Anomalous diffraction theory

Anomalous Diffraction Theory (ADT) - approximation developed by van de Hulst describing light scattering for optically soft spheres.

Anomalous diffractions approximation for extinction efficiency is valid for optically soft particles and large size parameter

$Q=2-{\frac {4}{p}}\sin {p}+{\frac {4}{p^{2}}}(1-\cos {p})$,

where Q is the efficiency factor of scattering, which is defined as the ratio of the scattering cross section and geometrical cross section πa²;
p = 4πa(n – 1)/λ has a physical meaning of the phase delay of the wave passed through the centre of the sphere;
a is the sphere radius, n is the ratio of refractive indices inside and outside of the sphere, and λ the wavelength of the light.
This set of equations was first described by Dutch astronomer van de Hulst. There are extensions to more complicated geometries of scattering target.