We propose an effective algorithm for surface profiling by white-light interferometry based on the so-called partial projection filter, which is a signal estimation technique from a finite number of noisy sampled data. The present authors' group has proposed a fast surface profiling algorithm called the SEST algorithm, in which the world's widest sampling interval of 1.425μm is used. The SEST algorithm, however, has the following problem. That is, when we reduce the sampling interval in order to improve the measurement accuracy, the performance does not increase. In order to solve this problem, the new algorithm has been proposed. That is, when the sampling interval of 1.425μm is used, the new algorithm achieves the same performance as the SEST algorithm. When a narrower sampling interval than 1.425μm is used, the new algorithm improves the accuracy. By computer simulations, the effectiveness of the new algorithm is confirmed.
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 600 nm and the bandwidth 60 nm is used. The SEST algorithm has been installed in a commercial system which achieved the world's fastest scanning speed of 42.75 micrometers /s. The height resolution of the system lies in the order of 10 nm for a measurement range of greater than 100 micrometers .