A note on equivalent circles, squares, and rectangles

Abstract

The scatter dose in the center of a circular beam of photons can be represented by a serial expansion, the first term of which is proportional to the radius. If this term only is used in a scatter integration, the expression becomes proportional to the average radius .hivin.r of the field contour, whatever its shape. For a square, the ratio between its side and the average diameter d = 2.hivin.r is s/d = 0.891, the relation between the equivalent circular and square fields for small fields. For rectangles, .hivin.r is given by the area-to-perimeter ratio multiplied by a function that increases slowly with the elongation ratio. The error term resulting from the use of only the linear term to describe scatter remains small under a variety of conditions.