Optimal Design of Optical Filter for White Light Interferometry based on Sampling Theory

Abstract

Vertical-scanning white light interferometry is a technique of profiling the surface topography of objects such as semiconductors, liquid crystal displays (LCDs), and so on. The profile is given by the “squared-envelope function” of the interference signal, which is called the interferogram. The world’s fastest surface profiling algorithm exploits a generalized sampling theorem that directly reconstructs the squared-envelope function from an infinite number of samples of the interferogram. The optical system of the white light interferometer is equipped with an optical filter. So far there were no guidelines for designing the optical filter’s characteristics. Field engineers empirically chose some combination of commercial optical filters by checking the corresponding interferograms. The main purpose of this paper is to provide a guideline for designing the optical filter’s characteristics. That is, we devise the optimal characteristics of the optical filter in the sense that, with a fixed passband of the optical filter, the second moment of the squared interferogram is minimized. Simulation results confirm the effectiveness of the optimal characteristics.