Nonlinear regression technique applied to generalized phase-shifting interferometry

Abstract

We develop a new approach involving nonlinear regression in phase-shifting interferometry with the hope of improving the accuracy of phase measurement in the presence of first-order piezoelectric transducer (PZT) calibration errors. The approach that uses the Levenberg–Marquardt method is shown to detect with high precision the value of the true phase step given to the PZT. The study shows that the method is also an efficient tool for determining the unknown phase steps even for a speckled intensity image. This is interesting and significant from the point of view of coherent optical metrology. Linear regression is subsequently applied for interference phase determination.

Acknowledgments

This research is funded by the Swiss National Science Foundation. We would also like to thank Rajesh L. V. V. L. for the fruitful discussion during the implementation of this algorithm.