Abstract

A system of functional differential equations arising from Fermat’s principle is used to study qualitative questions concerning the mathematical possibility of certain rotationally symmetric piecewise homogeneous optical systems. In particular, it is shown that, given two pairs of points on the optical axis, there exist precisely two systems of single-element lenses having prescribed axial thickness and index of refraction such that these points are perfect foci. This finding sharpens an earlier result. Embedding the solution in a one-parameter family permits the construction of an asymptotic solution that requires the solution of a single nonlinear ordinary differential equation. The leading-order solution corresponds to an optical system satisfying the Herschel condition. The existence and uniqueness results are extended to optical systems having three lens boundaries such as achromatic doublets.

© 1994 Optical Society of America

Full Article  |  PDF Article

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

Figures (6)

You do not have subscription access to this journal. Figure files 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 (76)

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