Lakshminarayanan V, Sridhar R, Jagannathan R
School of Optometry, University of Missouri at St. Louis 63121-4499, USA.
J Opt Soc Am A Opt Image Sci Vis. 1998 Sep;15(9):2497-503. doi: 10.1364/josaa.15.002497.
The dioptric power of an optical system can be expressed as a four-component dioptric power matrix. We generalize and reformulate the standard matrix approach by utilizing the methods of Lie algebra. This generalization helps one deal with nonlinear problems (such as aberrations) and further extends the standard matrix formulation. Explicit formulas giving the relationship between the incident and the emergent rays are presented. Examples include the general case of thick and thin lenses. The treatment of a graded-index medium is outlined.
光学系统的屈光力可以表示为一个四分量屈光力矩阵。我们利用李代数方法对标准矩阵方法进行了推广和重新表述。这种推广有助于处理非线性问题（如像差），并进一步扩展了标准矩阵公式。给出了入射光线和出射光线之间关系的显式公式。示例包括厚透镜和薄透镜的一般情况。概述了渐变折射率介质的处理方法。
