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 t
otal 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.
(ABRIDGED) We describe the first results of the ALHAMBRA survey which provides cosmic tomography of the evolution of the contents of the Universe over most of Cosmic history. Our approach employs 20 contiguous, equal-width, medium-band filters coveri
ng from 3500 to 9700 A, plus the JHKs bands, to observe an area of 4 sqdeg on the sky. The optical photometric system has been designed to maximize the number of objects with accurate classification by SED and redshift, and to be sensitive to relatively faint emission lines. The observations are being carried out with the Calar Alto 3.5m telescope using the cameras LAICA and O-2000. The first data confirm that we are reaching the expected magnitude limits of AB<~25 mag in the optical filters from the blue to 8300 A, and from AB=24.7 to 23.4 for the redder ones. The limit in the NIR is (Vega) K_s~20, H~21, J~22. We expect to obtain accurate redshift values, Delta z/(1+z) <~ 0.03 for about 5x10^5 galaxies with I<~25 (60% complete), and z_med=0.74. This accuracy, together with the homogeneity of the selection function, will allow for the study of the redshift evolution of the large scale structure, the galaxy population and its evolution with redshift, the identification of clusters of galaxies, and many other studies, without the need for any further follow-up. It will also provide targets for detailed studies with 10m-class telescopes. Given its area, spectral coverage and its depth, apart from those main goals, the ALHAMBRA-Survey will also produce valuable data for galactic studies.
