Phase-stepping interferometry: methods for reducing errors caused by camera nonlinearities.

Phase errors that arise in phase-stepping interferometry are discussed. Investigations were performed by use of a Twyman-Green interferometer equipped with a compensation plate with a variable and servo-controlled tilt angle. With this instrument, phase-stepping errors can be reduced to a negligible level. There are, however, phase errors that are caused by camera nonlinearities. Two methods for minimizing these errors are presented. The first method is based on the simple idea that the interference intensity at the output of a two-beam interferometer has an exact cosine shape. The camera signals were monitored as a function of the tilt angle of the compensation plate, and the deviation from the cosine form was used to produce a correction. The second method is based on the idea that, under specific conditions, errors of an average of two phase measurements may compensate for each other. Numerical calculations were performed and give evidence of this hypothesis. Each method, the signal-correction and the averaging method, drastically reduces errors in evaluation of phases. The combination of both methods is a powerful tool that allows precise phase data to be obtained with an uncertainty, in the range lambda/2000 approximately 0.3 nm, that is caused mainly by signal noise.