Depth-resolved holographic reconstructions by three-dimensional deconvolution: erratum.

Correction of Eq. (20) in our published article [Opt. Express18, 22527 (2010)10.

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.

Moiré structures in twisted bilayer graphene studied by transmission electron microscopy.

We investigate imaging of moiré structures in free-standing twisted bilayer graphene (TBG) carried out by transmission electron microscopy (TEM) in diffraction and in-line Gabor holography modes. Electron diffraction patterns of TBG acquired at typical TEM electron energies of 80-300 keV exhibit the diffraction peaks caused by diffraction on individual layers. However, diffraction peaks at the scattering angles related to the periodicity of the moiré structure have not been observed in such diffraction patterns.

Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval.

Coherent diffraction imaging (CDI) allows the retrieval of an isolated object's structure, such as a macromolecule, from its diffraction pattern. CDI requires the fulfillment of two conditions: the imaging radiation must be coherent and the object must be isolated. We discuss that it is possible to directly retrieve the molecular structure from its diffraction pattern, which was acquired neither with coherent radiation nor from an individual molecule.

Metal Adsorption and Nucleation on Free-Standing Graphene by Low-Energy Electron Point Source Microscopy.

The interaction of metals with carbon materials (and specifically with graphene) is of importance for various technological applications. In particular, the intercalation of alkali metals is believed to provide a means for tuning the electronic properties of graphene for device applications. While the macroscopic effects of such intercalation events can readily be studied, following the related processes at an atomic scale in detail and under well-defined experimental conditions constitutes a challenge.

Resolution enhancement in in-line holography by numerical compensation of vibrations.

Mechanical vibrations of components of the optical system is one of the sources of blurring of interference pattern in coherent imaging systems. The problem is especially important in holography where the resolution of the reconstructed objects depends on the effective size of the hologram, which is on the extent of the interference pattern, and on the contrast of the interference fringes. We discuss the mathematical relation between the vibrations, the hologram contrast and the reconstructed object.

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

While imaging individual atoms can routinely be achieved in high resolution transmission electron microscopy, visualizing the potential distribution of individually charged adsorbates leading to a phase shift of the probing electron wave is still a challenging task. Low-energy electrons (30 - 250 eV) are sensitive to localized potential gradients. We employed low-energy electron holography to acquire in-line holograms of individual charged impurities on free-standing graphene.

Imaging proteins at the single-molecule level.

Imaging single proteins has been a long-standing ambition for advancing various fields in natural science, as for instance structural biology, biophysics, and molecular nanotechnology. In particular, revealing the distinct conformations of an individual protein is of utmost importance. Here, we show the imaging of individual proteins and protein complexes by low-energy electron holography.

Direct Observation of Individual Charges and Their Dynamics on Graphene by Low-Energy Electron Holography.

Visualizing individual charges confined to molecules and observing their dynamics with high spatial resolution is a challenge for advancing various fields in science, ranging from mesoscopic physics to electron transfer events in biological molecules. We show here that the high sensitivity of low-energy electrons to local electric fields can be employed to directly visualize individual charged adsorbates and to study their behavior in a quantitative way. This makes electron holography a unique probing tool for directly visualizing charge distributions with a sensitivity of a fraction of an elementary charge.

Creating Airy beams employing a transmissive spatial light modulator.

We present a detailed study of two novel methods for shaping the light optical wavefront by employing a transmissive spatial light modulator (SLM). Conventionally, optical Airy beams are created by employing SLMs in the so-called all-phase mode. In the first method, a numerically simulated lens phase distribution is loaded directly onto the SLM, together with the cubic phase distribution.

Inverted Gabor holography principle for tailoring arbitrary shaped three-dimensional beams.

It is well known that by modifying the wavefront in a certain manner, the light intensity can be turned into a certain shape. However, all known light modulation techniques allow for limited light modifications only: focusing within a restricted region in space, shaping into a certain class of parametric curves along the optical axis or bending described by a quadratic-dependent deflection as in the case of Airy beams. We show a general case of classical light wavefront shaping that allows for intensity and phase redistribution into an arbitrary profile including pre-determined switching-off of the intensity.

Design and implementation of a micron-sized electron column fabricated by focused ion beam milling.

We have designed, fabricated and tested a micron-sized electron column with an overall length of about 700 microns comprising two electron lenses; a micro-lens with a minimal bore of 1 micron followed by a second lens with a bore of up to 50 microns in diameter to shape a coherent low-energy electron wave front. The design criteria follow the notion of scaling down source size, lens-dimensions and kinetic electron energy for minimizing spherical aberrations to ensure a parallel coherent electron wave front. All lens apertures have been milled employing a focused ion beam and could thus be precisely aligned within a tolerance of about 300 nm from the optical axis.

Practical algorithms for simulation and reconstruction of digital in-line holograms.

Here we present practical methods for simulation and reconstruction of in-line digital holograms recorded with plane and spherical waves. The algorithms described here are applicable to holographic imaging of an object exhibiting absorption as well as phase-shifting properties. Optimal parameters, related to distances, sampling rate, and other factors for successful simulation and reconstruction of holograms are evaluated and criteria for the achievable resolution are worked out.

Holography and coherent diffraction with low-energy electrons: A route towards structural biology at the single molecule level.

The current state of the art in structural biology is led by NMR, X-ray crystallography and TEM investigations. These powerful tools however all rely on averaging over a large ensemble of molecules. Here, we present an alternative concept aiming at structural analysis at the single molecule level.

Holographic time-resolved particle tracking by means of three-dimensional volumetric deconvolution.

Holographic particle image velocimetry allows tracking particle trajectories in time and space by means of holography. However, the drawback of the technique is that in the three-dimensional particle distribution reconstructed from a hologram, the individual particles can hardly be resolved due to the superimposed out-of-focus signal from neighboring particles. We demonstrate here a three-dimensional volumetric deconvolution applied to the reconstructed wavefront which results in resolving all particles simultaneously in three-dimensions.

Low-energy electron holographic imaging of gold nanorods supported by ultraclean graphene.

An ideal support for an electron microscopy should be as thin as possible and be able to interact as little as possible with the primary electrons. Since graphene is atomically thin and made up of carbon atoms arranged in a honeycomb lattice, the potential to use graphene as a substrate in electron microscopy is enormous. Until now graphene has hardly ever been used for this purpose because the cleanliness of freestanding graphene before or after deposition of the objects of interest was insufficient.

On artefact-free reconstruction of low-energy (30-250eV) electron holograms.

Low-energy electrons (30-250eV) have been successfully employed for imaging individual biomolecules. The most simple and elegant design of a low-energy electron microscope for imaging biomolecules is a lensless setup that operates in the holographic mode. In this work we address the problem associated with the reconstruction from the recorded holograms.

Graphene unit cell imaging by holographic coherent diffraction.

We have imaged a freestanding graphene sheet of 210 nm in diameter with 2 Å resolution by combining coherent diffraction and holography with low-energy electrons. The entire sheet is reconstructed from a single diffraction pattern displaying the arrangement of 660.000 individual graphene unit cells at once.

Resolution enhancement in digital holography by self-extrapolation of holograms.

It is generally believed that the resolution in digital holography is limited by the size of the captured holographic record. Here, we present a method to circumvent this limit by self-extrapolating experimental holograms beyond the area that is actually captured. This is done by first padding the surroundings of the hologram and then conducting an iterative reconstruction procedure.

When holography meets coherent diffraction imaging.

The phase problem is inherent to crystallographic, astronomical and optical imaging where only the intensity of the scattered signal is detected and the phase information is lost and must somehow be recovered to reconstruct the object's structure. Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered.

Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging.

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane.

Individual filamentous phage imaged by electron holography.

An in-line electron hologram of an individual f1.K phage was recorded with a purpose-built low energy electron point source (LEEPS) microscope. Cryo-microscopic methods were employed to prepare the specimen so that a single phage could be presented to the coherent low energy electrons: An aqueous phage suspension was applied to a thin carbon membrane with micro-machined slits.

Coherent low-energy electron diffraction on individual nanometer sized objects.

Today's structural biology techniques require averaging over millions of molecules to obtain detailed structural information. Derivation of the molecular structure from a scattering experiment with just one single 3D-molecule imposes major challenges. Coherent and damage-free radiation is needed to ensure sufficient elastic scattering events before destroying the molecule and a means to solve the phase problem is wanted.

Depth-resolved holographic reconstructions by three-dimensional deconvolution.

Methods of three-dimensional deconvolution with a point-spread function as frequently employed in optical microscopy to reconstruct true three-dimensional distribution of objects are extended to holographic reconstructions. Two such schemes have been developed and are discussed: an instant deconvolution using the Wiener filter as well as an iterative deconvolution routine. The instant 3d-deconvolution can be applied to restore the positions of volume-spread objects such as small particles.

Nondestructive imaging of individual biomolecules.

Radiation damage is considered to be the major problem that still prevents imaging an individual biological molecule for structural analysis. So far, all known mapping techniques using sufficient short wavelength radiation, be it x rays or high energy electrons, circumvent this problem by averaging over many molecules. Averaging, however, leaves conformational details uncovered.