Abstract
Lattice fringe spacing measurements have been used as a method of estimating local chemical composition. It is possible that, due to dynamical scattering, the fringe profile is influenced by atomic number difference and changes in specimen thickness and tilt as well as atomic displacements. Even if these other effects are negligible it is especially important to know whether the fringe spacing changes in the image exactly correspond to the lattice plane displacements in the specimen. In most experiments tilted illumination is used and the crystal is set at a Bragg condition for a low order reflection. In a high resolution microscope (Cs≃1.5mm) the transfer function should be sufficiently flat in the region of interest and aberrations can be neglected. Some insight into the nature of lattice fringes can be gained from a two-beam theory. Using the standard notation w = cot B = sξg, where s is the excitation error and ξg the extinction distance, the intensity of the fringes becomes:
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