A convolution method for constructing primary beam profiles in the presence of beam modifiers

Abstract

Empirical functions that describe primary beam profiles for radiotherapy treatment planning systems generally account for finite source size only on beams unmodified by blocks, wedges, or compensating filters. To incorporate the effects of extended sources on such modified beams and to treat the effect of an extended source consistent with the manner in which the unmodified beam is treated, the unmodified beam profile can be written as a convolution of an unknown source function with a collimator transmission profile. Using Fourier transforms, one can then solve for the source function. This source function is then convolved with a beam tranmission function that has been modified by blocks, wedges, or compensating filters to obtain a primary beam profile. A number of examples are presented that demonstrate the calculations of the effects of beam modifiers on primary beam profiles.