Noise in phase shifting interferometry

Abstract

Abstract:We present a theoretical analysis to estimate the amount of phase noise due to noisy interferograms in Phase Shifting Interferometry (PSI). We also analyze the fact that linear filtering transforms corrupting multiplicative noise in Electronic Speckle Pattern Interferometry (ESPI) into fringes corrupted by additive gaussian noise. This fact allow us to obtain a formula to estimate the standard deviation of the noisy demodulated phase as a function of the spectral response of the preprocessing spatial filtering combined with the PSI algorithm used. This phase noise power formula is the main result of this contribution.

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

“…But now we extend previous analysis [3][4][5][6][7][8] to phase-shifting interferometry corrupted by no-white (pink) additive noise. Moreover using Parseval's theorem we unify in a single theory our spectral approach [3,4] with previous non-spectral methods [5][6][7][8] which give the estimated phase variance as a formula depending upon the coefficients of the phase-shifting algorithm.…”

“…Here we use the PSA's FTF to find the estimated phase variance due to a sequence of interferograms corrupted by non-white additive noise. Moreover, for the special case of white additive noise, the equivalence between the noise analysis based on the PSA's spectrum [3,4], and on its coefficients [5][6][7][8] is also shown, and finally two interesting examples of its application is given.…”

“…In 2009 Servin et al [3,4] used the spectra of the PSAs to analyze their sensitivity to white additive noise. Non-spectral methods for noise analysis in PSI have been reported before [5][6][7][8] using: Taylor expansion of the fringe irradiance [5]; joint statistical distribution of the noise [6]; PSA's x-characteristic polynomial [7]; the derivative of the PSA's arctangent ratio [8].…”

“…As in our previous works [3,4], here we use spectral (FTF) techniques. But now we extend previous analysis [3][4][5][6][7][8] to phase-shifting interferometry corrupted by no-white (pink) additive noise.…”

Spectral analysis of phase shifting algorithms

“…In [7] we show that the phase noise in a PSI algorithm is proportional to the integral of |H(ω)| 2 . So at a glance one may estimate the noise rejection of two "competing" PSI algorithms by their area under |H(ω)| 2 for the same output signal's energy.…”