Projective Formulation of the Problems of Geometrical Optics II The Design of a Centered Optical System

Abstract

As an application of the theoretical procedure suggested in the first part of the paper, the design of a general optical system is considered. In order that the formulation may be useful, the general equations deduced in Part I, which merely expressed the classic laws of geometrical optics, should be supplemented by a number of equations expressing the elimination of the principal aberrations: this requires that a literal “ray tracing” be effected. In the tangential plane, this projective ray tracing is merely an application of elementary principles: in the extrameridian case, an artifice is introduced by which points and lines of a tridimensional space can be mapped in a plane through the use of complex coordinates. Though the discussion of such complex mapping requires some supplementary theory to be developed, the extrameridian ray tracing can eventually be performed without greater difficulty than that encountered in the tangential case.The conclusions are illustrated by the discussion of the design of a general Schmidt system.