Recognition and separation of fringe patterns in deflectometric measurement of transparent elements based on empirical curvelet transform.

• Fringe superposition is an essential challenge for the deflectometric measurement of transparent elements. • A general-purpose fringe separation strategy is proposed by the empirical curvelet based frequency domain filtering. • Over-separated patterns are recombined based on the weighted permutation entropy method to avoid phase distortion. In the deflectometric measurement of transparent elements, it is critical to separate the superposed fringes reflected from the front and rear surfaces to establish the pixel correspondences between the camera and screen pixels. But it is a challenging task due to the low reflectivity and uneven background of transparent elements. A reliable fringe separation method is proposed based on the empirical curvelet transform. The captured fringe images are decomposed into different modes according to their directions, periods, curvatures or modulation coefficients, and then a weighted-permutation-entropy-based fusing algorithm is developed to automatically aggregate those over-separated patterns. By employing the proposed method, the measurement accuracy is significantly improved, the number of demanded images is effectively reduced, and high-precision, automatic, and rapid measurement is thereby achieved. The measurement accuracy of spherical and cylindrical lenses can achieve 73 nm and 332 nm Root-of-Mean-Squares-Error, respectively. [ABSTRACT FROM AUTHOR]