[OPTICAL REVIEW Vol. 7, No. 6 (2000) 543-549]

Phase-Measuring Algorithms to Suppress Spatially Nonuniform PhaseModulation in a Two-Beam Interferometer

Kenichi HIBINO and Makoto YAMAUCHI

Mechanical Engineering Laboratory, Agency of Industrial Science and Technology, 1-2, Namiki, Tsukuba, Ibaraki, 305-8564 Japan

(Received May 13, 2000; Accepted July 5, 2000)

Phase modulation of presently used phase-shifting interferometers is assumed to be spatially uniform across the observing aperture. However, calibration errors or the configuration of an interferometer can cause a spatial nonuniformity in the phase modulation. Spatial nonuniformity causes a significant error in the measured phase when the phase modulator has nonlinear sensitivity. An even-order nonlinearity in the phase modulation in particular contributes to the errors. Lowest-order errors can be suppressed by adding a new symmetry to the sampling functions of the phase-shifting algorithm, however the algorithm suffers from large random noise. The random noise is shown to be decreased substantially by applying one more sampled frame to the algorithm. We derive new seven-sample and eight-sample algorithms that can compensate for a nonuniform phase shift and has much less random noise than the previous algorithm we proposed.

Key words : phase-shifting interferometry, phase-shift algorithm, nonlinear phase-shift, spatially nonuniform phase shift