A deep multicolor survey. VI. Near-infrared observations, selection effects, and number counts

I present near-infrared J (1.25 mum), H (1.65 mum), and K (2.2 mum) imaging observations of 185 arcmin(2) in 21 high galactic latitude fields. These observations reach limiting magnitudes of J similar to 21, H similar to 20, and K similar to 18.5 mag. The detection efficiency, photometric accuracy, and selection biases as a function of integrated object brightness, size, and profile shape are quantified in detail. I evaluate several popular methods for measuring the integrated light of faint galaxies and show that only aperture magnitudes provide an unbiased measure of the integrated light that is independent of apparent magnitude. These J, H, and K counts and near-infrared colors are in best agreement with passive galaxy formation models with at most a small amount of merging (for Omega (M) = 0.3 and Omega (Lambda) = 0.7).