Updates in<i>SASfit</i>for fitting analytical expressions and numerical models to small-angle scattering patterns

Abstract

Small-angle scattering is an increasingly common method for characterizing particle ensembles in a wide variety of sample types and for diverse areas of application. <i>SASfit</i> has been one of the most comprehensive and flexible curve-fitting programs for decades, with many specialized tools for various fields. Here, a selection of enhancements and additions to the <i>SASfit</i> program are presented that may be of great benefit to interested and advanced users alike: (<i>a</i>) further development of the technical basis of the program, such as new numerical algorithms currently in use, a continuous integration practice for automated building and packaging of the software, and upgrades on the plug-in system for easier adoption by third-party developers; (<i>b</i>) a selection of new form factors for anisotropic scattering patterns and updates to existing form factors to account for multiple scattering effects; (<i>c</i>) a new type of a very flexible distribution called metalog [Keelin (2016). <i>Decis. Anal.</i> <b>13</b>, 243-277], and regularization techniques such as the expectation-maximization method [Dempster <i>et al.</i> (1977). <i>J. R. Stat. Soc. Ser. B (Methodological)</i>, <b>39</b>, 1-22; Richardson (1972) <i>J. Opt. Soc. Am.</i> <b>62</b>, 55; Lucy (1974). <i>Astron. J.</i> <b>79</b>, 745; Lucy (1994). <i>Astron. Astrophys.</i> <b>289</b>, 983-994], which is compared with fits of analytical size distributions via the non-linear least-squares method; and (<i>d</i>) new structure factors, especially for ordered nano- and meso-scaled material systems, as well as the Ornstein-Zernike solver for numerical determination of particle interactions and the resulting structure factor when no analytical solution is available, with the aim of incorporating its effects into the small-angle scattering intensity model used for fitting with <i>SASfit</i>.