Design of phase shifting algorithms: fringe contrast maximum

In phase shifting interferometry, the fringe contrast is preferred to be at a maximum when there is no phase shift error. In the measurement of highly-reflective surfaces, the signal contrast is relatively low and the measurement would be aborted when the contrast falls below a threshold value. The fringe contrast depends on the design of the phase shifting algorithm. The condition for achieving the fringe contrast maximum is derived as a set of linear equations of the sampling amplitudes. The minimum number of samples necessary for constructing an error-compensating algorithm that is insensitive to the jth harmonic component and to the phase shift error is discussed. As examples, two new algorithms (15-sample and (3N - 2)-sample) were derived that are useful for the measurement for highly-reflective surfaces.