[Aavso-photometry] Converting Std Deviation in electrons tomagnitudes

[Brad Walter]

The reference is Howell, S.B., in "Stellar Photometry - Current Techniques
and Future Developments, eds. C.J. Butler & I. Elliott, IAU Colloquium 136,
Cambridge University Press, p.318.  

-----Original Message-----
From: Michael Newberry [mailto:mnewberry at mirametrics.com] 
Sent: Tuesday, December 25, 2007 6:34 PM
To: Brad Walter; aavso-photometry at mira.aavso.org
Subject: Re: [Aavso-photometry] Converting Std Deviation in electrons
tomagnitudes

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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