The aberrations of reflective optical systems with planar symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this second and last paper, closed-form expressions are derived for the aberrations created by an individual mirror. We study two-mirror off-axis telescopes and establish a new family of designs that we show is simultaneously free of constant coma, linear astigmatism, and quadratic distortions (including smile and keystone). Analytical expressions for the intrinsic aberrations of an astigmatic beam are also derived.

中文翻译：

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具有自由曲面的平面对称镜系统的像差。第二部分：闭式像差公式

在最一般的情况下，将研究具有平面对称性的反射光学系统的像差，这些像差具有自由曲面以及切线和矢状对象及图像的可能位置不同。在第二篇也是最后一篇文章中，针对单个反射镜创建的像差导出了封闭形式的表达式。我们研究了两面镜离轴望远镜，并建立了一个新的设计系列，我们展示了这些设计同时没有恒彗差，线性像散和二次失真（包括微笑和梯形失真）。还导出了像散光束的固有像差的解析表达式。