An accurate method for computer‐generating tungsten anode x‐ray spectra from 30 to 140 kV

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Abstract
A tungsten anode spectral model using interpolating polynomials (TASMIP) was used to compute x‐ray spectra at 1 keV intervals over the range from 30 kV to 140 kV. The TASMIP is not semi‐empirical and uses no physical assumptions regarding x‐ray production, but rather interpolates measured constant potential x‐ray spectra published by Fewell et al. [Handbook of Computed Tomography X‐ray Spectra (U.S. Government Printing Office, Washington, D.C., 1981)]. X‐ray output measurements (mR/mAs measured at 1 m) were made on a calibrated constant potential generator in our laboratory from 50 kV to 124 kV, and with 0–5 mm added aluminum filtration. The Fewell spectra were slightly modified (numerically hardened) and normalized based on the attenuation and output characteristics of a constant potential generator and metal‐insert x‐ray tube in our laboratory. Then, using the modified Fewell spectra of different kVs, the photon fluence Φ at each 1 keV energy bin over energies from 10 keV to 140 keV was characterized using polynomial functions of the form A total of 131 polynomial functions were used to calculate accurate x‐ray spectra, each function requiring between two and four terms. The resulting TASMIP algorithm produced x‐ray spectra that match both the quality and quantity characteristics of the x‐ray system in our laboratory. For photon fluences above 10% of the peak fluence in the spectrum, the average percent difference (and standard deviation) between the modified Fewell spectra and the TASMIP photon fluence was −1.43% (3.8%) for the 50 kV spectrum, −0.89% (1.37%) for the 70 kV spectrum, and for the 80, 90, 100, 110, 120, 130 and 140 kV spectra, the mean differences between spectra were all less than 0.20% and the standard deviations were less than ∼1.1%. The model was also extended to include the effects of generator‐induced kV ripple. Finally, the x‐ray photon fluence in the units of per mR was calculated as a function of HVL, kV, and ripple factor, for various (water‐equivalent) patient thicknesses (0, 10, 20, and 30 cm). These values may be useful for computing the detective quantum efficiency, of x‐ray detector systems. The TASMIP algorithm and ancillary data are made available on line at http://www.aip.org/epaps/epaps.html.