Inhomogeneity corrections in electron-beam dose planning. Limitations with the semi-infinite slab approximation

An investigation was made of the limitations of the semi-infinite slab approximation used in pencil-beam models for electron-beam dose planning. Comparison of measured and calculated dose distributions were made for one-, two- and three-dimensional air inhomogeneities in water. The two- and three-dimensional air cavities were cylindrical with the axis parallel to the incident beam. The radii of the cavities were between 11 and 46 mm and the incident electron energies between 10 and 20 MeV. The measurements were made with a silicon diode. In the calculations the semi-infinite slab approximation was applied to a Gaussian model of the beam and to a generalised Gaussian model. The latter also takes large-angle single scattering into account. By using an absorber in front of the cavity the different fluence contributions to the central axis dose could be measured separately. The result shows that a doubling of the dose may be obtained along the central axis for narrow deep cavities. The dose contribution from the electron transport into the cavity from the cylindrical wall is shown to be underestimated by the semi-infinite slab approximation. This is shown to give large errors especially at depths where the angular distribution of the electrons is large and the electrons have a long drift space in air.