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For the optical testing of a large mirror with a long radius of curvature, itis generally necessary to use a single-shot phase-shifting interferometer totake several measurements because the influence of air turbulence on airstratification prevention should be reduced for an accurate measurement. Inthis paper, a new technique that applies hierarchical clustering, whichclassifies a few clusters according to the pattern similarity of acquiredwrapped phases, is proposed. As the minority patterns of the wrapped phases areexcluded, the effects of unknown noises can be reduced. For each cluster, thecircular mean is used to calculate the denoised wrapped phases. The surfacefigure is obtained from the unwrapped phases. Because the running number of thephase-unwrapping algorithm becomes the same as the number of chosen clusters,the proposed technique is much faster than conventional procedures. In 500measurements using a spherical mirror with a diameter of 1.5 m, the measurementtime and standard deviation of the surface figure's root-mean-square error arereduced by up to approximately 23% and 15%, respectively, of the resultsobtained via the conventional procedure.

Phase retrieval by pattern classification and circular mean for robust optical testing