A semiempirical method to characterize the pencil-beam dose kernel is presented. Results from measurements are described by mathematical models of the applicable physical processes. The measurements were made with 6 and 25 MV x-ray beams from a linear accelerator. Broad-beam notations were used consistently, and the pencil-beam quantities were obtained by differentiation. The results were compared to pencil-beam kernels calculated by Monte Carlo techniques. The analysis of the measured data included a number of approximations. It was assumed that all the constituent pencil beams in the field are parallel, i.e., the divergence is ignored. Furthermore, the lateral variations of the incident photon fluence and the energy spectrum were disregarded. Monte Carlo calculations, on the other hand, are based on an average energy spectrum over the field, and are free from divergence and variations in the incident photon fluence. Measured and Monte Carlo calculated pencil beams nevertheless agreed well, and the approximations mentioned caused at maximum 2.7% discrepancies for the largest field size at 6 MV.
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