Optimization approach to the suppression of vibration errors in phase-shifting interferometry

An optimization-based strategy is introduced for suppressing errors due to vibration in phase-shifting-interferometry algorithms. A norm-square integral criterion of the error as a function of vibration frequency is used as the basis of the optimization procedure. Analytical results are obtained for certain classes of problems, and numerical algorithms are used when these are not available. It is also shown that the effect of vibration-induced errors in the computation of a time-averaged phase estimate diminishes as the measurements are averaged. Simulations are used to validate the analysis and demonstrate the overall efficacy of the approach. Generalizations to multiple objective optimization problems are briefly discussed.