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The Physics of the Accelerating Universe (PAU) survey at the William HerschelTelescope (WHT) will use a new optical camera (PAUCam) with a large set ofnarrow-band filters to perform a photometric galaxy survey with aquasi-spectroscopic redshift precision of \sigma(z)/(1 + z) ~ 0.0035 and mapthe large-scale structure of the universe in three dimensions up to i_AB <22.5-23.0. In this paper we present a detailed photo-z performance study usingphotometric simulations for 40 equally-spaced 12.5-nm-wide (FWHM) filters witha ~25% overlap and spanning the wavelength range from 450 nm to 850 nm,together with a ugrizY broad-band filter system. We then present the migrationmatrix r_ij, containing the probability that a galaxy in a true redshift bin jis measured in a photo-z bin i, and study its effect on the determination ofgalaxy auto- and cross-correlations. Finally, we also study the impact on thephoto-z performance of small variations of the filter set in terms of width,wavelength coverage, etc., and find a broad region where slightly modifiedfilter sets provide similar results, with the original set being close tooptimal.

Precise photometric redshifts with a narrow-band filter set: The PAU Survey at the William Herschel Telescope