Tunable phase-extraction formulae for simultaneous shape measurement of multiple surfaces with wavelength-shifting interferometry

The interferometric surface measurement of single or stacked parallel plates presents considerable technical difficulties due to multiple-beam interference. To apply phase-shifting methods, it is necessary to use a pathlength-dependent technique such as wavelength scanning, which separates interference signals from various surfaces in frequency space. The detection window for frequency analysis has to be optimized for maximum tolerance against frequency detuning due to material dispersion and scanning nonlinearities, as well as for suppression of noise from other frequencies. We introduce a new class of phase-shifting algorithms that fulfill these requirements and allow continuous tuning of phase detection to any frequency of interest. We show results for a four-surface stack of nearparallel plates, measured in a Fizeau interferometer.