A method for calculating the intensities of transmitted and diffracted waves at the bottom plane of a crystalline specimen when the incident electron beam interacts with the specimen. In the "Bethe's method," the energy of the electron wave is given, and the states of the electron waves (wave number vectors) allowed in the crystal are obtained by the Schroedinger equation, and finally the amplitudes of transmitted and diffracted waves at the exit plane are obtained by connecting these waves to the incident electron wave using the boundary condition. In this method, multiple scattering (dynamical diffraction) is taken into account. Since the equation to obtain the wave vectors takes the form of a matrix, the method is termed the matrix method or the eigenvalue method.
"Fermat's principle" states that light (electron beam) travels through a path whose optical path length is shortest (extremum). This principle gives the basics for discussing optics and electron optics. The law of reflection and the law of refraction are derived from the principle.
"Friedel's law" states that the intensities of the hkl reflection and the -h-k-l reflection are equal even for polar crystals. This law holds for X-ray diffraction to which kinematical diffraction can be applied; however does not hold for electron diffraction where the dynamical diffraction effect is strong. This fact implies that X-ray diffraction cannot distinguish polar and non-polar crystals unless anomalous dispersion is utilized, but electron diffraction can.
The Green's function, G(r, r'), provides a response at point r from a point scatterer located at r'. The Green's function in the case of the dynamical theory of electron diffraction is (-1/4π)･exp (i k|r - r'|)/|r - r'|.
The contrast of a high-resolution (HREM) image is lower than that expected from image simulation. "Stobb's factor" is used to adjust the simulated contrast to agree with the experimental contrast. The superposition of the background intensity due to thermal diffuse scattering (TDS) is considered to decrease the contrast of HREM images formed by elastic scattering.
Phase contrast from an amorphous specimen (granular structure) remarkably changes with the defocus amount. "Thon's curve" expresses how the spatial frequency (emphasized spacings), in which the phase of the waves are matched, changes with the defocus amount.