I need the mathematical expression for volume transformation PSD from scatter intensity PSD. I know all hypothesis for transformation but I don't know how volume PSD is calculated.
I was recently curious about it. It is said in Malvern manual that it internally uses the Mie scattering theory to calculate Volume and Number size distribution from Intensity data. I even tried to calculate by myself but got some strange results. Please take a look in the attached document. There are some formulas, how they calculate it althow the quality of the file is not very good.
There is a simplified mathematical expression for isotropic scattering in a technical note referenced in http://www.materials-talks.com/blog/2014/01/23/intensity-volume-number-which-size-is-correct/ The discrete size distribution just requires taking into account an appropriate weight for each segment of the histogram. Typically this is either the Mie or RGD scattering function, which expresses a normalized intensity versus scattering vector, also often refered to as the form factor, or P(q), where q is the scattering vector.
To compare your calculations with the software, you can export the histrogram data by displaying the appropriate graph in the software, then Edit-Copy Size Values and Ctrl-V into a spreadsheet program. This can be done for Intensity, Volume, and Number distributions. Good luck, Ulf