X‐ray spectrum unfolding using a regularized truncated SVD method

New procedures to characterize the x‐ray primary beam, obtaining an accurate assessment of the actual photon spectrum, are needed for quality control of x‐ray tubes for medical purposes. The Compton scattering technique is very useful for determining x‐ray spectra (in the 10–150 kV_p range), avoiding the pile‐up effect in the detector, since usually there is insufficient space available to apply other techniques. The Compton scattering procedure was simulated using the Monte Carlo method by means of the MCNP code. In order to validate the simulation model, experimental measurements were made at the Centro Nacional de Dosimetría (CND), Valencia, Spain, using a calibrated x‐ray tube. Different spectra were measured varying the operational parameters (kV, mA, Al). Furthermore, CND provided the theoretical spectra corresponding to the x‐ray measurement conditions. Using the developed model, a response matrix was obtained by simulating the interactions of different monoenergetic beams. During the construction of the primary photon spectrum it is necessary to calculate the inverse of the response matrix. Because this matrix is ill‐conditioned, its inversion is not a simple process. This problem was solved using a truncated singular value decomposition (TSVD), method together with variational regularization. The performance of the methodology was tested with experimental and simulated x‐ray spectra. Copyright © 2005 John Wiley & Sons, Ltd.