The original version of this page was put together by P. J. Flatau. I just rearranged it.
J. V. Dave: Scattering of electromagnetic radiation by a large, absorbing sphere. IBM J. Res. Dev. 1969, vol. 13(3), 302-313.
Details are provided for two subroutines with which one can compute the various characteristics of the electromagnetic radiation scattered by an absorbing, homogeneous sphere of any reasonable size. The necessary expressions for this purpose were first derived by Mie (1908). The method of computations used is the so-called method of logarithmic derivative of one of the complex functions, introduced by Infeld (1947). The main difference between the two subroutines is in the procedure used in computations of one of the functions. This function is computed by an upward recurrence procedure in one subroutine and by a downward recurrence procedure in the other. Sufficient results for demonstrating the reliability of these programs are presented and discussed for a sphere of 10µm radius illuminated by an unpolarized radiation of 0.4µm wavelength.
J. V. Dave: Coefficients of the Legendre and Fourier series for the scattering functions of spherical particles. Appl. Opt. 1970, vol. 9(8), 1888-1896
Results of computations are presented to show the variations of coefficients of four different Legendre series, one for each of the four scattering functions needed in describing directional dependence of the radiation scattered by a sphere. Values of the size parameter (x) covered for this purpose vary from 0.01 to 100.0. An adequate representation of the entire scattering function vs scattering angle curve is obtained after making use of about 2x+10 terms of the series. It is shown that a section of a scattering function vs scattering angle curve can be adequately represented by a Fourier series with less than 2x+10 terms. The exact number of terms required for this purpose depends upon values of the size parameter and refractive index, as well as upon the values of the scattering angles defining the section under study. Necessary expressions for coefficients of such Fourier series are derived with the help of the addition theorem of spherical harmonics.
B. Verner: Note on the recurrence between Mie's coefficients. J. Opt. Soc. Am. 1976, vol. 66(12), 1424-1425
Mie's coefficients an, bn, n=1,2,..., can be written in a form involving the Wronskian (wn, Wn respectively) of functions of alpha ( alpha =2 pi a/ lambda , where a=radius of the scattering sphere). It is shown that recurrent relationships can be found directly between the expressions wn, Wn; if the lowest values are known, all higher values can be calculated without need to first generate the Bessel functions.
B. Verner and M. Barta and B. Sedlacek: The fine structure of the Lorenz-Mie light scattering. J. Colloid Interface Sci. 1977, vol. 62(2), 348-349.
An important characteristic of the Lorenz-Mie light scattering is specific turbidity in which the Lorenz-Mie coefficients are parametrized by the relative refractive index m of the scattering sphere with respect to the external medium and by the parameter alpha = pi d lambda; d is the diameter of the sphere and lambda is the wavelength of incident light in the external medium. By analyzing the fine structure of calculated turbidity curves the authors show that at higher alpha and m the scattering characteristics cannot be interpolated in a simple way even between very close values without a considerable distortion of the theoretical curves.
W. J. Wiscombe: Improved Mie scattering algorithms. Appl. Opt. 1980, vol. 19(9), 1505-1509
Scattering of electromagnetic radiation from a sphere, so-called Mie scattering, requires calculations that can become lengthy and even impossible for those with limited resources. At the same time, such calculations are required for the widest variety of optical applications, extending from the shortest UV to the longest microwave and radar wavelengths. This paper briefly describes new and thoroughly documented Mie scattering algorithms that result in considerable improvements in speed by employing more efficient formulations and vector structure. The algorithms are particularly fast on the Cray-1 and similar vector-processing computers.
C. F. Bohren: Recurrence relations for the Mie scattering coefficients. J. Opt. Soc. Am. A, Opt. Image Sci.. 1987, vol. 4(3), 612-613
The Mie scattering coefficients satisfy recurrence relations- an-1, bn-1, an, and bn determine an+1 and bn+1. It is therefore possible, in principle, to generate the entire set from the first four, which has a simple interpretation. Each term in a multipole expansion of an electrostatic field can be obtained by differentiating the preceding term. The Mie coefficients are terms in a multipole expansion of a particular electromagnetic field, namely, that scattered by an arbitrary sphere. By analogy, it is not surprising that all these coefficients can be generated from the electric and magnetic dipole and quadrupole terms. Moreover, the recurrence relations for the Mie coefficients contain finite differences, in analogy with the infinitesimal differences (derivatives) in the multipole expansion of an electrostatic field.
V. E. Cachorro and L. L. Salcedo and J. L. Casanova: Program for the calculation of Mie scattering magnitudes. An. Fis. B, Apl. Metodos Instrum. 1989, vol. 85(2), 198-211
A Fortran program has been produced to compute the Mie scattering magnitudes, such as efficiency factors simple scattering albedo, asymmetry factor, complex scattering amplitudes, phase function, etc. It is based in a new improved algorithm that enables an accurate and fast computation without wavelength nor size and refractive index limitations.
V. E. Cachorro and L. L. Salcedo and J. L. Casonova: Scattered light intensities by a homogeneous sphere with the Lorentz-Mie theory. Opt. Pura Apl. 1989, vol. 22(1), 1-7
By means of the LVEC-MIE Code the forward scattered intensities produced by spherical transparent and opaque particles with radius from 0.5 to 100µm and for a useful range of forward scattering angles (0-20 degrees) are calculated using the exact Lorentz-Mie scattering theory. The reported results are of interest to the various scattering techniques of particle size and concentration measurements.
V. E. Cachorro and L. L. Salcedo: New improvements for Mie scattering calculations. J. Electromagn. Waves Appl. 1991, vol. 5(9), 913-926
New improvements to compute Mie scattering quantities are presented. They are based on a detailed analysis of the various sources of error in Mie computations and on mathematical justifications. The algorithm developed based on these improvements proves to be reliable and efficient, without size (x=2 pi R/ lambda ) nor refractive index (m=mR/-i mi) limitations, and the user has a choice to fix in advance the desired precision in the results. It also includes a new and efficient method to initiate the downward recurrences of Bessel functions.
J. A. Lock: Improved Gaussian beam-scattering algorithm. Appl. Opt. 1995, vol. 34(3), 559-570
The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
N. G. Volkov and V. Yu. Kovach: Light scattering by spherically symmetric heterogeneous aerosol particles. Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 1990, vol. 26(5), 517-523
Explicit expressions are obtained for the Mie coefficients of the scattering series a/sub n/ and b/sub n/ for spherically symmetric heterogeneous particles. An algorithm and FORTRAN computer program are developed for the calculation of extinction efficiency factors and for full and back scattering on a multilayered sphere with an arbitrary layers number. These quantities are calculated for the characteristic alteration laws of the refractive index of anthropogenic aerosol atmospheric particles.
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