Revisiting observability in polydisperse systems: “real” polydispersity

2011/07/17 // 1 Comment

edited on 2011-07-20 14:51 to add equation defining observability Of course I could not leave you hanging after the last post with that question “does the observability still scale with the radius squared for samples with more than two particles?”. Short answer: yes. Long answer: mostly, with some interesting lessons w.r.t. q-angles and limitations. Click “more” to read [...]

Observability in polydisperse systems. What is all the accuracy for?

2011/06/30 // 0 Comments

Abstract of this post: In this post, I will show that for a spherical two-particle system, the observability of the smaller particle scales with the inverse squared radius, quite different from the scattering power, which scales with the radius to the sixth power (volume squared). This means that scattering data with 1% error can be used to distinguish at most particles 1/20th the size of the largest particle present, and data with 0.1% error can be used to observe single particles at most 1/50th of the size of the largest particle. Beyond this, only proportional numbers of smaller particles can be observed. Additionally the point of maximum observability is determined to be at q*Rg~2.6 for numeric examples, and q*Rg~2.45 for an algebraic [...]

Does it matter part 2: polarization factor and spherical corrections

2011/06/12 // 2 Comments

In this series of posts, we take a quick look at some uncommon corrections you can do to your scattering patterns and we evaluate whether they are worththe trouble or not. The goal is to arrive at intensities which are within 1% of their correct values. In the previous post, we looked at the sample self-absorption behaviour. This turned out only to significantly affect the scattering patterns at very high absorptions and large scattering angles. Additionally, its complexity makes it difficult to implement for all types of samples (it was only derived for the simple case of a sheet-like sample, not for the more common capillary- or cylindrical shape). Thus, this correction should only be considered necessary to apply for highly absorbing samples scattering to angles above 5 degrees. Two other corrections to consider are the polarization correction and the spherical correction. The spherical correction, correcting for the differences in angular coverage by the detector pixels, was also [...]

Baby, and the perfect measurement made easier

2011/05/29 // 0 Comments

I apologise for my low activity in the last few weeks. Those of you who are following my Twats (Twitter messages) will probably be able to link this to our newborn baby. Now growing strongly for two weeks, having to wake up every four hours in what seems like the longest beamtime ever have left me feeling like a pinball at night. Despite that, the research continues, and I am happy to say that getting the Perfect measurement (or an approximation thereof at least, as described in the document of a few posts ago) will become maybe a little easier with some new software I wrote. The software draft is written in Matlab, but I am trying to learn Python to recode the essentials in free software (interested in helping? Let me know!). Why all this focus on the perfect measurement, you may ask? Well, it turns out that for most of the SAXS analyses to give you the correct answer (as opposed to just an answer), your data should be correct to within 1%. Most beamlines will not give you this [...]

Does it matter? part 1: sample direction-dependent absorption

2011/05/06 // 5 Comments

Figure 1: Scattered radiation traveling different distances through a sample 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, [...]

Work in Progress: How to do a SAXS measurement well

2011/04/06 // 3 Comments

Hi all. For a work-related project, I have been developing some software and writing some documentation. This documentation is still a work in progress (as is the software), and it lacks much graphics. However, I think it could serve as a good introduction to those who want to do a good SAXS measurement, or those who will join on an expedition to a SAXS beamline. Let me know what you think! The appendix is a chapter from my thesis. [...]