Technical note: Generation of a Cerenkov scatter function convolution kernel for a primary proton beam

To generate a Cerenkov scatter function (CSF) for a primary proton beam and to study the dependence of the CSF on the irradiated medium.

The MCNP 6.2 code was used to generate the CSF. The CSF was calculated for light-pigmented, medium-pigmented, and dark-pigmented stratified skin, as well as for a homogeneous optical phantom, which mimics the optical properties of human tissue. CSFs were generated by binning all of the Cerenkov photons which escape the back end (end opposite beam incidence) of a 20 × 20 × 20 cm phantom. A 4 × 4 cm, 500 × 500 bin grid was used to create a histogram of the Cerenkov photon flux on the simulated medium's back surface (surface opposite beam incidence). A triple Gaussian was then used to fit the data.

From the triple Gaussian fit, the coefficients of the CSF for the four phantom materials was generated. The individual CSF fit coefficient errors, with respect to the Gaussian representation, were found to be between 0.92% and 4.11%. The R² value for the fit was calculated to be 0.99. The phantom material was found to have a significant effect (63% difference between materials) on the CSF amplitude and full width at half maximum (195% difference between materials). The difference in these parameters for the three skin pigments was found to be small.

The CSF was obtained for a proton beam using the MCNP 6.2 code for a phantom constructed of light, medium, and dark stratified human skin, as well as for an optical phantom. The CSFs were then fit with a triple-Gaussian function. The coefficients can be used to generate a radially symmetric CSF, which can then be used to deconvolve a measured Cerenkov image to obtain the dose distribution.