Surface Profiling of Silicon Wafer Using Wavelength-Scanning Fizeau Interferometer and Gaussian Window Function

: Wavelength-scanning Fizeau interferometry is extensively utilized for measuring surface shapes. The phase distribution in a fringe pattern can be determined using a phase-shifting algorithm. Surrel's characteristic polynomial theory allows for the design of flexible phase-shifting algorithms by modifying the window function. As industry demands for higher measurement precision increase, the need to develop flexible phase-shifting algorithms with improved phase-shift error suppression has been increasing. Nevertheless, devising these algorithms poses significant challenges, primarily due to the complex derivation of their window functions, which are formulated as powers of M-sample characteristic polynomials. In this study, the Gaussian window function was developed by generalizing existing flexible phase-shifting algorithms. Ultimately, a 4-inch silicon wafer's surface shape was measured via a wavelength-scanning Fizeau interferometer employing the 10N - 9 algorithms, which are calculated by Gaussian phase-shifting algorithm.