Modeling the output ratio in air for megavoltage photon beams

The output ratio in air, OR, for a high-energy x-ray beam describes how the incident central axis photon fluence varies with collimator setting. For field sizes larger than 3 x 3 cm2, its variation is caused by the scatter of photons in structures in the accelerator head (primarily the flattening filter and the wedge, if one is used) and by the backscatter of radiation into the monitor ionization chamber. The objective of this study was to evaluate the use of an analytical function to parametrize OR for square collimator setting c: OR = (1 + a1.c).[1 + a2.erf(c/lambda)2].H0. For open beams, these parameters can be attributed to explicit physical meanings within the systematical uncertainty of the model: a1 accounts for backscatter into the monitor, a2 is the maximum scatter-to-primary ratio for head-scattered photons, and lambda represents the effective width of the "source" of head-scatter photons. H0 is a constant that sets OR = 1 for c = 10 cm. This formula also fits OR for wedge beams and a Co-60 unit, although the fitting parameters lose their physical interpretations. To calculate the output ratio for a rectangular field, cx x cy, an equivalent square can be used: c = (1 + k).cy x cx/(k.cx + cy), where k is a constant. The study included a number of different accelerators and a cobalt-60 unit. The fits for square fields agreed with measurements with a standard deviation (SD) of less than 0.5%. Using k = lx.(f - ly)/ly.(f - lx), where lx and ly are the source-to-collimator distances and f is the source-to-detector distance, measurements and calculations agreed within a SD of 0.7% for rectangular fields. Sufficient data for the three parameters are presented to suggest constraints that can be used for quality assurance of the measured output ratio in air.