Centre of Vision and Eye Research, Queensland University of Technology, Kelvin Grove, Queensland, Australia.
Ophthalmic Physiol Opt. 2021 Mar;41(2):401-408. doi: 10.1111/opo.12771. Epub 2021 Feb 20.
Third-order equations are well known for determining sagittal and tangential powers of a thin lens, corresponding to an eye rotating behind a lens to view objects away from the optical axis of the lens. These equations are referenced to the back surface of the lens and do not take into account the peripheral thickness of the lens. They do not give the same results as finite raytracing at small angles in which powers are referenced to the vertex sphere, which is the same distance from the centre-of-rotation for all object angles. Modified forms of the third-order sagittal and tangential image vergence error equations are developed to overcome the discrepancies. These are used to determine Tscherning ellipses for zero oblique astigmatism and zero mean oblique power error. While solutions to oblique astigmatism are not affected by the modifications, there are considerable changes to mean oblique error solutions.
三阶方程常用于确定薄透镜的矢状和切向力，这对应于眼睛在透镜后面旋转以观察远离透镜光轴的物体。这些方程参考了透镜的后表面，并未考虑透镜的周边厚度。与在小角度进行有限光线追踪时的结果不同，在小角度进行有限光线追踪时，力被参考到顶点球，对于所有物体角度，该顶点球距离旋转中心的距离相同。为了克服这些差异，开发了三阶矢状和切向像散误差方程的修正形式。这些方程用于确定零斜散光和零平均斜光误差的 Tscherning 椭圆。虽然斜散光的解决方案不受修改的影响，但平均斜误差解决方案有相当大的变化。
