During the recent ignition tuning campaign at the National Ignition Facility, layered cryogenic deuterium and tritium capsules were imploded via x-ray driven ablation. The hardened gated x-ray imager diagnostic temporally and spatially resolves the x-ray emission from the core of the capsule implosion at energies above ~8 keV. On multiple implosions, ~200-400 ps after peak compression a spherically expanding radiative shock has been observed. This paper describes the methods used to characterize the radial profile and rate of expansion of the shock induced x-ray emission.