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The interaction of metals with carbon materials, specifically with graphene, is of importance for various technological applications. In particular, 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. Here, we investigate in situ the adsorption and nucleation of the alkali metals K, Cs, and Li on free-standing graphene by means of low-energy electron point source microscopy. We find that alkali metals readily intercalate in between bilayer graphene. In fact, the equilibrium distribution of K and Cs favours a much higher particle density in between the bilayer than on the single layer graphene. We obtain a quantitative value for the difference of the free energy of binding between these two domains. Our study is completed with a control experiment introducing Pd as a representative of the non-alkali metals. Now, we observe cluster formation in equal measure on both, single and bilayer graphene, however no intercalation. Our investigations thus constitute the first in situ study of metal atom sorption of different specificity on free-standing graphene.

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.

We investigate imaging of moire 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 moire structure have not been observed in such diffraction patterns. We show that diffraction on moire structure can create intense diffraction peaks if the energy of the probing electrons is very low, in the range of a few tens of eV. Experimental diffraction patterns of TBG acquired with low-energy electrons of 236 eV exhibiting peaks attributed to the moire structure periodicity are shown. In holography mode, the intensity of the wave transmitted through the sample and measured in the far-field can be enhanced or decreased depending on the atomic arrangement, as for example AA or AB stacking. Thus, a decrease of intensity in the far-field must not necessarily be associated with some absorption inside the sample but can simply be a result of a particular atomic arrangement. We believe that our findings can be important for exploiting graphene as a support in electron imaging.

Coherent diffraction imaging (CDI) allows the retrieval of the structure of an isolated object, such as a macromolecule, from its diffraction pattern. CDI requires the fulfilment 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, provided the molecule exhibits periodicity in one direction, as in the case of fiber diffraction. We demonstrate that by applying iterative phase retrieval methods to a fiber diffraction pattern, the repeating unit, that is, the molecule structure, can directly be reconstructed without any prior modeling. As an example, we recover the structure of the DNA double helix in three-dimensions from its two-dimensional X-ray fiber diffraction pattern, Photograph 51, acquired in the famous experiment by Raymond Gosling and Rosalind Franklin, at a resolution of 3.4 Angstrom.

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, that 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. We show how vibrations can be post-filtered out from the hologram or from the reconstructed object assuming a Gaussian distribution of the vibrations. We also provide a numerical example of compensation for directional motion blur. We demonstrate our approach for light optical and electron holograms, acquired with both, plane- as well as spherical-waves. As a result of such hologram deblurring, the resolution of the reconstructed objects is enhanced by almost a factor of 2. We believe that our approach opens up a new venue of post-experimental resolution enhancement in in-line holography by adapting the rich database/catalogue of motion deblurring algorithms developed for photography and image restoration applications.

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. By applying an iterative phase retrieval reconstruction routine we recover the potential distribution of the localized charged impurities present on free-standing graphene.

We report angle-resolved electron transmission measurements through freestanding graphene sheets in the energy range of 18 to 30 eV above the Fermi level. The measurements are carried out in a low-energy electron point source microscope, which allows simultaneously probing the transmission for a large angular range. The characteristics of low-energy electron transmission through graphene depend on its electronic structure above the vacuum level. The experimental technique described here allows mapping the unoccupied band structure of freestanding two-dimensional materials as a function of energy and probing angle, respectively in-plane momentum. Our experimental findings are consistent with theoretical predictions of a resonance in the band structure of graphene above the vacuum level [V. U. Nazarov, E. E. Krasovskii, and V. M. Silkin, Physical Review B 87, 041405 (2013)].

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 behaviour in a quantitative way. This makes electron holography a unique probing tool for directly visualising charge distributions with a sensitivity of a fraction of an elementary charge. Moreover, spatial resolution in the nanometer range and fast data acquisition inherent to lens-less low-energy electron holography allows for direct visual inspection of charge transfer processes.

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. An Airy beam is generated at the focal plane of the numerical lens. We provide for the first time a quantitative properties of the formed Airy beam. We derive the formula for deflection of the intensity maximum of the so formed Airy beam, which is different to the quadratic deflection typical of Airy beams. We cross-validate the derived formula by both simulations and experiment. The second method is based on the fact that a system consisting of a transmissive SLM sandwiched between two polarisers can create a transmission function with negative values. This observation alone has the potential for various other wavefront modulations where the transmission function requires negative values. As an example for this method, we demonstrate that a wavefront can be modulated by passing the SLM system with transmission function with negative values by loading an Airy function distribution directly onto SLM. Since the Airy function is a real-valued function but also with negative values, an Airy beam can be generated by direct transfer of the Airy function distribution onto such an SLM system. In this way, an Airy beam is generated immediately behind the SLM. As both new methods do not employ a physical lens, the two setups are more compact than conventional setups for creating Airy beams. We compare the performance of the two novel methods and the properties of the created Airy beams.

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. Samples of individual proteins and protein complexes on ultraclean freestanding graphene were prepared by soft-landing electrospray ion beam deposition, which allows chemical- and conformational-specific selection and gentle deposition. Low-energy electrons do not induce radiation damage, which enables acquiring sub-nanometer resolution images of individual proteins (cytochrome C and bovine serum albumin) as well as of protein complexes (hemoglobin), which are not the result of an averaging process.

In coherent diffractive imaging (CDI) the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by post-extrapolation of coherent diffraction images, such as diffraction patterns or holograms. We demonstrate that a diffraction pattern can unambiguously be extrapolated from only a fraction of the entire pattern and that the ratio of the extrapolated signal to the originally available signal is linearly proportional to the oversampling ratio. While there could be in principle other methods to achieve extrapolation, we devote our discussion to employing iterative phase retrieval methods and demonstrate their limits. We present two numerical studies; namely the extrapolation of diffraction patterns of non-binary and that of phase objects together with a discussion of the optimal extrapolation procedure.

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. To create an arbitrary three-dimensional path of intensity, we represent the path as a sequence of closely packed individual point-like absorbers and simulate the in-line hologram of the created object set; when such a hologram is contrast inverted, thus giving rise to a diffractor, it creates the pre-determined three-dimensional path of intensity behind the diffractor under illumination. The crucial parameter for a smooth optical path is the sampling of the predetermined curves, which is given by the lateral and axial resolution of the optical system. We provide both, simulated and experimental results to demonstrate the power of this novel method.

We show that radiation damage to unstained biological specimens is not an intractable problem in electron microscopy. When a structural hypothesis of a specimen is available, quantum mechanical principles allow us to verify the hypothesis with a very low electron dose. Realization of such a concept requires precise control of the electron wave front. Based on a diffractive electron optical implementation, we demonstrate the feasibility of this new method by both experimental and numerical investigations., Comment: 8 pages, 3 figures

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. Experimentally, the final column shapes a quasi-planar wave front with a minimal full divergence angle of 4 mrad and electron energies as low as 100 eV.

Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object reconstructed from an experimental X-ray diffraction record which contains about 10% missing information, including the pixels in the center of the diffraction pattern. A diffraction pattern is extrapolated beyond the detector area and as a result, the object is reconstructed at an enhanced resolution and better agreement with experimental amplitudes is achieved. The optimal parameters for the iterative routine and the limits of the extrapolation procedure are discussed., Comment: 12 pages, 4 figures

We address the problem of reconstructing phase-shifting objects from their single shot in-line holograms. We show that a phase-shifting object cannot be reliably recovered from its in-line hologram by non-iterative reconstruction routines, and that an iterative reconstruction should be applied. We demonstrate examples of simulated in-line holograms of objects with the following properties: purely absorbing, both absorbing and phase shifting, and strong phase-shifting. We investigate the effects of noise and interference contrast in holograms on the reconstruction results and discuss details of an optimal iterative procedure to quantitatively recover the correct absorbing and phase-shifting properties of the object. We also review previously published reconstructions of experimental holograms and summarize the optimal parameters for retrieval of phase-shifting objects from their in-line holograms.

Modern structural biology relies on NMR, X-ray crystallography and cryo-electron microscopy for gaining information on biomolecules at nanometer, sub-nanometer or atomic resolution. All these methods, however, require averaging over a vast ensemble of entities and hence knowledge on the conformational landscape of an individual particle is lost. Unfortunately, there are now strong indications that even X-ray free electron lasers will not be able to image individual molecules but will require nanocrystal samples. Here, we show that non-destructive structural biology of single particles has now become possible by means of low-energy electron holography. As an example, individual tobacco mosaic virions deposited on ultraclean freestanding graphene are imaged at one nanometer resolution revealing structural details arising from the helical arrangement of the outer protein shell of the virus. Since low-energy electron holography is a lens-less technique and since electrons with a deBroglie wavelength of approximately 1 Angstrom do not impose radiation damage to biomolecules, the method has the potential for Angstrom resolution imaging of single biomolecules.

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. Moreover, we show that the numerical procedures for the reconstruction of holograms recorded with plane and spherical waves are identical under certain conditions. Experimental examples of holograms and their reconstructions are also discussed., Comment: with link to MATLAB codes

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. We show that by combining electron holography and coherent diffraction imaging estimations concerning the phase of the scattered wave become needless as the phase information is extracted from the data directly and unambiguously. Performed with low-energy electrons the resolution of this lens-less microscope is just limited by the De Broglie wavelength of the electron wave and the numerical aperture, given by detector geometry. In imaging freestanding graphene, a resolution of 2 Angstrom has been achieved revealing the 660.000 unit cells of the graphene sheet from one data set at once. Applied to individual biomolecules the method allows for non-destructive imaging and imports the potential to distinguish between different conformations of proteins with atomic resolution., Comment: 17 pages, 10 figures; Ultramicroscopy 2015

Interfacing graphene with solid-state devices and maintaining it free of contamination is a crucial step towards a functioning device, be it a semiconductor structure or any other device for technological applications. We take advantage of the catalytic properties of platinum metals to completely remove the polymer capping after the transfer of macroscopic graphene sheets to a solid-state device. For that purpose a platinum metal coated structure is brought in close proximity with the polymer capping. Subsequent annealing in air at a temperature between 175 and 350{\deg}C actuates a complete catalytic removal of the polymer. Finally, the platinum metal catalyst is removed revealing ultra clean graphene interfaced with an arbitrary device. Experiments to interface macroscopic graphene layers with oxidized silicon wafers demonstrate the general applicability of this approach. In repeating the procedure, multi-layer graphene sheets can also be produced. Direct evidence for the latter is provided by optical images of three overlapping graphene sheets. The exceeding level of cleanliness of the graphene is examined on the nanometer scale by means of low-energy electron transmission microscopy., Comment: arXiv admin note: text overlap with arXiv:1210.6824

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. Moreover, we apply the three-dimensional volumetric deconvolution to reconstructions of a time-dependent sequence of holograms of an ensemble of polystyrene spheres moving in water. From each hologram we simultaneously resolve all particles in the ensemble in three dimensions and from the sequence of holograms we obtain the time-resolved trajectories of individual polystyrene spheres., Comment: 11 pages, 7 figures

Previously reported crystalline structures obtained by an iterative phase retrieval reconstruction of their diffraction patterns seem to be free from displaying any irregularities or defects in the lattice, which appears to be unrealistic. We demonstrate here that the structure of a nanocrystal including its atomic defects can unambiguously be recovered from its diffraction pattern alone by applying a direct phase retrieval procedure not relying on prior information of the object shape. Individual point defects in the atomic lattice are clearly apparent. Conventional phase retrieval routines assume isotropic scattering. We show that when dealing with electrons, the quantitatively correct transmission function of the sample cannot be retrieved due to anisotropic, strong forward scattering specific to electrons. We summarize the conditions for this phase retrieval method and show that the diffraction pattern can be extrapolated beyond the original record to even reveal formerly not visible Bragg peaks. Such extrapolated wave field pattern leads to enhanced spatial resolution in the reconstruction., Comment: 10 pages, 4 figures

An ideal support for electron microscopy shall be as thin as possible and 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 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. We demonstrate here by means of low-energy electron holographic imaging that freestanding graphene prepared with the Platinum-metal catalysis method remains ultraclean even after re-exposure to ambient conditions and deposition of gold-nanorods from the liquid phase. In the holographic reconstruction of the gold particles the organic shell surrounding the objects is imaged while it is not detectable in SEM images of the very same sample, demonstrating the tremendous potential of low-energy electron holography for the imaging of graphene-supported single biomolecules.

Low-energy electrons (30-250 eV) 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. We discuss the twin image problem intrinsic to inline holography and the problem of the so-called biprism-like effect specific to low-energy electrons. We demonstrate how the presence of the biprism-like effect can be efficiently identified and circumvented. The presented sideband filtering reconstruction method eliminates the twin image and allows for reconstruction despite the biprism-like effect, which we demonstrate on both, simulated and experimental examples., Comment: 11 pages, 5 figures

A technique of pulsed low-energy electron holography is introduced that allows for recording highly resolved holograms within reduced exposure times. Therefore, stacks of holograms are accumulated in a pulsed mode with individual acquisition times as short as 50 {\mu}s. Subsequently, these holograms are aligned and finally superimposed. The resulting holographic record reveals previously latent high-order interference fringes and thereby pushing interference resolution into the sub-nanometer regime. In view of the non-damaging character of low-energy electrons, the method is of particular interest for structural analysis of fragile biomolecules., Comment: 13 pages, 5 figurs

Modern microscopy techniques are aimed at imaging an individual molecule at atomic resolution. Here we show that low-energy electrons with kinetic energies of 50-250 eV offer a possibility of overcome the problem of radiation damage, and obtaining images of individual biomolecules. Two experimental schemes for obtaining images of individual molecules, holography and coherent diffraction imaging, are discussed and compared. Images of individual molecules obtained by both techniques, using low-energy electrons, are shown., Comment: 17 pages, 9 figures. See for the full text at Springer website http://link.springer.com/chapter/10.1007%2F978-94-007-6232-9_29# Present and Future Methods for Biomolecular Crystallography, Springer, 2013

We have imaged a freestanding graphene sheet of 210 nm in diameter with 2 Angstrom resolution by combining coherent diffraction and holography with low-energy electrons. The entire sheet is reconstructed from just a single diffraction pattern displaying the arrangement of 660.000 individual graphene unit cells at once. Given the fact that electrons with kinetic energies of the order of 100 eV do not damage biological molecules, it will now be a matter to develop methods for depositing individual proteins onto such graphene sheets.

Conventional microscopic records represent intensity distributions whereby local sample information is mapped onto local information at the detector. In coherent microscopy, the superposition principle of waves holds; field amplitudes are added, not intensities. This non-local representation is spread out in space and interference information combined with wave continuity allows extrapolation beyond the actual detected data. Established resolution criteria are thus circumvented and hidden object details can retrospectively be recovered from just a fraction of an interference pattern., Comment: 11 pages, 4 figures

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. The wavefront beyond the experimentally detected area is thus retrieved and the hologram reconstruction shows enhanced resolution. To demonstrate the power of this concept, we apply it to simulated as well as experimental holograms., Comment: 11 pages, 6 figures, MATLAB code

While freestanding clean graphene is essential for various applications, existing technologies for removing the polymer layer after transfer of graphene to the desired substrate still leave significant contaminations behind. We discovered a method for preparing ultra-clean freestanding graphene utilizing the catalytic properties of platinum metals. Complete catalytic removal of polymer residues requires annealing in air at a temperature between 175 and 350{\deg}C. Low-energy electron holography investigations prove that this method results in ultra-clean freestanding graphene.

We investigated the utility of free-standing graphene as a transparent sample carrier for imaging nanometer-sized objects by means of low-energy electron holography. The sample preparation for obtaining contamination-free graphene as well as the experimental setup and findings are discussed. For incoming electrons with 66 eV kinetic energy graphene exhibits 27% opacity per layer. Hence, electron holograms of nanometer-sized objects adsorbed on free-standing graphene can be recorded and numerically reconstructed to reveal the object's shapes and distribution. Furthermore, a Moire effect has been observed with free-standing graphene multi-layers.

The mode of action of proteins is to a large extent given by their ability to adopt different conformations. This is why imaging single biomolecules at atomic resolution is one of the ultimate goals of biophysics and structural biology. The existing protein database has emerged from X-ray crystallography, NMR or cryo-TEM investigations. However, these tools all require averaging over a large number of proteins and thus over different conformations. This of course results in the loss of structural information. Likewise it has been shown that even the emergent X-FEL technique will not get away without averaging over a large quantity of molecules. Here we report the first recordings of a protein at sub-nanometer resolution obtained from one individual ferritin by means of low-energy electron holography. One single protein could be imaged for an extended period of time without any sign of radiation damage. Since ferritin exhibits an iron core, the holographic reconstructions could also be cross-validated against TEM images of the very same molecule by imaging the iron cluster inside the molecule while the protein shell is decomposed.

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. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, the reconstruction of the scattered complex-valued object wave is directly provided by a well-defined reference wave that must cover the entire detector area which often is an experimental challenge. CDI provides the highest possible, only wavelength limited, resolution, but the phase recovery is an iterative process which requires some pre-defined information about the object and whose outcome is not always uniquely-defined. Moreover, the diffraction patterns must be recorded under oversampling conditions, a pre-requisite to be able to solve the phase problem. Here, we report how holography and CDI can be merged into one superior technique: holographic coherent diffraction imaging (HCDI). An inline hologram can be recorded by employing a modified CDI experimental scheme. We demonstrate that the amplitude of the Fourier transform of an inline hologram is related to the complex-valued visibility, thus providing information on both, the amplitude and the phase of the scattered wave in the plane of the diffraction pattern. With the phase information available, the condition of oversampling the diffraction patterns can be relaxed, and the phase problem can be solved in a fast and unambiguous manner., Comment: 22 pages, 7 figures

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. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process., Comment: 13 pages, 7 figures

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. The iterative deconvolution can be applied to restore the distribution of complex and extended objects. Simulated and experimental examples are presented and demonstrate artifact and noise free three-dimensional reconstructions from a single two-dimensional holographic record. Keywords: digital holography, volumetric deconvolution, three-dimensional volumetric deconvolution, particle tracking, holographic particle tracking, resolution, PSF, Comment: including MATLAB code

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 wave-length radiation, be it X-rays or high energy electrons, circumvent this problem by averaging over many molecules. Averaging, however, leaves conformational details uncovered. Even the anticipated use of ultra-short but extremely bright X-ray bursts of a Free Electron Laser shall afford averaging over 10^6 molecules to arrive at atomic resolution. Here we present direct experimental evidence for non-destructive imaging of individual DNA molecules. In fact, we show that DNA withstands coherent low energy electron radiation with deBroglie wavelength in the Angstrom regime despite a vast dose of 10^8 electrons/nm^2 accumulated over more than one hour., Comment: 11 pages, 3 figures

We present a reconstruction technique for simultaneous retrieval of absorption and phase shifting properties of an object recorded by in-line holography. The routine is experimentally tested by applying it to optical holograms of a pure phase respectively amplitude object of micrometer dimensions that has been machined into a glass-plate using a focused ion beam. The method has also been applied to previously published electron holograms of single DNA molecules., Comment: 11 pages, 7 figures

While the invention of holography by Dennis Gabor truly constitutes an ingenious concept, it has ever since been troubled by the so called twin image problem limiting the information that can be obtained from a holographic record. Due to symmetry reasons there are always two images appearing in the reconstruction process. Thus, the reconstructed object is obscured by its unwanted out of focus twin image. Especially for emission electron as well as for x- and gamma-ray holography, where the source-object distances are small, the reconstructed images of atoms are very close to their twin images from which they can hardly be distinguished. In some particular instances only, experimental efforts could remove the twin images. More recently, numerical methods to diminish the effect of the twin image have been proposed but are limited to purely absorbing objects failing to account for phase shifts caused by the object. Here we show a universal method to reconstruct a hologram completely free of twin images disturbance while no assumptions about the object need to be imposed. Both, amplitude and true phase distributions are retrieved without distortion.