Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry.
ABSTRACT Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramér-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise.
- Optics and Lasers in Engineering 08/2012; 50(8):iii–x. · 1.70 Impact Factor
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ABSTRACT: An autoregressive method to analyze the fringe pattern observed in holographic interferometry is reported. Considering the impact of a 30 dB signal-to-noise ratio, we have shown that the reconstruction of the simulated symmetric profiles with 3, 4, and 5 fringes produces a maximum error of 0.300, 0.520, and 1.015 rad, respectively. The reconstruction of an asymmetric profile gives a larger error. The method was also applied to a recent fringe pattern. Our results are in qualitative agreement with those obtained using other methods.Optical Engineering 12/2011; 50(12):5801-. · 0.96 Impact Factor