Mathematical estimation of half-value layer thicknesses

The objective of this article is to introduce a simplified and swift method to satisfactorily estimate the half-value layers (HVL), quarter-value layer (QVL), and tenth-value layer (TVL) from the x-ray spectra emitted by any diagnostic radiology or kV radiotherapy x-ray tubes.

A CdTe x-ray and Gamma detector (X-123 CdTe, AmpTek Inc.) is used to measure the x-ray spectra at four different x-ray energies (low, mid, high energy x-rays) with different external filtering. The software "SpekCalc GUI" (Developed in McGill University, Montreal, Canada) is also used to obtain the simulated x-ray spectra. Both measured and simulated spectra are used to compute the HVL thicknesses of Aluminum by a mathematical method presented in this article. Next, the HVL thicknesses for corresponding tube potentials are also measured by calibrated ionization chamber and varying thicknesses of aluminum plates. Finally, the computed and measured HVL, QVL, and TVL thicknesses are compared to evaluate the efficacy of the presented method.

The results show acceptable concordance between computed and measured quantities. The disagreement rates between measured HVL and the values derived mathematically from the x-ray spectra are 10 to 90 micrometers of Aluminum at tube potentials of 31 kV to 120 kV. As it is shown, a negligible discrepancy is observed between the analytical estimation and the experimental assessments.

The HVL is an essential component in the evaluation of the quality of an x-ray beam. However, its measurement could occasionally be challenging, time-consuming, or uncertain due to some technical difficulties. Although the scope of this study is not to undermine the value of conventional and widely accepted practice to determine the HVL thickness, the introduced method provides the fast, more convenient, and comparably reliable technique to estimate the HVL, QVL, and TVL by employing the given x-ray spectrum.