Quantitative Assessment of the Conditioning of the Inversion of Quasi-Elastic and Static Light Scattering Data for Particle Size Distributions

The rank of the data transfer matrices is used as a quantitative criterion for the assessment of the degree of ill conditioning of the inversion of static, single-angle, and multiangle quasi-elastic light scattering (QELS) data for particle size distributions by intensity, number, and volume. It is shown that the simultaneous (constrained) inversion of three-angle and more angle data sets for distributions by volume can be well-conditioned. The inversion of QELS spectral data is hardly better conditioned compared to the inversion of correlation data. However it appears that spectral data require about 10 times slower sampling times in the data-collecting procedures. The inversion of static data for distributions by volume appears also to be well-conditioned.