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.

© 1972 Optical Society of America

Aberration Coefficients of Plane Symmetric Systems

P. J. Sands
J. Opt. Soc. Am. 62(10) 1211-1220 (1972)

Optical Aberration Coefficients. X. Theory of Concentric Optical Systems

H. A. Buchdahl
J. Opt. Soc. Am. 52(12) 1361-1367 (1962)

Optical Aberration Coefficients. IX. Theory of Reversible Optical Systems

H. A. Buchdahl
J. Opt. Soc. Am. 51(6) 608-616 (1961)

Optical Aberration Coefficients. XII. Remarks Relating to Aberrations of any Order

H. A. Buchdahl
J. Opt. Soc. Am. 55(6) 641-649 (1965)

Aberration coefficients of double-plane-symmetric systems

P. J. Sands
J. Opt. Soc. Am. 63(4) 425-430 (1973)