Determination of the Energy Spectra of Clinical X-Ray Beams Using Dose-Depth Datasets
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A method to determine the energy spectra of clinical x-ray beams based on dose-depth datasets measured in the absorber of known composition and thicknesses was developed, implemented by a computer and tested. An iterative perturbation method, originally proposed by Waggener, was implemented with some modification. The energy spectrum estimated by the iterative perturbation method often contains unrealistic spectral features, i.e. peaks and valleys, the number of which being proportional to the number of energy bins considered in the calculation. A method of smoothing the estimated energy spectra of x-ray beams, by means of polynomials of lowest possible degrees to eliminate the nonphysical features in the spectrum, was developed. The estimated energy spectra of x-ray beams after smoothing with polynomials were found to meet all the physical criteria of spectral shapes of therapeutic x-ray beams. Additionally, the use of polynomial t was found to yield the energy spectrum of an intense x-ray beam in terms of a single continuous function containing only a few parameters. The energy spectra of therapeutic x-ray beams with nominal energies of 6, 10, and 18 MVp, produced by Elekta's Versa-HD linear accelerator (linac), were estimated. Additionally, the energy spectra of lter-free x-ray beams with nominal energies of 6 MVp and 10 MVp produced by the same linac were also estimated. Two sets of dose-depth data were measured in each x-ray beam, one with aluminum and the other with copper absorbers of varying thicknesses. Measurements were obtained from an experimental setup designed to minimize the secondary x-rays that reach the detector by means of two collimators of appropriate dimensions. The dose-depth datasets measured with aluminum were used to estimate the energy spectra of x-ray beams whereas the datasets measured with copper were used to validate the estimated spectra. The estimated spectra were found to produce dose-depth datasets that matched corresponding measured dose-depth datasets within 0.1 to 2.5%.
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