Exact analytical solution of the convolution integral equation for a general profile fitting function and Gaussian detector kernel

One of the most important aspects in the metrology of radiation fields is the problem of the measurement of dose profiles in regions where the dose gradient is large. In such zones, the 'detector size effect' may produce experimental measurements that do not correspond to reality. Mathematically it can be proved, under some general assumptions or spatial linearity, that the disturbance induced in the measurement by the effect of the finite size of the detector is equal to the convolution of the real profile with a representative kernel of the detector. In this work the exact relation between the measured profile and the real profile is shown, through the analytical resolution of the integral equation for a general type of profile fitting function using Gaussian convolution kernels.