An approximate multi-beam form of the “ellipse” in high-resolution transmission electron microscopy

The concept of “ellipse”, appearing in recent studies of high-resolution transmission electron microscopy, is newly defined as the curves in the Fourier transform patterns of the images caused by many beams by plotting the intensities of diffracted beams vs. the transmitted beam. The present approximate ellipsoidal path can also be derived by using the phase-grating approximation and Sayreʹs relation, but without the two-Bloch-waves assumption. Its validity is examined from the data obtained by Fourier transforming the multi-slice simulated images of silicon 〈1 1 0〉, and gives a valuable issue for quantitative image analysis in diffraction space.