simulating_sas.html

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<title>Simulatung SAS</title>
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<h1>Calculating small-angle scattering of an object using randomly distributed points</h1>
<p>
SAXS and SANS data from a particle, e.g. a cylinder, can be simulated using various methods. One of them, used by <a href="https://somo.chem.utk.edu/shape2sas/" target="_blank">Shape2SAS</a>, is to fill the cylinder volume by randomly distributed points (or small spheres). The scattering can then be calculated by the <a href="https://pythoninchemistry.org/sim_and_scat/calculating_scattering/debye_equation.html" target="_blank"> Debye equation</a>.<br>
If enough points are fill into the volume, the scattering from these points corresponds to the scattering from the cylinder. It is a bit like pixels in an image: if the resolution is good enough (enough pixels), you do not see the pixels.<br>
The $q$-value defined which size we probe: small $q$ are large distances, and large $q$ probe small distances. So the larger $q$, you would like to simulate, the more points you need to fill into the cylinder volume. 

A cylinder is in fact a poor example, as the scattering from a cylinder can be calculated <a href="https://www.sasview.org/docs/user/models/cylinder.html" target="_blank">analytically</a>, which is faster than than filling with points, but other shapes may not have an analytical expression. This could, e.g., be the envelope of a protein.

<img src="cylinder_points.png" style="width:600px"/><br> 

<ul><b>Programs using beads or points to calculate saxs/sans data:</b>
<li>Shape2SAS (<a href="https://doi.org/10.1107/S1600576723005848" target="_blank">Larsen et al, 2023</a>).</li> 
<li>CDEF (<a href="https://doi.org/10.1107/S160057672200499X" target="_blank">Deumer et al, 2022</a>).</li>
<li>SPONGE (<a href="https://github.com/bamresearch/sponge" target="_blank">Pauw and Breßler, 2021</a>).</li>
<li>McSAS [no longer maintained, replaced by Shape2SAS] (<a href="https://doi.org/10.1107/S0021889890002801" target="_blank">Hansen, 1990</a>, <a href="https://journals.iucr.org/paper?S1600576714013156" target="_blank">Hansen, 2014</a>).</li>
<li>DAMMIF/DAMMIN (<a href="https://doi.org/10.1107/S0021889809000338" target="_blank">Franke and Svergun, 2009</a>).</li>
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