Analysis of Small-Angle Scattering Data from Spherical Particles by both the Indirect Transform Method and the Maximum-Entropy Method

In this paper extensive comparison studies of the indirect transform method (ITM) and the maximum-entropy method (MEM) were made for recovering the size distribution of spherical particles. Simulated small-angle scattering (SAS) data with different noise levels for various size distributions are tested. It is found that both the MEM and ITM are capable of accurately recovering the original size distributions for various types of size distributions from simulated SAS data with a 1% noise level. When the noise level of the simulated SAS data is increased to 6%, the size distributions recovered by both the ITM and MEM begin to have many noisy oscillations. It is also found that the MEM is more vulnerable to termination effects, i.e. when low-Q or high-Q data are not available. On the other hand, even for cases with limited-Q-range data the ITM can still accurately recover the original size distribution. This was clearly shown in the analysis of the measured small-angle X-ray scattering data, with a limited Q range, from a β-quenched zircaloy-4 specimen.