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On-line version ISSN 1870-9044

Polibits  n.45 México Jun. 2012


Demodulation of Interferograms based on Particle Swarm Optimization


Julio Jiménez*1, Humberto Sossa**1, Francisco Cuevas2, and Laura Gómez***1


1 Julio Jimenez, Humerto Sossa and Laura Gomez are with Centro de Investigación en Computación, Instituto Politécnico Nacional, México DF., 07738, Mexico (email: *, **, ***lenis45@hotmail).

2 Francisco Cuevas is with Centro de Investigaciones en Óptica, León, Guanajuato, 37150, Mexico (email:


Manuscript received on November 11, 2011.
manuscript accepted on December 15, 2011.



A parametric method to carry out fringe pattern demodulation by means of a particle swarm optimization is presented. The phase is approximated by the parametric estimation of an «th-grade polynomial so that no further unwrapping is required. A particle swarm is used to optimize the input parameters of the function that estimates the phase. A fitness function is established to evaluate the particles, which considers: (a) the closeness between the observed fringes and the recovered fringes, (b) the phase smoothness and c) the prior knowledge of the object, such as its shape and size. The swarm of particles evolves until a fitness average threshold is obtained. We demonstrate that the method is able to successfully demodulate fringe patterns and even a one-image closed-fringe pattern.

Key words: Phase retrieval; fringe analysis; optical metrology; evolutionary technique.





This paper has been prepared with financial support from the IPN and CONACYT under grants: SIP 20111016, SIP 20121311 and CONACYT 155014. We wish to thank the Centro de Investigación en Computación of the I.P.N. for supporting us on this major accomplishment. We would also like to take the time to give warm thanks for all the support and contribution that given to us by Centro de Investigaciones en Óptica. Additionally, special thanks to Lawrence Whitehill and Mario Ruiz for reviewing English in this document. Finally, thanks to the anonymous reviewers who have given us their constructive criticism on the improvement of this work.



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