Diffraction pattern from thermal neutron incoherent elastic scattering and the holographic reconstruction of the coherent scattering length distribution

The diffraction of spherical waves (S waves) interacting with a periodic scattering length distribution produces characteristic intensity patterns known as Kossel and Kikuchi lines (collectively called K lines). The K-line signal can be inverted to give the three-dimensional structure of the coherent scattering length distribution surrounding the source of S waves-a process known as "Gabor holography" or, simply, "holography." This paper outlines a kinematical formulation for the diffraction pattern of monochromatic plane waves scattering from a mixed incoherent and coherent S-wave scattering length distribution. The formulation demonstrates that the diffraction pattern of plane waves incident on a sample with a uniformly random distribution of incoherent scatterers is the same as that from a sample with a single incoherent scatterer per unit cell. In practice, one can therefore reconstruct the holographic data from samples with numerous incoherent S-wave scatterers per unit cell. Thus atomic resolution thermal neutron holography is possible for materials naturally rich in incoherent thermal neutron scatterers, such as hydrogen (e.g., biological and polymeric materials). Additionally, holographic inversions from single-wavelength data have suffered from the so-called conjugate or twin-image problem. The formulation presented for holographic inversion-different from those used previously [e.g., T. Gog et al., Phys. Rev. Lett. 76, 3132 (1996)]-eliminates the twin-image problem for single-wavelength data.