Equivalent squares for small field dosimetry

Abstract

The use of equivalent squares is of value when determining output and depth dose data for rectangular fields. We have looked at the variation with field shape of head scatter factors (S(c)), phantom scatter factors (S(p)) and tissue phantom ratios (TPRs) using measurements on a 6 MV linac with a Moduleaf mini-multileaf collimator. Measurements were made for fields with dimensions down to 1 cm. A different approach to calculating equivalent squares needs to be made depending on the quantity of interest. For TPRs, good agreement for rectangular fields can be obtained using the well established E = 2XY/(X+Y) formula where E is the equivalent square field size and X and Y are the field dimensions. For S(c) measurements, where a collimator exchange effect is observed, better agreement is obtained using E = (1+A)XY/(AX+Y), where A is an empirically determined constant. For S(p) measurements, E = 2XY/(X+Y) only gives agreement with measurements when the minimum field dimension is at least 2.5 cm. For smaller fields, the equivalent square overestimates S(p), with the difference being strongly related to the value of the smaller dimension. We propose an empirical formula, based on the size of the smaller dimension.