Least-squares method for data reconstruction from gradient data in deflectometry

Least-squares integration (LSI) and radial basis function integration (RBFI) methods are widely used to reconstruct specular surface shapes from gradient data in a deflectometry measurement. The traditional LSI method requires gradient data having a rectangular grid, and the RBFI method is effective at handling small size measurement data sets. Practically, the amount of gradient data is rather large, and data grids are in quadrilateral shapes. With this in mind, a new LSI method is proposed to integrate gradient data, which is based on an approximation that the normal vector of one point is perpendicular to the vectors connecting points at either side. A small measurement data set integrated by the RBFI method is employed as a supplementary constraint of the proposed method. Simulation and experimental results show that this proposed method is effective and accurate at handling deflectometry measurement.