On extinction. I. General formulation

A new formalism of the dynamical diffraction theory is proposed in order to take into account the statistical nature of lattice distortions. It is postulated that the observed intensity is given by an ensemble average of the intensity field derived from the wave equations of Takagi-Taupin type. The formalism leads to exactly the same results as those of the conventional dynamical theory for ideally perfect crystals and the results of the conventional kinematical theory for ideally imperfect crystals. The general relations are established among the integrated diffraction powers for three types of incident wave; namely, a spherical wave (narrow beam), a plane wave and the wave from an incoherent homogeneous source (wide beam). This paper is a preparation for the following one on secondary extinction [Kato, Acta Cryst. (1976) A32, 458-466].