Kaye Stephen B
St. Paul's Eye Unit, Royal Liverpool University Hospital, Liverpool, United Kingdom.
Optom Vis Sci. 2009 Apr;86(4):382-94. doi: 10.1097/OPX.0b013e31819895b8.
To provide a scalar measure of refractive error, based on geometric lens power through principal, orthogonal and oblique meridians, that is not limited to the paraxial and sag height approximations.
A function is derived to model sections through the principal meridian of a lens, followed by rotation of the section through orthogonal and oblique meridians. Average focal length is determined using the definition for the average of a function.
Average univariate power in the principal meridian (including spherical aberration), can be computed from the average of a function over the angle of incidence as determined by the parameters of the given lens, or adequately computed from an integrated series function. Average power through orthogonal and oblique meridians, can be similarly determined using the derived formulae.
The widely used computation for measuring refractive error, the spherical equivalent, introduces non-constant approximations, leading to a systematic bias. The equations proposed provide a good univariate representation of average lens power and are not subject to a systematic bias. They are particularly useful for the analysis of aggregate data, correlating with biological treatment variables and for developing analyses, which require a scalar equivalent representation of refractive power.
基于通过主、正交和斜子午线的几何透镜焦度，提供一种屈光不正的标量测量方法，该方法不限于傍轴和矢高近似。
推导一个函数来模拟透镜主子午线的截面，然后将该截面绕正交和斜子午线旋转。使用函数平均值的定义来确定平均焦距。
主子午线的平均单变量焦度（包括球差），可以根据给定透镜参数确定的入射角上的函数平均值来计算，或者通过积分级数函数充分计算。通过正交和斜子午线的平均焦度，可以使用推导公式类似地确定。
测量屈光不正时广泛使用的计算方法——球镜当量，引入了非恒定近似，导致系统偏差。所提出的方程提供了平均透镜焦度的良好单变量表示，并且不存在系统偏差。它们对于分析汇总数据、与生物治疗变量相关以及开发需要屈光力标量等效表示的分析特别有用。
