<title>Nonlinear excess fraction method: a robust temporal phase-unwrapping algorithm</title>

Abstract

Phase unwrapping, an unavoidable process in grating projection profilometry based on phase measurement, often manifests itself as the major obstacle that compromises measuring reliability and prevents automated profiling. In this paper, a robust temporal phase unwrapping algorithm, namely, non-linear excess fraction method (NLEFM) is proposed, which may enlarge the measuring range by dozens of times at no cost of accuracy. The algorithm presented in a general form demonstrates that the conventional linear excess fraction method can be readily extended into non-linear domain once certain condition is met. This novel method has been successfully applied to profiling complex objects with abrupt discontinuities and surface isolations. The multi-frequency grating projection profilometer based on NLEFM is promised to be developed into a robust, high accuracy and automated shape measurement system.