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Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms

JOURNAL OF OPTICS 2015年第2期17卷 025701-025701页

作者： Liu, Zhengjun Guo, Cheng Tan, Jiubin Wu, Qun Pan, Liqiang Liu, Shutian Harbin Inst Technol Dept Automat Test & Control Harbin 150001 Peoples R China Harbin Inst Technol Postdoctoral Mobile Stn Elect Sci & Technol Harbin 150001 Peoples R China Harbin Inst Technol Dept Phys Harbin 150001 Peoples R China Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Harbin Inst Technol Sch Comp Sci & Technol Harbin 150001 Peoples R China

For the iterative phase retrieval, multiple measured intensity images in output plane are only considered for accelerating the convergence. The amplitude and phase at the observed object plane of measurement system are unknown in this research. The observing system is composed of gyrator transform, in which several images are recorded by using several transform angles for the same input image. An amplitude-phase retrieval scheme is designed and tested. The numerical simulations have demonstrated that the amplitude and phase pattern within a very small error (less than 0.04 and 0.0005 for an 8-bit two-dimensional data) can be recovered after 1000 iterations.

关键词： phase retrieval multiple constraint planes abcd transforms

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Hyperbolic rotation of the Wigner distribution function

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APPLIED OPTICS 2015年第13期54卷 D8-D14页

作者： Gitin, A. V. Kalashnikov, M. P. Max Born Inst Nichtlineare Opt & Kurzzeitspect D-12489 Berlin Germany

The Wigner distribution function is a convenient way to describe image transformations in optical systems: spatial shearing, spatial frequency shearing, circular rotation, hyperbolic rotation, etc. The hyperbolic rotation can be represented as scaling of the Wigner distribution function with a separate scale factor for each axis direction. It is shown that if an optical system with positive lenses provides circular rotation of the WDF in the phase plane, with negative lenses it will provide hyperbolic rotation of the WDF function in this phase plane. (C) 2015 Optical Society of America

关键词： Paraxial wave optics abcd transforms Fractional Fourier transforms

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Propagation of Airy-related beams generated from flat-topped Gaussian beams through a chiral slab

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OPTICS AND LASERS IN ENGINEERING 2014年第1期52卷 13-18页

作者： Liu, Zhirong Zhao, Daomu Zhejiang Univ Dept Phys Hangzhou 310027 Zhejiang Peoples R China East China Jiaotong Univ Sch Basic Nanchang 330013 Peoples R China

We derived the analytical expression for the propagation of Airy-related beams generated from flattopped Gaussian beams through an abcd optical system, and use it to study the propagation of this type of beams through a chiral slab. Several influence factors, such as the optical beams order N and the chiral parameter gamma of the chiral medium, on the beam propagation properties both in near- and far-zones are discussed in detail. It is shown that the Airy tails of high order beams decay more quickly than those of low order beams in the chiral medium;the constructive interference effect between the LCP (left-circularly polarized) and RCP (right-circularly polarized) beams becomes more significant as the chiral parameter gamma increases;the LCP and RCP beams are not separated in the near-zone, while the two beams are obviously separated in the far-zone, and accordingly the interference peaks decrease as the propagation distance increases in the chiral slab. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： abcd transforms Chiral media Laser beam shaping Propagation

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Diffraction integral and propagation of Hermite-Gaussian modes in a linear refractive index medium

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2014年第5期31卷 914-919页

作者： Kovalev, A. A. Kotlyar, V. V. Zaskanov, S. G. Russian Acad Sci Image Proc Syst Inst Laser Measurements Lab Samara 443001 Russia

We derive a diffraction integral to describe the paraxial propagation of an optical beam in a graded index medium with the permittivity linearly varying with the transverse coordinate. This integral transformation is irreducible to the familiar abcd transformation. The form of the integral transformation suggests that, unlike a straight path in a homogeneous space, any paraxial optical beam will travel on a parabola bent toward the denser medium. By way of illustration, an explicit expression for the complex amplitude of a Hermite-Gaussian beam in the linear index medium is derived. (C) 2014 Optical Society of America

关键词： abcd transforms Fourier transforms Gaussian beams Light beams Light propagation Refractive index

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Two-dimensional nonseparable linear canonical transform: sampling theorem and unitary discretization

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2014年第12期31卷 2631-2641页

作者： Zhao, Liang Healy, John J. Sheridan, John T. Univ Coll Dublin Sch Elect Elect & Commun Engn Coll Engn & Architecture Commun & Optoelect Res CtrSFI Strateg Res Cluste Dublin 4 Ireland Maynooth Univ Dept Elect Engn Maynooth Kildare Ireland

The two-dimensional (2D) nonseparable linear canonical transform (NS-LCT) is a unitary, linear integral transform that relates the input and output monochromatic, paraxial scalar wave fields of optical systems characterized by a 4 x 4 ray tracing matrix. In addition to the obvious generalizations of the 1D LCT (which are referred to as separable), the 2D-NS-LCT can represent a variety of nonaxially symmetric optical systems including the gyrator transform and image rotation. Unlike the 1D LCT, the numerical approximation of the 2D-NS-LCT has not yet received extensive attention in the literature. In this paper, (1) we develop a sampling theorem for the general 2D-NS-LCT which generalizes previously published sampling theorems for the 1D case and (2) we determine which sampling rates may be chosen to ensure that the obvious discrete transform is unitary. (C) 2014 Optical Society of America

关键词： Numerical approximation and analysis abcd transforms Digital holography Discrete optical signal processing

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Signal reconstruction from partial information of discrete linear canonical transform

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OPTICAL ENGINEERING 2014年第3期53卷 1-7页

作者： Zhang, Feng Hu, Yang Tao, Ran Wang, Yue Beijing Inst Technol Dept Elect Engn Beijing 100081 Peoples R China

Signal reconstruction, especially for nonstationary signals, occurs in many applications such as optical astronomy, electron microscopy, and x-ray crystallography. As a potent tool to analyze the nonstationary signals, the linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. The reconstruction of a finite discrete-time signal from the partial information of its discrete LCT and some known samples under some restrictions is presented. The partial information about its discrete LCT that we have assumed to be available is the discrete LCT phase alone or the discrete LCT magnitude alone. Besides, a reconstruction example is provided to verify the effectiveness of the proposed algorithm. (C) The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

关键词： fractional Fourier transforms abcd transforms discrete optical signal processing

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Derivation and discrete implementation for analytic signal of linear canonical transform

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2013年第5期30卷 987-992页

作者： Pei, Soo-Chang Lai, Yun-Chiu Natl Taiwan Univ Grad Inst Commun Engn Taipei 10617 Taiwan

Analytic signal and Hilbert transform associated with linear canonical transform (LCT) have been developed [Opt. Commun. 281, 1468 (2008)]. However, the aforementioned paper has some drawbacks;for example, this kind of analytic signal cannot preserve the positive frequency bands of the original signal under LCT operations. In this paper, these drawbacks are pointed out, and a better definition for analytic signal associated with LCT is proposed. In addition, a discrete implementation for the analytic signal associated with discrete LCT is also provided. Several numerical examples, shown with both time and Wigner time-frequency domains, are demonstrated to illustrate the efficiency and accuracy of the proposed LCT analytic signal. (C) 2013 Optical Society of America

关键词： Fourier optics and signal processing Paraxial wave optics abcd transforms Spectrum analysis Fractional Fourier transforms

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Phase-space window and degrees of freedom of optical systems with multiple apertures

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2013年第4期30卷 682-690页

作者： Ozaktas, Haldun M. Oktem, Figen S. Bilkent Univ Dept Elect Engn TR-06800 Ankara Turkey Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its space-frequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss. (C) 2013 Optical Society of America

关键词： Fourier optics and signal processing abcd transforms Matrix methods in paraxial optics Apertures Fractional Fourier transforms Phase space in wave options

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Generation and propagation of an anomalous vortex beam

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OPTICS LETTERS 2013年第24期38卷 5418-5421页

作者： Yang, Yuanjie Dong, Yuan Zhao, Chengliang Cai, Yangjian Univ Elect Sci & Technol China Sch Astronaut & Aeronaut Chengdu 611731 Peoples R China Soochow Univ Sch Phys Sci & Technol Suzhou 215006 Peoples R China

A theoretical model is proposed to describe a novel vortex beam named anomalous vortex (AV) beam. Analytical propagation formula for the proposed beam passing through a paraxial abcd optical system is derived, and the propagation properties of such beam in free space are studied numerically. It is interesting to find that an AV beam will eventually become an elegant Laguerre-Gaussian beam in the far field (or in the focal plane) in free space. Furthermore, we report experimental generation of an AV beam and measure its propagation properties. Our experimental results are consistent with the theoretical predictions. (C) 2013 Optical Society of America

关键词： abcd transforms Propagation Optical vortices

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Differential commuting operator and closed-form eigenfunctions for linear canonical transforms

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2013年第10期30卷 2096-2110页

作者： Pei, Soo-Chang Liu, Chun-Lin Natl Taiwan Univ Dept Elect Engn Taipei 10617 Taiwan

The linear canonical transform (LCT) with a, b, c, d parameter plays an important role in quantum mechanics, optics, and signal processing. The eigenfunctions of the LCT are also important because they describe the self-imaging phenomenon in optical systems. However, the existing solutions for the eigenfunctions of the LCT are divided into many cases and they lack a systematic way to solve these eigenfunctions. In this paper, we find a linear, second-order, self-adjoint differential commuting operator that commutes with the LCT operator. Hence, the commuting operator and the LCT share the same eigenfunctions with different eigenvalues. The commuting operator is very general and simple when it is compared to the existing multiple-parameter differential equations. Then, the eigenfunctions can be derived systematically. The eigenvalues of the commuting operator have closed-form relationships with the eigenvalues of the LCT. We also simplify the eigenfunctions for vertical bar a + d vertical bar > 2 and a + d = +/- 2, b not equal 0 into the more compact closed form instead of the integral form. For vertical bar a + d vertical bar > 2, the eigenfunctions are related to the parabolic cylinder functions. (C) 2013 Optical Society of America

关键词： Fourier optics and signal processing Paraxial wave optics abcd transforms Fractional Fourier transforms

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