Aberration compensation design method of freeform reflection systems based on generalized aberration theory with...

With the growing demand for high-performance, miniaturized, and lightweight optical systems, off-axis reflective configurations incorporating freeform surfaces have emerged as crucial solutions for reconciling imaging quality with system compactness. However, the intricate mathematical representations and non-rotational symmetry inherent in freeform surfaces present substantial challenges to conventional design methodologies, necessitating innovative direct design approaches. To address these limitations, this paper proposes an advanced aberration compensation method (ACM) rooted in generalized aberration theory (GAT) with series expansion, enabling balanced full-field performance. Distinct from the traditional coefficient minimization method (CMM) that independently minimizes aberration coefficients at individual orders, ACM strategically exploits cross-order aberration compensation through synergistic interactions between lower- and higher-order aberrations. This leads to enhanced full-field imaging performance and better adaptability to asymmetric field layouts. The method is demonstrated on two representative three-mirror anastigmat (TMA) systems: a field-offset zig-zag configuration and a compact circular layout with a small F-number. In both cases, ACM achieves more balanced aberration correction, improved MTF performance, and acceptable computation time increases (under 10%) compared to CMM. These results validate ACM as a promising tool for the efficient and accurate design of freeform optical systems in future advanced applications.