MATRIX DECOMPOSITIONS FOR NONSYMMETRICAL OPTICAL-SYSTEMS

A new approach to the representation of nonsymmetrical optical systems by matrices is introduced. In the paraxial approximation each component of an optical system is represented by a 4 multiplied by 4 unitary matrix, and the product of those matrices yields the transfer matrix of the system. The transfer matrix that represents the propagation between two arbitrary planes through the system containing two independently rotated cylindrical lenses is decomposed into the product of three matrices. The eigenvalues of the submatrices in this factorized form determine the focal lengths of the equivalent system and the localization of the foci of the system with respect to these arbitrarily chosen planes.