Direct Correction of Residual Symmetric Aberrations in Electron Holograms of Weak Phase Objects

Thin TEM specimen are regarded as weak objects (WPO), if the amplitude variation of the electron wave by the specimen can be neglected and the phase modulation is very small (≪π). Large classes of topical materials can be described in this approximation, such as most 2D materials, organic semiconductor materials or biological specimen. Due to the lack of amplitude (and hence intensity) contrast, conventional TEM (CTEM) investigations on WPOs are commonly performed under a certain defocus, which transfers part of the phase information to the recorded intensity. This intermixing contrast transfer from amplitude to phase and vice versa is commonly described by the phase contrast transfer function (PCTF), while the non-mixing contrast transfer for amplitude and phase is referred to as amplitude contrast transfer function (ACTF). Due to the transfer gap in the PCTF, the CTEM contrast transfer at low spatial frequencies is degraded in defocused images of WPOs (Fig. 1). By employing electron holography, however, both amplitude and phase of the electron wave can be reconstructed without a transfer gap. Having the whole wave information also enables the a-posteriori correction of geometric aberrations as it was already proposed in D. Gabor’s seminal paper from 1948 [1]. The realization of his idea, however, remains challenging in the absence of additional knowledge about the sample, due to the lack of a criterion for a successful aberration correction.