OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 5 — May. 1, 2009
  • pp: 1235–1239

Analogy between generalized Coddington equations and thin optical element approximation

Michael A. Golub  »View Author Affiliations


JOSA A, Vol. 26, Issue 5, pp. 1235-1239 (2009)
http://dx.doi.org/10.1364/JOSAA.26.001235


View Full Text Article

Enhanced HTML    Acrobat PDF (144 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Local wavefront curvature transformations at an arbitrarily shaped optical surface are commonly determined by generalized Coddington equations that are developed here via a local thin optical element approximation. Eikonal distributions of the incident and refracted beams are calculated and related by an eikonal transfer function of a local thin optical element located in close proximity to a given point at a tangent plane of an optical surface. Main coefficients and terms involved in the generalized Coddington equations are derived and explained as a local nonparaxial generalization for the customary paraxial wavefront transformations.

© 2009 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(080.0080) Geometric optics : Geometric optics
(080.1510) Geometric optics : Propagation methods
(110.2990) Imaging systems : Image formation theory
(220.2740) Optical design and fabrication : Geometric optical design

History
Original Manuscript: January 23, 2009
Manuscript Accepted: March 21, 2009
Published: April 21, 2009

Citation
Michael A. Golub, "Analogy between generalized Coddington equations and thin optical element approximation," J. Opt. Soc. Am. A 26, 1235-1239 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-5-1235


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Kingslake, “Who discovered Coddington's equations?” Opt. Photonics News, May 1994, pp. 20-23.
  2. W. J. Smith, Modern Optical Engineering (McGraw-Hill Professional Publishing, 2000),Section 10.6.
  3. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972), pp. 136-179.
  4. S. A. Comastri and J. M. Simon, “Wavefront aberration function: its first and second field derivatives,” Optik 111, 249-260 (2000).
  5. A. E. Murray, “Skew astigmatism at toric surfaces, with special reference to spectacle lenses,” J. Opt. Soc. Am. 47, 599-601 (1957). [CrossRef]
  6. J. E. A. Landgrave and J. R. Moya-Cessa, “Generalized Coddington equations in ophthalmic lens design,” J. Opt. Soc. Am. A 13, 1637-1644 (1996). [CrossRef]
  7. D. G. Burkhard and D. L. Shealy, “Simplified formula for the illuminance of an optical system,” Appl. Opt. 20, 897-909 (1981). [CrossRef] [PubMed]
  8. J. Turunen, “Astigmatism in laser beam optical systems,” Appl. Opt. 25, 2908-2911 (1986). [CrossRef] [PubMed]
  9. D. DeJager and M. Noethen, “Gaussian beam parameters that use Coddington-based Y-NU paraprincipal ray tracing,” Appl. Opt. 31, 2199-2205 (1992). [CrossRef] [PubMed]
  10. V. Greco and G. Giusfredi, “Reflection and refraction of narrow Gaussian beams with general astigmatism at tilted optical surfaces: a derivation oriented toward lens design,” Appl. Opt. 46, 513-521 (2007). [CrossRef] [PubMed]
  11. W. Zou, K. P. Thompson, and J. P. Rolland, “Differential Shack-Hartmann curvature sensor: local principal curvature measurements,” J. Opt. Soc. Am. A 25, 2331-2337 (2008). [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999), Sec. 4.6. [PubMed]
  13. J. A. Kneisly II, “Local curvature of wavefronts in an optical system,” J. Opt. Soc. Am. 54, 229-235 (1964). [CrossRef]
  14. O. N. Stavroudis, “Simpler derivation of the formulas for generalized ray tracing,” J. Opt. Soc. Am. 66, 1330-1333 (1976). [CrossRef]
  15. N. Lindlein and J. Schwider, “Local wave fronts at diffractive elements,” J. Opt. Soc. Am. A 10, 2563-2572 (1993). [CrossRef]
  16. C. E. Campbell, “Generalized Coddington equations found via an operator method,” J. Opt. Soc. Am. A 23, 1691-1698 (2006). [CrossRef]
  17. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Sec. 5.1.
  18. M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A 16, 1194-1201 (1999). [CrossRef]
  19. M. Testorf, “On the zero-thickness model of diffractive optical elements,” J. Opt. Soc. Am. A 17, 1132-1133 (2000). [CrossRef]
  20. L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields, Course of Theoretical Physics, 4th ed. (Butterworth-Heinemann, 2003), Vol. 2, p. 159.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited