Optical fringe-reflection deflectometry with sparse representation

Optical fringe-reflection deflectometry is a surprisingly attractive scratch detection technique for specular surfaces owing to its unparalleled local sensibility. Full-field surface topography is obtained from a measured normal field using gradient integration. However, there may not be an ideal measured gradient field for deflectometry reconstruction in practice. Both the non-integrability condition and various kinds of image noise distributions, which are present in the indirect measured gradient field, may lead to ambiguity about the scratches on specular surfaces. In order to reduce misjudgment of scratches, sparse representation is introduced into the Southwell curl equation for deflectometry. The curl can be represented as a linear combination of the given redundant dictionary for curl and the sparsest solution for gradient refinement. The non-integrability condition and noise permutation can be overcome with sparse representation for gradient refinement. Numerical simulations demonstrate that the accuracy rate of judgment of scratches can be enhanced with sparse representation compared to the standard least-squares integration. Preliminary experiments are performed with the application of practical measured deflectometric data to verify the validity of the algorithm.