Suppressing ripple distortions and spurious pistons in phase-shifting interferometry.

In this paper, we present new phase-shifting algorithms (PSAs) that suppress the ripple distortions and spurious pistons in phase-shifting interferometry. These phase errors arise when non-uniform phase-shifting interferograms are processed with PSAs that assume uniform phase shifts. By modeling the non-uniform phase shifts as a polynomial of the unperturbed phase-shift value $\omega_0$ω0, we show that the conditions for eliminating the ripple distortion and the spurious piston are associated with the $m$mth derivative of the PSA's frequency transfer function (FTF). Thus, we propose an approach to design robust algorithms based on the FTF formalism and we present four ready-to-apply PSAs formulas. Finally, our conclusions are supported by computer simulations.

Phase measurement of nonuniform phase-shifted interferograms using the frequency transfer function.

In this paper, we propose a phase measurement method for interferograms with nonuniform phase shifts. First, we measure the phase shifts between consecutive interferograms. Second, we use these values to modify the spectrum of the interferogram data. Then, by analyzing this spectrum, we design a suitable phase-shifting algorithm (PSA) using the frequency transfer function formalism. Finally, we test our PSA with experimental data to estimate the surface of an aluminum thin film. Our result is better than those obtained using the Fourier transform method, the principal component analysis method, and the least-squares PSA.