Wavelength-modulation Fourier interferometry with elimination of DC phase error

Abstract

Wavelength-modulation Fourier interferometry has been employed to measure the thickness of a glass plate. However, nonlinear phase-modulation error causes a DC error in the evaluated phase distribution. In this study, a 5 N–2 phase-extraction algorithm was derived for the simultaneous measurement of the thickness and surface shape of a glass plate with eliminating the DC phase error. First, the condition for the error elimination on a complex plane was derived and a new algorithm polynomial was proposed to satisfy this condition. Next, using this condition and 5 N–4 algorithm, 5 N–2 algorithm was derived. The newly developed 5 N–2 algorithm was visualized in the frequency domain using the Fourier transform method. The DC error elimination ability of the 5 N–2 algorithm was confirmed through numerical error analysis. Finally, the surface shape and thickness of the glass plate were simultaneously measured using a large-aperture Fizeau interferometer and the 5 N–2 algorithm. The standard deviations of the thickness and surface shape profiling were 3.113 nm and 10.689 nm, respectively, which were smaller than those obtained using other phase-extraction algorithms.