Notes on the Transformation from Sphere to Plane Isotropic Source

The conditions are examined under which a well-known relation can be stated between the dose from a spherical source and that from a plane isotropic source whose intensity is the same as the emission from the sphere in the radial direction . On the basis of a homogeneous core and surrounding medium, a mathematical justification is given of the usual physical argument for this relation where the core is "opaque". The case of purely radial emission is discussed as an example in which the relation does not hold. To examine the transition from isotropic to radial emission, correction factors for two types of anisotropic distributions are discussed. It is shown how in principle the correction factor for any given angular distribution can be simply obtained by expanding in Legendre polynomials. It is also suggested that in certain cases total leakage may be a more useful measure of source strength than the radial leakage. Finally, the method of calculating the dose at great distances by using the angular distribution of particles emitted from the core is illustrated with a uniform spherical volume source.