Phase-shifting interferometry (PSI) is the preferred non-contact method for profiling sub-nanometer surfaces. Based on monochromatic light interference, the method computes the surface profile from a set of interferograms collected at separate stepping positions. Errors in the estimated profile are introduced when these positions are not located correctly. In order to cope with this problem, various algorithms that minimize the effects of certain types of stepping errors (linear, sinusoidal, etc.) have been developed. Despite the relatively large number of algorithms suggested in the literature, there is no unified way of characterizing their performance when additional unaccounted random errors are present. Here, we suggest a procedure for quantifying the expected behavior of each algorithm in the presence of independent and identically distributed (i.i.d.) random stepping errors, which can occur in addition to the systematic errors for which the algorithm has been designed. The usefulness of this method derives from the fact that it can guide the selection of the best algorithm for specific measurement situations.
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