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Applied Optics

Applied 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)

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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

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

Robert W. Hosken, "Circle of least confusion of a spherical reflector," Appl. Opt. 46, 3107-3117 (2007)

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  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.
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  14. Ref. 4; Eqs. (42) with z = 0 at vertex of mirror and θ1 is our θ*.
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  18. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961), pp. 22-24.

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