Noniterative unfolding algorithm for neutron spectrum measurements with Bonner spheres

The use of detectors moderated by Bonner spheres of different diameters is a relatively easy and inexpensive method of measuring the energy spectrum of neutron emission sources. Because the number of counts for each sphere diameter can be obtained by integration of the spectrum multiplied by a two-dimensional kernel, the spectrum is obtained from measurement data by means of a deconvolution or "unfolding" algorithm. Algorithms capable of solving this ill-posed "inverse" problem are based on iteration, requiring an initial spectrum estimate, extensive computation, and considerable experience on the part of the user. This paper presents a noniterative algorithm based on spectrum models with undetermined parameters. It computes the set of parameters that minimizes the error between the actual Bonner counts measured and those predicted by integration of the resulting spectrum. Examples based on ideal data show that to avoid large spectrum errors caused by small measurement errors, the number of parameters involved must be small, much less than the number of sphere diameters employed. This restriction limits resolution in the spectrum, but the limitation is believed to be inherent in the physical characteristics of the Bonner system, not a defect of the algorithm. The method appears effective, fast, and easy to use.