OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1864–1872

Branch-point-tolerant least-squares phase reconstructor

William W. Arrasmith  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1864-1872 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001864


View Full Text Article

Enhanced HTML    Acrobat PDF (553 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In reconstructing images from coherently illuminated objects, the far-field two-dimensional phase function in the entrance pupil plane (measurement plane) of a coherent imaging system has to contend with the presence of point discontinuities or branch points. The general class of least-squares phase reconstructors that use phase gradients (or phase differences) on a grid of points in the entrance pupil measurement plane fails to correctly determine the two-dimensional pupil phase when branch points are present. The phase estimation error results from the fact that the phase gradient or phase difference inputs to the least-squares reconstructor are being wrapped by the measurement system into the principal-value range [-π, π]. Recently, the existence and the determination of a hidden phase term was presented that accounts for branch-point effects [FriedD. L., J. Opt. Soc. Am. A 15, 2759 (1998)]. Fried’s hidden phase term is used in this study to present a branch-point-tolerant least-squares phase reconstructor for estimation of the two-dimensional measurement-plane phase function. Simulations of three different types of coherently illuminated object demonstrate the utility of this approach. The sensitivity of the reconstruction method to additive Gaussian noise is also presented.

© 1999 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(030.7060) Coherence and statistical optics : Turbulence
(070.4560) Fourier optics and signal processing : Data processing by optical means
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.1830) Image processing : Deconvolution
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(110.1650) Imaging systems : Coherence imaging

History
Original Manuscript: January 25, 1999
Revised Manuscript: March 24, 1999
Manuscript Accepted: March 24, 1999
Published: July 1, 1999

Citation
William W. Arrasmith, "Branch-point-tolerant least-squares phase reconstructor," J. Opt. Soc. Am. A 16, 1864-1872 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1864

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited