The original version of this page was put together by P. J. Flatau. I just rearranged it.

- Bohren 1987
- Cachorro 1989
- Cachorro 1989
- Cachorro 1991
- Dave 1969
- Dave 1970
- Lock 1995
- Verner 1976
- Verner 1977
- Volkov 1990
- Wiscombe 1980

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 2*x*+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 2*x*+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 a_{n}, b_{n}, n=1,2,..., can be
written in a form involving the Wronskian (w_{n}, W_{n}
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
w_{n}, W_{n}; 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-
a_{n-1}, b_{n-1}, a_{n}, and b_{n}
determine a_{n+1} and b_{n+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=m_{R}/-i m_{i}) 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.