Abstract

This paper concerns itself with certain general details of the “Lagrangian” theory of aberration coefficients previously developed by the author. They are: (i) the general relation between various types of contributions by spherical and aspherical surfaces; (ii) a property of the iteration formulas of any order when the surface is spherical; (iii) the “Principle of Duality” and some of its applications, in particular to the problem of computing a set of coefficients and their duals by means of a single program; (iv) equations for the intrinsic coefficients of spherical aberration of any order when the surface is spherical, and for a related set of coefficients (these being required for an application of the principle of duality); and (v) the groups of identities between aberration coefficients of any order.

© 1965 Optical Society of America

Optical Aberration Coefficients. XIV. Simplified Computational Form of Iteration Equations

H. A. Buchdahl
J. Opt. Soc. Am. 59(11) 1422-1426 (1969)

Optical Aberration Coefficients. IX. Theory of Reversible Optical Systems

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

Optical Aberration Coefficients. VIII. Coefficient of Spherical Aberration of Order Eleven

H. A. Buchdahl
J. Opt. Soc. Am. 50(7) 678-683 (1960)

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

H. A. Buchdahl
J. Opt. Soc. Am. 62(11) 1314-1324 (1972)

Optical Aberration Coefficients. X. Theory of Concentric Optical Systems

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