Image transfer with spatial coherence for aberration corrected transmission electron microscopes

The formula of spatial coherence involving an aberration up to six-fold astigmatism is derived for aberration-corrected transmission electron microscopy. Transfer functions for linear imaging are calculated using the newly derived formula with several residual aberrations. Depending on the symmetry and origin of an aberration, the calculated transfer function shows characteristic symmetries. The aberrations that originate from the field's components, having uniformity along the z direction, namely, the n-fold astigmatism, show rotational symmetric damping of the coherence. The aberrations that originate from the field's derivatives with respect to z, such as coma, star, and three lobe, show non-rotational symmetric damping. It is confirmed that the odd-symmetric wave aberrations have influences on the attenuation of an image via spatial coherence. Examples of image simulations of haemoglobin and Si [211] are shown by using the spatial coherence for an aberration-corrected electron microscope.