Design of an off-axis reflective imaging system using a weighted freeform surface superposition algorithm and the...

In this paper, the equal optical path condition is integrated with a weighted freeform surface superposition algorithm to design the initial layout of off-axis reflective freeform imaging systems. For a single field of view under uniform sampling conditions, the initial layouts of two off-axis four-mirror systems are directly constructed by applying the equal optical path condition in conjunction with an appropriate selection of virtual image points. The results show that, under the single field of view condition, the modulation transfer function (MTF) values of the initial layouts exceed 0.8 at a spatial frequency of 20 line pairs per millimeter (lps/mm). Subsequently, a weighted surface superposition algorithm is employed to superpose freeform surfaces designed for different field points, with optimal weighting factors determined using a simulated annealing algorithm. As a result, the resulting superposed surface maintains relatively high imaging quality across multiple field points, thereby providing a favorable starting point for subsequent optimization. To validate the effectiveness of the proposed method, two initial layouts of off-axis four-mirror systems were designed. Based on these initial designs, the MTF of the first system exceeds 0.6 at a spatial frequency of 20 lps/mm, and the MTF of the second system exceeds 0.8 at a spatial frequency of 20 lps/mm, achieving near diffraction-limited performance.