Correction of errors due to uneven intensity distribution and inaccurate phase shifts in prism-based simultaneous phase-shifting interferometry

Simultaneous phase-shifting interferometry (SPSI) is a suitable technique for dynamic surface measurement due to its rapid measurement capability. Based on whether there are obvious multiple phase-shifting channels in the setup, it can be divided into the multi-channel type and the pixelated phase-mask type. For the former type, two important error sources are the uneven intensity distribution among different phase-shifting channels and inaccurate phase shifts in each phase-shifting channel. In order to diminish the influence of these two error sources, several methods have been proposed. However, in some of these methods, only one error source of the two was considered and corrected. In the methods where the two error sources were both considered, some assumptions such as the uniform background intensity and fringe contrast are needed, so a complete and universal suppression method for both error sources is still needed in actual applications. In this paper, for a prism-based SPSI, we proposed such an error-correction method that mainly contains the following contributions. First, the intrinsic parameters of the system, including intensity distribution coefficients and relative phase shifts among phase-shifting channels, are calibrated in advance. We also checked the uniformity of phase shifts in each phase-shifting channel. Second, based on the obtained parameters, a corrected four-step phase-shifting algorithm is deduced to recover the more accurate measured phase. Results of both simulation and experiment verify the effectiveness of the proposed method.