Nonimaging Optics

Appendix D CONSERVATION OF ÉTENDUE FOR TWO-PARAMETER BUNDLES OF RAYS

The conservation of étendue belongs to a set of integral invariants applicable to the solutions of any Hamiltonian system. Several authors discovered some of these invariants independently. Henri Poincará (1957) recognized them as a part of a general statement. In this appendix we are going to see the applications to optics one of them, which we call conservation of étendue for two-parameter bundles of rays.

Different forms of this invariant have appeared in Geometrical Optics: The theorem of Malus and Dupin, the Lagrange invariant, the Herzberger’s (1944, 1958) fundamental optical invariants (Herzberger, 1958) express totally or partially this invariant (Miñano, 1984).

We ...