Optical design methods of non-rotationally symmetric optical systems with freeform surfaces

Nowadays freeform surfaces play important roles in improving the imaging per-formance in non-rotationally symmetric optical systems. However, there are currently no general rules for the design with freeform surfaces. In this work, the aim is to contribute to the workflow of non-rotationally symmetric system design with the initial system design method, the analysis and the correction of aberrations in the systems, and the position selection rules for freeform surfac-es. Firstly, an initial system design method is proposed based on nodal aberration theory and Gaussian brackets. A good initial system with minimum aberrations and reasonable structure is essential before adding freeform surfaces. The other already existing methods are limited to certain types of systems. The Gaussian brackets method is not limited to the system type or the number of surfaces. The aberrations are optimized using the nonlinear least-squares solver. The vectorial aberration theory is important for design strategies and the per-formance evaluation. Thus, design strategies for obtaining nodal points of co-ma and astigmatism are concluded in this work based on the vectorial aberra-tion theory. The surface position selection rules for aspheres and freeform sur-faces are also generated based on the different behaviors when the surface is located at or away from the pupil. Since the biconic surface is often used as the basic shape in the freeform sys-tem design, the aberrations generated by the biconic surface are derived in this work. Thus, it is concluded from the aberration theory that coma and astigma-tism generated by the biconic surface are decoupled, which is a benefit to ob-tain nodal points when designing initial systems. Based on the Gaussian brackets initial system design method, initial setups of TMA systems are designed to demonstrate the design procedure. An extended Yolo telescope with three mirrors is designed with a small f-number. The field-constant coma is corrected by the strategy based on nodal aberration theory. The large astigmatism is further corrected using biconic surfaces and higher order freeform polynomials. Based on the selection rules, a Scheimpflug sys-tem is designed in this work with two freeform surfaces. It is proved that the uniformity of Scheimpflug systems can be balanced only with freeform surfaces.