Glass thickness testing using Fizeau interferometer with suppression of environmental factors

Abstract

The phase extraction technique used for thickness profiling of transparent glass plates through wavelength-tuning interferometry is susceptible to nonlinear error in phase shift owing to environmental factors, such as vibration and temperature fluctuations. These phase shift nonlinearities cause fluctuations and constant errors in the calculated phase, thereby distorting the original phase information. To address this issue, this study proposed a novel algorithm design method known as the advanced averaging method. This method incorporates the successive averaging technique and complex analysis using Z-transform to suppress phase shift nonlinearity. Additionally, a (7 + 4)-frame phase analysis algorithm was derived by the newly proposed advanced averaging method. Based on numerical analysis, the novel advanced averaging (7 + 4)-frame algorithm outperforms other algorithms in suppressing errors resulting from phase shift nonlinearity. Finally, in a validation experiment, the thickness homogeneity of a precision glass plate was profiled using this newly developed algorithm in conjunction with a large-aperture wavelength-tuning Fizeau interferometer. The repeatability error of the measurement accuracy was 4.563 nm, which is significantly lower than that of other conventional algorithms.