Self-Supervised Deep Learning for Improved Image-Based Wave-Front Sensing

Phase retrieval from supervised learning neural networks is restricted due to the problem of obtaining labels. To address this situation, in the present paper, we propose a phase retrieval model of self-supervised physical deep learning combined with a complete physical model to represent the image-formation process. The model includes two parts: one is MobileNet V1, which is used to map the input samples to the Zernike coefficients, the other one is an optical imaging system and it is used to obtain the point spread function for training the model. In addition, the loss function is calculated based on the similarity between the input and the output to realize self-supervised learning. The root-mean-square (RMS) of the wave-front error (WFE) between the input and reconstruction is 0.1274 waves in the situation of D/r0 = 20 in the simulation. By comparison, The RMS of WFE is 0.1069 waves when using the label to train the model. This method retrieves numerous wavefront errors in real time in the presence of simulated detector noise without relying on label values. Moreover, this method is more suitable for practical applications and is more robust than supervised learning. We believe that this technology has great applications in free-space optical communication.