Studies of the focal region of a spherical reflector: Geometric optics

Abstract

The classical optics of the spherical reflector is reviewed and extended with particular application to the focal region. The caustic surface, axial caustic, and circle of least confusion are described in detail. The manner in which the reflected rays combine in the focal region is then developed. In general, three reflected rays intersect at any field point <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> on the interior of the caustic surface, but off the axial caustic). The points of incidence of the three rays and their optical path lengths from a common reference plane are calculated, providing the necessary phase and divergence information for the focal region.