Design of nonlinearly spaced phase-shifting algorithms using their frequency transfer function

Here we show how to design phase-shifting algorithms (PSAs) for nonuniform/nonlinear (NL) phase-shifted fringe patterns using their frequency transfer function (FTF). Assuming that the NL phase steps are known, we introduce the desired zeroes in the FTF to obtain the specific NL-PSA formula. The advantage of designing NL-PSAs based on their FTF is that one can reject many distorting harmonics of the fringes. We can also estimate the signal-to-noise ratio for interferograms corrupted by additive white Gaussian noise. Finally, for non-distorted noiseless fringes, the proposed NL-PSA retrieves the modulating phase error free, just as standard/linear PSAs do.