Uncorrelated Polydisperse Homogeneous Spheres

Let us now consider the 3D equivalent of the aforementioned example an ensemble of uncorrelated homogeneous spheres - with polydispersity, meaning that the observed CLD 

Do the moments reflect the requirement that is normalized to 1 and that the average chord length of a sphere with unit diameter is 

Bearing in mind the aim to determine structural parameters, we resort to the measured CLD, (r). By means of numerical integration we compute some of its moments, IJ.- (gobs) For the sought-after moments of the sphere-diameter distribution, ho (r), we again have according to Eq. (8.87) 

The common measure for the breadth of the sphere-diameter distribution is the standard deviation (cf. p. 5, Eq. (1.8). 

---