Design of phase-shifting algorithms by fine-tuning spectral shaping

To estimate the modulating wavefront of an interferogram in Phase Shifting Interferometry (PSI) one frequently uses a Phase Shifting Algorithm (PSA). All PSAs take as input N phase-shifted interferometric measures, and give an estimation of their modulating phase. The first and best known PSA designed explicitly to reduce a systematic error source (detuning) was the 5-steps, Schwider-Hariharan (SH-PSA) PSA. Since then, dozens of PSAs have been published, designed to reduce specific data error sources on the demodulated phase. In Electrical Engineering the Frequency Transfer Function (FTF) of their linear filters is their standard design tool. Recently the FTF is also being used to design PSAs. In this paper we propose a technique for designing PSAs by fine-tuning the few spectral zeroes of a PSA to approximate a template FTF spectrum. The PSA's spectral zeroes are moved (tuned) while gauging the plot changes on the resulting FTF's magnitude.