Solution of three dimensional inverse transport problems

A solution is developed for the problem of determining the cross sections of a physical system by irradiating its outer boundary with a known neutron flux, measuring the exiting flux, and then making suitable use of the known incident and exiting boundary fluxes. Our solution requires the use of delta function (pencil beam) incident boundary fluxes, and detectors that are capable of measuring exiting angular fluxes which are weak delta functions of angle (arising from a line source) over an infinitesimal angular interval comprising the support of the delta function. Our approach, which is significantly different from previously published solutions of this problem, is applicable in general geometries with spatial inhomogeneities