Equivalent squares of irregular photon fields

The tables of equivalent fields published by the British Journal of Radiology (BJR) are intended for calculation of depth-dose functions in rectangular photon fields. We have investigated the validity of the equivalent-field concept for fields of arbitrary shape over a range of photon energies, field sizes and depths. We show that the empirical scatter-radius function (Day function) used to generate the equivalent-field tables is a good approximation to the average over energy of normalized scatter-air ratios extracted from BJR beam data for depths up to 10 cm. However, this function tends to diverge from the data as depth increases. Accuracy can be improved by making the Day function depend on depth. Equivalent squares, determined by sector integration of the original or modified Day functions, are suitable for megavoltage photon-beam dose calculations at central-axis and off-axis points in irregular as well as rectangular fields.