Dear scatterers, Those of you who have been reading this weblog for a while now, may remember the calculation of the sample self-absorption correction for plate-like samples. The result of this was a straightforward equation which could be used to correct the scattering of strongly absorbing samples (>30%) with a plate-like geometry. It was mentioned then, that the calculation of this correction for capillary samples is more complicated, but would be good to have. This sample self-absorption of a capillary will show up as a butterfly-shaped shadow on your scattering pattern. In the latest issue of J. Appl. Cryst., there is a new paper discussing exactly this. Sulyanov et al. have (programmed) a solution to calculate the sample self-absorption factor for cylindrical samples. The code they provide is available in Fortran, and I will spend some time to try to transcode this into Python in the near future. Judging from their solutions, I am happy I did not try to solve it. The solution seems to be a little bit more complicated than I thought. Additionally, in the same issue, Zeidler has a solution for samples of spherical geometry. While I have not encountered a problem requiring this solution before, it is certainly noteworthy, and may be of use to some of you doing scattering from suspended objects. Lastly, there is a new video of one of my latest short presentations online here, explaining a little about my work as well as the monte-carlo analysis method. It’s very short, and there will be a more detailed MC method explanation shortly (as I have promised for quite a while now). Scatter well!
This series is part of a set to determine which corrections matter when. We all heard -or read- about corrections Small-angle Scatterers do not need to do, because they are supposedly negligible. Let’s look at some of them and determine if this is really true or not. The first looks at the sample direction-dependent absorption. This is the effect of scattered radiation travelling a slightly different distance through the sample (and therefore experiencing different levels of absorption) depending on the direction of scattering. Take, for example, the simplest case of a sample like a plate or sheet (c.f. Figure 1). From this figure, it can easily be seen that the radiation scattering to an angle has to travel longer through the sample than radiation passing straight through. Therefore, the scattered radiation suffers from more absorption. But how much more? In this document: plate_transmission, with the help of Samuel Tardif, we calculated the exact angle-dependent absorption of a plate-like sample. The short answer, for those who do not want to read the document: The sample absorption indeed accounts for less than a percent of deviation to a scattering angle of 10 degrees (degrees, as this effect is independent of the wavelength), if the sample absorption is lower than 75 % (which is already much more absorption than the max. 30% rule-of-thumb you were told by your senior scatterers). The full diagram is shown in Figure 2 (click to enlarge). So, on the grand scale of things, this correction is indeed negligible for most samples (watch out for the highly absorbing ones though!). However, given its simplicity, it should not be much trouble to implement for sheet-like samples at least. The correction is very straightforward to implement (see document) as you only need to know the transmission factor (which you knew anyway, because you measured it for the background subtraction, right?). This only applies to sheet-like or plate-like samples, the calculation for a capillary is a little bit more complicated. The capillaries also suffer from this, but this plate-like absorption is the maximum correction to apply for capillary geometry (in the direction parallel to the capillary axis). So also for capillaries, implementation is unnecessary unless you are hunting for the final fractions of a percent accuracy. Next time we discuss another one: the polarization correction!