Harris W F
Department of Optometry, Rand Afrikaans University, Johannesburg, SouthAfrica.
Ophthalmic Physiol Opt. 1989 Oct;9(4):415-9.
The dioptric power matrix of a single refracting surface is shown to be directly related to the differential form known in differential geometry as the second fundamental form. Consequently it is a complete description of the local refractive character of the surface. Generalized equations are derived for sagitta and lens thickness for surfaces of any form. The equations hold approximately for points close to the optical axis except in the case of paraboloidal surfaces: for paraboloidal surfaces they hold exactly. Lens thickness approximately obeys what is termed the principle of form independence. The value of the second fundamental form is approximately double the sagitta. Formal support is provided for Keating's concept of a generalized matric vergence of astigmatic wave-fronts.
单个折射面的屈光力矩阵被证明与微分几何中已知的作为第二基本形式的微分形式直接相关。因此，它是该表面局部折射特性的完整描述。推导了任意形状表面的矢高和透镜厚度的广义方程。除了抛物面的情况外，这些方程对于靠近光轴的点近似成立：对于抛物面，它们精确成立。透镜厚度大致遵循所谓的形状独立性原理。为基廷关于像散波前广义矩阵聚散度的概念提供了形式上的支持。
