In the recent years high-resolution off-axis electron holography made huge advancements. Electron microscopes with increased numbers of electron optical biprisms and electron lenses allow more flexible ray paths. Due to the combination of double biprism holography and higher magnification at the lower biprism, holograms in the high resolution regime are now recorded with negligible artifacts [1]. Furthermore, smart averaging schemes for hologram series allow to prolong the effective exposure time for a hologram to time scales, where the experimental errors are not dominated by the shot noise anymore [2].

One of the advantages of holography is the posterior correction of residual aberrations. However, the aberrations still have to be sufficiently known. By quantitative comparison of reconstructed wave functions with calculations the imaging parameters can be retrieved with sufficient precision allowing the reconstruction of aberration corrected exit-wave functions. Thus nowadays holograms with (sub-)angstrom resolution can be obtained on a regular basis.

In off-axis holography only the side-band channel of the information recorded in the hologram is reconstructed. As hologram series are recorded and the reconstructed wave function can be propagated to arbitrary defocus values anyway, also focal series of conventional images (center-band) can be obtained in the same measurement.

In the figures the reconstructed exit waves of a GaAs wedge, obtained by inline and off-axis holography are shown [3, 4]. While differences in the low-frequency reconstruction are expected, also significant differences in thicker specimen parts are found. The latter can be easily recognized on the left side of the linescan profiles, where the amplitudes signals at the columns positions exhibit different behaviours. There are several possible reasons for this discrepancy. The numerical inversion of the imaging process within the inline method becomes worse conditioned since the thicker parts exhibit stronger non-linear imaging. Thus the reconstruction algorithm might converge in a wrong minimum of the overall error figure. Also, any changes of the object during the acquisition of the series will exhibit different behaviour in the measurement. Furthermore, both channels (side-band and center-band) refer to different parts of the density matrix due to the different quantum-mechanical nature of the underlying interference experiment.

[1] F. Genz et al., Ultramicroscopy 147 (2014) 33

[2] T. Niermann et al., Micron 63 (2014) 28

[3] T. Niermann et al., J. Phys. D: Appl. Phys. 49 (2016) 194002

[4] The FEI TrueImage software packages was used for inline reconstruction.

Figures:

Exit waves of a GaAs crystal reconstructed by means of inline and off-axis holography. The arsenic columns can be found on left hand side of the "dumbbells", while the gallium columns are on the right hand side.

Linescan across arsenic columns from thicker specimen parts (left) to thinner parts (right). The positions of the columns are marked by vertical lines.

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