Harris W F
Optometric Science Research Group, Department of Optometry, University of Johannesburg, Johannesburg, South Africa.
Optom Vis Sci. 2006 Apr;83(4):249-53. doi: 10.1097/01.opx.0000214327.65375.5a.
The purposes of this article were, for any sequence of tilts applied to a thin lens, to calculate an equivalent turn and single tilt, to show how to use the equivalent turn and tilt to calculate the tilted power of the lens, and, given the desired tilted power, to calculate the power of the untilted lens necessary to compensate for the effects of tilt. The untilted lens may be stigmatic (spherical) or astigmatic (spherocylindrical).
The analysis makes use of rotation matrices to represent rotation in space and previous work in third-order optics on oblique central refraction.
Equations are presented for calculating the combination of turn and tilt that is equivalent to any sequence of tilts. They are specialized for the particular case of combinations of faceform and pantoscopic tilts and allow the decomposition of an arbitrary tilt into a combination of turn and pantoscopic and faceform tilts. The equations also lead to a procedure for calculating or compensating for the tilted power of a sequentially tilted thin lens.
Previous work on the effect of tilt on thin lenses has been generalized to handle combinations of arbitrary tilts.
本文的目的是，对于施加于薄透镜的任何倾斜序列，计算等效旋转和单次倾斜，展示如何使用等效旋转和倾斜来计算透镜的倾斜屈光力，以及在给定所需倾斜屈光力的情况下，计算为补偿倾斜效应所需的未倾斜透镜的屈光力。未倾斜透镜可以是无像散的（球面的）或有像散的（球柱面的）。
该分析利用旋转矩阵来表示空间中的旋转以及三阶光学中关于斜向中心折射的先前工作。
给出了用于计算等效于任何倾斜序列的旋转和倾斜组合的方程。它们针对面形倾斜和前倾倾斜组合的特定情况进行了专门化处理，并允许将任意倾斜分解为旋转与前倾和面形倾斜的组合。这些方程还引出了一种计算或补偿顺序倾斜薄透镜倾斜屈光力的方法。
先前关于倾斜对薄透镜影响的工作已得到推广，以处理任意倾斜的组合。
