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Trying to understand the resolution in the context of the standard error of the mean. An example in a book reads: "The energy resolution of a gamma ray detector used to investigate a decaying nuclear isotope is 50keV. If only one such decay is observed its energy is known to 50keV. If 100 are collected this improves to 5keV. To reach 1keV you would need to observe 2500 decays."

I understand that the standard error of the mean falls off like 1/sqrt(N). But I'm confused how this relates to the intrinsic resolution of the detector. Isn't its resolition a set thing? (Sorry I know I sound clueless, I think I actually am).

What determines the resolution of the detector for a single measurement? How can (why) this intrinsic property change as your sample number increases?

It all sounds to me like "your phone can take pictures of resolution x. If you take many pictures the resolution will improve".

Please don't assume prior knowledge of any kind in your answer (if that is possible at all).

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  • $\begingroup$ They would appear to be sloppy, and not considering the detector resolution. $\endgroup$
    – Jon Custer
    Nov 16, 2016 at 20:33
  • $\begingroup$ If you take many pictures the resolution will improve is kinda the premise behind lucky imaging (though the resolution is improved with post-processing of a multitude of images) $\endgroup$
    – Kyle Kanos
    Nov 16, 2016 at 20:35

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If we are talking about a scintillating detector or some kind of solid state charge collection device, then the 50 keV quoted to you is not the intrinsic resolution of the electronics but the random uncertainty that arises because the ionization and collection processes are stochastic.

That is, repeated events due to the same source will generate a random distribution of signals that is roughly normal, and whose mean is the thing that you calibrate. So the uncertainty of the mean is the limit of the quality of your measurement.

There generally is also a width due to the electronics, but it is usually much narrower and you rarely have enough statistics that you need to worry about that.

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  • $\begingroup$ Thanks, that is correct, I was thinking of a scintillating detector and I thought thr width was due to the electronics. If it is a statistical error it does make sense (algebraically at least). If you have some time could you please write a bit more about why the error exactly occurs (why is the collection stochastic)? $\endgroup$
    – Eva
    Nov 17, 2016 at 16:47
  • $\begingroup$ @Eva There are not that many photoelectrons coming off the photocathode of the PMT. If that is about 100 for a certain gamma energy causing a photopeak in the scintillator, next time it can be 112 or 93. That is the bottleneck where the stochastics cause a large uncertainty. $\endgroup$
    – user137289
    Nov 28, 2016 at 22:54

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