Particle swarm optimization-driven design of off-axis four-mirror optical systems with near-diffraction-limited aberration correction

Abstract Off-axis four-mirror optical systems exhibit enhanced design flexibility and superior aberration correction compared to their three-mirror counterparts, yet their design complexity remains a significant challenge in modern optical engineering. This study proposes a systematic methodology integrating Particle Swarm Optimization (PSO) and off-axis optimization to address these limitations. First, third-order aberration expressions for a coaxial four-mirror system are derived using classical aberration theory, establishing a theoretical foundation. A multi-constraint fitness function is formulated to quantify imaging quality, enabling the application of the PSO algorithm for global optimization. This process yields an optimized coaxial structure with initial geometric parameters, which serves as the baseline for subsequent off-axis transformations. In the second phase, off-axis optimization is implemented to eliminate central obscuration and stray light, while strategically introducing conic and aspheric surfaces to further suppress residual aberrations. The final off-axis four-mirror system achieves near-diffraction-limited performance across visible wavelengths, as evidenced by a modulation transfer function (MTF) exceeding 0.5 at 180 lp mm −1 . This work advances the automated design of freeform multi-mirror systems, offering a scalable framework for applications requiring compact, unobscured optical architectures with sub-λ wavefront control.