Thickness profiling of transparent plate using wavelength-tuned phase-shifting analysis

Abstract

Abstract In the interferometric phase-shifting analysis, the phase-shift nonlinearity causes both uniform and non-uniform phase errors in the phase distribution. In this research, a novel 13-frame phase-extraction algorithm that can suppress the uniform phase error was derived. The characteristics of the new 13-frame algorithm are discussed using a Fourier description. Additionally, the error suppression ability of the new 13-frame algorithm was performed by numerical error analysis, with comparisons to de Groot 13, Hibino 19, Hanayama 11, and 17-frame algorithms. Numerical analysis indicates that the new 13-frame algorithm shows the best performance (under 2 nm when 30% linear miscalibration and under 0.5 nm when the nonlinearity 10%). Finally, the variation in thickness of a transparent plate was profiled by the new 13-frame algorithm and a Fizeau interferometer. The repeatability standard deviation of experiments using the 13-fram algorithm was 3.344 nm, which shows the better performance that those of other conventional algorithms.