Following this idea, a median error of 0.15 mag/arcsec is derived
from the comparison of HST data with GAIA simulated data.
Now, remembering that the median -band surface brightness of the HST image
is 19.42 mag/arcsec, the expected standard error in surface
photometry at this surface brightness level can be calculated as indicated in
Section 5.7, thus obtaining 0.17 mag/arcsec, very
close to the value obtained from simulations.
This good agreement further demonstrates the convenience of statistical
formulae for use in the preliminary instrument design and mission planning,
while it validates the results of simulations.
Note that in this simple treatment the error originating from the subtraction
of the sky background was not considered, but it is believed
(see Section 5.5 that this would yield an error much lower than that
introduced by readnoise, so that the calculation is essentially correct.
Note also how the a posteriori accuracy in surface photometry obtained
with pixels/sample compares favourably with that obtained with
other sample sizes, as shown by Table 7.2.
The apparently contradictory lower accuracy obtained with pixels/sample can be understood as originating from the smearing of
bright features due to the wider PSF, whereas the decrease in accuracy for
sample sizes smaller than pixels is due to the increase in the
readnoise.