Abstract

We describe necessary and sufficient conditions for image transformations so that surfaces refracting or reflecting collimated beams exist. The surfaces are given by explicit formulas. When these conditions are not satisfied, we show that a surface can be found so that it minimizes the L2 distance between its gradient and the image transformation.

© 2011 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Reflection, refraction, and the Legendre transform

Cristian E. Gutiérrez
J. Opt. Soc. Am. A 28(2) 284-289 (2011)

Designing coupled free-form surfaces

R. Andrew Hicks and Christopher Croke
J. Opt. Soc. Am. A 27(10) 2132-2137 (2010)

Determining the intensities produced by reflected and refracted wave fronts in geometrical optics

Elsa Newman and Vladimir Oliker
J. Opt. Soc. Am. A 12(4) 784-793 (1995)

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 (2)

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 (35)

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