Three-beam interferogram analysis method for surface flatness testing of glass plates and wedges

When testing transparent plates with high quality flat surfaces and a small angle between them the three-beam interference phenomenon is observed. Since the reference beam and the object beams reflected from both the front and back surface of a sample are detected, the recorded intensity distribution may be regarded as a sum of three fringe patterns. Images of that type cannot be succesfully analyzed with standard interferogram analysis methods. They contain, however, useful information on the tested plate surface flatness and its optical thickness variations. Several methods were elaborated to decode the plate parameters. Our technique represents a competitive solution which allows for retrieval of phase components of the three-beam interferogram. It requires recording two images: a three-beam interferogram and the two-beam one with the reference beam blocked. Mutually subtracting these images leads to the intensity distribution which, under some assumptions, provides access to the two component fringe sets which encode surfaces flatness. At various stages of processing we take advantage of nonlinear operations as well as single-frame interferogram analysis methods. Two-dimensional continuous wavelet transform (2D CWT) is used to separate a particular fringe family from the overall interferogram intensity distribution as well as to estimate the phase distribution from a pattern. We distinguish two processing paths depending on the relative density of fringe sets which is connected with geometry of a sample and optical setup. The proposed method is tested on simulated and experimental data.