Strain maps obtained by phase-shifting interferometry: An uncertainty analysis

We used Moiré interferometry to evaluate the strains induced on a specimen subjected to a steady tensile load. The strains were evaluated by differentiating the whole-field phase values obtained by a phase-shifting algorithm. Because the direct differentiation of even slightly noisy data may lead to unacceptable derivative errors, the strain evaluation procedure included the application of a low-pass filter, which allowed us to smooth out local fluctuations in the phase data. In addition to the noise, the strain values were also affected by systematic errors in the phase values rendered by the phase-shifting algorithm as well as uncertainties in the determination of both the interferometer sensitivity and the magnification of the imaging system. In this paper, the influence of these error sources was assessed by applying a Monte Carlo-based uncertainty propagation technique; the strain uncertainty evaluation was based on simulating a large number of times, both the phase-shifting procedure and the post-image processing (which included the filter application). We found that the strain uncertainty strongly depends on the low-pass filter used to counteract the noise effect. Although we obtained the phase data from a Moiré pattern, the procedure presented to evaluate the strain uncertainty is valid independently of the techniques used to generate the fringe pattern or the algorithm applied to exploit the phase-shifting procedure.