The far-field spatial distributions of high-order harmonics in an ionized medium have been investigated using a computer model that includes both the single atom effects and the collective effects of the medium. The results show that depletion of the non-linear medium due to ionization and radial phase variations across the gas jet cause broadening and complicated structures in the far-field spatial distributions. These phase variations are due to three factors: focusing, ionization, i.e. depletion of the non-linear medium and electron dispersion, and intensity-dependent phase variations of the atomic dipoles.