The VLA-COSMOS Large Project has imaged the 2 sq.deg. COSMOS field with a
resolution of 1.5 arcsec and a sensitivity of about 11 microJy (1 sigma)
yielding to a catalog of about 3600 radio sources. In this paper we present a
further analysis of the VLA-COSMOS Large Project catalog of radio sources aimed
to: 1) quantify and correct for the effect of bandwidth smearing in the
catalog, 2) determine the incompleteness produced by the noise bias and the
resolution bias in the new catalog and 3) derive the radio source counts at 1.4
GHz. The effect of bandwidth smearing on the radio sources in the catalog was
quantified comparing the peak and total flux densities in the final mosaic and
in each of the individual pointings where the source was closest to the center
of the field. We find that the peak flux densities in the original VLA-COSMOS
Large Project catalog have to be divided by a factor about 0.8 or 0.9,
depending on the distance from the mosaic center. The completeness of the radio
catalog has been tested using samples of simulated radio sources with different
angular size distributions. These simulated sources have been added to the
radio image and recovered using the same techniques used to produce the radio
catalog. The fraction of missed sources as a function of the total flux density
is a direct measure of the incompleteness. Finally, we derived the radio source
counts down to 60 microJy with unprecedented good statistics. Comparison to the
findings of other surveys shows good agreement in the flux density range 0.06-1
mJy confirming the upturn at about 0.5 mJy and a possible decline of the source
counts below about 0.1 mJy.Comment: 23 pages, 6 figure. Accepted for publication in Astrophysical Journa