Phase reconstruction from difference equations: a branch point tolerant method

Gregory C. Dente; Michael L. Tilton; Laura J. Ulibarri

doi:10.1117/12.405788

31 October 2000 Phase reconstruction from difference equations: a branch point tolerant method

Gregory C. Dente, Michael L. Tilton, Laura J. Ulibarri

Proceedings Volume 4091, Imaging Technology and Telescopes; (2000) https://doi.org/10.1117/12.405788
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

Numerous optical engineering applications lead to two two- dimensional difference equations for the phase of a complex field. We will demonstrate that, in general, the solution for the phase can be decomposed into a regular, single-valued function determined by the divergence of the phase gradient, as well as a multi-valued 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 will present a solution method that gives both the regular and hidden parts of the phase. Finally, we will demonstrate the method with several examples from both speckle imaging and shearing interferometry.

Citation Download Citation

Gregory C. Dente, Michael L. Tilton, and Laura J. Ulibarri "Phase reconstruction from difference equations: a branch point tolerant method", Proc. SPIE 4091, Imaging Technology and Telescopes, (31 October 2000); https://doi.org/10.1117/12.405788

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