Spherical-wave dynamical theory: Ii. Takagi’s theory
This chapter describes Takagi's dynamical theory of the diffraction of incident spherical waves. It considers the crystal wave to be developed as a sum of modulated waves. The fundamental equations are generalized as a set of partial differential equations (Takagi's equations). Their solutions for an incident spherical wave are first obtained by the method of integral equations for both the transmission and reflection geometries. The hyperbolic nature of Takagi's equations is shown and their solution derived using the method of Riemann functions for a point source located on the entrance surface or away from the incident surface. An appendix describes the properties of hyperbolic partial differential equations.
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