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Poisson stats: signal to noise

  1. Oct 6, 2003 #1
    A star was measured to have an apparent magnitude m=16 with S/N=10 integrated over a minute. What is the uncertainty in the measurement?
    So, S/N=sqrt(fAt)
    How can I find fA?
    Hoping that K is arbitrary (please verify this), I choose K=0
    Then 16=-2.5log(fAt)
    So fA=3.98 e-7 J/s (units inconsequential)
    So, uncertainty =6.3 e-4
    Or, I can get N=uncertainty=sqrt(S/10)=sqrtS <--- something VERY wrong here
    Last edited: Oct 6, 2003
  2. jcsd
  3. Oct 7, 2003 #2
    Last edited by a moderator: Apr 20, 2017
  4. Oct 7, 2003 #3
    I think this is an exercise in error propagation.
    You could also write m=-2.5log(I)+K
    You have m, and I/dI=10. You want to find dm. (d means differential).

    m + dm = -2.5log(I + dI) + K.
    You could now substitute dI = I/10, and solve for m. That will work, since I will cancel.

    However, I suspect they talk about RMS noise.
    Which makes things a bit more complicated.
  5. Oct 7, 2003 #4
    Re: Re: Poisson stats: signal to noise

    No, actually. You're answer if perfect. We went over this today in class. It didn't make sense then, but I think it's finally making sense. I was trying to hard to find S.
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