Fitting contrast by least square method for phase-shifting interferometry of unknown and arbitrary phase-steps under high non-uniform illumination

This work presents a very robust and non-iterative algorithm for phase retrieval in phase-shifting interferometry of three unknown and unequal phase-steps under illumination conditions of high spatial non-uniformity. First, the background light is eliminated by subtraction of two interferograms, thereby two secondary patterns are obtained. Second, the object phase is algebraically eliminated from two secondary patterns to obtain only one equation in three unknowns: the modulation light, and the two phase-steps. Third, the square of modulation light is approximated to a polynomial of degree K, and then we demonstrate that it is possible to rewrite the equation in the form of an error function. Forth, the coefficients for the modulation approximation and the phase-steps are computed by applying the least squares method. Some advantages of this approach are its capacity to support high spatial variations in the illumination and the object phase.

[1]  Qiaofeng Tan,et al.  Phase extraction from interferograms with unknown tilt phase shifts based on a regularized optical flow method. , 2013, Optics express.

[2]  Cruz Meneses-Fabian,et al.  Common-path speckle interferometer for phase objects studies , 2013 .

[3]  C. Meneses-Fabian,et al.  Phase retrieval by Euclidean distance in self-calibrating generalized phase-shifting interferometry of three steps. , 2015, Optics express.

[4]  Cruz Meneses-Fabian,et al.  Generalized phase-shifting interferometry by parameter estimation with the least squares method , 2013 .

[5]  C. Meneses-Fabian,et al.  Double aperture common-path phase-shifting interferometry by translating a ruling at the input plane. , 2013, Optics letters.

[6]  K Larkin,et al.  A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns. , 2001, Optics express.

[7]  C. J. Morgan.  Least-squares estimation in phase-measurement interferometry. , 1982, Optics letters.

[8]  D. J. Brangaccio,et al.  Digital wavefront measuring interferometer for testing optical surfaces and lenses. , 1974, Applied optics.

[9]  C. Meneses-Fabian.  Self-calibrating generalized phase-shifting interferometry of three phase-steps based on geometric concept of volume enclosed by a surface , 2016 .

[10]  Michael A. Player,et al.  Phase step measurement and variable step algorithms in phase-shifting interferometry , 1992 .

[11]  K. Hibino,et al.  Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts , 1997 .

[12]  Toyohiko Yatagai,et al.  Generalized phase-shifting interferometry , 1990, Other Conferences.

[13]  J Vargas,et al.  Analysis of the principal component algorithm in phase-shifting interferometry. , 2011, Optics letters.

[14]  Fan Wu,et al.  Correction of phase extraction error in phase-shifting interferometry based on Lissajous figure and ellipse fitting technology. , 2015, Optics express.

[15]  J. Schwider,et al.  IV Advanced Evaluation Techniques in Interferometry , 1990 .

[16]  Cruz Meneses-Fabian,et al.  Common-path phase-shifting interferometer with binary grating , 2006 .

[17]  K. Creath.  V Phase-Measurement Interferometry Techniques , 1988 .

[18]  Chris L. Koliopoulos,et al.  Fourier description of digital phase-measuring interferometry , 1990 .

[19]  M A Player,et al.  Phase-step insensitive algorithms for phase-shifting interferometry , 1994 .

[20]  Seah Hock Soon,et al.  Phase-shifting windowed Fourier ridges for determination of phase derivatives. , 2003, Optics letters.

[21]  Matias R. Viotti,et al.  A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure , 2016, Optical Engineering + Applications.

[22]  Bongtae Han,et al.  Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms. , 2004, Optics letters.

[23]  Weimin Jin,et al.  Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method. , 2011, Optics express.

[24]  John E. Greivenkamp,et al.  Generalized Data Reduction For Heterodyne Interferometry , 1984 .