Phase-Shift Algorithm for Two Nonorthogonal Interferograms

The phase step method is widely used to analyze interferograms and extract the phase distribution from them. Its limitation is the large number of interferograms required for this purpose. The minimum number is three interferograms. This paper describes a general analysis algorithm that requires only two interferograms, the phase shifts between which may not be orthogonal. The idea of the paper is to obtain an additional interferogram by transforming a two-dimensional elliptical cross section that is formed by the two interferograms into a threedimensional cross section with respect to the base of some spatial cylinder. After determining the parameters of the ellipse, a projection vector parallel to the center axis of the cylinder is found. Then the two-dimensional section is projected onto a three-dimensional plane perpendicular to the center axis of the cylinder. Each of the projections of this plane onto the coordinate planes forms one of the interferograms. After obtaining three interferograms, phase demodulation was performed using a three-point algorithm. The RMS error of the phase calculation was 0.015 radians.