Phase-shift extraction from twice-normalized light intensity changes recorded with random phase shifts

A simple phase-shift extraction algorithm is proposed for interferograms recorded with random phase shifts that vary over at least 2π. The phase-shift-dependent changes in the intensity at two pixels having different phases, selected from one frame, are taken out and normalized. The sum and difference of the two normalized changes are calculated, and both the changes are normalized again along the phase shifts. The normalized sum and difference become the cosine and sine of a term including the random phase shift, respectively. Thereby, the phase shifts are extracted from both twice-normalized intensity changes. An experiment using an interference microscope equipped with a piezoelectric-transducer positioner of an objective lens is conducted to estimate the validity of the algorithm. The algorithm is verified to have satisfactory results when the multiple interferograms used have a sample size of more than 15 frames recorded with random phase shifts