  Scattering problems are important in describing light propagation in wide
ranging media such as the atmosphere, colloidal solutions, metamaterials, glass
ceramic composites, transparent polycrystalline ceramics, and surfaces. The
Rayleigh Gans Debye (RGD) approximation has enjoyed great success in describing
a wide range of scattering phenomena. We derive a generalized RGD formulation
from the perturbation of Maxwell equations. In contrast to most treatments of
RGD scattering, our formulation can model any soft scattering phenomena in
linear media, including scattering by stochastic process, lossy media, and by
anisotropic inhomogeneities occurring at multiple length scales. Our
first-principles derivation makes explicit underlying assumptions and provides
jumping off points for more general treatments. The derivation also facilitates
a deeper understanding of soft scattering. It is demonstrated that sources of
scattering are not interfaces as is often presumed, but excess accelerating
charges emitting uncompensated radiation. Approximations to the equations are
also presented and discussed. For example, the scattering coefficient in the
large size RGD limit is shown to be proportional to the correlation length and
the variance of a projected phase shift.
