The effects of divergence and nonuniformity on the x-ray pencil-beam dose kernel

The scattered-photon part of pencil-beam dose kernels for high-energy x-ray beams can be derived experimentally by differentiating the broad-beam scatter-to-primary dose ratio as a function of radius. Formally, this requires a uniform and parallel beam, and the procedure is complicated by the nonideal, actual beam conditions: the primary dose profile is not uniform, the beam quality is not constant, and the distance to the source is not infinite. The experimentally determined scatter-to-primary ratios can be corrected for these effects before they are differentiated to give the pencil-beam kernels. The correction factors were calculated and shown to reach as much as 5% of the true scatter-to-primary ratio. The effect on the pencil beam was evaluated and corrected pencil beams were determined.