Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global search.

A new phase-shifting interferometric technique that uses an unknown phase step is described in which the phase step is determined by use of an algorithm called Probabilistic Global Search Lausanne (PGSL). One of the main sources of error in phase stepping is piezoelectric device (PZT) nonlinearity. The PGSL algorithm identifies the characteristics of the response of the PZT to the applied voltage through matching predicted and measured responses. The unknown phase step is also calculated with 0.097% error. This approach overcomes the limitations of existing techniques to determine unknown phase steps. Linear regression is subsequently applied for interference phase determination.

[1]  P. Carré.  Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures , 1966 .

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

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

[4]  Ian F. C. Smith,et al.  A direct stochastic algorithm for global search , 2003, Appl. Math. Comput..

[5]  T. Yatagai,et al.  Generalized phase-shifting interferometry , 1991 .

[6]  Qian Kemao,et al.  Determination of the best phase step of the Carré algorithm in phase shifting interferometry , 2000 .

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

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

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

[10]  Paul Taylor,et al.  Multiphase fringe analysis with unknown phase shifts , 1994 .

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

[12]  H. Frankena,et al.  Linear approximation for measurement errors in phase shifting interferometry. , 1991, Applied optics.

[13]  S. W. Kim,et al.  Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting. , 1994, Applied optics.