OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 46, Iss. 16 — Jun. 1, 2007
  • pp: 3107–3117

Circle of least confusion of a spherical reflector

Robert W. Hosken  »View Author Affiliations


Applied Optics, Vol. 46, Issue 16, pp. 3107-3117 (2007)
http://dx.doi.org/10.1364/AO.46.003107


View Full Text Article

Enhanced HTML    Acrobat PDF (909 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A simple, tractable equation is provided for determining the size and location of the circle of least confusion of a concave spherical reflector. This method is exact for the object at infinity and with wave effects neglected. Designers of large radius Arecibo-like telescopes, both radio and optical, with symmetrical, spherical primaries should find the method useful. The mathematical results are valid for apertures with an angle of incidence up to 45°. Comparisons of the location of the disk of least confusion with longitudinal spherical aberration and the radius of the disk with transverse spherical aberration are presented.

© 2007 Optical Society of America

OCIS Codes
(080.1010) Geometric optics : Aberrations (global)
(080.1510) Geometric optics : Propagation methods
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design

ToC Category:
Geometrical optics

History
Original Manuscript: December 7, 2006
Manuscript Accepted: January 11, 2007
Published: May 15, 2007

Citation
Robert W. Hosken, "Circle of least confusion of a spherical reflector," Appl. Opt. 46, 3107-3117 (2007)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-16-3107


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. C. Spencer, "Focal region of a spherical reflector-circle of least confusion," Appl. Opt. 7, 1644-1645 (1968). [CrossRef] [PubMed]
  2. R. C. Spencer and G. Hyde, "Studies of the focal region of a spherical reflector: geometric optics," IEEE Trans. Antennas Propag. AP-16, 317-324 (1968).
  3. A. W. Love, ed., Reflector Antennas (IEEE Press, 1978), pp. 359-366.
  4. G. Silva-Ortigoza, J. Castro-Ramos, and A. Cordero-Davila, "Exact calculation of the circle of least confusion of a rotationally symmetric mirror. II," Appl. Opt. 40, 1021-1028 (2001). [CrossRef]
  5. A. Cordero-Dávila and J. Castro-Ramos, "Exact calculation of the circle of least confusion of a rotationally symmetric mirror," Appl. Opt. 37, 6774-6778 (1998). [CrossRef]
  6. J. Castro-Ramos, O. de Ita Prieto, and G. Silva-Ortigoza, "Computation of the disk of least confusion for conic mirrors," Appl. Opt. 43, 6080-6089 (2004). [CrossRef] [PubMed]
  7. R. K. Jungquist, "Optical design of the Hobby-Eberly telescope four mirror spherical aberration corrector," in Current Developments in Optical Design and Optical Engineering VIII, Proc. SPIE 3779, 2-16 (1999). [CrossRef]
  8. D. Korsch, Reflective Optics (Academic, 1991), pp. 115-116.
  9. A. W. Love, "Some highlights in reflector antenna development," Radio Sci. 11, 671-684 (1976).
  10. A. W. Love, ed., Reflector Antennas (IEEE Press, 1978), pp. 2-15.
  11. Spencer used an iterative solution to a six-degree polynomial in his parameter: σ @ (2 sin θ*/tan Θ).
  12. θ0 in Eq. (41) of Ref. 4 is our Θ.
  13. W. F. Osgood, Advanced Calculus (Macmillan, 1925), pp. 186-194.
  14. Ref. 4; Eqs. (42) with z = 0 at vertex of mirror and θ1 is our θ*.
  15. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986), pp. 113-116.
  16. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1966), pp. 386-387.
  17. A. M. Ostrowski, Solutions of Equations in Euclidean and Banach Spaces (Academic, 1973), pp. 38-60.
  18. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961), pp. 22-24.

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