Deconvolution of Doppler-broadened positron annihilation lineshapes by the generalised least-squares method

Deconvolution of the Doppler-broadened annihilation radiation lineshape has been carried out using the generalised least-squares method. The nondashlinear background subtraction is examined through tail stripping and step function fitting procedures. Spurious oscillations of the residual instrumental function are found not to produce an efficient inverse transformation. For this reason least-squares solutions are subjected to a nondashnegativity constraint in order to reduce the oscillations in the deconvoluted spectrum. This procedure improves the results dramatically and shows promise as regards quantitative studies of the local momentum distributions and defect characterisation at various depths of solids in future positron beam experiments.