Power vectors: An application of Fourier analysis to the description and statistical analysis of refractive error
Power vectors: An application of Fourier analysis to the description and statistical analysis of refractive error
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DOI：
10.1097/00006324-199706000-00019
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发表时间：
1997-06-01
影响因子：
1.4
通讯作者：
Horner, D
中科院分区：
文献类型：
--
作者：
Thibos, LN;Wheeler, W;Horner, D
本文从焦度分布的傅里叶分析的观点出发，对球柱透镜进行了描述。它表明，熟悉的正弦平方法自然导致一个傅立叶级数表示正好有三个傅立叶系数，代表薄透镜的自然参数。常数项对应于平均等效球镜度（MSE），而谐波的振幅和相位分别对应于杰克逊交叉柱面（JCC）透镜的度数和轴。以矩形形式表示傅立叶级数导致将任意球柱透镜表示为球面透镜和两个交叉柱体的和，一个在轴0度处，另一个在轴45度处。这三个组成镜片的光焦度可以解释为光焦度分布的矢量表示的（x，y，z）坐标。这种功率矢量表示的球柱体透镜的验光数据的数值和图形分析的优点，涉及透镜组合，比较不同的镜头，和屈光不正的统计分布的问题进行了说明。
The description of sphere-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphere-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degrees and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.