Conic-Surface-Enabling design of multi-mirror freeform imaging systems with flexible folding geometries

The design of reflective optical systems is often hindered by the absence of flexible and generic initialization methods, leading to constrained system performance and increased design complexity. This paper presents a generic Conic-Surface-Enabling method for designing multi-mirror freeform imaging systems with flexible folding geometries. This hybrid method integrates automated generation of initial confocal systems with efficient optimization of freeform system designs. Initial systems are generated by leveraging the confocal properties of generalized “focus type” off-axis conic surfaces, tailored to meet specific imaging requirements and packaging constraints. These designs serve as effective starting points for the subsequent optimization, enabling superior imaging performance through a user-defined freeform surface. The conic-based freeform surface is modified to accommodate diverse situations, facilitating a smooth transition from classical conic forms to freeform geometries. Several representative examples are presented to validate the flexibility and generality of the proposed method in tailoring multi-mirror designs with varying surface numbers and folding geometries. Simulation results further confirm the method's effectiveness, with a designed lithographic objective achieving an image-side numerical aperture of 0.35, an RMS wavefront error of 0.047λ, and distortion below 1 nm, highlighting its potential for advanced optical applications.