The scattering at zero angle in contrast variation

The scattering of neutrons, x-rays, or light by a polydisperse system of particles is studied. As is well known, for fixed wave vector q the scattering intensity I(q) is a quadratic function of the scattering length density of the external medium. The minimum of the parabola is the minimal scattering intensity Imin(q). It is shown that Imin(0) is, for a certain large class of particles, directly proportional to the width of the size distribution [so that Imin(0)=0 for strictly monodisperse particles]. Explicit formulas are presented which permit the measurement of the size distribution for spheres, disks, rods, and similar particles.