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.

Numerical Simulation of Anomalous Vortex Beams on Different Fractional Fourier Transform Planes

2014 ◽  
Vol 556-562 ◽  
pp. 3745-3748 ◽  
Author(s):  
Zhi Ping Dai ◽  
Zhen Feng Yang ◽  
Zhen Jun Yang ◽  
Zhao Guang Pang ◽  
Shu Min Zhang
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Fractional Order ◽  
Topological Charge ◽  
Fractional Fourier Transform ◽  
Analytical Expression ◽  
New Type ◽  
Vortex Beams ◽  
Beam Parameters

The properties of fractional Fourier transform of anomalous vortex beams are studied. A new type of analytical expression of fractional Fourier transform for anomolous vortex beams is obtained. The properties of anomolous vortex beams on different fractional Fourier transform planes with different parameters are illustrated. The results show that the anomolous vortex beams always has a doughnut profile, the distribution of intensity on different fractional Fourier transform planes highly depends on the fractional order and the beam parameters, such as the beam order and the topological charge.

Wavelet packets associated with linear canonical transform on spectrum

2021 ◽  
pp. 2150030
Author(s):  
M. Younus Bhat ◽  
Aamir H. Dar
Keyword(s):  
Fourier Transform ◽  
Multiresolution Analysis ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Integral Transforms ◽  
Wavelet Packets ◽  
Linear Canonical Transform ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Vector Valued

The linear canonical transform (LCT) provides a unified treatment of the generalized Fourier transforms in the sense that it is an embodiment of several well-known integral transforms including the Fourier transform, fractional Fourier transform, Fresnel transform. Using this fascinating property of LCT, we, in this paper, constructed associated wavelet packets. First, we construct wavelet packets corresponding to nonuniform Multiresolution analysis (MRA) associated with LCT and then those corresponding to vector-valued nonuniform MRA associated with LCT. We investigate their various properties by means of LCT.

scholarly journals Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials

2018 ◽  
Vol 9 ◽  
pp. 1828-1833 ◽  
Author(s):  
Daniela Dragoman
Keyword(s):  
Wave Function ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Berry Phase ◽  
Wave Functions ◽  
Electron Propagation ◽  
One Step ◽  
The Difference ◽  
Integrated Logic ◽  
The Fourier Transform

A tunable fractional Fourier transform of the quantum wave function of electrons satisfying either the Schrödinger or the Dirac equation can be implemented in an atomically thin material by a parabolic potential distribution applied on a direction transverse to that of electron propagation. The difference between the propagation lengths necessary to obtain a fractional Fourier transform of a given order in these two cases could be seen as a manifestation of the Berry phase. The Fourier transform of the electron wave function is a particular case of the fractional Fourier transform. If the input and output wave functions are discretized, this configuration implements in one step the discrete fractional Fourier transform, in particular the discrete Fourier transform, and thus can act as a coprocessor in integrated logic circuits.

Numerical Simulations of Fractional Fourier Transform of Hypergeometric-Gaussian Beam

2013 ◽  
Vol 765-767 ◽  
pp. 780-784 ◽  
Author(s):  
Zhen Feng Yang ◽  
Wen Dan Miao ◽  
Zhen Jun Yang ◽  
Shu Min Zhang
Keyword(s):  
Fourier Transform ◽  
Numerical Simulations ◽  
Gaussian Beam ◽  
Intensity Distribution ◽  
Fractional Fourier Transform ◽  
Focal Length ◽  
Beam Width ◽  
Laser Beams ◽  
New Type ◽  
Lens Focal Length

The fractional Fourier transform (FRFT) of a new type of laser beams called the hypergeometric-Gaussian beam (HyGGB) is investigated in detail. The analytical expression for the FRFT of a HyGGB is derived. The properties of a HyGGB in the FRFT plane with different parameters are illustrated. The results show that the intensity distribution of a HyGGB in the FRFT plane strongly depends on the fractional order, the lens focal length and the initial beam width.

scholarly journals Uncertainty principles invariant under the fractional Fourier transform

1991 ◽  
Vol 33 (2) ◽  
pp. 180-191 ◽  
Author(s):  
David Mustard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Intrinsic Property ◽  
Continuous Group ◽  
Uncertainty Principles ◽  
New Family ◽  
Special Cases ◽  
Fractional Fourier Transforms ◽  
The Fourier Transform

AbstractUncertainty principles like Heisenberg's assert an inequality obeyed by some measure of joint uncertainty associated with a function and its Fourier transform. The more groups under which that measure is invariant, the more that measure represents an intrinsic property of the underlying object represented by the given function. The Fourier transform is imbedded in a continuous group of operators, the fractional Fourier transforms, but the Heisenberg measure of overall spread turns out not to be invariant under that group. A new family is developed of measures that are invariant under the group of fractional Fourier transforms and that obey associated uncertainty principles. The first member corresponds to Heisenberg's measure but is generally smaller than his although equal to it in special cases.

Parameters Estimation and Waveform Reconstruction of Chirp Signal Based on FRFT

2014 ◽  
Vol 989-994 ◽  
pp. 3993-3996 ◽  
Author(s):  
Yan Jun Wu ◽  
Gang Fu ◽  
Fei Liu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Signal Reconstruction ◽  
Parameters Estimation ◽  
The Other ◽  
Fourier Domain ◽  
Chirp Signal ◽  
The Fourier Transform ◽  
Definition Of ◽  
Noisy Background

The fractional Fourier transform (FRFT) is a generalization of the Fourier transform. The article first introduces the definition of FRFT transformation; then analyzed FRFT Chirp signal based on this humble proposed restoration Chirp signal in a noisy background in two ways: one is based on parameter estimation, and the other is based on the scores Fourier domain filtering to achieve signal reconstruction; Finally, simulation verify the feasibility of the above analysis.

scholarly journals The scale of the Fourier transform: a point of view of the fractional Fourier transform

2017 ◽  
Vol 792 ◽  
pp. 012044
Author(s):  
C J Jimenez ◽  
J M Vilardy ◽  
S Salinas ◽  
L Mattos ◽  
C O Torres
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Point Of View ◽  
The Fourier Transform

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.

scholarly journals A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

2013 ◽  
Vol 23 (3) ◽  
pp. 685-695 ◽  
Author(s):  
Navdeep Goel ◽  
Kulbir Singh
Keyword(s):  
Fourier Transform ◽  
Quantum Mechanics ◽  
Fractional Fourier Transform ◽  
Integral Transform ◽  
Linear Canonical Transform ◽  
Product Theorem ◽  
Special Cases ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Representation Transformation

Abstract The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution and product theorem in the LCT domain derived by a representation transformation in quantum mechanics, which seems a convenient and concise method. It is compared with the existing convolution theorem for the LCT and is found to be a better and befitting proposition. Further, an application of filtering is presented by using the derived results.

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.

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