1 Introduction

Understanding the formation of structure in the Universe is one of the most pressing questions in modern cosmology. The Sloan and 2dF surveys currently in progress (Colless 1998; Gunn 1995) will provide an accurate picture of large-scale structures in the local Universe but presently our knowledge of galaxy clustering at z>0.5 is poorly constrained. This is entirely a consequence of the technical limitations in imaging and spectroscopic equipment, which (until recently) have had fields of view $\sim$50 arcmin²; in all cosmologies this translates to <1 h^-1 Mpc at z>0.5. Covering a substantial enough area to provide meaningful statistics on larger ( 10-20 h^-1 Mpc) scales at higher redshifts ($z\sim1$) has been prohibitively expensive in telescope time. Consequently, many galaxy clustering measurements made at these redshifts have been dominated by the effects of sample variance, and also have only been able to investigate the highly non-linear regime where the predictions of theoretical models for the clustering of galaxies are strongly dependent on the biasing schemes employed. Other studies, such as investigating the variation of clustering amplitude by galaxy type or intrinsic luminosity, or the accurate measurement of higher-order statistics such as S₃ have been even more challenging.

However, with the advent of wide-field multi-object spectrographs like VIRMOS and DEIMOS (Le Fèvre et al. 2000; Davis & Faber 1998), in addition to wide-field mosaic cameras on 4 m-telescopes, this situation is changing. In this paper we detail a new survey, the Canada-France Deep Fields (CFDF) project which has been carried out using the University of Hawaii's wide field ( $28'\times28'$) 8K mosaic camera, UH8K. This survey has targeted three of the original fields of the Canada-France redshift survey (Lilly et al. 1995). In total the CFDF consists of four independent deep fields, each of area 0.25 deg². All of these have VI colours, three BVI and two and a half UBVI. The survey reaches a limiting magnitude ( $3\sigma,3''$aperture) of $I_{AB}\sim25.5$ and at least one magnitude fainter in UBV (Table 1). The $\sim$10⁵ galaxies in the survey, coupled with 1000 spectroscopic redshifts present throughout our fields, allows us to investigate with unprecedented accuracy the evolution of galaxy clustering to $z\sim1$ (the survey's median redshift at its completeness limit of $I_{AB}\sim25.5$). Moreover, our four widely separated fields also ensure that we can estimate the effect of cosmic variance on our results.

To date, there have been many studies of $\omega (\theta )$ carried out using deep imaging surveys conducted using charge-coupled-device (CCD)-based detectors (McCracken et al. 2000; Woods & Fahlman 1997; Hudon & Lilly 1996; Brainerd et al. 1994; Roche et al. 1993). These works have generally focussed on one or two fields, usually covering $\sim$50 arcmin² each and typically reaching limiting magnitudes of $I{_{AB}\sim25}$. Several authors have also attempted to cover larger areas (>1 deg²) by mosaicing together many separate pointings (Roche & Eales 1999; Postman et al. 1998), although these surveys reach much shallower limiting magnitudes ( $I_{AB} \sim 22$). In contrast, the CFDF survey, by virtue of its depth and angular coverage, is able to provide an accurate measurement of $\omega (\theta )$ in the range 18.5 < I_AB < 25.0.

Normally the results from these surveys have been interpreted in terms of the "$\epsilon-$'' formalism first introduced to explain clustering amplitudes observed at bright magnitudes on photographic plates (Groth & Peebles 1977; Phillipps et al. 1978). With this approach, an assumed redshift distribution ${\rm d}N/{\rm d}z$ (or one measured from an independent spectroscopic survey) and cosmology is coupled with a model for the evolution of $\xi(r,z)$ (parametrised by $\epsilon$). In this way it is possible to predict the amplitude of $\omega (\theta )$ at any magnitude limit, based on these assumptions. One can then conclude which value of $\epsilon$ is most appropriate for any given set of observations. Based on comparisons between $\omega (\theta )$measurements in deeper CCD surveys and photographic measurements at brighter magnitudes, many authors concluded that, for z<1 at least, growth of galaxy clustering was consistent with $0<\epsilon<2$(Brainerd, Smail, & Mould Brainerd et al. 1994). More recently, direct measurements of r₀(z) have been attempted at z<1 using spectroscopic samples (Carlberg et al. 2000; Small et al. 1999; Le Fèvre et al. 1996; Cole et al. 1994). These works have demonstrated the importance of sample selection in measuring galaxy clustering evolution; $\epsilon$ has been shown to be sensitive to the range of intrinsic galaxy luminosities and spectral types selected. Attempts have also been made using photometric redshifts computed using either ground-based or space-based imaging data to measure the growth of clustering (Teplitz et al. 2001; Brunner, Szalay, & Connolly Brunner et al. 2000; Arnouts et al. 1999a; Connolly, Szalay, & Brunner Connolly et al. 1998). However, the finding that clustering amplitudes for Lyman-break galaxies was similar to some classes of galaxies found locally (Adelberger et al. 1998; Giavalisco et al. 1998) has provided the clearest evidence to date that this simple formalism could not fully account for the observations of clustering at $z\sim3$.

In this paper, the first in a series, we will introduce the CFDF survey, explain in detail our data reduction strategy and demonstrate its robustness. As a first application of this dataset, we will present a measurement of the projected galaxy correlation function $\omega (\theta )$. The angular size and depth of the CFDF allows us to make a reliable determination of $\omega (\theta )$ over a large magnitude range ( $18 < I_{AB-{\rm med}} < 24$). Moreover the four separate fields allows us to make an estimate of the field-to-field variance in the galaxy clustering signal. Finally we will discuss how appropriate the "epsilon'' formalism is to describe the evolution of galaxy clustering measured in our data.

In a future paper (Foucaud et al., in preparation) we will describe our measurements of the clustering length r₀ at $z\sim3$ from a sample of $\sim$2000 Lyman-break galaxies derived from the CFDF dataset. By adding R- and Z-band data from the new CFH12K camera (Starr et al. 2000) we expect to sufficiently increase the accuracy of the photometric redshifts in the range 0<z<1 to allow a direct measurement of r₀(z) in this interval; however, in this paper we will concern ourselves only with measurement of $\omega (\theta )$ and its dependence on apparent magnitude and colour.