Re: Database error estimates

[Stupendous Man <richmond@stupendous.cis.rit.edu>]

  Andrew wrote:

> For example, selecting MV in 11.9 to 12.1 I find a
> range of standard deviations in the Database from
> 0.012 to 0.091 mags with clusters around 0.020,
> 0.040 and up, implying a wide range of
> exposure times. Not true, I think?

  Not true, indeed.

  The values stored in the database are calculated for
each instrumental magnitude extracted from each image.
They are based on simple photon statistics: an aperture
of radius N pixels contains a total signal of E counts
above the background level B.  If we know the conversion
factor from counts to electrons (the gain factor, which
should be in the FITS header of each image), we can
figure out the typical uncertainties in the signal
caused ONLY by the random statistical variations in the
number of electrons one would expect from a mean level
of sky B and star E.

  These values are almost always much smaller than the
true uncertainties in measurement due to systematic
effects in the data acquisition and measurement.  
This is especially true for bright stars: based on
photon statistics, one might expect variations of only
0.003 mag from one image to the next ... but the real
variation is closer to 0.03.

  As one goes to the faint end, with smaller signals,
the random photon statistics predict larger and larger
uncertainties; eventually, these tend to dominate
the systematic effects.  The database values for
faint stars are probably not very far from the actual
night-to-night variations.

> The case that I can check, because I have the raw
> data is Day 2452605: files HV/IRA2604797-863.
> Specifically for a star of MV 12.0 near the centre of
> HVRA2604797 I estimate a standard deviation of
> 0.061 mags for my least squares PSF fitting method
> and around 0.064 to 0.067 mags for aperture methods,
> depending on the size of the aperture.

> The standard deviations in the Database are 0.019
> to 0.022 mags for MV 11.9 to 12.1 in this image.

  Hmmmm.  The database values are taken from the pipeline,
which performs aperture photometry on the image.
You are performing aperture photometry on the image.
If you pick the same aperture sizes, and if you use the
same gain values, then you ought to end up with uncertainties
which agree with the database.

  This is perhaps puzzling ....

> I used:
> Background s.d. 28.56 digits excluding sky background
> Sky background 1886.3 digits
> MV 12.0 equals 3321 digits total, 175.8 digits peak pixel

  Aha.  Perhaps you are assuming that the gain is 1.0 electrons
per pixel?  If so, you won't get the same value as the pipeline,
as it is using a gain of something like 3 electrons per pixel.
Tom, can you remind us of the gain value for the Mark IV units?
It should appear in one of the *.param files which accompanies
all pipeline output.

  I'm guessing that a combination of different gain (mostly)
and different apertures (slightly) may explain why Andrew's
own aperture magnitude calculations do not yield the same
uncertainty estimates as the Mark IV pipeline.

                                          Michael