3D modeling of SAS data
This page discusses 3D reconstruction of scatterer shapes from 1D SAS data — which methods exist, what they assume, and where to find the tools.
3D modeling of the shapes and arrangement of particles (scatterers) provides the most understandable presentation for humans. Being able to see something that resembles the visual images we are used to — either 2D images (~microscopy) or 3D volume images (voxelgrams, ~tomography) — helps us process the results and visualize the scattering system in our heads. It is especially valuable for comparing two or more scattering systems, where seeing different images or voxelgrams may be far more understandable than comparing aggregate numerical values such as average scatterer sizes, size distributions, or specific surface areas.
A necessary warning
Reconstruction of 3D structure from its 1D representation (measured in a limited scattering vector range and with limited resolution) is, logically, challenging. It does not take high mathematics to realize that the amount of information in 1D data is significantly less than what is needed to correctly reconstruct a 3D voxelgram. These methods therefore need to make a lot of assumptions to be able to create a unique 3D representation of the scattering system. It is critical that users understand under what conditions a specific method can be used. If your scattering system is NOT of the type a specific model assumes, the assumptions are not satisfied and you are generating pure garbage. DO NOT GENERATE GARBAGE — there is already too much of it in the world...
That said, these methods have been around for a long time and, in bioSAXS for example, are highly successful. This page provides explanation and guidance for using some of these models in non-bio SAXS areas.
KEEP IN MIND THAT IN ORDER TO BE MEANINGFUL, YOUR SCATTERING SYSTEM MUST MATCH THE MODEL REQUIREMENTS.
Monodispersed dilute systems
This is the typical bioSAXS application, and the same methods can be applied to non-bio SAXS (SAS in general). What is needed is for the scattering system to be a dilute system of one type of particle, monodispersed (all exactly the same size and shape), with no aggregation and no contamination by other "stuff". If your system looks like this, you can use the well-known suite of programs ATSAS (EMBL Hamburg, not our software). I have successfully applied DAMMIN and DAMMIF to some inorganic scattering systems and it worked really well.
Mass Fractal Aggregates
Mass Fractal Aggregates (MFA) are easily imagined as resembling snowflakes. Scattering from MFAs is usually analyzed using the Unified fit (Greg Beaucage; see many of his papers). In the paper "A. Mulderig et al., Quantification of branching in fumed silica", Andrew Mulderig, Greg's student, detailed how MFA model parameters can be calculated from real or computer-generated structures. Alex McGlasson from the same group created Igor code that generates MFAs using a Monte Carlo method. This method is included in Irena — read the manual page on this method for details. It has also been ported to pyIrena as the Fractals tool.
Two-phase solids
If the sample scattering comes from a system with ONLY two phases and a sharp interface between them, you can try this model. There are other practical limits as well — for example, the size distribution of features must be relatively limited (perhaps a decade). In this case one can use the methods described in the SAXSMorph paper or the Quintanilla GRF paper. The method calculates the Debye autocorrelation function and uses Gaussian Random Fields to generate one of the infinite number of 3D distributions of matter that have the same 1D small-angle scattering as the sample.
The method ported from SAXSMorph is part of Irena and now also of pyIrena (SAXS Morph tool, pyirena-saxsmorph, with an optional 3D voxelgram viewer installed via pip install pyirena[gui3d]).