The computation of the nanoparticles volume distribution function and the specific surface area based on the small-angle X-ray scattering indicatrix by the method of the statistical regularization

A modification of the method of statistical regularization to restore the volume distribution function of the particle radius of gyration given by small-angle X-ray scattering indicatrix is developed. The criteria to select grid nodes along the radius of gyration together with the choice of the optimal value of the regularization parameter is described.
The effectiveness of the method is confirmed in tests of the particle distribution of the three shapes with symmetrical cross-section (ellipsoid, rectangular parallelepiped, right cylinder) and anisometry in the range 0,5 $\dots$ 2. Integral ambiguity of reconstruction of the distribution function does not exceeds 4%.
The method of calculating the specific surface area on the basis of the reconstructed distribution function is represented. The obtained specific surface depends weakly on the assumed anisometry and is depends strongly on different proposed forms of the particles.