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Hybrid deconvolution for small-angle inelastic multiple scattering

Based on a method previously reported for retrieval of angle-independent inelastic scattering probabilities from energy loss spectra, a hybrid approach to the inversion problem for angle-resolved spectroscopy is proposed. The energy loss spectrum is expanded into Legendre polynomials with respect to the scattering angle, leading to a set of decoupled matrix equations, each of which determines a generalised Fourier coefficient of the angle-resolved single scattering loss function. This hybrid approach combines the advantage of the matrix formulation (no need to sample a spectrum up to energies where the intensity tends to zero) with the advantage of the Fourier transform for small-angle scattering. By way of example it is shown that the method is feasible for a variety of applications.