Precision Surface Shape Measurement of Transparent Plate Using Wavelength- Tuning Interferometry

When measuring the surface shape and thickness of a transparent plate using the wavelength-tuning interferometry, many types of phase errors occur owing to laser stability, interferometer instability, and environmental uncertainty. In this study, we developed a 15-sample phase extraction algorithm that effectively compensates these phase errors. Among several methods for developing the phase-extraction algorithm, it was developed using linear equation theory, and the algorithm was visualized in the frequency domain and complex plane using the Fourier transform and characteristic polynomial theory, respectively. In addition, the ability of the algorithm to suppress phase-shift linear errors and nonlinear errors was verified through numerical analysis. Finally, the surface-shape profiling of the transparent plate was measured using a wavelength-tuning Fizeau interferometer and the proposed 15-sample phase extraction algorithm.