Diagnosis of aberrations from crystalline samples in scanning transmission electron microscopy

The Ronchigrams, or shadow images, observed from a thin crystalline sample in a scanning transmission electron microscope characteristically present many sets of fringes, which appear thanks to the coherent interference between the various Bragg-diffracted discs as they overlap in the diffraction plane. A particular region of such patterns can be shown to be independent of the defocus at which they are recorded. The intensity along this so-called achromatic ring depends on the microscope aberrations and can be used to diagnose the wave aberration coefficients, a crucial first step in the operation of an aberration-corrected microscope. A new algorithm is presented that allows the accurate determination of all non-cylindrically symmetric aberrations up to fourth-order from a crystalline sample using this property of the Ronchigram. An experimental procedure for determining the position of and intensity along the achromatic lines, as well as examples of diagnosis from two different crystalline structures, are detailed.