[Aavso-photometry] Errors on AIP

Wed Jul 14 16:17:09 EDT 2004

> Finally, yeah, I'm not sure how to integrate the read noise into the 
> noise equation. I'm just adding it in quadrature now. Otherwise the 
> noise equation makes sense to me.

To integrate read noise, you need to take into account your aperture; each 
pixel contributes read noise.

If your aperture has N pixels, and the read noise is R electrons, the 
total read noise contribution is RN = R * sqrt(N). To combine in your 
equation, you need to express it as a relative error (so divide it by the 
star flux).

I have a rather complete model for noise that takes most factors into 
account at:

http://astro.corlan.net/gcx/html/node8.html#SECTION00083000000000000000

It's not necessarily easy to follow i'm afraid ;-).

Radu

> 
> Cheers,
> Michael Koppelman
> http://www.lolife.com/astronomy/
> 
> 
> 
> On Jul 14, 2004, at 2:45 PM, Pertti Pääkkönen wrote:
> 
> > Michael,
> >
> > I have been working with the same problem. AIP does not save the sky 
> > backgound STD
> > in
> > the photometry, which is needed for uncertainty estimates. 
> > Furthermore, we should
> > speak about uncertainty here, not error. When we reduce our 
> > measurements into
> > standard system, (where the Comp stars are measured) we can speak 
> > about measurement
> > error. And this reduction introduces another uncertainties.
> >
> > I looked through your file, and these are my comments (please, don't 
> > take it as
> > ultimate truth :-)
> >
> > - Your uncertainty formula seems reasonable, provided that SNR is 
> > correct.
> >
> > - Why do you add K-C STD when you calculate the final uncertainty for 
> > V-C? It may
> > give correct results, if C and K are of same brightness. However, it 
> > DOES give you a
> > good indication of your uncertainty for V-C provided that V and K are 
> > of same
> > brightness.
> >
> > - There is something weird in your SNR formula. Under square root you 
> > coadd
> > StarCount
> > times Gain, AverageSkyBackgound times StarApertureArea, 
> > StarApertureRadius squared
> > times StarApertureArea (=Pi times StarAperture^4), and finally 
> > ReadOutNoise. This
> > does not make sense to me...
> >
> > I have found a reasonable formula, which is discussed in the 
> > references of AAVSO CCD
> > Observing Manual. Please find the Newberry article "Signal-to-Noise 
> > Considerations
> > for Sky-Subtracted CCD Data" (1991), or alternatively the article 
> > "Measuring the
> > Signal-to-Noise Ratio S/N of the CCD Image of a Star or Nebula", found 
> > at:
> > http://www.phys.vt.edu/~jhs/phys3154/snr20040108.pdf . In this article 
> > there is a
> > nice explanation how SNR is calculated. It also gives a formula to 
> > calculate the
> > SNR.
> >
> > I have applied your excel sheet to my series of U Gem in case of 
> > bright and dim V
> > star. In AIP_Err_bright C is star #1 and V is star #2 in ugem.seq by 
> > Henden and
> > Sumner. In AIP_Err_dim C star is #1 and V is star 11. Thus, in the 
> > first run B-V is
> > about 0.5 and in the second B-V is about 4.1. For SNR calculation I 
> > add measured STD
> > of the Sky Annulus in column P (measured by my own software), SNR 
> > calculated using
> > Newberry formula in column Q, and finally uncertainty 
> > 2.5*log10(1+1/SNR).
> >
> > In AIP_Err_bright there is practically no difference bitween yours and 
> > my results.
> > This is because SNR is dominated by photon noise sqrt(StarCount). In 
> > AIP_Err_dim
> > there is some difference between SNR's. But still, if you look mean 
> > values of
> > calculated uncertainties (Err), they are equal.
> >
> > I suspect that there is something wrong with your SNR formula. It 
> > takes account
> > ReadOutNoise, but not actual noise in the image SkyBackground. This 
> > means that it
> > will not take into account changing observing conditions nor random 
> > effects like
> > gamma rays etc. If the STD of SkyBackground is used, then photon 
> > noise, thermal
> > noise, ReadOut noise and random effects are taken into account. But 
> > this is
> > practically significant only with poor SNR (<50 or so).
> >
> > When playing with uncertainties, it is adviced to compare your 
> > estimates to STD of
> > your measurements. With reasonably large amount of measurements the 
> > uncertainty and
> > STD should be equal regardless of star SNR. However, in my studies the 
> > ratio DeltaV
> > / STD(V) appears to be close to 0.6 (cross-checked with Arto's 
> > MaximDL).
> >
> > I wanted to start discussion about what is correct way to give error 
> > esitmates in
> > AAVSO WebObs. I have learned that the same discussion was there just 
> > one year
> > earlier.
> >
> > I hope this helps. Please find attached zipped two files with my 
> > photometry.
> >
> > Well, still 6 weeks when we can think about observing because of 
> > summer here in
> > Finland...
> >
> > Cheers,
> >
> > Pertti
> >
> >
> > Lainaus Michael Koppelman <lolife at bitstream.net>:
> >
> >> This is an experiment. I know a lot of people use AIP for photometry
> >> and it doesn't calculate the signal-to-noise ratio (SNR). I have
> >> created a spreadsheet where you simply paste your AIP data into it and
> >> it calculates the "total" error in your photometry using the equation:
> >>
> >> Err = sqrt( (1/snr)^2 + comp_sigma^2 )
> >>
> >> It also calculates your comp star (K-C) sigma for you and tells you 
> >> the
> >> SNR and "total" error for each data point.
> >>
> >> I would appreciate it is people who use AIP could test it out and let
> >> me know how it works. I would also appreciate it if those people who
> >> have a good understanding of SNR could double-check my math.
> >>
> >> The spreadsheet is here:
> >>
> >> http://www.lolife.com/astronomy/AIP_Err.xls
> >>
> Cheers,
> Michael Koppelman
> http://www.lolife.com/astronomy/
> 
> >> _______________________________________________
> >> Aavso-photometry mailing list
> >> Aavso-photometry at mira.aavso.org
> >> http://www.aavso.org/mailman/listinfo/aavso-photometry
> >>
> >
> >
> > -- 
> > Pertti Pääkkönen, PhD, Laboratory engineer
> > University of Joensuu, Department of Physics
> > Tel: +358 13 351 3238
> > Fax: +358 13 251 3290<AIP_Err.zip>
> 
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> 
> 

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