Previous implementations of the iterative phase shifting method, in which the phase of a test object is computed from measurements using a phase shifting interferometer with unknown positions of the reference, do not provide an accurate way of knowing when convergence has been attained. We present a new approach to this method that allows us to deterministically identify convergence. The method is tested with a home-built Fizeau interferometer that measures optical surfaces polished to lambda/100 using the Hydra tool. The intrinsic quality of the measurements is better than 0.5 nm. Other possible applications for this technique include fringe projection or any problem where phase shifting is involved.
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