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