Role of scattering-factor anisotropy in electron, positron, and photon holography

We have studied the angular anisotropy in the scattering factor of electrons, positrons, and photons in solids. We show that as a function of angle, the maximum number of dips in the scattering factor close-quote s magnitude and jumps of near π in its phase are related to the angular momenta of the bound and resonance states of the potential. The effect of the scattering factor close-quote s anisotropy on low-energy electron and positron holographic wave-front reconstruction is discussed. Applying the variable-axis small-cone method, a good-quality reconstructed image is only possible within angular regions where the scattering factor is near isotropic. Thus the usable window for low-energy electron wave-front reconstruction is element dependent; the window size decreases as the atomic number increases. Positrons, on the other hand, are like photons and are not bound by the potential. For positrons or photons, there is no elemental dependence of the usable window and the entire backscattering regime is suitable for holographic reconstruction. We have established two rules that predict the maximum number of magnitude dips and phase jumps in the scattering factor for any element. copyright 1998 The American Physical Society