Looking for the first galaxies: lensing or blank fields?

Context. The identification and study of the first galaxies remains one of the most exciting topics in observational cosmology. The determination of the best possible observing strategies is a very important choice in order to build up a representative sample of spectroscopically confirmed sources at high-z (z greater than or similar to 7), beyond the limits of present-day observations. Aims. This paper is intended to precisely adress the relative efficiency of lensing and blank fields in the identification and study of galaxies at 6 less than or similar to z less than or similar to 12. Methods. The detection efficiency and field-to-field variance are estimated from direct simulations of both blank and lensing fields observations. Present known luminosity functions in the UV are used to determine the expected distribution and properties of distant samples at z greater than or similar to 6 for a variety of survey configurations. Different models for well known lensing clusters are used to simulate in details the magnification and dilution effects on the backgound distant population of galaxies. Results. The presence of a strong-lensing cluster along the line of sight has a dramatic e. ect on the number of observed sources, with a positive magnification bias in typical ground-based shallow surveys (AB less than or similar to 25.5). The positive magnification bias increases with the redshift of sources and decreases with both depth of the survey and the size of the surveyed area. The maximum efficiency is reached for lensing clusters at z similar to 0.1-0.3. Observing blank fields in shallow surveys is particularly inefficient as compared to lensing fields if the UV LF for LBGs is strongly evolving at z greater than or similar to 7. Also in this case, the number of z greater than or similar to 8 sources expected at the typical depth of JWST (AB similar to 28-29) is much higher in lensing than in blank fields (e. g. a factor of similar to 10 for AB less than or similar to 28). All these results have been obtained assuming that number counts derived in clusters are not dominated by sources below the limiting surface brightness of observations, which in turn depends on the reliability of the usual scalings applied to the size of high-z sources. Conclusions. Blank field surveys with a large field of view are needed to prove the bright end of the LF at z greater than or similar to 6-7, whereas lensing clusters are particularly useful for exploring the mid to faint end of the LF.