Introduction

The evaluation of the radiative transfer equation requires a detailed knowledge of the extinction and scattering properties of atmospheric particles. In most cases we rely on theoretical calculations assuming that the scattering particles have a spherical shape. In order to carry out the calculations we must specify the particle size and the wavelength-dependent complex index of refraction. The required calculations are known as Mie calculations while the entire theory is called the Mie theory. This goes back to Gustav Mie who published the whole theory in 1908. Nowadays a large number of reliable computer programs are available to provide the required information without understanding the theory behind it. This might be sufficient in some cases, but it is more valuable to comprehend the theoretical background which will be presented in the following sections.

The Mie theory of light scattering by homogeneous spheres is based on the formal solution of Maxwell's equations using proper boundary conditions. In this text we will follow Stratton's discussion of the Electromagnetic Theory (1941). In van De Hulst's (1957) treatise Light Scattering by Small Particles many mathematical details of the Mie theory are omitted, but numerous helpful physical explanations are given. In particular he gives a number of approximate formulas for special cases.