[Aavso-photometry] Converting Std Deviation in electrons tomagnitudes

[Michael Newberry]

Merry Christmas Brad,

The relation between SNR and sigma(m) is indeed as simple as Steve shows. It 
comes from the definition of magnitude, m, as  m = K - 2.5 * log(F), where F 
is flux and K is a zero point constant. When you turn this into a 
differential equation to see how a small change in flux relates to a small 
change in magnitude, and then you identify SNR = F / sigma(F), you obtain 
the simple formula sigma(m) = 1.0857 / SNR. This comes from pure algebra and 
simple differential calculus, and it involves no astronomy and nothing about 
how the magnitude is calculated or how the various noise sources combine. If 
you want to break down SNR into its noise components, then it gets 
interesting, however!

I think you are assuming that the formula needs to be more complex because 
the noise is actually coming from various sources which must be taken into 
account. In fact, the SNR stated is the final one into which the various 
noise sources have been included. When dealing with the "final" SNR, it does 
not matter where the noise components comes from; then the conversion to 
magnitude error is trivial, as shown above.

As a side point, what is the reference you mention?

Michael

----- Original Message ----- 
From: "Brad Walter" <bswalter at hughes.net>
To: <aavso-photometry at mira.aavso.org>
Sent: Tuesday, December 25, 2007 5:05 PM
Subject: [Aavso-photometry] Converting Std Deviation in electrons 
tomagnitudes


>
>
> I have been perusing Handbook of CCD Astronomy by Steve Howell and came
> across a formula in Section 4.4 (page 78 in my paperback version) that
> mystifies me. Steve uses a conversion factor of 1.0857 as a conversion
> factor from Sigma = 1/SNR in electrons to sigma in magnitudes. With a 
> little
> fiddling I was able to deduce that the conversion factor equals (to the
> least significant digit given) 2.5/LN(10). I don't understand how a 
> constant
> conversion factor can be correct. It seems to me that the conversion would
> be more like the following
>
> Sigma(mag)= -2.5*Log(1 + 1/SNR)/2 + 2.5*Log(1 - 1/SNR)/2
>
> where using Steve Howell's terminology
>  SNR = Nstar/SQRT(Nstar + P)
>  Nstar is the signal in electrons
>  P is made up of the noise terms other than the Poisson noise of the flux
> from the star.
>
> Can anyone explain Steve's conversion formula? I can't find the reference 
> he
> cites on-line
>
>
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