Calculation of x-ray spectra emerging from an x-ray tube. Part II. X-ray production and filtration in x-ray targets.

A new approach to the calculation of the x-ray spectrum emerging from an x-ray tube is proposed. Theoretical results for the bremsstrahlung cross section appearing in the literature are summarized. Four different treatments of electron penetration, based on the work presented in Part I, are then used to generate bremsstrahlung spectra. These spectra are compared to experimental data at 50, 80 and 100 kVp tube potentials. The most sophisticated treatment of electron penetration was required to obtain good agreement. With this treatment both the National Institute of Standards and Technology bremsstrahlung cross sections, based on accurate partial wave calculations, and the Bethe-Heitler cross section [H. A. Bethe and W. Heitler, Proc R. Soc. London, Ser. A. 146, 83-112 (1934)] corrected by a modified Elwert factor [G. Elwert, Ann. Phys. (Leipzig) 426, 178-208 (1939)], provided good agreement to measured data. An approximate treatment of the characteristic spectrum is suggested. The dependencies of the bremsstrahlung and characteristic outputs of an x-ray tube on tube potential are compared to experimentally derived data for 70-140 kVp potentials. Agreement is to within a few percent of the total output over the entire range. The spectral predictions of the semiempirical models of Birch and Marshall [R. Birch and M. Marshall, Phys. Med. Biol. 24, 505-513 (1979)] (IPEM Report 78) and of Tucker et al. [D. M. Tucker, G. T. Barnes, and D. P. Chakraborty, Med. Phys. 18, 211-218 (1991).] are also assessed. The predictions of Tucker et al. are very close to the model developed here. The predictions of IPEM Report 78 are similar, but consistently harder for the range of tube potentials examined (50-100 kV). Unlike the semiempirical models, the model proposed here requires the introduction of no empirical and unphysical parameters in the differential bremsstrahlung cross section, bar an overall normalization factor which is close to unity.