Aberration measurement using the Ronchigram contrast transfer function

The bright field contrast transfer function is one of the most useful concepts in conventional transmission electron microscopy. However, the electron Ronchigram contrast transfer function, as derived by Cowley, is inherently more complicated since it is not isoplanatic. Here, we derive a local contrast transfer function for small patches in a Ronchigram and demonstrate its utility for the direct measurement of aberrations from single Ronchigrams of an amorphous film. We describe the measurement of aberrations from both simulated and experimental images and elucidate the effects due to higher-order aberrations, separating those arising from the pre- and post-sample optics, and partial coherence.