Stabilization of ill-posed nonlinear regression model and its application to interferogram reduction

James S. Slepicka; Soyoung Stephen Cha

doi:10.1117/12.57442

1 December 1991 Stabilization of ill-posed nonlinear regression model and its application to interferogram reduction

Proceedings Volume 1554, Second International Conference on Photomechanics and Speckle Metrology; (1991) https://doi.org/10.1117/12.57442
Event: San Diego, '91, 1991, San Diego, CA, United States

Abstract

In the past, various techniques have been developed for fringe reduction of conventional interferograms. Most typical ones utilize maximum/minimum or side tracking based on conventional image processing. These methods, however, pose a resolution limitation, not allowing acquisition of fractional fringe order numbers. The Fourier Transform method, requiring a relatively large number of fringes or injection of carrier fringes, also has limitations in some applications. The regression method, while simple, confronts a stability problem. That is, the ill-posed nonlinear intensity function cannot provide unique solutions. Here, we present a new approach and some of the test results for the regression method. It is based on iterative independent estimation of the individual terms that appear in the nonlinear model. The test results demonstrate stable convergence and accurate phase extraction by the new regression approach.

Citation Download Citation

James S. Slepicka and Soyoung Stephen Cha "Stabilization of ill-posed nonlinear regression model and its application to interferogram reduction", Proc. SPIE 1554, Second International Conference on Photomechanics and Speckle Metrology, (1 December 1991); https://doi.org/10.1117/12.57442

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