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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 9 — Sep. 1, 2013
  • pp: 1814–1824

Explicit representations of all refractive optical interfaces without spherical aberration

Juan Camilo Valencia Estrada, Álvaro Hernán Bedoya Calle, and Daniel Malacara Hernández  »View Author Affiliations


JOSA A, Vol. 30, Issue 9, pp. 1814-1824 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001814


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Abstract

The following explicit model, valid for high aperture refraction with homogenous and isotropic materials, encompasses all explicit solutions of the first-order nonlinear differential equation representing the perfect image-forming process of any axial object point into its axial image point. Solutions include well-known cases, such as flats, spheres, prolate ellipsoids, prolate hyperboloids, and other sections of nondegenerate Cartesian ovals of revolution, now classified according to the recurrent explicit solution introduced herein. We also present some series expansions, given in cylindrical coordinates z(r), for more efficient computation. Explicit solutions allow accurate and expedite thickness calculation as compared to the regular series, parametric, or implicit solutions commonly used. The results of this study are useful in the design of centered optical systems that are perfectly aligned.

© 2013 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.1010) Geometric optics : Aberrations (global)
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(220.1250) Optical design and fabrication : Aspherics
(080.4225) Geometric optics : Nonspherical lens design

ToC Category:
Geometric Optics

History
Original Manuscript: May 7, 2013
Revised Manuscript: July 23, 2013
Manuscript Accepted: July 24, 2013
Published: August 21, 2013

Citation
Juan Camilo Valencia Estrada, Álvaro Hernán Bedoya Calle, and Daniel Malacara Hernández, "Explicit representations of all refractive optical interfaces without spherical aberration," J. Opt. Soc. Am. A 30, 1814-1824 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-9-1814


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References

  1. R. Descartes, Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences (Ian Maire, 1637).
  2. S. Hawking, God Created Integers (Editorial Crítica, 2005).
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  9. The word “focus” is generally used to indicate geometrical optics real or virtual points where light rays converge or diverge as the image of an object at infinity. In this document it will also be used to indicate the position of the image, regardless of whether the object is located at an infinite or finite distance. Therefore, it is equivalent to declaring the “focal length” f as the image distance measured from the origin.
  10. D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011). [CrossRef]
  11. J. Valencia and A. Bedoya, “Lentes asféricas ovales,” Mexican patent application. Instituto mexicano de la propiedad industrial (IMPI). MX/a/2012/010025 (August30, 2012).

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