The physical basis for empirical rules used to determine equivalent fields for phantom scatter

Abstract

Simple empirical rules are widely employed to determine the size of the square radiation field which is equivalent to either a rectangular field or a circular field with respect to phantom scatter. For a rectangular field, the area divided by the perimeter of the rectangle is equated to the area divided by the perimeter of the equivalent square. For circular fields, the area of the circle is sometimes equated to the area of the equivalent square. These empirical rules are very simple and remarkably accurate. They have been in daily use for 30 years, yet there is little discussion in the literature of their fundamental physical basis. An equation is derived for the equivalence of rectangular fields which has the form of the area over perimeter result multiplied by a "correction" factor. This equation is based on fundamental physical principles and it agrees better, within its domain of applicability, with published data than the area over perimeter rule. It is also shown that what appear to be different arbitrary rules for circles and rectangles both emerge from the same underlying physical analysis.