Harris W F
Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa.
Optom Vis Sci. 1996 Sep;73(9):606-12.
The geometry of the astigmatic wavefront is derived from the symplectic nature of linear optics. It is shown to be paraboloidal. Equations are derived that govern the propagation of such wavefronts through astigmatic systems in general and through thin lenses and across refracting interfaces and homogeneous gaps in particular. The equations allow the generalization of the concept of wavefront curvature or vergence to astigmatic systems. In particular they show how the step-along method of calculating wavefront curvature is generalized. Not only are Keating's earlier conclusions on this topic confirmed but also they are shown to hold under more general circumstances. They hold even when the system contains gradient-index elements such as the natural lens of the eye. Some of the premises used in the earlier study are shown not to be necessary: they are a consequence of symplecticity. The analysis also provides a step-along procedure for calculating wave-front direction. A numerical example in the Appendix shows the application of the step-along method to a particular separated astigmatic system: the back-vertex power of the system is determined as is the equation of the emergent wavefront for a distant object point.
像散波前的几何形状源自线性光学的辛特性。结果表明它是抛物面的。推导了一般情况下此类波前通过像散系统、特别是通过薄透镜以及跨越折射界面和均匀间隙时的传播方程。这些方程使得波前曲率或聚散度的概念能够推广到像散系统。特别地，它们展示了计算波前曲率的逐点法是如何推广的。不仅证实了基廷在此主题上的早期结论，而且表明这些结论在更一般的情况下也成立。即使系统包含诸如眼睛的自然晶状体等梯度折射率元件，这些结论依然成立。早期研究中使用的一些前提条件被证明并非必要：它们是辛性的结果。该分析还提供了一种计算波前方向的逐点程序。附录中的一个数值示例展示了逐点法在一个特定的分离像散系统中的应用：确定了系统的后顶点屈光力以及远处物点的出射波前方程。
