1-Norm character of phase shifting interferograms and its application in phase shift extraction

Aiming at the situation that the fringe number in the interferogram is less than one, a novel phase shift extraction algorithm is proposed. By introducing the 1-norm of a sequence of phase-shifting interferograms and analyzing its character, which changes in the cosine form with the phase shift, the phase shift can be extracted from an arccosine function easily. Specially, so long as the fringe number in the interferogram is less than 0.5, both the simulation calculation and experimental research show that the phase shift with high precision can be obtained directly and rapidly in the proposed algorithm.