Concatenation of symmetric systems in Hamiltonian optics

The calculation of restricted characteristic functions of symmetric optical systems is investigated using the process of concatenation. The characteristic functions under consideration take the form of a power series in the rotation invariants. A new set of variables (replacing the intermediate rotation invariants) is introduced, which permits the problem to be expressed in a form that has become familiar from the study of the concatenation of systems without symmetries. An appropriate general formalism is developed and implemented in a FORTRAN program that enables the characteristic functions of systems composed of simple subsystems (whose charactertistic functions may be determined directly) to be calculated to arbitrary orders.