scholarly journals Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings

1999 ◽  
Vol 55 (4) ◽  
pp. 659-676 ◽  
Author(s):  
Massimo Nespolo ◽  
Hiroshi Takeda ◽  
Toshihiro Kogure ◽  
Giovanni Ferraris
Keyword(s):  
Fourier Transform ◽  
Computer Program ◽  
Intensity Distribution ◽  
Structural Model ◽  
Reciprocal Space ◽  
Stacking Sequence ◽  
Periodic Intensity ◽  
The Fourier Transform

Following a preliminary revisitation of the nomenclatures in use for mica polytypes, the properties of the periodic intensity distribution (PID) function, which represents the Fourier transform of the stacking sequence, are analysed. On the basis of the relative rotations of neighbouring layers, mica polytypes are classified into three types; for each type, the PID exists in different subspaces of the reciprocal space. A revised procedure to compute the PID, in which further restrictions on the structural model orientation are introduced, is presented. A unifying terminology based upon the most common symbols used to describe mica polytypes (RTW, Z and TS) is derived; these symbols represent the geometrical basis for the computation of the PID. Results are presented for up to four layer polytypes and are compared with the reflection conditions derived by means of Zvyagin's functions. Both the PID values and the reflection conditions are expressed in suitable axial settings and compared with previous partial reports, revealing some errors in previous analyses. A computer program to compute PID from the stacking symbols is available.

Phase Analyse of Non-Vortical and Vortical Beams in Fractional Fourier Transform System

2014 ◽  
Vol 602-605 ◽  
pp. 3648-3651
Author(s):  
Zhi Ping Dai ◽  
Zhen Jun Yang
Keyword(s):  
Fourier Transform ◽  
Intensity Distribution ◽  
Topological Charge ◽  
Fractional Fourier Transform ◽  
Phase Distribution ◽  
Dark Region ◽  
Strong Intensity ◽  
Beam Parameters ◽  
The Fourier Transform ◽  
Phase Analyse

The phase of vortical beams is very different from that of non-vortical beams. The phase of non-vortical and vortical beams in fractional Fourier transform system is investigated by selecting different parameters of the anomalous vortical beam. It is found that although the intensity distribution is similar except nearby the Fourier transform plane for the non-vortical and the vortical beams, the phase distribution is very different even the beam parameters are the same except the topological charge. The different phases bring different intensity distributions especially at the Fourier transform plane, i.e the center of non-vortical beams is a very strong intensity peaks, however the center of vortical beams is a dark region.

scholarly journals 27. Intensity distribution across the Cygnus and Cassiopeia sources

1957 ◽  
Vol 4 ◽  
pp. 159-161
Author(s):  
R. C. Jennison
Keyword(s):  
Fourier Transform ◽  
Angular Distribution ◽  
Intensity Distribution ◽  
Phase Measurement ◽  
Frame Of Reference ◽  
Absolute Amplitude ◽  
A New Technique ◽  
The Fourier Transform ◽  
Aerial Systems ◽  
Phase Angles

Measurements of the angular distribution of intensity across the intense discrete sources in Cassiopeia and Cygnus have previously been handicapped by lack of knowledge of the phase of the Fourier transform at very long aerial spacings. The technical difficulties of measuring the phase of the transform and also of calibrating the absolute amplitude have been solved by a new technique involving three stations. This method enables the phase to be measured relative to a frame of reference within the source and obviates the need for retaining the phase angles accurately constant on the removal of one of the aerial systems to a new site. The phase measurement is not limited to observations of the central fringe, and useful measurements may be made on all the fringes contained within the aerial polar diagrams.

Fourier crystal diffractometry based on refractive optics

2013 ◽  
Vol 46 (5) ◽  
pp. 1475-1480 ◽  
Author(s):  
Petr Ershov ◽  
Sergey Kuznetsov ◽  
Irina Snigireva ◽  
Vyacheslav Yunkin ◽  
Alexander Goikhman ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Intensity Distribution ◽  
Focal Plane ◽  
Bragg Reflection ◽  
Si Substrate ◽  
X Ray ◽  
Spatial Intensity Distribution ◽  
Reflection Geometry ◽  
The Fourier Transform

X-ray refractive lenses are proposed as a Fourier transformer for high-resolution X-ray crystal diffraction. By employing refractive lenses the wave transmitted through the object converts into a spatial intensity distribution at its back focal plane according to the Fourier-transform relations. A theoretical consideration of the Fourier-transform technique is presented. Two types of samples were studied in Bragg reflection geometry: a grating made of strips of a thin SiO2film on an Si substrate and a grating made by profiling an Si crystal. Fourier patterns recorded at different angles along the rocking curves of the Si 111 Bragg reflection were analysed.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Sign in / Sign up

Export Citation Format

Share Document