Statistical properties of phase-shift algorithms

Statistical properties of phase-shift algorithms are investigated for the case of additive Gaussian intensity noise. Based on a bivariate normal distribution, a generally valid probability-density function for the random phase error is derived. This new description of the random phase error shows properties that cannot be obtained through Gaussian error propagation. The assumption of a normally distributed phase error is compared with the derived probability-density function. For small signal-to-noise ratios the assumption of a normally distributed phase error is not valid. Additionally, it is shown that some advanced systematic-error-compensating algorithms have a disadvantageous effect on the random phase error.

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

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

[3]  N Streibl,et al.  Accuracy of phase shifting interferometry. , 1988, Applied optics.

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

[5]  Jumpei Tsujiuchi,et al.  Accuracy of phase determination with unequal reference phase shift , 1988 .

[6]  J. Wyant,et al.  Effect of piezoelectric transducer nonlinearity on phase shift interferometry. , 1987, Applied optics.

[7]  Jumpei Tsujiuchi,et al.  An analysis of systematic phase errors due to nonlinearity in fringe scanning systems , 1986 .

[8]  Xianyu Su,et al.  Automated phase-measuring profilometry using defocused projection of a Ronchi grating , 1992 .

[9]  Chris P. Brophy,et al.  Effect of intensity error correlation on the computed phase of phase-shifting interferometry , 1990 .

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

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

[12]  Kenneth H. Womack,et al.  Interferometric Phase Measurement Using Spatial Synchronous Detection , 1983 .

[13]  Kieran G. Larkin,et al.  Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function , 1993, Optics & Photonics.

[14]  W. Macy,et al.  Two-dimensional fringe-pattern analysis. , 1983, Applied optics.

[15]  Chong Liu.  A method of eliminating the measurement error for phase shifting interferometry , 1993, International Commission for Optics.

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

[17]  Kieran G. Larkin,et al.  Design and assessment of symmetrical phase-shifting algorithms , 1992 .

[18]  R. Thalmann,et al.  Heterodyne and quasi-heterodyne holographic interferometry , 1985 .

[19]  J C Wyant,et al.  Phase shifter calibration in phase-shifting interferometry. , 1985, Applied optics.

[20]  J Schwider,et al.  Phase shifting interferometry: reference phase error reduction. , 1989, Applied optics.

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

[22]  Chris L. Koliopoulos,et al.  Interferometric optical phase measurement techniques , 1981 .

[23]  J. Bruning.  Fringe Scanning Interferometers , 1978 .

[24]  P L Ransom,et al.  Interferogram analysis by a modified sinusoid fitting technique. , 1986, Applied optics.

[25]  W. Bennett.  Methods of Solving Noise Problems , 1956, Proceedings of the IRE.

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

[27]  H. Böhme,et al.  Phase-determination of Fizeau interferences by phase-shifting interferometry , 1989 .