipurpose RTOF Fourier diffractometer at the ET-RR-1 reactor
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Tiitta, A.T.
1993-09-01
The present work represents a further study of the basic RTOF Fourier multipurpose diffractometer, to start with, at the ET-RR-1 reactor. The functions of the suggested arrangement are thoroughly discussed and the possibilities if its expansion are also assessed. The flexibility of the arrangement allows its further expansion both for stress measurement at 90 deg. scattering angle with two detector banks at opposite sides of the incident beam and for operation in the transmission diffraction mode. (orig.). (19 refs., 10 figs., 1 tab.)
A time-focusing Fourier chopper time-of-flight diffractometer for large scattering angles
International Nuclear Information System (INIS)
Heinonen, R.; Hiismaeki, P.; Piirto, A.; Poeyry, H.; Tiitta, A.
1975-01-01
A high-resolution time-of-flight diffractometer utilizing time focusing principles in conjunction with a Fourier chopper is under construction at Otaniemi. The design is an improved version of a test facility which has been used for single-crystal and powder diffraction studies with promising results. A polychromatic neutron beam from a radial beam tube of the FiR 1 reactor, collimated to dia. 70 mm, is modulated by a Fourier chopper (dia. 400 mm) which is placed inside a massive boron-loaded particle board shielding of 900 mm wall thickness. A thin flat sample (5 mm x dia. 80 mm typically) is mounted on a turntable at a distance of 4 m from the chopper, and the diffracted neutrons are counted by a scintillation detector at 4 m distance from the sample. The scattering angle 2theta can be chosen between 90deg and 160deg to cover Bragg angles from 45deg up to 80deg. The angle between the chopper disc and the incident beam direction as well as the angle of the detector surface relative to the diffracted beam can be adjusted between 45deg and 90deg in order to accomplish time-focusing. In our set-up, with equal flight paths from chopper to sample and from sample to detector, the time-focusing conditions are fulfilled when the chopper and the detector are parallel to the sample-plane. The time-of-flight spectrum of the scattered neutrons is measured by the reverse time-of-flight method in which, instead of neutrons, one essentially records the modulation function of the chopper during constant periods preceding each detected neutron. With a Fourier chopper whose speed is varied in a suitable way, the method is equivalent to the conventional Fourier method but the spectrum is obtained directly without any off-line calculations. The new diffractometer is operated automatically by a Super Nova computer which not only accumulates the synthetized diffraction pattern but also controls the chopper speed according to the modulation frequency sweep chosen by the user to obtain a
International Nuclear Information System (INIS)
Trunov, V.A.
1997-01-01
In paper detail information of the development and construction of the efficient neutron high resolution diffractometer with using of original version of Fourier method - reverse time-of-flight Fourier method - are presented. The advantages of dignities of method are demonstrated by help of numeral structural studies (rare-earth formates, hexaborides, high-Tc superconductors, catalyses). The part of the scientific results are presented for the first time
International Nuclear Information System (INIS)
Aksenov, V.L.; Balagurov, A.M.; Bokuchava, G.D.; Simkin, V.G.; Taran, Yu.V.; Shamsutdinov, N.R.; ); Bulkin, A.P.; Kudryashov, V.A.; Trunov, V.A.; Shrajber, Yu.
1997-01-01
A high resolution Fourier diffractometer was applied to study elastic properties of austenitic steel Kh6CrNiTi1810 under external uniaxial load and residual internal stresses, resulted from material fatigue, to determine residual stresses in two-layer tubes manufactured by weld-surfacing austenitic stainless steel with a ferritic one as well as to measure residual stresses in Al 2 O 3 /Al cermets. The data on stress distribution in the specimens investigated are presented. It is concluded about a good agreement between results of diffraction studies and mechanical tests [ru
Correlation Fourier diffractometry: 20 Years of experience at the IBR-2 reactor
Balagurov, A. M.; Bobrikov, I. A.; Bokuchava, G. D.; Zhuravlev, V. V.; Simkin, V. G.
2015-05-01
The high-resolution Fourier diffractometer (HRFD) was commissioned at the IBR-2 pulsed reactor at FLNP JINR in 1994. The specific feature of the HRFD design is the use of fast Fourier chopper for modulating the primary neutron beam intensity and the correlation method of diffraction data acquisition. This allowed to reach with HRFD extremely high resolution (Δ d/ d ≈ 0.001) over a wide range of inter-planar spacings at a relatively short flight path between chopper and sample ( L = 20 m). Over time, a lot of diffraction experiments on crystalline materials, the main goal of which was to study their atomic and magnetic structures, were performed at HRFD. Successful implementation of the Fourier diffractometry technique at the IBR-2 reactor stimulated the construction of yet another Fourier diffractometer intended for internal mechanical stress studies in bulk materials (FSD, Fourier Stress Diffractometer). In this paper the experience of using this technique at the IBR-2, which is a long-pulse neutron source, is considered, the examples of HRFD studies are given, and possible solutions for existing technical problems of using correlation diffractometry and ways of increasing the intensity and resolution of HRFD are discussed.
FSD: Frequency Space Differential measurement of CMB spectral distortions
Mukherjee, Suvodip; Silk, Joseph; Wandelt, Benjamin D.
2018-04-01
Although the Cosmic Microwave Background agrees with a perfect blackbody spectrum within the current experimental limits, it is expected to exhibit certain spectral distortions with known spectral properties. We propose a new method, Frequency Space Differential (FSD) to measure the spectral distortions in the CMB spectrum by using the inter-frequency differences of the brightness temperature. The difference between the observed CMB temperature at different frequencies must agree with the frequency derivative of the blackbody spectrum, in the absence of any distortion. However, in the presence of spectral distortions, the measured inter-frequency differences would also exhibit deviations from blackbody which can be modeled for known sources of spectral distortions like y & μ. Our technique uses FSD information for the CMB blackbody, y, μ or any other sources of spectral distortions to model the observed signal. Successful application of this method in future CMB missions can provide an alternative method to extract spectral distortion signals and can potentially make it feasible to measure spectral distortions without an internal blackbody calibrator.
Genomic structure, expression and association study of the porcine FSD2.
Lim, Kyu-Sang; Lee, Kyung-Tai; Lee, Si-Woo; Chai, Han-Ha; Jang, Gulwon; Hong, Ki-Chang; Kim, Tae-Hun
2016-09-01
The fibronectin type III and SPRY domain containing 2 (FSD2) on porcine chromosome 7 is considered a candidate gene for pork quality, since its two domains, which were present in fibronectin and ryanodine receptor. The fibronectin type III and SPRY domains were first identified in fibronectin and ryanodine receptor, respectively, which are candidate genes for meat quality. The aim of this study was to elucidate the genomic structure of FSD2 and functions of single nucleotide polymorphisms (SNPs) within FSD2 that are related to meat quality in pigs. Using a bacterial artificial chromosome clone sequence, we revealed that porcine FSD2 consisted of 13 exons encoding 750 amino acids. In addition, FSD2 was expressed in heart, longissimus dorsi muscle, psoas muscle, and tendon among 23 kinds of porcine tissues tested. A total of ten SNPs, including four missense mutations, were identified in the exonic region of FSD2, and two major haplotypes were obtained based on the SNP genotypes of 633 Berkshire pigs. Both haplotypes were associated significantly with intramuscular fat content (IMF, P meat color, affecting yellowness (P = 0.002). These haplotype effects were further supported by the alteration of putative protein structures with amino acid substitutions. Taken together, our results suggest that FSD2 haplotypes are involved in regulating meat quality including IMF, MP, and meat color in pigs, and may be used as meaningful molecular makers to identify pigs with preferable pork quality.
Benford's law and the FSD distribution of economic behavioral micro data
Villas-Boas, Sofia B.; Fu, Qiuzi; Judge, George
2017-11-01
In this paper, we focus on the first significant digit (FSD) distribution of European micro income data and use information theoretic-entropy based methods to investigate the degree to which Benford's FSD law is consistent with the nature of these economic behavioral systems. We demonstrate that Benford's law is not an empirical phenomenon that occurs only in important distributions in physical statistics, but that it also arises in self-organizing dynamic economic behavioral systems. The empirical likelihood member of the minimum divergence-entropy family, is used to recover country based income FSD probability density functions and to demonstrate the implications of using a Benford prior reference distribution in economic behavioral system information recovery.
Which are the male factors associated with female sexual dysfunction (FSD)?
Maseroli, E; Fanni, E; Mannucci, E; Fambrini, M; Jannini, E A; Maggi, M; Vignozzi, L
2016-09-01
It has been generally assumed that partner's erectile dysfunction, premature, and delayed ejaculation play a significant role in determining female sexual dysfunction (FSD). This study aimed to evaluate the role of the male partner's sexual function, as perceived by women, in determining FSD. A consecutive series of 156 heterosexual women consulting our clinic for FSD was retrospectively studied. All patients underwent a structured interview and completed the Female Sexual Function Index (FSFI). FSFI total score decreased as a function of partner's age, conflicts within the couple, relationship without cohabitation and the habit of engaging in intercourse to please the partner; FSFI total score increased as a function of frequency of intercourse, attempts to conceive and fertility-focused intercourse. FSFI total score showed a negative, stepwise correlation with partner's perceived hypoactive sexual desire (HSD) (r = -0.327; p libido, FSFI total score was significantly lower when their partner's libido was low (p = 0.041); the correlation disappeared if the patient also experienced HSD. In conclusion, the presence of erectile dysfunction, premature, and delayed ejaculation of the partner may not act as a primary contributing factor to FSD, as determined by FSFI scores; conversely, women's sexuality seems to be mostly impaired by the perceived reduction in their partner's sexual interest. © 2016 American Society of Andrology and European Academy of Andrology.
Fiber-optic sensor demonstrator (FSD) for the monitoring of spacecraft subsystems on ESA's PROBA-2
Kruzelecky, Roman V.; Zou, Jing; Mohammed, Najeeb; Haddad, Emile; Jamroz, Wes; Ricci, Francesco; Lamorie, Joshua; Edwards, Eric; McKenzie, Iain; Vuilleumier, Pierrik
2017-11-01
MPB Communications (MPBC) is developing solutions to the monitoring requirements of spacecraft based on its fiber-laser and Fiber Bragg Grating expertise. This is cumulating in the Fiber Sensor Demonstrator for ESA's Proba-2 that is scheduled for launch in 2007. The advantages of the MPBC approach include a central interrogation system that can be used to control a variety of different fiber-optic sensors including temperature, pressure, actuator status, and propellant leakage. This paper reviews the design and ground qualification of the FSD system in preparation for integration with Proba-2. The FSD will provide monitoring for various Proba-2 subsystems, including a hybrid propulsion system. Some of the challenges associated with using fiber-optics in space are discussed.
EXCED - epithermal neutron diffractometer at KENS
Kuwahara, K; Iwasa, K; Kohgi, M; Nakamura, M; Inamura, Y; Arai, M; Kunii, S
2002-01-01
A new epithermal neutron diffractometer (EXCED) was installed at the KENS spallation pulsed-neutron source. EXCED is designed to be a small scattering angle diffractometer using an incident neutron energy of about propor to 1 eV for determining the crystal and magnetic structures of materials containing high-absorption elements. Using this diffractometer, we have been able to measure the nuclear and magnetic Bragg peaks of Gd compounds, which are known as the best absorber of thermal neutrons. The instrumental details and the preliminary results of the neutron diffraction from a single crystal of GdB sub 6 are reported. (orig.)
The engineering materials diffractometer 'TAKUMI'
International Nuclear Information System (INIS)
Aizawa, Kazuya; Harjo, Stefanus; Ito, Takayoshi
2010-01-01
The construction of the Engineering Materials Diffractometer, TAKUMI in J-PARC has been finished on March 2009, and the commissioning has been started from September 2008 being parallel with the final stage of the construction. In the commissioning, after checking the validity and the stability of the detectors and the data acquisition system, powder diffraction data of an austenitic steel alloy with 10 mm diameter without beam collimation (high intensity mode) was measured, and the resolution Δd/d of 0.4% was confirmed, as designed. Further commissioning was done also with 2 mm diameter of annealed piano wire with combination of beam collimation (high resolution mode), and the resolution Δd/d of less than 0.2% was confirmed to be achieved. TAKUMI adopted an event mode data recording method. It was found that this recording method is very useful to manipulate data as we like, for instance, detector range, time of flight binning width and time resolved data, even the experiment has been finished. (author)
Female sexual dysfunction (FSD): Prevalence and impact on quality of life (QoL).
Nappi, Rossella E; Cucinella, Laura; Martella, Silvia; Rossi, Margherita; Tiranini, Lara; Martini, Ellis
2016-12-01
Female sexual dysfunction (FSD) and quality of life (QOL) are both multidimensional and have a bidirectional relationship across the reproductive life span and beyond. Methodological difficulties exist in estimating the real prevalence of FSD because it is hard to determine the level of distress associated with sexual symptoms in a large-scale survey. Approximately 40-50% of all women report at least one sexual symptom, and some conditions associated with hormonal changes at menopause, such as vulvovaginal atrophy (VVA) and hypoactive sexual desire disorder (HSDD), have a significant impact on sexual function and QOL. Sexual distress peaks at midlife, declines with age and is strongly partner-related. Many postmenopausal women are still sexually active, especially if they are in a stable partnership. Even though sexual functioning is impaired, a variety of psychosocial factors may maintain sexual satisfaction. That being so, health care providers (HCPs) should proactively address sexual symptoms at midlife and in older women, from a balanced perspective. Adequate counselling should be offered. Women with distressing symptoms may benefit from tailored hormonal and non-hormonal therapies, whereas women without distress related to their sexual experiences should not receive any specific treatment. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Instrumentation of a manually programmed neutron diffractometer
DEFF Research Database (Denmark)
Hansen, K.B.; Neisig, K.E.
1966-01-01
This paper describes essentially the digital part of the instrumentation for a neutron diffractometer in which the measuring procedure is governed by a control unit involving a fixed number of program points. A simultaneously running test program monitors the information transfer from the data...
Instrumentation of a manually programmed neutron diffractometer
DEFF Research Database (Denmark)
Hansen, K.B.; Neisig, K.E.
1966-01-01
This paper describes essentially the digital part of the instrumentation for a neutron diffractometer in which the measuring procedure is governed by a control unit involving a fixed number of program points. A simultaneously running test program monitors the information transfer from the data...... sources and to the print-out in table form. The experimental conditions must be set by a panel switch selected program, which allows a desired parameter program to be executed....
IBARAKI Materials Design Diffractometer for J-PARC
Ishigaki, Toru; Harjo, Stefanus; Yonemura, Masao; Kamiyama, Takashi; Aizawa, Kazuya; Oikawa, Kenichi; Sakuma, Takashi; Morii, Yukio; Arai, Masatoshi; Ebata, Kazuhiro; Takano, Yoshiki; Kasao, Takuro
2006-11-01
Ibaraki prefecture, the local government of the area for J-PARC site, has decided to build a versatile powder diffractometer (IBARAKI Materials Design Diffractometer) to promote industrial applications for neutron beams in J-PARC. This diffractometer is designed to be a high throughput one enabling materials scientists to use it like the chemical analytical instruments in their material development processes. It covers in d range 0.18industrial application, a utilization system for this diffractometer is required. We will establish a support system for both academic and industrial users who are willing to use neutron but have not been familiar with neutron diffraction.
Powder neutron diffractometers HRPT and DMCG
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.; Doenni, A.; Staub, U.; Zolliker, M. [Lab. for Neutron Scattering ETH Zurich, Zurich (Switzerland) and Paul Scherrer Institute, Villigen (Switzerland)
1996-11-01
Basic properties and applications of SINQ powder neutron diffractometers are described. For optimum use of the continuous neutron beams these instruments are equipped with position sensitive detectors, and both high-intensity and high-resolution modes of operation are possible. HRPT attaining resolutions {delta}d/d{<=}10{sup -3}, d=lattice spacing, at a thermal neutron channel of the target station and DMCG at a cold neutron guide coated with m=2 supermirrors, are complementary concerning the applications: the former will be mainly used for structural studies and the latter to investigate magnetic ordering phenomena. (author) figs., tabs., refs.
Powder neutron diffractometers HRPT and DMCG
International Nuclear Information System (INIS)
Fischer, P.; Doenni, A.; Staub, U.; Zolliker, M.
1996-01-01
Basic properties and applications of SINQ powder neutron diffractometers are described. For optimum use of the continuous neutron beams these instruments are equipped with position sensitive detectors, and both high-intensity and high-resolution modes of operation are possible. HRPT attaining resolutions δd/d≤10 -3 , d=lattice spacing, at a thermal neutron channel of the target station and DMCG at a cold neutron guide coated with m=2 supermirrors, are complementary concerning the applications: the former will be mainly used for structural studies and the latter to investigate magnetic ordering phenomena. (author) figs., tabs., refs
IBARAKI materials design diffractometer (iMATERIA)—Versatile neutron diffractometer at J-PARC
Ishigaki, T.; Hoshikawa, A.; Yonemura, M.; Morishima, T.; Kamiyama, T.; Oishi, R.; Aizawa, K.; Sakuma, T.; Tomota, Y.; Arai, M.; Hayashi, M.; Ebata, K.; Takano, Y.; Komatsuzaki, K.; Asano, H.; Takano, Y.; Kasao, T.
2009-02-01
Ibaraki prefecture, the local government of the area for J-PARC site, was decided to build a versatile neutron diffractometer (IBARAKI Materials Design Diffractometer, iMATERIA) to promote an industrial application for neutron beam in J-PARC. iMATERIA is planned to be a high throughput diffractometer so that materials engineers and scientists can use it like the chemical analytical instruments in their materials development process. It covers in d range 0.18industrial application, a utilization system for this diffractometer is required. We will establish a support system for both academic and industrial users who are willing to use neutron but have not been familiar with neutron diffraction. The analysis software is also very important for powder diffraction, we will also prepare a software package consisting of combination of several powder-diffraction software, structural databases and visualization. The construction of iMATERIA will be completed in the end of April 2008, as one of day-one instruments for J-PARC.
Instrumentation for PSD-based neutron diffractometers at Dhruva ...
Indian Academy of Sciences (India)
positions and data is acquired simultaneously from all the PSDs. Throughput is further improved by using multiple PSDs at each position. Various instruments like the powder diffractometer, high-Q diffractometer, polarized neutron reflectometer, quasi-elastic neutron spectrometer, small-angle neutron spectrometer all use ...
IBARAKI Materials Design Diffractometer for J-PARC
International Nuclear Information System (INIS)
Ishigaki, Toru; Harjo, Stefanus; Yonemura, Masao; Kamiyama, Takashi; Aizawa, Kazuya; Oikawa, Kenichi; Sakuma, Takashi; Morii, Yukio; Arai, Masatoshi; Ebata, Kazuhiro; Takano, Yoshiki; Kasao, Takuro
2006-01-01
Ibaraki prefecture, the local government of the area for J-PARC site, has decided to build a versatile powder diffractometer (IBARAKI Materials Design Diffractometer) to promote industrial applications for neutron beams in J-PARC. This diffractometer is designed to be a high throughput one enabling materials scientists to use it like the chemical analytical instruments in their material development processes. It covers in d range 0.18< d(A)<5 with Δd/d=0.16% at the high-resolution scattering detector bank, and covers 5< d(A)<800 with gradually changing resolution. Typical measuring time to obtain a 'Rietveld-quality' data is several minutes for the sample size of laboratory X-ray diffractometer. To promote industrial application, a utilization system for this diffractometer is required. We will establish a support system for both academic and industrial users who are willing to use neutron but have not been familiar with neutron diffraction
VULCAN - The engineering diffractometer at the SNS
Energy Technology Data Exchange (ETDEWEB)
Wang, X.-L. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 379831-6474 (United States)]. E-mail: wangxl@ornl.gov; Holden, T.M. [Northern Stress Technology, Deep River, Ont., Canada KOJ1P0 (Canada); Rennich, G.Q. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 379831-6474 (United States); Stoica, A.D. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 379831-6474 (United States); Liaw, P.K. [Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996-2200 (United States); Choo, H. [Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996-2200 (United States); Hubbard, C.R. [Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 379831-6064 (United States)
2006-11-15
The VULCAN diffractometer at the Spallation Neutron Source (SNS) is designed to tackle a broad range of problems in materials science and engineering, including spatial mapping of the residual stress distribution in components, deformation behavior under static and cyclic loadings, and the kinetics of the phase transformation. The optics design features a focusing neutron guide, wide-angular detector coverage for diffraction, and an area detector for small angle scattering. By employing an interchangeable neutron guide-collimator system, the instrument can be optimally configured for individual experiments with desired resolution. The performance of the instrument was estimated using Monte Carlo simulation. A suite of specialized sample environments is also under construction as an integrated part of the instrument.
Diffractometer for neutron crystallography in biology
International Nuclear Information System (INIS)
Niimura, Nobuo
1993-01-01
Since the structure-function relationship of proteins is dominated by the behavior of hydrogen atoms, it is important to know the structural information of hydrogen atoms. Neutron diffraction provides an experimental method of directly locating hydrogen atoms. So, we have had a project to construct the dedicated diffractometer for the neutron crystallography in biology at JRR-3M in JAERI (Japan Atomic Energy Research Institute). The diffraction intensity from the protein crystal is weaker than that from most of inorganic materials. In order to overcome the intensity problem, three items should be considered carefully. Those are (1) how to get a large single crystal, (2) how to get intense neutron flux on a sample position, and (3) how to get a genuine detector system. (author)
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
The development of a time of flight diffractometer, FIONA
International Nuclear Information System (INIS)
Goodyear, A.G.; Miller, R.J.R.
1975-11-01
A neutron diffractometer, FIONA, has been built at AWRE in order to study structure and equation of state data of materials at high pressures and elevated temperatures. It is required that the sample should be subjected to pressures up to 60 kbar and temperatures up to 800 0 K. There is a further requirement that the diffractometer should have a multi-detector system to make the maximum use of the neutrons available from the 5 MW HERALD reactor. Both these requirements can be met by using a time of flight diffractometer. The instrument is described. (author)
Resolution of the neutron diffractometer of the Mexican Nuclear Center
International Nuclear Information System (INIS)
Macias B, L.R.; Garcia C, R.M.; Ita T, A. De
2003-01-01
The neutron diffractometer has three collimators and a monochromator of which it depends the resolution of the same one and exists a commitment between the resolution of the diffractometer and its intensity; if it is sought to work with more resolution, the intensity will diminish, and also, if one has little volume of the material, the diffracted light it is diminished, so the selection of the values of the collimators is this way important to have an unique value of the resolution of the diffractometer. (Author)
Directory of Open Access Journals (Sweden)
Chiara Borghi
2017-03-01
Full Text Available Female Sexual Disorders (FSD include a complex, multidimensional, individual experience that can change as an individual age, suggesting that these problems are caused by multiple factors including psychosocial factors, personal relationships, pathologic changes caused by diseases, and pharmacologic influences. Menopause is an important time for middle aged women and postmenopausal physiological changes could have a significant role in the development of FSD. Few is still known about their correct definition and treatment. Their incidence, prevalence and risk factors are difficult to define because of a high level of overlap in the experience of problems with desire, arousal, and orgasm. Little evidences are known about the best therapeutic approach, and both non-pharmacological and pharmacological treatment options have been described. Among these, phosphodiesterase type 5 inhibitors could be an effective option for many subtypes of female sexual disorders, with an improvement in different aspects of sexual function, such as desire, arousal, orgasm and sexual satisfaction. In this paper authors reviewed what is already known about the use of these vasoactive agents, particularly tadalafil, as a treatment option for female sexual disturbances.
A control and recording system for a neutron diffractometer
International Nuclear Information System (INIS)
Czech, Z.; Turek, L.; Wierzewski, K.
1982-01-01
A digital system for automatic control and data recording being a part of a neutron diffractometer designed for measurement of the angular distribution of monochromatic neutrons is described. The system is built using digital TTL integrated circuits. Particular attention is drawn to the interesting design of the optimized cross-matrix which selects the elements subjected to recording. The system successfully works with the neutron diffractometer at the EWA reactor. (author)
Stade, Eric
2005-01-01
A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of ap
Hoch, Jeffrey C.
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.
Hoch, Jeffrey C
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.
Development of engineering diffractometer at J-PARC
Moriai, Atsushi; Torii, Shuki; Suzuki, Hiroshi; Harjo, Stefanus; Morii, Yukio; Arai, Masatoshi; Tomota, Yo; Suzuki, Tetsuya; Akiniwa, Yoshiaki; Kimura, Hidehiko; Akita, Koich
2006-11-01
An engineering diffractometer for investigations of stresses and crystallographic structures within engineering components is now being developed at J-PARC project. The diffractometer is designed to view a decoupled-poisoned liquid H 2 moderator providing neutrons with good symmetrical diffraction profiles in the acceptable wavelength range. The diffractometer will have a primary flight path of 40 m and a secondary flight path of 2.0 m for 90° scattering detector banks, and will include a curved supermirror neutron guide to avoid intensity loss due to the long flight path and to reduce backgrounds from fast neutrons and gamma rays. Therefore, stresses with sufficient accuracies in many engineering studies are quite promising. The diffractometer involves a sample translator which is able to handle large and heavy real industrial-scaled components. Detailed design works are being continuously promoted. The optimization of the diffractometer has been performed with a Monte Carlo simulation, and an appropriate resolution of less than 0.2% in Δ d/ d has been confirmed.
Thermoluminescent dosemeter in a X-ray diffractometer
International Nuclear Information System (INIS)
Mendoza A, D.; Gonzalez M, P.; Falcon B, T.; Castano, V.M.
1999-01-01
In this work it was presented the results obtained of the dosimetry which was realized in a X-ray diffractometer for powders, trademark Siemens D5000, using the thermoluminescent signal generated by the X-rays in the commercial dosemeter TLD-100 of Harshaw, US. In according to the results obtained, the radiation quantity received by an analysed material in the diffractometer, will be proportional to exposure time and it can vary from unities until tenths of grays. These results are very outstanding when are analysed crystalline materials in a diffractometer, for knowing the present crystalline phases, mainly if these are highly sensitive to the ionizing radiation, as it is the case of the thermoluminescent materials. (Author)
A high resolution powder diffractometer using focusing optics
Indian Academy of Sciences (India)
sample environment of very low temperatures and high magnetic fields using a 7 Tesla cryogen-free superconducting magnet with a VTI having a temperature range of 1.5–. 320 K. The special sample environment and high resolution make this neutron powder diffractometer a very powerful facility for studying magnetic ...
A high resolution powder diffractometer using focusing optics
Indian Academy of Sciences (India)
. Keywords. Neutron diffraction; Bragg diffraction optics. PACS Nos 61.05.fm; 61.05.F; 03.75.Be. 1. Introduction. The design and construction of a neutron powder diffractometer is mainly governed by the scientific purpose, the constraint that the ...
First Results from the VULCAN Diffractometer at the SNS
Energy Technology Data Exchange (ETDEWEB)
Wang, Xun-Li [ORNL; Holden, T. M. [Northern Stress Technology; Stoica, Alexandru Dan [ORNL; An, Ke [ORNL; Skorpenske, Harley David [ORNL; Rennich, George Q [ORNL; Iverson, Erik B [ORNL; Jones, Amy Black [ORNL
2010-01-01
On Friday June 26, 2009, the neutron beam shutter for the VULCAN diffractometer at the SNS was opened for the first time. Initial measurements to characterize the instrument performance are reported. It is shown that the measurement results are by and large in agreement with design calculations. New research opportunities with VULCAN are discussed.
Instrumentation for PSD-based neutron diffractometers at Dhruva ...
Indian Academy of Sciences (India)
or stepper motor controller connected over GPIB or RS232 are also integrated in the data acquisition system. The data ... system the PSD is moved using a motor and data is acquired at different positions. In order to achieve .... The powder diffractometer for polycrystals is built at the beam port T-1013 in the Dhruva reactor ...
A high resolution powder diffractometer using focusing optics
Indian Academy of Sciences (India)
The instrument provides sample environment of very low temperatures and high magnetic fields using a 7 Tesla cryogen-free superconducting magnet with a VTI having a temperature range of 1.5–320 K. The special sample environment and high resolution make this neutron powder diffractometer a very powerful facility for ...
Write-up for the diffractometer D1 at Risoe
International Nuclear Information System (INIS)
Bundgaard, J.; Krebs Larsen, F.; Lebech, B.; Nielsen, M.H.; Skaarup, P.
1982-05-01
Manual for the crystallographic program system used to control the 4-circle neutron diffractometer D1/TASII at DR3, Risoe. The mechanical part of the diffractometer consists of a monochromator part which allows an easy change of incident neutron wavelenght and a four-circle HUBER goniostate consisting of an Euler cradle (HUBER 512) and two horizontal goniometers (HUBER 440 and HUBER 430). The goniostate is computer controlled by a PDP-11/34 interfaced via CAMAC modules. The PDP-11/34 computer has a 128 k byte memory, two hard magnetic disc stations, a fast DEC-writer terminal and a screen terminal. The diffractometer can be operated remotely via modem and telephone line connections from remote stations such as the University of Aarhus and ILL, Grenoble. Minor parts of the software used to control the diffractometer were developed at Risoe while the major parts were a generous gift to Risoe from College 5, the diffraction group, at the Institute Laue-Langevin, Grenoble, France. (editors)
Indian Academy of Sciences (India)
(Exercise !)) The subject of Fourier series finds a wide range of applications from crystallography to spectroscopy. It is one of the most powerful theories in the history of mathematics and has stimulated the .... satisfy the wave equation and following physical ideas Bernoulli suggested solutions of the form u ex,t) = l:ak ...
Indian Academy of Sciences (India)
assuming a lot of Lebesgue theory of integration. We would like to conclude this article with the following result. ofFejer which treats the class of continuous functions as a whole. As we know, given any point to there is a function in this class whose Fourier series diverges at that point. In 1904, the Hungarian mathematician ...
Measuring, Acquiring and recording of the neutron flux intensity at the cairo fourier diffractometer
Maayouf, R M A; Abdel-Hamid, A S
2003-01-01
A simple and low cost, data acquisition system is presented for measuring, acquiring and recording the instant variations of the neutron flux. The system applies especially designed PC acquisition board and software driver to acquire, periodically, the number of digital pulses that arrive from one or more neutron detectors during short sampling time intervals. It has been verified that the data collected from the detectors, using the present system, can be preserved and available for software analysis and statistical operations; such as computing the average and integral neutron flux during any time period.
Instrumentation for PSD based neutron diffractometers at Dhruva reactor
International Nuclear Information System (INIS)
Pande, S.S.; Borkar, S.P.; Prafulla, S.; Srivastava, V.D.; Behare, A.; Mukhopadhyay, P.K.; Ghodgaonkar, M.D.; Kataria, S.K.
2004-01-01
Linear position sensitive detectors (PSDs) are widely used to configure neutron diffractometers and other instruments. Necessary front-end electronics and a data acquisition system is developed to cater to such instruments built around the Dhruva research reactor in BARC. These include three diffractometers with multiple PSDs and four with single PSD. The front-end electronics consists of high voltage units, preamplifiers, shaping amplifiers, ratio ADCs (RDC). The data acquisition system consists of an interface card and software. Commercially available hardware like temperature controller or stepper motor controller connected over GPIB or RS232 are also integrated in the data acquisition system. The data acquisition is automated so that it can continue unattended for control parameter like temperature, thus enabling optimum utilization of available beam time. The instrumentation is scalable and can be easily configured for various instrumental requirements. The front-end electronics and the data acquisition system are described here. (author)
Instrumentation for PSD-based neutron diffractometers at Dhruva reactor
Pande, S. S.; Borkar, S. P.; Prafulla, S.; Srivastava, V. D.; Behare, A.; Mukhopadhyay, P. K.; Ghodgaonkar, M. D.; Kataria, S. K.
2004-08-01
Linear position sensitive detectors (PSDs) are widely used to configure neutron diffractometers and other instruments. Necessary front-end electronics and a data acquisition system [1] is developed to cater to such instruments built around the Dhruva research reactor in BARC. These include three diffractometers with multiple PSDs and four with single PSD. The front-end electronics consists of high voltage units, preamplifiers [2], shaping amplifiers, ratio ADCs (RDC) [3]. The data acquisition system consists of an interface card and software. Commercially available hardware like temperature controller or stepper motor controller connected over GPIB or RS232 are also integrated in the data acquisition system. The data acquisition is automated so that it can continue unattended for control parameter like temperature, thus enabling optimum utilization of available beam time. The instrumentation is scalable and can be easily configured for various instrumental requirements. The front-end electronics and the data acquisition system are described here.
X-ray diffractometer configurations for thin film analysis
Energy Technology Data Exchange (ETDEWEB)
Haase, A. [Rich. Seifert and Co., Analytical X-ray Systems, Ahrensburg (Germany)
1996-09-01
A presentation of various configurations of focusing Seemann-Bohlin diffractometer, parafocusing Bragg-Brentano diffractometer and parallel beam are demonstrated. Equipped with different thin film attachments a comparison to conventional measurements are given. The application of different detector types like scintillation, gas proportional, electroluminescence (LUX) and solid state are described. Typical instrument set-ups for reflectometry, grazing incidence diffraction, total reflection, high resolution X-ray diffraction are explained. Different elements like slits, soller slits, pinhole collimators, crystal monochromators, monofiber (FOX) and polycapillaries (multifiber lens, Kumakhov lens`), flat or curved multilayer with constant or variable d-spacing, and their combinations are presented. The comparison of different beam conditioners in peak-to-background ratios are given. Wavelength dispersive scans show the energy discrimination possibilities of different beam optics.
User guide for the POLARIS powder diffractometer at ISIS
International Nuclear Information System (INIS)
Hull, S.; Mayers, J.
1989-11-01
The POLARIS spectrometer at ISIS is currently being scheduled for use as a high intensity, medium resolution powder diffractometer. The particularly high neutron flux on POLARIS enables experiments to be performed with comparatively short counting times or on small sample volumes. This ability has been exploited during kinetic experiments of phase changes, where diffraction data is collected whilst the furnace is heating up. The provision of a large detector bank at 2 θ ∼ 90 0 is particularly important for studies of powder samples at high pressures. This scattering geometry has significant advantages for experiments of this kind, as suitable collimation of the incident and outgoing beams eliminates scattering from the surrounding pressure transmitting medium. This guide is intended to give a short description of the POLARIS powder diffractometer and to provide the basic information required to perform a powder diffraction experiment. (author)
Development of BATAN’s texture diffractometer (current status)
Energy Technology Data Exchange (ETDEWEB)
Priyanto, T. H., E-mail: thardi@batan.go.id; Bharoto,; Mugirahardjo, H.; Muslih, R.; Ramadhani, A.; Sairun [Center for Nuclear Industrial Material Technology (PTBIN) National Nuclear Energy Agency (BATAN) Kawasan Puspiptek Serpong, Tangerang Selatan (Indonesia)
2015-04-16
Texture Diffractometer, called DN2, is one of neutron diffractometers in BATAN which is dedicated for texture measurement using neutron diffraction method. To obtain better performance of the DN2, a flight tube goniometer have been installed between the monochromator and sample position. By adjusting the flight tube goniometer, defocusing effect at direct beam and background effect could be reduced significantly. Some experiments have been carried out to characterize DN2 performance. The flight tube goniometer alignment and neutron wavelength calibration were characterized using silicon standard sample Si640d. Data refinement of diffraction pattern was analyzed using MAUD software and it is obtained reliability factor with background, R{sub wpb}, reduced significantly, from 42.53 % to 19.36 % after setting of flight tube goniometer. Reliability factor without background (R{sub wp}) was reduced from 27.41% to 21.36%. Calibrated of neutron wavelengh, λ = 1,2799 Angstrom is obtained.
Neutron diffractometer RSND for residual stress analysis at CAEP
Li, Jian; Wang, Hong; Sun, Guangai; Chen, Bo; Chen, Yanzhou; Pang, Beibei; Zhang, Ying; Wang, Yun; Zhang, Changsheng; Gong, Jian; Liu, Yaoguang
2015-05-01
Residual Stress Neutron Diffractometer (RSND) has been built at China Academy of Engineering Physics (CAEP) in Mianyang. Due to its excellent flexibility, the residual stress measurement on different samples, as well as in-situ study for materials science, can be carried out through RSND. The basic tests on its intensity and resolution and some preliminary experimental results under mechanical load, demonstrate the high quality of RSND.
User guide for the ECN stress-diffractometer facility
International Nuclear Information System (INIS)
Helmholdt, R.B.
1994-01-01
This report contains a description of the experimental set-up for residual stress measurements at beam hole HB4 of the High Flux Reactor at Petten. With this manual an experimentalist familiar with the properties of neutrons, diffraction techniques and the phenomenon (residual) stress will be able to operate the diffractometer, to check all the components on their proper operation and, if necessary, to repeat the alignment procedures. (orig.)
Tricks and tips on handling a powder diffractometers
Energy Technology Data Exchange (ETDEWEB)
Veroli, C. [CNR, Montelibretti, Rome (Italy). Istituto Chimica dei Materiali
1996-09-01
In the present work, the authors illustrate the procedure to be followed when small quantities of powder have to be analysed, and they also report how to generally reduce the measurement background. In addition, they describe how the diffractometer can be used to collect thin-film spectra. The experimental procedure requires careful handling because inappropriate or careless use of the instrument can lead to its damage.
High-speed single-crystal television diffractometer (software)
International Nuclear Information System (INIS)
Thomas, D.J.
1982-01-01
Area-detector diffractometers make possible almost ideal diffraction experiments. Until recently the performance of such instruments has been limited in practice by the available software. This general account discusses an unconventional way of indexing a lattice which is more appropriate for the calculations needed with normal-beam rotation geometry, and asserts the need to perform a continuous 'real-time' adaptive refinement to monitor the condition of the crystal and the detector. (orig.)
Concept for a new high resolution high intensity diffractometer
Energy Technology Data Exchange (ETDEWEB)
Stuhr, U. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-09-01
A concept of a new time-of-flight powder-diffractometer for a thermal neutral beam tube at SINQ is presented. The design of the instrument optimises the contradictory conditions of high intensity and high resolution. The high intensity is achieved by using many neutron pulses simultaneously. By analysing the time-angle-pattern of the detected neutrons an assignment of the neutrons to a single pulse is possible. (author) 3 figs., tab., refs.
On the origins of the weak folding cooperativity of a designed ββα ultrafast protein FSD-1.
Directory of Open Access Journals (Sweden)
Chun Wu
Full Text Available FSD-1, a designed small ultrafast folder with a ββα fold, has been actively studied in the last few years as a model system for studying protein folding mechanisms and for testing of the accuracy of computational models. The suitability of this protein to describe the folding of naturally occurring α/β proteins has recently been challenged based on the observation that the melting transition is very broad, with ill-resolved baselines. Using molecular dynamics simulations with the AMBER protein force field (ff96 coupled with the implicit solvent model (IGB = 5, we shed new light into the nature of this transition and resolve the experimental controversies. We show that the melting transition corresponds to the melting of the protein as a whole, and not solely to the helix-coil transition. The breadth of the folding transition arises from the spread in the melting temperatures (from ∼325 K to ∼302 K of the individual transitions: formation of the hydrophobic core, β-hairpin and tertiary fold, with the helix formed earlier. Our simulations initiated from an extended chain accurately predict the native structure, provide a reasonable estimate of the transition barrier height, and explicitly demonstrate the existence of multiple pathways and multiple transition states for folding. Our exhaustive sampling enables us to assess the quality of the Amber ff96/igb5 combination and reveals that while this force field can predict the correct native fold, it nonetheless overstabilizes the α-helix portion of the protein (Tm = ∼387K as well as the denatured structures.
High resolution neutron diffractometer HRND at research reactor CMRR
Zhang, J.; Xia, Y.; Wang, Y.; Xie, C.; Sun, G.; Liu, L.; Pang, B.; Li, J.; Huang, C.; Liu, Y.; Gong, J.
2018-01-01
The high resolution neutron diffractometer HRND is located at the 20 MW China Mianyang Research Reactor (CMRR), which is a neutron powder diffractometer especially dedicated to crystal and magnetic structure studies for polycrystalline powder samples. A vertical focusing Ge (511) monochromator produce a monochromatic neutron beam with a wavelength of 1.885 Å at a fixed take-off angle of 120o. An array of 64 equidistant 3He filled proportional counters can acquire diffraction patterns with a large-scale diffraction angle range over 160o. As all the Soller slit collimators of HRND have a collimation angle of 10' and the monochromator has an average mosaicity of 0.359o, HRND obtains a best resolution of about 1.6\\textperthousand based on experiments, which makes the resolution of HRND can compete with the mainstream-level high resolution neutron powder diffractometers in the world. Equipped with a cryostat and a furnace, HRND allows structural characterization in an extremely broad temperature range. The details of the configuration and performance of the instrument are reported along with its specifications and performance assessments in the present paper.
Automation of angular movement of the arm neutron diffractometer
International Nuclear Information System (INIS)
Aguilar H, F.; Herrera A, E.; Quintana C, G.; Torres R, C. E.; Reyes V, M.
2015-09-01
A technique to determine the crystal structure of some materials is the neutron diffraction. This technique consists on placing the material in question in a monoenergetic neutron beam obtained by neutron diffraction in a monochromator crystal. The neutron energy depends of the diffraction angle. The Instituto Nacional de Investigaciones Nucleares has a neutron diffractometer and monochromator crystals of pyrolytic graphite. This crystal can be selecting the neutron energy depending on the angle of diffraction in the glass. The radiation source for the neutron diffractometer is the TRIGA Mark III reactor of the Nuclear Center Dr. Nabor Carrillo Flores. During their operation are also obtained besides neutrons, β and γ radiation. The interest is to have thermal neutrons, so fast neutrons and γ rays are removed using appropriate shielding. The average neutron fluxes of the radial port RE2 of neutron diffractometer at power 1 MW are: heat flow 2,466 x 10 8 n cm -2 sec -1 and fast flow 1,239 x 10 8 n cm -2 sec -1 . The neutron detector is housed in a shield mounted on a mechanical linkage with which the diffraction angle is selected, and therefore the energy of the neutrons. The movement of this joint was performed by the equipment operator manually, so that accuracy to select the diffraction angle was not good and the process rather slow. Therefore a mechanical system was designed, automated by means of a motor as an actuator, a system of force transmission and an electronic control in order that the operator will schedule the diffraction angles and allow the count in the neutrons detection system in a simple manner. (Author)
Write-up for the Diffractometer D1 at Risø
DEFF Research Database (Denmark)
Bundgaard, Jørgen; Krebs Larsen, F.; Lebech, Bente
Manual for the crystallographic program system used to control the 4-circle neutron diffractometer D1/TASII at DR3, Risø. The mechanical part of the diffractometer consists of a monochromator part which allows an easy change of incident neutron wavelength and a four-circle HUBER goniostate...... terminal. The diffractometer can be operated remotely via modem and telephone line connections from remote stations such as the University of Århus and ILL, Grenoble. Minor parts of the software used to control the diffractometer were developed at Risø while the major parts were a generous gift to Risø...
Design of Data Acquisition System for High Resolution Powder Diffractometer
International Nuclear Information System (INIS)
Yu Zhouxiang; Sun Kai; Liu Yuntao; Chen Dongfeng; Gan Shaojian
2009-01-01
The holistic design and hardware components of data acquisition system for high resolution powder diffractometer based on China Advanced Research Reactor (Carr) were introduced. The structures and features of each unit circuit were described in detail. The circuit was debugged using input signal and the performance was tested. The results satisfy the requirements of pre-design. The whole system including detector, preamplifier, main amplifier, discriminator, counter and computer fulfill the process of signal acquiring, amplifying, shaping, discriminating, counting and storing. Besides, the data acquisition system with up to 65 channels has been successfully manufactured. (authors)
Enhancement of TOF diffractometer Sirius with 90 detector bank
Oikawa, K; Torii, S; Mochiku, T
2002-01-01
A TOF powder diffractometer, Sirius, installed at the Neutron Science Laboratory (KENS) of the High Energy Accelerator Research Organization (KEK), has realized both high resolution and high intensity with its large backward detector bank together with supermirror guide. Sirius also has a large 90 detector bank (0.54 str), which is used for diffraction studies under special environments, such as high pressure, high temperature, and so on. Recent works using a high-pressure cell (Paris-Edinburgh cell) and a high-temperature furnace with a gas-control device (modeled on the Miller Furnace at IPNS) are presented. (orig.)
Study of single crystals by neutron diffractometer KSN-2
International Nuclear Information System (INIS)
Jirak, Z.
1976-01-01
The experimental technique is described of measuring neutron diffraction on monocrystals using diffractometer KSN-2 of Polish manufacture located by the WWR-S reactor at Rez. For structural measurements crystals are used with the largest possible mosaic spread parameter to allow for minimum correction on the secondary extinction at relatively large dimensioned samples. It is stated that mosaic spread parameter of the samples and thereby their usability for structural studies may be estimated in the course of measuring from half-widths of diffraction curves. (Oy)
High-pressure-low-temperature x-ray power diffractometer.
Syassen, K; Holzapfel, W B
1978-08-01
A high-pressure technique for x-ray diffraction studies at low temperatures is described. The system consists of a Bridgman anvil type high-pressure device with either tungsten carbide or boron carbide anvils, a liquid He cryostat, and x-ray diffractometer operating in Debye-Scherrer geometry. The newly developed boron carbide anvil cell is capable of containing a liquid pressure transmitting medium. The precision of the lattice parameter determination is discussed and the effect of nonisostatic stress components on the diffraction pattern is examined.
Soft X-ray diffractometer for synchrotron radiation
Gau, T S; Liu, K Y; Chung, C H; Chen, C K; Lai, S C; Shu, C H; Huang, Y S; Chao, C H; Lee, Y R; Chen, C T; Chang, S L
2001-01-01
An ultra-high vacuum soft X-ray diffractometer has been constructed and commissioned at the Synchrotron Radiation Research Center (SRRC) to investigate materials structures in mesoscale. The diffractometer, housed in a UHV tank, consists of a 6-circle goniometer, together with the systems for beam-collimation, signal detection, vacuum, and control panels. The kappa-phi (cursive,open) Greek-psi goniostat is adopted for the sample orientation. Crystal samples can be rotated along a given reciprocal lattice vector by using psi scan. Two orthogonal axes, gamma (or 2 theta) and delta, are used to move the detector. The detector is a semiconductor pin diode, which can be used in UHV ambient. This 6-circle goniometer allows for sample scanning of a wide range in the momentum space. The motors used for goniometer rotation and slit selection are UHV compatible. The UHV tank is placed on an XYZ table capable of positioning the center of the goniometer onto the incident beam. Test experiments have been carried on the 1-...
Portable X-ray diffractometer equipped with XRF for archaeometry
International Nuclear Information System (INIS)
Uda, M.; Ishizaki, A.; Satoh, R.; Okada, K.; Nakajima, Y.; Yamashita, D.; Ohashi, K.; Sakuraba, Y.; Shimono, A.; Kojima, D.
2005-01-01
A portable X-ray diffractometer equipped with an X-ray fluorescence spectrometer was improved so as to get a diffraction pattern and a fluorescence spectrum simultaneously in air from one and the same small area on a specimen. Here, diffraction experiments were performed in two modes, i.e. an angle rotation mode and an energy dispersive mode. In the latter a diffraction pattern and a fluorescence spectrum were simultaneously recorded in a short time, 100 s or less, on one display. The diffractometer was tested in the field to confirm its performance. Targets chosen for this purpose were a bronze mirror from the Eastern Han Dynasty (25-220), and a stupa and its pedestal which are part of the painted statue of 'Tamonten holding a stupa' from the Heian Period (794-1192), enshrined in the Engyouji temple founded in 996. The bronze mirror was identified as a product of the Han Dynasty from its chemical composition and the existence of the δ phase in the Cu-Sn alloy. The stupa and its pedestal were decorated with gold powder and gold leaf, respectively. From the XRF data of the pedestal, the underlying layer of gold leaf seems to have been painted with emerald green
Portable X-ray diffractometer equipped with XRF for archaeometry
Uda, M.; Ishizaki, A.; Satoh, R.; Okada, K.; Nakajima, Y.; Yamashita, D.; Ohashi, K.; Sakuraba, Y.; Shimono, A.; Kojima, D.
2005-09-01
A portable X-ray diffractometer equipped with an X-ray fluorescence spectrometer was improved so as to get a diffraction pattern and a fluorescence spectrum simultaneously in air from one and the same small area on a specimen. Here, diffraction experiments were performed in two modes, i.e. an angle rotation mode and an energy dispersive mode. In the latter a diffraction pattern and a fluorescence spectrum were simultaneously recorded in a short time, 100 s or less, on one display. The diffractometer was tested in the field to confirm its performance. Targets chosen for this purpose were a bronze mirror from the Eastern Han Dynasty (25-220), and a stupa and its pedestal which are part of the painted statue of "Tamonten holding a stupa" from the Heian Period (794-1192), enshrined in the Engyouji temple founded in 996. The bronze mirror was identified as a product of the Han Dynasty from its chemical composition and the existence of the δ phase in the Cu-Sn alloy. The stupa and its pedestal were decorated with gold powder and gold leaf, respectively. From the XRF data of the pedestal, the underlying layer of gold leaf seems to have been painted with emerald green.
Neutron Time-of-Flight Diffractometer HIPPO at LANSCE
Vogel, Sven; Williams, Darrick; Zhao, Yusheng; Bennett, Kristin; von Dreele, Bob; Wenk, Hans-Rudolf
2004-03-01
The High-Pressure Preferred Orientation (HIPPO) neutron diffractometer is the first third-generation neutron time-of-flight powder diffractometer to be constructed in the United States. It produces extremely high intensity by virtue of a short (9 m) initial flight path on a high intensity water moderator and 1380 3He detector tubes covering 4.5 m2 of detector area from 10' to 150' in scattering angles. HIPPO was designed and manufactured as a joint effort between LANSCE and University of California with the goals of attaining world-class science and making neutron powder diffractometry an accessible and available tool to the national user community. Over two decades of momentum transfer are available (0.1-30 A-1) to support studies of amorphous solids; magnetic diffraction; small crystalline samples; and samples subjected to extreme environments such as temperature, pressure, or magnetic fields. The exceptionally high data rates of HIPPO also make it useful for time-resolved studies. In addition to the standard ancillary equipment (100-position sample/texture changer, closed-cycle He refrigerator, furnace), HIPPO has unique high-pressure cells capable of achieving pressures of 30 GPA at ambient and high (2000 K) temperature with samples up to 100 mm3 in volume.
An in-vacuum diffractometer for resonant elastic soft x-ray scattering
Hawthorn, D. G.; He, F.; Davis, H.; Achkar, A. J.; Zhang, J.; Sutarto, R.; Wadati, H.; Radi, A.; Wilson, T.; Wright, G.; Shen, K. M.; Geck, J.; Zhang, H.; Novak, V.; Sawatzky, G. A.; Venema, L.C.
We describe the design, construction, and performance of a 4-circle in-vacuum diffractometer for resonant elastic soft x-ray scattering. The diffractometer, installed on the resonant elastic and inelastic x-ray scattering beamline at the Canadian Light Source, includes 9 in-vacuum motions driven by
VULCAN-The engineering diffractometer at the SNS
Energy Technology Data Exchange (ETDEWEB)
Wang, Xun-Li [ORNL; Holden, T. M. [Northern Stress Technology; Rennich, George Q [ORNL; Stoica, A. D. [Oak Ridge Associated Universities (ORAU); Liaw, Peter K [University of Tennessee, Knoxville (UTK); Choo, Hahn [ORNL; Hubbard, Camden R [ORNL
2006-01-01
The VULCAN diffractometer at the Spallation Neutron Source (SNS) is designed to tackle a broad range of problems in materials science and engineering, including spatial mapping of the residual stress distribution in components, deformation behavior under static and cyclic loadings, and the kinetics of the phase transformation. The optics design features a focusing neutron guide, wide-angular detector coverage for diffraction, and an area detector for small angle scattering. By employing an interchangeable neutron guide-collimator system, the instrument can be optimally configured for individual experiments with desired resolution. The performance of the instrument was estimated using Monte Carlo simulation. A suite of specialized sample environments is also under construction as an integrated part of the instrument.
NIEMELÄ, EERO
2008-01-01
Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...
Directory of Open Access Journals (Sweden)
Zhen Cao
2014-01-01
Full Text Available Fourier transform infrared spectroscopy (FTIR technique was used to classify 16 species from three moss families (Mielichhoferiaceae, Bryaceae, and Mniaceae. The FTIR spectra ranging from 4000 cm−1 to 400 cm−1 of the 16 species were obtained. To group the spectra according to their spectral similarity in a dendrogram, cluster analysis and principal component analysis (PCA were performed. Cluster analysis combined with PCA was used to give a rough result of classification among the moss samples. However, some species belonging to the same genus exhibited very similar chemical components and similar FTIR spectra. Fourier self-deconvolution (FSD was used to enhance the differences of the spectra. Discrete wavelet transform (DWT was used to decompose the FTIR spectra of Mnium laevinerve and M. spinosum. Three scales were selected as the feature extracting space in the DWT domain. Results showed that FTIR spectroscopy combined with DWT was suitable for distinguishing different species of the same genus.
The high resolution powder diffractometer (HRPD) at ISIS - a user guide
International Nuclear Information System (INIS)
Ibberson, R.M.; David, W.I.F.; Knight, K.S.
1992-05-01
This guide is intended to give a short description of the High Resolution Powder Diffractometer, HRPD, at ISIS and to provide the basic information required in order to perform a routine powder diffraction experiment. (Author)
Neutron diffractometers for structural biology at spallation neutron sources
International Nuclear Information System (INIS)
Schoenborn, B.P.; Pitcher, E.
1994-01-01
Spallation neutron sources are ideal for diffraction studies of proteins and oriented molecular complexes. With spoliation neutrons and their time dependent wavelength structure, it is easy to electronically select data with an optimal wavelength bandwidth and cover the whole Laue spectrum as time (wavelength) resolved snapshots. This optimized data quality with best peak-to-background ratios and provides adequate spatial and energy resolution to eliminate peak overlaps. The application of this concept will use choppers to select the desired Laue wavelength spectrum and employ focusing optics and large cylindrical 3 He detectors to optimize data collection rates. Such a diffractometer will cover a Laue wavelength range from 1 to 5 Angstrom with a flight path length of 10m and an energy resolution of 0.25 Angstrom. Moderator concepts for maximal flux distribution within this energy range will be discussed using calculated flux profiles. Since the energy resolution required for such timed data collection in this super Laue techniques is not very high, the use of a linac only (LAMPF) spoliation target is an exciting possibility with an order of magnitude increase in flux
Data acquisition system for linear position sensitive detector based neutron diffractometer
International Nuclear Information System (INIS)
Pande, S.S.; Borkar, S.P.; Behere, A.; Prafulla, S.; Srivastava, V.D.; Mukhopadhyaya, P.K.; Ghodgaonkar, M.D.; Kataria, S.K.
2003-03-01
This data acquisition system is developed to serve the requirements of various linear 1PSD based neutron diffractometers. A neutron diffractometer uses a neutron beam as a probe to study the crystallographic properties of materials. Presently two multi-PSD and two single-PSD diffractometers are commissioned and a few more are being installed in Dhruva. This data acquisition system is installed at each of these - diffractometers. Different requirements of individual diffractometers were studied and reconciled to design a single data acquisition system, which can be easily configured or customized for individual setups. The charge division in a linear PSD is converted to a position output with the help of an RDC (Ratio ADC). The ftont-end electronics, which consist of preamplifiers and shaping amplifiers, provide an interface between a PSD and an RDC. A PC add-on card is designed around a Transputer. It can interface 16 RDCs, a few motor controls and on/off controls. Data acquisition and other controls are implemented in the Transputer program. A front-end Windows98 application merges the raw data of different RDCs to obtain the equiangular data. Through software the data acquisition system can be configured for diffetent diffractometers. Commercially available hardware is also integrated as,a part of the data acquisition system in some of the setups. The data acquisition system is working reliably as a part of two single PSD and two multi-PSD diffractometers. It can handle data rates upto 15 K/Sec without any loss of counts. It has played a significant role in providing improved throughput and utilization ofvarious diffractometers. The'data acquisition system and its different applications are presented in this report. (author)
An X-ray diffractometer specimen holder for use with reactive and toxic materials
International Nuclear Information System (INIS)
Huyton, A.; Munden, A.B.
1979-04-01
An X-ray diffractometer specimen holder has been designed for analysis of reactive sodium compounds which will satisfactorily seal the sample from the atmosphere. The holder can be readily filled in a glove-box and is easily transported for mounting on a vertical Philips PW 1051 X-ray diffractometer. It is considered that this holder could also be applied to a wide range of other reactive and toxic materials, e.g. plutonium or its compounds. (author)
Indian Academy of Sciences (India)
digital methods of spectrum estimation which influenced the research in almost every field of engineering and science. In this article, we will first introduce the conti- nuous-time Fourier transform (eFT), discrete-time Fourier transform and discrete Fourier transform (DFT) and then present an example to illustrate the relation ...
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
design and Application of Neutron Residual Stress Diffractometer for China Advanced Research Reactor
International Nuclear Information System (INIS)
Li Junhong; Gao Jianbo; Li Jizhou; Han Songbai; Zu Yong; Liu Rongdeng; Liu Xiaolong; Liu Yuntao; Chen dongfeng
2010-01-01
The neutron residual stress diffractometer for China Advanced Research Reactor (CARR) is the first instrument in China for the residual stress measurement using neutron diffraction method. Its sample table and some affiliated equipment were relocated from Sweden. According to the situation of CARR, the conceptional and physical design and mechanism fabrication were finished. Now the whole instrument is going to be put in commissioning. The take-off angle of new monochromator's shielding could be continuously changeable from 41 degree to 109 degree. The position of monochromator could be adjusted conveniently and flexibly by a five axis table. The resolution of this diffractometer could reach 0.2% using the double focusing Si(311) monochromator. The technical specification of one dimension neutron position sensitive detector ORDELA 1128N is better than that of ORDELA 1150N used on REST. The various affiliated equipment of instrument enable the diffractometer to measure the texture and tensional experiment in situ. (authors)
Energy Technology Data Exchange (ETDEWEB)
Mendoza A, D.; Gonzalez M, P.; Falcon B, T. [Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, Mexico D.F. (Mexico); Castano, V.M. [Instituto de Fisica, UNAM, Laboratorio Juriquilla, A.P. 1-1010, C.P. 76001, Queretaro (Mexico)
1999-07-01
In this work it was presented the results obtained of the dosimetry which was realized in a X-ray diffractometer for powders, trademark Siemens D5000, using the thermoluminescent signal generated by the X-rays in the commercial dosemeter TLD-100 of Harshaw, US. In according to the results obtained, the radiation quantity received by an analysed material in the diffractometer, will be proportional to exposure time and it can vary from unities until tenths of grays. These results are very outstanding when are analysed crystalline materials in a diffractometer, for knowing the present crystalline phases, mainly if these are highly sensitive to the ionizing radiation, as it is the case of the thermoluminescent materials. (Author)
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
D2B, a new high resolution neutron powder diffractometer at ILL Grenoble
International Nuclear Information System (INIS)
Hewat, A.W.
1987-01-01
Applications of high resolution neutron powder diffraction to materials science have grown rapidly in the past 10 years, with the development of Rietveld methods of profile refinement, and new high resolution diffractometers and multidetectors. Materials studied range from catalysts to zeolites, and from battery electrodes to prestressed superconducting wires. Although the techniques have now been adapted for X-ray and synchrotron radiation, neutron powder diffraction retains unique advantages. In this paper we describe the design and first test measurements on the latest high resolution powder diffractometer D2B at ILL Grenoble. A review of the applications is published in Chemica Scripta (1986). (author) 9 refs., 6 figs., 2 tabs
X-ray diffractometers for examining and inspecting stressed-strained materials (review)
International Nuclear Information System (INIS)
Myasnikov, Y.G.; Bol'shakov, P.P.; Komyak, N.I.; Lifshits, V.A.
1986-01-01
The application of modern detectors and automation of measurements based on computers have increased the productivity and accuracy of the x-ray method, which has become an effective means of technological inspection of objects of complicated configuration and arbitrary dimensions. Various recording methods are described in this paper that are used in the goniometric devices of the diffractometers for determining the stresses, including: a fixed detector, parafocusing, Zeeman-Blin method, parallel beam, and side-inclined beam. Work is being continued on the development of x-ray diffractometers for macrostress measurements using computers for automating the process of measurement and processing the experimental data
An adjustable in-pile fan collimator for focusing at a neutron diffractometer
Stüsser, N
2002-01-01
An adjustable in-pile fan collimator was built and tested in a neutron diffraction set-up with a large horizontally curved monochromator for focusing in real and reciprocal space. For small samples, enhancements of intensity up to a factor of five without losing 2 theta-resolution are possible in comparison to a conventional diffractometer equipped with Soller-type collimators. Our geometry will be discussed and compared to both the conventional diffractometer and a focusing arrangement using an in-pile diaphragm.
Powder neutron diffraction studies by means of the KSN-2 diffractometer
International Nuclear Information System (INIS)
Vratislav, S.; Dlouha, M.
1998-01-01
Placed at the 2nd horizontal beam tube of the LVR-15 research reactor, KSN-2 is a double axis powder diffractometer used for structure and texture experiments with polycrystalline samples. The diffractometer is equipped with auxiliary devices such as a cryogenic apparatus, heater furnace, and texture goniometer. The diffraction patterns are treated by Rietveld analysis, and complete structural parameters are determined. Research activities are focused on neutron scattering in solid state physics and materials science. Applications to condensed matter cover a wide range, from the location of light atoms and cation distributions to magnetic structures and phase transitions. Some promising materials such as zeolites, perovskites and high-temperature superconductors were investigated
Improvement of detector system of the two-axis neutron powder diffractometer
International Nuclear Information System (INIS)
Xue Yanjie; Guo Liping; Chen Dongfeng; Zhang Baisheng; Chen Na; Zhang Li; Sun Kai; Xiao Hongwen; Zhang Lingfei; Wang Hongli; Li Junhong; Wu Erdong; Yuan Xuezhong
2005-01-01
The detector system of the two-axis neutron powder diffractometer at the Heavy Water Research Reactor of China Institute of Atomic Energy was improved by increasing the number of detectors from one to four and by installing the third Soller collimators with horizontal divergence of 20'. The measurements of Fe powder diffraction patterns show that the counting rate of the diffractometer is increased by a factor of 2.3 and the resolution is also improved at the lower and mediate scattering angle region. (author)
Angle calculations for a z-axis/(2S+2D) hybrid diffractometer
DEFF Research Database (Denmark)
Bunk, Oliver; Nielsen, Martin Meedom
2004-01-01
calculations are presented for a new 'hybrid' diffractometer consisting of a base instrument that can be combined with two different detector arms. With one of the detector arms, the instrument is a standard z-axis diffractometer as commonly used in surface studies. The other detector arm is designed...... for a heavy two-dimensional detector. The calculations are formulated in a general framework making it easy to incorporate, e. g. a second sample rotation stage, whereby it is possible to perform reflectivity and standard surface-crystallography measurements in the same geometry....
Control program of the neutron four-circle-diffractometer P32 at the SILOE reactor/CEN Grenoble
International Nuclear Information System (INIS)
Guth, H.; Paulus, H.; Reimers, W.; Heger, G.
1983-09-01
The four-circle diffractometer P32 for elastic neutron scattering on single crystals was installed at the SILOE reactor/CEN Grenoble in 1981. The control program, presented here, is a new update of the former program versions used at the FR2 reactor/Kernforschungszentrum Karlsruhe. Important improvements concerning reliability and handling of the diffractometer are added. (orig.) [de
Control program of the neutron four-circle-diffractometer P110 at the ORPHEE reactor/CEN Saclay
International Nuclear Information System (INIS)
Guth, H.; Paulus, H.; Reimers, W.; Heger, G.
1984-05-01
The four-circle diffractometer P110 for elastic neutron scattering on single crystals was installed at the ORPHEE reactor/CEN Saclay in 1982. The control progam, presented here, is a new update of the former program versions used at the FR2 reactor. Important improvements concerning reliability and handling of the diffractometer are added. (orig./HP) [de
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…
Fourier Transform Spectrometer
National Aeronautics and Space Administration — The Fourier Transform Spectrometer project demonstrates the efficacy of a miniaturized spectrometer for flight applications.A spectrometer is an instrument used to...
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
JAX: a micro-computer based X-ray diffractometer controller
International Nuclear Information System (INIS)
Naval, P.C. Jr.
1987-05-01
This paper describes a micro-computer based X-ray diffractometer controller and explores its possibilities in simplifying acquisition and analysis of X-ray powder diffraction data. The interrupt-driven controller can operate in both present time and present count data acquisition modes and allows a data analysis program to execute concurrently with data collection. (Auth.). 16 figs.; 2 tabs
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
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....
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Energy Technology Data Exchange (ETDEWEB)
Macias B, L.R. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico); Garcia C, R.M. [Administracion Central de Laboratorio y Servicios Cientificos, Legaria 608, Col. Irrigacion, 11500 Mexico D.F. (Mexico); Ita T, A. De [UAM-A, San Pablo 180, Col. Reynosa Tamaulipas, 02200 Mexico D.F. (Mexico)
2003-07-01
The neutron diffractometer has three collimators and a monochromator of which it depends the resolution of the same one and exists a commitment between the resolution of the diffractometer and its intensity; if it is sought to work with more resolution, the intensity will diminish, and also, if one has little volume of the material, the diffracted light it is diminished, so the selection of the values of the collimators is this way important to have an unique value of the resolution of the diffractometer. (Author)
Determination of precise X-ray diffraction angles by fast Fourier transform
International Nuclear Information System (INIS)
Tokita, S.; Kojima, T.
1987-01-01
A new analytical method is presented for the separation of two or more closely overlapping X-ray diffraction lines using the narrowly distributed Gaussian function and one-dimensional fast Fourier transform pair. To test the method, the diffraction lines associated with characteristic Kα 1 and Kα 2 rays are measured by an X-ray diffractometer using a Brazilian quartz powder as a standard sample. It is found that the observed diffraction lines can be completely separated into Kα 1 and Kα 2 lines and that the accuracy of those diffraction angles is better than 2x10 -4 . (orig.)
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)
Fast Fourier orthogonalization
L. Ducas (Léo); T. Prest; S.A. Abramov; E.V. Zima; X-S. Gao
2016-01-01
htmlabstractThe classical fast Fourier transform (FFT) allows to compute in quasi-linear time the product of two polynomials, in the {\\em circular convolution ring} R[x]/(x^d−1) --- a task that naively requires quadratic time. Equivalently, it allows to accelerate matrix-vector products when the
International Nuclear Information System (INIS)
Hoelzel, M.; Gilles, R.; Schlapp, M.; Boysen, H.; Fuess, H.
2004-01-01
The new structure powder diffractometer (SPODI), currently built up in the experimental hall of the FRM-II in Garching, near Munich, is optimised to achieve high-resolution diffraction at high neutron flux with good profile shapes. Highly developed components, such as a composite monochromator, three different collimators in front of the sample and a position sensitive detector enable a usage of the instrument in various configurations. This contribution gives an insight in instrumental variations to optimize the diffractometer. Monte Carlo simulations were performed to figure out the influences of sample height, sample collimation, detector height and wavelength on flux, resolution and profile shape. Based on these calculations, the most suitable instrument configuration for a specific task will be selected
Single crystal diffractometer for solid state physics at pulsed neutron source
International Nuclear Information System (INIS)
Takahashi, Miwako; Abe, Hiroshi; Ishigaki, Toru
2002-05-01
KEK Neutron Diffraction Facility held this meeting on September 1, 2002. The objects of meeting were to discuss themes and future of single crystal diffraction of pulsed neutron source, because 3GeV/1MW intense neutron beam will be produced by the high intensity proton accelerator project after 4 year. This report was made to discuss needs of the single crystal diffractometer in the high intensity proton accelerator project for research of solid-state physics. Paper, needs of this apparatus, suggestions to how to put forward proposal and themes are included. 16 papers were read in this meeting. The subjects of these papers consisted of the neutron diffractometer such as FOX, FONDER, EXCED, SXD and it by intense pulsed neutron source, powder, MRP, high Tc superconductors, and binary alloy. (S.Y.)
Instrumentation for Position Sensitive Detector-Powder diffractometer at CENM-Maamora
International Nuclear Information System (INIS)
Messous, M.-Y.; Belhorma, B.; Labrim, H.; El-Bakkari, B.; Jabri, H.
2013-06-01
Linear position sensitive detectors are widely used to configure neutron diffractometer and other instruments. Necessary front-end electronics and data acquisition system was developed to fulfil such instruments built around the research reactor. In this paper, the front-end electronics dedicated to the neutron powder diffractometer which will be installed in the axial beam port of the Triga Mark II research reactor (Center of Nuclear Studies of Maamora) is described. It consists of High voltage power supply, a Position-decoder and a Multichannel analyzer and data acquisition software. The 3 He-PSD detector response exposed to the neutron flow emitted by 252 Cf source held in paraffin spheres with distinct thicknesses for moderation effect, is shown. Monte-Carlo N Particles code (MCNP) simulations were also performed to study both the detector performance and the paraffin efficiency. (authors)
Calibration of X-Ray diffractometer by the experimental comparison method
Energy Technology Data Exchange (ETDEWEB)
Dudka, A. P., E-mail: dudka@ns.crys.ras.ru [Russian Academy of Sciences, Shubnikov Institute of Crystallography (Russian Federation)
2015-07-15
A software for calibrating an X-ray diffractometer with area detector has been developed. It is proposed to search for detector and goniometer calibration models whose parameters are reproduced in a series of measurements on a reference crystal. Reference (standard) crystals are prepared during the investigation; they should provide the agreement of structural models in repeated analyses. The technique developed has been used to calibrate Xcalibur Sapphire and Eos, Gemini Ruby (Agilent) and Apex x8 and Apex Duo (Bruker) diffractometers. The main conclusions are as follows: the calibration maps are stable for several years and can be used to improve structural results, verified CCD detectors exhibit significant inhomogeneity of the efficiency (response) function, and a Bruker goniometer introduces smaller distortions than an Agilent goniometer.
Application of the X-ray diffractometer DRON to the study of long period structures
International Nuclear Information System (INIS)
Gordelij, V.I.; Lushchikov, V.I.; Syrykh, A.G.; Cherezon, V.G.
1991-01-01
It is shown that the stock-produced X-ray diffractometer DRON can be adapted for the study of long period structures up to ∼150 A. The experimental data on small-angle diffraction spectra, measured on it, from both lamellar and lateral structures of biological and lipid membranes are reported. The data show that lattice constants of these structures could be determined within the accuracy of 1 A. 15 refs.; 7 figs
Using NIST Crystal Data Within Siemens Software for Four-Circle and SMART CCD Diffractometers
Byram, Susan K.; Campana, Charles F.; Fait, James; Sparks, Robert A.
1996-01-01
NIST Crystal Data developed at The National Institute for Standards and Technology has been incorporated with Siemens single crystal software for data collection on four-circle and two-dimensional CCD diffractometers. Why this database is useful in the process of single crystal structure determination, and how the database is searched, are described. Ideas for future access to this and other databases are presented. PMID:27805166
[Beginning of use of a new biological neutron diffractometer (iBIX) in J-PARC].
Tanaka, Ichiro; Kusaka, Katsuhiro; Hosoya, Takaaki; Ohhara, Takashi; Kurihara, Kazuo; Niimura, Nobuo
2010-05-01
Ibaraki Prefectural Government together with Ibaraki University and Japan Atomic Energy Agency (JAEA) has almost finished constructing a time-of-flight (TOF) neutron diffractometer for biological macromolecules for industrial use at J-PARC, IBARAKI Biological Crystal Diffractometer (iBIX). Since 2009, Ibaraki University has been asked to operate this machine in order for users to do experiments by Ibaraki Prefecture. The diffractometer is designed to cover sample crystals which have their cell edges up to around 150 A. It is expected to measure more than 100 samples per year if they have 2 mm(3) in crystal volume, and to measure even around 0.1 mm(3) in crystal volume of biological samples. The efficiency of iBIX is also expected about 100 times larger than those of the present high performance diffractometers at JRR-3 in JAEA when 1MW power realizes in J-PARC. Since December 2008, iBIX has been open to users and several proteins and organic compounds were tested under 20 kW proton power of J-PARC. It was found that one of their proteins was diffracted up to 1.4 A in d-spacing, which was nearly comparable resolution to that of BIX-3 in JRR-3 when used the same crystal as at iBIX for reasonable exposure time. In May 2009, 14 detector units were set up. By the end of fiscal year 2009, the basic part of data reduction software will be finished and an equipment blowing low temperature gas to the sample will be installed with the cooperation of JAEA.
A comparison between Engin and Engin-X, a new diffractometer optimized for stress measurement
International Nuclear Information System (INIS)
Dann, J.A.; Daymond, M.R.; Edwards, L.; James, J.A.; Santisteban, J.R.
2004-01-01
Engineering diffractometers are used extensively by both engineers and materials scientists for the measurement of strain within polycrystalline materials, both metallic and ceramic. In the past neutron diffractometers have generally been built as 'all-purpose' instruments, with designs that are compromises, balancing competing requirements to measure the intensities, positions and widths of diffraction peaks simultaneously. In contrast the newly constructed diffractometer ENGIN-X was designed with the single aim of making engineering strain measurements; essentially the accurate measurement of polycrystalline lattice parameters, at a precisely determined position. Under this design philosophy, considerable performance improvements have been obtained compared to the existing instrument. This paper details the design philosophy of this instrument, including tuneable incident resolution, together with the approaches used to realise the performance required. The improved instrument performance is demonstrated here, with results obtained during the commissioning of ENGIN-X. These results include strain mapping experiments, and demonstrate the influence of resolution on required count times, and provide a direct comparison with measurements from the existing ENGIN instrument at ISIS
Time-of-flight Extreme Environment Diffractometer at the Helmholtz-Zentrum Berlin
Prokhnenko, Oleksandr; Stein, Wolf-Dieter; Bleif, Hans-Jürgen; Fromme, Michael; Bartkowiak, Maciej; Wilpert, Thomas
2015-03-01
The Extreme Environment Diffractometer (EXED) is a new neutron time-of-flight instrument at the BER II research reactor at the Helmholtz-Zentrum Berlin, Germany. Although EXED is a special-purpose instrument, its early construction made it available for users as a general-purpose diffractometer. In this respect, EXED became one of the rare examples, where the performance of a time-of-flight diffractometer at a continuous source can be characterized. In this paper, we report on the design and performance of EXED with an emphasis on the unique instrument capabilities. The latter comprise variable wavelength resolution and wavelength band, control of the incoming beam divergence, the possibility to change the angular positions of detectors and their distance to the sample, and use of event recording and offline histogramming. These features combined make EXED easily tunable to the requirements of a particular problem, from conventional diffraction to small angle neutron scattering. The instrument performance is demonstrated by several reference measurements and user experiments.
Ortega-Cerda, Joaquim; Seip, Kristian
2000-01-01
We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges' theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a classical inequality of H. Landau as a consequence of Pavlov's description of Riesz bases of complex ex...
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Independent task Fourier filters
Caulfield, H. John
2001-11-01
Since the early 1960s, a major part of optical computing systems has been Fourier pattern recognition, which takes advantage of high speed filter changes to enable powerful nonlinear discrimination in `real time.' Because filter has a task quite independent of the tasks of the other filters, they can be applied and evaluated in parallel or, in a simple approach I describe, in sequence very rapidly. Thus I use the name ITFF (independent task Fourier filter). These filters can also break very complex discrimination tasks into easily handled parts, so the wonderful space invariance properties of Fourier filtering need not be sacrificed to achieve high discrimination and good generalizability even for ultracomplex discrimination problems. The training procedure proceeds sequentially, as the task for a given filter is defined a posteriori by declaring it to be the discrimination of particular members of set A from all members of set B with sufficient margin. That is, we set the threshold to achieve the desired margin and note the A members discriminated by that threshold. Discriminating those A members from all members of B becomes the task of that filter. Those A members are then removed from the set A, so no other filter will be asked to perform that already accomplished task.
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
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.
Fourier multispectral imaging.
Jia, Jie; Ni, Chuan; Sarangan, Andrew; Hirakawa, Keigo
2015-08-24
Current multispectral imaging systems use narrowband filters to capture the spectral content of a scene, which necessitates different filters to be designed for each application. In this paper, we demonstrate the concept of Fourier multispectral imaging which uses filters with sinusoidally varying transmittance. We designed and built these filters employing a single-cavity resonance, and made spectral measurements with a multispectral LED array. The measurements show that spectral features such as transmission and absorption peaks are preserved with this technique, which makes it a versatile technique than narrowband filters for a wide range of multispectral imaging applications.
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
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
Design of an oscillating radial collimator for use in a neutron diffractometer
International Nuclear Information System (INIS)
Deshpande, S.K.; Goyal, P.S.
2003-01-01
An oscillating radial collimator (ORC) has been designed for use at the IUC-DAEF neutron diffractometer that is being set up at the upcoming neutron beamline at Dhruva reactor, BARC. The design incorporates cadmium-plated stainless steel blades mounted between aluminium flanges in a vertical venetian blinds type arrangement. The oscillations are driven by a stepper motor using a worm and wheel segment. The design satisfies the requirements of high visibility over the small sample region but good cut-off away from it. (author)
International Nuclear Information System (INIS)
Hu Rui; Liu Yuntao; Wang Wei; Liu Zhongxiao; Li Junhong; Gao Jianbo; Wang Hongli; Chen Dongfeng
2015-01-01
The double focusing Si monochromator was designed, simulated and tested for the neutron residual stress diffractometer on China Advanced Research Reactor. The optimal vertical curvature and the optimal thickness of Si wafers were obtained by SIMRES simulation program. In addition, the figure of merit in dependence on the scattering angle, monochromator horizontal curvature and wavelength was also determined by this program. The neutron beam test results indicate that the intensity of neutron increases by 15 times by using double focusing Si monochromator in comparison with Cu monochromator. (authors)
Design and construction of a data acquisition system for a neutron diffractometer
International Nuclear Information System (INIS)
Baeza F, Lorena M.
1995-01-01
This work presents the design and construction of a data acquisition system for the neutron diffractometer of the La Reina Nuclear Studies Center. The system counts simultaneously the events produced in 17 detection channels, in 128 time channels with 10 μs duration, synchronized with a external signal. The event counting is performed by associating each detection and time channel to a binary code which determine a storage memory. The system is operated by a computer which controls the data acquisition and transfer. The designed software allows the data acquisition and storage in a file for later processing
Implementation of a new Cryopad on the diffractometer POLI at MLZ.
Hutanu, V; Luberstetter, W; Bourgeat-Lami, E; Meven, M; Sazonov, A; Steffen, A; Heger, G; Roth, G; Lelièvre-Berna, E
2016-10-01
A new polarized neutron single crystal diffractometer POLI (Polarization Investigator) has been developed at the Maier-Leibnitz Zentrum, Garching, Germany. After reviewing existing devices, spherical neutron polarimetry has been implemented on POLI as a main experimental technique using a third-generation cryogenic polarization analysis device (Cryopad) built in cooperation between RWTH University and Institut Laue-Langevin. In this report we describe the realization and present the performance of the new Cryopad on POLI. Some improvements in the construction as well as details regarding calibrations of Cryopad and its practical use are discussed. The reliable operation of the new Cryopad on POLI is also demonstrated.
The high resolution powder diffractometer at ISIS - an introductory user's guide
International Nuclear Information System (INIS)
David, W.I.F.; Akporiaye, D.E.; Ibberson, R.M.; Wilson, C.C.
1988-12-01
This manual is intended to fulfil the role of an introductory users' guide for High Resolution Powder Diffractometer (HRPD). We hope, in addition to providing a general overview of the machine, that the manual will help users to run the instrument routinely and handle most aspects of data assessment and analysis. The contents are divided into six sections including: HRPD at ISIS, the experimental running of HRPD, Neutron Powder Diffraction data analysis at ISIS-practical and scientific aspects, data assessment and crystal structure plotting programs. (author)
A data acquisition system for a high intensity powder diffractometer at HANARO
International Nuclear Information System (INIS)
Cheon, Jong-Kyu; Moon, Myung-Kook; Lee, Chang-Hee; Em, V. T; Lee, Seong-Su; Nam, Uk-Won; Yi, Jung-Hwan; Park, Je-Geun; Kim, Hong-Ju
2010-01-01
A data acquisition (DAQ) and control system for the high intensity powder diffractometer (HIPD) at High-flux Advanced Neutron Application ReactOr (HANARO) is developed in this paper. The HIPD provides the advantage of wide-angle coverage of neutron diffraction operations, which can reduce the time that is required for experiments. The HIPD DAQ and control system was commissioned into operation and the diffraction data of Al 2 O 3 was recorded successfully. The details of the detector, the data acquisition process and the instrument controls system used in the operation of the HIPD are presented.
USB port compatible virtual instrument based automation for x-ray diffractometer setup
International Nuclear Information System (INIS)
Jayapandian, J.; Sheela, O.K.; Mallika, R.; Thiruarul, A.; Purniah, B.
2004-01-01
Windows based virtual instrument (VI) programs in graphic language simplify the design automation in R and D laboratories. With minimal hardware and maximum support of software, the automation becomes easier and user friendly. A novel design approach for the automation of SIEMENS make x-ray diffractometer setup is described in this paper. The automation is achieved with an indigenously developed virtual instrument program in labVIEW ver.6.0 and with a simple hardware design using 89C2051 micro-controller compatible with PC's USB port for the total automation of the experiment. (author)
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.
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).
Kusaka, K.; Hosoya, T.; Tanaka, I.; Niimura, N.; Kurihara, K.; Ohhara, T.
2010-11-01
Since 2004, Ibaraki prefecture has constructed the TOF neutron biological diffractometer (iBIX) at J-PARC for industrial use. Since the end of 2008, Ibaraki University has operated iBIX in order to support the experiment of users and to improve the instruments. The diffractometer is designed to measure samples with their cell edges up to around 150Å. In the beginning of December in 2008, the basic optics, the support system of detectors and the three detectors were completed for the diffraction experiments. We have tried to measure the TOF diffraction data of several proteins and organic compounds in order to estimate the efficiency and characteristics of the diffcactometer. The TOF diffraction data of Ribonuclease A can be measured under the following conditions, beam power: 20kW, pulse repetition: 25Hz, range of wavelength: 0.5~4Å, exposure time: 18.7 hours. About one hundred Bragg reflections could be observed clearly on all detectors. The reflection of 1.58Å in minimum d-spacing which Iobs/γ(Iobs) > 7 was observed. This result implies that the efficiency of the iBIX will become 50~100 times higher than that of the present high performance diffracatometer BIX-3 in JAEA after 1MW operation of J-PARC.
GLAD: The IPNS (Intense Pulsed Neutron Source) Glass, Liquid, and Amorphous materials Diffractometer
International Nuclear Information System (INIS)
Crawford, R.K.; Price, D.L.; Haumann, J.R.; Kleb, R.; Montague, D.G.; Carpenter, J.M.; Susman, S.; Dejus, R.J.
1989-01-01
A number of years of experience in diffraction from amorphous materials has now been accumulated at various pulsed neutron sources. Workshops t IPNS and elsewhere have distilled some of this experience to provide a set of criteria for a new diffractometer dedicated to an optimized for structural studies of amorphous materials. This paper discusses the instrument GLAD (Glass, Liquid, and Amorphous Materials Diffractometer) which has been designed to meet these criteria and is now being built at IPNS. This instrument involves the use of relatively short-wavelength neutrons and a sophisticated neutron detection and acquisition system. A preliminary, simplified version of the instrument has been constructed while the final version is still under design, in order to develop the data acquisition and analysis techniques and to develop methods for collection of data with adequate quality (low background) at short wavelengths. This paper will briefly outline the final instrument envisioned and its calculated performance, but will focus mostly on the details of the detection/acquisition system and the calibration and data collection procedures which have been developed. The brief operating experience which has been gained to data with the preliminary instrument version will also be summarized. 6 refs., 12 figs
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Ultrasonic Transducers for Fourier Analysis.
Greenslade, Thomas B., Jr.
1995-01-01
Describes an experiment that uses the ultrasonic transducer for demonstrating the Fourier components of waveshapes such as the square and triangular waves produced by laboratory function generators. (JRH)
Fourier-Hermite communications; where Fourier meets Hermite
Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria
A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency
International Nuclear Information System (INIS)
Balagurov, A.M.; Bokuchava, G.D.; Papushkin, I.V.; Sumin, V.V.; Venter, A.M.
2010-01-01
Neutron diffraction is widely used for investigations of residual and applied stresses in bulk materials and components. The most important factor in these investigations is the high penetration depth of neutrons (up to 2 cm for steel). At the IBR-2 pulsed reactor in Dubna the Fourier stress diffractometer (FSD) has been constructed to optimize the internal stress measurements. The FSD design satisfies the requirements of high luminosity, high resolution and specific sample environment. The collimator system guarantees a minimum gauge volume of 2x2x2 mm. A mechanical testing machine allows in-situ tension or compression measurements up to a load of 20 kN and sample temperatures up to 800 deg C. In the paper the current status of FSD is reported and potentialities are demonstrated with several examples of investigations performed
DEFF Research Database (Denmark)
Christensen, Finn Erland; Hornstrup, Allan; Jacobsen, E.
1987-01-01
A versatile X-ray diffractometer for the study of X-ray optical elements such as grazing incidence mirrors, crystals and X-ray gratings has been built and put into operation at the Danish Space Research Institute. The diffractrometer is built on a 1.5 m long granite bench with the X-ray source...
Braun, Daniel; Monjid, Younes; Rougé, Bernard; Kerr, Yann
2018-02-01
We investigated whether correlations between the Fourier components at slightly shifted frequencies of the fluctuations of the electric field measured with a one-dimensional antenna array on board a satellite flying over a plane allow one to measure the two-dimensional brightness temperature as a function of position in the plane. We found that the achievable spatial resolution that resulted from just two antennas is on the order of h χ , with χ = c / ( Δ r ω 0 ) , both in the direction of the flight of the satellite and in the direction perpendicular to it, where Δ r is the distance between the antennas, ω0 is the central frequency, h is the height of the satellite over the plane, and c is the speed of light. Two antennas separated by a distance of about 100 m on a satellite flying with a speed of a few km/s at a height of the order of 1000 km and a central frequency of order GHz allow, therefore, the imaging of the brightness temperature on the surface of Earth with a resolution of the order of 1 km. For a single point source, the relative radiometric resolution is on the order of √{ χ} , but, for a uniform temperature field in a half plane left or right of the satellite track, it is only on the order of 1 / χ 3 / 2 , which indicates that two antennas do not suffice for a precise reconstruction of the temperature field. Several ideas are discussed regarding how the radiometric resolution could be enhanced. In particular, having N antennas all separated by at least a distance on the order of the wave-length allows one to increase the signal-to-noise ratio by a factor of order N but requires averaging over N2 temperature profiles obtained from as many pairs of antennas.
A design for a high resolution very-low-Q time-of flight diffractometer
International Nuclear Information System (INIS)
Hjelm, R. P.
1998-01-01
The design of a high resolution view low-Q time of flight diffractometer was motivated by the anticipated need to perform small-angle neutron scattering measurements at far lower momentum transfer and higher precision than currently available at either pulsed or steady state sources. In addition, it was recognized that flexibility in the configuration of the instrument and ease in which data is acquired are important. The design offers two configurations, a high intensity/very low Q geometry employing a focusing mirror and a medium to high Q-precision/low Q configuration using standard pinhole collimation geometry. The quality of the mirror optics is very important to the performance of the high intensity/very low Q configuration. We believe that the necessary technology exists to fabricate the high quality mirror optics required for the instrument
International Nuclear Information System (INIS)
Blakeley, M.P.; Andersen, K.; Kreuz, M.; Giroud, B.; McSweeney, S.; Mitchell, E.; Teixeira, S.C.M.; Forsyth, V.T.
2011-01-01
We propose to construct a novel protein diffractometer at position H112B. The new instrument will deliver major efficiency gains, as well as offering greatly extended flexibility through the option of several easily interchangeable modes of operation. This proposal builds on the demonstrable need to extend ILL's capacity for high resolution structural studies of protein systems, as well as a need to widen the scope of biological crystallography - in particular for monochromatic studies at both high and low resolution. The development will be carried out in close collaboration with structural biologists at the ESRF, and engineered in such a way that the user interface of the instrument (from sample to software) will be transparently identifiable to a large, dynamic, and driven community of European synchrotron X-ray macromolecular crystallographers. (authors)
Wombat: The high-intensity powder diffractometer at the OPAL reactor
Energy Technology Data Exchange (ETDEWEB)
Studer, Andrew J [Bragg Institute, ANSTO, PMB 1 Menai 2234 (Australia)]. E-mail: ajs@ansto.gov.au; Hagen, Mark E. [Bragg Institute, ANSTO, PMB 1 Menai 2234 (Australia); Noakes, Terrence J. [Bragg Institute, ANSTO, PMB 1 Menai 2234 (Australia)
2006-11-15
The Wombat powder diffractometer will be located on the TG1 thermal guide at the OPAL reactor. A variable vertically focusing monochromator will provide a flux of up to {approx}10{sup 8} ns{sup -1} cm{sup -2} at the sample position. A compact curved 2D position sensitive detector will allow simultaneous acquisition of 120 deg. in 2{theta}, with {approx}10{sup 6} s{sup -1} count rate capability and time resolution down to the microsecond level. Wombat is designed for experiments requiring rapid real time acquisition (time-resolved environmental or kinetics experiments) or very good signal to noise (experiments with difficult sample environments or small sample volumes)
Measurement of the neutron intensity data using the HANARO four circle diffractometer
Energy Technology Data Exchange (ETDEWEB)
Lee, Jin Ho; Lee, Chang Hee; Seong, Baek Seok; Lee, Jeong Soo; Shim, Hae Seop; Hong, Kwang Pyo; Song, Su Ho; Suh, Il Hwan
1999-04-01
As the four circle diffractometer(FCD) has been set up in HANARO, it has become possible to study single crystal structures by means of the neutron diffraction. By introducing the constitution and characteristics of FCD, it has been shown that the feature of neutron diffraction experiment are different from that of X-ray or electronic beam. Besides we have explained the processes of determining experimental information in order to acquire intensity data and constructed the experimental system based on geometry of the FCD. As the computer programme performing all experimental processes automatically has been installed and the accuracy of experimental processes were confirmed by KCl single crystal experiment, the original experimental system for single crystal experiments and analyses by the neutron diffraction method using FCD has been established. (Author). 12 refs., 2 tabs., 11 figs.
The Performance of Fine Resolution Neutron Powder Diffractometer at PTBIN-BATAN
Directory of Open Access Journals (Sweden)
A. Fajar
2010-04-01
Full Text Available We describe the performance of a fine resolution neutron powder diffractometer, DN3, which has been installed at the neutron guide (NG2 in the Neutron Guide Hall about 71 m away from the Multipurpose G. A. Siwabessy reactor core. DN3 has a multi-detector system which consists of 32 3He neutron detectors and soller-type collimation. The resolution curve of the instrument was found to have little variation over a wide angular region. The best resolution is Δ2θ (FWHM of 0.23º and Δd / d of 5x10-3, where 2θ and d are scattering angle and d-spacing, respectively. The instrument provides sample environment of low temperatures using a cryostat having a temperature range of 10-300K. Several experimental results, interlaboratory comparison study and he next activities to improve the performance of DN3 equipment have also been discussed.
Performance improvement of the high resolution neutron diffractometer at CAEP with Geant4 simulation
International Nuclear Information System (INIS)
Zhang, J.; Xia, Y.; Zhang, Y.; Pang, B.; Sun, G.; Li, J.; Huang, C.; Wang, Y.; Pan, J.; Xie, C.
2017-01-01
The newly-built high resolution neutron diffractometer (HRND) at China Academy of Engineering Physics (CAEP) could not acquire high-quality diffraction patterns. In order to solve the problem, the present work introduces the Monte Carlo method based software called Geant4 which is rarely applied in the field of neutron diffraction. The geometrical structure of HRND has been structured by Geant4, thus simulation results can not only re-display the problems of HRND but help to solve such problems as well. According to the simulation results, some effective measures have been carried out to obtain higher instrument performance. It is found that the performance of HRND is improved eventually after new experimental diffraction patterns are acquired.
Performance improvement of the high resolution neutron diffractometer at CAEP with Geant4 simulation
Zhang, J.; Xia, Y.; Zhang, Y.; Pang, B.; Sun, G.; Li, J.; Huang, C.; Wang, Y.; Pan, J.; Xie, C.
2017-10-01
The newly-built high resolution neutron diffractometer (HRND) at China Academy of Engineering Physics (CAEP) could not acquire high-quality diffraction patterns. In order to solve the problem, the present work introduces the Monte Carlo method based software called Geant4 which is rarely applied in the field of neutron diffraction. The geometrical structure of HRND has been structured by Geant4, thus simulation results can not only re-display the problems of HRND but help to solve such problems as well. According to the simulation results, some effective measures have been carried out to obtain higher instrument performance. It is found that the performance of HRND is improved eventually after new experimental diffraction patterns are acquired.
Design and implementation of low-Q diffractometers at spallation sources
International Nuclear Information System (INIS)
Seeger, P.A.; Hjelm, R.P.
1993-01-01
Low-Q diffractometers at spallation sources that use time of flight methods have been successfully implemented at several facilities, including the Los Alamos Neutron Scattering Center. The proposal to build new, more powerful, advanced spallation sources using advanced moderator concepts will provide luminosity greater than 20 times the brightest spallation source available today. These developments provide opportunity and challenge to expand the capabilities of present instruments with new designs. The authors review the use of time of flight for low-Q measurements and introduce new designs to extend the capabilities of present-day instruments. They introduce Monte Carlo methods to optimize design and simulate the performance of these instruments. The expected performance of the new instruments are compared to present day pulsed source- and reactor-based small-angle neutron scattering instruments. They review some of the new developments that will be needed to use the power of brighter sources effectively
Development of SPICA, new dedicated neutron powder diffractometer for battery studies
International Nuclear Information System (INIS)
Yonemura, M; Kamiyama, T; Torii, S; Nagao, M; Ishikawa, Y; Mori, K; Fukunaga, T; Onodera, Y; Adipranoto, D S; Arai, H; Ogumi, Z; Uchimoto, Y
2014-01-01
SPICA, a new special environment powder neutron diffractometer was built at BL09 in the Material and Life science Facility (MLF) of the Japan Proton Accelerator Research Complex (J-PARC). This is the first instrument dedicated solely to the study of next-generation batteries in J-PARC and is optimized for in situ measurements to clarify structural changes of materials in batteries. The basic design and instrumentation of SPICA have been completed. The highest Δd/d resolution achieved at the commissioning stage was 0.09% at the back scattering bank of SPICA. The reliability of the diffraction data has achieved a sufficiently high level for the structural analysis of materials using the Rietveld method. The air scattering banks with the blades made of B 4 C for in situ measurements also function very well.
Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer
International Nuclear Information System (INIS)
Misumi, I; Gonda, S; Sato, O; Huang, Q; Kurosawa, T
2005-01-01
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology (NMIJ/AIST) have designed nanometric lateral scales with a pitch of less than 100 nm for atomic force microscope (AFM), scanning electron microscope (SEM) and optical diffractometer. The pitches of the scales were calibrated by nanometrological AFM with differential laser interferometer (DLI-AFM) and the uncertainty in the pitch measurements was evaluated. The average pitches were quite close to the designed pitches and the expanded uncertainty (k = 2) was less than 0.5% of the nominal pitch. It became clear that proposed nanometric lateral scales had sufficiently high quality as candidate certified reference materials (CRMs). A domestic intercomparison of the nanometric lateral scales is underway
Residual stress diffractometer KOWARI at the Australian research reactor OPAL: Status of the project
Brule, Alain; Kirstein, Oliver
2006-11-01
Neutron scattering using diffraction techniques is now recognized as the most precise and reliable method of mapping sub-surface residual stresses in materials or even components, which are not only of academic but also of industrial-economic relevance. The great potential of neutrons in the field of residual stresses was recognized by ANSTO and its external Beam Instrument Advisory Group for the new research reactor OPAL. The recommendation was to build the dedicated strain scanner KOWARI among the first suite of instruments available to users. We give an update on the overall project and present the current status of the diffractometer. It is anticipated that the instrument will be commissioned in mid 2006 and available to users at the end of the OPAL project.
Residual stress diffractometer KOWARI at the Australian research reactor OPAL: Status of the project
International Nuclear Information System (INIS)
Brule, Alain; Kirstein, Oliver
2006-01-01
Neutron scattering using diffraction techniques is now recognized as the most precise and reliable method of mapping sub-surface residual stresses in materials or even components, which are not only of academic but also of industrial-economic relevance. The great potential of neutrons in the field of residual stresses was recognized by ANSTO and its external Beam Instrument Advisory Group for the new research reactor OPAL. The recommendation was to build the dedicated strain scanner KOWARI among the first suite of instruments available to users. We give an update on the overall project and present the current status of the diffractometer. It is anticipated that the instrument will be commissioned in mid 2006 and available to users at the end of the OPAL project
SENJU: a new time-of-flight single-crystal neutron diffractometer at J-PARC.
Ohhara, Takashi; Kiyanagi, Ryoji; Oikawa, Kenichi; Kaneko, Koji; Kawasaki, Takuro; Tamura, Itaru; Nakao, Akiko; Hanashima, Takayasu; Munakata, Koji; Moyoshi, Taketo; Kuroda, Tetsuya; Kimura, Hiroyuki; Sakakura, Terutoshi; Lee, Chang-Hee; Takahashi, Miwako; Ohshima, Ken-Ichi; Kiyotani, Tamiko; Noda, Yukio; Arai, Masatoshi
2016-02-01
SENJU is a new single-crystal time-of-flight neutron diffractometer installed at BL18 at the Materials and Life Science Experimental Facility of the Japan Accelerator Research Complex (J-PARC). The diffractometer was designed for precise crystal and magnetic structure analyses under multiple extreme sample environments such as low temperature, high pressure and high magnetic field, and for diffraction measurements of small single crystals down to 0.1 mm 3 in volume. SENJU comprises three choppers, an elliptical shape straight supermirror guide, a vacuum sample chamber and 37 scintillator area detectors. The moderator-to-sample distance is 34.8 m, and the sample-to-detector distance is 800 mm. The wavelength of incident neutrons is 0.4-4.4 Å (first frame). Because short-wavelength neutrons are available and the large solid angle around the sample position is covered by the area detectors, a large reciprocal space can be simultaneously measured. Furthermore, the vacuum sample chamber and collimator have been designed to produce a very low background level. Thus, the measurement of a small single crystal is possible. As sample environment devices, a newly developed cryostat with a two-axis (ω and φ axes) goniometer and some extreme environment devices, e.g. a vertical-field magnet, high-temperature furnace and high-pressure cell, are available. The structure analysis of a sub-millimetre size (0.1 mm 3 ) single organic crystal, taurine, and a magnetic structure analysis of the antiferromagnetic phase of MnF 2 have been performed. These results demonstrate that SENJU can be a powerful tool to promote materials science research.
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Fourier reconstruction with sparse inversions
Zwartjes, P.M.
2005-01-01
In seismic exploration an image of the subsurface is generated from seismic data through various data processing algorithms. When the data is not acquired on an equidistantly spaced grid, artifacts may result in the final image. Fourier reconstruction is an interpolation technique that can reduce these artifacts by generating uniformly sampled data from such non-uniformly sampled data. The method works by estimating via least-squares inversion the Fourier coefficients that describe the non-un...
Fourier transform nuclear magnetic resonance
International Nuclear Information System (INIS)
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)
Energy Technology Data Exchange (ETDEWEB)
Mayr, Sina, E-mail: sina.mayr@frm2.tum.de [Technische Universität München, Physik-Department E21, James-Franck-Str. 1, 85748 Garching (Germany); Randau, Christian [Georg-August-Universität Göttingen, Fakultät für Geowissenschaften und Geologie, Abteilung Isotopengeologie Außenstelle MLZ (FRM II), Lichtenbergstr. 1, 85748 Garching (Germany); Kreuzpaintner, Wolfgang [Technische Universität München, Physik-Department E21, James-Franck-Str. 1, 85748 Garching (Germany)
2017-05-21
A proxy software was developed which allows the Siemens D500 x-ray diffractometer to be upgraded with add-ons that have never been officially available for it. For demonstration, we designed and integrated an automatic attenuator option and demonstrated the feasibility of our upgrade path by typical comparative x-ray measurements, which would usually saturate the x-ray detector, if no attenuator is used.
Mayr, Sina; Randau, Christian; Kreuzpaintner, Wolfgang
2017-05-01
A proxy software was developed which allows the Siemens D500 x-ray diffractometer to be upgraded with add-ons that have never been officially available for it. For demonstration, we designed and integrated an automatic attenuator option and demonstrated the feasibility of our upgrade path by typical comparative x-ray measurements, which would usually saturate the x-ray detector, if no attenuator is used.
International Nuclear Information System (INIS)
Mayr, Sina; Randau, Christian; Kreuzpaintner, Wolfgang
2017-01-01
A proxy software was developed which allows the Siemens D500 x-ray diffractometer to be upgraded with add-ons that have never been officially available for it. For demonstration, we designed and integrated an automatic attenuator option and demonstrated the feasibility of our upgrade path by typical comparative x-ray measurements, which would usually saturate the x-ray detector, if no attenuator is used.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
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.
The Wide Angle Neutron Diffractometer (WAND) at HFIR: possibilities and future
Frontzek, Matthias; Andrews, Katie M.; Chakoumakos, Bryan C.
The Wide Angle Neutron Diffractometer (WAND) at the High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory (ORNL) has been built and continues to be, a joint project between ORNL and the Japan Atomic Energy Agency. Equipped with a 1-dimensional position sensitive detector (PSD), the instrument is a multi-purpose instrument for both powder and single crystal diffraction. WAND is currently in the process of a 2-phase upgrade to become a world class, general purpose instrument. In phase 1, finished in the beginning of 2016, the whole instrument was practically re-built from scratch, keeping only the front end and the 1-D PSD. Phase 2 will replace the 1-D PSD with the state of the art BNL120 2D-PSD which comes from the Lujan Neutron Scattering Center. We are currently integrating the detector off-line into the data acquisition architecture at HFIR. The new instrument, WAND2, will be available for general users in the proposal call 2018A. In our contribution we present results from experiments on WAND after phase 1. The upgrade now allows mounting the whole suite of available sample environment (50 mK to 1500 K, magnetic fields (5 T), high pressures (4 GPa)). We will further discuss the scientific impact the new capabilities of WAND2 will have.
International Nuclear Information System (INIS)
Ganguly, S.; James, J.A.; Fitzpatrick, M.E.; Tanguy, A.
2010-01-01
Residual stress measurement using neutron diffraction is becoming an increasingly important tool in engineering stress analysis. To this effect, a new generation of dedicated engineering strain instruments are being built at neutron sources, offering considerable improvements in both counting time and spatial resolution. Alongside these improvements, measurements in complex geometry prototype components are increasingly in demand. As a result, there is a strong drive towards integrated sample positioning systems that allow for simplified setup and operating of experiments on components with complex geometries. The present study details work carried out at the ENGIN-X instrument at the UK's ISIS pulsed neutron source, on measurements in a prototype metal matrix composite (MMC) aircraft wheel, forged from a billet produced through a powder-metallurgy route. The measurement was designed to obtain the macrostress and misfit stresses developed in the matrix and in the reinforcement phase in the wheel during fabrication. The study also demonstrates the use of the SScanSS software for experimental design and implementation, which was developed to complement the advances in the instrumentation of new strain mapping diffractometers. SScanSS simplifies the precise spatial location of the measuring gauge volume inside such complex components. (orig.)
Position controller for the arm of a neutron diffractometer using fuzzy logic
International Nuclear Information System (INIS)
Ayala P, G.F.
1994-01-01
The neutron diffractometer is an important instrument coupled to one of the radial outlets of the TRIGA-3-Salazar Reactor and is used mainly to analyze textures and crystal lattices. One of its main components is the velocity analysis goniometer which controls in a tangential way the movements of the sensor requiring for this a resolution of a hundredth of degree, but at the same time wide displacements are required. It is necessary to design and construct a system on the basis of a micro controller which control the long movements in a rapid way and with the needed accuracy. In this work, a proposition is presented: to replace the A.C. motor with a D.C. motor with a wide range of velocity and supplied with a card (DAC) to control the velocity by means of digital data. Moreover, a programmed micro controller with an algorithm based on fuzzy logic receiving data in BCD will be use. The use of micro controller will allow to set free the personal computer of the position of the goniometer; nevertheless, the system will report to the P C and its control program about the present position of the goniometer and the time when the desired position is reached. It is also consider that the user will be away from the system (a minimum of 15 meters) in order to avoid the zone with a high intensity of background radiation. (Author)
International Nuclear Information System (INIS)
Stalick, J.K.; Prince, E.; Santoro, A.; Schroder, I.G.; Rush, J.J.
1995-01-01
The new high-resolution neutron powder diffractometer BT-1 at the NIST reactor has proven to be a powerful and versatile instrument in its first year of operation. With 32 detectors arranged at 5 degree intervals and a 12 degree 2θ scan range, powder diffraction patterns can be collected to 167 degree 2θ. There is a choice of three monochromator take-off angles (75 degree, 90 degree, and 120 degree) so that the peak-width minimum can be matched to the d-spacing range that is most important for each sample; all choices have a wavelength close to 1.54 angstrom. Data can be collected on sample sizes ranging from 200 mg to 30 g. Temperatures of 0.3 K to 1,400 K are routinely available, and a magnetic field of 7T can be applied with a superconducting magnet. Typical data collection times range from 1--12 hours depending upon sample size and desired resolution. Examples are given of a variety of materials applications
In situ surface/interface x-ray diffractometer for oxide molecular beam epitaxy
Energy Technology Data Exchange (ETDEWEB)
Lee, J. H. [Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA; Tung, I. C. [Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA; Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA; Chang, S. -H. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Bhattacharya, A. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Fong, D. D. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA; Freeland, J. W. [Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA; Hong, Hawoong [Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
2016-01-01
In situ studies of oxide molecular beam epitaxy by synchrotron x-ray scattering has been made possible by upgrading an existing UHV/molecular beam epitaxy (MBE) six-circle diffractometer system. For oxide MBE growth, pure ozone delivery to the chamber has been made available, and several new deposition sources have been made available on a new 12 in. CF (ConFlat, a registered trademark of Varian, Inc.) flange. X-ray diffraction has been used as a major probe for film growth and structures for the system. In the original design, electron diffraction was intended for the secondary diagnostics available without the necessity of the x-ray and located at separate positions. Deposition of films was made possible at the two diagnostic positions. And, the aiming of the evaporation sources is fixed to the point between two locations. Ozone can be supplied through two separate nozzles for each location. Also two separate thickness monitors are installed. Additional features of the equipment are also presented together with the data taken during typical oxide film growth to illustrate the depth of information available via in situ x-ray techniques.
In situ surface/interface x-ray diffractometer for oxide molecular beam epitaxy
Energy Technology Data Exchange (ETDEWEB)
Lee, J. H.; Freeland, J. W.; Hong, Hawoong, E-mail: hhong@aps.anl.gov [Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Tung, I. C. [Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Chang, S.-H.; Bhattacharya, A.; Fong, D. D. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
2016-01-15
In situ studies of oxide molecular beam epitaxy by synchrotron x-ray scattering has been made possible by upgrading an existing UHV/molecular beam epitaxy (MBE) six-circle diffractometer system. For oxide MBE growth, pure ozone delivery to the chamber has been made available, and several new deposition sources have been made available on a new 12 in. CF (ConFlat, a registered trademark of Varian, Inc.) flange. X-ray diffraction has been used as a major probe for film growth and structures for the system. In the original design, electron diffraction was intended for the secondary diagnostics available without the necessity of the x-ray and located at separate positions. Deposition of films was made possible at the two diagnostic positions. And, the aiming of the evaporation sources is fixed to the point between two locations. Ozone can be supplied through two separate nozzles for each location. Also two separate thickness monitors are installed. Additional features of the equipment are also presented together with the data taken during typical oxide film growth to illustrate the depth of information available via in situ x-ray techniques.
A high resolution, high efficiency neutron powder diffractometer: test refinement of Al2O3
International Nuclear Information System (INIS)
Hewat, A.W.; Bailey, I.
1975-01-01
Modifications to the ILL high-resolution powder diffractometer D1A will improve its efficiency by an order of magnitude. Novel features include a monochromator take-off angle of 122deg giving high resolution at high angles, a bank of eight 20 x 100 mm high efficiency mylar collimators with He 3 counters, and the possibility of working at high pressures (up to 45 kbar), or low and very high temperatures (1.5K to 2800K). The performance expected of the instrument is illustrated by the refinement of data collected on a standard Al 2 O 3 sample supplied by the Neutron Diffraction Commission. Anisotropic vibrational amplitudes as well as atomic co-ordinates have been determined quite precisely. When completed, D1A will be unique for the precise measurement of moderately complex crystal structures under 'difficult' conditions, especially for the study of phase transitions. But in fact, it is only an indication of a type of more powerful machine described recently in Nuclear Instruments and Methods which could be built on a beam tube of a high-flux reactor
Benafan, O; Padula, S A; Skorpenske, H D; An, K; Vaidyanathan, R
2014-10-01
A gripping capability was designed, implemented, and tested for in situ neutron diffraction measurements during multiaxial loading and heating on the VULCAN engineering materials diffractometer at the spallation neutron source at Oak Ridge National Laboratory. The proposed capability allowed for the acquisition of neutron spectra during tension, compression, torsion, and/or complex loading paths at elevated temperatures. The design consisted of age-hardened, Inconel(®) 718 grips with direct attachment to the existing MTS load frame having axial and torsional capacities of 100 kN and 400 N·m, respectively. Internal cooling passages were incorporated into the gripping system for fast cooling rates during high temperature experiments up to ∼1000 K. The specimen mounting couplers combined a threaded and hexed end-connection for ease of sample installation/removal without introducing any unwanted loads. Instrumentation of this capability is documented in this work along with various performance parameters. The gripping system was utilized to investigate deformation in NiTi shape memory alloys under various loading/control modes (e.g., isothermal, isobaric, and cyclic), and preliminary results are presented. The measurements facilitated the quantification of the texture, internal strain, and phase fraction evolution in NiTi shape memory alloys under various loading/control modes.
New POLDI - project of reincarnation of a polarized neutron diffractometer at the reactor PIK
Zobkalo, I.; Gavrilov, S.; Matveev, V.; Fenske, J.
2017-06-01
The project of a considerable modernization of the polarized neutron diffractometer POLDI is discussed. It assumes the adoption of POLDI to a broader range of magnetic investigations such as determination of magnetic structures, detailed investigation of complex magnetic structures, studies of magnetic domains, study of the magnetization density maps, magnetic form-factor particularities, local susceptibility, etc. The flexible construction should permit to use either spherical neutron polarimetry technique or flipping ratio technique. Different types of polarization system were analyzed. Original focusing fan-like bender is proposed as polarizer unit. Our simulations give evidence that for the wavelength range 1.3 - 3 Å and with suitable size, such a device can give much better efficiency than 3He cells, which are often in use. The higher flux at the sample position of a factor of at least 3.3, with lower divergence and good polarization degree from 98% (1.3 Å) to above 94% (3 Å) makes the bender set-up favorable over the layout with a 3He-cell.
Resolution of the USANS diffractometer at the FRJ-2 research reactor in Juelich
International Nuclear Information System (INIS)
Borbely, S.; Heiderich, M.; Schwahn, D.
1999-01-01
Channel cut perfect crystals are used in double crystal diffractometers (DCD) for ultra small angle scattering in order to reduce background scattering coming from the tails of the Darwin reflection curve. To approach the theoretically predicted resolution curve one has also to consider reflections from the backfront of the crystals. Our new crystals with the (111) lattice planes parallel to the surface were designed to avoid that single reflected neutrons from the backfront could enter the detector. Actually, the crystals are functioning in a mode of triple and fivefold reflections as we operate the DCD with λ = 4.48 A neutrons and the corresponding diffraction angle of 91 deg. The experimental resolution curve gave a Δλ = 25.8 μrad FWHM and an intensity ratio of 3 x 10 -4 at twice the Δδ angle with respect to the maximum intensity at δ = 0. This is an improvement of nearly two orders of magnitude in comparison with our old version and is in agreement with the results of by using a Cd absorber. The capabilities of the instrument are demonstrated by measurements of a model latex dispersion and of giant amphiphilic aggregates. (author)
Design and performance of a gamma-ray diffractometer at 0.12A
International Nuclear Information System (INIS)
Alkire, R.W.
1982-01-01
Gamma-ray diffractometry is a relatively new field in which radioisotopes are used to provide highly penetrating, monoenergetic radiation for diffraction experiments. The first part of this work details the design of a gamma-ray diffractometer using the 103 keV gamma-rays from 153 Sm (γ = 0.12A). Complete description of source material, transport cask, full circle, detector and associated electronics is presented along with alignment and testing procedures. The second part of this work covers theoretical advantages and disadvantages afforded by 0.12A radiation, and experimental capabilities are tested by determining the absolute structure factor for the forbidden 222 reflection in silicon. F(222) was determined to be 1.456 +- 0.008 which is in excellent agreement with previous studies but with a reduction in error of between two and ten. General applications of 0.12A gamma radiation are also explored, including mosaic characterizations, structural phase transformations, electron density mapping, powder diffraction and experiments in special environmental devices
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...
International Nuclear Information System (INIS)
Zorina, M.V.; Mironov, V.L.; Mironov, S.V.
2005-01-01
A model is developed, which enables computation of the the angular dependences of X-ray reflection, with taking into account the finiteness of sample sizes and the diffractometer alignment errors. It is shown that the angular dependences of refraction for glass and quartz wafers calculated with account of possible errors of the diffractometer optical system alignment are in good agreement with the experimental curves in the entire range of angles [ru
Synthetic Fourier transform light scattering.
Lee, Kyeoreh; Kim, Hyeon-Don; Kim, Kyoohyun; Kim, Youngchan; Hillman, Timothy R; Min, Bumki; Park, Yongkeun
2013-09-23
We present synthetic Fourier transform light scattering, a method for measuring extended angle-resolved light scattering (ARLS) from individual microscopic samples. By measuring the light fields scattered from the sample plane and numerically synthesizing them in Fourier space, the angle range of the ARLS patterns is extended up to twice the numerical aperture of the imaging system with unprecedented sensitivity and precision. Extended ARLS patterns of individual microscopic polystyrene beads, healthy human red blood cells (RBCs), and Plasmodium falciparum-parasitized RBCs are presented.
Fourier series in orthogonal polynomials
Osilenker, Boris
1999-01-01
This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness).The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
This study considers the application of Fourier series analysis (FSA) to seasonal time series data. The ultimate objective of the study is to construct an FSA model that can lead to reliable forecast. Specifically, the study evaluates data for the assumptions of time series analysis; applies the necessary transformation to the ...
Fourier reconstruction with sparse inversions
Zwartjes, P.M.
2005-01-01
In seismic exploration an image of the subsurface is generated from seismic data through various data processing algorithms. When the data is not acquired on an equidistantly spaced grid, artifacts may result in the final image. Fourier reconstruction is an interpolation technique that can reduce
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 2. Uncertainty Principles and Fourier Analysis. Alladi Sitaram. General Article Volume 4 Issue 2 February 1999 pp 20-23. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/004/02/0020-0023 ...
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-01-01
Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…
Fourier analysis for rotating-element ellipsometers.
Cho, Yong Jai; Chegal, Won; Cho, Hyun Mo
2011-01-15
We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.
International Nuclear Information System (INIS)
Bennett, K.; Dreele, R.B. von; Wenk, H.R.
2001-01-01
United States National Laboratory researchers and University of California faculty, representing a broad range of scientific disciplines, is building a novel time-of-flight (TOF) neutron diffractometer and associated in situ equipment at the Manuel Lujan Jr. Neutron Scattering Center (Lujan Center), under the auspices of the United States Department of Energy. The goal with the High-Pressure Preferred Orientation Instrument (HIPPO) is to investigate dynamic processes in heterogeneous bulk materials in a variety of environments. The instrument, which will become available in summer 2001, has the extremely high count-rates necessary to study time-dependent processes in small (1-mm diameter) and large (2-cm diameter) samples, and in a large variety of environmental conditions (10-2000 K cryostats and furnaces, 0-20 GPa pressure vessels, straining cells, goniometers, magnets, etc.). The 3-D arrangement of detectors allows direct measurements of crystal orientation distributions in polycrystalline materials. The analysis of TOF diffraction patterns with versatile Rietveld codes provides simultaneous information on crystal structure, texture, microstructure and phase proportions. While this instrument has many applications in materials science, it is also of great interest for geology and geophysics. Some applications include: kinetics of reactions, structure of silicate glasses and melts, high-pressure investigations of complex systems, evolution of texture and anisotropy during deformation and recrystallization. The Lujan Center aims at creating an instrument with high data through-put and easy access to researchers and students. While the HIPPO instrument will be part of the national user facility operated by the Lujan Center, the scientific program will be guided by the University of California consortium with the goal of satisfying national priorities and establishing an environment of scientific excellence. (author)
Energy Technology Data Exchange (ETDEWEB)
Bennett, K.; Dreele, R.B. von [Manuel Lujan Jr. Neutron Scattering Center, Los Alamos, NM (United States); Wenk, H.R. [Department of Geology and Geophysics, Univ. of California, Berkely, CA (United States)
2001-03-01
United States National Laboratory researchers and University of California faculty, representing a broad range of scientific disciplines, is building a novel time-of-flight (TOF) neutron diffractometer and associated in situ equipment at the Manuel Lujan Jr. Neutron Scattering Center (Lujan Center), under the auspices of the United States Department of Energy. The goal with the High-Pressure Preferred Orientation Instrument (HIPPO) is to investigate dynamic processes in heterogeneous bulk materials in a variety of environments. The instrument, which will become available in summer 2001, has the extremely high count-rates necessary to study time-dependent processes in small (1-mm diameter) and large (2-cm diameter) samples, and in a large variety of environmental conditions (10-2000 K cryostats and furnaces, 0-20 GPa pressure vessels, straining cells, goniometers, magnets, etc.). The 3-D arrangement of detectors allows direct measurements of crystal orientation distributions in polycrystalline materials. The analysis of TOF diffraction patterns with versatile Rietveld codes provides simultaneous information on crystal structure, texture, microstructure and phase proportions. While this instrument has many applications in materials science, it is also of great interest for geology and geophysics. Some applications include: kinetics of reactions, structure of silicate glasses and melts, high-pressure investigations of complex systems, evolution of texture and anisotropy during deformation and recrystallization. The Lujan Center aims at creating an instrument with high data through-put and easy access to researchers and students. While the HIPPO instrument will be part of the national user facility operated by the Lujan Center, the scientific program will be guided by the University of California consortium with the goal of satisfying national priorities and establishing an environment of scientific excellence. (author)
New developments of TOF neutron diffraction at the IBR-2 pulsed reactor
International Nuclear Information System (INIS)
Balagurov, Anatoli M.
2001-01-01
Development of high-resolution RTOF Fourier technique for powder neutron diffraction studies is being continued at the IBR-2 pulsed reactor in Dubna. Besides some technical improvements in the operating HRFD instrument, a new dedicated instrument, Fourier Strain Diffractometer (FSD), for investigation of residual stresses in bulk materials has been constructed at IBR-2 in 1999. With a new HRFD Fourier chopper smaller than 10 μs TOF contribution in a resolution function was obtained in the experiment with perfect Si single crystal. A series of diffraction experiments with the beams from a new methane cold neutron moderator installed at the IBR-2 in 1999 is discussed. A comparison with the results obtained with the conventional water comb-like moderator shows that for various types of experiments, which are performed at HRFD and DN-2 diffractometers, the methane cold neutron source provides better conditions. (author)
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.
DEFF Research Database (Denmark)
Silva, M A F M da; Sosman, L P; Yokaichiya, F
2012-01-01
and MgGa 2 O 4 and relate structural changes observed in MgGa 2 O 4 -Ga 2 O 3 system to the optical properties, and secondly, to compare the neutron powder diffraction results obtained using two diffractometers: D2B located at the ILL (Grenoble, France) and Aurora located at IPEN (SÃ£o Paulo, Brazil......Optical materials that emit from the visible to the near-infrared spectral region are of great interest due to their possible application as tunable radiation sources, as signal transmission, display, optoelectronics signal storage, cellulose industry as well as in dosimetry. One important family...
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Energy Technology Data Exchange (ETDEWEB)
Aguilar H, F.; Herrera A, E.; Quintana C, G. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Torres R, C. E.; Reyes V, M., E-mail: fortunato.aguilar@inin.gob.mx [Instituto Tecnologico de Toluca, Av. Tecnologico s/n, Ex-Rancho La Virgen, Metepec, Estado de Mexico (Mexico)
2015-09-15
A technique to determine the crystal structure of some materials is the neutron diffraction. This technique consists on placing the material in question in a monoenergetic neutron beam obtained by neutron diffraction in a monochromator crystal. The neutron energy depends of the diffraction angle. The Instituto Nacional de Investigaciones Nucleares has a neutron diffractometer and monochromator crystals of pyrolytic graphite. This crystal can be selecting the neutron energy depending on the angle of diffraction in the glass. The radiation source for the neutron diffractometer is the TRIGA Mark III reactor of the Nuclear Center Dr. Nabor Carrillo Flores. During their operation are also obtained besides neutrons, β and γ radiation. The interest is to have thermal neutrons, so fast neutrons and γ rays are removed using appropriate shielding. The average neutron fluxes of the radial port RE2 of neutron diffractometer at power 1 MW are: heat flow 2,466 x 10{sup 8} n cm{sup -2} sec{sup -1} and fast flow 1,239 x 10{sup 8} n cm{sup -2} sec{sup -1}. The neutron detector is housed in a shield mounted on a mechanical linkage with which the diffraction angle is selected, and therefore the energy of the neutrons. The movement of this joint was performed by the equipment operator manually, so that accuracy to select the diffraction angle was not good and the process rather slow. Therefore a mechanical system was designed, automated by means of a motor as an actuator, a system of force transmission and an electronic control in order that the operator will schedule the diffraction angles and allow the count in the neutrons detection system in a simple manner. (Author)
Energy Technology Data Exchange (ETDEWEB)
Kamal, I., E-mail: imtiaz-kamal26@yahoo.com; Yunus, S. M., E-mail: yunussm11@yahoo.com; Datta, T. K., E-mail: tk-datta4@yahoo.com; Zakaria, A. K. M.; Das, A. K.; Aktar, S.; Hossain, S. [Institute of Nuclear Science and Technology, Atomic Energy Research Establishment, Ganakbari, Savar, Dhaka (Bangladesh); Berliner, R., E-mail: RB@instrumentationAssociates.com [Instrumentation Associates, Durham, North Carolina (United States); Yelon, W. B., E-mail: yelonwb@hotmail.com [Oak Ridge National Laboratory, Oak Ridge, Tennessee (United States)
2016-07-12
A high performance neutron diffractometer called Savar Neutron Diffractometer (SAND) was built and installed at radial beam port-2 of TRIGA Mark II research reactor at AERE, Savar, Dhaka, Bangladesh. Structural studies of materials are being done by this technique to characterize materials crystallograpohically and magnetically. The micro-structural information obtainable by neutron scattering method is very essential for determining its technological applications. This technique is unique for understanding the magnetic behavior in magnetic materials. Ceramic, steel, electronic and electric industries can be benefited from this facility for improving their products and fabrication process. This instrument consists of a Popovicimonochromator with a large linear position sensitive detector array. The monochromator consists of nine blades of perfect single crystal of silicon with 6 mm thickness each. The monochromator design was optimized to provide maximum flux on 3 mm diameter cylindrical sample with a relatively flat angular dependence of resolution. Five different wave lengths can be selected by orienting the crystal at various angles. A sapphire filter was used before the primary collimator to minimize the first neutron. The detector assembly is composed of 15 linear position sensitive proportional counters placed at either 1.1 m or 1.6 m from the sample position and enclosed in a air pad supported high density polythene shield. Position sensing is obtained by charge division using 1-wide NIM position encoding modules (PEM). The PEMs communicate with the host computer via USB. The detector when placed at 1.1 m, subtends 30° (2θ) at each step and covers 120° in 4 steps. When the detector is placed at 1.6 m it subtends 20° at each step and covers 120° in 6 steps. The instrument supports both low and high temperature sample environment. The instrument supports both low and high temperature sample environment. The diffractometer is a state-of-the art technology
Kamal, I.; Yunus, S. M.; Datta, T. K.; Zakaria, A. K. M.; Das, A. K.; Aktar, S.; Hossain, S.; Berliner, R.; Yelon, W. B.
2016-07-01
A high performance neutron diffractometer called Savar Neutron Diffractometer (SAND) was built and installed at radial beam port-2 of TRIGA Mark II research reactor at AERE, Savar, Dhaka, Bangladesh. Structural studies of materials are being done by this technique to characterize materials crystallograpohically and magnetically. The micro-structural information obtainable by neutron scattering method is very essential for determining its technological applications. This technique is unique for understanding the magnetic behavior in magnetic materials. Ceramic, steel, electronic and electric industries can be benefited from this facility for improving their products and fabrication process. This instrument consists of a Popovicimonochromator with a large linear position sensitive detector array. The monochromator consists of nine blades of perfect single crystal of silicon with 6mm thickness each. The monochromator design was optimized to provide maximum flux on 3mm diameter cylindrical sample with a relatively flat angular dependence of resolution. Five different wave lengths can be selected by orienting the crystal at various angles. A sapphire filter was used before the primary collimator to minimize the first neutron. The detector assembly is composed of 15 linear position sensitive proportional counters placed at either 1.1 m or 1.6 m from the sample position and enclosed in a air pad supported high density polythene shield. Position sensing is obtained by charge division using 1-wide NIM position encoding modules (PEM). The PEMs communicate with the host computer via USB. The detector when placed at 1.1 m, subtends 30˚ (2θ) at each step and covers 120˚ in 4 steps. When the detector is placed at 1.6 m it subtends 20˚ at each step and covers 120˚ in 6 steps. The instrument supports both low and high temperature sample environment. The instrument supports both low and high temperature sample environment. The diffractometer is a state-of-the art technology
International Nuclear Information System (INIS)
Kamal, I.; Yunus, S. M.; Datta, T. K.; Zakaria, A. K. M.; Das, A. K.; Aktar, S.; Hossain, S.; Berliner, R.; Yelon, W. B.
2016-01-01
A high performance neutron diffractometer called Savar Neutron Diffractometer (SAND) was built and installed at radial beam port-2 of TRIGA Mark II research reactor at AERE, Savar, Dhaka, Bangladesh. Structural studies of materials are being done by this technique to characterize materials crystallograpohically and magnetically. The micro-structural information obtainable by neutron scattering method is very essential for determining its technological applications. This technique is unique for understanding the magnetic behavior in magnetic materials. Ceramic, steel, electronic and electric industries can be benefited from this facility for improving their products and fabrication process. This instrument consists of a Popovicimonochromator with a large linear position sensitive detector array. The monochromator consists of nine blades of perfect single crystal of silicon with 6 mm thickness each. The monochromator design was optimized to provide maximum flux on 3 mm diameter cylindrical sample with a relatively flat angular dependence of resolution. Five different wave lengths can be selected by orienting the crystal at various angles. A sapphire filter was used before the primary collimator to minimize the first neutron. The detector assembly is composed of 15 linear position sensitive proportional counters placed at either 1.1 m or 1.6 m from the sample position and enclosed in a air pad supported high density polythene shield. Position sensing is obtained by charge division using 1-wide NIM position encoding modules (PEM). The PEMs communicate with the host computer via USB. The detector when placed at 1.1 m, subtends 30° (2θ) at each step and covers 120° in 4 steps. When the detector is placed at 1.6 m it subtends 20° at each step and covers 120° in 6 steps. The instrument supports both low and high temperature sample environment. The instrument supports both low and high temperature sample environment. The diffractometer is a state-of-the art technology
International Nuclear Information System (INIS)
Stuhr, U.; Bauer, G.S.; Wagner, W.
1997-01-01
A Time-of-Flight Diffractometer with high pulse rates, allowing multiple frame overlap, is a completely novel design of an instrument dedicated for high resolution strain-field mapping. We elaborated a detailed concept of this instrument applying analytical calculations and Monte Carlo computer simulations. Having established the instrument concept, the computer simulations will now be extended to optimize the total performance of the instrument. To illustrate the necessity and possibilities of applying modem tools for instrument design, we describe, as an example, the different steps towards the development of the detailed design of this instrument, which we intend to build at the Swiss spallation. source SINQ in the near future
International Nuclear Information System (INIS)
Dura, Joseph A.; Pierce, Donald J.; Majkrzak, Charles F.; Maliszewskyj, Nicholas C.; McGillivray, Duncan J.; Loesche, Mathias; O'Donovan, Kevin V.; Mihailescu, Mihaela; Perez-Salas, Ursula; Worcester, David L.; White, Stephen H.
2006-01-01
An elastic neutron scattering instrument, the advanced neutron diffractometer/reflectometer (AND/R), has recently been commissioned at the National Institute of Standards and Technology Center for Neutron Research. The AND/R is the centerpiece of the Cold Neutrons for Biology and Technology partnership, which is dedicated to the structural characterization of thin films and multilayers of biological interest. The instrument is capable of measuring both specular and nonspecular reflectivity, as well as crystalline or semicrystalline diffraction at wave-vector transfers up to approximately 2.20 A -1 . A detailed description of this flexible instrument and its performance characteristics in various operating modes are given
Dura, Joseph A.; Pierce, Donald J.; Majkrzak, Charles F.; Maliszewskyj, Nicholas C.; McGillivray, Duncan J.; Lösche, Mathias; O'Donovan, Kevin V.; Mihailescu, Mihaela; Perez-Salas, Ursula; Worcester, David L.; White, Stephen H.
2011-01-01
An elastic neutron scattering instrument, the advanced neutron diffractometer/reflectometer (AND/R), has recently been commissioned at the National Institute of Standards and Technology Center for Neutron Research. The AND/R is the centerpiece of the Cold Neutrons for Biology and Technology partnership, which is dedicated to the structural characterization of thin films and multilayers of biological interest. The instrument is capable of measuring both specular and nonspecular reflectivity, as well as crystalline or semicrystalline diffraction at wave-vector transfers up to approximately 2.20 Å−1. A detailed description of this flexible instrument and its performance characteristics in various operating modes are given. PMID:21892232
DEFF Research Database (Denmark)
Shen, Yanbin; Pedersen, Erik Ejler; Christensen, Mogens
2014-01-01
to operate and maintain. Test examples on lithium insertion/extraction in two spinel-type LIB electrode materials (Li4Ti5O12 anode and LiMn2O4 cathode) are presented as well as first results on sodium extraction from a layered SIB cathode material (Na0.84Fe0.56Mn0.44O2).......An electrochemical cell has been designed for powder X-ray diffraction (PXRD) studies of lithium ion batteries (LIB) and sodium ion batteries (SIB) in operando with high time resolution using conventional powder X-ray diffractometer. The cell allows for studies of both anode and cathode electrode...
Fourier techniques in X-ray timing
van der Klis, M.
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Improved Fourier-transform profilometry
International Nuclear Information System (INIS)
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
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.
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..
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
International Nuclear Information System (INIS)
Yamashita, Daisuke; Ishizaki, Atsushi; Uda, Masayuki
2009-01-01
A portable X-ray diffractometer equipped with an X-ray fluorescence spectrometer was improved so as to obtain a diffraction pattern and a fluorescence spectrum in air from one and the same small area of a specimen. The reason why the portable XRD with an XRF spectrometer was specially designed for archaeology may be understood from the following facts: (1) some objects exhibited in museums are not allowed to be transferred from the open air to a vacuum, even if their volumes are small; (2) some objects are very difficult to move from their original sites; (3) some parts of exhibits are extremely fragile and cannot be examined in a vacuum; and (4) information on the chemical composition and structure from the same area of an object offers a better understanding of the constitutive materials of the object. Some examples of the use of a portable X-ray diffractometer equipped with an X-ray fluorescence spectrometer in the field are also introduced. Experimental results of Sho-kannon, Snew's mask and Tutankhamun's golden mask are shown here. (author)
Paszkowicz, Wojciech
2005-10-01
During the past two decades, 1D and 2D semiconductor photon-counting detectors found applications, e.g., in detection of elementary particles and in medicine. More recent is their use for the X-ray diffraction and spectroscopy, where they become highly competitive with other detector types. Practical applications of such 1D detectors, built from up to about a hundred (at laboratory diffractometers) to several hundred (at a synchrotron beamline) of strips of size of the order 0.1×10 mm, to diffraction purposes started at the turn of the century. In the present study, selected properties of a laboratory X-ray powder diffractometer equipped with a linear photon-counting detector and a primary-beam Johansson monochromator are described. Aberrations characteristic to Bragg-Brentano instruments equipped with linear detectors are experimentally shown to be weak for 2.1° angular range covered by the detector used in this study. The counting statistics provided by this setting is shown to largely outperform that obtained with the settings equipped with point detectors. Consequently, diffraction peaks are detectable down to the level of 0.1% intensity, permitting for identification of minor impurity phases. Using illustrative examples, it is demonstrated that, with the described instrument, phase analysis of bulk polycrystals and thin polycrystalline layers is facilitated, and that structure refinement of collected data can be successfully performed.
Fourier Spectroscopy: A Bayesian Way
Directory of Open Access Journals (Sweden)
Stefan Schmuck
2017-01-01
Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.
Dual Comb Fourier Transform Spectroscopy
Hänsch, T. W.; Picqué, N.
2010-06-01
The advent of laser frequency combs a decade ago has already revolutionized optical frequency metrology and precision spectroscopy. Extensions of laser combs from the THz region to the extreme ultraviolet and soft x-ray frequencies are now under exploration. Such laser combs have become enabling tools for a growing tree of applications, from optical atomic clocks to attosecond science. Recently, the millions of precisely controlled laser comb lines that can be produced with a train of ultrashort laser pulses have been harnessed for highly multiplexed molecular spectroscopy. Fourier multi-heterodyne spectroscopy, dual comb spectroscopy, or asynchronous optical sampling spectroscopy with frequency combs are emerging as powerful new spectroscopic tools. Even the first proof-of-principle experiments have demonstrated a very exciting potential for ultra-rapid and ultra-sensitive recording of complex molecular spectra. Compared to conventional Fourier transform spectroscopy, recording times could be shortened from seconds to microseconds, with intriguing prospects for spectroscopy of short lived transient species. Longer recording times allow high resolution spectroscopy of molecules with extreme precision, since the absolute frequency of each laser comb line can be known with the accuracy of an atomic clock. The spectral structure of sharp lines of a laser comb can be very useful even in the recording of broadband spectra without sharp features, as they are e.g. encountered for molecular gases or in the liquid phase. A second frequency comb of different line spacing permits the generation of a comb of radio frequency beat notes, which effectively map the optical spectrum into the radio frequency regime, so that it can be recorded with a single fast photodetector, followed by digital signal analysis. In the time domain, a pulse train of a mode-locked femtosecond laser excites some molecular medium at regular time intervals. A second pulse train of different repetition
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...
Mozgai, Viktória; Szabó, Máté; Bajnóczi, Bernadett; Weiszburg, Tamás G.; Fórizs, István; Mráv, Zsolt; Tóth, Mária
2017-04-01
During material analysis of archaeological metal objects, especially their inlays or corrosion products, not only microstructure and chemical composition, but mineralogical composition is necessary to be determined. X-ray powder diffraction (XRD) is a widely-used method to specify the mineralogical composition. However, when sampling is not or limitedly allowed due to e.g. the high value of the object, the conventional XRD analysis can hardly be used. Laboratory micro-XRD instruments provide good alternatives, like the RIGAKU Dmax Rapid II micro-X-ray diffractometer, which is a unique combination of a MicroMax-003 third generation microfocus, sealed tube X-ray generator and a curved 'image plate' detector. With this instrument it is possible to measure as small as 10 µm area in diameter on the object. Here we present case studies for the application of the micro-XRD technique in the study of archaeological metal objects. In the first case niello inlay of a Late Roman silver augur staff was analysed. Due to the high value of the object, since it is the only piece known from the Roman Empire, only non-destructive analyses were allowed. To reconstruct the preparation of the niello, SEM-EDX analysis was performed on the niello inlays to characterise their chemical composition and microstructure. Two types of niello are present: a homogeneous, silver sulphide niello (acanthite) and an inhomogeneous silver-copper sulphide niello (exsolution of acanthite and jalpaite or jalpaite and stromeyerite). The micro-X-ray diffractometer was used to verify the mineralogical composition of the niello, supposed on the base of SEM results. In the second case corrosion products of a Late Roman copper cauldron with uncertain provenance were examined, since they may hold clues about the burial conditions (pH, Eh, etc.) of the object. A layer by layer analysis was performed in cross sections of small metal samples by using electron microprobe and micro-X-ray diffractometer. The results
Tunable fractional-order Fourier transformer
International Nuclear Information System (INIS)
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)
Fourier transform n.m.r. spectroscopy
International Nuclear Information System (INIS)
Shaw, D.
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-04-19
Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Fourier's law: insight from a simple derivation.
Dubi, Y; Di Ventra, M
2009-04-01
The onset of Fourier's law in a one-dimensional quantum system is addressed via a simple model of weakly coupled quantum systems in contact with thermal baths at their edges. Using analytical arguments we show that the crossover from the ballistic (invalid Fourier's law) to diffusive (valid Fourier's law) regimes is characterized by a thermal length scale, which is directly related to the profile of the local temperature. In the same vein, dephasing is shown to give rise to classical Fourier's law, similarly to the onset of Ohm's law in mesoscopic conductors.
International Nuclear Information System (INIS)
Terada, Noriki
2016-01-01
Recently, we have developed the experimental setup for high pressure neutron diffraction experiment with using Hybrid-Anvil-Cell in combination with high flux cold neutron time of flight (TOF) diffractometer WISH at ISIS. By using this unique setup, we have succeeded in measuring pressure induced magnetic Bragg reflections for the multiferroic compounds CuFeO 2 and TbMnO 3 . The former shows pressure induced polar magnetic phases up to 7.9 GPa. For the latter compound, we have determined the magnetic structures under not only high pressure (5 GPa) but also high magnetic field (8T) condition. In this article, I would like to show utilization of the combination, and encourage researchers in other fields as well as multiferroics to use the unique combination. (author)
International Nuclear Information System (INIS)
Rodríguez-Velamazán, J Alberto; Campo, Javier; Rodríguez-Carvajal, Juan; Noguera, Pedro
2011-01-01
Neutron diffraction has unique capabilities for scientific research under extreme conditions, mainly in two large areas: crystallography/geosciences and magnetism/solid-state physics. The growing interest in these fields is attested by the quantity and quality of publications, by the number of experiments proposed at the different neutron sources and by the new instrumentation projects under development all around the world. Therefore, the Spanish scientific community and the ILL are considering the construction of a CRG 'eXtreme conditions Diffractometer (XtremeD)' for both single crystals and powders, operating at high pressures (up to 50 GPa) and high magnetic fields (up to 15 Tesla). At the present time we are working on the finalization of the technical project, and the construction phase is expected to start in 2011. The scientific areas in which the projected instrument can make significant contributions and the main technical characteristics of the project are discussed in this paper.
Stone, Christopher; Williams, Derrick; Price, Jeremy
2016-01-01
The Extended Q-range Small-angle Neutron Scattering Diffractometer (EQ-SANS) instrument at the spallation neutron source (SNS), Oak Ridge, Tennessee, incorporates a 69 m 3 detector vessel with a vacuum system which required an upgrade with respect to performance, ease of operation, and maintenance. The upgrade focused on improving pumping performance as well as optimizing system design to minimize opportunity for operational error. This upgrade provided the following practical contributions: •Reduced time required to evacuate from atmospheric pressure to 2 mTorr from 500 to 1000 min to 60-70 min•Provided turn-key automated control with a multi-faceted interlock for personnel and machine safety.
Bartkowiak, Maciej; Stüßer, Norbert; Prokhnenko, Oleksandr
2015-10-01
The Extreme Environment Diffractometer is a neutron time-of-flight instrument, designed to work with a constant-field hybrid magnet capable of reaching fields over 26 T, unprecedented in neutron science; however, the presence of the magnet imposes both spatial and technical limitations on the surrounding instrument components. In addition to the existing diffraction and small-angle neutron scattering modes, the instrument will operate also in an inelastic scattering mode, as a direct time-of-flight spectrometer. In this paper we present the Monte Carlo ray-tracing simulations, the results of which illustrate the performance of the instrument in the inelastic-scattering mode. We describe the focussing neutron guide and the chopper system of the existing instrument and the planned design for the instrument upgrade. The neutron flux, neutron spatial distribution, divergence distribution and energy resolution are calculated for standard instrument configurations.
Jin, Xinzhe; Nakamoto, Tatsushi; Harjo, Stefanus; Hemmi, Tsutomu; Umeno, Takahiro; Ogitsu, Toru; Yamamoto, Akira; Sugano, Michinaka; Aizawa, Kazuya; Abe, Jun; Gong, Wu; Iwahashi, Takaaki
2013-06-01
To prepare for projects such as the Large Hadron Collider upgrade, International Thermonuclear Experimental Reactor and Demonstration reactor, it is important to form a clear understanding of stress-strain properties of the materials that make up superconducting magnets. Thus, we have been studying the mechanical properties of superconducting wires using neutron diffraction measurements. To simulate operational conditions such as temperature, stress, and strain, we developed a cryogenic load frame for stress-strain measurements of materials using a neutron diffractometer at Japan Proton Accelerator Research Complex (J-PARC) Takumi beam line. The maximum load that can be applied to a sample using an external driving machine is 50 kN. Using a Gifford-MacMahon cryocooler, samples can be measured down to temperatures below 10 K when loaded. In the present paper, we describe the details of the cryogenic load frame with its test results by using type-304 stainless steel wire.
International Nuclear Information System (INIS)
Parente, C.B.R.; Mazzocchi, V.L.
1999-01-01
Application of neutron diffractometer at the Instituto de Pesquisas Energeticas Nucleares, Sao Paulo, Brazil, in the structural investigations of advanced ceramics was presented. Methodology of the analysis of neutron diffraction patterns was tested with BaLiF 3 single crystals and also doped with Ni 2+ or Pb 2+ ions. The same methodology was used to investigate the HTSC phases in the system Bi-Sr-Ca-Cu-O. The system Bi 1.7 Pb 0.3 Sr 2 Ca 2.2 Cu 3.5 O 10.6 was also investigated. Addition of Pb 2+ ions increased the fraction of high-T c phase 2223. Symmetry in neutron multiple diffraction patterns, obtained for aluminium single crystal, was elaborated. Crystal lattice parameter for aluminium single crystal was determined at different temperatures using neutron multiple diffraction. (author)
Fourier analysis and synthesis tomography.
Energy Technology Data Exchange (ETDEWEB)
Wagner, Kelvin H. (University of Colorado at Boulder, Boulder, CO); Sinclair, Michael B.; Feldkuhn, Daniel (University of Colorado at Boulder, Boulder, CO)
2010-05-01
Most far-field optical imaging systems rely on a lens and spatially-resolved detection to probe distinct locations on the object. We describe and demonstrate a novel high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially-integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth-of-field and working-distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. Finally, we present for the first time two-dimensional high-resolution image reconstructions demonstrating a three-orders-of-magnitude improvement in depth-of-field over conventional lens-based microscopy.
Fourier Spectroscopy: A Simple Analysis Technique
Oelfke, William C.
1975-01-01
Presents a simple method of analysis in which the student can integrate, point by point, any interferogram to obtain its Fourier transform. The manual technique requires no special equipment and is based on relationships that most undergraduate physics students can derive from the Fourier integral equations. (Author/MLH)
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
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.
Scheibler, Robin; Hurley, Paul
2012-03-01
We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.
Walter, Jens M.; Randau, Christian; Stipp, Michael; Leiss, Bernd; Ullemeyer, Klaus; Klein, Helmut; Hansen, Bent T.; Kuhs, Werner F.
2013-04-01
For the investigation of fabric development in mono- and polyphase rocks and their deformation kinematics the quantitative analysis of the crystallographic preferred orientation (CPO) is a common tool. Furthermore, bulk texture measurements also allow the quantitative characterisation of the anisotropic physical properties of rocks. As neutrons have large penetration capabilities of several cm in geological sample materials neutron diffraction is a strong tool for geoscientific texture analysis. The new POWTEX (POWder and TEXture) Diffractometer at the neutron research reactor FRM II in Garching, Germany is designed as a high-intensity (~1 x 107 n/cm2s) time-of-flight diffractometer. The combination of high flux, the utilization of wavelength frames (TOF) and the large detector coverage ( 9.8 sr) allow fast and effective texture measurements. As the cylindrical detector provides sufficient angular resolution also for sharp recrystallisation textures, POWTEX offers unique possibilities for in-situ time-resolved texture measurements during deformation and recrystallisation experiments on rock materials as large sample environments can be placed inside the detector system. The in-situ deformation apparatus is a new design to minimize shadowing effects inside the cylindrical detector and is operated by a uniaxial spindle drive with a maximum axial load of 250 kN. The HT deformation experiments will be carried out in uniaxial compression or extension and an upgrade to triaxial deformation conditions is envisaged. The apparatus can alternatively be used for ice deformation by inserting a cryostat cell for temperatures down to 77 K with a triaxial apparatus allowing also simple shear experiments. Strain rates range between 10-8 and 10-3 s-1 reaching to at least 50 % axial strain. The deformation apparatus is designed for continuous long-term deformation experiments and can be exchanged between in-situ and ex-situ placements during continuous operation inside and outside
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
X-ray interferometric Fourier holography
International Nuclear Information System (INIS)
Balyan, M.K.
2016-01-01
The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
Mapped Fourier Methods for stiff problems in toroidal geometry
Guillard , Herve
2014-01-01
Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...
International Nuclear Information System (INIS)
Iwata, Yutaka; Mitani, Shigeshi; Shibuya, Iwao
1994-01-01
Summary is made on the single crystal neutron diffraction works carried out over the past 30 years using 4-circle neutron diffractometer installed at B-3 beam hole of the Kyoto University Reactor. Subjects dealt with are studies on structure determinations and investigations on phase transition mechanism in various ferroelectric materials and related substances. New applications are also introduced on neutron diffraction method for investigating molecular dynamics and behavior of hydrogens in crystals. (author) 83 refs
Energy Technology Data Exchange (ETDEWEB)
Suh, Il Hwan; Kim, Moon Jib; Kim, Jin Gyu [Chungnam National University, Taejon (Korea)
2000-04-01
As the four circle diffractometer (FCD) has been set up in HANARO, it has become possible to study the single crystal structures by means of the neutron diffraction. Taking account of the geometry of the FCD, a program for the control of te FCD and neutron data acquisition operating under Windows' circumstance has been accomplished. Also, a computer program which can automatically measure the diffraction intensity data has been developed. All data obtained from the FCD are processed automatically for further work and a software for the single crystal structure analyses has been prepared. A KC1 single crystal was selected as first test sample for a structure analysis had been successfully performed on the FCD using in-house developed program and accordingly their functionings with precision were confirmed. For regular single crystal diffraction experiments, the structure analyses of chrysoberyl and Zr(Y)0{sub 1.87} single crystals were performed using both neutron and X-ray diffraction methods, and the result showed that the neutron diffraction work is superior to the X-ray one from the viewpoint of certain crystallographic information obtainable only from the former one. 24 refs., 15 figs., 15 tabs. (Author)
Losko, Adrian; Vogel, Sven
2012-10-01
Automation of sample changes is essential on neutron diffractometers with short count times per sample (as little as 1min for steel samples), such as the high pressure preferred orientation (HIPPO) instrument at the Los Alamos Neutron Science Center (LANSCE), to allow for a high sample throughput. Efficient use of available neutron flux is indispensable and reduces the instrument downtime and workload of beamline personnel. High precision motion in cartesian coordinates permits accurate sample alignment and increased coverage of sample directions for texture measurements. Using geometrical properties of diffraction by crystals, corrections in sample displacements in strain measurements will minimize the artificial strain due to misalignment of the sample position to determine the center of ``gravity'' of the diffraction signal by utilizing a sample rotation that will ensure that the same grain population will diffract in two different detectors, allowing to determine any sample position offset. Those corrections are only achievable with a combination of high precision sample positioning and a large detector coverage as on HIPPO. Here we present the capabilities of the new robotic sample changer to help improve texture and strain measurements on the HIPPO instrument.
Development of Mössbauer diffractometer by using nuclear resonant scattering at SPring-8 BL11XU
Energy Technology Data Exchange (ETDEWEB)
Nakamura, Shin, E-mail: shin@koala.mse.teikyo-u.ac.jp [Teikyo University, Department of Science and Engineering (Japan); Mitsui, Takaya [National Institutes for Quantum and Radiological Science and Technology (Japan); Fujiwara, Kosuke; Ikeda, Naoshi [Okayama University (Japan); Kobayashi, Yasuhiro [Kyoto University, Research Reactor Institute (Japan); Shimomura, Susumu [Kyoto Sangyo University (Japan)
2016-12-15
A Mössbauer diffractometer has been developed by using {sup 57}Fe nuclear resonant scattering apparatus at SPring-8 BL11XU in order to obtain a crystal-site-selective Mössbauer spectrum. A #Mathematical Italic Small Theta#-2#Mathematical Italic Small Theta# goniometer was newly installed between the nuclear monochromator and a detector. From a single crystal Fe{sub 3}O{sub 4} mounted on the goniometer, the 111, 222, and 220 reflected γ-rays were used to collect the diffraction spectra at room temperature. The intensity ratio of the two subspectra, corresponding to A- and B-site Fe ions, changes notably according to the reflection index. The diffraction spectrum is composed of a major absorption spectrum and a minor emission spectrum. The former is given by the γ-ray due to the electron scattering and nuclear absorption, whereas the latter is given by the γ-ray due to the nuclear resonant scattering. Interference effects between these two γ-rays are also seen as line broadenings, asymmetric line shapes, and slope of the base lines. These features can be successfully expressed by a Fano function. We consider that the emission spectrum due to the nuclear resonant scattering represents crystal-site-selective Mössbauer spectrum.
International Nuclear Information System (INIS)
Parente, C.B.R.; Mazzocchi, V.L.; Mestnik-Filho, J.; Mascarenhas, Y.P.; Berliner, R.
2010-01-01
A high-resolution powder diffractometer (HRPD) was installed on the IEA-R1 research reactor at IPEN-CNEN/SP, Sao Paulo, SP, Brazil. It is an extensive upgrade of the old IPEN-CNEN/SP multipurpose neutron diffractometer which used a single boron trifluoride (BF 3 ) detector and a flat mosaic single crystal copper monochromator. The main modifications introduced were the installation of a position sensitive detector (PSD) and a focusing silicon monochromator. Placed at a distance of 1600 mm from sample, the PSD spans an angular range of 20 o of a diffraction pattern. An extensive powder diffraction pattern can be obtained by collecting data in contiguous 20 o segments. The double-focusing perfect single crystal silicon monochromator, installed in a take-off angle of 84 o , can be positioned to produce 4 different wavelengths, namely 1.111, 1.399, 1.667 and 2.191 A (nominal values). Diffraction patterns, obtained with the instrument, have shown a quite good resolution. Curves full width at half maximum (FWHM) vs. scattering angle (2θ) have been measured with powdered alumina using three vanadium sample holders 1/8, 1/4 and 3/8 in. in diameter. Such curves give the resolution that can be expected from the instrument in an interval 2θ from 5 o to 130 o . In comparison to the former instrument, the new diffractometer has much better resolution and is, per intensity point, ca. 600 times faster in data acquisition.
Fourier phasing with phase-uncertain mask
International Nuclear Information System (INIS)
Fannjiang, Albert; Liao, Wenjing
2013-01-01
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
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
Practical Fourier analysis for multigrid methods
Wienands, Roman
2004-01-01
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the detai...
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
On nonlinear Fourier transform: towards the nonlinear superposition
Saksida, Pavle
2017-01-01
In the paper we consider the nonlinear Fourier transform associated to the AKNSZS systems. In particular, we discuss the construction of the nonlinear Fourier modes of this transform by means of a perturbation scheme. The linearization of the AKNS-ZS nonlinear Fourier transform is the usual, linear Fourier transform and the linearization of a nonlinear Fourier mode of frequency d is the linear Fourier mode of the same frequency. We show that the first non-trivial term in the perturbation expression of any nonlinear Fourier mode is given by the dilogarithm function.
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
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.
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.
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
A Fourier analysis approach for capillary polarimetry.
Markov, Dmitry A; Swinney, Kelly; Norville, Kristin; Lu, David; Bornhop, Darryl J
2002-03-01
A new method of fringe interrogation based on Fourier analysis was implemented and tested for a capillary polarimetry detector. It has significant advantages over the previously employed depth of modulation (DOM) approach, including speed and alignment insensitivity. The new and old methods were compared using a set of interference fringes typically used to facilitate nanoliter volume polarimetric determinations. Polarimetric response was calculated with both methods over the range from 0 degrees to 180 degrees. The results were found to be in good agreement with Malus Law and indicate that an fast Fourier transform (fft) could be used for real-time capillary scale polarimetry in a probe volume of 40 nL.
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.
Interferogram analysis using Fourier transform techniques
Roddier, Claude; Roddier, Francois
1987-01-01
A method of interferogram analysis is described in which Fourier transform techniques are used to map the complex fringe visibility in several types of interferograms. Algorithms are developed for estimation of both the amplitude and the phase of the fringes (yielding the modulus and the phase of the holographically recorded object Fourier transform). The algorithms were applied to the reduction of interferometric seeing measurements (i.e., the estimation of the fringe amplitude only), and the reduction of interferometric tests (i.e., estimation of the fringe phase only). The method was used to analyze scatter-plate interferograms obtained at NOAO.
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Fourier Series The Mathematics of Periodic Phenomena
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 10. Fourier Series The Mathematics of Periodic Phenomena. S Thangavelu ... Author Affiliations. S Thangavelu1. Department of Mathematics and Statistics, University of New Mexico, Humanities Building 419, Albuquerque, NM 87131-1141, USA ...
An Uncertainty Principle for Quaternion Fourier Transform
BAHRI, Mawardi; HITZER, Eckhard S. M; HAYASHI, Akihisa; ASHINO, Ryuichi
2008-01-01
We review the quaternionic Fourier transform(QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT.This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.
Fourier series models through transformation | Omekara | Global ...
African Journals Online (AJOL)
This study considers the application of Fourier series analysis (FSA) to seasonal time series data. The ultimate objective of the study is to construct an FSA model that can lead to reliable forecast. Specifically, the study evaluates data for the assumptions of time series analysis; applies the necessary transformation to the ...
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
The periodogram at the Fourier frequencies
Kokoszka, P; Mikosch, T
In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,
Spatially incoherent single channel digital Fourier holography.
Kelner, Roy; Rosen, Joseph
2012-09-01
We present a new method for recording digital Fourier holograms under incoherent illumination. A single exposure recorded by a digital camera is sufficient to record a real-valued hologram that encodes the complete three-dimensional properties of an object.
Fast Fourier Transform Spectral Analysis Program
Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.
1969-01-01
Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.
Fourier Multiplier Theorems Involving Type and Cotype
Rozendaal, J.; Veraar, M.C.
2017-01-01
In this paper we develop the theory of Fourier multiplier operators (Formula presented.), for Banach spaces X and Y, (Formula presented.) and (Formula presented.) an operator-valued symbol. The case (Formula presented.) has been studied extensively since the 1980s, but far less is known for
Fourier Analysis Of Vibrations Of Round Structures
Davis, Gary A.
1990-01-01
Fourier-series representation developed for analysis of vibrations in complicated, round structures like turbopump impellers. Method eliminates guesswork involved in characterization of shapes of vibrational modes. Easy way to characterize complicated modes, leading to determination of responsiveness of given mode to various forcing functions. Used in conjunction with finite-element numerical simulation of vibrational modes of structure.
Fourier Analysis and the Rhythm of Conversation.
Dabbs, James M., Jr.
Fourier analysis, a common technique in engineering, breaks down a complex wave form into its simple sine wave components. Communication researchers have recently suggested that this technique may provide an index of the rhythm of conversation, since vocalizing and pausing produce a complex wave form pattern of alternation between two speakers. To…
Fourier phase demodulation of interferometric fiber sensor
Fu, Xin; Lu, Ping; Liu, Deming; Zhang, Jiangshan
2017-10-01
A novel demodulation method for interferometric fiber sensor is proposed in this paper. The physical parameters to be measured by the sensor is obtained by calculating the phase variation of the interference components. The phase variation is computed with the assist of the fast Fourier analysis. For fiber interferometers, most of the energy is contained in the few spatial frequencies corresponding to the components that produce the interference. Therefore, the information of the interference fringe can be presented by the Fourier results at those intrinsic frequencies. Based on this assumption, we proposed a novel method to interrogate the fiber interferometer by calculating the Fourier phase at the spatial frequency. Theoretical derivation proves that the Fourier phase variation is equal to the phase change of the interferometer. Simulation results demonstrate the ability of noise resistance of the proposed method since the information of all wavelength sampling points are adopted for the demodulation process. A Sagnac interferometer based on a section of polarization-maintaining photonic crystal fiber is utilized to verify the feasibility of the phase demodulation technique by lateral pressure sensing. Experimental results of -0.069rad/kPa is acquired.
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.
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
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
International Nuclear Information System (INIS)
Rodríguez-Velamazán, J Alberto; Noguera, Pedro
2011-01-01
The Spanish community of neutron scatterers and the ILL are considering the construction of a CRG e xtreme conditions Diffractometer (XtremeD)for both single crystals and powders, operating at high pressures (up to 50 GPa) and high magnetic fields (up to 15 Tesla). High pressure studies require reduced sample volumes. This makes the focusing optics a crucial part of the instrument, in order to have increased flux and to avoid the scattering from the sample environment. The different solutions at different levels of the instrument, which are being studied, will be discussed in this paper.
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
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
Fourier analysis: from cloaking to imaging
International Nuclear Information System (INIS)
Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan
2016-01-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers. (review)
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Fourier Transform Fabry-Perot Interferometer
Snell, Hilary E.; Hays, Paul B.
1992-01-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
The PROSAIC Laplace and Fourier Transform
International Nuclear Information System (INIS)
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
Fourier transform of momentum distribution in vanadium
International Nuclear Information System (INIS)
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.)
Correcting sample drift using Fourier harmonics.
Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L
2018-04-21
During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.
Complete way to fractionalize Fourier transform
Yeung, Daniel S.; Ran, Qiwen; Tsang, Eric C. C.; Teo, Kok Lay
2004-01-01
We propose a complete way to fractionalize Fourier transform. This fractionalization can perfectly extend the fractional Fourier transform (FRFT) defined in [C.C. Shih, Opt. Commun. 118 (1995) 495] to the original one in [V. Namias, J. Inst. Math. Appl. 25 (1980) 241]. The new FRFT proposed in this paper can have any integer M(⩾3)-periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform, and it will be reduced to the FRFT in [Namias, loc. cit.; Shih, loc. cit.; S. Liu, J. Jiang, Y. Zhang, J. Zhang, J. Phys. A: Math. Gen. 30 (1997) 973] at the three limits with M=+∞, M=4, M=4 k ( k is a natural number), respectively.
Laser Field Imaging Through Fourier Transform Heterodyne
Energy Technology Data Exchange (ETDEWEB)
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.
1999-04-05
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Fourier Transform Spectrometer Controller for Partitioned Architectures
DEFF Research Database (Denmark)
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....
Study of Fourier descriptors statistical features
Darwish, Ahmed M.; Mohamed, Emad-Eldin H.
1993-12-01
In this paper we present a new approach to reduce the computations involved in recognition applications. Fourier descriptors are treated as a occurrence of a complex random variable. Statistical function measures are then used to characterize the behavior of the complex variable. A study of pattern regeneration based on these statistical features was carried out. Some of these statistical measures were found to comprehend most of the object global features. Thus, they could be used for classification and recognition purposes.
Fourier analysis of the SOR iteration
Leveque, R. J.; Trefethen, L. N.
1986-01-01
The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. It is shown that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants.
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-01-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Sets of Fourier coefficients using numerical quadrature
International Nuclear Information System (INIS)
Lyness, J. N.
2001-01-01
One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)
The derivative-free Fourier shell identity for photoacoustics.
Baddour, Natalie
2016-01-01
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.
International Nuclear Information System (INIS)
Nowak, D. E.; Blasini, D. R.; Vodnick, A. M.; Blank, B.; Tate, M. W.; Deyhim, A.; Smilgies, D.-M.; Abruna, H.; Gruner, S. M.; Baker, S. P.
2006-01-01
A new diffractometer system was designed and built for the G2 experimental station at the Cornell High Energy Synchrotron Source (CHESS). A six-circle κ goniometer, which provides better access to reciprocal space compared to Eulerian cradles, was chosen primarily to perform large angle Bragg diffraction on samples with preferred crystallographic orientations, and can access both horizontal and vertical diffraction planes. A new atmosphere- and temperature-controlled sample stage was designed for thin film thermomechanical experiments. The stage can be operated in ultrahigh vacuum and uses a Be dome x-ray window to provide access to all scattering vectors above a sample's horizon. A novel design minimizes sample displacements during thermal cycling to less than 160 μm over 900 deg. C and the stage is motorized for easy height adjustments, which can be used to compensate for displacements from thermal expansion. A new area detector was built and a new line detector was purchased. Both detectors cover a large region in reciprocal space, providing the ability to measure time-resolved phenomena. A detailed description of the design and technical characteristics is given. Some capabilities of the diffractometer system are illustrated by a strain analysis on a thin metal film and characterization of organic thin films with grazing incidence diffraction. The G2 experimental station, as part of CHESS, is a national user facility and is available to external users by application
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
Fourier spectral simulations for wake fields in conducting cavities
International Nuclear Information System (INIS)
Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.
2007-01-01
We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.
A Note on Fourier and the Greenhouse Effect
Postma, Joseph E.
2015-01-01
Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...
Some Applications of Fourier's Great Discovery for Beginners
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…
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",…
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
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
Validation of Fourier analysis of videokeratographic data.
Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios
2017-06-15
The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.
Bruzzo, Ugo; Maciocia, Antony
2017-12-01
This special issue celebrates the 34 years since the discovery of the Fourier-Mukai Transform by Shigeru Mukai. It mostly contains papers presented at the conference held in the Mathematics Research Centre of the University of Warwick, 15th to 19th June 2015 as part of a year long Warwick symposium on Derived categories and applications. The conference was also the annual conference of the Vector Bundles on Algebraic Curves series led by Peter Newstead. The symposium was principally supported by the Engineering and Physical Sciences Research Council of the UK and there was further funding from the London Mathematical Society and the Foundation Compositio.
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.
Doppler-free Fourier transform spectroscopy.
Meek, Samuel A; Hipke, Arthur; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie
2018-01-01
Sub-Doppler broadband multi-heterodyne spectroscopy is proposed and experimentally demonstrated. Using two laser frequency combs of slightly different repetition frequencies, we have recorded Doppler-free two-photon dual-comb spectra of atomic rubidium resonances of a width of 6 MHz, while simultaneously interrogating a spectral span of 10 THz. The atomic transitions are uniquely identified via the intensity modulation of the observed fluorescence radiation. To the best of our knowledge, these results represent the first demonstration of Doppler-free Fourier transform spectroscopy and extend the range of applications of broadband spectroscopy towards precision nonlinear spectroscopy.
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
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....
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Analysis method for Fourier transform spectroscopy
Park, J. H.
1983-01-01
A fast Fourier transform technique is given for the simulation of those distortion effects in the instrument line shape of the interferometric spectrum that are due to errors in the measured interferogram. The technique is applied to analyses of atmospheric absorption spectra and laboratory spectra. It is shown that the nonlinear least squares method can retrieve the correct information from the distorted spectrum. Analyses of HF absorption spectra obtained in a laboratory and solar CO absorption spectra gathered by a balloon-borne interferometer indicate that the retrieved amount of absorbing gas is less than the correct value in most cases, if the interferogram distortion effects are not included in the analysis.
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 ...
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.
Digital Fourier microscopy for soft matter dynamics
International Nuclear Information System (INIS)
Giavazzi, Fabio; Cerbino, Roberto
2014-01-01
Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method. (topical review)
International Nuclear Information System (INIS)
Randau, C.; Brokmeier, H.G.; Gan, W.M.; Hofmann, M.; Voeller, M.; Tekouo, W.; Al-hamdany, N.; Seidl, G.; Schreyer, A.
2015-01-01
The materials science neutron diffractometer STRESS-SPEC located at FRM II is a dedicated instrument for strain and pole figure measurements. Both methods make complementary demands on sample handling. On one hand pole figure measurements need a high degree of freedom to orient small samples and on the other hand in strain investigations it is often necessary to handle large and heavy components. Therefore a robot based sample positioning system was developed, which has the capability to provide both possibilities. Based on this new robot system further developments like a full automated sample changer system for texture measurements were accomplished. Moreover this system opens the door for combined strain and texture analysis at STRESS-SPEC
International Nuclear Information System (INIS)
Radulescu, Aurel; Pipich, Vitaliy; Ioffe, Alexander
2012-01-01
Following the shutdown of FRJ-2 research reactor in Jülich, the pinhole small-angle neutron diffractometers KWS-1 and KWS-2 have been moved to the research reactor FRM II in Garching. The installation of these 40 m long instruments required the design and setup of new neutron guides with geometrical and optical features imposed by the instruments' positioning in the neutron guide hall, such as, the predetermined length and beam height as well as the foreseen improvement of the instrument performance. We report here about the quality assessment of the newly constructed neutron guides with respect to the optical, geometrical and alignment characteristics and the positioning of the velocity selector integrated in the neutron guide system by comparing the features of the measured neutron beams (in terms of neutron flux, intensity distribution and beam profile) with the results of the simulations of optimal neutron guide systems.
Energy Technology Data Exchange (ETDEWEB)
Randau, C. [Institute for Materials Science and Engineering, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld (Germany); Brokmeier, H.G., E-mail: heinz-guenter.brokmeier@tu-clausthal.de [Institute for Materials Science and Engineering, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld (Germany); Institute of Materials Research, Helmholtz-Centre Geesthacht, D-21502 Geesthacht (Germany); Gan, W.M. [Institute of Materials Research, Helmholtz-Centre Geesthacht, D-21502 Geesthacht (Germany); Hofmann, M.; Voeller, M. [Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II), TU München, D-85747 Garching (Germany); Tekouo, W. [Institute for Machine Tools and Industrial Management, TU München, D-85747 Garching (Germany); Al-hamdany, N. [Institute for Materials Science and Engineering, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld (Germany); Seidl, G. [Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II), TU München, D-85747 Garching (Germany); Schreyer, A. [Institute of Materials Research, Helmholtz-Centre Geesthacht, D-21502 Geesthacht (Germany)
2015-09-11
The materials science neutron diffractometer STRESS-SPEC located at FRM II is a dedicated instrument for strain and pole figure measurements. Both methods make complementary demands on sample handling. On one hand pole figure measurements need a high degree of freedom to orient small samples and on the other hand in strain investigations it is often necessary to handle large and heavy components. Therefore a robot based sample positioning system was developed, which has the capability to provide both possibilities. Based on this new robot system further developments like a full automated sample changer system for texture measurements were accomplished. Moreover this system opens the door for combined strain and texture analysis at STRESS-SPEC.
Randau, C.; Brokmeier, H. G.; Gan, W. M.; Hofmann, M.; Voeller, M.; Tekouo, W.; Al-hamdany, N.; Seidl, G.; Schreyer, A.
2015-09-01
The materials science neutron diffractometer STRESS-SPEC located at FRM II is a dedicated instrument for strain and pole figure measurements. Both methods make complementary demands on sample handling. On one hand pole figure measurements need a high degree of freedom to orient small samples and on the other hand in strain investigations it is often necessary to handle large and heavy components. Therefore a robot based sample positioning system was developed, which has the capability to provide both possibilities. Based on this new robot system further developments like a full automated sample changer system for texture measurements were accomplished. Moreover this system opens the door for combined strain and texture analysis at STRESS-SPEC.
International Nuclear Information System (INIS)
Hong, Hawoong; Chiang, T.-C.
2007-01-01
A new ultrahigh vacuum (UHV) surface diffractometer system equipped with molecular beam epitaxy (MBE) capabilities has been developed. It has a versatile 6-circle configuration for defining the diffraction geometry, and a three-axis translation stage for controlling the sample position. Rugged mechanical components are employed in the design to allow accurate diffraction measurements. Sample cooling is facilitated by passing liquid nitrogen into a reservoir in the base of a sample mount. The sample can be heated to very high temperatures by either direct current heating or electron beam bombardment. During film growth and processing, the sample temperature, monitored by thermocouples, can be continuously and rapidly varied between ∼110 K to above room temperature. A charge coupled device (CCD) camera, attached to the μ circle, allows rapid reciprocal space mapping for real time studies of sample growth and evolution during deposition and annealing. A beam stop and a baffle are implemented to minimize stray scattered radiation
International Nuclear Information System (INIS)
Nomura, Katsuhiro
2008-01-01
Perovskite-type proton conductors can be used as the electrolyte materials in fuel cells, hydrogen sensors, hydrogen separation apparatus, and the other electrochemical devices. In this paper, the crystal structure analysis of perovskite-type proton conductors under cell operating conditions by using a laboratory X-ray diffractometer with a parallel beam optics are introduced. The crystal structures of A 3+ B 3+ O 3 -type perovskite proton conductors, (La 0.9 Sr 0.1 )M III O 3-δ (M III =Sc, In, and Lu) are reported, and the expected change in proton conduction path is discussed with an increase in tilting angles of BO 6 (=M IIO 6 ) octahedra. In addition, the electron density distribution of (La 0.8 Sr 0.2 )ScO 3-δ compound is shown. (author)
Choi, Yong Nam; Kim, Shin Ae; Kim, Sung Kyu; Kim, Sung Baek; Lee, Chang-Hee; Mikula, Pavel
2004-07-01
In a conventional diffractometer having single monochromator, only one position, parallel position, is used for the diffraction experiment (i.e. detection) because the resolution property of the other one, anti-parallel position, is very poor. However, a bent perfect crystal (BPC) monochromator at monochromatic focusing condition can provide a quite flat and equal resolution property at both parallel and anti-parallel positions and thus one can have a chance to use both sides for the diffraction experiment. From the data of the FWHM and the Delta d/d measured on three diffraction geometries (symmetric, asymmetric compression and asymmetric expansion), we can conclude that the simultaneous diffraction measurement in both parallel and anti-parallel positions can be achieved.
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.
Multicomplementary operators via finite Fourier transform
International Nuclear Information System (INIS)
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
Ion cyclotron resonance spectrometer with fourier transformation
International Nuclear Information System (INIS)
Pikver, R.; Suurmaa, Eh.; Syugis, A.; Tammik, A.; Lippmaa, Eh.
1983-01-01
The ion cyclotron resonance spectrometer with Fourier transformation intended for investigating mass specta and chemical reaction kinetics in the gaseous phase is described. The mass-spectrum of CO and N 2 positive ions is shown. The spectrometer consists of an electromagnet with power supply, a vacuum system, a cell with electronic equipment and a minicomputer. In the vacuum system (5x10 -9 Torr) there is a cubic measuring cell heated up to 400 deg C. The spectrometer mass resolution is of the 10 5 order. The spectrometer is able to operate as a high-resolution analytical mass-spectrometer of positive and negative ions. The experience of the spectrometer operation confirms its effectiveness for investigating ion-molecular reactions, in particular, proton transfer reactions
Fourier transform and its application to 1D and 2D NMR
International Nuclear Information System (INIS)
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
Assessment of Nutrient Composition of Fore-Stomach Digesta (FSD ...
African Journals Online (AJOL)
acer
animals subsist on very poor quality forages, leading to very low levels of performance. (Steinbach, 1997). These and other factors such as rise in the price of conventional feed and feed ingredients limited the productivity of livestock in Nigeria. It therefore becomes imperative to look for alternative sources of feeds in order to.
Full system decontamination (FSD) for sustainable dose reduction
International Nuclear Information System (INIS)
Stiepani, Christoph; Sempere-Belda, Luis; Topf, Christian; Basu, Ashim
2012-09-01
Nuclear power plants experience an increase in dose rates during operation due to the build-up of the activity inventory. The activity build-up is influenced by the construction materials, past and present water chemistries, and the individual operating history of the plant. Depending on these factors the dose levels in an operating plant may reach a point in which concrete actions to reduce the overall radiation exposure become necessary. In the past dose reduction plans were performed, based on - Modification in coolant water chemistry - Substitution of Cobalt containing materials - Outage optimization program - Installation of permanent shielding - Decontamination The dose rate reduction took several years and today a stagnation of further dose rate reduction can be seen. Therefore AREVA has developed the Concept for Sustainable Dose Reduction in Operating BWRs and PWRs. This is a program of joint corrective measures to minimize dose levels rapidly and keep them low for continued operation. It can be applied in plants from all constructors and designs. The concept is based fully on the application of proven technologies, including: - Full System Decontamination with AREVA's decontamination process HP/CORD UV to minimize the activity inventory - The formation of new, very stable protective oxides on the system surfaces including injection of depleted zinc - Introduction of advanced water chemistry for maintaining the low dose levels achieved during ongoing operation The implementation of this program is particularly interesting for plants with a long operation history, especially when considering life extension. The latest application was performed successfully at the German PWR Grafenrheinfeld in 2010. In this paper the concept for sustainable dose reduction will be outlined and the site application detailed and the achieved results at PWR Grafenrheinfeld will be described. The recontamination after one cycle will be outlined in a second paper. (authors)
On a General Class of Trigonometric Functions and Fourier Series
Pavao, H. Germano; Capelas de Oliveira, E.
2008-01-01
We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
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.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
Realization of quantum Fourier transform over ZN
International Nuclear Information System (INIS)
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)
Fast algorithm of adaptive Fourier series
Gao, You; Ku, Min; Qian, Tao
2018-05-01
Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.
Fourier transform spectroscopy for future planetary missions
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
Exploring Fourier Series and Gibbs Phenomenon Using Mathematica
Ghosh, Jonaki B.
2011-01-01
This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…
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
Fourier transform in multimode systems in the Bargmann representation
International Nuclear Information System (INIS)
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
Lacunary Fourier Series and a Qualitative Uncertainty Principle for ...
Indian Academy of Sciences (India)
We define lacunary Fourier series on a compact connected semisimple Lie group . If f ∈ L 1 ( G ) has lacunary Fourier series and vanishes on a non empty open subset of , then we prove that vanishes identically. This result can be viewed as a qualitative uncertainty principle.
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Present work illustrates a scheme of quantitative description of the shape of the skull outlines of temnospondyl amphibians using bilaterally symmetric closed Fourier curves. Some special points have been identified on the Fourier fits of the skull outlines, which are the local maxima, or minima of the distances from the ...
Infrared Fourier spectres of pectin obtained from pumpkin
International Nuclear Information System (INIS)
Usmanova, S.R.; Dzhonmurodov, A.S.; Nazirova, Kh.I.; Mukhidinov, Z.K.
2015-01-01
Present article is devoted to infrared Fourier spectres of pectin obtained from pumpkin. The analysis of pectin obtained from pumpkin was conducted by means of infrared spectrophotometer with Fourier transformation. The infrared spectroscopic study of pectin polysaccharide fraction of pectin matter, as well as pectin helium and micro helium obtained by means of fast extraction was conducted.
Fourier transforms of Dini-Lipschitz functions on Vilenkin groups
Directory of Open Access Journals (Sweden)
M. S. Younis
1992-01-01
Full Text Available In [4] we proved some theorems on the Fourier Transforms of functions satisfying conditions related to the Dini-Lipschitz conditions on the n-dimensional Euclidean space Rn and the torus group Tn. In this paper we extend those theorems for functions with Fourier series on Vilenkin groups.
Fourierdimredn: Fourier dimensionality reduction model for interferometric imaging
Kartik, S. Vijay; Carrillo, Rafael; Thiran, Jean-Philippe; Wiaux, Yves
2016-10-01
Fourierdimredn (Fourier dimensionality reduction) implements Fourier-based dimensionality reduction of interferometric data. Written in Matlab, it derives the theoretically optimal dimensionality reduction operator from a singular value decomposition perspective of the measurement operator. Fourierdimredn ensures a fast implementation of the full measurement operator and also preserves the i.i.d. Gaussian properties of the original measurement noise.
Geometric interpretations of the Discrete Fourier Transform (DFT)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
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.
The relationship between shock response spectrum and fast Fourier transform
International Nuclear Information System (INIS)
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)
Double Fourier analysis for Emotion Identification in Voiced Speech
International Nuclear Information System (INIS)
Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.
2016-01-01
We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Applied Fourier analysis from signal processing to medical imaging
Olson, Tim
2017-01-01
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. Fo...
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
A transformada de Fourier em basic The Fourier transform (FFT in basic
Directory of Open Access Journals (Sweden)
Mauricio Gomes Constantino
2000-06-01
Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.
Energy Technology Data Exchange (ETDEWEB)
Kim, Moon Jib [Soonchunhyang University, Asan (Korea); Suh, Il Hwan [Chungnam National University, Taejon (Korea)
1999-06-01
We have been studied to find out the experimental methods and procedures for neutron diffraction method for neutron diffractometer in HANARO -the atomic research reactor in KAERI. We have studied experimental process for the neutron diffraction data analysis, using computer soft-wares such as SHELXS for the calculation the initial phase of crystal structure, SHELXL for refinement of atomic coordinate using least-squares method, ORTEP for the display of the calculated positions of molecule, and PATSEE for the calculation of the phase from the expected structure. In these studies, we analyzed the structure of test sample using these programs, and prepare the user's manual for these soft-wares. We have also studied on bending effect of monochromator in order to increase the intensity of neutron beam, and designed HRPD - High Resolution Powder Diffractometers. 7 refs., 6 figs. (Author)
Directory of Open Access Journals (Sweden)
David . R Allan
2017-11-01
Full Text Available Herein, we describe the development of a novel dual air-bearing fixed-χ diffractometer for beamline I19 at Diamond Light Source. The diffractometer is designed to facilitate the rapid data collections possible with a Dectris Pilatus 2M pixel-array photon-counting detector, while allowing remote operation in conjunction with a robotic sample changer. The sphere-of-confusion is made as small as practicably possible, through the use of air-bearings for both the ω and φ axes. The design and construction of the new instrument is described in detail and an accompanying paper by Johnson et al. (also in this issue will provide a user perspective of its operation.
International Nuclear Information System (INIS)
Macias B, L.R.
1991-05-01
The objective of this work consists on determining the calibration in the angular parameters and the neutron wavelength used in the neutron diffractometer of the TRIGA Mark III reactor, through some readings in that a well-known sample is used by means of a Fortran computer program that is used in the CYBER computer of the ININ in Mexico, and/or in micro computers compatible with IBM. The program was also designed to determine the zero of the 2 θ angle of the goniometer of the diffractometer. The generated data were proven by means of well-known data of the Powder Diffraction File of the Joint Committee on Powder Diffraction Standards (JCPDS). (Author)
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
Precision Fourier Neutron Diffraction Study of the High-Temperature Superconductor Y(44Ca)Ba2Cu4O8
International Nuclear Information System (INIS)
Balagurov, A.M.; Simkin, V.G.; Kaganovich, T.Yu.; Trunov, V.A.
1994-01-01
The high-temperature superconductor, YBa 2 Cu 4 O 8 , with partial substitution of Ca for Y was investigated with a high-resolution Fourier neutron diffractometer over a wide temperature range. The 44 Ca isotope was used to increase neutron contrast. Structural analysis was performed for the spectra measured at 135, 165, and 293 K; the temperature dependence of the lattice parameters was determined from the points measured within the range of 8 to 288 K. The presence of a structural anomaly in the proximity of 150 K was confirmed. It manifests itself by a sharp change in the expansion coefficient along the b axis, irregular behaviour of the orthorhombicity coefficient, and a noticeable change in bond length. The most distinct change is a contraction of the distance between the Cu2 copper atom and the apical O1 oxygen, as well as change in the distance between the O2 and O3 atom chains in the CuO 2 layer. 8 refs., 4 figs., 3 tabs
International Nuclear Information System (INIS)
2002-01-01
The purpose of the workshop was to: inform the Australian research organizations and universities of the capabilities of an engineering and materials science instrument; promote the use of neutron diffraction to map and investigate strains/stresses in materials and components for industrial applications and research; identify the future needs and opportunities in this area; present the options for a stress mapping diffractometer at the Replacement Research Reactor and receive feedback on these options; identify the ancillary equipment and facilities required. Presented papers and discussions at the workshop indicated that there are a number of important benefits to Australia in the building of a first-class instrument for materials science and engineering and many residual stress-related problems in a wide variety of fields in Australia, such as the manufacturing industries, mining, oil and gas, rail transport, defense and life extension. Stress scanning provides another tool for solving problems to complement facilities at the major research institutes, CSIRO, AMIRA, DSTO, ANSTO and the universities. It will create a regional pool of experts who may tap into the pool of expertise internationally. The turn around time for tests for Australian customers will be reduced thus avoiding having to go overseas to have the tests performed. From an educational perspective the instrument will build expertise in Australia and will help to attract graduates into engineering. A detailed list of the attendees and affiliations is in Appendix C
International Nuclear Information System (INIS)
Bolze, J.
2011-01-01
We present the application of the small-angle X-ray scattering (SAXS) technique for the structural characterization of nano materials. This technique has become available in the laboratory on a multipurpose X-ray diffractometer platform and yields information that is complementary to what can be deduced from XRD (or WAXS) data. Among others SAXS is used for the determination of the size distribution, shape, specific surface area, inner structure and aggregation behavior of nanoparticles. It may also be applied to investigate pore size distributions in meso porous materials as well as ordered nano structures. Several application examples dealing with the characterization of photo catalytic nano powders, porous materials, polymer nano composites, colloidal dispersions, surfactants and related samples will be given. Furthermore, the SAXS technique will be compared and contrasted to complementary experimental techniques, such as dynamic light scattering, ultracentrifugation, electron microscopy, BET measurements and mercury intrusion porosimetry. Whereas this presentation focuses on the application examples of the SAXS technique, a more fundamental and practical introduction will be given within the workshop. (author)
Image reconstruction from pairs of Fourier-transform magnitude
International Nuclear Information System (INIS)
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
Fourier mode analysis of source iteration in spatially periodic media
International Nuclear Information System (INIS)
Zika, M.R.; Larsen, E.W.
1998-01-01
The standard Fourier mode analysis is an indispensable tool when designing acceleration techniques for transport iterations; however, it requires the assumption of a homogeneous infinite medium. For problems of practical interest, material heterogeneities may significantly impact iterative performance. Recent work has applied a Fourier analysis to the discretized two-dimensional transport operator with heterogeneous material properties. The results of these analyses may be difficult to interpret because the heterogeneity effects are inherently coupled to the discretization effects. Here, the authors describe a Fourier analysis of source iteration (SI) that allows the calculation of the eigenvalue spectrum for the one-dimensional continuous transport operator with spatially periodic heterogeneous media
Development of Fourier domain optical coherence tomography
Wang, Rui
Fourier domain optical coherence tomography (FD-OCT) is a high-speed, high-resolution, and noninvasive imaging technique that can obtain cross-sectional images of light scattering medium, such as biomedical tissues. In this thesis, I report three novel methods in FD-OCT technique including common-path endoscopic FD-OCT, streak-mode FD-OCT, and Doppler streak-mode FD-OCT. Finally, I apply the streak mode FD-OCT to ultrahigh-speed, noninvasive, live imaging of embryonic chick hearts. An extension of conventional FD-OCT technique is endoscopic FD-OCT, which can access internal organs by utilizing a miniaturized catheter design. However, its image signal suffers from the bending of the endoscopic catheter. To address this problem, a common-path endoscopic FD-OCT system was developed to avoid the polarization mismatch. Consequently, the OCT images were immune to the catheter bending. In addition, a Microelectromechanical system (MEMS) motor was integrated into the miniaturized probe to achieve circumferential scanning within lumen samples. In conventional FD-OCT, the imaging speed is limited by the slow line-scan rate of the camera. We developed the streak-mode FD-OCT technique, in which an area-scan camera is used instead of a line-scan camera to record the FD-OCT spectrum. Using this technique, high temporal resolution of 1000--2000 cross-sectional images of the sample were obtained in one second. Doppler FD-OCT is a functional extension of FD-OCT technique, which can measure the flow velocity within biomedical tissues. However, conventional techniques are not available to measure high speed flow due to slow imaging speed, phase wrapping, and fringe wash out issues. Based on the streak mode FD-OCT, a novel Doppler technique was developed that addressed these problems. It has been well established that cardiac dynamics play an important role in the early development of an embryonic heart. However, the mechanism by which cardiac dynamics affect the development of a
Fourier transform spectroscopy of semiconductor materials
International Nuclear Information System (INIS)
Jonak-Auer, I.
1996-11-01
In order to determine the type of charge carriers, i.e. electrons or holes, participating in optical transitions, cyclotron resonance experiments using circularly polarized radiation were performed on strained-layer [111]-oriented InGaAs/(Al)GaAs multiple quantum wells and on a [100]-oriented InAs/GaSb double-heterostructure. Because of the rather complicated band-structures of these samples it is a priori unknown which carriers take part in transitions. The measurements yield the surprising result, that for the InGaAs/GaAs multiple quantum well the experimentally observed cyclotron resonance appears in the electron-active polarization in the frequency-regime of the Far Infrared (FIR), but in the hole-active polarization in the range of millimeter waves, whereas for the InGaAs/AlGaAs sample the resonance is caused by holes also in the FIR. Since by theoretical considerations the possibility of electrons causing the FIR cyclotron resonance could be excluded, the measurements are interpreted as being caused by holes due to broken selection rules. In the InAs/GaSb sample hole cyclotron resonance could for the first time be measured on a double-heterostructure. As for the application oriented measurements, they comprised a study of the hydrogen content of amorphous silicon nitride layers, and were performed in collaboration with Austria Mikro Systeme International AG. Fourier spectroscopy is a fast and non-destructive means for determining impurity concentrations. Radiation in the Mid Infrared regime stimulates N-H and Si-H stretching vibrations which lead to absorption peaks and can directly be attributed to the hydrogen concentration via calibration factors taken from the literature. In comparison with recommended procedures in the literature, a much higher accuracy in determining the areas of the absorption peaks could be gained in the course of this thesis by a proper polynomial fit of the background spectrum outside the absorption lines. The hydrogen content of
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
On Sums of Numerical Series and Fourier Series
Pavao, H. Germano; de Oliveira, E. Capelas
2008-01-01
We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)
Extending Single-Molecule Microscopy Using Optical Fourier Processing
2015-01-01
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
. © Indian Academy of Sciences. Embedding relations connected with strong approximation of Fourier series. BOGDAN SZAL. Faculty of Mathematics, Computer Science and Econometrics,. University of Zielona Góra, 65-516 Zielona Góra, ul.
Surface Fourier-transform lens using a metasurface
International Nuclear Information System (INIS)
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)
Almost everywhere convergence over cubes of multiple trigonometric Fourier series
International Nuclear Information System (INIS)
Antonov, N Yu
2004-01-01
Under certain conditions on a function φ:[0,+∞)→[0,+∞) we prove a theorem asserting that the convergence almost everywhere of trigonometric Fourier series for all functions of class φ(L) [-π,π) implies the convergence over cubes of the multiple Fourier series and all its conjugates for an arbitrary function f element of φ(L)(log + L) d-1 ) [-π,π) d , d element of N. It follows from this and an earlier result of the author on the convergence almost everywhere of Fourier series of functions of one variable and class L(log + L)(log + log + log + L)) [-π,π) that if f element of L(log + L) d (log + log + log + L)) [-π,π) d , d element of N, then the Fourier series of f and all its conjugates converge over cubes almost everywhere
On the physical relevance of the discrete Fourier transform
CSIR Research Space (South Africa)
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...
On the Equisummability of Hermite and Fourier Expansions
Indian Academy of Sciences (India)
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-02-01
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo\\'s laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier\\'s law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.
Electro-Optic Imaging Fourier Transform Spectral Polarimeter, Phase I
National Aeronautics and Space Administration — Boulder Nonlinear Systems, Inc. (BNS) proposes to develop an Electro-Optic Imaging Fourier Transform Spectral Polarimeter (E-O IFTSP). The polarimetric system is...
A fourier transform quality measure for iris images
CSIR Research Space (South Africa)
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...
Space-charge calculations with the fast Fourier transform
International Nuclear Information System (INIS)
Vaughan, J.R.
1978-01-01
A method is described for calculating linear accelerator beam trajectories in traveling wave tubes. A grid is placed over the region of interest in which there is space charge. A matrix of the Fourier potential coefficients is obtained, and a straight Fourier synthesis is used to add these with the appropriate trigonometric multipliers to obtain the potential matrix. The pulses on a particle for the next trajectory step are found by interpolating and differencing the potentials on that matrix
A New Nonlinear Unit Root Test with Fourier Function
Güriş, Burak
2017-01-01
Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...
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.
On the Mathematics of Music: From Chords to Fourier Analysis
Lenssen, Nathan; Needell, Deanna
2013-01-01
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from recorded music. We begin with a light introduction to the theory of music and motivate the use of Fourier analysis in audio processing. We introduce the discrete and continuous Fourier transforms and investigate their use in extracting important information...
Simple optical setup implementation for digital Fourier transform holography
International Nuclear Information System (INIS)
De Oliveira, G N; Rodrigues, D M C; Dos Santos, P A M
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.
Li, Shu-Nan; Cao, Bing-Yang
2017-09-01
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
Self-Fourier functions and coherent laser combination
International Nuclear Information System (INIS)
Corcoran, C J; Pasch, K A
2004-01-01
The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)
Radulescu, Aurel; Szekely, Noemi Kinga; Appavou, Marie-Sousai; Pipich, Vitaliy; Kohnke, Thomas; Ossovyi, Vladimir; Staringer, Simon; Schneider, Gerald J.; Amann, Matthias; Zhang-Haagen, Bo; Brandl, Georg; Drochner, Matthias; Engels, Ralf; Hanslik, Romuald; Kemmerling, Günter
2016-01-01
The KWS-2 SANS diffractometer is dedicated to the investigation of soft matter and biophysical systems covering a wide length scale, from nm to µm. The instrument is optimized for the exploration of the wide momentum transfer Q range between 1x10-4 and 0.5 Å-1 by combining classical pinhole, focusing (with lenses), and time-of-flight (with chopper) methods, while simultaneously providing high-neutron intensities with an adjustable resolution. Because of its ability to adjust the intensity and the resolution within wide limits during the experiment, combined with the possibility to equip specific sample environments and ancillary devices, the KWS-2 shows a high versatility in addressing the broad range of structural and morphological studies in the field. Equilibrium structures can be studied in static measurements, while dynamic and kinetic processes can be investigated over time scales between minutes to tens of milliseconds with time-resolved approaches. Typical systems that are investigated with the KWS-2 cover the range from complex, hierarchical systems that exhibit multiple structural levels (e.g., gels, networks, or macro-aggregates) to small and poorly-scattering systems (e.g., single polymers or proteins in solution). The recent upgrade of the detection system, which enables the detection of count rates in the MHz range, opens new opportunities to study even very small biological morphologies in buffer solution with weak scattering signals close to the buffer scattering level at high Q. In this paper, we provide a protocol to investigate samples with characteristic size levels spanning a wide length scale and exhibiting ordering in the mesoscale structure using KWS-2. We present in detail how to use the multiple working modes that are offered by the instrument and the level of performance that is achieved. PMID:28060296
Iterative wave-front reconstruction in the Fourier domain.
Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry
2017-05-15
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.
Fast Fourier single-pixel imaging via binary illumination.
Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang
2017-09-20
Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Ballooning modes or Fourier modes in a toroidal plasma?
International Nuclear Information System (INIS)
Connor, J.W.; Taylor, J.B.
1987-01-01
The relationship between two different descriptions of eigenmodes in a torus is investigated. In one the eigenmodes are similar to Fourier modes in a cylinder and are highly localized near a particular rational surface. In the other they are the so-called ballooning modes that extend over many rational surfaces. Using a model that represents both drift waves and resistive interchanges the transition from one of these structures to the other is investigated. In this simplified model the transition depends on a single parameter which embodies the competition between toroidal coupling of Fourier modes (which enhances ballooning) and variation in frequency of Fourier modes from one rational surface to another (which diminishes ballooning). As the coupling is increased each Fourier mode acquires a sideband on an adjacent rational surface and these sidebands then expand across the radius to form the extended mode described by the conventional ballooning mode approximation. This analysis shows that the ballooning approximation is appropriate for drift waves in a tokamak but not for resistive interchanges in a pinch. In the latter the conventional ballooning effect is negligible but they may nevertheless show a ballooning feature. This is localized near the same rational surface as the primary Fourier mode and so does not lead to a radially extended structure
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Spectrums Transform Operators in Bases of Fourier and Walsh Functions
Directory of Open Access Journals (Sweden)
V. V. Syuzev
2017-01-01
Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel
Some applications of Fourier's great discovery for beginners
International Nuclear Information System (INIS)
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations. (paper)
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
On the Alignment of Shapes Represented by Fourier Descriptors
DEFF Research Database (Denmark)
Sjöstrand, Karl; Ericsson, Anders; Larsen, Rasmus
2006-01-01
The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has many benefits and is applicable for describing a range of medical structures in two dimensions. Delineations in medical applications often...... consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss an alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding...... represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects...
International conference Fourier Analysis and Pseudo-Differential Operators
Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
2014-01-01
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Fixed-point error analysis of Winograd Fourier transform algorithms
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Special affine Fourier transformation in frequency-domain
Cai, L. Z.
2000-11-01
Special affine Fourier transformation (SAFT) can be considered as an extension of the fractional Fourier transformation (FRT) and the most general linear mapping in phase space. A general formula for SAFT in frequency-domain is derived, which gives a direct relationship between the input and output spatial frequency spectra of a light field. It shows that the SAFT has similar and symmetric feature in both space- and frequency-domains. As its special cases, Collins formula in frequency-domain, the spatial frequency representations of the almost-FRT, almost-Fresnel and almost-Fourier transformations are explicitly obtained. These formulae may provide a tool for investigating the performance of a lossless optical system including small deformations in both domains in a unified way within the framework of linear theory.
Shape Recognition in Presence of Occlusion from Fourier Plane Processing
Pohit, Mausumi; Goel, Alpana
2011-10-01
A new technique for recognition of objects in presence of occlusion is presented in this paper. The Fourier spectrum of a partially occluded shape differs from that of the whole object shape thereby decreasing the 2D correlation between two images. The present method is based on 1D correlation of Fourier Spectrum slices taken from the 2D Fourier Transform of the reference and the test object. For small occlusion, some of the slices are affected depending on the nature of occlusion. Responses of the rest of the slices are unaffected. This study shows that this method not only identify the object in presence of occlusion but at the same time has good discrimination capability.
Fourier domain asymmetric cryptosystem for privacy protected multimodal biometric security
Choudhury, Debesh
2016-04-01
We propose a Fourier domain asymmetric cryptosystem for multimodal biometric security. One modality of biometrics (such as face) is used as the plaintext, which is encrypted by another modality of biometrics (such as fingerprint). A private key is synthesized from the encrypted biometric signature by complex spatial Fourier processing. The encrypted biometric signature is further encrypted by other biometric modalities, and the corresponding private keys are synthesized. The resulting biometric signature is privacy protected since the encryption keys are provided by the human, and hence those are private keys. Moreover, the decryption keys are synthesized using those private encryption keys. The encrypted signatures are decrypted using the synthesized private keys and inverse complex spatial Fourier processing. Computer simulations demonstrate the feasibility of the technique proposed.
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.
Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda
2017-09-13
This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ......The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...
A Fourier Optical Model for the Laser Doppler Velocimeter
DEFF Research Database (Denmark)
Lading, Lars
1972-01-01
The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....
Fourier analysis of the aerodynamic behavior of cup anemometers
International Nuclear Information System (INIS)
Pindado, Santiago; Pérez, Imanol; Aguado, Maite
2013-01-01
The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)
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
Quantitative aspects of near-infrared Fourier transform Raman spectroscopy
Walder, F. T.; Smith, M. J.
Three fundamental behaviors of vibrational spectroscopy data manipulation routinely associated with Fourier transform infrared (FTIR) spectroscopy are evaluated for near-infrared (NIR) Fourier transform Raman spectroscopy. Spectral reproducibility, spectral subtraction and sensitivity are examined relative to the NIR FT-Raman experiment. Quantitative predictive ability is compared for identical sets of samples containing mixtures of the three xylene isomers. Partial least-squares analysis is used to compare predictive ability. IR performance is found to be better than Raman, though the potential for method development using NIR FT-Raman is shown to be quite promising.
On L1-convergence of Walsh-Fourier series
Directory of Open Access Journals (Sweden)
C. W. Onneweer
1978-01-01
Full Text Available Let G denote the dyadic group, which has as its dual group the Walsh(-Paley functions. In this paper we formulate a condition for functions in L1(G which implies that their Walsh-Fourier series converges in L1(G-norm. As a corollary we obtain a Dini-Lipschitz-type theorem for L1(G convergence and we prove that the assumption on the L1(G modulus of continuity in this theorem cannot be weakened. Similar results also hold for functions on the circle group T and their (trigonometric Fourier series.
Application of Fourier analysis to multispectral/spatial recognition
Hornung, R. J.; Smith, J. A.
1973-01-01
One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
An introduction to Lebesgue integration and Fourier series
Wilcox, Howard J
1995-01-01
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects.The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate
Neural network signature verification using Haar wavelet and Fourier transforms
McCormack, Daniel K. R.; Brown, B. M.; Pedersen, John F.
1993-08-01
This paper discusses the use of neural network's for handwritten signature verification using the Fourier and Haar wavelet transforms as methods of encoding signature images. Results will be presented that discuss a neural network's ability to generalize to unseen signatures using wavelet encoded training data. These results will be discussed with reference to both Backpropagation networks and Cascade-Correlation networks. Backpropagation and Cascade- Correlation networks are used to compare and contrast the generalization ability of Haar wavelet and Fourier transform encoded signature data.
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
Energy Technology Data Exchange (ETDEWEB)
Rodriguez Z, G.; Rodriguez V, R.; Luna C, A. [Centro de Investigaciones en Optica, Apartado Postal 948, 37000 Leon, Guanajuato (Mexico)
1999-05-01
The introduction of tomography as an advanced topic to be included in a Fourier optics course at graduated level is proposed. It is shown a possible presentation sequence which features the use of typical Fourier optics techniques, as well as some well known opto-mechanical devices as examples. Finally, a simplified apparatus which illustrates the central Fourier theorem as an experimental project on Fourier optics is described. Corresponding experimental results are also shown. (Author)
Fourier analysis and signal processing by use of the Moebius inversion formula
Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.
1990-01-01
A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.
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
Fourier coefficientes computation in two variables, a distributional version
Directory of Open Access Journals (Sweden)
Carlos Manuel Ulate R.
2015-01-01
Full Text Available The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.
Multipliers for the absolute Euler summability of Fourier series
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
(Math. Sci.), Vol. 111, No. 2, May 2001, pp. 203–219. Printed in India. Multipliers for the absolute Euler summability of Fourier series. PREM CHANDRA. School of Studies in Mathematics, Vikram University, Ujjain 456 010, India. MS received 30 December 1999; revised 30 October 2000. Abstract. In this paper, the author ...
Non-spectral fractal measures with Fourier frames
Lai, Chun-Kit; Wang, Yang
2015-01-01
We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal exponentials (and hence it does not admit any exponential orthonormal bases), but it still admits Fourier frames.
Fourier transform infrared spectroscopic estimation of crystallinity in ...
Indian Academy of Sciences (India)
Wintec
quartz in rock samples and estimate the mining quality of quartz mineral, which is substantiated by calculating the crystallinity index. ... procedure which can be used to estimate the distribution of quartz in various rocks for mining purpose. ... coal was reported by several workers (Heaney et al. 1994). Fourier transform ...
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Unknown
[Sengupta P D, Sengupta D and Ghosh P 2005 Bilaterally symmetric Fourier approximations of the skull outlines of temnospondyl amphibians and their ... The outlines of the vertebrate skulls are variable and they help in recognizing the ..... Carrol R L 1988 Vertebrate paleontology and evolution (New York: Freeman) pp 698.
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ...
Coupling of column liquid chromatography and Fourier transform infrared spectrometry
Somsen, G.W; Gooijer, C; Velthorst, N.H; Brinkman, U.A Th
1998-01-01
This paper provides an extensive overview of the literature on the coupling of column liquid chromatography (LC) and Fourier transform infrared spectrometry (FT-IR). Flow-cell-based FT-IR detection and early solvent-elimination interfaces for LC-FT-IR are discussed in brief. A comprehensive
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
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 ...
Application of Migration Velocity Using Fourier Transform Approach ...
African Journals Online (AJOL)
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 ...
Fourier-transform infrared spectroscopic studies of dithia ...
Indian Academy of Sciences (India)
Unknown
limited region 1000–1150 cm–1.10 Therefore, in the present paper we report and analyse Fourier-trans- form infrared (FT-IR) spectra of S2TPP and its chemically prepared cation. 2. Experimental. Dithia tetraphenyl porphyrine was received from. Professor A L Verma as a gift and used without fur- ther purification. However ...
Grating-assisted superresolution of slow waves in Fourier space
DEFF Research Database (Denmark)
Thomas, N. Le; Houdré, R.; Frandsen, Lars Hagedorn
2007-01-01
with a high numerical aperture Fourier space imaging set-up. A high-resolution spectroscopy of the far-field emission diagram allows us to accurately and efficiently determine the dispersion curve and the group-index dispersion of planar photonic waveguides operating in the slow light regime....
Properties of the Simpson discrete fourier transform | Singh ...
African Journals Online (AJOL)
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 ...
Fourier transform infrared spectroscopic estimation of crystallinity in ...
Indian Academy of Sciences (India)
Wintec
Fourier transform infrared spectroscopic estimation of crystallinity in SiO2 based rocks. BHASKAR J SAIKIA. †. , G PARTHASARATHY* and N C SARMAH. †. National Geophysical Research Institute, Council of Scientific and Industrial Research, Hyderabad 500 007, India. †. Department of Physics, Dibrugarh University, ...
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
Fourier transformation methods in the field of gamma spectrometry
Indian Academy of Sciences (India)
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.
Fourier transform infrared microspectroscopy as a diagnostic tool for ...
Indian Academy of Sciences (India)
Fourier transform infrared (FTIR) microspectroscopy can be considered to be a fast and non-invasive tool for distinguishing between normal and cancerous cells and tissues without the need for laborious and invasive sampling procedures. Gastric samples from four patients (age, 65±2 years) were analysed. Samples were ...
A new analytical solution to the diffusion problem: Fourier series ...
African Journals Online (AJOL)
This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.
Nonlinear Fourier transform for dual-polarization optical communication system
DEFF Research Database (Denmark)
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...
Synthetic aperture ultrasound Fourier beamformation using virtual sources
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2016-01-01
An efficient Fourier beamformation algorithm is presented for multistatic synthetic aperture ultrasound imaging using virtual sources (FBV). The concept is based on the frequency domain wavenumber algorithm from radar and sonar and is extended to a multi-element transmit/receive configuration using...
Overcoming Spurious Regression Using time-Varying Fourier ...
African Journals Online (AJOL)
Non-stationary time series data have been traditionally analyzed in the frequency domain by assuming constant amplitudes regardless of the timelag. A new approach called time-varying amplitude method (TVAM) is presented here. Oscillations are analyzed for changes in the magnitude of Fourier Coefficients which are ...
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
ing only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl. 11(4) (2008) 749–756] which is a generalization of Tikhonov's results [Anal. Math. 31 (2005) 183–194]. We also ...
Novel properties of the Fourier decomposition of the sinogram
International Nuclear Information System (INIS)
Edholm, P.R.; Lewitt, R.M.; Lindholm, B.
1986-01-01
The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency ω (continuous) and angular harmonic number n (discrete). For absolute value of ω large, the Fourier coefficients on the line n=kω of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed
Free Sixteen Harmonic Fourier Series Web App with Sound
Ruiz, Michael J.
2018-01-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The…
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms(FT). This very general technique gives us a lot of insight intosolving first order differential equations with source terms dependingon time. In itself, the RC circuit is by far the mostcommonplace entity in modern ...
Fourier beamformation of multistatic synthetic aperture ultrasound imaging
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2015-01-01
A new Fourier beamformation (FB) algorithm is presented for multistatic synthetic aperture ultrasound imaging. It can reduce the number of computations by a factor of 20 compared to conventional Delay-and-Sum (DAS) beamformers. The concept is based on the wavenumber algorithm from radar and sonar...
Fourier transform infrared spectrophotometry and X-ray powder ...
African Journals Online (AJOL)
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 ...
The linogram algorithm and direct fourier method with linograms
International Nuclear Information System (INIS)
Edholm, P.R.
1990-01-01
This text is an attempt to describe the linogram algorithm based on a somewhat simplified mathematical description of the algorithm which is also more similar to the actual digital implementation. Another algorithm with linograms, which may be called a direct fourier method is also presented. (K.A.E.)
Education and Utopia: Robert Owen and Charles Fourier
Leopold, David
2011-01-01
The aims of education, and the appropriate means of realising them, are a recurring preoccupation of utopian authors. The utopian socialists Robert Owen (1771-1858) and Charles Fourier (1772-1837) both place human nature at the core of their educational views, and both see education as central to their wider objective of social and political…
Fourier transform infrared (FTIR) spectroscopy for identification of ...
African Journals Online (AJOL)
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 ...
Multipliers for the Absolute Euler Summability of Fourier Series
Indian Academy of Sciences (India)
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
L1-convergence of complex double Fourier series
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
L1-convergence of complex double Fourier series. KULWINDER KAUR, S S BHATIA and BABU RAM. ∗. School of Mathematics and Computer Applications, Thapar Institute of Engineering and Technology, Post Box No. 32, Patiala 147 004, India. ∗. Department of Mathematics, Maharshi Dayanand University, Rohtak, India.
Fourier-transform Infrared Characterization of Kaolin, Granite ...
African Journals Online (AJOL)
Fourier-transform Infrared Characterization of Kaolin, Granite, Bentonite and Barite. ... Diazonium salts at the peak region frequency of 3200-3100cm-1, organic substance at peak region of 2900-2700cm-1, by comparing the spectra obtained with those ... Keywords: characterization; clays; infrared; minerals; spectroscopy ...
Optimal Fourier Inversion in Semi-analytical Option Pricing
R. Lord (Roger); Ch. Kahl
2006-01-01
textabstractAt the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
Holograms; security holograms; optical security; extended fractional Fourier transforms. PACS Nos 42.40.-i; 42.40. ... cost-effective scheme for the development of security hologram, we noticed that two reference beams holography [10] can ..... couragement, support and for permission to publish this work. They wish to thank.
Transformation of a Free-Wilson matrix into Fourier coefficients
Czech Academy of Sciences Publication Activity Database
Holík, M.; Halámek, Josef
2002-01-01
Roč. 20, - (2002), s. 422 - 428 ISSN 0931-8771 Institutional research plan: CEZ:AV0Z2065902 Keywords : Free-Wilson matrix * Fourier transform * multivariate regression Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.558, year: 2002
Construction of a pulsed nozzle fourier transform microwave ...
Indian Academy of Sciences (India)
Administrator
Construction of a pulsed nozzle fourier transform microwave spectrometer to study the lithium bond. A P TIWARI 1, B J MUKKADA 1, E ARUNAN 1 and P C MATHIAS 2. 1Department of Inorganic and Physical Chemistry, Indian Institute of. Science, Bangalore 560 012, India. 2Sophisticated Instruments Facility, Indian Institute ...
Discrete frequency identification using the HP 5451B Fourier analyser
International Nuclear Information System (INIS)
Holland, L.; Barry, P.
1977-01-01
The frequency analysis by the HP5451B discrete frequency Fourier analyser is studied. The advantages of cross correlation analysis to identify discrete frequencies in a background noise are discussed in conjuction with the elimination of aliasing and wraparound error. Discrete frequency identification is illustrated by a series of graphs giving the results of analysing 'electrical' and 'acoustical' white noise and sinusoidal signals [pt
Quantifying complex shapes: elliptical fourier analysis of octocoral sclerites.
Carlo, Joseph M; Barbeitos, Marcos S; Lasker, Howard R
2011-06-01
Species descriptions of most alcyonacean octocorals rely heavily on the morphology of sclerites, the calcium carbonate spicules embedded in the soft tissue. Sclerites provide taxonomic characters for species delineation but require qualitative descriptions, which introduce ambiguities in recognizing morphological features. Elliptical Fourier analysis of the outline of sclerites was used to quantify the morphology of eight species of gorgoniid octocoral in the genus Pseudopterogorgia. Sclerites from one to seven colonies of each species were compared. Scaphoids and spindles were examined separately; rods and octoradiates were excluded from the analyses because of their morphologic similarity across all species. Discriminant analysis of elliptical Fourier descriptors (EFDs) was used to determine whether the elliptical Fourier analysis could be used to identify the specimens. Sclerites were highly variable even within a single colony. Correct species assignments of individual sclerites were greater than 50% for both scaphoids and spindles. Species assignments based on averages of the EFDs for each colony approached 90%. Elliptical Fourier analysis quantifies morphological differences between species and measures colony variance in sclerite size and shape among colonies and species. Phylogenetic analysis based on EFDs did not capture monophyletic groups. The quantification of complex shapes such as sclerites provides an important tool in alpha taxonomy but may be less useful in phylogenetic analyses.
HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS
Directory of Open Access Journals (Sweden)
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.
An introduction to non-harmonic Fourier series
Young, Robert M
2001-01-01
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
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.
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Unknown
2000; Steyer 2003) to study shape changes through onto- geny. However, in all the cases only the complete or nearly- ..... (iii) Energy-phase summary of Fourier coefficients. After analysing several samples we find the following .... luga-land in northern Russia; Ann. Soc. Pal. Russie 8 49–76. Romer A S 1947 Review of the ...
Fourier ptychographic microscopy at telecommunication wavelengths using a femtosecond laser
Ahmed, Ishtiaque; Alotaibi, Maged; Skinner-Ramos, Sueli; Dominguez, Daniel; Bernussi, Ayrton A.; de Peralta, Luis Grave
2017-12-01
We report the implementation of the Fourier Ptychographic Microscopy (FPM) technique, a phase retrieval technique, at telecommunication wavelengths using a low-coherence ultrafast pulsed laser source. High quality images, near speckle-free, were obtained with the proposed approach. We demonstrate that FPM can also be used to image periodic features through a silicon wafer.
A functional program for the Fast Fourier Transform
Vries, F.-J. de
This paper is written as a contribution to the Parallel Reduction Machine Project. Its purpose is to present a functional program for a well-known application of the fundamental algorithmic method Fast Fourier Transform for multiplication of polynomials. This in order to verify experimentally two
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
Abstract. This paper describes a simple method for making dual beam encoded ex- tended 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 ...
Accelerated radial Fourier-velocity encoding using compressed sensing
International Nuclear Information System (INIS)
Hilbert, Fabian; Han, Dietbert
2014-01-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Accelerated radial Fourier-velocity encoding using compressed sensing.
Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert
2014-09-01
Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus
Accelerated radial Fourier-velocity encoding using compressed sensing
Energy Technology Data Exchange (ETDEWEB)
Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)
2014-10-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Dudka, A. P.; Antipin, A. M.; Verin, I. A.
2017-09-01
Huber-5042 diffractometer with a closed-cycle Displex DE-202 helium cryostat is a unique scientific instrument for carrying out X-ray diffraction experiments when studying the single crystal structure in the temperature range of 20-300 K. To make the service life longer and develop new experimental techniques, the diffractometer control is transferred to a new hardware and software platform. To this end, a modern computer; a new detector reader unit; and new control interfaces for stepper motors, temperature controller, and cryostat vacuum pumping system are used. The system for cooling the X-ray tube, the high-voltage generator, and the helium compressor and pump for maintaining the desired vacuum in the cryostat are replaced. The system for controlling the primary beam shutter is upgraded. A biological shielding is installed. The new program tools, which use the Linux Ubuntu operating system and SPEC constructor, include a set of drivers for control units through the aforementioned interfaces. A program for searching reflections from a sample using fast continuous scanning and a priori information about crystal is written. Thus, the software package for carrying out the complete cycle of precise diffraction experiment (from determining the crystal unit cell to calculating the integral reflection intensities) is upgraded. High quality of the experimental data obtained on this equipment is confirmed in a number of studies in the temperature range from 20 to 300 K.
On the finite Fourier transforms of functions with infinite discontinuities
Directory of Open Access Journals (Sweden)
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.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
Directory of Open Access Journals (Sweden)
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.
Meso-optical Fourier transform microscope with double focusing
International Nuclear Information System (INIS)
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
Fourier-based magnetic induction tomography for mapping resistivity
International Nuclear Information System (INIS)
Puwal, Steffan; Roth, Bradley J.
2011-01-01
Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.
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.
Limitations on continuous variable quantum algorithms with Fourier transforms
International Nuclear Information System (INIS)
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.
Time-of-flight Fourier Spectrometry with UCN
Kulin, G. V.; Frank, A. I.; Goryunov, S. V.; Geltenbort, P.; Jentschel, M.; Bushuev, V. A.; Lauss, B.; Schmidt-Wellenburg, Ph.; Panzarella, A.; Fuchs, Y.
2016-09-01
The report presents the first experience of using a time-of-flight Fourier spectrometer of ultracold neutrons (UCN). The description of the spectrometer design and first results of its testing are presented. The results of the first experiments show that the spectrometer may be used for obtaining UCN energy spectra in the energy range of 60÷200 neV with a resolution of about 5 neV. The application of TOF Fourier spectrometry technique allowed us to obtain the energy spectra from the diffraction of monochromatic ultracold neutrons on a moving grating. Lines of 0, +1 and +2 diffraction orders were simultaneously recorded, which had previously been impossible to be done by other methods. These results have made it possible to make a comparison with the recent theoretical calculations based on the dynamical theory of neutron diffraction on a moving phase grating.
Jones matrix treatment for optical Fourier processors with structured polarization.
Moreno, Ignacio; Iemmi, Claudio; Campos, Juan; Yzuel, Maria J
2011-02-28
We present a Jones matrix method useful to analyze coherent optical Fourier processors employing structured polarization. The proposed method is a generalization of the standard classical optical Fourier transform processor, but considering vectorial spatial functions with two complex components corresponding to two orthogonal linear polarizations. As a result we derive a Jones matrix that describes the polarization output in terms of two vectorial functions defining respectively the structured polarization input and the generalized polarization impulse response. We apply the method to show and analyze an experiment in which a regular scalar diffraction grating is converted into equivalent polarization diffraction gratings by means of an appropriate polarization filtering. The technique is further demonstrated to generate arbitrary structured polarizations. Excellent experimental results are presented.
An introduction to Laplace transforms and Fourier series
Dyke, Phil
2014-01-01
Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...
Absolute Measurement of Tilts via Fourier Analysis of Interferograms
Toland, Ronald W.
2004-01-01
The Fourier method of interferogram analysis requires the introduction of a constant tilt into the interferogram to serve as a carrier signal for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.
A time Fourier analysis of zonal averaged ozone heating rates
Wang, P.-H.; Wu, M.-F.; Deepak, A.; Hong, S.-S.
1981-01-01
A time-Fourier analysis is presented for the yearly variation of the zonal averaged ozone heating rates in the middle atmosphere based on a model study. The ozone heating rates are determined by utilizing two-dimensional ozone distributions, the altitude and latitude, and by including the effect of the curved earth's atmosphere. In addition, assumptions are introduced to the yearly variations of the ozone distributions due to the lack of sufficient existing ozone data. Among other results, it is shown that the first harmonic component indicates that the heating rates are completely out of phase between the northern and southern hemispheres. The second Fourier component shows a symmetric pattern with respect to the equator, as well as five distinct local extreme values of the ozone heating rate. The third harmonic component shows a pattern close to that of the first component except in the regions above 70 deg between 45-95 km in both hemispheres.
Spectrometer calibration for spectroscopic Fourier domain optical coherence tomography
Szkulmowski, Maciej; Tamborski, Szymon; Wojtkowski, Maciej
2016-01-01
We propose a simple and robust procedure for Fourier domain optical coherence tomography (FdOCT) that allows to linearize the detected FdOCT spectra to wavenumber domain and, at the same time, to determine the wavelength of light for each point of detected spectrum. We show that in this approach it is possible to use any measurable physical quantity that has linear dependency on wavenumber and can be extracted from spectral fringes. The actual values of the measured quantity have no importance for the algorithm and do not need to be known at any stage of the procedure. As example we calibrate a spectral OCT spectrometer using Doppler frequency. The technique of spectral calibration can be in principle adapted to of all kind of Fourier domain OCT devices. PMID:28018723
On frame properties for Fourier-like systems
DEFF Research Database (Denmark)
Christensen, Ole; Osgooei, Elnaz
2013-01-01
structure. An attractive class of frames is formed by letting the window functions be trigonometric polynomials, restricted to compact intervals. We prove, under weak conditions, that such systems generate a frame with a dual that is also generated by a trigonometric polynomial. For polynomial windows......, a result of this type does not hold. Throughout the paper the results are related to the well established theory for Gabor systems.......Fourier-like systems are formed by multiplying a class of exponentials with a set of window functions. Via the Fourier transform they are equivalent to shift-invariant systems. We present sufficient and easily verifiable conditions for such systems to form a frame with a dual frame having the same...
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
Fourier-positivity constraints on QCD dipole models
Directory of Open Access Journals (Sweden)
Bertrand G. Giraud
2016-09-01
Full Text Available Fourier-positivity (F-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position space r. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical F-positivity constraints on the limit r→0 behavior of the dipole amplitudes, we identify the common origin of the violation of F-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior r2+ϵ, ϵ>0 softer, even slightly, than color transparency. F-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant α(r.
Fractional fourier-based filter for denoising elastograms.
Subramaniam, Suba R; Hon, Tsz K; Georgakis, Apostolos; Papadakis, George
2010-01-01
In ultrasound elastography, tissue axial strains are obtained through the differentiation of axial displacements. However, the application of the gradient operator amplifies the noise present in the displacement rendering unreadable axial strains. In this paper a novel denoising scheme based on repeated filtering in consecutive fractional Fourier transform domains is proposed for the accurate estimation of axial strains. The presented method generates a time-varying cutoff threshold that can accommodate the discrete non-stationarities present in the displacement signal. This is achieved by means of a filter circuit which is composed of a small number of ordinary linear low-pass filters and appropriate fractional Fourier transforms. We show that the proposed method can improve the contrast-to-noise ratio (CNR(e)) of the elastogram outperforming conventional low-pass filters.
Group-based sparse representation for Fourier ptychography microscopy
Zhang, Yongbing; Cui, Ze; Zhang, Jian; Song, Pengming; Dai, Qionghai
2017-12-01
Fourier ptychography microscopy (FPM), which employs alternative projection between spatial and Fourier domains to stitch low-resolution images captured under angularly varying illumination, reconstructs one image with high-resolution and wide field of view (FOV) to bypass the limitation of the space-bandwidth product (SBP) of the traditional optical system. However, system noises such as pupil aberrations, LEDs misalignment and so on, are inevitably introduced in the process of capturing low-resolution images. To address this problem, we propose a new method to insert the Group-based sparse representation (GSR) into the convergence-related metric of FPM as the regularization term in this paper. We have carried out the experiments over both synthetic and real captured images, and the results demonstrate that the proposed method is able to have promising performance while inhibiting the noises efficiently.
High resolution integral holography using Fourier ptychographic approach.
Li, Zhaohui; Zhang, Jianqi; Wang, Xiaorui; Liu, Delian
2014-12-29
An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.
Free sixteen harmonic Fourier series web app with sound
Ruiz, Michael J.
2018-03-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The program is free for non-commercial use and can also be downloaded for running offline.
Visible Imaging Fourier Transform Spectrometer: Design and Calibration
International Nuclear Information System (INIS)
Wishnow, E.H.; Wurtz, R.; Blais-Ouellette, S.; Cook, K.H.; Carr, D.; Lewis, I.; Grandmont, F.; Stubbs, C.W.
2002-01-01
We present details of the design, operation and calibration of an astronomical visible-band imaging Fourier transform spectrometer (IFTS). This type of instrument produces a spectrum for every pixel in the field of view where the spectral resolution is flexible. The instrument is a dual-input/dual-output Michelson interferometer coupled to the 3.5 meter telescope at the Apache Point Observatory. Imaging performance and interferograms and spectra from calibration sources and standard stars are discussed
On One Application of Fourier Analysis in Plastic Surgery
Rakhimov, Abdumalik; Zainuddin, Hishamuddin
In present paper, we discuss the spectral methods of measurement of the degree of speech and/or quality of sound by comparing the coefficient of performance indicators depending on energy distributions, ratio of energy of the fundamental tone and energy of overtones. Such a method is very efficient for string oscillation with different initial conditions and it is useful for justification of applications of Fourier analysis in plastic surgery in treatment of some medical diseases.
Vanishing dissipation limit for the Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2016-01-01
Roč. 14, č. 6 (2016), s. 1535-1551 ISSN 1539-6746 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : inviscid limit * compressible fluid * Navier–Stokes–Fourier system Subject RIV: BA - General Mathematics Impact factor: 1.425, year: 2016 http://intlpress.com/site/pub/pages/journals/items/cms/content/vols/0014/0006/a004/index.html
Dimension reduction for the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Březina, J.; Kreml, Ondřej; Mácha, Václav
2017-01-01
Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link.springer.com/article/10.1007%2Fs00021-016-0301-6
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.
Dimension reduction for the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Březina, J.; Kreml, Ondřej; Mácha, Václav
2017-01-01
Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link. springer .com/article/10.1007%2Fs00021-016-0301-6
Fourier analysis of multi-tracer cosmological surveys
Abramo, L. Raul; Secco, Lucas F.; Loureiro, Arthur
2015-01-01
We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feld...
FTIS compact Fourier transform imaging spectrometer for remote sensing
Posselt, W.; Holota, K.; Tittel, H. O.; Rost, M.; Harnisch, B.
2017-11-01
The feasibility of a compact Fourier-Transform-Imaging-Spectrometer (FTIS) for small satellite remote sensing missions is currently being studied under ESA contract. Compared to classical hyperspectral imagers using dispersive spectrometers the major advantages of the FTIS is the compact optics module and the tolerable higher detector temperature, thus easing the instrument thermal design. The feasibility of this instrument concept will be demonstrated by breadboarding.
Approximation by weighted means of Walsh-Fourier series
Directory of Open Access Journals (Sweden)
F. Móricz
1996-01-01
Full Text Available We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1. We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.
Lacunary Fourier series and a qualitative uncertainty principle for ...
Indian Academy of Sciences (India)
Since Ff vanishes on an open set, by Lemma 2.1, Ff vanishes identically. It follows that Trace(π( f )) is zero for π ∈ ˆG. Next, notice that any translate of f has lacunary Fourier series. If g varies in a small enough neighborhood of the identity in G, then applying the above argument to the trans- lated function g f (x) = f (gx) we ...
Fast Fourier transform analysis of rotor-bearing systems
Choy, K. C.; Gunter, E. J.; Allaire, P. E.
1978-01-01
Nonlinear transient analysis of rotor-bearing systems is becoming increasingly important in the analysis of modern-day rotating machinery to model such phenomena as oil film whirl. This paper develops an analysis technique incorporating modal analysis and fast Fourier transform techniques to analyze rotors with residual shaft bow and realistic nonlinear bearings. The technique is demonstrated on single-mass and three-mass rotor examples. Comparisons of the theoretical results with experimental data give excellent agreement.
Fourier expansions and multivariable Bessel functions concerning radiation programmes
International Nuclear Information System (INIS)
Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.
1996-01-01
The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)
Fourier transform profilometry by using digital dc subtraction
Wongjarern, J.; Widjaja, J.; Sangpech, W.; Thongdee, N.; Santisoonthornwat, P.; Traisak, O.; Chuamchaitrakool, P.; Meemon, P.
2014-06-01
A new method for eliminating unwanted background of Fourier transform profilometry (FTP) by using simple dc bias and background eliminations from the deformed grating images is proposed. The proposed method has an advantage over a conventional FTP in that the 3-D object profile can be accurately measured although original fundamental spectra are corrupted by a zeroth-order spectrum. Experimental verifications of the proposed method are presented.
Vanishing dissipation limit for the Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2016-01-01
Roč. 14, č. 6 (2016), s. 1535-1551 ISSN 1539-6746 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : inviscid limit * compressible fluid * Navier–Stokes–Fourier system Subject RIV: BA - General Mathematics Impact factor: 1.425, year: 2016 http://intlpress.com/site/pub/pages/ journals /items/cms/content/vols/0014/0006/a004/index.html
Fourier-Malliavin volatility estimation theory and practice
Mancino, Maria Elvira; Sanfelici, Simona
2017-01-01
This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study. .
A Fourier space algorithm for solving quadratic assignment problems
Kondor, Risi
2010-01-01
The quadratic assignment problem (QAP) is a central problem in combinatorial optimization. Several famous computationally hard tasks, such as graph matching, partitioning, and the traveling salesman all reduce to special cases of the QAP. In this paper we propose a new approach to the QAP based on the theory of non–commutative Fourier analysis on the symmetric group. Specifically, we present a branch–and–bound algorithm that performs both the branching and the bound...
Solving singular convolution equations using the inverse fast Fourier transform
Czech Academy of Sciences Publication Activity Database
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/
Evaluation of gastric motility by Fourier analysis of condensed images
International Nuclear Information System (INIS)
Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K.
2000-01-01
In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)
Fourier acceleration in lattice gauge theories. I. Landau gauge fixing
International Nuclear Information System (INIS)
Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.
1988-01-01
Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations
Periodic transonic flow simulation using fourier-based algorithm
International Nuclear Information System (INIS)
Mohaghegh, Mohammad Reza; Malekjafarian, Majid
2014-01-01
The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.
Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.
Caple, Jodi; Byrd, John; Stephan, Carl N
2017-11-01
The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.
Diamond-Based Magnetic Imaging with Fourier Optical Processing
Backlund, Mikael P.; Kehayias, Pauli; Walsworth, Ronald L.
2017-11-01
Diamond-based magnetic field sensors have attracted great interest in recent years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond has been previously demonstrated in condensed matter, biological, and paleomagnetic applications. Vector magnetic imaging with NV ensembles typically requires a significant applied field (>10 G ) to resolve the contributions from four crystallographic orientations, hindering studies of magnetic samples that require measurement in low or independently specified bias fields. Here we model and measure the complex amplitude distribution of NV emission at the microscope's Fourier plane and show that by modulating this collected light at the Fourier plane, one can decompose the NV ensemble magnetic resonance spectrum into its constituent orientations by purely optical means. This decomposition effectively extends the dynamic range at a given bias field and enables wide-field vector magnetic imaging at arbitrarily low bias fields, thus broadening potential applications of NV imaging and sensing. Our results demonstrate that NV-based microscopy stands to benefit greatly from Fourier optical approaches, which have already found widespread utility in other branches of microscopy.
Evaluation of gastric motility by Fourier analysis of condensed images
Energy Technology Data Exchange (ETDEWEB)
Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K. [Dept. of Nuclear Medicine, Univ. of Munich, Munich (Germany)
2000-10-01
In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)
Chebyshev-Fourier Spectral Methods for Nonperiodic Boundary Value Problems
Directory of Open Access Journals (Sweden)
Bojan Orel
2014-01-01
Full Text Available A new class of spectral methods for solving two-point boundary value problems for linear ordinary differential equations is presented in the paper. Although these methods are based on trigonometric functions, they can be used for solving periodic as well as nonperiodic problems. Instead of using basis functions periodic on a given interval −1,1, we use functions periodic on a wider interval. The numerical solution of the given problem is sought in terms of the half-range Chebyshev-Fourier (HCF series, a reorganization of the classical Fourier series using half-range Chebyshev polynomials of the first and second kind which were first introduced by Huybrechs (2010 and further analyzed by Orel and Perne (2012. The numerical solution is constructed as a HCF series via differentiation and multiplication matrices. Moreover, the construction of the method, error analysis, convergence results, and some numerical examples are presented in the paper. The decay of the maximal absolute error according to the truncation number N for the new class of Chebyshev-Fourier-collocation (CFC methods is compared to the decay of the error for the standard class of Chebyshev-collocation (CC methods.
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Error Analysis for Fourier Methods for Option Pricing
Häppölä, Juho
2016-01-06
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.
International Nuclear Information System (INIS)
Long, L.L.
1976-01-01
Fourier series and statistical communication theory techniques are utilized in the estimation of river water temperature increases caused by external thermal inputs. An example estimate assuming a constant thermal input is demonstrated. A regression fit of the Fourier series approximation of temperature is then used to forecast daily average water temperatures. Also, a 60-day prediction of daily average water temperature is made with the aid of the Fourier regression fit by using significant Fourier components
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
"Cracking Open the Natural Teleology": Walter Benjamin, Charles Fourier and the Figure of the Child
Dolbear, Sam; Proctor, Hannah
2016-01-01
The French utopian socialist Charles Fourier is a key figure in Walter Benjamin's "Arcades Project". For Benjamin, one of the most significant aspects of Fourier's utopian vision was its conceptualisation of work as a form of play. According to Fourier it would be possible to build a world around people's inherent desires. In such a…
On the Cooley-Turkey Fast Fourier algorithm for arbitrary factors ...
African Journals Online (AJOL)
Atonuje and Okonta in [1] developed the Cooley-Turkey Fast Fourier transform algorithm and its application to the Fourier transform of discretely sampled data points N, expressed in terms of a power y of 2. In this paper, we extend the formalism of [1] Cookey-Turkey Fast Fourier transform algorithm. The method is developed ...
Introduction to partial differential equations from Fourier series to boundary-value problems
Broman, Arne
2010-01-01
This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.
Insights into Fourier Synthesis and Analysis: Part I--Using Simple Programs and Equipment.
Moore, Guy S. M.
1988-01-01
Introduced is a unique generation method of Fourier series requiring simple mathematical skills and using computer programs. Discusses Fourier synthesis by microcomputer, and Fourier analysis with simple equipment. Shown are a circuit diagram, computer programs, monitor displays and tables of data. (YP)
Mei, Liang; Svanberg, Sune
2015-03-20
This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.
Quantitative lung perfusion evaluation using Fourier decomposition perfusion MRI.
Kjørstad, Åsmund; Corteville, Dominique M R; Fischer, Andre; Henzler, Thomas; Schmid-Bindert, Gerald; Zöllner, Frank G; Schad, Lothar R
2014-08-01
To quantitatively evaluate lung perfusion using Fourier decomposition perfusion MRI. The Fourier decomposition (FD) method is a noninvasive method for assessing ventilation- and perfusion-related information in the lungs, where the perfusion maps in particular have shown promise for clinical use. However, the perfusion maps are nonquantitative and dimensionless, making follow-ups and direct comparisons between patients difficult. We present an approach to obtain physically meaningful and quantifiable perfusion maps using the FD method. The standard FD perfusion images are quantified by comparing the partially blood-filled pixels in the lung parenchyma with the fully blood-filled pixels in the aorta. The percentage of blood in a pixel is then combined with the temporal information, yielding quantitative blood flow values. The values of 10 healthy volunteers are compared with SEEPAGE measurements which have shown high consistency with dynamic contrast enhanced-MRI. All pulmonary blood flow (PBF) values are within the expected range. The two methods are in good agreement (mean difference = 0.2 mL/min/100 mL, mean absolute difference = 11 mL/min/100 mL, mean PBF-FD = 150 mL/min/100 mL, mean PBF-SEEPAGE = 151 mL/min/100 mL). The Bland-Altman plot shows a good spread of values, indicating no systematic bias between the methods. Quantitative lung perfusion can be obtained using the Fourier Decomposition method combined with a small amount of postprocessing. Copyright © 2013 Wiley Periodicals, Inc.
Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity.
Jubery, Talukder Z; Shook, Johnathon; Parmley, Kyle; Zhang, Jiaoping; Naik, Hsiang S; Higgins, Race; Sarkar, Soumik; Singh, Arti; Singh, Asheesh K; Ganapathysubramanian, Baskar
2016-01-01
Soybean canopy outline is an important trait used to understand light interception ability, canopy closure rates, row spacing response, which in turn affects crop growth and yield, and directly impacts weed species germination and emergence. In this manuscript, we utilize a methodology that constructs geometric measures of the soybean canopy outline from digital images of canopies, allowing visualization of the genetic diversity as well as a rigorous quantification of shape parameters. Our choice of data analysis approach is partially dictated by the need to efficiently store and analyze large datasets, especially in the context of planned high-throughput phenotyping experiments to capture time evolution of canopy outline which will produce very large datasets. Using the Elliptical Fourier Transformation (EFT) and Fourier Descriptors (EFD), canopy outlines of 446 soybean plant introduction (PI) lines from 25 different countries exhibiting a wide variety of maturity, seed weight, and stem termination were investigated in a field experiment planted as a randomized complete block design with up to four replications. Canopy outlines were extracted from digital images, and subsequently chain coded, and expanded into a shape spectrum by obtaining the Fourier coefficients/descriptors. These coefficients successfully reconstruct the canopy outline, and were used to measure traditional morphometric traits. Highest phenotypic diversity was observed for roundness, while solidity showed the lowest diversity across all countries. Some PI lines had extraordinary shape diversity in solidity. For interpretation and visualization of the complexity in shape, Principal Component Analysis (PCA) was performed on the EFD. PI lines were grouped in terms of origins, maturity index, seed weight, and stem termination index. No significant pattern or similarity was observed among the groups; although interestingly when genetic marker data was used for the PCA, patterns similar to canopy
Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity
Jubery, Talukder Z.; Shook, Johnathon; Parmley, Kyle; Zhang, Jiaoping; Naik, Hsiang S.; Higgins, Race; Sarkar, Soumik; Singh, Arti; Singh, Asheesh K.; Ganapathysubramanian, Baskar
2017-01-01
Soybean canopy outline is an important trait used to understand light interception ability, canopy closure rates, row spacing response, which in turn affects crop growth and yield, and directly impacts weed species germination and emergence. In this manuscript, we utilize a methodology that constructs geometric measures of the soybean canopy outline from digital images of canopies, allowing visualization of the genetic diversity as well as a rigorous quantification of shape parameters. Our choice of data analysis approach is partially dictated by the need to efficiently store and analyze large datasets, especially in the context of planned high-throughput phenotyping experiments to capture time evolution of canopy outline which will produce very large datasets. Using the Elliptical Fourier Transformation (EFT) and Fourier Descriptors (EFD), canopy outlines of 446 soybean plant introduction (PI) lines from 25 different countries exhibiting a wide variety of maturity, seed weight, and stem termination were investigated in a field experiment planted as a randomized complete block design with up to four replications. Canopy outlines were extracted from digital images, and subsequently chain coded, and expanded into a shape spectrum by obtaining the Fourier coefficients/descriptors. These coefficients successfully reconstruct the canopy outline, and were used to measure traditional morphometric traits. Highest phenotypic diversity was observed for roundness, while solidity showed the lowest diversity across all countries. Some PI lines had extraordinary shape diversity in solidity. For interpretation and visualization of the complexity in shape, Principal Component Analysis (PCA) was performed on the EFD. PI lines were grouped in terms of origins, maturity index, seed weight, and stem termination index. No significant pattern or similarity was observed among the groups; although interestingly when genetic marker data was used for the PCA, patterns similar to canopy