The calculation of transmission through a photon beam attenuator using sector integration

A calculational scheme is presented for the prediction of the transmitted fraction (TR) through an attenuator of known material and physical dimensions, at any point in a photon beam, for a beam of any shape or size. The method considers the total TR to be composed of scatter and primary components and computes the scatter component by sector integration. The input for the calculations consists of measured narrow- and broad-beam transmitted fractions through lead in air for various circular fields, thicknesses of the attenuator, and angles from the central axis, in a geometry approximating typical treatment conditions. The method has been tested for the case of a uniform half slab and a 45 degree wedge in a 4-MV photon beam. It was found that the use of TR values obtained by the above method reduced the maximum absorbed dose computation error from 8% computed with a commercially available algorithm to 3%, in a typical treatment setup. This method is generally applicable to any shaped attenuator such as a wedge or compensator covering whole or part of a radiation field.