André Guinier proved a small angle scattering curve can be approximated to $$ I = I_0 exp(-q²Rg²/3) $$ at low $q$, where Rg is the radius of gyration of the scatterer.
The difficult part is to be able to find the Guinier-region, i.e. where this approximation is valid. FreeSAS implement 3 ways of selecting this region:
- autogpa: Guinier peak analysis by Christopher D. Putnam J. Appl. Cryst. (2016). 49, 1412–1419 Ti fits sqrt(q²Rg²)*exp(-q²Rg²/3)*I0/Rg to the curve I*q = f(q²) The Guinier region goes arbitrary from 0.5 to 1.3 q·Rg
- autorg: Heavily inspired from Jesse Hopkins’ BioXTAS RAW Journal of applied crystallography vol. 50,Pt 5 1545-1553.
- auto-guinier: home brewed version: the main difference is that one does not search for the “best region” but rather focuses on the most likely start and end-points.