Fast surface profiler by white-light interferometry using a new algorithm, the SEST algorithm

We devise a fast algorithm for surface profiling by white-light interferometry. It is named the SEST algorithm after Square Envelope function estimation by Sampling Theory. Conventional methods for surface profiling by white-light interferometry based their foundation on digital signal processing technique, which is used as an approximation of continuous signal processing. Hence, these methods require narrow sampling intervals to achieve good approximation accuracy. In this paper, we introduce a totally novel approach using sampling theory. That is, we provide a generalized sampling theorem that reconstructs a square envelope function of a white-light interference fringe from sampled values of the interference fringe. A sampling interval in the SEST algorithm is 6-14 times wider than those of conventional methods when an optical filter of the center wavelength 600nm and the bandwidth 60nm is used. The SEST algorithm has been installed in a commercial system which achieved the world's fastest scanning speed of 42.75mum/s. The height resolution of the system lies in the order of 10nm for a measurement range of greater than 100mum.