3D modeling of SAS data
This page is specific discussion on 3D scatterer shape reconstruction form 1D SAS data.
3D modeling of shapes and arrangement of particles (scatterers) provides the most understandable presentation for humans. Being able to see something which resembles visual images of type we are used to - either 2D image (~microscopy) or 3D volume images (voxelgrams, ~tomography) - makes us process the results better and visualize in our head the scattering system. Especially valuable it is for comparing two or more scattering systems, where seeing different images/voxelgrams may be lot more understandable than seeing aggregate/numerical values, such as average scatter sizes, size distributions, or specific surface areas.
Reconstruction of 3D data from their 1D representation (measured in 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 reconstruct correctly 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. Therefore, it is critical that users of these methods understand under what conditions a specific method can be used. If scattering system is NOT of the type a specific model/method, assumptions made by the model/method are NOT satisfied, and user is generating pure garbage. DO NOT GENERATE GARBAGE, there is already too much of it in the world...
However, these methods have been around for long time and, in bioSAXS (for example) are highly successful. This page provides explanation and guidance for some of these models use 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 typical example of application in bioSAXS and same methods can be easily applied to non-bio SAXS (SAS in general). What is needed is for the scattering system to be dilute system of one type of particles, monodispersed (all exactly the same size and shape), with no aggregation and no contamination by other "stuff". If the system looks like this, you can use well know suite of programs ATSAS. I have successfully applied "DAMMIN" or "DAMMIF" to some inorganic scattering and it worked really well.
Mass Fractal Aggregate
Mass Fractal Aggregates (MFA) are easily imagined as resembling snowflakes. The scattering from MFAs is usually analyzed by using Unified fit (Greg Beaucage, see many of his papers) and in recent paper "A. Mulderig, et.al, Quantiﬁcation of branching in fumed silica" Andrew, greg's student, detailed how the MFA model parameters can be calculated from real or computer generated structures. Alex McGlasson from the same group has created Igor code which can generate MFA using Monte Carlo method. This method is now included in Irena (May2019 BETA version). If you are interested in use of this method, install Irena BETA version May2019 or later. Read the manual page on this method for details.
Two Phase Solid
If the sample scattering is created by system, where there are ONLY two phases and the interface between the phases is sharp, one can try this model. There are also other practical limits to this model - for example, the size distribution of features must be relatively limited (may be decade). But in this case one can use methods described in SAXSMorph paper or Quintanilla GRF paper. In this method we calculate Debye Autocorrelation function and use Gaussian Random Fields to generate one of infinite number of 3D distributions of matter which has same 1D small-angle scattering as the sample has.
The method ported from SAXSMorph is now part of Irena (May2019 BETA version). If you want to use it, install Irena BETA version May2019 or later.
Also, SAXSMorph program has lost its "home" location and with permission of the author, Bridget Ingham, I am posting here last SAXSMorph versions. They are provided without any warranty and without any support/maintenance. SAXSmorph for Windows, SAXSmorph in Java, SAXSMorph manual and SAXSMorph paper. Users are free to download and use.