Fig. 1. Whole optical design framework based on deep learning.

Fig. 2. Illustration of the fundamental data set generation and feedback strategy.

Fig. 3. Illustration of input and output parameters of DNN. The superscripts i, o, and tar denote input, output, and target, respectively. The output and target surface and structure parameters values are used to construct the mean square error (MSE) and then construct the supervised loss function L_super.

Fig. 4. Sketch of the parameter space and subspace pair SPΦ(i) and SPψ(i). A 2D space (only two system parameters and two structure parameters are considered, respectively) is plotted here for clarity, but actual parameter spaces should be high-dimensional spaces. Four subspaces are plotted here as an example. The subspaces plotted in same color form a subspace pair SPΦ(i)-SPψ(i). φ and ψ of reference system RSYS(i) are at the center of SPΦ(i) and SPψ(i).

Fig. 5. Illustration of the training mode of combined supervised and unsupervised training.

Fig. 6. Fast generation process of multiple-solution freeform imaging systems using FreeformNet.

Fig. 7. (a) The selected folding geometry of freeform off-axis three-mirror imaging system and its structure constraints. (b) Sketch of the concept of structure parameters range.

Fig. 8. Typical predicted systems when system parameters and structure parameters were all provided.

Fig. 9. Average RMS spot diameter and maximum relative distortion of normal systems in case one (system numbers were arranged in ascending order according to the average RMS spot diameter).

Fig. 10. Typical predicted systems when all system parameters and partial structure parameters were provided.

Fig. 11. Average RMS spot diameter, maximum relative distortion, and system volume of normal systems in the second case (the system numbers were arranged in ascending order according to the average RMS spot diameter).

Fig. 12. Typical predicted systems when partial system parameters were provided.