Imaging the potential distribution of individual charged impurities on graphene by low-energy electron holography

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.

Phase Reconstruction of Low-Energy Electron Holograms of Individual Proteins

Low-energy electron holography (LEEH) is one of the few techniques capable of imaging large and complex three-dimensional molecules, such as proteins, on the single-molecule level at subnanometer resolution. During the imaging process, the structural information about the object is recorded both in the amplitude and in the phase of the hologram. In low-energy electron holography imaging of proteins, the object's amplitude distribution, which directly reveals molecular size and shape on the single-molecule level, can be retrieved via a one-step reconstruction process. However, such a one-step reconstruction routine cannot directly recover the phase information encoded in the hologram. In order to extract the full information about the imaged molecules, we thus implemented an iterative phase retrieval algorithm and applied it to experimentally acquired low-energy electron holograms, reconstructing the phase shift induced by the protein along with the amplitude data. We show that phase imaging can map the projected atomic density of the molecule given by the number of atoms in the electron path. This directly implies a correlation between reconstructed phase shift and projected mean inner potential of the molecule, and thus a sensitivity to local changes in potential, an interpretation that is further substantiated by the strong phase signatures induced by localized charges.

Gabor's holography: seven decades influencing optics [Invited]

Dennis Gabor's seminal idea of a simple all-optical setup aimed at reconstructing the object wavefront stored on a photographic plate gave birth a little over seven decades ago to the field of holography. In 1971 Gabor obtained the Nobel Prize in Physics for this invention. Still, the road in the early days after his two first papers on the subject was one full of obstacles, so his scientific and engineering contemporaries put his idea to rest for more than 10 years, until the invention of the laser. This fact made his holographic concept take off to new and unsuspected applications. This invited review paper is a homage to Dennis Gabor's 50th anniversary of his Nobel Prize accolade. For this purpose, the review departs from the typical common route, i.e., those written following a timeline fashion, and instead is written with the intent to cover only a few of the holography applications in optics while scanning the electromagnetic spectrum. In doing this, the authors are aware that other invited papers for this special issue will tackle other subjects not dealt with in this review non-timeline paper.

Holography and Coherent Diffraction Imaging with Low-(30-250 eV) and High-(80-300 keV) Energy Electrons: History, Principles, and Recent Trends

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

Direct visualization of charge transport in suspended (or free-standing) DNA strands by low-energy electron microscopy

Low-energy electrons offer a unique possibility for long exposure imaging of individual biomolecules without significant radiation damage. In addition, low-energy electrons exhibit high sensitivity to local potentials and thus can be employed for imaging charges as small as a fraction of one elementary charge. The combination of these properties makes low-energy electrons an exciting tool for imaging charge transport in individual biomolecules. Here we demonstrate the imaging of individual deoxyribonucleic acid (DNA) molecules at the resolution of about 1 nm with simultaneous imaging of the charging of the DNA molecules that is of the order of less than one elementary charge per nanometer. The cross-correlation analysis performed on different sections of the DNA network reveals that the charge redistribution between the two regions is correlated. Thus, low-energy electron microscopy is capable to provide simultaneous imaging of macromolecular structure and its charge distribution which can be beneficial for imaging and constructing nano-bio-sensors.