Comparison of multiframe phase-shifting algorithms with unknown value of phase shift

Our work analyses several multiframe phase-shifting algorithms with unknown values of phase shifts. The presented paper offers new algorithms for evaluation of phase values in interferometric measurements. Nonlinear multi-frame phase-shifting algorithms, which use five, six and seven intensity frames to determine phase values in interferometric measurements, are described theoretically. The proposed algorithms compensate for linear phase-shift errors, i.e. miscalibration of phase-shift, which are very common in practice of interferometric measurements. The phase-shift value is assumed unknown but constant in these algorithms, so that at least four phase shifted intensity frames have to be recorded. An advantage of the described algorithms is a possibility of pointwise phase-shift calculation. An analysis of proposed algorithms with respect to possible influences on the process of interferometric measurements is also carried out. Several important potential error sources were chosen and the sensitivity and accuracy of phase evaluation algorithms was compared. The algorithms derived in this work can be used in any phase-shifting measurement technique and they offer the advantage of insensitivity to the linear phase-shift errors.