Interpretation of mean free path values derived from off-axis electron holography amplitude measurements

In this work, we have explored the factors which govern mean free path values obtained from off-axis electron holography measurements. Firstly, we explore the topic from a theoretical perspective, and show that the mean amplitude reconstructed from off-axis holograms is due to the coherent portion of the direct, central object-transmitted beam only - it is not affected by the presence or absence of other scattered beams. Secondly, we present a detailed experimental study which compares mean free path values obtained from hologram sideband, centreband, EELS, and TEM measurements as a function of optical collection angle and energy-loss-filtering. These results confirm that the coherent portion of the direct beam defines the mean amplitude, and additionally show that the coherent portion corresponds to the conventional energy-filtered signal (with threshold 5 eV in this work). Finally, we present summary measurements from a selection of different materials, and compare the results against a simple electron scattering model. This study reinforces the claim that the mean amplitude is defined by the energy-filtered direct beam, and confirms that the contributions of elastic and inelastic scattering to the total mean free path are broadly in line with theoretical expectations for these different materials. These results in aggregate indicate that neither experimental collection angles nor enhanced sensitivity to low-loss phonon scattering affect the mean amplitude signal arising from off-axis holography reconstructions, nor the associated mean free path values which are derived from this mean amplitude.