Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method

Transparent optical elements play a significant role in optical imaging and sensing, and the form qualities of these elements are critical to the functionalities of opto-electrical equipment. Therefore, rapid measurement of advanced transparent optical devices is urgently needed. Deflectometry, as a commonly used measurement method, has broad applications in form measurement. However, there are some challenges in the reflective deflectometric measurement of transparent elements, such as fringe superposition, low reflectivity, and non-uniform backgrounds, which severely affect the measurement accuracy. To address these issues, a single-frame fringe separation method is proposed for the deflectometric measurement of transparent elements. A fast iterative filtering method is utilized for coarse fringe separation and a convolutional neural network is adopted to solve the information leakage and incomplete fringe separation. The construction of the neural network involves improving and refining the filtering method to achieve precise separation of fringes. The proposed method achieves fringe separation and forms reconstruction of the upper and lower surfaces. Through simulations and experiments, the effectiveness and robustness of the proposed method are demonstrated, and the measurement accuracy can achieve 65 nm root-of-mean-squared-error (RMSE).