[Aavso-photometry] Different ways of averaging data

[Wolfgang Renz]

What about averaging before doing the lightquants/electrons/counts
to mag conversion ?
Or while converting temporarily back to intensities ?

Photometry is about measuring intensities but mags are logarithmic
intensities that have the property that equal mag differences represent
equal intensity factors. So averaging the logarithmic mags should
always give a bit too faint mean mag value and introduces an additional
systematic error depending on the mag differences.

Example A: Slow changing target and/or high SNR (500) data
    intensity I   -2.5*log(I) mag
       9980        - 9.9978263...
      10000        -10.0000000...
      10020        -10.0021693...
      -----        --------------
avg   10000        - 9.99999855...
Converting back the avg mag gives a intensity of 9999.986. The
difference is pretty small.

Example B:  Fast changing target or low SNR (10) data
    intensity I   -2.5*log(I) mag
       9000        - 9.8856062...
      10000        -10.0000000...
      11000        -10.1034817...
      -----        --------------
avg   10000        - 9.9963626...
Converting back the avg mag gives a intensity of 9966. The
difference is still small but already significant (see also discussion
about using SNR+ and SNR- for error estimates)

Example C: Sparse data with highly differing intensities
    intensity I   -2.5*log(I) mag
       5000        - 9.2474250...
      10000        -10.0000000...
      15000        -10.4402281...
      -----        --------------
avg   10000        - 9.8958843...
Converting back the avg mag gives a intensity of 9086. The
difference is more than significant and the additional error due
to averaging in the mag space is larger than 0.1 mag.

* Whats the 'official' recommendation when to start averaging in
  the intensity space ?
*Are the AAVSO ten-days-mean of the miras still averaged in
  the mag space ?


There exists an other issue related to intensity and mag space:
When you measure a variable with a much brighter companion that
can not be resolved.
While the measured differential intensities might be significant, the
differential mags of both together will decrease with brighter
companions. Subtracting an incorrect mag of the companion will
enlarge or reduce the real amplituide of the variable. Just the
differential intensities stay what they are. So in these cases just a
differential intensity vs. time graph is not affected by the magnitude
of the unresolved, bright companion.


Clear skies
  Wolfgang

-- 
Wolfgang Renz, Karlsruhe, Germany
Rz.BAV = WRe.vsnet = RWG.AAVSO



----- Original Message ----- 
From: "arne" <arne at aavso.org>
To: "Pedro Pastor" <pps at dlsi.ua.es>
Cc: <pps at ua.es>; <aavso-photometry at aavso.org>
Sent: Sunday, June 05, 2005 1:57 AM
Subject: Re: [Aavso-photometry] Different ways of averaging data


> Pedro Pastor wrote:
> 
> >I've done a high rate sampling on a Delta Scuti (NSV 3063). While
> >processing data I saw that, although single point data precision is
> >around 0.002 mag., data dispersion along the whole series is high.
> > 
> >As long as my sampling rate was high, I thought of averaging measures
> >(every 5 points). Then, a big doubt rose in my mind. What would be
> >better to average: differential photometry data or raw images (in order
> >to raise SNR) and then calibrating the result image and get the
> >differential photometry measure?
> > 
> >I've done some tests in order to compare both methods, but my results
> >don't shed any light on the question. Maybe both procedures are
> >equivalent?
> > 
> >Could anybody provide me with some information (or results) about this
> >point?
> > 
> >Thank you very much.
> > 
> >  
> >
> Since your Poisson error is in the 0.002 range, you are Poisson-noise
> limited and sky/readnoise are negligible contributions.  This means
> you will get the same results whether you stack frames and measure,
> or do individual measures and average.  There is one exception
> that I can think of immediately.  During stacking, if your software
> averages the frames and then has a 16-bit frame as output, you lose
> some signal/noise (you want either a 32-bit integer sum or a
> floating-point result).
>   The primary source of noise when taking high time cadence images
> is scintillation.  Averaging several measures will decrease this
> error at the cost of time resolution.
>   I usually find averaging the individual measures to be easier
> than to stack frames, as long as you are not skynoise or readnoise
> dominated.  When the object gets faint, you usually have to be
> more careful.
> Arne