OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 31 — Nov. 1, 2010
  • pp: 5977–5982

Signal processing approach to designing gradient index correctors for wide-field, concentric lenses

William Stoner  »View Author Affiliations

Applied Optics, Vol. 49, Issue 31, pp. 5977-5982 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (889 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The signal processing method used in transaxial tomography, reconstruction from projections, is applied to the design of a spherical gradient index corrector for the concentric “noflare” lens. The method yields a spherical gradient index lens that corrects the entire field of the lens. Motivation for the method is provided by a comparison of the Schmidt and super-Schmidt camera designs.

© 2010 Optical Society of America

OCIS Codes
(110.2760) Imaging systems : Gradient-index lenses
(110.6960) Imaging systems : Tomography
(220.1000) Optical design and fabrication : Aberration compensation
(220.3620) Optical design and fabrication : Lens system design
(080.6755) Geometric optics : Systems with special symmetry

Original Manuscript: July 13, 2010
Revised Manuscript: September 18, 2010
Manuscript Accepted: September 20, 2010
Published: October 21, 2010

William Stoner, "Signal processing approach to designing gradient index correctors for wide-field, concentric lenses," Appl. Opt. 49, 5977-5982 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. M. Mercereau and A. V. Oppenheim, “Digital reconstruction of multidimensional signals from their projections,” Proc. IEEE 62, 1319–1338 (1974). [CrossRef]
  2. A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, 1995), pp. 332 and 394.
  3. Walther’s reference to Hekker’s discussion of the “noflare” lens isF. Hekker, “On concentric optical systems,” Ph.D. thesis (Delft University of Technology, 1947).
  4. J. G. Baker, “Schmidt image former with spherical aberration corrector,” U.S. patent 2,458,132 (4 January 1949).
  5. F. L. Whipple, “The Harvard Photographic Meteor Program,” Sky Telesc. 8, 90 (1949).
  6. H. C. King, The History of the Telescope (Dover, 1979), pp. 365–369.
  7. H. Goldstein, Classical Mechanics (Addison-Wesley, 1950), pp. 81–82.
  8. The term “impact parameter” has been previously introduced in the optics literature with the refractive index as a multiplicative factor. See C. M. Vest, “Interferometry of strongly refracting axisymmetric phase objects,” Appl. Opt. 14, 1601–1606 (1975). [CrossRef] [PubMed]
  9. R. N. Bracewell, “Strip integration in radio astronomy,” Aust. J. Phys. 9, 198–217 (1956). [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics (Pergamon, 1969), p. 122.
  11. H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambridge U. Press, 1970), p. 7.
  12. M. Born and E. Wolf, Principles of Optics (Pergamon, 1969), pp. 147–149.
  13. J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H-S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83(1995). [CrossRef]
  14. V. D. Shargorodsky, V. P. Vasiliev, N. M. Soyuzova, V. B. Burmistrov, I. S. Gashkin, M. S. Belov, T. I. Khorosheva, and E. Nikolaev, “Experimental spherical retroreflector on board of the Meteor-3M satellite,” presented at the 12th International Workshop on Laser Ranging, Matera, Italy, 13–17 November 2000, http://cddis.gsfc.nasa.gov/lw12/index.html.
  15. J. P. Oakley, “Whole-angle spherical retroreflector using concentric layers of homogeneous optical material,” Appl. Opt. 46, 1026–1031 (2007). [CrossRef] [PubMed]
  16. B. E. Bernacki, N. C. Anheier, K. Krishnaswami, B. D. Cannon, and K. B. Binkley, “Design and fabrication of efficient miniature retroreflectors for the mid-infrared,” Proc. SPIE 6940, 69400X (2008). [CrossRef]
  17. K. Kikuchi, T. Morikawa, J. Shimada, and K. Sakurai, “Cladded radially inhomogeneous sphere lenses,” Appl. Opt. 20, 388–394 (1981). [CrossRef] [PubMed]
  18. K. Kikuchi, T. Morikawa, J. Shimada, and K. Sakurai, “Graded-index sphere lens with hemispherical rod cladding,” Appl. Opt. 21, 2734–2738 (1982). [CrossRef] [PubMed]
  19. Y. Koike, Y. Sumi, and Y. Ohtsuka, “Spherical gradient-index sphere lens,” Appl. Opt. 25, 3356–3363 (1986). [CrossRef] [PubMed]
  20. Y. Koike, A. Kanemitsu, Y. Shioda, E. Nihei, and Y. Ohtsuka, “Spherical gradient-index polymer lens with low spherical aberration,” Appl. Opt. 33, 3394–3400 (1994). [CrossRef] [PubMed]
  21. V. Handerek, H. McArdle, T. Willats, N. Psaila, and L. Laycock, “Experimental retroreflectors with very wide field of view,” Proc. SPIE 5986598611 (2005). [CrossRef]
  22. A. E. Conrady, Applied Optics and Optical Design, Part One (Dover, 1992), pp. 6–7.
  23. M. Kidger, Fundamental Optical Design (SPIE, 2002), p. 7.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited