Because a movement (mobility; diffusion coefficient) is measured based on Brownian motion and a ‘size’ can be inferred from the motion. This motion can be converted to an equivalent size based on the Stokes-Einstein equation which has the assumption of a sphere for the conversion. Mobilities of irregular particles are much harder to model (although for some systems such as cylinders this has been achieved). All particle size techniques make some assumption of the shape (usually spherical equivalent) to allow data to be processed statistically. Thus some form of imaging (manual or electron microscopy) is required in addition to a technique such as light scattering.

Thanks Alan

as Alan F Rawle explained, the hydrodynamic radius is calculated from the diffusion coefficient by the Stokes-Einstein equation.

To calculate the diffusion coefficient, the decay of scattering intensity in correlation with time is processed as intensity-time auto-correlation function with a Fourier Transform. Thus, the decay constants and fluctuations on the intensity of the backscattered light are correlated with the mobility of the particles to measure, which results in an average value.

Thanks Rebeca