International Nuclear Information System (INIS)
Kuz'min, E.S.; Balagurov, A.M.; Bokuchava, G.D.; Zhuk, V.V.; Kudryashev, V.A.; Bulkin, A.P.; Trunov, 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 stresses 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 the tested modules in comparison with a detector of the previous generation are presented and advantages of the new detector design for high-resolution diffractometry are discussed
Residual Stress Studies Using the Cairo Fourier Diffractometer Facility
International Nuclear Information System (INIS)
Maayouf, R.M.A.; El-Shaer, Y.H.
2002-01-01
The present paper deals with residual stress studies using the Cairo Fourier diffractometer facility CFDF. The CFDF is a reverse - time of -flight (RTOF) diffractometer; applies a Fourier chopper. The measurements were performed for copper samples in order to study the residual stress after welding. The maximum modulation of the Fourier chopper during the measurements was 136 khz; leading to a time resolution half-width of about 7 μ s. It has been found from the present measurements that, the resulting diffraction spectra could be successfully used for studying the residual stress; in the wavelength range between 0.7-2.9 A degree at ∼ 0.45 % relative resolution
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.
The new fourier diffractometer at the IBR-2 reactor: design and first results
International Nuclear Information System (INIS)
Aksenov, V.L.; Balagurov, A.M.; Simkin, V.G.
1992-01-01
A high-resolution neutron powder Fourier diffractometer has been constructed at the pulsed reactor IBR-2 in Dubna. Preliminary results have confirmed resolution predictions indicating that Δd/d can be as small as 5x10 -4 over a wide d range with a good data accumulation rate. 3 refs.; 10 figs.; 1 tab
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
Energy Technology Data Exchange (ETDEWEB)
Maayouf, R M.A.; El-Kady, A S.I.; El-Shaer, Y H [Reactor and Neutron physics Dept., NRC, Atomic Energy Authority, Cairo (Egypt)
1997-12-31
This work deals with optimization of a detector system for use with the fourier reverse time of flight (RTOF) diffractometer facility recently installed at the ETRR-1 reactor. The detector system of the diffractometer was designed for detecting neutrons scattered from the sample. It consists of 4 independent scintillation detector elements arranged according to the time focusing geometry in order to increase the luminosity of the diffractometer for the given resolution. Each of the detector elements is made of 1 mm thick {sup 6} Li-glass scintillator (NE-912) whose surface area is 200 mm{sup 2}. The present detector system ensures reliable identification and separation of thermal neutron pulses from fast neutrons and gamma- quanta. It was found from measurements with Fe sample that it is possible to make neutron diffraction measurement, within one hour using the present detector system and with resultion 0.5%. 6 FIGS.
ASTACUS, a time focussing neutron diffractometer based on the reverse Fourier principle
International Nuclear Information System (INIS)
Tiitta, A.; Hiismaeki, P.
1979-01-01
Design principles, technical realization, and performance of a new time-of-flight neutron diffractometer, built for high resolution powder work and successfully operated for one year, are reported. The range of lattice spacings covered by the instrument extends from 0.3 down to 0.04 nm while the resolution varies from about 0.16% up to 0.8% respectively as dicated by the 10 μs time resolution and about 8 m flight path. (Auth.)
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Abdel-Latif, I.; El-Kady, A.; El-Shafey, A.; Khalil, M.; El-Shaer, Y.
1997-05-01
This report represents the results of measurements performed recently with the Cairo Fourier diffractometer facility (CFDF). The main components of the CFDF were supplied by the IAEA according to the technical assistance project EGY/1/022. The CFDF performance is assessed and the main parameters are given. The neutron guide system attached to the CFDF provides a thermal neutron flux ∼ 10 6 n/cm 2 .sec at the sample position; free from fast neutrons and gamma rays background. It has been found, from measurements with different powder samples, that such value of the thermal neutron flux is adequate for neutron diffraction measurements, at scattering angle 2θ 90 deg. and D values between 0.7A and 2.5A; with 52% resolution. (author). 26 refs, 10 figs, 2 tabs
The DSP-based RTOF-correlator for high resolution Fourier diffractometers
Energy Technology Data Exchange (ETDEWEB)
Butenko, V A; Drozdov, V A; Kirilov, A S [Frank Lab. of Neutron Physics of the Academy of Sciences of Slovakia, Bratislava (Slovakia)
1996-12-31
To improve efficiency of the time-of-flight analysis, the correlation and the Fourier methods are used with a preliminary neutron flux modulation. In this case the elastically scattered neutron spectrum is calculated as a function of the cross-correlation of the detector signal and the neutron flux modulation. 10 refs.; 5 figs.
Powder neutron diffractometers
International Nuclear Information System (INIS)
Adib, M.
2002-01-01
Basic properties and applications of powder neutron Diffractometers are described for optimum use of the continuous neutron beams. These instruments are equipped with position sensitive detectors, neutron guide tubes, and both high intensity and high resolution modes of operation are possible .The principles of both direct and Fourier reverse time-of-flight neutron Diffractometers are also given
International Nuclear Information System (INIS)
Aksenov, V.L.; Balagurov, A.M.; Taran, Yu.V.
1995-01-01
The results of estimating residual stresses in cold rolled iron disks by measurements with the high resolution Fourier diffractometer (HRFD) at the IBR-2 pulsed reactor are presented. These measurements were made for calibration of magnetic and ultrasonic measurements carried out at the Fraunhofer-Institute for Nondestructive Testing in Saarbrucken (Germany). The tested objects were cold rolled steel disks of 2.5 mm thickness and diameter of about 500 mm used for forming small, gas pressure tanks. Neutron diffraction experiments were carried out at the scattering angle 2θ=+152 d eg with resolution Δd/d=1.5·10 -3 . The gauge volume was chosen according to the magnetic measurements lateral resolution 20x20 mm 2 . In the nearest future the neutron diffraction measurements with cold rolled iron disks at the scattering angle 2θ=±90 0 are planned. Also the texture analysis will be included in the Rietveld refinement procedure for more correct calculation of residual stress fields in the cold rolled materials. 8 refs., 10 figs., 1 tab
High-resolution diffractometer MINI-SFINKS
International Nuclear Information System (INIS)
Trunov, W.A.; Kudryaschev, W.A.; Uljanov, W.A.; Bulkin, A.P.; Muratov, W.G.; Korotkova, T.K.; Schebetov, A.F.
1991-01-01
The theoretical principles of the RTOF (reverse time-of-flight) method as well as the basic equations, the optimization of the neutron guides with Fourier chopper and the time-focussing detector setup are outlined. The powder diffractometer is described and some experimental results are given. The report was used as conceptual design basis for the FSS spectrometer at FRG-1 (GKSS Research Center) which has been optimized for non-destructive determination of residual stress. (orig.) With 18 figs., 3 tabs [de
Neutron Diffractometer; Neutronski difraktometar
Energy Technology Data Exchange (ETDEWEB)
Zivadinovic, M [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Serbia and Montenegro)
1961-12-15
RA nuclear reactor is considered as a relatively strong neutron source producing the thermal neutron flux of about 3x10{sup 13} n/cm{sup 2} sec when operating at nominal power of 6.5 MW. Neutron diffraction method is applied in the field of solid state physics, material science, crystallography, magnetism, nuclear physic. Neutron diffractometer at the RA reactor consists of: system for obtaining collimated neutron beam from the horizontal experimental channel neutron monochromator; goniometer and electronic equipment for measurements and collecting the the measurement data. Nuklearni reaktor RA koji pri radu na snazi od 6,5 MW ima fluks termalnih neutrona oko 3x10{sup 13} n/cm{sup 2} sec predstavlja relativno jak izvor neutrona. Tehnika difrakcije neutrona primenjuje se u istrazivanjima fizike crvstog stanja, strukture materijala, kristalografije, magnetizma, nuklearne fizike. Neutronski difraktometar na reaktoru RA sastoji se od sistema za dobijanje kolimisanog snopa neutrona kroz horizontalni kanal reaktora; neutroskog monohromatora; goniometra i elektronskih uredjaja za merenja i registrovanje rezultata. Ovaj izvestaj sadrzi detaljan opis i seme neutronskog difraktometra sa pratecom opremom i elektronskim komponentama.
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.
Full system decontamination (FSD) at NPP Stade prior to dismantling activities
International Nuclear Information System (INIS)
Christoph Stiepani; Karl Seidelmann
2006-01-01
Full text of publication follows: Introduction: Minimization of personnel dose rates and generation of material free for release is of the highest priority and requires Full System Decontamination (FSD) as a first and important measure when decommissioning Nuclear Power Plants. Framatome ANP has many years experience with Full System Decontaminations for operating nuclear power plants in general and for decommissioning in particular. The latest decommissioning project was the FSD at the PWR Stade which was permanently shut down in November 2003 after 31 years of operation. FSD was scheduled within a short period after shutdown and prior to decommissioning activities. Full System Decontamination at Stade: The PWR Stade is a 4 loop design. FSD included the entire primary circuit with RPV and the auxiliary systems (RHR, VCS and RWCU). The decontamination circuit had a total volume of ∼310 m 3 and an overall surface of ∼17000 m 2 . The Framatome ANP decontamination process HP/CORD R UV was selected for application. The decontamination was performed by using NPP systems in combination with the Framatome mobile decontamination equipment AMDA R (Automated Mobile Decontamination Appliance). A total of 4 decontamination cycles were performed and excellent results were obtained. The average decontamination factor (DF) was 160 for the steam generators with an outstanding ambient dose reduction factor (DRF) of 75. Conclusions: FSD at the PWR Stade has shown that the HP/CORD UV process yields excellent results in primary and auxiliary systems. The significant ambient dose reduction factor of 75 is remarkable. This very high DRF, no other decontamination application came even close, will result in excellent cost-benefit ratios for additional decommissioning activities at Stade. The applied HP/CORD UV process is not a specific decontamination process for decommissioning. Therefore the obtained decontamination and dose reduction factors demonstrate the advantage/potential for
Multiwire area x-ray diffractometers
International Nuclear Information System (INIS)
Hamlin, R.
1985-01-01
The multiwire proportional counter is at this writing the only type of two-dimensional position-sensitive X-ray detector capable of collecting diffraction data accurate enough for solution of new protein structures. The first diffractometer system to use this type of detector (the Mark I diffractometer system) was assembled at the University of California, San Diego and has collected the data used to solve for four new protein structures. Similar diffractometer systems using a single thin, flat multiwire counter are now being constructed in several other laboratories around the world, and several of these should routinely be collecting good diffraction data from protein and perhaps even virus crystals by 1986. A table describing some of these other systems is included later in this chapter. The next step in the evolution of area diffractometer systems based on the multiwire proportional counter is more complete coverage of the solid angle of the diffraction pattern - more complete than the 10 - 40% coverage possible with one flat multiwire counter. The phenomenon called ''parallax'' makes it impractical to intercept the whole diffraction pattern with one flat, xenon-filled multiwire counter. Two strategies for dealing with parallax are now being pursued. One strategy involves adding a spherical drift region to the front of a flat multiwire counter and a detector using this idea will be described. The other strategy, one being pursued by the author, involves building an array of flat detectors arranged to approximate a section of the surface of a sphere. The array of flat detectors gives more flexibility in crystal-to-detector distance and distributes the dead time over many detectors, thereby allowing the full array to have a high counting rate capacity even using only medium speed (2 μsec) position readout circuits for each individual detector
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 (iMATERIA)-Versatile neutron diffractometer at J-PARC
International Nuclear Information System (INIS)
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.
2009-01-01
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 0.18< d (A)<5 with Δd/d=0.16% at high resolution bank, and covers 5< d (A)<800 with gradually changing resolution at three detector bank (90 deg., low angle and small angle). Typical measuring time to obtain a 'Rietveld-quality' data is several minutes with 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. 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.
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.
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.
TOF powder diffractometer on a reactor source
International Nuclear Information System (INIS)
Bleif, H.J.; Wechsler, D.; Mezei, F.
1999-01-01
Complete text of publication follows. The performance of time-of-flight (TOF) methods on Long Pulse Spallation Sources can be studied at a reactor source. For this purpose a prototype TOF monochromator instrument will be installed at the KFKI reactor in Budapest. The initial setup will be a powder diffractometer with a resolution of δd/d down to 2 x 10 -3 at a wavelength of 1 A. The instrument uses choppers to produce neutron pulses of down to 10 μs FWHM. The optimal neutron source for a chopper instrument is a Long Pulse Spallation Source, but even on a continuous source simulations have shown that this instrument outperforms a conventional crystal monochromator powder diffractometer at high resolution. The main components of the TOF instrument are one double chopper defining the time resolution and two single choppers to select the wavelength range and to prevent frame overlap. For inelastic experiments a further chopper can be added in front of the sample. The neutron guide has a super-mirror coating and a curvature of 3500m. The total flight path is 20m and there are 24 single detectors in backscattering geometry. (author)
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 dysfunction, premature and delayed ejaculation. In an age-adjusted model, partner's HSD was negatively related to FSFI total score (Wald = 9.196, p = 0.002), arousal (Wald = 7.893, p = 0.005), lubrication (Wald = 5.042, p = 0.025), orgasm (Wald = 9.293, p = 0.002), satisfaction (Wald = 12.764, p sexual pleasure, and with a higher frequency of masturbation, even after adjusting for age. In patients not reporting any reduction in 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.
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
Control of an X-ray diffractometer
International Nuclear Information System (INIS)
Bleif, H.J.; Degenhardt, K.H.; Herdam, G.
1980-09-01
As to the four-axis diffractometer control the following problems have beeen solved by using CAMAC-instrumentation: 1) Orientation of the crystal and adjustment of the limit switch are possible by manual operation. 2) The temperature of the crystal is adjusted and controlled by a process computer. 3) The computer controls the measuring sequence as follows: a) the crystal and the detector are put in the calculated position; b) measuring of the intensity with the measuring time being determined by a monitor counter (impulse pre-selection) or by a timer (time pre-selection); c) analog output of intensity; d) storing of the data on a data file. (orig./HP)
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.
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)
Design of Double PG Crystal Neutron Diffractometer
International Nuclear Information System (INIS)
Adib, M.; Habib, N.; El-Mesiry, M.S.; Fathallah, M.
2011-01-01
The design of a diffractometer containing two pyrolytic graphite (PG) crystals to select monochromatic neutrons in the range of wavelengths longer than 0.26 nm is given. The first crystal is high oriented pyrolytic graphite (HOPG) set at glancing angle to reflect monochromatic neutrons with a selected wavelength. The second is a low quality PG crystal filter, set at take-off-angle such that, it transmits the selected monochromatic neutrons and rejects the higher order contaminations accompanying the first order reflection. It was shown that, 2 mm thick of PG crystal having 0.30 FWHM on mosaic spread are the optimum parameters of monochromator PG crystal. While the optimum thickness and mosaic spread of the PG crystal filter were selected to have low contamination factor of higher order reflections. The optimum parameters of the PG filter crystal were calculated using the computer package Graphite recently developed in our laboratory. Calculation shows that, 3 cm thick PG filter (20 on mosaic spread) is sufficient to almost eliminate the higher order contaminations accompanying the main monochromatic neutrons with
Instrumentation for PSD-based neutron diffractometers at Dhruva ...
Indian Academy of Sciences (India)
These include three diffractometers with multiple PSDs and four with single ... causes ionization in the gas, the charge is collected at both ends of the wire and .... terface required for data acquisition, control, presentation and system setup. The.
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)
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
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
Energy Technology Data Exchange (ETDEWEB)
Moriai, Atsushi [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki, 319-1195 (Japan)]. E-mail: atsushi.moriai@jaea.go.jp; Torii, Shuki [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki, 319-1195 (Japan); Suzuki, Hiroshi [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki, 319-1195 (Japan); Harjo, Stefanus [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki, 319-1195 (Japan); Morii, Yukio [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki, 319-1195 (Japan); Arai, Masatoshi [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki, 319-1195 (Japan); Tomota, Yo [Ibaraki University, Hitachi-shi, Ibaraki, 316-8511 (Japan); Suzuki, Tetsuya [Ibaraki University, Hitachi-shi, Ibaraki, 316-8511 (Japan); Akiniwa, Yoshiaki [Nagoya University, Nagoya-shi, Aichi, 464-8603 (Japan); Kimura, Hidehiko [Nagoya University, Nagoya-shi, Aichi, 464-8603 (Japan); Akita, Koich [Musashi Institute of Technology, Setagaya-ku, Tokyo, 158-8557 (Japan)
2006-11-15
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{sub 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{sup o} 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 {delta}d/d has been confirmed.
Time-of-flight neutron diffractometer for monocrystal study
International Nuclear Information System (INIS)
Anan'ev, B.N.; Balagurov, A.M.; Barabash, I.P.; Georgiu, Z.; Shibaev, V.D.
1979-01-01
The design of a neutron diffractometer is discussed. It is used for structural analysis of single crystals on the basis of time-of-flight measurements. The diffractometer is positioned along the axis of a beam of the IBR-30 pulse reactor, its average power is 29 kW. The mechanical part of the diffractometer consists of a massive foundation with a threeaxial goniometer, a rotatable platform with a collimator and a 3 He counter. The flowsheet of a control unit is given, which is used to position the rotatable platform of the diffractometer. The control unit includes a 14 digic binary counter for rotation angle recording, a parallel-to-series converter, a control signal shaper, two position shift registers, and a servo mechanism. The accuracy of diffraction maxima is evaluated. It is found that the ratio D(t)sup(1/2)/t (D(t) is a time dispersion of diffraction maxima, t is total time-of-flight time), which characterize the resolution of the diffractometer, is equal to 0.5% at the Bragg angle Q=45 deg and the neutron wavelength Λ=1 A
Development of engineering diffractometer at J-PARC
International Nuclear Information System (INIS)
Moriai, Atsushi; Torii, Shuki; Suzuki, Hiroshi; Harjo, Stefanus; Morii, Yukio; Arai, Masatoshi; Tomota, Yo; Suzuki, Tetsuya; Akiniwa, Yoshiaki; Kimura, Hidehiko; Akita, Koich
2006-01-01
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 o 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 Δd/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)
International Nuclear Information System (INIS)
Stellwag, Bernhard; Hoffmann-Wankerl, Stephan; Schuetz, Sigrid; Jacob, Astrid
2012-09-01
Full-system decontamination (FSD) or replacement of steam generators (SG) and other large components in mature PWR plants results in large bare metal surfaces in the reactor system. The AREVA chemistry concept for sustainable dose rate reduction at such plants includes a passivation treatment for formation of high-quality oxide films in the reactor system and high pH operation in combination with zinc injection during subsequent power operation. The effectiveness of these measures has been proven by plant operation experience. The systematic evaluation of plant-specific experience is used for further optimization of the concept. These measures were also applied at the 1350 MW-class 4-loop PWR Grafenrheinfeld after an FSD with the AREVA decontamination process HP/CORD R UV in 28 th outage. The passivation treatment consisted of zinc injection during plant heat-up and parallel adjustment of a high pH value. It was carried out in the plant operation condition 'subcritical hot' for 200 hours and a pH (300 deg. C) of 7.1. During the cycle, the pH value was increased to 7.4 and zinc injection was continued. This paper evaluates the recontamination of the plant inclusive the first refueling outage since the FSD. The evaluation is based on routine chemistry and dose rate surveillance data and on the results of special measurement programs conducted at the plant before and after the FSD. Results of surface gamma activity measurements and fuel crud analyses are also described. Data is evaluated with regard to release, transport and deposition of corrosion products and nuclides in the reactor system. The plant-specific contamination sources and their pathways are outlined. Compared to the first refueling outage of the plant in 1983, the dose rate level at the main loops could be more than halved in spite of already activated core internals and crud on fuel assemblies, the in-core instrumentation and the control rods including guide assemblies and drive rods. The FSD
A high resolution powder diffractometer using focusing optics
Indian Academy of Sciences (India)
E-mail: siruguri@csr.ernet.in. Abstract. In this paper, we describe the design, construction and performance of a new high resolution neutron powder diffractometer that has been installed at the Dhruva reactor, Trombay, India. The instrument employs novel design concepts like the use of bent, perfect crystal monochromator ...
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)
Slit and phase grating diffraction with a double crystal diffractometer
International Nuclear Information System (INIS)
Treimer, Wolfgang; Hilger, Andre; Strobl, Markus
2006-01-01
The lateral coherence properties of a neutron beam (λ=0.5248nm) in a double crystal diffractometer (DCD) were studied by means of single slit diffraction and by diffraction by different perfect Silicon phase gratings. Perfect agreements were found for the lateral coherence length measured with the slit and for the one determined by Silicon phase gratings, however, some peculiarities are still present
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
Indian Academy of Sciences (India)
The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...
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
International Nuclear Information System (INIS)
Haase, A.
1996-01-01
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
X-ray diffraction analysis with diffractometer DRON-1
International Nuclear Information System (INIS)
Bochenin, V.I.
1978-01-01
Rapid methods of phase quantitative analysis of wolframite (FeMn)WO 4 and molybdenite MoS 2 in industrial materials using DRON-1 diffractometer are suggested. Diffractometer with spectrometric attachment was used for determination of (FeMn)WO 4 in industrial raw materials. Results of the above analysis have been compared with the data of chemical analysis, their good agreement has been shown. Time of wolframite determination in one sample is 8-10 min. Method of standard background with respect to absorption properties of medium has been developed for MoS 2 rapid determination in enriched molybdenum ore. Time of molybdenite determination in one sample is 3-4min., error is 4 % rel. in MoS 2 concentration range from 15.4 to 36.7 %
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.
A nanoscale ordered materials diffractometer for the SNS
International Nuclear Information System (INIS)
Neuefeind, Joerg; Chipley, Kenneth K.; Tulk, Chris A.; Simonson, J. Michael; Winokur, Michael J.
2006-01-01
The Nanoscale Ordered Materials Diffractometer (NOMAD) is one of five neutron scattering instruments being managed within the Spallation Neutron Source (SNS) Instruments-Next Generation (SING) project. NOMAD is designed as a high-flux, medium-resolution diffractometer using a large bandwidth of neutron energies and extensive detector coverage to perform structural determinations of local order in crystalline and amorphous materials. The instrument will enable studies of a large variety of samples ranging from liquids, solutions, glasses, polymers, and nanocrystalline materials to long-range ordered crystals and will allow unprecedented access to high-resolution pair distribution functions, small-contrast isotope substitution experiments, small sample sizes, and parametric studies. Project completion for the instrument is anticipated in 2010 and a review of the design status will be given
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.
Data acquisition system for linear PSD based neutron diffractometer
International Nuclear Information System (INIS)
Pande, S.S.; Borkar, S.P.; Behere, Anita; Ghodgaonkar, M.D.
2001-01-01
Single or multi-PSD configurations are used in different neutron diffractometer setups. A data acquisition system is developed to serve the gross requirements of all the diffractometer setups. It is also customized to specific requirements of different setups. The hardware is developed as a Transputer based add-on card. Most of the hardware functionality is handled in the Transputer program thus improving throughput of the system. The card can handle 16 RDCs, a few motor controls and on/off controls. The software comprises of a front-end Windows98 application, a Transputer program and a device driver. The data acquisition system performs data acquisition, analysis, display and storage. Analysis includes converting raw data of linear PSD to equiangular format, merging and clubbing the data to make a continuous equiangular spectrum. Calibration of individual PSD is a crucial activity in correctly merging the data coming from PSDs. (author)
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)
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.)
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.
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.
Zhang, Dawei; Lazim, Raudah; Mun Yip, Yew
2017-09-01
We conducted an all-atom ab initio folding of FSD-EY, a protein with a ββα configuration using non-polarizable (AMBER) and polarizable force fields (PHB designed by Gao et al.) in implicit solvent. The effect of reducing the polarization effect integrated into the force field by the PHB model, termed the PHB0.7 was also examined in the folding of FSD-EY. This model incorporates into the force field 70% of the original polarization effect to minimize the likelihood of over-stabilizing the backbone hydrogen bonds. Precise folding of the β-sheet of FSD-EY was further achieved by relaxing the REMD structure obtained in explicit water.
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.
App. 1. Fourier series and Fourier transform
International Nuclear Information System (INIS)
Anon.
1977-01-01
Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr
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)
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.)
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
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.
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
New diffractometers at ILL Grenoble - the millennium program
International Nuclear Information System (INIS)
Hewat, A. W.
2000-01-01
Full text: New techniques for constructing detectors and monochromators are being used to build a number of new diffractometers at ILL Grenoble to provide an order of magnitude gain in efficiency, and higher resolution. Similar techniques might be applied at the new Australian reactor to provide world-class neutron instruments. These projects include a high resolution multi-detector powder diffractometer super-D2B, a modular microstrip detector for liquids and amorphous materials D4c, an array of 2D microstrip detectors for large molecular structures and fibre diffraction D19, a large high flux microstrip detector D20, a neutron image plate camera for structural and magnetic transitions T-LADI, and a dedicated neutron strain-scanner built with a large grant from the UK EPSRC. The super-D2B project will consist of 128 linear wire detectors behind an array of very fine Soeller collimators, which will provide a horizontal resolution of 5x10 -4 in d-spacing. Vertical resolution by charge division along the 300mm detector length will be used to correct for the curvature of the diffraction cones, greatly increasing the useful vertical acceptance angle. Prototype collimators and detectors have already been constructed. The new D4c detector is being installed in June 2000 on the liquids and amorphous materials diffractometer D4. It consists of a bank of 9 individual microstrip detectors covering a total of 160 degrees, with each detector containing 64 microstrip 'wires'. The complete diffraction pattern will be obtained with 2 positions of this detector bank, which is very efficient for short wavelength neutrons, and highly stable, as needed to measure small differences between amorphous materials using for example isotope contrast. The world's first microstrip powder diffractometer D20 is currently being re-built, and will be available again in October 2000. It consists of 1600 microstrip 'wires' in a single 160-degree chamber. The machine is so fast that it can follow
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 consis...
The IPEN/CNEN-SP PSD neutron diffractometer
International Nuclear Information System (INIS)
Parente, Carlos Benedicto Ramos; Mazzocchi, Vera Lucia; Mascarenhas, Yvonne Primerano
2004-01-01
Full text: A new IPEN-CNEN/SP neutron powder diffractometer is under construction at the 4 MW thermal IEA-R1m research reactor. It is an upgrading of the old IPEN-CNEN/SP multipurpose neutron diffractometer. The main modifications introduced in the old instrument are: installation of a position sensitive detector (PSD) and a bent perfect single crystal monochromator (a focusing Si monochromator). The PSD is formed by eleven linear detector elements, clamped together at each end to form a rigid plane. The PSD is installed in a detector shielding which is supported by two arms fixed in a large rotary table. This table provides the instrument with the 2θ angular movement. A smaller rotary table, placed underneath and concentric with the larger one, provides the ω(θ) movement. Both tables are driven by a computer controlled geared mechanism. The computer also makes the data acquisition. A rotating-oscillating collimator, placed at the entrance to the detector shielding, eliminates parasitic scattering from furnace or cryorefrigerator heat shields in the vicinity of the sample. The collimator also makes the PSD less sensitive to ambient background. The PSD spans an angular range of 20 deg of a diffraction pattern, resulting in a quite good resolution for the instrument. An extended powder diffraction pattern can be obtained by moving the detector and collecting the data in 20 deg segments. With a take-off angle of 84 deg, the monochromator can be positioned to produce 4 different wavelengths, namely 1.111, 1.399, 1.667 and 2.191 A. Other parts constructed for the new instrument are: a in-pile collimator, a monochromatic beam collimator and a neutron shield, large enough to accommodate the monochromator, a beam shutter and the monochromatic beam collimator. In comparison to the former instrument, the new diffractometer will have better resolution and will be ca. 600 times faster in data acquisition. At the present time, the new instrument is in the final steps of
IPNS time-of-flight single crystal diffractometer
International Nuclear Information System (INIS)
Schultz, A.J.; Teller, R.G.; Williams, J.M.
1983-01-01
The single crystal diffractometer (SCD) at the Argonne Intense Pulsed Neutron Source (IPNS) utilizes the time-of-flight (TOF) Laue technique to provide a three-dimensional sampling of reciprocal space during each pulse. The instrument contains a unique neutron position-sensitive 6 Li-glass scintillation detector with an active area of 30 x 30 cm. The three-dimensional nature of the data is very useful for fast, efficient measurement of Bragg intensities and for the studies of superlattice and diffuse scattering. The instrument was designed to achieve a resolution of 2% or better (R = δQ/Q) with 2 THETA > 60 0 and lambda > 0.7A
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...
Neutron diffractometers for structural biology at spallation neutron sources
Energy Technology Data Exchange (ETDEWEB)
Schoenborn, B.P.; Pitcher, E. [Los Alamos National Laboratory, NM (United States)
1994-12-31
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 {sup 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.
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
DREAM — a versatile powder diffractometer at the ESS
International Nuclear Information System (INIS)
Schweika, W; Violini, N; Lieutenant, K; Nekrassov, D; Zendler, C; Henry, P F; Houben, A; Jacobs, P
2016-01-01
The instrument DREAM, in construction at the long pulse European Spallation Source (ESS), is a new type of neutron time-of-flight powder diffractometer, which utilizes additional choppers to meet the typical high resolution requests. Pulses will be of symmetric shape and their width can be varied from 10 μs to 1 ms, providing an unprecedented flexibility from highest to low resolution with optimized intensities at the superior brightness of the 5 MW source. The design is driven particularly by the needs and challenges for small and complex samples, large unit cell materials, thermoelectric cage structures or metal-organic framework structures, multiphase battery materials and complex magnetic structures. Therefore, the chosen wavelength bandwidth of 3.7 Å may cover well the peak intensities of the thermal and cold moderator used simultaneously and provides a sufficient Q (and d ) range for obtaining diffraction patterns in a single setting. VITESS simulations show a performance that is about two orders of magnitude higher than current best instruments. (paper)
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)
A computer-controlled CAMAC system for the operation of a neutron diffractometer
International Nuclear Information System (INIS)
Zwoll, K.; Mueller, K.D.; Will, G.
1976-01-01
The paper describes a computer-controlled four-circle diffractometer for the investigation of single crystals by neutron diffraction. The hardware is based on the internationally standardised CAMAC system. This makes the system described here independent of the type of computer used and also largely independent of the mechanical equipment used. The software is written in the interpretative language FOCAL which is easy to learn and ensures high flexibility in programming and thus also in the use of the diffractometer. (orig.) [de
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)
Computer-controlled CAMAC system for the operation of a neutron diffractometer
Energy Technology Data Exchange (ETDEWEB)
Zwoll, K; Mueller, K D [Kernforschungsanlage Juelich G.m.b.H. (Germany, F.R.). Zentrallabor fuer Elektronik; Will, G [Bonn Univ. (Germany, F.R.). Mineralogisches Inst.
1976-10-01
The paper describes a computer-controlled four-circle diffractometer for the investigation of single crystals by neutron diffraction. The hardware is based on the internationally standardised CAMAC system. This makes the system described here independent of the type of computer used and also largely independent of the mechanical equipment used. The software is written in the interpretative language FOCAL which is easy to learn and ensures high flexibility in programming and thus also in the use of the diffractometer.
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)
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.
On the origins of the weak folding cooperativity of a designed ββα ultrafast protein FSD-1.
Wu, Chun; Shea, Joan-Emma
2010-11-18
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.
Zhang, Nan; Fan, Zhaoyang; Luo, Nan; Bi, Xiaoming; Zhao, Yike; An, Jing; Liu, Jiayi; Chen, Zhong; Fan, Zhanming; Li, Debiao
2016-02-01
To evaluate the feasibility and diagnostic performance of flow-sensitive dephasing (FSD)-prepared steady-state free precession (SSFP) MR angiography (MRA) for imaging infragenual arteries at 3.0T, with contrast enhanced MR angiography (CE MRA) as reference. Twenty consecutive patients with suspicion of lower extremity arterial disease undergoing routine CE MRA were recruited. FSD MRA was performed at calf before CE MRA. Image quality and stenosis degree of infragenual arteries from both techniques were independently evaluated and compared. Six patients in this study underwent DSA examination. Three undiagnostic segments were excluded with severe venous contamination in CE MRA. A total of 197 calf arterial segments images were analyzed. No significant difference existed in the relative signal intensity (rSI) of arterial segments between FSD MRA and CE MRA techniques (0.92 ± 0.09 versus 0.93 ± 0.05; P = 0.207). However, the subjective image quality score was slightly higher in FSD MRA (3.66 ± 0.81 versus 3.49 ± 0.87; P = 0.050). With CE MRA images as reference standard, slight overestimation existed in FSD MRA (2.19 ± 1.24 versus 2.09 ± 1.18; P = 0.019), with total agreement of 84.3% on the basis of all arterial segments. The sensitivity, specificity, negative predictive value, and positive predictive value of FSD MRA was 96.4%, 93.0%, 98.5%, and 84.1%. No significant difference in the stenosis degree score was detected between MRA (FSD MRA and CE MRA) and DSA (P > 0.05). FSD MRA performed on at 3.0T without the use of contrast medium provides diagnostic images allowing for arterial stenosis assessment of calf arteries that was highly comparable with CE MRA. Moreover, venous contamination was less problematic with FSD MRA. © 2015 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Hallenga, K.
1991-01-01
This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs
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 ...
D1A, a high resolution neutron powder diffractometer with a bank of mylar collimators
International Nuclear Information System (INIS)
Hewat, A.W.; Bailey, I.
1976-01-01
This paper describes a first attempt at following the design criteria set out earlier for a high resolution conventional powder diffractometer. An existing machine, D1A, has been modified using a bank of ten high pressure 3 He counters and almost perfect 10minutes of arc mylar foil collimators. The system is more successful than earlier multicollimator arrangements because each of the collimator/counters is virtually identical; this permits automatic addition of the intensities so that a single high resolution profile, up to X40 times as intense as on the original diffractometer, is obtained just as easily as on a single counter machine. A comparison is made with the other powder diffractometers, D1B and D2 at the ILL. (Auth.)
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)
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
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....
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)
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
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
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…
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
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...
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
Simple methods of aligning four-circle diffractometers with crystal reflections
Energy Technology Data Exchange (ETDEWEB)
Mitsui, Y [Tokyo Univ. (Japan). Faculty of Pharmaceutical Sciences
1979-08-01
Simple methods of aligning four-circle diffractometers with crystal reflections are devised. They provide the methods to check (1) perpendicularity of chi plane to the incident beam, (2) zero point of 2theta and linearity of focus-chi center-receiving aperture and (3) zero point of chi.
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
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…
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...
Fourier Transform Mass Spectrometry
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-01-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802
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....
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.
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)
Fourier transformation for engineering and natural science
International Nuclear Information System (INIS)
Klingen, B.
2001-01-01
The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)
Analysis of a drum chopper for use on a new small angle diffractometer at IPNS
International Nuclear Information System (INIS)
Crawford, R.K.; Epperson, J.E.; Thiyagarajan, P.; Carpenter, J.M.
1990-01-01
Light-weight drum choppers rotating at 15 Hz have been in use on the IPNS powder diffractometers for several years, where they serve to eliminate the delayed-neutron background from much of the spectral region of interest. Monte Carlo simulations indicate that a similar chopper operated at 15 Hz should do an excellent job of delayed-neutron removal in the new small-angle diffractometer being designed at IPNS. The simulations also show that when the same chopper is operated at 7.5 Hz it performs quite successfully as a frame-elimination chopper, effectively eliminating neutrons from alternate pulses and allowing extension of the useful wavelength range of the instrument to ∼28 Angstrom. Thus the incorporation of such a chopper should add considerably to the range and flexibility of the new instrument. 7 refs., 9 figs
International Nuclear Information System (INIS)
Graf, H.A.
1983-08-01
The computer program MONREF was written for calculating the integrated intensity and the k-vector distribution produced by mosaic-crystal monochromators in neutron diffractometers of given geometries. The program treats flat and horizontally curved monochromators in Bragg reflection. Its basic algorithm is derived from Zachariasen's coupled differential equations which were modified to include the case of asymmetrically cut crystals. The calculations are restricted to the scattering in the experimental plane. In the first part of the report the program and its applications are described. In the second part a compilation of intensities is presented, calculated for crystals of Cu, Si, Ge and pyrolytic graphite commonly used as monochromators, in a standard diffractometer configuration. (orig.)
Automation of an X-ray diffractometer using a manually preset control system
International Nuclear Information System (INIS)
Berry, T.; Prentice, P.C.
1978-11-01
The measurements of lattice parameters of beta silicon carbide nuclear reactor temperature monitors at Dounreay were formerly carried out using an X-ray diffractometer connected to a simple step scan control system with an analysis time of 8 hours per specimen. A system is described whereby the step scan throughout of the X-ray diffractometer is increased by using an automatic sample charger and additional control electronics, allowing round-the-clock analysis. The original system which used Harwell 2000 series electronic units has been expanded to include an AERE designed goniometer control unit, a Philips sample changer with control unit, and a Honeywell chart recorder. The integrated circuit logic used, interconnections of modules, and operating instructions are given in appendices. (UK)
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)
HiQ - A high-Q diffractometer for PDF measurements
International Nuclear Information System (INIS)
Brunelli, M.; Fischer, H.E.; Gaehler, R.; Chatterji, T.
2011-01-01
The local structure of many important functional materials is often different from the average structure, as revealed by diffraction, due to, e.g. doping, mixed site occupancy, or formation of time-dependent local distortions. To get information on both the average and the local structures one needs to perform a joint Rietveld and PDF (Pair Distribution Function) analysis of the total scattering, for which we need data to Q = 30 - 35 Angstroms with Δd/d ∼ 3*10 -3 . Here, we describe how the hot-source diffractometer D4 can be adapted to achieve this capability, and outline one possible design of a dedicated high-Q diffractometer at the ILL (Laue Langevin Institute), using the vacant inclined hot-neutron beam IH2. (authors)
High-efficiency transmision neutron polarizer for high-resolution double crystal diffractometer
International Nuclear Information System (INIS)
Ioffe, A.; Krist, T.; Mezei, F.; Gordeev, G.; Ibrayev, B.
1997-01-01
An efficient transmission geometry neutron polarizer for the high-resolution double crystal diffractometer at HMI (λ=4.8 A) is described. A polarization of about 94% was achieved and the polarized neutron beam intensity amounts to 40% of the nonpolarized beam intensity. This opens up wide possibilities for the study of magnetic small-angle scattering for extremely small momentum transfer (Q∝10 -5 A -1 ). (orig.)
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
Data transmission from the DRON-2 X-ray diffractometers to a computer
International Nuclear Information System (INIS)
Abramov, V.G.; Monov, N.A.; Sazonov, V.F.; Chernomorskaya, E.A.
1991-01-01
The circuit of data transmission from DRON-2 X-ray diffractometer to a measurement-computation complex based on UVK SM-3 computer and CAMAC crate is described. The data is transmitted along two-wire TRP 1x2 telephone line of 'current loop type'. Pulses from intensity channel outlet are transmitted as unipolar mark pulses of ∼1 μs duration. The channels are separated by amplitudes
Data acquisition and processing software for linear PSD based neutron diffractometers
International Nuclear Information System (INIS)
Pande, S.S.; Borkar, S.P.; Ghodgaonkar, M.D.
2003-01-01
As a part of data acquisition system for various single and multi-PSD diffractometers software is developed to acquire the data and support the requirements of diffraction experiments. The software is a front-end Windows 98 application on PC and a transputer program on the MPSD card. The front-end application provides entire user interface required for data acquisition, control, presentation and system setup. Data is acquired and the diffraction spectra are generated in the transputer program. All the required hardware control is also implemented in the transputer program. The two programs communicate using a device driver named VTRANSPD. The software plays a vital role in customizing and integrating the data acquisition system for various diffractometer setups. Also the experiments are effectively automated in the software which has helped in making best use of available beam time. These and other features of the data acquisition and processing software are presented here. This software is being used along with the data acquisition system at a few single PSD and multi-PSD diffractometers. (author)
International Nuclear Information System (INIS)
Burattini, E.; Simeoni, S.
1991-01-01
A high resolution powder diffractometer, connected to the wiggler magnet line BX1, is now operative at the Adone storage ring in Frascati. A Si channel-cut monochromator on the line allows operation in the range 1-3 A. To achieve the desired high resolution in the diffraction spectra, a 'triple-axis configuration' has been chosen: a vertical standing goniometer supports a flat Ge(111) crystal analyzer on the 2O arm. With this configuration, a value of less than 0.02 o for the FWHM of the diffraction peaks has been reached. The special design solutions adopted for a Seifer MZ VI goniometer and the microstep technology used in the stepper motor actuation assure a mechanical resolution better than 0.001 o . A special supporting table, with six degrees of freedom, has been made for the diffractometer orientation in front of the X-ray beam. An IBM-PC is dedicated to the diffractometer positioning control and preliminary data collection. As a Macintosh IICX provides for the data processing, a special software package, named 'Mac Dust', has been developed and is continuously updated. The first experimental results collected on-line during the instrument check-up are presented. (author) 5 figs., 1 tab., 11 refs
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
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.
Fourier plane imaging microscopy
Energy Technology Data Exchange (ETDEWEB)
Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)
2014-09-14
We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.
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)
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
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...
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...
Neutron diffractometer for bio-crystallography (BIX) with an imaging plate neutron detector
Energy Technology Data Exchange (ETDEWEB)
Niimura, Nobuo [Japan Atomic Energy Research Inst., Ibaraki-ken (Japan)
1994-12-31
We have constructed a dedicated diffractometer for neutron crystallography in biology (BIX) on the JRR-3M reactor at JAERI (Japan Atomic Energy Research Institute). The diffraction intensity from a protein crystal is weaker than that from most inorganic materials. In order to overcome the intensity problem, an elastically bent silicon monochromator and a large area detector system were specially designed. A preliminary result of diffraction experiment using BIX has been reported. An imaging plate neutron detector has been developed and a feasibility experiment was carried out on BIX. Results are reported. An imaging plate neutron detector has been developed and a feasibility test was carried out using BIX.
Software of structure experiMents in a neutron time-of-flight diffractometer
International Nuclear Information System (INIS)
Balagurov, A.M.; Dlouga, M.; Zlokazov, V.B.; Mironova, G.M.
1978-01-01
A set of programs is discussed to be used in diffraction experiment in a neutron time-of-flight diffractometer. The DIFRAT program, which processes spectra of poly and monocrystals, locates all spectrum maxima and assesses their width on the basis of given experimental data and elementary cell parameters. Accurate location of maxima, evaluation of their area and width is done by the IREAK program. The most important feature of this program is a capability to set an experimental model of maxima patterns. The EXPDAT program is developed to investigate structural characteristics of a sample. It calculates corrections for absorbtion and extinction
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
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)
The D18 diffractometer for neutron interferometry at the I.L.L
International Nuclear Information System (INIS)
Bauspiess, W.
1978-01-01
Three things are needed for neutron interferometry: an interferometer (a crystal in the case of Bragg diffraction interferometry), a neutron source, and a device to select and handle the neutrons that shall be used. It is this last technical aspect of neutron interferometry which is discussed in the paper, using as an example the new diffractometer for neutron interferometry that is being built at the I.L.L. Results of performance tests are not presently available but its characteristics are visible from the design. The experimental figures given in the paper refer to experiments performed with the prototype machine, or are extrapolated from said experiments
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.
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
Initial results from the high resolution powder diffractometer HRPD at ISIS
International Nuclear Information System (INIS)
David, W.I.F.; Harrison, W.T.A.; Johnson, M.W.
1986-07-01
The paper reviews the initial commissioning of the high resolution time-of-flight neutron powder diffractometer, HRPD, on the Spallation Neutron Source, ISIS, at the Rutherford Appleton Laboratory. Preliminary results have confirmed both intensity and resolution predictions indicating that (Δd/d) lies between 0.04% and 0.08% for all d-spacings between 0.2 and 5A. The scientific potential of this increased resolution over existing time-of-flight diffractometers has been demonstrated in the successful ab initio structure determination of an unknown inorganic material, FeAsO 4 , and the detailed study of subtle symmetry changes in NiO. The true instrumental resolution, however, has been observed in only a small number of experiments: sample broadening is often seen to play a dominant role in the determination of the peak shape, particularly at longer d-spacings. This leads to additional useful information about macroscopic properties, such as anisotropic crystallite size, strain distribution and sample homogeneity, but also results in a significant increase in complexity of peak-shape description and data-analysis strategy. (author)
A new high resolution neutron powder diffractometer at the Brookhaven high flux beam reactor
International Nuclear Information System (INIS)
Passell, L.; Bar-Ziv, S.; Gardner, D.W.; Cox, D.E.; Axe, J.D.
1991-01-01
A high resolution neutron powder diffractometer under construction at the Brookhaven HFBR is expected to be completed by mid-1991. The new machine will have a Ge (511) monochromator with a take-off angle of 120 o (λ=1.89A) and 64 3 He counters in the detector bank. There will be interchangeable collimators before the monochromator allowing a choice of 5 or 11' horizontal divergence, and 10 cm-high, 5' collimators in front of the detectors. In the higher resolution mode, Δd/d is expected to be about 6x10 -4 at the resolution minimum. The diffractometer is generally similar to D2B at the Institut Laue-Langevin except for the monochromator. This will consist of a vertically focussing array of segments 3x1.27 cm in dimensions cut from stacks of 20 0.43 mm wafers that have been pressed and brazed together. Preliminary measurements indicate that a mosaic width of 0.1-0.15 o and a peak reflectivity of 25% can be achieved in this way. (author) 2 figs., 22 refs
Universal crystal cooling device for precession cameras, rotation cameras and diffractometers
International Nuclear Information System (INIS)
Hajdu, J.; McLaughlin, P.J.; Helliwell, J.R.; Sheldon, J.; Thompson, A.W.
1985-01-01
A versatile crystal cooling device is described for macromolecular crystallographic applications in the 290 to 80 K temperature range. It utilizes a fluctuation-free cold-nitrogen-gas supply, an insulated Mylar crystal cooling chamber and a universal ball joint, which connects the cooling chamber to the goniometer head and the crystal. The ball joint is a novel feature over all previous designs. As a result, the device can be used on various rotation cameras, precession cameras and diffractometers. The lubrication of the interconnecting parts with graphite allows the cooling chamber to remain stationary while the crystal and goniometer rotate. The construction allows for 360 0 rotation of the crystal around the goniometer axis and permits any settings on the arcs and slides of the goniometer head (even if working at 80 K). There are no blind regions associated with the frame holding the chamber. Alternatively, the interconnecting ball joint can be tightened and fixed. This results in a set up similar to the construction described by Bartunik and Schubert where the cooling chamber rotates with the crystal. The flexibility of the systems allows for the use of the device on most cameras or diffractometers. THis device has been installed at the protein crystallographic stations of the Synchrotron Radiation Source at Daresbury Laboratory and in the Laboratory of Molecular Biophysics, Oxford. Several data sets have been collected with processing statistics typical of data collected without a cooling chamber. Tests using the full white beam of the synchrotron also look promising. (orig./BHO)
A Novel X-ray Diffractometer for the Florida Split Coil 25 Tesla Magnet
Wang, Shengyu; Kovalev, Alexey; Suslov, Alexey; Siegrist, Theo
2014-03-01
At National High Magnetic Field Laboratory (NHMFL), we are developing a unique X-ray diffractometer for the 25 Tesla Florida Split Coil Magnet for scattering experiments under extremely high static magnetic fields. The X-ray source is a sealed tube (copper or molybdenum anode), connected to the magnet by an evacuated beam tunnel. The detectors are either an image plate or a silicon drift detector, with the data acquisition system based on LabVIEW. Our preliminary experimental results showed that the performance of the detector electronics and the X-ray generator is reliable in the fringe magnetic fields produced at the highest field of 25 T. Using this diffractometer, we will make measurements on standard samples, such as LaB6, Al2O3 and Si, to calibrate the diffraction system. Magnetic samples, such as single crystal HoMnO3 and stainless steel 301 alloys will be measured subsequently. The addition of X-ray diffraction to the unique split coil magnet will significantly expand the NHMFL experimental capabilities. Therefore, external users will be able to probe spin - lattice interactions at static magnetic fields up to 25T. This project is supported by NSF-DMR Award No.1257649. NHMFL is supported by NSF Cooperative Agreement No. DMR-1157490, the State of Florida, and the U.S. DoE.
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
Mechanical design of a high-resolution x-ray powder diffractometer at the Advanced Photon Source.
Energy Technology Data Exchange (ETDEWEB)
Shu, D.; Lee, P.; Preissner, C.; Ramanathan, M.; Beno, M.; VonDreele, R.; Ranay, R.; Ribaud, L.; Kurtz, C.; Jiao, X.; Kline, D.; Jemian, P.; Toby, B.
2007-01-01
A novel high-resolution x-ray powder diffractometer has been designed and commissioned at the bending magnet beamline 11-BM at the Advanced Photon Source (APS), Argonne National Laboratory (ANL). This state-of-the-art instrument is designed to meet challenging mechanical and optical specifications for producing high-quality powder diffraction data with high throughput. The 2600 mm (H) X 2100 mm (L) X 1700 mm (W) diffractometer consists of five subassemblies: a customized two-circle goniometer with a 3-D adjustable supporting base; a twelve-channel high-resolution crystal analyzer system with an array of precision x-ray slits; a manipulator system for a twelve scintillator x-ray detectors; a 4-D sample manipulator with cryo-cooling capability; and a robot-based sample exchange automation system. The mechanical design of the diffractometer as well as the test results of its positioning performance are presented in this paper.
Mechanical design of a high-resolution x-ray powder diffractometer at the Advanced Photon Source
International Nuclear Information System (INIS)
Shu, D.; Lee, P.; Preissner, C.; Ramanathan, M.; Beno, M.; VonDreele, R.; Ranay, R.; Ribaud, L.; Kurtz, C.; Jiao, X.; Kline, D.; Jemian, P.; Toby, B.
2007-01-01
A novel high-resolution x-ray powder diffractometer has been designed and commissioned at the bending magnet beamline 11-BM at the Advanced Photon Source (APS), Argonne National Laboratory (ANL). This state-of-the-art instrument is designed to meet challenging mechanical and optical specifications for producing high-quality powder diffraction data with high throughput. The 2600 mm (H) X 2100 mm (L) X 1700 mm (W) diffractometer consists of five subassemblies: a customized two-circle goniometer with a 3-D adjustable supporting base; a twelve-channel high-resolution crystal analyzer system with an array of precision x-ray slits; a manipulator system for a twelve scintillator x-ray detectors; a 4-D sample manipulator with cryo-cooling capability; and a robot-based sample exchange automation system. The mechanical design of the diffractometer as well as the test results of its positioning performance are presented in this paper.
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
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.
Fast Fourier transform telescope
International Nuclear Information System (INIS)
Tegmark, Max; Zaldarriaga, Matias
2009-01-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
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).
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.
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
Energy Technology Data Exchange (ETDEWEB)
Tamalonis, A. [Materials Development, Inc., Arlington Heights, Illinois 60004 (United States); Weber, J. K. R., E-mail: rweber@anl.gov; Alderman, O. L. G. [Materials Development, Inc., Arlington Heights, Illinois 60004 (United States); Argonne National Laboratory, Argonne, Illinois 60439 (United States); Neuefeind, J. C.; Carruth, J. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 (United States); Skinner, L. B. [Materials Development, Inc., Arlington Heights, Illinois 60004 (United States); Argonne National Laboratory, Argonne, Illinois 60439 (United States); Stony Brook University, Stony Brook, New York 11794 (United States); Benmore, C. J. [Argonne National Laboratory, Argonne, Illinois 60439 (United States)
2015-09-15
Five neutron collimator designs were constructed and tested at the nanoscale ordered materials diffractometer (NOMAD) instrument. Collimators were made from High Density PolyEthylene (HDPE) or 5% borated HDPE. In all cases, collimators improved the signal to background ratio and reduced detection of secondary scattering. In the Q-range 10-20 Å{sup −1}, signal to background ratio improved by factors of approximately 1.6 and 2.0 for 50 and 100 mm deep collimators, respectively. In the Q-range 40-50 Å{sup −1}, the improvement factors were 1.8 and 2.7. Secondary scattering as measured at Q ∼ 9.5 Å{sup −1} was significantly decreased when the collimators were installed.
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)
Use of a CCD-based area detection system of a fibre diffractometer
International Nuclear Information System (INIS)
Hanna, S.; Windle, A.H.
1995-01-01
We describe a new X-ray fibre diffractometer, consisting of a commercial X-ray sensitive video camera coupled to a conventional 3 goniometer in place of a more traditional single-point detector. The active element of the video camera is a charge-coupled device (CCD). Diffraction images, obtained at various goniometer settings, are transformed into reciprocal space, and combined to give a complete section through the origin and parallel to the symmetry axis of cylindrically averaged reciprocal space. A greater density of measurements is needed in the vicinity of the reciprocal fibre axis in order to avoid information loss due to the curvature of the Ewald sphere. The pros and cons of using CCD's as X-ray detectors are discussed and sample results from polymer fibers are shown. 17 refs., 5 figs
The new powder diffractometer D1B of the Institut Laue Langevin
Puente Orench, I.; Clergeau, J. F.; Martínez, S.; Olmos, M.; Fabelo, O.; Campo, J.
2014-11-01
D1B is a medium resolution high flux powder diffractometer located at the Institut Laue Langevin, ILL. D1B a suitable instrument for studying a large variety of polycrystalline materials. D1B runs since 1998 as a CRG (collaborating research group) instrument, being exploited by the CNRS (Centre National de la Recherche Scientifique, France) and CSIC (Consejo Superior de Investigaciones Cientificas, Spain). In 2008 the Spanish CRG started an updating program which included a new detector and a radial oscillating collimator (ROC). The detector, which has a sensitive height of 100mm, covers an angular range of 128°. Its 1280 gold wires provide a neutron detection point every 0.1°. The ROC is made of 198 gadolinium- based absorbing collimation blades, regular placed every 0.67°. Here the present characteristics of D1B are reviewed and the different experimental performances will be presented.
Sensitivity of triple-crystal X-ray diffractometers to microdefects in silicon
International Nuclear Information System (INIS)
Molodkin, V.B.; Olikhovskii, S.I.; Len, E.G.; Kislovskii, E.N.; Kladko, V.P.; Reshetnyk, O.V.; Vladimirova, T.P.; Sheludchenko, B.V.
2009-01-01
The dynamical theory, which describes both diffraction profiles and reciprocal space maps measured from imperfect crystals with account for instrumental factors of triple-crystal diffractometer (TCD), has been developed for adequate quantitative characterization of microdefects. Analytical expressions for coherent and diffuse scattering (DS) intensities measured by TCD in the Bragg diffraction geometry have been derived by using the generalized statistical dynamical theory of X-ray scattering in real single crystals with randomly distributed defects. The DS intensity distributions from single crystals containing clusters and dislocation loops have been described by explicit analytical expressions. Particularly, these expressions take into account anisotropy of displacement fields around defects with discrete orientations. Characteristics of microdefect structures in silicon single crystals grown by Czochralsky- and float-zone methods have been determined by analyzing the measured TCD profiles and reciprocal space maps. The sensitivities of reciprocal space maps and diffraction profiles to defect characteristics have been compared. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Measurement of the neutron intensity data using the HANARO four circle diffractometer
International Nuclear Information System (INIS)
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
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
On fractional Fourier transform moments
Alieva, T.; Bastiaans, M.J.
2000-01-01
Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
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.
Better powder diffractometers. II—Optimal choice of U, V and W
Cussen, L. D.
2007-12-01
This article presents a technique for optimising constant wavelength (CW) neutron powder diffractometers (NPDs) using conventional nonlinear least squares methods. This is believed to be the first such design optimisation for a neutron spectrometer. The validity of this approach and discussion should extend beyond the Gaussian element approximation used and also to instruments using different radiation, such as X-rays. This approach could later be extended to include vertical and perhaps horizontal focusing monochromators and probably other types of instruments such as three axis spectrometers. It is hoped that this approach will help in comparisons of CW and time-of-flight (TOF) instruments. Recent work showed that many different beam element combinations can give identical resolution on CW NPDs and presented a procedure to find these combinations and also find an "optimum" choice of detector collimation. Those results enable the previous redundancy in the description of instrument performance to be removed and permit a least squares optimisation of design. New inputs are needed and are identified as the sample plane spacing ( dS) of interest in the measurement. The optimisation requires a "quality factor", QPD, chosen here to be minimising the worst Bragg peak separation ability over some measurement range ( dS) while maintaining intensity. Any other QPD desired could be substituted. It is argued that high resolution and high intensity powder diffractometers (HRPDs and HIPDs) should have similar designs adjusted by a single scaling factor. Simulated comparisons are described suggesting significant improvements in performance for CW HIPDs. Optimisation with unchanged wavelength suggests improvements by factors of about 2 for HRPDs and 25 for HIPDs. A recently quantified design trade-off between the maximum line intensity possible and the degree of variation of angular resolution over the scattering angle range leads to efficiency gains at short wavelengths. This
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...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
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
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Automated IBM PC/XT/AT based measurement and control system for the DRON-3M X-ray diffractometer
International Nuclear Information System (INIS)
Tulaev, A.B.
1989-01-01
An automated IBM PC/XT/AT based measurement and control system for the DRON-3M X-ray diffractometer is decribed. The system permits carrying out of real time diffractometer control automatic X-spectra measurement and data acquisition, as well as experimental information computing and representation. The electronic of the system consists of a CAMAC crate with analog and power modules, and a control and measurement organization module, performed as a single bord in the standard of PC electronics. The system provides X-spectra acquisition with volume up to 4K in the angle range from 100 to 160 degrees with a resolution of 0.01 degree, a dead time less than 1mks and an exposition time from tenths of a second to dozens of minutes. 3 refs.; 5 figs
International Nuclear Information System (INIS)
Tanaka, Ichiro; Hosoya, Takaaki; Kusaka, Katsuhiro; Niimura, Nobuo; Yamada, Taro; Tomoyori, Katsuaki; Yokoyama, Takeshi; Ohhara, Takashi; Kurihara, Kazuo; Ohnishi, Yuki; Yoshimura, Masashi; Kawamura, Takahiro; Oosumi, Takashi; Uchida, Hirohisa; Suzuki, Eiichiro; Kashiwagi, Tatsuki; Miyamoto, Akio; Furukawa, Yasunori
2011-01-01
IBARAKI Biological Crystal Diffractometer (iBIX), a new neutron diffractometer for protein crystallography, was constructed as a next generation neutron source in J-PARC (Japan Proton Accelerator Research Complex) and it has begun operation since December 2008. During a fiscal year of 2009, 14 detector units, the basic part of data reduction software and an equipment of cryostream cooler to 20K became available, and measurements and structural analysis of an organic standard crystal were succeeded. Since 120kW accelerator operation in December 2009, neutron measurements for structural analysis of several crystals of inorganic, organic compounds and proteins including industrial users' have been carried out and some of these data sets have been analyzed to the degree that positions of the hydrogen and the hydrated water could be identified. (author)
International Nuclear Information System (INIS)
Waldecker, Lutz; Bertoni, Roman; Ernstorfer, Ralph
2015-01-01
We present the design and implementation of a highly compact femtosecond electron diffractometer working at electron energies up to 100 keV. We use a multi-body particle tracing code to simulate electron bunch propagation through the setup and to calculate pulse durations at the sample position. Our simulations show that electron bunches containing few thousands of electrons per bunch are only weakly broadened by space-charge effects and their pulse duration is thus close to the one of a single-electron wavepacket. With our compact setup, we can create electron bunches containing up to 5000 electrons with a pulse duration below 100 fs on the sample. We use the diffractometer to track the energy transfer from photoexcited electrons to the lattice in a thin film of titanium. This process takes place on the timescale of few-hundred femtoseconds and a fully equilibrated state is reached within 1 ps
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)
The time-of-flight small-angle neutron diffractometer (SAD) at IPNS, Argonne National Laboratory
International Nuclear Information System (INIS)
Thiyagarajan, P.; Epperson, J.E.; Crawford, R.K.; Carpenter, J.M.; Klippert, T.E.; Wozniak, D.G.
1997-01-01
The design, development and performance of the time-of-flight (TOF) small-angle diffractometer (SAD) at the Intense Pulsed Neutron Source (IPNS) at Argonne National Laboratory are described. Similar TOF-SANS instruments are in operation at the pulsed neutron sources at Los Alamos National Laboratory, USA, at Rutherford Appleton Laboratory, England, and at KEK, Japan. These instruments have an advantage by comparison with their steady-state counterparts in that a relatively wide range of momentum transfer (q) can be monitored in a single experiment without the need to alter the collimation or the sample-to-detector distance. This feature makes SANS experiments easy and very effective for studying systems such as those undergoing phase transitions under different conditions, samples that cannot be easily reproduced for repetitive experiments, and systems under high temperature, pressure or shear. Three standard samples are used to demonstrate that the quality of the SANS data from SAD is comparable with those from other established steady-state SANS facilities. Two examples are given to illustrate that the wide q region accessible in a single measurement at SAD is very effective for following the time-dependent phase transitions in paraffins and temperature- and pressure-dependent phase transitions in model biomembranes. (orig.)
High-Resolution Powder Diffractometer HRPT for Thermal Neutrons at SINQ
International Nuclear Information System (INIS)
Fischer, P.; Koch, M.; Koennecke, M.; Pomjakushin, V.; Schefer, J.; Schlumpf, N.
1999-01-01
The new neutron powder diffractometer at the Swiss continuous spallation neutron source SINQ is designed as a flexible instrument for high resolution [best values δd/d: ( -3 with d = lattice spacing in the high resolution or high intensity modes, respectively]. It uses large scattering angles 2Θ M = 120 deg or 90 deg of the monochromator, a 28 cm high, vertically focusing wafer type Ge(hkk) monochromator and a position-sensitive 3 He detector(3.6 bar) produced by Cerca at Romans, France. It has 1600 (25x64) detectors with an angular separation of 0.1 deg and includes modern electronics developed by E. Berruyer, Cerca and PSI. The SICS software of PSI controls the instrument with a server running on an unix workstation and clients written in Java through the TCP/IP network. The design principles and first experiences are presented. The interdisciplinary applications of HRPT will permit high-resolution refinement of chemical and magnetic structures as well as phase analysis including the detection of defects and internal microstrain. In particular real-time investigations of chemical or structural changes and of magnetic phase transitions in crystalline, quasicrystalline, amorphous and liquid samples including technically interesting new materials are possible. (author)
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.
Design of a microcomputer-based X-ray diffractometer controller
International Nuclear Information System (INIS)
Naval, P.C. Jr.
1988-01-01
This work describes the design of an Apple II-based X-ray diffractometer controller capable of acquiring and analyzing X-ray powder diffraction data. The controller's interrupt-drivers hardware includes an on-based scaler for counting X-ray pulses, a closed-loop stepper motor driver for Philips PW 1050 Vertical Goniometer, and circuits for present data collection and safety. ACQUIRE - data acquisition program for the controller coordinates its various devices so that it can perform sample scanning in any of the following modes: continuous, present tome or present count scanning. This program watches over the scanning process and will try to correct any error it detects. Any fault monitored is logged on disk. The collected diffraction data are stored on disk together with its data acquisition parameters and may be transported to another computer. Data analysis is done by ANALYZE a program that operates on the output file generated by ACQUIRE. Its 15 single-keystroke commands permit panning and zooming of the sample's diffractogram, data smoothing, data peak search, peak report generation, and digital plotting. Data smoothing uses a third-degree Savitzky-Golay Convoluting Filter of user defined width. For peak detection, the peak search algorithm examines the diffractograms second derivative for any Gaussian resemblance and checks the peaks' area for statistical significance. The hard copy plot is available from any on-line digital plotted supporting EPSON's Mode D Plotter Commands. (Author). 15 refs. Appendixes p. 85-163
In situ surface/interface x-ray diffractometer for oxide molecular beam epitaxy
International Nuclear Information System (INIS)
Lee, J. H.; Freeland, J. W.; Hong, Hawoong; Tung, I. C.; Chang, S.-H.; Bhattacharya, A.; Fong, D. D.
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
International Nuclear Information System (INIS)
Benafan, O.; Padula, S. A.; Skorpenske, H. D.; An, K.; Vaidyanathan, R.
2014-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Benafan, O., E-mail: othmane.benafan@nasa.gov [NASA Glenn Research Center, Structures and Materials Division, Cleveland, Ohio 44135 (United States); Advanced Materials Processing and Analysis Center, Materials Science and Engineering Department, University of Central Florida, Orlando, Florida 32816 (United States); Padula, S. A. [NASA Glenn Research Center, Structures and Materials Division, Cleveland, Ohio 44135 (United States); Skorpenske, H. D.; An, K. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); Vaidyanathan, R. [Advanced Materials Processing and Analysis Center, Materials Science and Engineering Department, University of Central Florida, Orlando, Florida 32816 (United States)
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{sup ®} 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.
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)
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.
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
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.
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.
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.
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...
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)
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...
Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.
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
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
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)
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.
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.
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.
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.
International Nuclear Information System (INIS)
Andersen, Ken H.; Marero, David Martin y; Barlow, Michael J.
2001-01-01
OSIRIS combines a long-wavelength powder diffractometer with a polarisation analysis backscattering spectrometer. The diffractometer can access wavelengths up to 70 A with a resolution of better than 1% Δd/d. The very high counting-rate at shorter wavelengths is ideal for in-situ, real-time and parametric experiments. The spectroscopy section incorporates an array of graphite crystals arranged in near-backscattering to give a high counting rate with 25 μeV energy resolution. The incident beam is polarised using a supermirror bender and the scattered beam is polarisation-analysed by a 3 He spin-filter in the process of being constructed. The spin-filter system consists of a fibre laser, a peristaltic pump and a wide-angle banana-shaped quartz cell in a continuous-flow setup. The scattered beam passes twice through the spin-filter cell, thus doubling the optical path length in the cell. The aim is to achieve 70% nuclear polarisation with no variation in time. (author)
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)
Energy Technology Data Exchange (ETDEWEB)
Park, Yang-Soon; Han, Sun-Ho; Kim, Jong-Goo; Jee, Kwang-Yong; Kim, Won-Ho [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2006-10-15
An X-ray diffractometer for spatially resolved X-ray diffraction measurements was developed to identify phase in the narrow (micron-scaled) region of high burn-up fuels and some nuclear materials. The micro-SRD was composed of an X-ray microbeam alignment system and a sample micro translation system instead of a normal slit and a fixed sample stage in a commercial XRD. The X-ray microbeam alignment system was fabricated with a microbeam concentrator having two Ni deposited mirrors, a vertical positioner, and a tilt table for the generation of a concentrated microbeam. The sample micro translation system was made with a sample holder and a horizontal translator, allowing movement of a specimen at 5 {mu}m steps. The angular intensity profile of the microbeam generated through a concentrator was symmetric and not distorted. The size of the microbeam was 4,000 x 20{mu}m and the spatial resolution of the beam was 47 {mu}m at the sample position. When the diffraction peaks were measured for a UO{sub 2} pellet specimen by this system, the reproducibility (2{theta} = {+-}0.01 .deg.) of the peaks was as good as a conventional X-ray diffractometer. For the cross section of oxidized titanium metal, not only TiO{sub 2} in an outer layer but also TiO near an oxide-metal interface was observed.
Properties of the distributional finite Fourier transform
Carmichael, Richard D.
2016-01-01
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
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 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
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..
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
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.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
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)
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...
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
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
A simple approach to Fourier aliasing
International Nuclear Information System (INIS)
Foadi, James
2007-01-01
In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and structured, introductions to the topic, commonly met in advanced, specialized books
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
Energy Technology Data Exchange (ETDEWEB)
Shaw, D [Varian Ltd., Walton (UK)
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.
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-06-01
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.
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
On the inverse windowed Fourier transform
Rebollo Neira, Laura; Fernández Rubio, Juan Antonio
1999-01-01
The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.; Boashash, B.
2003-01-01
We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept
The fractional Fourier transform and applications
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
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
International Nuclear Information System (INIS)
Da Silva, M A F M; Sosman, L P; Yokaichiya, F; Henry, P F; Bordallo, H N; Mazzocchi, V L; Parente, C B R; Mestnik-Filho, J
2012-01-01
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 of such systems are the spinel compounds doped with Cr 3+ , in which the physical the properties are related to the insertion of punctual defects in the crystalline structure. The purpose of our work is two fold. First, we compare the luminescence of the MgGa 2 O 4 -Ga 2 O 3 system with the single phase Ga 2 O 3 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 (São Paulo, Brazil). In the configuration chosen, Aurora shows an improved resolution, which is related to the design of its silicon focusing monochromator.
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.
Energy Technology Data Exchange (ETDEWEB)
Katsuya, Yoshio; Tanaka, Masahiko [Synchrotron X-ray Station at SPring-8, National Institute for Materials Science (NIMS), 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Song, Chulho [Synchrotron X-ray Station at SPring-8, National Institute for Materials Science (NIMS), 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Global Research Center for Environment and Energy based Nanomaterials Science (GREEN), Lithium Air Battery Specially Promoted Research Team, NIMS, 1-1 Namiki, Tsukuba, Ibaraki 305-0044 (Japan); Ito, Kimihiko; Kubo, Yoshimi [Global Research Center for Environment and Energy based Nanomaterials Science (GREEN), Lithium Air Battery Specially Promoted Research Team, NIMS, 1-1 Namiki, Tsukuba, Ibaraki 305-0044 (Japan); Sakata, Osami, E-mail: SAKATA.Osami@nims.go.jp [Synchrotron X-ray Station at SPring-8, National Institute for Materials Science (NIMS), 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Global Research Center for Environment and Energy based Nanomaterials Science (GREEN), Lithium Air Battery Specially Promoted Research Team, NIMS, 1-1 Namiki, Tsukuba, Ibaraki 305-0044 (Japan); Synchrotron X-ray Group, Quantum Beam Unit, NIMS, 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan)
2016-01-15
An X-ray powder diffractometer has been developed for a time-resolved measurement without the requirement of a scattering angle (2θ) scan. Six one-dimensional detector modules are asymmetrically arranged in a vertical line at a designed distance of 286.5 mm. A detector module actually covers a diffraction angle of about 12° with an angular resolution of 0.01°. A diffracted intensity pattern is simultaneously recorded in a 2θ angular range from 1.63° to 74.37° in a “one shot” measurement. We tested the performance of the diffractometer with reference CeO{sub 2} powders and demonstrated diffraction measurements from an operating lithium-air battery.
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)
International Nuclear Information System (INIS)
Petrun'kin, S.P.; Garavina, E.V.; Trostin, V.N.
1995-01-01
A container (cell) and a temperature-control system have been designed enabling one to carry out x-ray diffraction study of liquid samples both at a fixed temperature and within a certain temperature range using a commercial DRON-UMl x-ray diffractometer. Special features of the cell and the materials used for it allow one to study both chemically inert and corrosive liquids
Replica Fourier Transform: Properties and applications
International Nuclear Information System (INIS)
Crisanti, A.; De Dominicis, C.
2015-01-01
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
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.
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
New focus on Fourier optics techniques
Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.
2004-01-01
We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
On the Scaled Fractional Fourier Transformation Operator
International Nuclear Information System (INIS)
Hong-Yi, Fan; Li-Yun, Hu
2008-01-01
Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched
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...
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
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...
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)
Direct fourier method reconstruction based on unequally spaced fast fourier transform
International Nuclear Information System (INIS)
Wu Xiaofeng; Zhao Ming; Liu Li
2003-01-01
First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)
Fourier optical cryptosystem using complex spatial modulation
International Nuclear Information System (INIS)
Sarkadi, T; Koppa, P
2014-01-01
Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Projective Fourier duality and Weyl quantization
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs
Fourier duality as a quantization principle
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs
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...
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
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
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.
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.
Fourier analysis in several complex variables
Ehrenpreis, Leon
2006-01-01
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh
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
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.
Kohara, S; Kashihara, Y; Matsumoto, N; Umesaki, N; Sakai, I
2001-01-01
A horizontal two-axis diffractometer for glasses and liquids, installed at SPring-8 bending magnet beamline BL04B2, operated at 8 GeV electron energy, is described. Photon energies of 37.8 and 61.7 keV were obtained using a bent Si (1 1 1) crystal and a bent Si (2 2 0) crystal, respectively. The instrument has been successfully applied to measure diffraction spectra of vitreous SiO sub 2 in transmission geometry up to scattering vector Q=36 A sup - sup 1 , and measured total structure factor S(Q) was well reproduced by reverse Monte Carlo modelling.
International Nuclear Information System (INIS)
Kohara, Shinji; Suzuya, Kentaro; Kashihara, Yasuharu; Matsumoto, Norimasa; Umesaki, Norimasa; Sakai, Ichiro
2001-01-01
A horizontal two-axis diffractometer for glasses and liquids, installed at SPring-8 bending magnet beamline BL04B2, operated at 8 GeV electron energy, is described. Photon energies of 37.8 and 61.7 keV were obtained using a bent Si (1 1 1) crystal and a bent Si (2 2 0) crystal, respectively. The instrument has been successfully applied to measure diffraction spectra of vitreous SiO 2 in transmission geometry up to scattering vector Q=36 A -1 , and measured total structure factor S(Q) was well reproduced by reverse Monte Carlo modelling
DEFF Research Database (Denmark)
Shen, Yanbin; Pedersen, Erik Ejler; Christensen, Mogens
2014-01-01
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...... 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)....
DEFF Research Database (Denmark)
Christensen, Finn Erland; Hornstrup, Allan; Schnopper, H. W.
1988-01-01
methods is that they are bandwidth-limited. A crucial point in the analysis of data is, therefore, to specify accurately the wavelength bandwidth limitation and to determine the surface autocorrelation function within this bandwidth. The authors present a number of scattering measurements obtained using...... a triple-axis perfect-crystal X-ray diffractometer and the results of an autocorrelation function analysis. Furthermore, they present some measurements of integrated reflectivity, which they believe provide evidence for microroughness in the range from a few angstroms to tens of microns...
International Nuclear Information System (INIS)
Hjelm, R.P. Jr.; Seeger, P.A.
1992-01-01
The implementation of small-angle (Low-momentum transfer) neutron scattering at pulsed spallation sources, using time of flight methods, has meant the introduction of some new ideas in instrument design, data acquisition, data reduction and computer management of the experiment and the data. Here we recount some of the salient aspects of solutions for implementing time of fight small-angle neutron scattering instruments at pulsed sources, as realized on the Low-Q Diffractometer, LQD, at Los Alamos. We consider, fortlier, some of the problems that are yet to be solved, and take a short excursion into the future of SANS instrumentation at pulsed sources
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,
Pi, Fourier Transform and Ludolph van Ceulen
Vajta, Miklos
2000-01-01
The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as
Fourier transform infrared spectrometery: an undergraduate experiment
International Nuclear Information System (INIS)
Lerner, L
2016-01-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory. (paper)
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.
2001-01-01
The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution
The Fourier transform of tubular densities
Prior, C B; Goriely, A
2012-01-01
molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
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...
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...
The Fourier modal method for aperiodic structures
Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.
2010-01-01
This paper extends the area of application of the Fourier modal method from periodic structures to non-periodic ones illuminated under arbitrary angles. This is achieved by placing perfectly matched layers at the lateral boundaries and reformulating the problem in terms of a contrast field.
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....
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
1999-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we
Fractional-Fourier-domain weighted Wigner distribution
Stankovic, L.; Alieva, T.; Bastiaans, M.J.
2001-01-01
A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the
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.
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
Automatic Fourier transform and self-Fourier beams due to parabolic potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2015-12-15
We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.
(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
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 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)
Multichannel Dynamic Fourier-Transform IR Spectrometer
Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.
2017-09-01
A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.
Discrete Fourier transform in nanostructures using scattering
International Nuclear Information System (INIS)
Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.
2004-01-01
In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed
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
2018-07-01
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.
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)
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-09-01
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 covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
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....
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 resampling: Theory and application
International Nuclear Information System (INIS)
Hawkins, W.G.
1996-01-01
One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)
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.
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...
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
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",…
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
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.
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.
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.
Fourier optics treatment of classical relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2006-08-15
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
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,
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 ...
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.
Noise figure of amplified dispersive Fourier transformation
International Nuclear Information System (INIS)
Goda, Keisuke; Jalali, Bahram
2010-01-01
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
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.
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Functional Fourier transforms and the loop equation
International Nuclear Information System (INIS)
Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.
1986-01-01
The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables
Fourier transform spectroscopy of six stars
Energy Technology Data Exchange (ETDEWEB)
Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia
1981-01-01
This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.
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-transforming with quantum annealers
Directory of Open Access Journals (Sweden)
Itay eHen
2014-07-01
Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.
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.
Fourier transform ion cyclotron resonance mass spectrometry
Marshall, Alan G.
1998-06-01
As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.
Approximate modal analysis using Fourier decomposition
International Nuclear Information System (INIS)
Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana
2010-01-01
The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.
Fourier transform inequalities for phylogenetic trees.
Matsen, Frederick A
2009-01-01
Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.
The Fourier transform of tubular densities
International Nuclear Information System (INIS)
Prior, C B; Goriely, A
2012-01-01
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)
Fourier transform zero field NMR and NQR
International Nuclear Information System (INIS)
Zax, D.B.
1985-01-01
In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI
Resolution optimization with irregularly sampled Fourier data
International Nuclear Information System (INIS)
Ferrara, Matthew; Parker, Jason T; Cheney, Margaret
2013-01-01
Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer–Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications. (paper)
Fourier transform spectra of quantum dots
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
On localization for double Fourier series
Goffman, Casper; Waterman, Daniel
1978-01-01
The localization theorems for Fourier series of functions of a single variable are classical and easy to prove. The situation is different for Fourier series of functions of several variables, even if one restricts consideration to rectangular, in particular square, partial sums. We show that the answer to the problem can be obtained by considering the notion of generalized bounded variation, which we introduced. Given a nondecreasing sequence {λn} of positive numbers such that Σ 1/λn diverges, a function g defined on an interval I of R1 is said to be of Λ-bounded variation (ΛBV) if Σ|g(an) — g(bn)|/λn converges for every sequence of nonoverlapping intervals (an, bn) [unk]I. If λn = n, we say that g is of harmonic bounded variation (HBV). The definition suitably modified can be extended to functions of several variables. We show that in the case of two variables the localization principle holds for rectangular partial sums if ΛBV = HBV, and that if ΛBV is not contained in HBV, then the localization principle does not hold for ΛBV even in the case of square partial sums. PMID:16592492
The prosaic Laplace and Fourier transform
International Nuclear Information System (INIS)
Smith, G.A.
1995-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics
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)
Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.
1997-01-01
Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be
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
Fourier rebinning algorithm for inverse geometry CT.
Mazin, Samuel R; Pele, Norbert J
2008-11-01
Inverse geometry computed tomography (IGCT) is a new type of volumetric CT geometry that employs a large array of x-ray sources opposite a smaller detector array. Volumetric coverage and high isotropic resolution produce very large data sets and therefore require a computationally efficient three-dimensional reconstruction algorithm. The purpose of this work was to adapt and evaluate a fast algorithm based on Defrise's Fourier rebinning (FORE), originally developed for positron emission tomography. The results were compared with the average of FDK reconstructions from each source row. The FORE algorithm is an order of magnitude faster than the FDK-type method for the case of 11 source rows. In the center of the field-of-view both algorithms exhibited the same resolution and noise performance. FORE exhibited some resolution loss (and less noise) in the periphery of the field-of-view. FORE appears to be a fast and reasonably accurate reconstruction method for IGCT.
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
Fractional Fourier transform for confluent hypergeometric beams
International Nuclear Information System (INIS)
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-01-01
Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.
Rotational Fourier tracking of diffusing polygons.
Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G
2011-11-01
We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.
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.
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.)
Reducing Approximation Error in the Fourier Flexible Functional Form
Directory of Open Access Journals (Sweden)
Tristan D. Skolrud
2017-12-01
Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
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.
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)
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)
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
Energy Technology Data Exchange (ETDEWEB)
Ayala P, G F [Instituto Nacional de Investigaciones Nucleares, Mexico City (Mexico)
1994-12-31
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).
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 ...
Fourier transformations for difference analogs of the harmonic oscillator
International Nuclear Information System (INIS)
Askey, R.; Atakishiyev, N.M.
1995-01-01
The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs
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
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.
Time-of-flight Fourier spectrometry of UCN
International Nuclear Information System (INIS)
Kulin, G.V.; Frank, A.I.; Goryunov, S.V.; Kustov, D.V.; Geltenbort, P.; Jentshel, M.; Strepetov, A.N.; Bushuev, V.A.
2014-01-01
The results of preliminary experiments on TOF Fourier UCN spectrometry are presented. The description of the new Fourier spectrometer that may be used for the measurement of the UCN spectra arising from diffraction by a moving grating is given. The results of preliminary experiments and Monte Carlo calculations give reason to hope for the success of the planned experiment.
Fourier path-integral Monte Carlo methods: Partial averaging
International Nuclear Information System (INIS)
Doll, J.D.; Coalson, R.D.; Freeman, D.L.
1985-01-01
Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects
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…
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
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
International Nuclear Information System (INIS)
Nogueira, Pedro H F; Castro, Antonio S de
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)
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.
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)
First order deformations of the Fourier matrix
Energy Technology Data Exchange (ETDEWEB)
Banica, Teodor, E-mail: teo.banica@gmail.com [Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise (France)
2014-01-15
The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.
Three dimensional image reconstruction in the Fourier domain
International Nuclear Information System (INIS)
Stearns, C.W.; Chesler, D.A.; Brownell, G.L.
1987-01-01
Filtered backprojection reconstruction algorithms are based upon the relationship between the Fourier transform of the imaged object and the Fourier transforms of its projections. A new reconstruction algorithm has been developed which performs the image assembly operation in Fourier space, rather than in image space by backprojection. This represents a significant decrease in the number of operations required to assemble the image. The new Fourier domain algorithm has resolution comparable to the filtered backprojection algorithm, and, after correction by a pointwise multiplication, demonstrates proper recovery throughout image space. Although originally intended for three-dimensional imaging applications, the Fourier domain algorithm can also be developed for two-dimensional imaging applications such as planar positron imaging systems
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)
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...
Solution of 3-dimensional diffusion equation by finite Fourier transformation
International Nuclear Information System (INIS)
Krishnani, P.D.
1978-01-01
Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)
Fourier convergence analysis applied to neutron diffusion Eigenvalue problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2004-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge
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.
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)
The Scope Of Fourier Transform Infrared (FTIR)
Hirschfeld, T.
1981-10-01
Three auarters of a century after its inception, a generation after its advantages were recognized, and a decade after its first commercialization, FT-IR dominates the growth of the IR market, and reigns alone over its high performance end. What lies ahead for FT-IR now? On one hand, the boundary between it and the classical scanning spectrometers is becoming fuzzy, as gratings attempt to use as much of FT-IR's computer technology as they can handle, and smaller FT systems invade the medium cost instrument range. On the other hand, technology advances in IR detectors, non-Fourier interference devices, and the often announced tunable laser are at long last getting set to make serious inroads in the field (although not necessarily in the manner most of us expected). However, the dominance of FT-IR as the leading edge of IR spectroscopy seems assured for a good many years. The evolution of FT-IR will be dominated by demands not yet fully satisfied such as rapid sample turnover, better quantitation, automated interpretation, higher GC-IR sensitivity, improved LC-IR, and, above all else, reliability and ease of use. These developments will be based on multiple small advances in hardware, large advances in the way systems are put together, and the traditional yearly revolutionary advances of the computer industry. The big question in the field will, however, still be whether our ambition and our skill can continue to keep up with the advances of our tools. It will be fun.
Fourier transform based scalable image quality measure.
Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien
2012-08-01
We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.
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.
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.
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
The application and improvement of Fourier transform spectrometer experiment
Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning
2017-08-01
According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.
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 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...
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 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.
q-Generalization of the inverse Fourier transform
International Nuclear Information System (INIS)
Jauregui, M.; Tsallis, C.
2011-01-01
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.
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.)
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...
Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems
Leuschner, Matthias; Fritzen, Felix
2017-11-01
Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.
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.
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
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-01-01
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
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...
Error Analysis for Fourier Methods for Option Pricing
Hä ppö lä , Juho
2016-01-01
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
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)
Fourier-Based Transmit Beampattern Design Using MIMO Radar
Lipor, John; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting
The Fourier law in a momentum-conserving chain
Giardinà, C.; Kurchan, J.
2005-01-01
We introduce a family of models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases the Fourier law is verified in one dimension.
Innovative design method of automobile profile based on Fourier descriptor
Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei
2017-10-01
Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.
Fourier transform wavefront control with adaptive prediction of the atmosphere.
Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre
2007-09-01
Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.
Fourier analysis in dynamic non periodic phenomena in nuclear medicine
International Nuclear Information System (INIS)
Constantinesco, A.; Lallot, C.
1984-01-01
The success of Fourier analysis in assessing cardiac function has led us to investigate other possible uses of this technique. We show that phase analysis applied to dynamic non periodic activity changes gives useful parametric functional images. The phase image is comparable to a transit time image, the amplitude image is comparable to the maximum variations of activity and the mean image corresponds to a normalized sum of images. Exemples of this powerful application of Fourier analysis are discussed [fr
Simple optical setup implementation for digital Fourier transform holography
Energy Technology Data Exchange (ETDEWEB)
De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)
2011-01-01
In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.
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.
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)
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.
Elf, F; Artus, G R J; Roth, S
2002-01-01
The expected diffraction patterns of the new powder diffractometer SPODI, currently under construction at the FRM-II in Garching, will be smeared Debye-Scherrer rings as depicted by Monte Carlo (MC) simulations. To overcome this disadvantage, a concept based on the combination of MC simulations and empirical approximation methods is developed to reverse the smearing by deconvolution and then summing up along the rings, including corrections for different arc lengths, resulting in conventional one-dimensional diffraction patterns suitable for Rietveld-refinement programs without further processing. (orig.)
International Nuclear Information System (INIS)
Spaccavento, J.
1993-01-01
As a Department of Energy Teacher Research Associate at Los Alamos National Laboratory this past summer, the author was given the opportunity to exit the class-room and enter the world of intense scientific research for an eight week period. In this paper the author briefly describes the Manual Lujan Jr. Neutron Scattering Center at Los Alamos, then focuses specifically on the Low-Q Diffractometer which was the instrument he worked on. The author details one specific experimental technique namely open-quotes Contrast Variation,close quotes and closes by briefly presenting several other interesting applications of neutron scattering
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.
Electro-Optical Imaging Fourier-Transform Spectrometer
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
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.
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
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.
Screening retinal transplants with Fourier-domain OCT
Rao, Bin
2009-02-01
Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.
Fourier imaging of non-linear structure formation
International Nuclear Information System (INIS)
Brandbyge, Jacob; Hannestad, Steen
2017-01-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
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 imaging of non-linear structure formation
Energy Technology Data Exchange (ETDEWEB)
Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)
2017-04-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
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 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.
The Fourier U(2 Group and Separation of Discrete Variables
Directory of Open Access Journals (Sweden)
Kurt Bernardo Wolf
2011-06-01
Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.
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)
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.”
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.
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.
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.
Advantage of Fast Fourier Interpolation for laser modeling
International Nuclear Information System (INIS)
Epatko, I.V.; Serov, R.V.
2006-01-01
The abilities of a new algorithm: the 2-dimensional Fast Fourier Interpolation (FFI) with magnification factor (zoom) 2 n whose purpose is to improve the spatial resolution when necessary, are analyzed in details. FFI procedure is useful when diaphragm/aperture size is less than half of the current simulation scale. The computation noise due to FFI procedure is less than 10 -6 . The additional time for FFI is approximately equal to one Fast Fourier Transform execution time. For some applications using FFI procedure, the execution time decreases by a 10 4 factor compared with other laser simulation codes. (authors)
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
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
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
Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions
DEFF Research Database (Denmark)
Cleanthous, Galatia; Georgiadis, Athanasios; Nielsen, Morten
2018-01-01
A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operat......A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity...
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)....
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...
Connection between Fourier coefficient and Discretized Cartesian path integration
International Nuclear Information System (INIS)
Coalson, R.D.
1986-01-01
The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established
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.
Decay of the Fourier transform analytic and geometric aspects
Iosevich, Alex
2014-01-01
The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
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)
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.
Fiber-optic Sensor Demonstrator (FSD) integration with PROBA-2
Reutlinger, Arnd; Glier, Markus; Zuknik, Karl-Heinz; Hoffmann, Lars; Müller, Mathias; Rapp, Stephan; Kurvin, Charles; Ernst, Thomas; McKenzie, Iain; Karafolas, Nikos
2017-11-01
Modern telecommunication satellites can benefit from the features of fiber optic sensing wrt to mass savings, improved performance and lower costs. Within the course of a technology study, launched by the European Space Agency, a fiber optic sensing system has been designed and is to be tested on representative mockups of satellite sectors and environment.
FSD-HSO Optimization Algorithm for Closed Fringes Interferogram Demodulation
Directory of Open Access Journals (Sweden)
Ulises H. Rodriguez-Marmolejo
2016-01-01
Full Text Available Due to the physical nature of the interference phenomenon, extracting the phase of an interferogram is a known sinusoidal modulation problem. In order to solve this problem, a new hybrid mathematical optimization model for phase extraction is established. The combination of frequency guide sequential demodulation and harmony search optimization algorithms is used for demodulating closed fringes patterns in order to find the phase of interferogram applications. The proposed algorithm is tested in four sets of different synthetic interferograms, finding a range of average relative error in phase reconstructions of 0.14–0.39 rad. For reference, experimental results are compared with the genetic algorithm optimization technique, obtaining a reduction in the error up to 0.1448 rad. Finally, the proposed algorithm is compared with a very known demodulation algorithm, using a real interferogram, obtaining a relative error of 1.561 rad. Results are shown in patterns with complex fringes distribution.
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.
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
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 ...
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 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.
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.
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 ...
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 ...
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.
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
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
Beschrijving van een computerprogramma voor Fourier-analyse
Sannes, A.jr.
1975-01-01
During my practical work at the NIOZ Texel, from May until August 1974, I have been engaged with the Fourier- transformation. The direct motive was the problem of a guest-investigator who studied the regularity in the frequency of pulsations of the hearts of guillemots. A computerprogram that can
Power filtering of nth order in the fractional Fourier domain
International Nuclear Information System (INIS)
Alieva, Tatiana; Calvo, Maria Luisa; Bastiaans, Martin J.
2002-01-01
The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from intensity distributions only is proposed. The optical configuration for the experimental realization of the method is discussed. (author)
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
Prototypes and matrix relevance learning in complex fourier space
Straat, M.; Kaden, M.; Gay, M.; Villmann, T.; Lampe, Alexander; Seiffert, U.; Biehl, M.; Melchert, F.
2017-01-01
In this contribution, we consider the classification of time-series and similar functional data which can be represented in complex Fourier coefficient space. We apply versions of Learning Vector Quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger
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.
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.
SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design
Dool, T.C. van den; Kruizinga, B.; Braam, B.C.; Hamelinck, R.F.M.M.; Loix, N.; Loon, D. van; Dams, J.
2012-01-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme in 2022. JAXA leads the development
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.
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
The RC Circuit: An Approach with Fourier Transforms. Classroom Volume 21 Issue 11 November 2016 pp 1029-1042 ... But a lot of things, (including the complex impedanceitself, and some insight into complex analysis) can be understoodbetter if we use the FT approach to solve the differentialequations that come up in ...
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 ...
Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm
Catterall, S.; Karamov, S.
2001-01-01
We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.
Critical points of multidimensional random Fourier series: variance estimates
Nicolaescu, Liviu I.
2013-01-01
To any positive number $\\varepsilon$ and any nonnegative even Schwartz function $w:\\mathbb{R}\\to\\mathbb{R}$ we associate the random function $u^\\varepsilon$ on the $m$-torus $T^m_\\varepsilon:=\\mathbb{R}^m/(\\varepsilon^{-1}\\mathbb{Z})^m$ defined as the real part of the random Fourier series $$ \\sum_{\
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
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.
Fourier coefficientes computation in two variables, a distributional version
Carlos Manuel Ulate R.
2015-01-01
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.
Closed form fourier-based transmit beamforming for MIMO radar
Lipor, John J.; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform
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 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.)
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...
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...
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....
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...
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…
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…
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
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
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
Application of Fourier transforms for microwave radiometric inversions
Holmes, J. J.; Balanis, C. A.; Truman, W. M.
1975-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.
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.
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.
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
On frame properties for Fourier-like systems
DEFF Research Database (Denmark)
Christensen, Ole; Osgooei, Elnaz
2013-01-01
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...... 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-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.
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 ...
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-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.
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.
The Fourier transform for certain hyperkähler fourfolds
Shen, Mingmin
2016-01-01
Using a codimension-1 algebraic cycle obtained from the PoincarÃ© line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of HyperkÃ¤hler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.
Fourier acceleration of iterative processes in disordered systems
International Nuclear Information System (INIS)
Batrouni, G.G.; Hansen, A.
1988-01-01
Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria
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.
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.
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
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.
Some studies on Fourier analysis in students experiment
大崎, 正雄
2016-01-01
Here we give some troubles in teaching and their solutions occured during the Software Science Experiment course, which is opened for the 4th semester in the Department of Software Science. One of the subjects of this experiment course is Fourier analysis using MyPC. Some students are not familiar with calculating the integration of sinusoidal function, and also some need support for drawing graphs with MS Excel. Typical mistakes and their settlements are given.
Symmetrized neutron transport equation and the fast Fourier transform method
International Nuclear Information System (INIS)
Sinh, N.Q.; Kisynski, J.; Mika, J.
1978-01-01
The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations
An algorithm for the basis of the finite Fourier transform
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
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)
Optically compressed sensing by under sampling the polar Fourier plane
International Nuclear Information System (INIS)
Stern, A; Levi, O; Rivenson, Y
2010-01-01
In a previous work we presented a compressed imaging approach that uses a row of rotating sensors to capture indirectly polar strips of the Fourier transform of the image. Here we present further developments of this technique and present new results. The advantages of our technique, compared to other optically compressed imaging techniques, is that its optical implementation is relatively easy, it does not require complicate calibrations and that it can be implemented in near-real time.
Fast Fourier transformation results from gamma-ray burst profiles
Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.
1992-01-01
Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
Swinyard, Bruce; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.- P.; Bendo, G. J.; Ferlet, M.; Griffin, Matthew Jason; Lim, T. L.; Makiwa, G.
2014-01-01
The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of ∼450–1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a sp...
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-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. .
The Convergence Acceleration of Two-Dimensional Fourier Interpolation
Directory of Open Access Journals (Sweden)
Anry Nersessian
2008-07-01
Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.
Fourier and wavelet analysis of skin laser doppler flowmetry signals
Qi, Wei
2011-01-01
ObjectiveThis thesis examines the measurement of skin microvascular blood flows from Laser Doppler Flowmetry (LDF) signals. Both healthy subjects and those with features of the metabolic syndrome are studied using signal processing techniques such as the Fourier and Wavelet transforms. An aim of this study is to investigate whether change in blood flow at rest can be detected from the spectral content of the processed signals in the diferent subject groups. Additionally the effect of insulin ...
Ghost telescope and ghost Fourier telescope with thermal light
International Nuclear Information System (INIS)
Gong Wenlin; Han Shensheng
2011-01-01
As important observation tools, telescopes are very useful in remote observations. We report a proof-of-principle experimental demonstration of ghost telescope scheme and show that, by measuring the intensity correlation of two light fields and only changing the position of the detector in the reference path, ghost telescope and ghost Fourier telescope can be obtained even if a single-pixel detector is fixed in Fresnel region of the object. Differences between conventional telescope and ghost telescope are also discussed.
An OTDM-To-WDM Converter Using Optical Fourier Transformation
Khin Su Myat Min; Zaw Myo Lwin; Hla Myo Tun
2015-01-01
We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements ar...
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/