We report on the analysis of the spatial beam profile of high-order harmonic radiation originating from a semi-infinite gas cell (SIGC). We experimentally assign contributions of electron trajectories to different spatial regions of the harmonic radiation beam. The angular divergence of the harmonic radiation is studied for the first time in a SIGC as a function of different phase-matching parameters. We relate the ratio of the dipole phase coefficients to the coherence time and divergence angle measurements. Simulations, including high-order-harmonic propagation, give further insight into the generation process and the influence of phase matching. The analysis reveals that the SIGC enables tuning of the cutoff frequency by altering the absorption of the generating medium. © 2013 American Physical Society.