Statistical self-calibrating algorithm for three-sample phase-shift interferometry

Abstract

A new self-calibrating algorithm is described that succeeds in reconstructing an almost error-free wavefront from only three interferograms. The algorithm is based on the assumption that the optical phase, taken modulo , is quasi-uniformly distributed in the range [0, ) over the field of the interferograms. When the actual reference phases differ from those considered in the phase computation program a non-uniform histogram of the computed phase results. An analysis of this histogram allows a fitting procedure to find the actual phase shifts. Eventually an accurate shape of the wavefront can be calculated or a corrected signal can be sent to the phase-shifting device.