High-Precision Construction of Off-Axis Multi-Reflective Systems for a Single Field of View Based on a Stable Initialization Seed Curve Extension Algorithm

Freeform optical design is regarded as a key approach to overcoming the performance limits of traditional imaging systems. However, the existing Seed Curve Expansion (SCE) algorithm has two major limitations. First, the initial and ideal image points are selected randomly, causing unstable optical performance and low construction accuracy, especially under finite object distance and non-paraxial incidence. Multiple trials are often needed, reducing efficiency and repeatability. Second, the algorithm cannot constrain aperture, focal length, or geometry; thus, despite good imaging quality, the final system parameters often deviate from design requirements, limiting engineering applicability. To address these issues, this work proposes a Stable Initialization Seed Curve Expansion (SI-SCE) algorithm based on ray tracing and Fermat’s principle. The method accurately calibrates the initial point and the ideal image point, eliminating uncertainties caused by randomness. A virtual auxiliary surface strategy is introduced to achieve high-precision freeform construction under finite object distance. In addition, a parameter constraint mechanism is embedded in the algorithm, enabling the designed off-axis multi-reflective freeform system to directly meet specified requirements on pupil diameter, focal length, and geometric size. The feasibility of the SI-SCE algorithm was demonstrated by designing a freeform off-axis three-mirror imaging system with a rectangular 6°×6° field of view and a moderate F-number. The final system features an F-number of 3.4 and an entrance pupil diameter of 60 mm. It achieves diffraction-limited performance across the Visible–NIR 0.38−2 μm wavelength range.