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Limitations of iterative least squares methods in phase shifting interferometry in presence of vibrations

Least square (LS) methods are an alternate approach to phase shifting interferometry algorithms for object shape measurement in the presence of unequal phase steps. One of the sources of unequal steps is vibrations. We study the influence of vibrations on intensity data and compare the obtained results with a LS and classic PSI algorithms. We find that in the case when no vibrations are present, both methods give similar results, while when vibrations are present LS methods generated slightly better results than the PSI algorithm. The results for both methods worsen significantly as the amplitude of the vibrations increases. We also show that a different set of phase steps than those found by LS method, while not generating minimal error function, can yield a better phase result with no residual phase error.