OPTIMIZATION OF RESOLUTION FUNCTIONS FOR NEUTRON-SCATTERING

We study the relationship between the information content of a neutron scattering experiment and the resolution function of the spectrometer. By deconvolving simulated data, we provide counterexamples to popular approaches to spectrometer optimization which include only the intensity and width of the resolution function. For example, we find that asymmetric functions often yield greater information about the scattering law than symmetric functions with the same intensity and width. More generally, we show that the sharpness of the resolution function, or alternatively the spread of its Fourier spectrum, is the most important factor controlling the reconstruction of the scattering law from data. We provide a simple argument based on average signal-to-noise ratios to suggest that the information content of an experiment is related to the achievable bandwidth of the reconstruction. We propose an analytic expression for a new "figure-of-merit" of a resolution function which agrees qualitatively with our simulations, and which can be used to optimize neutron scattering spectrometers. © 1990.