Circle of least confusion of a spherical reflector
Applied Optics, Vol. 46, Issue 16, pp. 3107-3117 (2007)
http://dx.doi.org/10.1364/AO.46.003107
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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
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References
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- 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).
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- A. W. Love, ed., Reflector Antennas (IEEE Press, 1978), pp. 2-15.
- Spencer used an iterative solution to a six-degree polynomial in his parameter: σ @ (2 sin θ*/tan Θ).
- θ_{0} in Eq. (41) of Ref. 4 is our Θ.
- W. F. Osgood, Advanced Calculus (Macmillan, 1925), pp. 186-194.
- Ref. 4; Eqs. (42) with z = 0 at vertex of mirror and θ_{1} is our θ*.
- W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986), pp. 113-116.
- W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1966), pp. 386-387.
- A. M. Ostrowski, Solutions of Equations in Euclidean and Banach Spaces (Academic, 1973), pp. 38-60.
- G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961), pp. 22-24.
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