A geometric calculation of square and circular size equivalents for rectangular radiation fields in radiotherapy

In radiotherapy the volume of irradiated tissue is determined by the cross-section of a beam of radiation that strikes the skin of a patient. The radiation dose delivered at a given depth is a function of this cross-section, known as the radiation field. The computing of that dose for rectangular fields can be simplified using a small number of data corresponding to square or circular fields. This procedure is called the equivalent field method. Two fields are said to be equivalent if they give equal doses of radiation at a given depth in tissue. In this work the equivalent circular and square fields are determined by the condition that the solid angle subtended by the field in the skin, as viewed from the exposed point, be the same.