Calculation of the small‐angle distribution of scattered photons in diagnostic radiology using a Monte Carlo collision density estimator

Calculations of various physical quantities pertaining to scattered photons in diagnostic radiology are conveniently carried out using the Monte Carlo technique. Some quantities, e.g., the small-angle distribution of scattered photons transmitted through the patient, are difficult to obtain with sufficient precision using straightforward simulation of physical experiments. By mixing the simulation of random trajectories with analytical calculations, the efficiency of deriving values for a particular field quantity may be drastically improved. This work describes a Monte Carlo collision density estimator that increases the efficiency of calculating the small-angle distribution of transmitted scattered photons by a factor of more than 50. Examples of such distributions outside laterally infinite water slabs are given for x rays generated at 40-70 kV and for various slab thicknesses (10-200 mm). Comparison with experimental results from the literature shows that cross sections for coherent scattering which take diffraction phenomena in liquid water into account must be used to get accurate results. A discrepancy between the experimental and calculated distributions of photons transmitted at very small (less than 3 degrees) angles to the normal to the slab may be interpreted in terms of experimental difficulties or insufficient accuracy in the differential scattering cross sections used in the calculations.