I decided I can do better than before, not so much in terms of the quality of the matching, but in terms of the usefulness. The executive summary is that the distortion corrections are polynomial fits, which apply over the entire overlap region between the UDS and the appropriate SXDF image, instead of just the region where the SXDF image is the "best" one to use (i.e., the one where the coordinates are furthest from the edge of the image). This has the benefit of allowing you to use a different optical image if the "best" one suffers from CCD bleed or another artifact.
So I repeat Part 2 of the DR1 matching, omitting step 2. This gives me the RA and Dec distortions as a function of UDS coordinates for each of the 5 SXDF images. I then perform a surface fit (using IDL's SFIT routine) to each of the 10 distortion maps (5 fields, 2 coordinate axes), with a range of polynomial orders from 1 to 15, and investigate the deviations between the polynomial fit and the distortions. I choose the lowest polynomial order for which the rms deviation is less than 25mas. This is shown in the figure below: the solid lines indicate the deviation in right ascension, and the dashes lines the deviation in declination; the upper traces show the maximum deviation, while the lower traces show the rms.
The celestial coordinates of each UDS source are used to compute a distortion correction for each of the 5 SXDF images. These distortions are applied and the new coordinates converted to pixel positions in that SXDF image. If this pixel location is within the image, photometry is performed (as with the previous matching, photometry is performed on modified images where slow background variations have been removed). Although the polynomials are well-behaved over the areas occupied by the SXDF images, they do get out of control if used at inappropriate locations, so a check is made to ensure that the distortion is less than 5 arcseconds.
Photometry was performed with the IRAF PHOT task. Sky noise has been estimated by subdividing each SXDF image into an 8x10 grid (approx 1000 pixels on a side) and performing photometry in 5000 randomly-placed apertures of diameters 1,2,3" within each grid element. A histogram was made of the results and a parabola fitted to the log of the number of objects per bin to give the sky noise.
Rather than perform random sky photometry for every size aperture in the DR3 catalogue, I applied an empirical solution determined from my 3 apertures. If sky noise is the dominant source of noise, it should vary linearly with aperture radius. However, the SXDF images are deep enough for confusion to be important, and the variation of confusion noise with aperture size depends on the shape of the source counts: for steep counts, the noise is caused by Poisson fluctuations in the number of very faint objects in the aperture, and is again linear with aperture radius; for flat counts, the noise depends on whether or not you have a brighter object in the aperture, and is linear with aperture area. Optical source counts are quite flat at the magnitudes probed by the SXDF data, so we expect the noise to vary more rapidly than linearly with radius. Empirically, it is found that noise ~ (aperture radius)^1.71. Performing the same analysis including larger apertures (4" and 5") produced an index of 1.82, although the ability to infer sky noise from 5" apertures is quite difficult as most apertures include significant object flux. After a bit of thought, it was decided to calculate the sky noise by scaling the measured 2" aperture noise by the 1.75th power of the aperture radius.
In many cases, there is only imaging data from one SXDF image: if so, this photometry is used. Sometimes, however, there may be data from two, or even three, images, and a choice has to be made. The following procedure is used:
In this context, the FOM is defined as the smallest distance to the SXDF image edge (since the astrometric solution will likely be worse there). A photometric point is considered to be discrepant among three points if it is more than 10 times further from the median as the other datapoint.
For your consideration: this might not be the best thing to do. In particular, this algorithm will choose to measure photometry from a clean image where the larger apertures go off-image in preference to one which is entirely on-image but masked in small apertures. Since the masking regions are a little conservative, there may be good data despite the masking flags. Note also that photometric results are returned for apertures which extend beyond the edge of the image by assuming that there is zero flux from the off-image region.
For those objects which are in the overlap regions between SXDF images, the photometry from different images has been compared. As seen in the plot below, the agreement is generally very good (there are 16,653 objects here, where the flags are zero on both images). The few extreme objects at intermediate magnitudes (the differences at bright magnitudes are due to saturation effects) are typically faint objects close to brighter ones where the photometry is uncertain; little can be done about these. It is also worth noting that the estimated photometry uncertainties are in good agreement with the scatter seen -- at R=25, the error is estimated to be 0.08 mag.
