Abstract

Runge–Kutta integration schemes are well suited to the determination of ray trajectories in inhomogeneous media. There is a fundamental difference, however, between Runge–Kutta schemes and many other schemes for numerically integrating ordinary differential equations: Runge–Kutta schemes are not based on approximating the continuous trajectory by a polynomial. Consequently, these schemes do not implicitly provide a continuous trajectory; they yield only a series of points through which the ray passes, together with the ray direction at those points. A supplementary method must be devised when a continuous trajectory is required. The accuracy of a continuous trajectory for Runge–Kutta schemes is limited by the error introduced in a single iteration of the integrator. A trajectory that attains this limit is referred to here as optimal. The existing method of calculating trajectories for a widely used Runge–Kutta scheme is, in fact, not optimal. Accordingly, an efficient method of determining optimal intermediate trajectories is presented. This new technique is shown to be superior to the existing method for locating ray–surface intersections and allows accuracy doubling (a recently proposed method for accelerating the analysis of systems with inhomogeneous elements) to be used to full advantage.

© 1990 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Differential ray tracing in inhomogeneous media

Bryan D. Stone and G. W. Forbes
J. Opt. Soc. Am. A 14(10) 2824-2836 (1997)

Ray-tracing method for isotropic inhomogeneous refractive-index media from arbitrary discrete input

Yohei Nishidate, Takashi Nagata, Shin-ya Morita, and Yutaka Yamagata
Appl. Opt. 50(26) 5192-5199 (2011)

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 (3)

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 (30)

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