Abstract

In this paper, we introduce an iterative scheme for phase demodulation of interferograms with nonuniformly spaced phase shifts. Our proposal consists of two stages: first, the phase map is obtained through a least squares fitting; second, the phase steps are retrieved using a statistical robust estimator. In particular, we use Tukey’s biweighted M-estimator because it can cope with both noisy data and outliers in comparison with the ordinary least squares estimator. Furthermore, we provide the frequency description of the algorithm and the phase demodulation allowing us to analyze the procedure and estimation according to the frequency transfer function (FTF) formalism for phase-shifting algorithms. Results show that our method can accurately retrieve the phase map and phase shifts, and it converges by the 10th iteration.

© 2020 Optical Society of America

Phase measurement of nonuniform phase-shifted interferograms using the frequency transfer function

Ivan Choque, Manuel Servin, Moises Padilla, Miguel Asmad, and Sotero Ordones
Appl. Opt. 58(15) 4157-4162 (2019)

Suppressing ripple distortions and spurious pistons in phase-shifting interferometry

Ivan Choque, Moises Padilla, Manuel Servin, Miguel Asmad, and Sotero Ordones
J. Opt. Soc. Am. A 37(4) 614-620 (2020)

Design of nonlinearly spaced phase-shifting algorithms using their frequency transfer function

Manuel Servin, Moises Padilla, Guillermo Garnica, and Gonzalo Paez
Appl. Opt. 58(4) 1134-1138 (2019)

Phase-shift extraction of multiple-frame randomly phase-shifted interferograms by analysis of the amplitude of the analytic signal

Hubing Du, Zhouxuan He, Pu Ma, Xiaodong Chen, and Peili Yin
Appl. Opt. 59(31) 9844-9849 (2020)

Fast and accurate tilt-shift-immune phase-shifting algorithm based on self-adaptive selection of interferogram subblocks and principal component analysis

Shuai Yang, Weiqian Zhao, Lirong Qiu, Yun Wang, and Songmei Tian
Appl. Opt. 59(9) 2906-2913 (2020)