Phase-shifting interferometry corrupted by white and non-white additive noise

Abstract

Abstract:The standard tool to estimate the phase of a sequence of phaseshifted interferograms is the Phase Shifting Algorithm (PSA). The performance of PSAs to a sequence of interferograms corrupted by nonwhite additive noise has not been reported before. In this paper we use the Frequency Transfer Function (FTF) of a PSA to generalize previous white additive noise analysis to non-white additive noisy interferograms. That is, we find the ensemble average and the variance of the estimated phase in a general PSA when interferograms corrupted by non-white additive noise are available. Moreover, for the special case of additive white-noise, and using the Parseval's theorem, we show (for the first time in the PSA literature) a useful relationship of the PSA's noise robustness; in terms of its FTF spectrum, and in terms of its coefficients. In other words, we find the PSA's estimated phase variance, in the spectral space as well as in the PSA's coefficients space.

Profilometry with digital fringe-projection at the spatial and temporal Nyquist frequencies

“…Nn Mb   . These results were derived for M-step LS-PSAs, which are defined univocally by their frequency transfer function [4,12]:…”

“…(3) are distorted by a zero-mean additive white-Gaussian noise (AWGN) having a flat power spectral density: ( , , ) ( , , ) ( , , ), n I x y t I x y t n x y t (14)Applying Eq. (13) to ( , , ) n I x y t , we obtain the following analytic signal:  for low-energy noise (a reasonable assumption for FPP), and variance of the noisy phase were derived for M-step LS-PSAs, which are defined univocally by their frequency transfer function[4,12]: 10) and (16) is obvious that our phase-demodulation method uses the 2-step LS-PSA. Typically M-step LS-PSAs are restricted to 3 M  in order to fulfill all quadrature conditions (see Eq.(6)).…”