Objective The testability of mirror surface shape error is a fundamental requirement for high-precision optical systems from design to application, failure to test means that it can't be manufactured. Currently, many optical system design methods focus on improving system performance and imaging quality. The public reporting on methods for directly assessing surface shape error testability during the design process is limited. Traditionally, the design of optical systems and the testing of optical elements often occur sequentially, without direct feedback on the testability during optical design. For high-performance optical systems, this can lead to the situation where the system design is excellent, but the difficulty of element testing is too high, resulting in bottlenecks in the practical application. Integrating relevant theoretical methods for testing into the process of optical systems design is an important way to solve the testability of optical component surface shape error. This approach has significant implications for reducing testing difficulties, fully exploring the potential of optical design and improving the feasibility of optical systems.

Methods In theoretical research, the research starts with the design of an off-axis three-mirror optical system as the theoretical entry point, using Computer Generated Holograms (CGH) as the test tool for optical element surface shapes error. Based on the surface shape characterization equation and CGH testing principles, mathematical relationships between the optical design parameters and CGH-related parameters are derived. This relationship act as a bridge for the testability of optical system surface shapes, thereby establishing a design method for off-axis three-mirror optical systems based on surface shape testability evaluation. In the design validation stage, an off-axis three-mirror optical system with a focal length of 800 mm, an F-number of 4, and a field of view of 14°×2° is taken as an example to validate the proposed design method based on surface shape testability evaluation

Results and Discussions The final result of the off-axis three-mirror optical system is shown in Figure 10. The system meets the requirements for image quality and design specifications, with the value of the Modulation Transfer Function (MTF) at 100 lp/mm exceeding 0.4 across all fields of view. Using this design method, the minimum line width of CGH used to test the system's tertiary mirrors has been increased from 4.84 μm to 14.34 μm, enhancing both the testability of optical system surface shapes and the manufacturability of CGH.

Conclusions Based on the principles of CGH testing and the surface characterization equations of optical elements, mathematical relationships between optical system design parameters of optical systems and the relevant parameters of CGH have been derived and a design method for off-axis three-mirror optical systems based on surface shape testability evaluation is proposed. Using this method, an off-axis three-mirror optical system with a focal length of 800 mm, an F-number of 4, and a field of view of 14°×2° was designed. The system shows good image quality, with MTF values exceeding 0.40 at 100 lp/mm across all fields of view. The design results demonstrate that compared to conventional off-axis three-mirror optical systems, this design method not only ensures imaging quality but also achieves calculation and control of the CGH-related parameters. It significantly enhances the testability of surface shapes and holds certain significance in reducing the difficulty of optical element testing and improving the feasibility of optical systems.