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Applied Optics

Applied Optics


  • Vol. 39, Iss. 10 — Apr. 1, 2000
  • pp: 1480–1485

Speckle imaging and hidden phase

Gregory C. Dente  »View Author Affiliations

Applied Optics, Vol. 39, Issue 10, pp. 1480-1485 (2000)

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The Knox–Thompson, or cross-spectrum, method provides two two-dimensional difference equations for the phase of the object spectrum. We demonstrate that, in general, the object spectrum phase can be decomposed into a regular, single-valued function determined by the divergence of the phase gradient, as well as a multivalued function determined by the circulation of the phase gradient; this second function has been called the hidden phase. The standard least-squares solution to the two-dimensional difference equations will always miss this hidden phase. We present a solution method that gives both the regular and the hidden parts of the object spectrum phase. Finally, we illustrate several examples of imaging through turbulence and postprocessing with the Knox–Thompson method, including the hidden phase.

© 2000 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(110.0110) Imaging systems : Imaging systems
(110.4280) Imaging systems : Noise in imaging systems
(110.6150) Imaging systems : Speckle imaging

Original Manuscript: August 30, 1999
Revised Manuscript: November 24, 1999
Published: April 1, 2000

Gregory C. Dente, "Speckle imaging and hidden phase," Appl. Opt. 39, 1480-1485 (2000)

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