Deconvolution of neutron scattering data: a new computational approach

In this paper we address the problem of reconstructing the scattering function SQ(E) from neutron spectroscopy data which represent a convolution of the former function with an instrument dependent resolution function. It is well known that this kind of deconvolution is an ill-posed problem. Therefore, we apply the Tikhonov regularization technique to get an estimate of SQ(E) from the data. Special features of the neutron spectroscopy data require modifications of the basic procedure, the most important one being a transformation to a non-linear problem. The method is tested by deconvolution of actual data from the IN6 time-of-flight spectrometer (resolution: 90 μeV) and simulated data. As a result the deconvolution is shown to be feasible down to an energy transfer of ≈ 100 μeV for this instrument without recognizable error and down to ≈ 20 μeV with 10% relative error.