Harris W F
Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa.
Optom Vis Sci. 1996 Jun;73(6):418-23. doi: 10.1097/00006324-199606000-00010.
The application of the concept of ray vector fields to optical systems is reexamined. Paraxial or linear optics defines a four-dimensional ray vector field for any optical system: the vector field maps the incident ray vector into the emergent ray vector. In the case of thin systems, including thin astigmatic lenses, one can define a vector field of reduced dimensionality: the vector field is two-dimensional and maps the ray's incident position into the change in reduced direction. When the index of refraction is the same before and after a thin system, the change in reduced direction is the reduced deflection through the system or the reduced prismatic effect. Contrary to what has recently been claimed, this type of two-dimensional vector field does not apply in general to thick systems. However, a number of different types of two-dimensional vector fields can be defined for various particular classes of optical systems. Thick systems differ qualitatively from thin systems. They do not have equivalent thin lenses and cannot generally be replaced by thin lenses. Equations are derived for the change in reduced direction and deflection for a ray through optical systems in general and through separated two- and three-lens systems in particular.
重新审视了光线矢量场概念在光学系统中的应用。傍轴或线性光学为任何光学系统定义了一个四维光线矢量场：该矢量场将入射光线矢量映射为出射光线矢量。在薄系统的情况下，包括薄像散透镜，可以定义一个降维的矢量场：该矢量场是二维的，将光线的入射位置映射为降维方向的变化。当薄系统前后的折射率相同时，降维方向的变化就是光线通过该系统的降维偏折或降维棱镜效应。与最近所宣称的相反，这种二维矢量场一般并不适用于厚系统。然而，对于各种特定类型的光学系统，可以定义多种不同类型的二维矢量场。厚系统与薄系统在性质上有所不同。它们没有等效薄透镜，通常也不能用薄透镜来替代。推导了光线通过一般光学系统以及特别是通过分离的双透镜和三透镜系统时降维方向变化和偏折的方程。
