Scanning interferometric phase-calculation formula for simultaneous topographic profiling of thickness and surface of optical flats

With the rapid development of industrial technologies, both the thickness irregularity and surface shape of transparent optical flats should be profiled precisely to maintain the performance of industrial equipment. When measuring the optical flat thickness using an interferometer, the profiling uncertainty can deteriorate owing to a constant phase error. In this study, a new 3N phase-extraction formula that can compensate for the Zernike piston error was developed for the simultaneous measurement of thickness and surface. Using Fourier representation, the characteristics of the 3N formula were shown in the frequency domain. Subsequently, the combined and Zernike piston error suppression ability of the 3N formula was verified by comparison with the other formulas. Finally, the thickness and surface of the optical flats were measured using the 3N formula and a wavelengthscanning Fizeau interferometer. The standard deviations of the thickness and surface profiling measurements were 4.435 nm and 9.654 nm, respectively, which were much smaller than those calculated using other phasecalculation formulas.