Abstract
Phase-shift deflectometry is a widely used high-precision gradient measurement method for assessing the topography of specular objects. The calibration of phase-shift deflectometry measurement systems involves establishing the phase-slope mapping relationship. This paper analyzes the causes of phase variations at different calibration points in existing phase-slope analysis models. Based on the fact that changes in height simultaneously produce phase variations in two perpendicular directions, a decoupling method is proposed to address the phase ambiguity problem to some extent. Through simulation, the variation in height phase and slope distribution were quantitatively analyzed for a unidirectional inclined plane to validate the proposed algorithm. Additionally, measurement experiments were performed on a unidirectional inclined plane with an inclination angle of −2.584° and a concave mirror with a curvature radius of 779.87 mm. Based on the findings, the decoupling method reduced the relative root-mean-square error of the gradient measurement for the inclined plane in the inclined direction by 2.206% and improved the error range of the curvature radius for the concave mirror from [0.55%, 4.1%] to [0.22%, 3.86%]. By comparing with the existed method, the decoupling method showed a certain advantage in practicality.
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