A fast algorithm for determining the Gaussian filtered mean line in surface metrology☆

Abstract

A fast recursive algorithm for determining the Gaussian filtered mean line was deduced using the central limit theorem and an approximation method. This recursive algorithm uses a small number of multiplications per loop and otherwise such simple computer operations as addition and subtraction, and therefore, can achieve a very high computational speed. Special cases are also presented in which the relatively inefficient multiplication operation in the computer can be replaced by the efficient digit shifting operation, and the filtering computational efficiency is enhanced further. High-order algorithms are proposed for practical use to improve filtering accuracy. The “forward filtering” and “backward filtering” implementation of the recursive algorithm results in zero phase distortion of the filtered mean line. A new relationship between the Gaussian filtering method and the classical 2RC filtering method is also established using this algorithm.