The dose response functions of ionization chambers in photon dosimetry - Gaussian or non-Gaussian?

This study is concerned with the spatial resolution of air-filled ionization chambers in photon-beam dosimetry, i.e. with their dose response functions. These act as convolution kernels K(x,y), transforming true dose profiles D(x,y) into the measured signal profiles M(x,y). One-dimensional dose response functions have been experimentally determined for nine types of cylindrical ionization chambers both in their lateral and longitudinal directions, as well as across two plane-parallel chambers and for the single chambers of two 2D arrays. All these 1D dose response functions are closely described by Gaussian functions. The associated energy-dependent values of the standard deviations σ have been measured for 6 and 15 MV photons with an uncertainty of 0.02mm. At depths beyond secondary electron fluence build-up, there was no detectable depth dependence of the σ values. The general occurrence of Gaussian dose response functions, their extension beyond the geometrical boundaries of the chambers, and the energy dependence of their standard deviations can be understood by considering the underlying system of convolutions, which is the origin of the influences of secondary electron transport. Monte-Carlo simulations of the convolution kernels for a cylindrical, a square, and a flat ionization chamber and their Fourier analysis have been employed to show that the Gaussian convolution kernels are approximations to the true dose response functions, valid in the clinically relevant domain of the spatial frequency. This paper is conceived as the starting point for the deconvolution methods to be described in a further publication.