Averaged Intensities in the Many-Beam Dynamical Theory of Electron Diffraction. I. Cases of Nondegenerate Characteristic Values

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Abstract
A many-beam dynamical theory is developed by using a matrix method for a parallel-plate crystal in the Laue case. This formulation gives an expression for the amplitude of any reflected wave in terms of characteristic values of “Anpassung.” The expression is proved to be equivalent to the result obtained by Fujimoto (J. Phys. Soc. Japan 14 (1959) 1558) and Niehrs (Z. Naturforsch. 14a (1959) 504) from Sylvester's theorem in matrix algebra. The averaged intensity is calculated exactly from the expression without solving the equation of the dispersion surface. The theory also makes possible the calculation of the factor appearing in the intensity formula for the Kikuchi pattern from a thick or wedge-shaped crystal.