Electron spectrum reconstruction as nonlinear programming model using micro-adjusting algorithm

In accurate radiotherapy, the electron spectra should be considered to improve the accuracy of dose calculation, because the electron beams that reach the surface traveling through the collimation system of the accelerator are not monoenergetic. For determinining the energy spectra of Clinical electron beams effectively, the nonlinear programming model and a new inversion algorithm "micro-adjusting algorithm" were studied, by using the measued percent depth dose (PDD). The key issue was how to reconconstruct the energy spectra from an ill-pose integral equation linking with the measured PDD, energy spectra and monoenergetic PDD. The monoenergetic PDD was calculated by bipatition model. And the nonlinear programming model with micro-adjusting algorithm was developed to solve this ill-pose integral equation. Testing samples for a Varian Clinac 1800 medical accelerator that considered and ignored the photon contanmination were both used to test this method. The reconstructed results showed even if including 5% photon contanmination the reconstructed energy spectra still agreed well with the original spectra - error of reconstructed PDD was less than 0.05%, while the one that substracted photon contamination was less than 0.006%. It could be concluded that the method of the nonlinear programming model with the micro-adjusting algorithm was feasible to reconstruct electron energy spectra.