Simultaneous interferometric profilometry of surface and thickness of transparent plate using wavelength-modulation

Abstract

Wavelength-modulation interferometers have been widely used to measure the geometric characteristics of transparent plates. However, several errors can be generated by multiple reflections of the laser beams and environmental uncertainties when the wavelength is modulated. In this research, two novel phase-calculation formulas with the same number of interference fringes (15) are proposed to measure the geometric characteristics of a transparent plate. First, a 15s-sample phase-calculation formula for measuring the surface shape of a transparent wedge plate was developed using a system of linear equations. Second, a 15t-sample phase-calculation formula for measuring the optical thickness irregularity of transparent parallel plate was developed by using the characteristic-polynomial theory. The two 15-sample formulas were visualized in the frequency domain and complex plane to confirm the properties of their error-compensation ability. Furthermore, the two formulas were compared with conventional phase-calculation formulas through the numerical analysis. Finally, the surface profile of the wedge plate and optical thickness irregularity of the parallel plate were measured via the two proposed formulas using wavelength-modulation Fizeau interferometer. The standard deviations of 15s-sample formula and the 15t-sample formula were confirmed as 4.3616 nm and 1.2875 nm, respectively. Using these formulas to measure the geometric properties of transparent plate on nanoscale can contribute to the production of high-performance semiconductor devices.