Multislice formula for inclined illumination

A multislice formula for many-beam calculation of dynamical electron diffraction amplitudes which may be applied for inclined illumination has been derived based on the Schrödinger equation. This formula clearly shows the following points: a specimen should be considered as sliced parallel to the entrance surface; a spherical propagation function should be used, giving the exact excitation error measured along the surface normal; the interaction constant in the phase-grating function should be changed; the phase grating should be projected along the beam direction. A new parameter for the strength of the upper-layer interaction in the case of the inclined illumination is proposed in terms of the excitation error of the reciprocal-lattice points used to define the projected potential. It is pointed out that the potential projected along the beam direction may better represent the upper-layer interactions for the inclined illumination.