Angular Mie Scattering
JOSA, Vol. 52, Issue 4, pp. 402-406 (1962)
http://dx.doi.org/10.1364/JOSA.52.000402
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Abstract
The basic Mie formulas are explained and several useful scattering functions are defined, such as the angular Mie scattering coefficients i_{θ} and the Mie phase function p_{M}. Finally, the scattering pattern for the forward, sideward, and backward area is surveyed, based on data for the refractive index n = 1.33.
Citation
RUDOLF PENNDORF, "Angular Mie Scattering," J. Opt. Soc. Am. 52, 402-406 (1962)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-52-4-402
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References
- G. Mie, Ann. Physik. (4) 25, 377 (1908).
- Or rather, the distance of observation is large compared to the radius of the particle (far-field solution).
- The a_{m}, b_{m}, π_{m}, and τ_{m} differ from those tabulated, such a^{S} A. Lowan [Tables of Scattering Functions for Spherical Particles' (U. S. Natl. Bur. Standards, 1949) Appl. Math. Ser. NR. 4], R. O. Gumprecht and C. M. Sliepcevich [Light Scattering Functions for Spherical Particles (University of Michigan Press, Ann Arbor Michigan, 1951)], and R. Penndorf and B. Goldberg ["New tables of scattering functions for spherical particles," Geophys. Research Paper No. 45, parts 1–5 (1956)], and others. If the author's own tabulated values are denoted with a_{m}^{T}, b_{m}^{T}, π_{m}^{T}, and τ_{m}^{T}, the above defined a_{m}, b_{m}, π_{m}, and τ_{m} can be computed from the tabulated values as follows: a_{m}=(-1)^{m}ia_{m}^{T}, b_{m}=(-1)^{m+1}ib_{m}^{T}, π_{m}=(-1)^{m+1}π_{m}^{T}/m(m+1), τ_{m}=(-1)^{m}τ_{m}^{T}/m(m+1).
- H. E. Van de Hulst, Light Scattering by Small Spheres (John Wiley & Sons, Inc. New York, 1957).
- In radar application, i_{θ} is called the bistatic scattering coefficient.
- From now on, only i_{1} and i_{2} will be written, but the variables still are {α,n,θ} as expressed by Eq. (4).
- S. Chandrasekhar, Radiative Transfer (Oxford University Press, Oxford, 1950), p. 5.
- Ch.-M. Chu, G. C. Clark, and S. W. Churchill, "Tablesof Angular distribution coefficients for light-scattering by spheres", Eng. Research Inst., University of Michigan, Ann Arbor (1957).
- H. Walter, Optik 14, 130 (1957).
- H. Walter, Optik 16, 401 (1959).
- R. O. Gumprecht and C. M. Sliepcevich, J. Phys. Chem. 57, 90 (1953).
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