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Title: Holographic phase retrieval and reference design

Abstract

Here, a general mathematical framework and recovery algorithm is introduced 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 additionally 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.

Authors:
ORCiD logo [1];  [1];  [1];  [2];  [1]
  1. Stanford Univ., CA (United States)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1562461
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Inverse Problems
Additional Journal Information:
Journal Volume: 35; Journal Issue: 9; Journal ID: ISSN 0266-5611
Publisher:
IOPscience
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Barmherzig, David A., Sun, Ju, Li, Po-Nan, Lane, T. J., and Candès, Emmanuel J. Holographic phase retrieval and reference design. United States: N. p., 2019. Web. doi:10.1088/1361-6420/ab23d1.
Barmherzig, David A., Sun, Ju, Li, Po-Nan, Lane, T. J., & Candès, Emmanuel J. Holographic phase retrieval and reference design. United States. doi:10.1088/1361-6420/ab23d1.
Barmherzig, David A., Sun, Ju, Li, Po-Nan, Lane, T. J., and Candès, Emmanuel J. Tue . "Holographic phase retrieval and reference design". United States. doi:10.1088/1361-6420/ab23d1.
@article{osti_1562461,
title = {Holographic phase retrieval and reference design},
author = {Barmherzig, David A. and Sun, Ju and Li, Po-Nan and Lane, T. J. and Candès, Emmanuel J.},
abstractNote = {Here, a general mathematical framework and recovery algorithm is introduced 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 additionally 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.},
doi = {10.1088/1361-6420/ab23d1},
journal = {Inverse Problems},
number = 9,
volume = 35,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
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Works referenced in this record:

Reconstruction of an object from the modulus of its Fourier transform
journal, January 1978