On differentiation of the scattering matrix in dynamical transmission electron diffraction

High-energy transmission electron diffraction from thin crystals under conditions of multiple scattering is considered. An expression is derived for the Jacobian of the scattering-matrix mapping, containing all partial derivatives of the scattering-matrix elements with respect to structure-matrix elements. (This structure matrix describes the scattering crystal and incident-beam direction). These results may be used to determine the regions of convergent-beam electron-diffraction (CBED) patterns which are most sensitive to changes in particular structure-factor amplitudes and phases (due, for example, to the effects of crystal bonding) and to develop more-efficient CBED algorithms based, for example, on a perturbation series in the incident-beam direction. A two-beam example is given.