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

White-light interferometry is a technique of profiling surface topography of objects such as semiconductors, liquid crystal displays (LCDs), and so on. The world fastest surface profiling algorithm utilizes a generalized sampling theorem that reconstructs the squared-envelope function r(z) directly from an infinite number of samples of the interferogram f(z). In practical measurements, however, only a finite number of samples of the interferogram g(z) = f(z) + C with a constant C are acquired by an interferometer. We have to estimate the constant C and to truncate the infinite series in the sampling theorem. In order to reduce both the truncation error and the estimation error for C, we devise an optimal characteristic of the optical filter installed in the interferometer in the sense that the second moment of the square of the interferogram is minimized. Simulation results confirm the effectiveness of the optimal characteristic of the optical filter.