Analysis of method of 3D shape reconstruction using scanning deflectometry

This work presents a scanning deflectometric approach to solving a 3D surface reconstruction problem, which is based on measurements of a surface gradient of optically smooth surfaces. It is shown that a description of this problem leads to a nonlinear partial differential equation (PDE) of the first order, from which the surface shape can be reconstructed numerically. The method for effective finding of the solution of this differential equation is proposed, which is based on the transform of the problem of PDE solving to the optimization problem. We describe different types of surface description for the shape reconstruction and a numerical simulation of the presented method is performed. The reconstruction process is analyzed by computer simulations and presented on examples. The performed analysis confirms a robustness of the reconstruction method and a good possibility for measurements and reconstruction of the 3D shape of specular surfaces.

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