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Proceedings Paper

Unwrapping of noisy phase maps: a comparison of two methods
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Paper Abstract

The unwrapping of experimental phase maps is not a straightforward process and much research has been devoted recently to the development of robust algorithms that can remove 2ir phase discontinuities in the presence of noise, phase inconsistencies, missing data and holes or shadows. In this paper, the performance of two recently developed phase unwrapping methods are compared. The first uses a least squares minimization formulation whose solution is provided by a fast discrete cosine transform. Areas ofbad data are removed from the differential equation by means of a weighting matrix and the unwrapped phase distribution is evaluated using an iterative approach. The second is a path-independent method based in the Thikonov regularization theory. This theory finds solutions that correspond to minimizers of positive definite quadratic cost functionals. The solution to the unwrapping problem by this method is a generalization of classical least-squares . The introduction of a regularization term permits the reduction of noise and the interpolation over regions with invalid data in a stable and controlled way. The performance ofboth methods are compared in their application to computer generated and experimental phase maps. Their main advantages and limitations are discussed. Keywords: Optical metrology, fringe analysis, cosine transform, regularization methods.

Paper Details

Date Published: 17 July 1996
PDF: 11 pages
Proc. SPIE 2860, Laser Interferometry VIII: Techniques and Analysis, (17 July 1996); doi: 10.1117/12.276337
Show Author Affiliations
Ramon Rodriguez-Vera, Ctr. de Investigaciones en Optica, A.C. (Mexico)
Guillermo H. Kaufmann, Instituto de Fisica Rosario (Argentina)
Manuel Servin Guirado, Ctr. de Investigaciones en Optica, A.C. (Mexico)
Andrew John Moore, Ctr. de Investigaciones en Optica, A.C. (United Kingdom)

Published in SPIE Proceedings Vol. 2860:
Laser Interferometry VIII: Techniques and Analysis
Malgorzata Kujawinska; Ryszard J. Pryputniewicz; Mitsuo Takeda, Editor(s)

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