Systems Without Symmetries: Foundations of a Theory of Lagrangian Aberration Coefficients

Abstract

This paper lays the foundations of the lagrangian aberration theory of systems without symmetries, i.e., of systems of arbitrarily situated refracting or reflecting surfaces of arbitrary shapes, separating homogeneous, isotropic media. Basically it relies upon the existence of a certain generic quasi-invariant, which leads to the possibility of writing down the exact relations between the ray coordinates and the local ray variables. A process of iteration can be based upon these relations; this makes it feasible to compute higher-order (i.e., third, fourth,. . .) aberration coefficients. The theory is, therefore, a wide-ranging generalization of that previously developed only for the symmetric system.