Automated construction of unobscured off-axis four-mirror imaging systems with the IACO_ℝ-NM hybrid global algorithm

Obtaining an unobscured starting point for off-axis four-mirror imaging systems is a non-trivial task that traditionally relies heavily on designer expertise and extensive trial-and-error. To address this challenge, we propose an automated framework capable of efficiently constructing initial off-axis four-mirror structures with diverse geometries. An evaluation function is formulated by combining first-order constraints, third-order aberration constraints using nodal aberration theory (NAT), and a "ray-quadrangle" obscuration error function. A hybrid global optimization strategy, named IACO_R-NM, is proposed by integrating the Improved ant colony optimization for continuous domains (IACO_R) with the Nelder-Mead (NM) simplex method, enabling designer-independent global exploration and rapid obtain unobscured systems. The IACO_R quickly locates an unobscured, coarse global optimum, upon which NM performs refined local optimization. This framework allows designers to efficiently assess the optimization potential of different initial structures and rapidly select suitable geometries for further optimization. Using this method, a compact off-axis four-mirror freeform imaging system is constructed, achieving diffraction-limited performance. Moreover, comparative studies against other global optimizers and gradient-based local methods demonstrate the superior optimization capability of the proposed hybrid algorithm.