In this paper, a method of how to construct a freeform surface directly in an off-axis reflective image system is proposed. The method includes both the seed curve extension algorithm and simulated annealing algorithm. Firstly, the sample points on the unkown freeform surface were be obtained quickly by the seed curve extension algorithm. Then the continuity of the freeform surface is evaluated by calculating the angle between the normal vectors at the adjacent sample points. At last the freeform surface was fitted to an extended polynomials using simulated annealing algorithm. The method is employed to construct a freeform surface directly which is used as a primary mirror in an initial layout of an off-axis two-mirror system.

中文翻译：

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通过种子曲线扩展和模拟退火算法直接在离轴反射图像系统的初始布局中构造自由曲面

本文提出了一种在离轴反射图像系统中直接构造自由曲面的方法。该方法包括种子曲线扩展算法和模拟退火算法。首先，通过种子曲线扩展算法快速获得未知的自由曲面上的采样点。然后，通过计算相邻样本点处的法向矢量之间的角度来评估自由曲面的连续性。最后，使用模拟退火算法将自由曲面拟合到扩展多项式。该方法用于直接构造自由曲面，该自由曲面在离轴两面镜系统的初始布局中用作主镜。