Design of compact off-axis freeform imaging systems based on optical-digital joint optimization

Using a freeform optical surface can effectively reduce the imaging system weight and volume while maintaining good performance and advanced system specifications. But it is still very difficult for traditional freeform surface design when ultra-small system volume or ultra-few elements are required. Considering the images generated by the system can be recovered by digital image processing, in this paper, we proposed a design method of compact and simplified off-axis freeform imaging systems using optical-digital joint design process, which fully integrates the design of a geometric freeform system and the image recovery neural network. This design method works for off-axis nonsymmetric system structure and multiple freeform surfaces with complicated surface expression. The overall design framework, ray tracing, image simulation and recovery, and loss function establishment are demonstrated. We use two design examples to show the feasibility and effect of the framework. One is a freeform three-mirror system with a much smaller volume than a traditional freeform three-mirror reference design. The other is a freeform two-mirror system whose element number is reduced compared with the three-mirror system. Ultra-compact and/or simplified freeform system structure as well as good output recovered images can be realized.