Spherical Wave Theory of Moiré Fringes Produced under Conditions of Borrmann Transmission by Two Crystals Separated by a Gap

Abstract

The spherical wave theory of Kato is applied to calculate the intensity field in the moire fringe pattern produced by two perfectly aligned simultaneously reflecting crystals separated by a gap when only anomalously transmitted waves need be taken into account. Under practical experimental conditions the incident wavefront curvature adds significantly to the phase difference between interfering waves. This contribution, together with a previously omitted term involving the ratio of gap width to sum of the crystal thicknesses, should be added to the argument of the trigonometric interference term used by previous workers in deriving structure factors from gap-fringe spacings. Expressed directly in terms of a change in the 220 structure factor, use of our revised interference term would reduce Hart and Milne's measured value for silicon by ½% and Baker, Hart and Helliar's measured value for germanium by 1.3%.