Fig. 1. Rapid design of spherical multi-lens optical system based on deep neural network AI methods^[34-35]. (a) Flow chart of the algorithm based on deep neural network. “Inference”: fast inference to realize optical system design. The DNN network in “Inference” is obtained by the two training steps of “Unsupervised traning” and “Supervised traning”. “Unsupervised traning” and “Supervised traning” are training processes that only need to be done once. In AI optical design, designers only need to carry out the “Inference” process to quickly design spherical multi-lens optical systems. (b) Architecture of the deep neural network. The input parameters are the first-order specifications of the optical system (entrance pupil diameter EPD, half height field of view HFOV, and vignetting coefficient threshold, etc.). A deep network can achieve dynamic iterative updates. The output parameters are the structural parameters of the lens (curvature, refractive index, and spacing, etc.)

Fig. 2. “Lens design extrapolation method” based on deep neural networks realizes designing various types of microscope objectives^[36] (the input parameters are the first-order specifications of the microscope objective lens and the qualitative arrangement description of the lens, and the output parameters are the structural parameters of the microscope objectives, such as curvature, refractive index, and spacing)

Fig. 3. Design off-axis flight visual display system based on deep learning neural network^[38]. In the database (upper dotted box), the input parameters are the first-order specifications of the off-axis flight visual display system, such as X-direction field of view, Y-direction field of view, pupil position and size, and object distance, and the output parameters are polynomial function of the off-axis free-form surface. In testing and practical use (the dotted box below), the deep neural network can quickly output the initial structure of the off-axis free-form surface, which can be further optimized later

Fig. 4. Design of off-axis three-mirror free-form surface imaging system based on deep learning neural network^[40]. In the “Dataset generation”, the input parameters are the first-order specifications of the imaging system (field of view, effective focal length, and F#), and the output parameters are surface structural data, such as off-axis free-form surface shape, interval, and tilt angles. In practical use, after the first-order specifications of the system are input, the deep neural network can quickly output the initial structure of the off-axis free-form surface, which can be further optimized later

Fig. 5. Diagram of the deep learning network architecture used in Fig.4 ^[40] (SSP: system specifications; OSD: output surface data)

Fig. 6. Design of various optical systems based on a general artificial intelligence framework^[41]. (a) Off-axis triple-mirror imaging system; (b) off-axis four-mirror afocal telephoto system with free-form surface; (c) free-form prism system for augmented reality near-eye display

Fig. 7. Free-space diffractive optical system enables optical computing digital sorting and imaging^[43]. (a) Schematic of deep diffraction networks; (b) free-space optical computing digital classification system based on diffractive neural networks; (c) free-space conjugate imaging system based on diffractive neural networks; (d) comparison between diffractive neural networks and conventional neural networks

Fig. 8. Computational classification system for optoelectronic hybrid based on diffractive neural network^[44]. (a) Schematic of optoelectronic hybrid network; (b) phase distribution maps of five diffractive layers

Fig. 9. Singlet lens computational imaging cameras

Fig. 10. “End-to-end” optoelectronic system design method with joint optimization of optical design and computational imaging^[63-64]

Fig. 11. Large depth-of-field (DOF) singlet lens imaging system^[68] (In optical design, maintain the consistency of PSF within a large DOF. After the digital image is acquired, the image contrast is further enhanced by deconvolution method)

Fig. 12. Flowchart of metasurface imaging combined with computational algorithms in white visible light spectrum^[69]

Fig. 13. Computational imaging of complex light-field based on metasurface diffuser^[70]

Fig. 14. Singlet lens microscopic imaging system based on circularly symmetric aberration functions^[71-72]. (a) Schematic of singlet lens microscopic imaging system; (b) three-dimensional schematic of portable color singlet lens computational microscopic imaging device

Fig. 15. Comparison of “end-to-end” joint optimization optoelectronic imaging system methods^[79]. (a) Post deconvolution computational imaging method can significantly improve the image quality of the optical lens (Cooke Triplets); (b) comparison of imaging capabilities based on different optimization criteria