The tuning of a Zernike phase plate with defocus and variable spherical aberration and its use in HRTEM imaging

With the advent of the double-hexapole aberration corrector in transmission electron microscopy the spherical aberration of the imaging system has become a tunable imaging parameter like the objective lens defocus. Now Zernike phase plates, altering the phase of the diffracted electron wave, can be approximated more perfectly than with the lens defocus alone, and the amount of phase change can be adjusted within wide limits. The tuning of the phase change allows an optimum contrast transfer in high-resolution imaging even for thick crystalline objects, thus surpassing the limits of the well-known Scherzer λ/4 phase plate to the imaging of thin objects. The optimum values for the spherical aberration and the lens defocus are derived, and the limits and imperfections of the approximation explored. A mathematical link to the channelling approximation of high-energy electron diffraction shows how the image contrast of atomic columns can be improved systematically within wide thickness limits. Depending on the specimen thickness different combinations of spherical aberration and defocus are favourable: positive spherical aberration with an underfocus, zero spherical aberration with zero defocus, as well as negative spherical aberration with an overfocus.