Surface flatness measurement of quasi-parallel plates employing three-beam interference with strong reference beam

Abstract

A big challenge for standard interferogram analysis methods such as Temporal Phase Shifting or Fourier Transform is a parasitic set of fringes which might occur in the analyzed fringe pattern intensity distribution. It is encountered, for example, when transparent glass plates with quasi-parallel surfaces are tested in Fizeau or Twyman-Green interferometers. Besides the beams reflected from the plate front surface and the interferometer reference the beam reflected from the plate rear surface also plays important role; its amplitude is comparable with the amplitude of other beams. In result we face three families of fringes of high contrast which cannot be easily separated. Earlier we proposed a competitive solution for flatness measurements which relies on eliminating one of those fringe sets from the three-beam interferogram and separating two remaining ones with the use of 2D Continuous Wavelet Transform. In this work we cover the case when the intensity of the reference beam is significantly higher than the intensities of two object beams. The main advantage of differentiating beam intensities is the change in contrast of individual fringe families. Processing of such three-beam interferograms is modified but also takes advantage of 2D CWT. We show how to implement this method in Twyman-Green and Fizeau setups and compare this processing path and measurement procedures with previously proposed solutions.