On Sat, Jun 22, 2013 at 1:56 PM, Ian Tickle <ianj...@gmail.com> wrote:
> On 22 June 2013 18:04, Douglas Theobald <dtheob...@brandeis.edu> wrote: > >> --- but in truth the Poisson model does not account for other physical >> sources of error that arise from real crystals and real detectors, such as >> dark noise and read noise (that's why I would prefer a gamma distribution). >> > > A photon counter is a digital device, not an analogue one. It starts at > zero and adds 1 every time it detects a photon (or what it thinks is a > photon). Once added, it is physically impossible for it to subtract 1 from > its accumulated count: it contains no circuit to do that. It can certainly > miss photons, so you end up with less than you should, and it can certainly > 'see' photons where there were none (e.g. from instrumental noise), so you > end up with more than you should. However once a count has been > accumulated in the digital memory it stays there until the memory is > cleared for the next measurement, and you can never end up with less than > that accumulated count and in particular not less than zero; the bits of > memory where the counts are accumulated are simply not programmed to return > negative numbers. It has nothing to do with whether the crystal is real or > not, all that matters is that photons from "somewhere" are arriving at and > being counted by the detector. The accumulated counts at any moment in > time have a Poisson distribution since the photons arrive completely > randomly in time. > I might add that if you are correct --- that the naive Poisson model is appropriate (perhaps true for the latest and greatest detectors, evidently Pilatus has no read-out noise or dark current) --- then the ML solution I outlined is a good one (much better than the crude Ispot-Iback background subtraction), and it provides rigorous SD estimates too.
