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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1662–1669

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

J. Miao, D. Sayre, and H. N. Chapman  »View Author Affiliations


JOSA A, Vol. 15, Issue 6, pp. 1662-1669 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001662


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Abstract

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× in each dimension (i.e., oversampling by 4× for 2D and 8× 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.

© 1998 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.0100) Image processing : Image processing
(100.5070) Image processing : Phase retrieval

Citation
J. Miao, D. Sayre, and H. N. Chapman, "Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects," J. Opt. Soc. Am. A 15, 1662-1669 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-6-1662

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