New solutions of the refraction integral
JOSA, Vol. 65, Issue 6, pp. 676-678 (1975)
http://dx.doi.org/10.1364/JOSA.65.000676
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Abstract
In a spherically symmetric inhomogeneous system, certain relations between refractive index and distance from the center of symmetry give closed solutions in elementary functions of the refraction integral. A careful formulation of the fundamental equations reveals that all such solutions reduce to special cases of one of eight standard forms, and that the theory of plane-parallel systems is mathematically identical. One special case gives a better representation of the Earth’s atmosphere than the traditionally used hypotheses of Cassini and Simpson.
Citation
R. White, "New solutions of the refraction integral," J. Opt. Soc. Am. 65, 676-678 (1975)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-65-6-676
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References
- Equation (1) is rigorously derived by Kerr (Ref. 5).
- Some authors have used the term differently, as meaning the actual displacement in arc of the image from the true direction of the body. The definitions coincide for a body infinitely distant from the center of symmetry, i. e., for astronomical refraction.
- Note that in order to secure these elegant symmetrical relationships of δ_{12} and θ_{12}, I have set the limits of integration in Eq. (2) so that δ_{12} is negative if At decreases continuously outwards.
- The quantities δ_{12}, etc., should be read "delta one, two," etc.
- Propagation of Short Radio Waves, edited by D. E. Kerr (Radiation Laboratory Series) (McGraw-Hill, New York, 1951).
- A. I. Mahan, Appl. Opt. 1, 497 (1962).
- The equivalent homogeneous atmsophere is that which has the same density throughout its depth as has the real atmosphere at the Earth's surface, and the same total mass.
- Refraction Tables in The Nautical Almanac (any recent edition) (U.S. Government Printing Office, Washington, D.C. 20402, and H. M. Stationery Office, London).
- B. Garfinkel, Astron. J. 72, 235 (1967).
- I have used the data: height of equivalent homogeneous atmosphere = 7.99 km, radius of Earth = 6370.9km, constant of refraction = 58. 294 arcseconds.
- A. Fletcher, Mon. Not. R. Astron. Soc. 91, 559 (1931).
- H. C. Plummer, Mon. Not. R. Astron. Soc. 92, 25 (1931).
- R. S. Heath, Geometrical Optics (Cambridge U. P., Cambridge, England, 1897).
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