THE RAY-TRACING AND ENERGY-CONSERVATION EQUATIONS FOR MIRROR SYSTEMS WITH 2 REFLECTING SURFACES

We consider specular reflector systems with two mirrors and an energy source which is either a point source or a collimator. For such systems, we derive here second order partial differential equations of Monge-Ampere type expressing the ray tracing and energy conservation laws. By specializing certain parameters in these equations, one obtains explicit expressions for energy patterns produced by the output wavefront on receiver surfaces of arbitrary geometry. The resulting differential equations can be used for analysis and synthesis of reflector systems that have applications in electromagnetics and optics.