Holographic phase retrieval and reference design

David A. Barmherzig; Ju Sun; Po Nan Li; T. J. Lane; Emmanuel J. Candès

doi:10.1088/1361-6420/ab23d1

Holographic phase retrieval and reference design

David A. Barmherzig, Ju Sun, Po Nan Li, T. J. Lane, Emmanuel J. Candès

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a 'reference' portion of the signal to be recovered via phase retrieval is a priori known from experimental design. A generic formula is also derived for the expected recovery error when the measurement data is corrupted by Poisson shot noise. This facilitates an optimization perspective towards reference design and analysis. We employ this optimization perspective towards quantifying the performance of various reference choices.

Original language	English (US)
Article number	094001
Journal	Inverse Problems
Volume	35
Issue number	9
DOIs	https://doi.org/10.1088/1361-6420/ab23d1
State	Published - Aug 20 2019
Externally published	Yes

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Publisher Copyright:
© 2019 IOP Publishing Ltd.

Keywords

coherent diffraction imaging
holography
optimization
phase retrieval

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AU - Sun, Ju

AU - Li, Po Nan

AU - Lane, T. J.

AU - Candès, Emmanuel J.

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AB - A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a 'reference' portion of the signal to be recovered via phase retrieval is a priori known from experimental design. A generic formula is also derived for the expected recovery error when the measurement data is corrupted by Poisson shot noise. This facilitates an optimization perspective towards reference design and analysis. We employ this optimization perspective towards quantifying the performance of various reference choices.

KW - coherent diffraction imaging

KW - holography

KW - optimization

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Holographic phase retrieval and reference design

Abstract

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Keywords

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