Study on the measurement error and scope of analytical gradient model in phase measuring deflectometry

The existing analytical gradient models in phase measuring deflectometry (PMD) usually suffer in the ambiguous problem. To solve this problem, simplification/assumption is often given to the surface shape, which causes non-ignorable measurement error in certain situations. In order to analyze the relation between the surface shape and measurement error when simplification/assumption is used, a ray tracing simulation model is developed in this paper. For any given PMD system setup, the relation between the height/slope variations of test surface and measurement accuracy can be carried out. The corresponding experiment work proves the correctness of this simulation model. The increasing of either the height or slope of object will lead to the exponential aggravating of measurement error. For our experiment setup, the measurement gradient error will be less than 0.5% if the ratio of the distance between the LCD (Liquid Crystal Display) screen and the reference plane and the STD (standard derivation) of object height is larger than 200. Keywords: Phase measuring deflectometry, Optical 3D measurement, Error analysis, Ray tracing model