RESUMO
The standard tool to estimate the phase of a sequence of phase-shifted interferograms is the Phase Shifting Algorithm (PSA). The performance of PSAs to a sequence of interferograms corrupted by non-white 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.
RESUMO
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.
Assuntos
Algoritmos , Interferometria/métodos , Modelos Estatísticos , Refratometria/métodos , Simulação por ComputadorRESUMO
A technique is presented for filtering and normalizing noisy fringe patterns, which may include closed fringes, so that single-frame demodulation schemes may be successfully applied. It is based on the construction of an adaptive filter as a linear combination of the responses of a set of isotropic bandpass filters. The space-varying coefficients are proportional to the envelope of the response of each filter, which in turn is computed by using the corresponding monogenic image [Felsberg and Sommer, IEEE Trans. Signal Process. 49, 3136 (2001)]. Some examples of demodulation of real Electronic Speckle Pattern Interferometry (ESPI) images patterns are presented.