So it seems science has beaten us to the punch once again. Remember last week’s optimistic story on how you can make better use of your (measurement) time? Turns out it has been done (at least once) before. The year was 1993, the authors were M. Steinhart and J. Pleštil, and they did the same from a different perspective . Credit where credit is due, their yet un-cited paper contains a good study of measurement stability and its effects on inferred information, and indeed has the equation for effective time-expenditure available (though written up in a confusing way). So all sadness on our side aside (as there is now no short-sweet-and-quick publication possible on this), please use your time wisely and cite that 1993 paper as it deserves. Do not let good methods like this be covered by years of dust. To give you some more ammunition for your citation-gun, here is a good paper detailing dead-time correction, and how Poisson statistics fail when these corrections are applied . I found that I should not blindly square-root my photons (real and imaginary), but that I should use the equations they provided where applicable. If you have a Pilatus detector, there is no reason to sweat much, as this correction is only applied in the very extreme count-rate regions . As always: let us know what you think and leave a comment!  STEINHART, M., & Plestil, J. (1993). Possible Improvements in the Precision and Accuracy of Small-Angle X-Ray-Scattering Measurements. Journal Of Applied Crystallography, 26, 591–601.  Laundy, D., & Collins, S. (2003). Counting statistics of X-ray detectors at high counting rates. J. Synchrotron Rad (2003). 10, 214-218 [doi:10.1107/S0909049503002668], 1–5. International Union of Crystallography. doi:10.1107/S0909049503002668  Kraft, P., Bergamaschi, A., Broennimann, C., Dinapoli, R., Eikenberry, E. F., Henrich, B., Johnson, I., et al. (2009). Performance of single-photon-counting PILATUS detector modules. Journal Of Synchrotron Radiation, 16, 368–375. doi:10.1107/S0909049509009911
Often, especially when measuring on big facilities, you are given a limited amount of time. So when it comes to measuring the sample and the background, this limited time has to be divided between a measurement of the sample, and a measurement of the background. Normally, one would spend about 50% of the time on a sample, and 50% on the background, or even more time on the background “because the counts are so low” (I know, I did the same!). There must be a better way to calculate the optimum division of time! So me and a colleague, Samuel Tardif, spent a little bit of time jotting down some equations, and plotting the result. The result is that for large differences in the signal-to-noise ratio (c.q. sample count rate to background count rate), significant reductions in uncertainty can be obtained through better division of time for any small-angle scattering measurement. In the case of a Bonse-Hart camera or a step-scan small-angle scattering measurement, each measurement point can be tuned to the optimal dwell time for the sample and background, after a quick initial scan to determine the signal-to-noise ratio at each point. Please let me know how it works for you! The calculation can be checked from this document where we wrote up the results: ideal_background
Hello dear readers, As a followup on my previous story, a colleague of mine sent me this paper that helps explain the standard deviation, standard error and confidence intervals. A useful, and funny read: Click here. The second noteworthy item is that I have, as of November 1st, started working at the National Institute for Materials Science (NIMS) as a (limited time) independent researcher. From now on, I will be working on a variety of stuff, which revolves around developing anisotropic SAS analysis methodologies. Naturally, I will post items of interest on this site as always, so keep checking in!. Also, don’t hesitate to leave a comment! B.
Everybody hates statistics … … but it can be of major importance in our small angle world. While very few papers on small-angle scattering discuss statistics, they can tell you whether your observations are real or just imaginary. In addition, statistics will let you know whether you have been able to describe your scattering pattern with your model or not. All in all, nice to have. I will briefly discuss two statistical concepts which could be of great use, as they have been for me. While I never really could understand all the concepts during statistics lectures at university (a situation which may sound familiar), I can try to explain some simple concepts. By the by, if you (dear reader) are a statistician, I would be happy to get in touch with you. The first concept is the most straightforward, and involves the uncertainties on fitting parameters. Secondly I will discuss statistics on collected intensity and how to retrieve them for a variety of detectors.