  Scattered neutron spectroscopy is a diagnostic technique commonly used to
measure areal density in ICF experiments. Deleterious areal density asymmetries
modify the shape of the scattered neutron spectrum. In this work a novel
analysis is developed which can be used to fit the shape change. This allows
scattered neutron spectroscopy to directly infer the amplitude and mode of the
areal density asymmetries, with little sensitivity to confounding factors which
affect other diagnostics for areal density. The model is tested on spectra
produced by a neutron transport calculation with both isotropic and anisotropic
primary fusion neutron sources. Multiple lines of sight are required to infer
the areal density distribution over the whole sphere -- we investigate the
error propagation and optimal detector arrangement associated with this
inference.
