Irregular field calculation on the central beam axis of photon beams using sector-integration

A method is proposed for calculation of irregular field factors on the central beam axis and homogeneous medium for x-ray beams. The irregular field factor is introduced as the ratio of the output of a field with and without blocks on the central beam axis. The algorithm is based on the sector-integration method and the circular field quantities are calculated from in-phantom measurements. These circular field quantities are the output per beam monitor unit for circular fields defined by a hypothetical secondary collimator and reduced to a circular field by blocking. A derivation of the sector-integration equation is given from first principles. As it is shown, the circular field quantities are evaluated from data measured for rectangular, block shaped fields. Such quantities contain all beam components, including photons scattered from the blocks, the block tray, and photons scattered in the phantom. Consequently, the so called primary and secondary beam components are readily incorporated in this approach. Once the circular field quantities have been determined from rectangular field data, the irregular field factors for other geometry can be calculated. Irregular field factors for square, rectangular and circular block-shaped fields were calculated for 6 MV photon beams and compared with measured values. The results agree within 0.7%, even for heavy blocked field cases, i.e., a 40 x 40 cm2 collimator field blocked to a 5 x 5 cm2 field. The method was tested for a particular source to surface distance, depth, phantom composition, and source to block distance. Calculation of irregular field factors in another set up conditions requires the measurement of the appropriate input data.