Linear error analysis of differential phase shifting algorithms

Abstract An important process in optical metrology is the determination of the difference between test and reference states. Direct calculation of the optical phase difference encoded in two fringe patterns can be done by using differential phase shifting algorithms (DPSAs). If the phase difference does not reach a complete period, DPSAs provide directly its continuous values and the known limitations of the unwrapping stage are avoided. This work presents a generic design protocol of DPSAs obtained by a least squares fitting that combines phase shifting algorithms (PSAs) in a suitable non-linear way. Results are also provided that quantitatively characterize the effect on some representative DPSAs by the main systematic error sources. The goodness of the analyzed DPSAs is contrasted with the experimental results for wavefront distortion evaluation using phase-shifted Mach–Zehnder fringe patterns.

[1]  J. Schwider,et al.  Digital wave-front measuring interferometry: some systematic error sources. , 1983, Applied optics.

[2]  Ignacio Lira,et al.  Whole-field analysis of uniaxial tensile tests by Moiré interferometry , 2005 .

[3]  B V Dorrío,et al.  REVIEW ARTICLE: Phase-evaluation methods in whole-field optical measurement techniques , 1999 .

[4]  Mahendra P. Kothiyal,et al.  Two-wavelength micro-interferometry for 3-D surface profiling , 2009 .

[5]  Guillermo H. Kaufmann,et al.  A portable digital speckle pattern interferometry device to measure residual stresses using the hole drilling technique , 2006 .

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

[7]  James E. Millerd,et al.  Phase-shifting multiwavelength dynamic interferometer , 2004, SPIE Optics + Photonics.

[8]  D. Malacara.  Optical Shop Testing , 1978 .

[9]  B. V. Dorrio,et al.  A multiplicative analogical moiré phase-shifting Twyman-Green technique for Nd:YAG rod wavefront distortion measurement , 2001 .

[10]  Higinio González-Jorge,et al.  Error propagation in differential phase evaluation. , 2010, Optics express.

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

[12]  C Joenathan,et al.  Phase-measuring interferometry: new methods and error analysis. , 1994, Applied optics.

[13]  B V Dorrío,et al.  Fizeau phase-measuring interferometry using the moiré effect. , 1995, Applied optics.

[14]  M. Owner-Petersen.  Digital speckle pattern shearing interferometry: limitations and prospects. , 1991, Applied optics.

[15]  J Burke,et al.  Complex division as a common basis for calculating phase differences in electronic speckle pattern interferometry in one step. , 1998, Applied optics.

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

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

[18]  Mahendra P. Kothiyal,et al.  A comparative study of phase-shifting algorithms in digital speckle pattern interferometry , 2008 .

[19]  Katherine Creath,et al.  Error sources in phase-measuring interferometry (Invited Paper) , 1992, Other Conferences.

[20]  Benito V. Dorrío,et al.  Characteristic polynomial theory of two-stage phase shifting algorithms , 2012 .

[21]  Masato Shibuya,et al.  Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating. , 2008, Applied optics.

[22]  Marta Miranda,et al.  Fourier analysis of two-stage phase-shifting algorithms. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[23]  W. R. Brohinsky,et al.  Electrooptic holography and its application to hologram interferometry. , 1985, Applied optics.

[24]  Cruz Meneses-Fabian,et al.  Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry. , 2008, Optics express.

[25]  Katherine Creath,et al.  Error sources in phase-measuring interferometry , 2010 .

[26]  C. S. Vikram,et al.  Algorithm for phase-difference measurement in phase-shifting interferometry. , 1993, Applied optics.

[27]  Matt Novak,et al.  Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer. , 2005, Applied optics.

[28]  Salah Karout,et al.  Two-dimensional phase unwrapping , 2007 .

[29]  J. Briers,et al.  Optical testing: a review and tutorial for optical engineers , 1999 .

[30]  Benito V. Dorrío,et al.  Monte Carlo based techniques of two-stage phase shifting algorithms , 2011 .

[31]  Tomás Belenguer,et al.  Optical inspection of liquid crystal variable retarder inhomogeneities. , 2010, Applied optics.

[32]  K A Stetson,et al.  Fourier-transform evaluation of phase data in spatially phase-biased TV holograms. , 1996, Applied optics.

[33]  Anand Asundi,et al.  Algorithm for directly retrieving the phase difference: a generalization , 2003 .

[34]  Angel F. Doval,et al.  Transparent object analysis in a Mach-Zehnder interferometer using the multiplicative analogical moire phase-shifting method , 1999, Other Conferences.

[35]  D. Malacara,et al.  Interferogram Analysis for Optical Testing , 2018 .

[36]  Babak Saif,et al.  Dynamic phase-shifting electronic speckle pattern interferometer , 2005, SPIE Optics + Photonics.