Abstract

The essentially Hamiltonian process of order doubling is incorporated into a Lagrangian method for the determination of the chromatic aberration coefficients of symmetric systems composed of homogeneous lenses and mirrors. In dealing with chromatic aberration coefficients, the prescription for weighted truncation of power series has been found to be of great value. Accordingly, in this paper we are initially concerned with the general principles of order doubling when weighted truncation is employed. These considerations give rise to the idea of weighted order doubling, which follows simply from a condition corresponding to Fermat’s principle. In the context of aberration theory, it is shown that, by using only the knowledge of a general ray path that includes terms up to order m in a chromatic coordinate, say ω, the configuration of this general ray at the initial or final base surface can be determined (by means of a characteristic function) including terms of order 2m + 1 in ω. A process is devised that incorporates these ideas into an efficient scheme for the determination of the Taylor coefficients of characteristic functions. As expected, the explicit inclusion of the chromatic dependence gives methods that are far superior to the corresponding monochromatic procedures.

© 1984 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Order doubling in the computation of aberration coefficients

G. W. Forbes
J. Opt. Soc. Am. 73(6) 782-788 (1983)

Automatic computation of optical aberration coefficients

T. Brender Andersen
Appl. Opt. 19(22) 3800-3816 (1980)

Seidel aberration coefficients: an alternative computational method

Psang Dain Lin and R. Barry Johnson
Opt. Express 27(14) 19712-19725 (2019)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (34)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription