N-step linear phase-shifting algorithms with optimum signal to noise phase demodulation

Abstract

A common way to test an optical wavefront is to use a phase-shifting interferometer along with (for example) a three-step linear phase-shifting algorithm (PSA). The following fundamental question arises: what phase step should be used? Typically, , or are used and, in fact, any phase step within the open interval can be employed. In the absence of any measuring noise, all these phase shifts yield the same estimate for the modulating phase. However, which of these phase steps ω 0 is the best to obtain the least noisy phase estimation from a temporal set of three noisy interferograms? Working in frequency space, a general procedure to obtain the optimum phase step ω 0 of a given linear N-step PSA is presented. This general procedure is exemplified for some particular linear PSAs, notably 3-, 5-, 7-, and 27-step PSAs.