Product representations of teletherapy dose distributions

Product representations are frequently used for teletherapy dose distributions. For example, the dose in a central plane is often written as the product of two factors, one dependent on the depth and the other on the transverse variable. We have answered the following question: given a (two-dimensional) set of data, how closely is it possible to represent these data by a product of two such factors, and what factors would give a best-fit representation? We thus have developed a quantitative test with which to judge any proposed product representation, for a given set of data. As an example, we have applied our method in analyzing the accuracy of a model proposed by van de Geijn for representing central-plane Cobalt-60 dose data through a product representation on decrement lines intersecting the source.