Uncertainty analysis of whole-field phase-differences retrieved from ESPI fringe patterns by using the Fourier transform method (FTM)

We have evaluated the uncertainty associated with the whole-field phase-differences retrieved by using the Fourier transform method (FTM), from a fringe pattern generated by electronic speckle pattern interferometry (ESPI). The phase-differences were induced by applying load to an elastic sample. The FTM involved the Fourier transform application to the fringe pattern, the isolation of the term carrying the phase information by applying a band-pass filter in the spatial frequency domain, and then the inverse Fourier transform application. Since the fringes in the analyzed pattern were adequately open, the FTM outcomes were presumed to be mainly affected by errors in the determination of both the width and the location of the applied filter mask. The influence of these error sources was assessed by using a Monte Carlo-based computer simulation. It implied evaluating the phase-differences a large number of times under the influence of the involved error sources. We found that the phase uncertainty depends strongly on the width of the applied filter mask; the influence of the other error sources considered into the uncertainty propagation was significantly smaller.