Fast recovery of sparse fringes in unknown freeform surface interferometry

In the adaptive freeform surface interferometer, the adaptive algorithms were equipped to find the required aberration compensation, making interferogram with dark areas (incomplete interferogram) sparse. However, traditional blind search-based algorithms are limited by convergence rate, time consumption, and convenience. As an alternative, we propose an intelligent approach composed of deep learning and ray tracing technology, which can recover sparse fringes from the incomplete interferogram without iterations. Simulations show that the proposed method has only a few seconds time cost with the failure rate less than 4‰. At the same time, the proposed method is easy to perform because it does not require the manual intervention of internal parameters before execution as in traditional algorithms. Finally, the feasibility of the proposed method was validated in the experiment. We believe that this approach is much more promising in the future.