Solution to the slope-height ambiguity problem in phase measuring deflectometry based on a co-axial telecentric optical path

Abstract

In recent years, phase measuring deflectometry (PMD) has become a popular method to measure the shapes of specular surfaces. However, the inherent slope-height ambiguity problem, which indicates the phase of the recorded fringe pattern is determined by both the height and slope of the test surface, causes considerable ambiguity errors in the measurement results. Existing error reduction methods usually require the initial shape information of the test surface or additional equipment to assist the measurement. These requirements make measurement inflexible in some situations. In this paper, the slope-height ambiguity problem in PMD is modelled and analyzed analytically for the first time, and the system geometry requirements of minimizing the ambiguity error are carried out accordingly. To meet these requirements, a co-axis optical path setup with a telecentric imaging system is proposed. In our simulation and experiment, this system reduces the phase and height errors by up to two orders of magnitude, compared to those from the normally employed system geometry setup.