New Computation of the Mie Scattering Functions for Spherical Particles

BERNICE GOLDBERG Geophysics Research Directorate, Air Force Cambridge Research Center,

Air Research and Development Command, Cambridge, Massachusetts (Received August 14, 1953)

EXTENSIVE computations have been made on the Mie Scattering Function K using the IBM 701 Electronic Data

Processing Machine, which show in detail the nature of the function.

Values of the functions

and

have been computed for 0<α≤30 .0 in steps of ∆α=0.1, for values of 1 7 0 ° ≤ γ ≤ 1 7 0 ° in steps of 5° and 170°≤γ≤ 180° in steps of 1° and for indexes of refraction m=1.33,1.40,1.44,1.486, and 1.50.

The terms in the series are defined as follows:

z takes on the values α or β.

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 43, NUMBER 12 DECEMBER, 1053

FIG. 1. Mie scattering coefficients for M = 1.33.

where r is the radius of the particle, X is the wavelength of the impinging radiation, and m is the index of refraction of the medium.

i 2 2 2 B O O K R E V I E W S Vol.43

where Pn is the Legendre polynomial of degree n, γ is the angle the scattered radiation makes with the incident radiation x=COSΓ.

These computations are much more detailed than any made previously and show very clearly the oscillatory nature of the function K and the location of the maxima and the minima. Lowan1 only gives values of these functions up to α=6 and at more widely spaced intervals, and Gumprecht and Sliepcevich2

have computed the functions for a much wider range, but at intervals ∆α=5 . Various other computations have been made, but not with the same systematic approach.

The curves given below show K, the total scattering coefficient for m=1.33 and for the range 0≤α≤30 .0 . For convenience, the interval was broken into three parts with overlapping regions. Complete tables of these functions will be available in the near future.

1 A. N. Lowan, Tables of Scattering Functions for Spherical Particles (National Bureau of Standards, Washington, D. C., 1949), Applied Math. Series 4.

2 R. O. Gumprecht and C. M. Sliepcevich, Light Scattering Functions for Spherical Particles (University of Michigan, Ann Arbor, Michigan, 1951).