Three-Dimensional Image Reconstruction with Application in Positron Annihilation

Abstract

Some remarks are made on Cormack's method and on the possibility of its application to two‐dimensional angular correlation of positron annihilation radiation data. The fulfilment of the consistency condition is studied on the example of the experimental data. It is shown that this condition, imposed on the experimental data, improves them making additional advantage of Cormack's method. Some remarks concerning a way of practical using this method are given. Test reconstructions for two anisotropic models and for positron annihilation data are presented. It is demonstrated that even strongly anisotropic model densities can be reproduced from a small number of their linear projections.

Elliptical hole pockets in the Fermi surfaces of unhydrated and hydrated sodium cobalt oxides

“…24,25 For each Compton profile, ϳ600 000 counts in the peak data channel were accumulated, and each Compton profile was corrected for possible multiple-scattering contributions. A twodimensional momentum density, representing a projection down the c axis of the full three-dimensional density, was reconstructed from each set of five profiles using tomographic techniques 26 and then folded back into the first BZ using the Lock-Crisp-West procedure 27,28 to obtain the occupation density from which the occupied parts of the BZ could be inferred. The occupation density is shown for each composition in Fig.…”

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

“…It was generally supposed that Fourier transform methods need a knowledge of many projections [44][45][46][47][48][49], whereas, as shown in the paper [12], the CM allows to reconstruct ρ(p) basing on a small number of measured spectra. It was explained in the paper [50] where we showed that the necessity of integration with a small ∆ϕ (Eq.…”

“…Cormack's method (CM), adopted for symmetry systems [12], has been applied many times for reconstructing electron-positron momentum densities from 2D ACAR data [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] as well as for reconstructing line dimensions of the Fermi surface from Compton scattering profiles (i.e. conversion: from 1D to 2D) [29][30][31][32].…”

Methods of Extracting Electron-Positron Enhancement Factors from Experimental ACAR Data

“…Socalled "consistency condition" for 2D data was discussed in Ref. [11] where it was shown that this condition suppresses the noise in the data.…”