A FOUNDATION FOR THE STATISTICAL DYNAMIC THEORY OF DIFFRACTION

The statistical dynamical theory [Kato (1980). Acta Cryst. A36, 763-769] is reformulated on a sounder basis. The starting wave equation is free from the so-called Takagi-Taupin (T-T) approximation. Functional calculus, an operational technique and the concept of the Green function are used as mathematical tools. Integro-differential equations are derived for the coherent (averaged) wave field and the energy flow vector of the incoherent intensity field. The formulae are exact except for assuming a model in which the fluctuation of the lattice phase is a set of Gaussian random variables defined in three-dimensional space. The general framework of the previous theory is justified within the T-T approximation. In general, however, new terms must be added and some terms have to be revised by introducing a Green function matrix. The theory may be used as a starting point when any approximate theory is developed for practical purposes.