Interpolated local model fitting method for accurate and fast single-shot surface profiling

Abstract

The local model fitting (LMF) method is a useful single-shot surface profiling algorithm based on spatial carrier frequency fringe patterns. The measurement principle of the LMF method relies on the assumption that the target surface is locally flat. In this paper, we first analyze the measurement error of the LMF method caused by violation of the locally flat assumption. More specifically, we theoretically prove that the measurement error is zero at fringe intensity extrema in an interference pattern even when the locally flat assumption is violated. Based on this theoretical finding, we propose a new surface profiling method called the interpolated LMF (iLMF) algorithm, which is more accurate and computationally efficient than the original LMF method. The practical usefulness of the iLMF method is shown through experiments.