OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 46, Iss. 11 — Nov. 1, 1956
  • pp: 927–932

Scattering from a Point Source in Plane Clouds

PAUL I. RICHARDS  »View Author Affiliations


JOSA, Vol. 46, Issue 11, pp. 927-932 (1956)
http://dx.doi.org/10.1364/JOSA.46.000927


View Full Text Article

Acrobat PDF (825 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A previously proposed modified form of diffusion theory [Phys. Rev. 100, 517 (1955)] is applied to problems involving point sources and plane clouds over an absorbing ground. A general but formal solution is first presented. Some analytic results are then obtained for a point source at the edge of a semi-infinite (half-space) cloud; specific formulas are given for the photon density at the edge of the cloud and for the net photon current there; asymptotic results are obtained for large distances inside the cloud along the source axis. Finally, numerical results are presented for the photon density at the mid-plane of an infinite plane cloud with thickness equal to two (transport) mean free paths and a point source at the center. An appendix summarizes analytic results of the modified theory for: a point source in an infinite medium, a point source at the center of a finite sphere, the albedo and transmission of an infinite plane slab with parallel (";solar";) illumination at an arbitrary angle, the albedo of the combination of a plane cloud over a ground plane with arbitrary albedo, and a rough analysis of ambient light levels in the ocean.

Citation
PAUL I. RICHARDS, "Scattering from a Point Source in Plane Clouds," J. Opt. Soc. Am. 46, 927-932 (1956)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-46-11-927


Sort:  Author  |  Journal  |  Reset

References

  1. Paul I. Richards, Phys. Rev. 100, 517 (1955).
  2. G. N. Watson, Theory of Bessel Functions (Cambridge University Press, Cambridge, 1944), second edition.
  3. A. Erdelyi, editor, Tables of Integral Transforms (McGraw-Hill Book Company, Inc., New York, 1954), Vols. I and II.
  4. W. Magnus and F. Oberhettinger, Functions of Mathematical Physics (Chelsea Publishing Company, New York, 1954).
  5. D. V. Widder, Advanced Calculus (Prentice-Hall, Inc., New York, 1947).
  6. It is understood on the right-hand side that ƒ[(t2-y2)½]=0 for t<y.
  7. In this and subsequent manipulations the following identity is frequently useful:(a2+b2)½-a=b2[(a2+b2)½+a]-1.
  8. The notation O(g) denotes a quantity whose absolute values remains less than some constant times the absolute value of g.
  9. Diffusion theory applied to the same problem gives ρ=0 unless the "extrapolated end point" is used, in which case the result corresponding to expression (31) is ρ~3/2r3, using the standard extrapolation distance (0.7104λ).
  10. G. Doetsch, Theorie und Anwendung der Laplacetransformation (Dover Publications, New York, 1945), p. 231.
  11. Diffusion theory, using the 0.7104λ extrapolated end point, gives 4.26/z2 in near agreement with Eq. (33).

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