A symmetrical optical system consists of a series of vertex to vertex intervals separating coaxial refracting or reflecting surfaces of revolution. This paper develops two types of matrices composed of constant elements, one representing intervals and the other surfaces. These matrices are multiplied together in the same order as the corresponding intervals and surfaces occur in the optical system. The resultant product matrix expresses the paraxial, aberrational and chromatic behavior of the system.
Such a formulation may be applied mechanically by unskilled computers, and suggests a passive electrical network analogue to optical systems. The surfaces are not limited to spheres.
CLYDE W. HARRIS, "Optical Design by a Matrix Method," J. Opt. Soc. Am. 40, 819-820 (1950)