[OPTICAL REVIEW Vol. 1, No. 2 (1994) 270-272]

## Phase Shifting Algorithms for Non-Sinusoidal Waveforms with Phase Shift Errors

Kenichi HIBINO,^{1} Bob F. OREB,^{2} David I. FARRANT^{2} and Kieran G. LARKIN^{3}

^{1}Mechanical Engineering Laboratory, Tsukuba, Ibaraki, 305 Japan, ^{2}Division of Applied Physics, CSIRO, NSW 2070, Australia, ^{3}Department of Physical Optics, School of Physics, University of Sydney, NSW 2006, Australia

(Accepted September 12, 1994)

In phase shifting interferometry, phase errors due to harmonic components of a fringe signal can be minimized by applying synchronous phase shifting algorithms with more than four samples. However, when the phase shift calibration is inaccurate, these algorithms cannot eliminate the effects of a non-sinusoidal waveform. It is shown that by taking a number of samples beyond one period of the fringe pattern, phase errors due to the harmonic components of the fringe signal can be eliminated, even when there exists a constant error in the phase shift interval. A general procedure for constructing phase shifting algorithms that eliminate these errors is derived. A seven-sample phase shifting algorithm is derived as an example, in which the effect of the second harmonic component can be eliminated in the presence of a constant error in the phase shift interval.

Key words : interferometry, fringe analysis, phase shift, phase shift error, harmonic signal