Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

Abstract

We present mathematical methods of computerized tomography, based on an analytical inversion of the Radon transform either in terms of the Fourier transforms or series of orthogonal polynomials. These techniques, so-called transform methods, are discussed for reconstructing electronic densities from both line and plane projections measured either in the two-dimensional angular correlations of annihilation radiation or in onedimensional angular correlations of annihilation radiation and the Compton scattering experiments. This paper is devoted to review all of the papers where such techniques were applied for studying electronic momentum densities and the Fermi surface of solids by angular correlations of annihilation radiation and the Compton scattering experiments.

Fermiology via the electron momentum distribution (Review Article)

“…Transform methods consist in the analytical inversion of the Radon transform. These methods, applied to the image reconstruction of momentum densities from 1D and 2D projections, shortly described in Chapter 3, are presented in the paper [13] with references of their applications to study electron (or e-p) momentum densities.…”