Optimal filter systems for photometric redshift estimation

In the next years, several cosmological surveys will rely on imaging data to estimate the redshift of galaxies, using traditional filter systems with 4-5 optical broad bands; narrower filters improve the spectral resolution, but strongly reduce the total system throughput. We explore how photometric redshift performance depends on the number of filters n_f, characterizing the survey depth through the fraction of galaxies with unambiguous redshift estimates. For a combination of total exposure time and telescope imaging area of 270 hrs m^2, 4-5 filter systems perform significantly worse, both in completeness depth and precision, than systems with n_f >= 8 filters. Our results suggest that for low n_f, the color-redshift degeneracies overwhelm the improvements in photometric depth, and that even at higher n_f, the effective photometric redshift depth decreases much more slowly with filter width than naively expected from the reduction in S/N. Adding near-IR observations improves the performance of low n_f systems, but still the system which maximizes the photometric redshift completeness is formed by 9 filters with logarithmically increasing bandwidth (constant resolution) and half-band overlap, reaching ~0.7 mag deeper, with 10% better redshift precision, than 4-5 filter systems. A system with 20 constant-width, non-overlapping filters reaches only ~0.1 mag shallower than 4-5 filter systems, but has a precision almost 3 times better, dz = 0.014(1+z) vs. dz = 0.042(1+z). We briefly discuss a practical implementation of such a photometric system: the ALHAMBRA survey.