A flux-preserving non-linear inline holography reconstruction algorithm for partially coherent electrons.

Retrieving low spatial frequency components of the phase of the complex-valued exit-face wave function in a transmission electron microscope by reconstruction of a focal series of images requires a large defocus range to be used. In an aberration corrected TEM or at sufficiently low resolution the effect of spherical and higher order aberrations on the spatial coherence term in the transmission cross coefficient may be neglected for an appropriate choice of objective aperture. Applying this approximation, a computationally efficient and flux-preserving iterative computer algorithm has been designed which allows the reconstruction of focal series recorded over a large focal range and arbitrary degrees of spatial coherence. The reconstruction from an experimental data set will be presented. Since a flux-preserving description of image formation is consistent with the transport of intensity equation (TIE), I will also discuss the implications for the application of the TIE under the condition of partial spatial coherence. Finally, a comparison with off-axis holography will be made.