Fast measurement of mid-spatial-frequency error on optical surfaces with convolutional neural networks

Mid-spatial-frequency (MSF) error on optical surfaces can do great harm to high-performance laser systems. A non-interferometric way of measuring it is phase retrieval, which has already proved its effectiveness in previous studies. However, the performance of phase retrieval is limited by its long-time iterative process and relies heavily on reliable initial solution. Therefore, in this paper, we put forward a method for fast measurement of MSF error, by introducing advanced deep learning technique into traditional computational imaging methods. Results show that the proposed method simultaneously gains an improvement on convergence speed and a reduction on residual error. The proposed method takes much fewer iterations to converge to the same error level, and has much smaller average residual error than that of the conventional algorithm in the numerical experiments.