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A new dosimetric quantity, the lateral build-up ratio (LBR), has been introduced to calculate depth dose distribution for any shaped field. Factors to account for change in incident fluence with collimation are applied separately. The LBR data for a small circular field are used to extract radial spread of the pencil beam, sigma(r), as a function of depth and energy. By using the relationship between LBR, sigma(r), energy and depth, a formalism is developed to calculate dose per monitor unit for any shaped field. Criteria for lateral scatter equilibrium are also developed which are useful in clinical dosimetry.

The Fermi-Eyges theory of electron scattering overestimates the scattering of electron beams used in radiation therapy. The reason for this overestimate is the neglect of the loss of electrons which are scattered into highly oblique paths and removed from the beam at relatively shallow depths. A modification of Eyges' solution to Fermi's equation is presented to take this loss of electrons into account. Equations for the calculation of isodose distributions for any medium using pencil beams are developed. Experimental confirmation is presented for electron beams of 13 and 18 MeV in homogeneous water, polystyrene, Lucite, and aluminum phantoms.

Central axis electron beam depth dose distributions can be transformed by replacing dose by fluence and depth by a measure of angular dispersion. This transformation was applied to a set of broad beam central axis depth dose distributions calculated by Monte Carlo code for beams with initial energies ranging from 1 to 60 MeV in homogeneous media of water, aluminum, and copper. The resulting fluence distributions belong to a family of curves that can be parametrized by a single-valued function of initial beam energy and medium and can be used to calculate fluence distributions for accelerators. Fluence curves can be easily transformed to depth dose curves.

Uneven air gaps, beam obliquity, or sloping contours create complex dosimetry problems in electron beam treatment planning. We find that the depth dose distribution in an obliquely incident beam can be calculated from the data for a normally incident beam by using inverse square law and obliquity factors. The obliquity factors have been determined for various energy beams in the range of 6-22 MeV and can be used for manual treatment planning.

Using a 13 MeV electron beam as an example, transmission curves for various thicknesses of lead were measured. The data indicated that the choice of shielding thickness depends greatly on the depth at which the measurements are made. The importance of this reference depth and criteria for shield design when shields of minimum thickness are required is discussed.