Spherical-wave theory of the zero-absorption LLL X-ray or neutron interferometer

Amplitude and intensity distributions within the outgoing beams of the triple-Laue-case (LLL) interferometer have been calculated for the case of zero absorption, which in practice is predominantly encountered with thermal neutrons. The type-1 wavefield with antinodes on the atomic sites, which with X-rays is quite frequently anomalously attenuated in the lattice, is here fully taken into account together with the type-2 wavefield of anomalous low absorption. After the combined diffraction by beam splitter, mirror, and analyser crystal of the interferometer for an incident plane wave has been solved, the solution for an incident spherical wave is developed by Fourier expansion, by a similar method to that first given by Kato [Acta Cryst. (1961), 14, 526-532] for just one diffracting crystal plate. In order to optimize the interferometer geometry spatial intensity profiles as functions of the geometric dimensions of the interferometer and of the phase shift between the interfering beams are calculated. The influence of deviations from the ideal geometry is investigated. Deviations of the order of the extinction length can result in a drastic reduction of interference contrast. Very good energy-converging and contrast properties are found if tM = 2t_S= 2t_A where t_M, t_S, t_A are the thicknesses of mirror, beam splitter, and analyser respectively. The calculated intensity profiles are in agreement with preliminary experimental profiles obtained recently with a silicon interferometer at the HFR in Grenoble.