The adaptive interferometer has been recently proposed to realize the metrology of unknown freeform surfaces with several restructured algorithms for feedback control. The adaptive moment estimation (Adam) stochastic parallel gradient descent (SPGD) algorithm is employed in this paper for fringes release. The proposed algorithm makes considerable progress in relieving conflict of the convergence rate, speed, and parameters intervention. Simulations and experiments show its 37% time saving and 99% convergence rate, with arbitrarily configured parameter increment, compared with the SPGD algorithm. It would have great potential in in-process tests in freeform surface fabrication or large-volume testing.

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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.