Sampling Theory in White-Light Interferometry

We devise generalized sampling theorems for scanning white-light interferometry. It is a technique used to obtain surface profiles of objects such as semiconductors, liquid crystal displays (LCDs), and so on. The sampling theorems reconstruct a squared-envelope function of an interference fringe by using sampled values of the interference fringe, not from those of the squared-envelope function itself. We extend the so-called second-order sampling so that an infinite number of sampling intervals can be used. As a result, less truncation error is achieved. Based on the theorems, we propose a surface profiling algorithm. This algorithm has been installed in a commercial system which achieved the world’s fastest vertical scanning speed, 6-14 times faster than those of the conventional systems.