Sampling theorem for surface profiling by white-light interferometry

White-light interferometry is a technique to measure surface topology of objects such as semiconductors, liquid crystal displays (LCDs), plastic films, and precision machinery parts. We devise a generalized sampling theorem for white-light interferometry. It reconstructs a square envelope function of an interference fringe directly from sampled values of the interference fringe, not from those of the square envelope function itself. The reconstruction formula requires only arithmetical calculations, no transcendental calculations except for only one cosine function. It has been installed in a commercial system that achieved the world’s fastest vertical scanning speed, 42μm/s, 6-14 times faster than conventional methods.