Topic

# Phase retrieval

About: Phase retrieval is a research topic. Over the lifetime, 5250 publications have been published within this topic receiving 112064 citations.

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TL;DR: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.

Abstract: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input-output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.

5,210 citations

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TL;DR: In this article, an algorithm is presented for the rapid solution of the phase of the complete wave function whose intensity in the diffraction and imaging planes of an imaging system are known.

5,197 citations

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TL;DR: This work demonstrates simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object and solves the twin‐image problem of in‐line holography and is capable of analysing data obtained using X‐ray microscope, electron microscopy, neutron microscopy or visible‐light microscopy.

Abstract: We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin-image problem of in-line holography and is capable of analysing data obtained using X-ray microscopy, electron microscopy, neutron microscopy or visible-light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non-iterative and computationally efficient method is applied to data obtained using an X-ray phase contrast ultramicroscope.

1,589 citations

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TL;DR: In this article, the propagation of phase and irradiance are derived, and a Green's function solution for the phase in terms of irradiance and perimeter phase values is given A measurement scheme is discussed, and the results of a numerical simulation are given Both circular and slit pupils are considered.

Abstract: Equations for the propagation of phase and irradiance are derived, and a Green’s function solution for the phase in terms of irradiance and perimeter phase values is given A measurement scheme is discussed, and the results of a numerical simulation are given Both circular and slit pupils are considered An appendix discusses the local validity of the parabolic-wave equation based on the factorized Helmholtz equation approach to the Rayleigh–Sommerfeld and Fresnel diffraction theories Expressions for the diffracted-wave field in the near-field region are given

1,310 citations

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TL;DR: It is shown that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques, and it is proved that the methodology is robust vis‐à‐vis additive noise.

Abstract: Suppose we wish to recover a signal \input amssym $\font\abc=cmmib10\def\bi#1{\hbox{\abc#1}} {\bi x} \in {\Bbb C}^n$ from m intensity measurements of the form , ; that is, from data in which phase information is missing. We prove that if the vectors are sampled independently and uniformly at random on the unit sphere, then the signal x can be recovered exactly (up to a global phase factor) by solving a convenient semidefinite program–-a trace-norm minimization problem; this holds with large probability provided that m is on the order of , and without any assumption about the signal whatsoever. This novel result demonstrates that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques. Finally, we also prove that our methodology is robust vis-a-vis additive noise. © 2012 Wiley Periodicals, Inc.

1,190 citations