Fringe analysis for thickness estimation of optical glass plate using Fizeau interferometer

Shift error of modulation frequency generated from the refractive-index dispersion of a transparent glass plate and the nonlinear properties of phase modulation during wavelength tuning need to be suppressed for determining the homogeneity in optical thickness of the glass plate with wavelength tuning. In this study, we develop a new method to eliminate the dispersive error of refractive index and the nonlinear error of the phase modulation simultaneously. Moreover, a new 21-sample phase-extraction algorithm is derived using the proposed method. Characteristics of the newly designed algorithm are visualized in the frequency domain and on the complex plane. Numerical analysis show that the 21-sample algorithm has a greater error-suppression ability than other classical algorithms. The homogeneity in optical thickness of the transparent glass plate is determined by combining the proposed 21-sample algorithm and Fizeau-type interferometer. The standard deviation of thickness profiling measurement is 5.658 nm. This is significantly smaller than the standard deviation of other algorithms. Furthermore, the two-dimensional thickness distributions demonstrated that the proposed 21-sample algorithm can suppress residual ripples more effectively compared with other algorithms.