Accurate PSF-matched photometry and photometric redshifts for the Extreme Deep Field with the Chebyshev-Fourier functions

Photometric redshifts, which have become the cornerstone of several of the largest astronomical surveys like PanStarrs, DES, J-PAS or the LSST, require precise measurements of galaxy photometry in different bands using a consistent physical aperture. This is not trivial, due to the variation in the shape and width of the Point Spread Function (PSF) introduced by wavelength differences, instrument positions and atmospheric conditions. Current methods to correct for this effect rely on a detailed knowledge of the PSF characteristics as a function of the survey coordinates, which can be difficult due to the relative paucity of stars tracking the PSF behaviour. Here we show that it is possible to measure accurate, consistent multicolour photometry without knowing the shape of PSF. The Chebyshev-Fourier Functions (CHEFs) can fit the observed profile of each object and produce high signal-to-noise integrated flux measurements unaffected by the PSF. These total fluxes, which encompass all the galaxy populations, are much more useful for Galaxy Evolution studies than aperture photometry. We compare the total magnitudes and colours obtained using our software to traditional photometry with SExtractor, using real data from the COSMOS survey and the Hubble Ultra Deep Field. We also apply the CHEFs technique to the recently published Extreme Deep Field and compare the results to those from ColorPro on the HUDF. We produce a photometric catalogue with 35732 sources (10823 with S/N>5), reaching a photometric redshift precision of 2% due to the extraordinary depth and wavelength coverage of the XDF images.