Wavelength-modulation Fourier interferometry with elimination of DC phase error.

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. • New 5 N –2 algorithm is proposed. • The characteristics of 5 N –2 algorithm is estimated in the frequency domain. • The phase errors calculated by 5 N –2 algorithm is compared with those by other algorithms. • The surface shape and optical thickness of a transparent multi-layer plate was measured by using wavelength-tuning Fizeau interferometer and the 5 N –2 algorithm. [ABSTRACT FROM AUTHOR]