Restricted characteristic functions tor general optical configurations

Hamilton’s six-variable characteristic functions are unwieldy for many practical applications. However, the desired optical characterization can often be given in the form of a simpler, restricted characteristic function of four variables. It is shown here that, as conventionally defined, these four-variable characteristics are incomplete for general analyses: They must be supplemented by information about ray sense. In fact, the functional form of each of the point, mixed, and angle characteristics is shown to involve the ray sense explicitly. The characterization of a homogeneous region is studied in detail to provide the foundation for a Hamiltonian analysis of generally configured systems of mirrors and homogeneous lenses.