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Freeform optical elements are increasingly used in practical optical systems, enabled by advances in fabrication and metrology. The automated design of off-axis freeform reflective systems under multi-field constraints remains difficult because aberrations are strongly coupled, and the design space is high-dimensional. We present an automated design workflow that combines multi-field seed-curve extension with constrained nonlinear least-squares refinement. The initial freeform geometry is constructed under global field constraints to embed the desired ray mapping. The freeform coefficients are then optimized using the Levenberg–Marquardt algorithm to improve image quality while controlling distortion. We demonstrate the method by designing a vehicle head-up display (HUD) system and validating it in Zemax OpticStudio. The optimized design achieves a maximum distortion below 3% and an MTF above 0.3 at 6 lp/mm across the full eye box. The results demonstrate that the proposed workflow is effective for the HUD design example studied in this work and is promising for similar off-axis reflective imaging systems.
Fu et al. (2026) studied this question.