In a system composed of distinct mesoscopic particles, all small-angle scattering can be understood as arising from surfaces or interfaces.
Normally, SAS is measured in order to detect correlations between different interfaces, and in particular, between remote surface segments of one and the same particle.
If the interface is flat, then Porod's law predicts the scattering intensity where S is the surface area of the particles, which can in this way be experimentally determined.
[note 1] Since the advent of fractal mathematics it has become clear that Porod's law requires adaptation for rough interfaces because the value of the surface S may be a function of q (the yardstick by which it is measured).
For a specific model system, e.g. a dispersion of uncorrelated spherical particles, one can derive Porod's law by computing the scattering function S(q) exactly, averaging over slightly different particle radii, and taking the limit