Deconvolution of neutron scattering data: a new computational approach

Abstract

In this paper we address the problem of reconstructing the scattering function S Q ( 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 S Q ( 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.