Particle Size Distributions from Fraunhofer Diffraction

Abstract

It is well known¹ that the mean intensity per steradian diffracted by a random distribution of N opaque particles is given, in the Fraunhofer region, by

$$I(s)=I_o\sum_{i=1}^{N}\frac{a_{i}^{2}J_{1}^{2}(ka_is)}{s^2}$$

((1))

where a _i is the radius of the particle i, k is the wave-vector of the radiation and s is the scattering angle. In the absence of noise an annular detector or segment of an annulus will respond with a current g(s) proportional to sI(s).