Deal F C, Toop J
Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland.
Optom Vis Sci. 1993 May;70(5):409-13. doi: 10.1097/00006324-199305000-00012.
Because the set of thin spherocylindrical lenses forms a vector space, any such lens can be expressed in terms of its cartesian coordinates with respect to whatever set of basis lenses we may choose. Two types of cartesian coordinate systems have become prominent, those having coordinates associated with the lens power matrix and those having coordinates associated with the Humphrey Vision Analyzer. This paper emphasizes the value of a particular cartesian coordinate system of the latter type, and the cylindrical coordinate system related to it, by showing how it can simplify the trigonometry of adding lenses and how it preserves symmetry in depicting the sets of all spherical lenses, all Jackson crossed-cylinders, and all cylindrical lenses. It also discusses appropriate coordinates for keeping statistics on lenses and shows that an easy extension of the lens vector space to include general optical systems is not possible.
由于薄球柱面透镜集合构成一个向量空间，所以任何这样的透镜都可以根据其相对于我们所选择的任何一组基透镜的笛卡尔坐标来表示。两种笛卡尔坐标系已变得突出，一种是其坐标与透镜屈光力矩阵相关联的坐标系，另一种是其坐标与汉弗莱视觉分析仪相关联的坐标系。本文通过展示它如何能简化透镜相加的三角学运算以及在描绘所有球面透镜、所有杰克逊交叉柱镜和所有柱面透镜集合时如何保持对称性，强调了后一种类型的特定笛卡尔坐标系及其相关圆柱坐标系的价值。它还讨论了用于透镜统计的合适坐标，并表明将透镜向量空间轻松扩展以纳入一般光学系统是不可能的。
