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Many scientific and technological areas associated with industrial process, diagnostic radiation images and radiation therapy demand high levels of accuracy and practicality for the measurement of X-ray energy spectra. The energy spectra of an X-ray beam can be determined either a direct or indirect measurement. Direct measurement uses a high energy resolution detector placed along the direction of the beam. Indirect measurement is based on the transmission curve of the beam and Laplace transforms. For this, i) a complete and exhaustive description of the mathematical derivation of the energy spectrum was carried out; ii) it was used the multistart algorithm along with the lsqnonlin function of MATLAB for the reconstruction of the spectrum; iii) the reconstruction of the spectrum was validated by comparing the half-value layer of the spectrum and the attenuation curve. The results showed that the half-value layer values of the spectrum and the attenuation curve were close to each other and the calculation time of the spectrum was considerably short. Therefore, it is concluded that the indirect determination of the X-ray spectrum from its attenuation curve by means of the novelty usage of the multistart-lsqnonlin synergy is a demonstrably simpler, faster and as effective alternative as the direct spectrum measurement.

Determinación del espectro de energía de un haz de rayos X terapéutico de kilovoltaje a partir de su curva de atenuación