Blind self-calibrating algorithm for phase-shifting interferometry by use of cross-bispectrum.

A blind self-calibrating algorithm for phase-shifting interferometry is presented, with which the nonlinear interaction introduced by phase shift errors, between the reconstructed phases and the reconstructed amplitudes of the reference wave, is measured with cross-bispectrum. Minimizing an objective function based on this cross-bispectrum allows accurately estimating the true phase shifts from only three interferograms in the absence of any supplementary assumptions and knowledge about these interferograms.

[1]  K. S. Lii,et al.  Cross-Bispectrum Computation and Variance Estimation , 1981, TOMS.

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

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

[4]  O. Kwon,et al.  Multichannel phase-shifted interferometer. , 1984, Optics letters.

[5]  T. Eiju,et al.  Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm. , 1987, Applied optics.

[6]  Katsuyuki Okada,et al.  Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry , 1991 .

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

[8]  J. Schwider,et al.  New compensating four-phase algorithm for phase-shift interferometry , 1993 .

[9]  Y. Surrel Phase stepping: a new self-calibrating algorithm. , 1993, Applied optics.

[10]  In-Bok Kong,et al.  General algorithm of phase-shifting interferometry by iterative least-squares fitting , 1995 .

[11]  X Chen,et al.  Phase-shifting interferometry with uncalibrated phase shifts. , 2000, Applied optics.

[12]  M. Chen,et al.  Algorithm immune to tilt phase-shifting error for phase-shifting interferometers. , 2000, Applied optics.

[13]  J. Bokor,et al.  Fourier-transform method of phase-shift determination. , 2001, Applied optics.

[14]  L. Cai,et al.  Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps. , 2003, Optics letters.

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

[16]  L. Cai,et al.  Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors , 2004 .

[17]  Gleb Vdovin,et al.  Phase extraction from three and more interferograms registered with different unknown wavefront tilts. , 2005, Optics express.

[18]  L Z Cai,et al.  Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry. , 2006, Optics letters.

[19]  Yingjie Yu,et al.  Blind phase shift estimation in phase-shifting interferometry. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  Mingyi Chen,et al.  Efficient iterative algorithm for phase-shifting interferometry , 2007 .

[21]  Baoli Yao,et al.  Phase-shift extraction for generalized phase-shifting interferometry. , 2009, Optics letters.