Coherent imaging with low-energy electrons, quantitative analysis.

Low-energy electrons (20-300eV) hold the promise for low-dose, non-destructive, high-resolution imaging, but at the price of challenging data analysis. This study provides theoretical considerations and models for the quantitative analysis of experimental data observed in low-energy electron transmission microscopy and in-line holography. The scattering of low-energy electrons and the imaging parameters, such as the inelastic mean free path, point spread function, depth of focus, and resolution, are quantitatively described. It is shown that unlike high-energy electrons (20-300 keV), low-energy electrons (20-300eV) introduce a large phase shift into the probing electron waves. Using the projected potentials formalism, the maximal phase shift acquired by a 120eV electron wave scattered by a carbon atom is theoretically estimated to be 5.03 radian and experimentally measured to be between 3 and 7.5 radian. The point spread function evaluated for low-energy electrons shows that they diffract much stronger than high-energy electrons, and that only very thin objects of up to 3Å in thickness can be imaged in focus. Thus, when imaging an object of finite thickness, such as a macromolecule, the obtained image will always be blurred due to the out-of-focus signal. This can provide an explanation for a long-standing problem of limited resolution in low-energy electron holography of macromolecules. As for imaging of a macromolecule's structure, it is shown that the amplitude of the wavefront reconstructed from the sample's hologram provides the best match to the projected potential distribution of the macromolecule. To evaluate the absorption properties, the inelastic mean free path (IMFP) is considered. The IMFP values calculated from theoretical models agree with the measured values. The IMFP of about 5Å was measured by transmission through graphene of 50-200eV electrons. This result implies that the internal structure of only very thin samples can be imaged in transmission mode. A simple method to quantitatively evaluate the absorption of a specimen from its in-line hologram without the need to reconstruct the hologram is presented.