A problem in rotation therapy with X rays

The radiation field required to produce a dose distribution in rotation therapy may, in a certain approximation, be calculated using an integral equation, that is, the solution of the equation predicts the intensities needed to produce the dose distribution. The nature of this approximation is discussed and is shown to be connected with a Radon-type problem for circles through the origin provided the beam can be continuously modified during the rotation. The lowest order approximation provides a vivid geometrical way of looking at treatment planning which may be useful in novel situations and which will persist, to some extent, in higher-order approximations. Questions of scattering, and of the extension of the problem to a full three dimensional treatment are discussed.