Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

Journal Article · Mon Jun 01 04:00:00 EDT 1998 · Journal of the Optical Society of America, Part A: Optics and Image Science

DOI:https://doi.org/10.1364/JOSAA.15.001662· OSTI ID:604421

Miao, J; Sayre, D; Chapman, H N ^[1]

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1. Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States)

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2{times} in each dimension (i.e., oversampling by 4{times} for 2D and 8{times} for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. {copyright} 1998 Optical Society of America

• OSTI ID: 604421
• Journal Information: Journal of the Optical Society of America, Part A: Optics and Image Science, Journal Name: Journal of the Optical Society of America, Part A: Optics and Image Science Journal Issue: 6 Vol. 15; ISSN 0740-3232; ISSN JOAOD6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
CRYSTALLOGRAPHY
ELECTRON DIFFRACTION
FOURIER TRANSFORMATION
IMAGE PROCESSING
INFORMATION RETRIEVAL
NEUTRON DIFFRACTION
NOISE
PHASE STUDIES
X-RAY DIFFRACTION