Modal shape reconstruction method for deflectometry based on deep learning

Deflectometry is a slope-based technique to measure specular surfaces. Modal reconstruction methods fit the surface shape with a certain mathematical model based on expansion polynomials and their coefficients. The coefficients are obtained by linear equations, which are consisted of the gradient of the polynomials and the measured slope data. Nevertheless, computing the large linear equations is time-consuming work and the noises and outliers will decrease the reconstruction accuracy. This paper uses the Chebyshev polynomials as the basis set and proposes a modal reconstruction method based on the deep convolutional neural network to directly output the corresponding Chebyshev coefficients. Compared with the conventional modal reconstruction method, the results demonstrate that the reconstruction accuracy and the computational efficiency are improved effectively using the proposed method.