7.6 Accuracy in Surface Photometry

As a verification of the simulation procedure, and to roughly estimate the accuracy in surface photmetry of the flux maps, a comparison between the surface brightness values in HST original image and in GAIA simulated flux map was carried out. In order to do so, the median value of the residuals between HST WFPC2 electron counts and simulated GAIA BBP electron counts were computed taking into account the different exposure time of the two images. The value thus obtained can then be compared with the accuracy in surface photometry expected a priori from flux maps, as it was derived in Section 5.7 on the basis of statistical considerations.

Following this idea, a median error of 0.15 mag/arcsec$^2$ is derived from the comparison of HST data with GAIA simulated data. Now, remembering that the median $V$-band surface brightness of the HST image is 19.42 mag/arcsec$^2$, 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$^2$, 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 $6\times4$ pixels/sample compares favourably with that obtained with other sample sizes, as shown by Table 7.2. The apparently contradictory lower accuracy obtained with $6\times8$ 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 $6\times4$ pixels is due to the increase in the readnoise.

Table 7.2: Accuracy in surface photometry estimated from simulations. Median error in $V$-band surface photometry of GAIA simulated flux map data with respect to HST data for different sample sizes. Sample size expressed in pixels, median error in mag/arcsec$^2$.

$6\times8$	$6\times4$	$6\times2$	$1\times8$
0.190	0.149	0.249	0.311