Electron interferometry and interference electron microscopy

Noise-resistant phase imaging with intensity correlation

Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.

X-ray bi-prism interferometry-A design study of proposed novel hardware

PURPOSE

Advances in X-ray phase-contrast imaging can obtain excellent soft-tissue contrast of phase-shift, attenuation, and small-angle scatter. Here, we present fringe patterns for different design parameters of X-ray bi-prism interferometry imaging systems. Our aim is to develop bi-prism interferometry imaging systems with excellent polychromatic performance that produce high-contrast fringes with spatially incoherent X-ray illumination. We also introduce a novel X-ray tube design that uses temporal multiplexing to provide simultaneous virtual "electronic phase stepping" that replace "mechanical phase stepping" popular with grating-based interferometry setups.

METHODS

In our investigation, we develop expressions for the irradiance distribution pattern of a bi-prism interferometer composed of multiple point sources and multiple bi-prisms. These expressions are used to plot fringe patterns for X-ray design parameters, including size of point source, number of point sources, and point source separation, and bi-prism design parameters including material, angle, number of bi-prisms, period, and bi-prism array to X-ray source and detector distances.

RESULTS

Results show that the fringe patterns for a bi-prism interferometry system are not longitudinally periodic as with grating interferometers that produce a Talbot-Lau carpet. It is also shown that at 59 keV X-rays the bi-prism material should be something comparable to nickel to obtain reasonable fringe visibility.

CONCLUSION

The irradiance distribution pattern demonstrates that bi-prism interferometry may provide comparable or improved fringe visibility to that of gratings. Special care is given to present our findings within the context of previous advancements. A single-shot image acquisition approach using a temporal multiplexed, high-power X-ray source provides virtual electronic phase stepping without focal spot sweeping. This provides multiple images, each at the same exposure and the same projection view, from different fringe locations that allow one to derive the attenuation, phase, and dark-field images of the sample without mechanical phase stepping of a grating.

Tomography of dark-field scatter including single-exposure Moiré fringe analysis with X-ray biprism interferometry-A simulation study

PURPOSE

In this work, we present tomographic simulations of a new hardware concept for X-ray phase-contrast interferometry wherein the phase gratings are replaced with an array of Fresnel biprisms, and Moiré fringe analysis is used instead of "phase stepping" popular with grating-based setups.

METHODS

Projections of a phantom consisting of four layers of parallel carbon microfibers is simulated using wave optics representation of X-ray electromagnetic waves. Simulated projections of a phantom with preferential scatter perpendicular to the direction of the fibers are performed to analyze the extraction of small-angle scatter from dark-field projections for the following: (1) biprism interferometry using Moiré fringe analysis; (2) grating interferometry using phase stepping with eight grating steps; and (3) grating interferometry using Moiré fringe analysis. Dark-field projections are modeled as projections of voxel intensities represented by a fixed finite vector basis set of scattering directions. An iterative MLEM algorithm is used to reconstruct, from simulated projection data, the coefficients of a fixed set of seven basis vectors at each voxel representing the small-angle scatter distribution.

RESULTS

Results of reconstructed vector coefficients are shown comparing the three simulated imaging configurations. The single-exposure Moiré fringe analysis shows not only an increase in noise because of one-eighth the number of projection samples but also is obtained with less dose and faster acquisition times. Furthermore, replacing grating interferometry with biprism interferometry provides better contrast-to-noise.

CONCLUSION

The simulations demonstrate the feasibility of the reconstruction of dark-field data acquired with a biprism interferometry system. With the potential of higher fringe visibility, biprism interferometry with Moiré fringe analysis might provide equal or better image quality to that of phase stepping methods with less imaging time and lower dose.

Tailoring Multiloop Atom Interferometers with Adjustable Momentum Transfer

Multiloop matter-wave interferometers are essential in quantum sensing to measure the derivatives of physical quantities in time or space. Because multiloop interferometers require multiple reflections, imperfections of the matter-wave mirrors create spurious paths that scramble the signal of interest. Here, we demonstrate a method of adjustable momentum transfer that prevents the recombination of the spurious paths in a double-loop atom interferometer aimed at measuring rotation rates. We experimentally study the recombination condition of the spurious matter waves, which is quantitatively supported by a model accounting for the coherence properties of the atomic source. We finally demonstrate the effectiveness of the method in building a cold-atom gyroscope with a single-shot acceleration sensitivity suppressed by a factor of at least 50. Our study will impact the design of multiloop atom interferometers that measure a single inertial quantity.

The Young-Feynman controlled double-slit electron interference experiment

The key features of quantum mechanics are vividly illustrated by the Young-Feynman two-slit thought experiment, whose second part discusses the recording of an electron distribution with one of the two slits partially or totally closed by an aperture. Here, we realize the original Feynman proposal in a modern electron microscope equipped with a high brightness gun and two biprisms, with one of the biprisms used as a mask. By exciting the microscope lenses to conjugate the biprism plane with the slit plane, observations are carried out in the Fraunhofer plane with nearly ideal control of the covering of one of the slits. A second, new experiment is also presented, in which interference phenomena due to partial overlap of the slits are observed in the image plane. This condition is obtained by inserting the second biprism between the two slits and the first biprism and by biasing it in order to overlap their images.

Development of a SEM-based low-energy in-line electron holography microscope for individual particle imaging

A new SEM-based in-line electron holography microscope has been under development. The microscope utilizes conventional SEM and BF-STEM functionality to allow for rapid searching of the specimen of interest, seamless interchange between SEM, BF-STEM and holographic imaging modes, and makes use of coherent low-energy in-line electron holography to obtain low-dose, high-contrast images of light element materials. We report here an overview of the instrumentation and first experimental results on gold nano-particles and carbon nano-fibers for system performance tests. Reconstructed images obtained from the holographic imaging mode of the new microscope show substantial image contrast and resolution compared to those acquired by SEM and BF-STEM modes, demonstrating the feasibility of high-contrast imaging via low-energy in-line electron holography. The prospect of utilizing the new microscope to image purified biological specimens at the individual particle level is discussed and electron optical issues and challenges to further improve resolution and contrast are considered.

A nanofabricated, monolithic, path-separated electron interferometer

Progress in nanofabrication technology has enabled the development of numerous electron optic elements for enhancing image contrast and manipulating electron wave functions. Here, we describe a modular, self-aligned, amplitude-division electron interferometer in a conventional transmission electron microscope. The interferometer consists of two 45-nm-thick silicon layers separated by 20 μm. This interferometer is fabricated from a single-crystal silicon cantilever on a transmission electron microscope grid by gallium focused-ion-beam milling. Using this interferometer, we obtain interference fringes in a Mach-Zehnder geometry in an unmodified 200 kV transmission electron microscope. The fringes have a period of 0.32 nm, which corresponds to the [1̄1̄1] lattice planes of silicon, and a maximum contrast of 15%. We use convergent-beam electron diffraction to quantify grating alignment and coherence. This design can potentially be scaled to millimeter-scale, and used in electron holography. It could also be applied to perform fundamental physics experiments, such as interaction-free measurement with electrons.

Depth profilometry via multiplexed optical high-coherence interferometry

Depth Profilometry involves the measurement of the depth profile of objects, and has significant potential for various industrial applications that benefit from non-destructive sub-surface profiling such as defect detection, corrosion assessment, and dental assessment to name a few. In this study, we investigate the feasibility of depth profilometry using an Multiplexed Optical High-coherence Interferometry MOHI instrument. The MOHI instrument utilizes the spatial coherence of a laser and the interferometric properties of light to probe the reflectivity as a function of depth of a sample. The axial and lateral resolutions, as well as imaging depth, are decoupled in the MOHI instrument. The MOHI instrument is capable of multiplexing interferometric measurements into 480 one-dimensional interferograms at a location on the sample and is built with axial and lateral resolutions of 40 μm at a maximum imaging depth of 700 μm. Preliminary results, where a piece of sand-blasted aluminum, an NBK7 glass piece, and an optical phantom were successfully probed using the MOHI instrument to produce depth profiles, demonstrate the feasibility of such an instrument for performing depth profilometry.

Vortex beam production and contrast enhancement from a magnetic spiral phase plate

Electron vortex beam probes offer the possibility of mapping magnetic moments with atomic resolution. In this work we consider using the stray magnetic field produced from a narrow ferromagnetic rod magnetised along its long axis to produce a vortex beam probe, as an alternative to the currently used holographic apertures or gratings. We show through numerical modelling, electron holography observations and direct imaging of the electron probe, that a long narrow ferromagnetic rod induces a phase shift in the wave-function of passing electrons that approximately describes a helix in the regions near its ends. Directing this rod towards the optical axis of a charged-particle beam probe forming system at a limiting aperture position, with the free-end sufficiently close to the axis, is shown to offer a point spread function composed of vortex modes, with evidence of this appearing in observations of the electron probe formed from inserting a micro-fabricated CoFe rod into the beam path of a 300 keV transmission electron microscope (TEM). If the rod is arranged to contain the magnetic flux of h/e, thus producing a maximum phase shift of 2π, it produces a simple spiral-like phase contrast transfer function for weak phase objects. In this arrangement the ferromagnetic rod can be used as a phase plate, positioned at the objective aperture position of a TEM, yielding enhanced image contrast which is simulated to be intermediate between comparable Zernike and Hilbert phase plates. Though this aspect of the phase plate performance is not demonstrated here, agreement between our observations and models for the probe formed from an example rod containing a magnetic flux of ~2.35h/e, indicate this phase plate arrangement could be a simple means of enhancing contrast and gaining additional information from TEM imaged weak phase samples, while also offering the capability to produce vortex beam probes. However, steps still need to be taken to either remove or improve the support membrane for the rod in our experiments to reduce any effects from charging in the phase plate.

Axial resonance of periodic patterns by using a Fresnel biprism

This paper proposes a method for the generation of high-contrast localized sinusoidal fringes with spatially noncoherent illumination and relatively high light throughput. The method, somehow similar to the classical Lau effect, is based on the use of a Fresnel biprism. It has some advantages over previous methods for the noncoherent production of interference fringes. One is the flexibility of the method, which allows the control of the fringe period by means of a simple axial shift of the biprism. Second is the rapid axial fall-off in visibility around the high-contrast fringe planes. And third is the possibility of creating fringes with increasing or with constant period as the light beam propagates. Experimental verifications of the theoretical statements are also provided.

Coherent electron interference from amorphous TEM specimens

For the first time, the electron intensity on the diffraction plane from amorphous transmission electron microscope (TEM) specimens has been found to have sufficient coherence to produce fringes in interferograms that were created using a wavefront splitting method of diffracted beam interferometry. The fringes were found to exist from low to high electron-scattering angles. Their spatial frequency depended on the angular overlap of the interfering beams, which was controlled by an electron biprism. From these interferograms, phase information of amorphous materials, which is information now lacking and required for determining their atomic structures, was obtained. An immediate application of this interference is a new method to determine the spatial resolution of the TEM that occurs at the shear angle for fringe disappearance.

A fully coherent electron beam from a noble-metal covered W(111) single-atom emitter

In quantum mechanics, a wavefunction contains two factors: the amplitude and the phase. Only when the probing beam is fully phase coherent, can complete information be retrieved from a particle beam based experiment. Here we use the electron beam field emitted from a noble-metal covered W(111) single-atom tip to image single-walled carbon nanotubes (SWNTs) in an electron point projection microscope (PPM). The interference fringes of an SWNT bundle exhibit a very high contrast and the fringe pattern extends throughout the entire beam width. This indicates good phase correlation at all points transverse to the propagation direction. Application of these sources can significantly improve the performance and expand the capabilities of current electron beam based techniques. New instrumentation based on the full spatial coherence may allow determination of the three-dimensional atomic structures of nonperiodic nanostructures and make many advanced experiments possible.

Single-particle diffraction and interference at a macroscopic scale

A droplet bouncing on a vertically vibrated bath can become coupled to the surface wave it generates. It thus becomes a "walker" moving at constant velocity on the interface. Here the motion of these walkers is investigated when they pass through one or two slits limiting the transverse extent of their wave. In both cases a given single walker seems randomly scattered. However, diffraction or interference patterns are recovered in the histogram of the deviations of many successive walkers. The similarities and differences of these results with those obtained with single particles at the quantum scale are discussed.

Diffraction of 0.5keV electrons from free-standing transmission gratings

A nanostructured grating was used to diffract a low-energy (500 eV) electron beam, and the current transmitted into the zeroth diffraction order was greater than 5% of the incident beam current. This diffraction efficiency indicates that the 55-nm-wide grating bars absorb electrons but the 45-nm-wide slots between bars transmit electron de Broglie waves coherently. The diffraction patterns can be asymmetric, and can be explained by a model that incorporates an electrostatic potential energy for electrons within 20 nm of the grating structure calculated by the method of images.

Electron optical phase-shifts by Fourier methods: Analytical versus numerical calculations

The theoretical framework for the computation of electromagnetic fields and electron optical phase-shifts in Fourier space has been recently applied to objects with long-range fringing fields, such as reverse-biased p-n junctions and magnetic stripe domains near a specimen edge. In addition to new analytical results, in this work, we present a critical comparison between numerical and analytical computations. The influence of explicit and implicit boundary conditions on the phase shifts and phase-contrast images is also investigated in detail.

Quantitative evaluation of spatial coherence of the electron beam from low temperature field emitters

By using multiwalled carbon nanotubes as an element of a nanobiprism, we evaluated quantitatively the coherence of electrons emitted from tungsten tips at room temperature and 78 K, and found an enhancement of coherence at 78 K. The increase of the transverse coherence length of the electron beam agreed well with that of the inelastic mean free path of electrons in solids, demonstrating the direct relationship between the coherences of the electron beam and the original electronic states. On the basis of this experimental fact, we comment on the interpretation of recent Hanbury Brown-Twiss type experiments for electrons reported by Kiesel et al. [Nature (London) 418, 392 (2002)]].

A Fourier approach to fields and electron optical phase-shifts calculations

The Fourier method is applied to calculate fields and electron optical phase shifts in specimens having long-range electromagnetic fields, like reverse biased p-n junctions or stripe magnetic domains. It is shown that this approach not only allows to take into account rather easily the effect of the fringing fields protruding in the space around the specimen, but also to obtain solutions to interesting models in analytical form.

An introduction to off-axis electron holography

The technique of off-axis electron holography is introduced and reviewed. The history of the topic is discussed briefly looking at the origin of electron holography and the reasons for its growth in recent years around the world. The formation and numerical reconstruction of the hologram is discussed in detail on a theoretical and practical level. The spread of holography is illustrated through a number of applications ranging from ultra high resolution studies of crystal structures, the imaging of magnetic and electric fields, the determination of sample composition and morphology and the use of holography for imaging biological specimens.

Electron microscopy of reverse biased p-n junctions

The aim of this paper is to present and discuss the recent results obtained in the investigation of reverse-biased p-n junctions by means of the out-of-focus method. It will be shown how the interpretation of the experimental images is not in agreement with the expectations based on the bulk p-n junction theory. The possible causes of this discrepancy will be discussed: among them a significant reason could be the finite specimen thickness with the associated surface states, which influences the width and shape of the depletion layer in the thinned specimen.