Abstract

Exact expressions are derived for Hamilton’s angle characteristic for a single reflecting or refracting surface of toric or conic form. The configuration of the base planes and the initial and final coordinates are all ultimately defined with respect to a base ray that is neither assumed to be normally incident nor taken to be incident at an axial or equatorial point. The expressions that emerge form a basis for several aspects of the modeling and design of systems without symmetries. Significant simplifications are realized by appropriately subdividing the derivation, and one of the principal components is a study of the change in the form of the restricted angle characteristic when the coordinates and base planes are reconfigured.

© 1993 Optical Society of America

Restricted characteristic functions for general optical configurations

G. W Forbes and Bryan D. Stone
J. Opt. Soc. Am. A 10(6) 1263-1269 (1993)

Generalization of Hamilton’s formalism for geometrical optics

M. A. Alonso and G. W. Forbes
J. Opt. Soc. Am. A 12(12) 2744-2752 (1995)

Foundations of first-order layout for asymmetric systems: an application of Hamilton’s methods

Bryan D. Stone and G. W. Forbes
J. Opt. Soc. Am. A 9(1) 96-109 (1992)

Foundations of second-order layout for asymmetric systems

Bryan D. Stone and G. W. Forbes
J. Opt. Soc. Am. A 9(11) 2067-2082 (1992)

Image formation by a general optical system, using Hamilton’s method

C. H. F. Velzel
J. Opt. Soc. Am. A 4(8) 1342-1348 (1987)