An analytical simulator for Compton tomographic measurements

A critical point of several reconstruction and analysis algorithms in x-ray experiments is a fast simulation of the interaction of radiation with matter. This kind of simulations are usually based on Monte Carlo techniques, which follows each particle individual trajectory. Since the maximum number of interactions is a user-definable integer, Monte Carlo simulations allow to obtain an arbitrary precision. However, in several experiments the flux of photons that reach the detector after the interaction in the volume of interest (VOI) is very low, therefore the simulation time may be very large. Simple experiments of x-ray tomography may require several days to obtain a reasonable statistics with the faster Monte Carlo codes. Particularly, in x-y scanning tomography both the detector and the x-ray tube are highly collimated. In such cases, conventional Monte Carlo techniques are inadequate. As a possible alternative, we propose an analytical spectrum generator, which evaluates the detected signal through the differential cross-section for the single interaction with corrections for absorption of the beam (before the interaction point) and of the scattered photon (after the interaction point). It will be shown that the analytical projector proposed in this paper is several order faster than Monte Carlo based simulators. Nevertheless, the signal is evaluated with a precision that is adequate for Compton tomography and for several other experiments that involve x-ray detection. As an example a 60 per 60 pixel matrix, with a 1mm collimation of both the detector and the x-ray generator, is simulated in few minutes, while Monte Carlo based simulations cannot produce a reasonable statistics even after several days. The present work reports some of the results obtained through the analytical projector and compares them with the performances of Monte Carlo based simulations.