Abelman Herven, Abelman Shirley
University of the Witwatersrand, Johannesburg, School of Computational and Applied Mathematics, Private Bag 3, Wits 2050, South Africa.
J Biomed Opt. 2009 Jan-Feb;14(1):014025. doi: 10.1117/1.3079809.
We seek to analyze the geometry and explain how bounds and intervals of nonzero purely cylindrical powers are obtained and applied in symmetric dioptric power space and envisaged in the clinic. The principal powers at zero and at the focus at the cylinder power of a lens are subject to the same uncertainty when measured. Accompanying these uncertainties is an error in axis position. Error cells are constructed for typical cylinder axes and an associated power. The geometry contains an elegant clinical determination for cross-cylinder compensation of astigmatism in terms of calculation friendly quantities. The extreme positions in the error cells define bounds for the cross-cylinder powers and their meridians. When clinical powers in a chosen error cell are transposed, the new powers are within a different cell. This ambiguous cell pair maps to a single cell in an antistigmatic plane around cross-cylinder powers.
我们试图分析其几何结构，并解释非零纯柱面屈光力的界限和区间是如何在对称屈光力空间中得到并应用的，以及在临床中是如何设想的。当测量透镜柱面屈光力为零时和焦点处的主子午面屈光力时，会受到相同的不确定性影响。伴随这些不确定性的是轴位误差。针对典型的柱面轴和相关的屈光力构建误差单元。该几何结构包含了一种简洁的临床方法，可根据便于计算的量来确定散光的交叉柱镜补偿。误差单元中的极端位置定义了交叉柱镜屈光力及其子午线的界限。当所选误差单元中的临床屈光力进行转换时，新的屈光力位于不同的单元内。这种模糊的单元对映射到围绕交叉柱镜屈光力的反散光平面中的单个单元。
