Quality control of measured x-ray beam data

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Abstract
The purpose of this study was to examine whether the quality of measured x-ray beam data can be judged from how well the data agree with a semiempirical formula. Tissue-phantom ratios (TPR) and output factors for several accelerators in the energy range 4-25 MV were fitted to the formula, separating the dose contributions from primary and phantom-scattered photons. The former was described by exponential attenuation in water, with beam hardening, and the latter by the scatter-to-primary dose ratio using two parameters related to the probability and the directional distribution of the scattered photons. Electron disequilibrium was not considered. Two approaches were evaluated. In one, the attenuation and hardening coefficients were determined from measurements in a narrow-beam geometry; in the other, they were extracted by the fitting procedure. Measured and fitted data agreed within +/- 2% in both cases. The differences were randomly distributed and had a standard deviation of typically 0.7%. Singular points with errors were easily identified. Systematic errors were revealed by increased standard deviation. However, when the attenuation was derived by the fitting algorithm, the attenuation coefficient deviated significantly from the experimental value. It is concluded that the semiempirical formula can serve to evaluate and verify beam data measured in water and that the physically most accurate description requires that the attenuation and hardening coefficients be determined in a narrow-beam geometry. The attenuation coefficient is an excellent measure of both the primary and the scatter dose component, i.e., of beam quality.