Photon output factor calculation from the inverse of the sector-integration equation

A method to predict rectangular field output factors (OFs) of photon open beams for the Saturne 41 linear accelerator has been developed. The procedure is similar to the sector-integration method but the radiotherapy quantities corresponding to circular fields (circular functions) are calculated from one-dimensional OFs. In this case the one-dimensional OFs are defined as rectangular field OFs, where one side remains constant and equal to the maximum field size. The circular quantities are numerically obtained by inversion of the sector-integration equation which relates both the one-dimensional OFs and the circular function. Two one-dimensional OFs were used to take into account the asymmetry between the x and y collimator systems (collimator exchange effect). The resulting pair of circular functions corresponds to the x and y collimator systems, respectively. They contain all the information relative to head, air, and medium (phantom) scatter and, consequently, there is no need to account for the geometry of the head or fitting parameters. Using the sector-integration method, the OFs for any rectangular field can be calculated by integrating the obtained circular functions. To improve results, a procedure is given to account for corner collimators overlapping. Results agree with data to within approximately 0.4% at 6-15 MV photon beams. The proposed method is thus clinically acceptable for routine calculation. Furthermore, the circular function calculation algorithm could be extended to other radiotherapy quantities.