The design of an optical system can be understood as a process of seeking optimal solutions of parameters. There is a complex nonlinear relationship between optical aberration and structural parameters of an optical system. Traditional optical design usually selects an initial structure similar to the expected structure on the basis of experience or from a public lens library. Then, the initial structure is optimized by local optimization algorithms such as damped least squares and the adaptive method, and global optimization algorithms such as simulated annealing, the genetic algorithm, the escape algorithm, and the particle swarm optimization algorithm. Therefore, selecting an appropriate initial structure is essential for subsequent optimization effect and efficiency. However, the current initial structure design method is usually similar to a trial-and-error process, and designers mainly rely on design experience to determine the most appropriate initial structure for different design requirements. This method limits the design efficiency and subsequent optimization of the optical system to a certain extent. In this paper, the proposed optimal design method for the initial structure of a refractive optical system based on deep learning provides designers with a way to choose the initial structure and improves the efficiency of optical design.

First, the structural characteristic data of the reference lens in the optical lens library are learned through supervised training. Then, an unsupervised training model based on ray tracing is constructed. The corresponding general formula for solving optical parameters is derived, and the structure of the optical system under a specific focal length is optimized by unsupervised training. After that, unsupervised training is combined with supervised training to ensure the correctness of the training results and improve the generalization ability of the network model. The super parameters of the network model are adjusted, and the rationality of the system structure is compared before and after the training. Finally, the gap between the output of the network model and the reference lens is compared through the cross-validation experiment, and the generalization ability of the deep learning network model for the design of the initial structure of the optical system under different focal lengths is verified.

Before the training, the size of the super parameter is dynamically adjusted. The comparison of different loss curves in Fig. 4 indicates that the training loss curve 1 drops faster than the training loss curve 3. This is because the learning rate of the training loss curve 3 decreases, which can increase the learning time but ensure the stability and accuracy of the deep learning training process. After deep learning, the optimized optical system is designed. Lens parameters are selected reasonably, and the distance between surfaces is appropriate. The system can perform normal imaging on the image surface (Fig. 5). After cross-validation training (Fig. 8), the comparison shows that the root-mean-square (RMS) spot radius of the lens designed by deep learning is similar to that of the reference lens, and some of the RMS spot radii of the deep learning lenses are even smaller than that of the reference lens. This indicates that the network model can design the initial structure of the refractive optical system that meets the requirements of the actual imaging quality. Finally, the initial structures under different entrance pupil distortions (EPDs) and fields of view (FOVs) are designed, and the success rate of optimal design is better than 96.403%. This indicates that the network model has a good generalization ability.

In this work, a deep learning method for the optimal design of the initial structure of the refractive optical system is proposed, combining supervised training with unsupervised training. Supervised training helps the deep neural network model to learn the structural characteristics of the optical system, and unsupervised training introduces ray tracing and the general formula derived in this paper into the deep learning framework to optimize more optical systems at a set focal length. After 2×105 times of training, the network model can design the initial structure of the optical system with the same optical properties as the reference lens. The simulation shows that under different focal lengths, the network model can generate one million groups of initial optical system structures within the specified EPD and FOV, and the design success rate is better than 96.403% under the specified RMS spot radius. This indicates that the network model has a certain generalization ability after deep learning. The proposed optimal design method for the initial structure of the refractive optical system based on deep learning in this paper provides designers with a way to choose the initial structure, improves the efficiency of optical design, and renders a new optimization method and optimization idea for optical optimal design.