Phase-measuring deflectometry based on the exponential orthogonal grating method

Phase-measuring deflectometry (PMD) is widely applied in three-dimensional (3D) shape measurement because of its high precision and simple hardware configuration. The orthogonal grating method, which encodes phase information in both horizontal and vertical directions, effectively reduces the number of required projection patterns. However, this approach is highly sensitive to system nonlinearities, which can lead to significant phase errors between the two orthogonal directions and compromise measurement accuracy. To address this issue, this paper proposes a phase acquisition method based on exponential orthogonal grating. By leveraging the mathematical properties of exponential functions, the proposed method theoretically compensates for nonlinear distortions induced by the gamma effect. Both simulation and experimental results demonstrate that the proposed method, when compared with the conventional non-composite sinusoidal fringe method and the sinusoidal orthogonal grating method, significantly improves measurement accuracy under nonlinear conditions. Moreover, it reduces the number of required projection patterns, thereby enhancing overall measurement efficiency.