NONLINEAR HOLOGRAPHIC CRYSTALLOGRAPHY

We point out the limitations of linear computer reconstruction algorithms employed previously in holographic crystallography. We show that many of the undesirable artifacts on prior holographic reconstruction of atom positions from point-source diffraction patterns may be traced directly to the nonlinear object-wave terms neglected in traditional holography. This problem is particularly severe in the so-called forward-scattering geometry, represented by, e.g., a subsurface B-atom emitter in the Si(111)-3 × 3 B surface. We show that, even in this case, unlike the prior linear schemes, the nonlinear algorithm ''atomic-position recovery by iterative optimization of reconstructed intensities'' is capable of recovering a very accurate, artifact-free and twin-image-free, three-dimensional reconstruction of the positions of nearby scattering atoms even for a single diffraction pattern. © 1994 The American Physical Society.