TY - JOUR
AU - Tanigaki,, Toshiaki
AB - Abstract Electron holography was invented for correcting aberrations of the lenses of electron microscopes. It was used to observe the atomic arrangements in crystals after decades of research. Then it was combined with a hardware aberration corrector to enable high-resolution and high-precision analysis. Its applications were further extended to magnetic observations with sub-nanometer resolution. High-resolution electron holography has become a powerful technique for observing electromagnetic distributions in functional materials. transmission electron microscope, electron holography, aberration corrector, high-resolution imaging, magnetic imaging Introduction In 1948, Gabor [1] proposed the concept of holography as an ‘electron interference microscope’. The resolution of electron microscopes was limited by the fourth root of the spherical aberration coefficient (Cs) of the electron lens [2]. To overcome this limitation, he proposed a two-step process for improving the resolution, which is completely different from the improvement of electron lenses. First, an object is illuminated with a coherent electron wave, and the interference between the coherent part of the waves scattered by the object and the illumination waves that are transmitted without being disturbed by the object is recorded on a photographic plate (hologram) (Fig. 1). Then, by illuminating the hologram with coherent light, a wave similar to that emitted from the object can be reconstructed by light. This is because both the phase and amplitude of the wave are recorded in the hologram. In principle, the aberration of the electron lens can be corrected in the reconstruction process, and it should be possible to reproduce an object wave at 100 000 times (the ratio of wavelength of light to electron) higher magnification compared with an optical microscope. However, in Gabor’s era, there was no coherent electron source, and the invention of lasers made holography practical in the field of optics. On the other hand, the practical use of the field emission (FE) electron source, which is an excellent coherent electron source, and the invention of the electron biprism have enhanced the applicability of electron holography. Today, off-axis image holography is used in high-resolution holography in addition to in-line holography originally invented by Gabor. We review high-resolution electron holography from early attempts to recent combinations with aberration correctors. Fig. 1 Open in new tabDownload slide Concept of hologram (Reprinted from Fig. 1 of Nature (1948) 161, 777–778). Fig. 1 Open in new tabDownload slide Concept of hologram (Reprinted from Fig. 1 of Nature (1948) 161, 777–778). High-resolution electron holography To verify the principle of high-resolution holography, spherical aberration was corrected by adjusting the optical lens system during reconstruction. Tonomura et al. [3] created an in-focus hologram of a gold particle using a field-emission transmission electron micr-oscope (TEM). During the correction process, the effect of spherical Fig. 3 Open in new tabDownload slide 0.136-nm dumbbell structure of Si in aberration-corrected phase image (Reprinted from Fig. 7 of Ultramicroscopy (1994) 54, 310–316). Fig. 3 Open in new tabDownload slide 0.136-nm dumbbell structure of Si in aberration-corrected phase image (Reprinted from Fig. 7 of Ultramicroscopy (1994) 54, 310–316). Fig. 4 Open in new tabDownload slide Aberration-corrected amplitude (a) and phase (b) images of InP. (Reprinted from Fig. 3 of Phys. Rev. Lett. (1992) 69, 293–296.). Fig. 4 Open in new tabDownload slide Aberration-corrected amplitude (a) and phase (b) images of InP. (Reprinted from Fig. 3 of Phys. Rev. Lett. (1992) 69, 293–296.). Fig. 5 Open in new tabDownload slide Aberration-corrected phase image of MgO(001) surface. (a) Phase image restored with Cs = 1.7 mm and df = −165 nm. (b) Simulated image for t = 8 nm (indicated with arrow pair in (a)) and Cs = df = 0. (Reprinted from Fig. 4 of J. Electron Microsc. (1994) 43, 318–321). Fig. 5 Open in new tabDownload slide Aberration-corrected phase image of MgO(001) surface. (a) Phase image restored with Cs = 1.7 mm and df = −165 nm. (b) Simulated image for t = 8 nm (indicated with arrow pair in (a)) and Cs = df = 0. (Reprinted from Fig. 4 of J. Electron Microsc. (1994) 43, 318–321). Fig. 6 Open in new tabDownload slide After comprehensive restoration of object exit-wave, amplitude (top) and phase (bottom) can be evaluated quantitatively and independently. Line profiles along atomic columns of (111)-plane give are evidence that interpretation in terms of atomic signals is much easier in phase shift: starting from specimen edge, atomic signal increases in steps of about 2π/12 corresponding to increase in specimen thickness by single gold atoms, whereas amplitude signal does not allow such conclusion because of its complicated behavior. Furthermore, signal between atomic positions proves that atomic phase shift is much more localized compared with amplitude signal. (Reprinted from Fig. 6 of Ultramicroscopy (2012) 116, 13). Fig. 6 Open in new tabDownload slide After comprehensive restoration of object exit-wave, amplitude (top) and phase (bottom) can be evaluated quantitatively and independently. Line profiles along atomic columns of (111)-plane give are evidence that interpretation in terms of atomic signals is much easier in phase shift: starting from specimen edge, atomic signal increases in steps of about 2π/12 corresponding to increase in specimen thickness by single gold atoms, whereas amplitude signal does not allow such conclusion because of its complicated behavior. Furthermore, signal between atomic positions proves that atomic phase shift is much more localized compared with amplitude signal. (Reprinted from Fig. 6 of Ultramicroscopy (2012) 116, 13). aberration of the conjugate reconstruction wave was canceled by the spherical aberration of the optical lens system. In the reconstructed image, Bragg-reflected beams were separated into left and right parts from the transmitted image due to the spherical aberration of the electron lens (Fig. 2(a)). In the corrected image, these were focused at the position of the transmitted image (Fig. 2(b)). However, optical processing is limited in reproduction accuracy and application conditions. From the late 1980s to the 1990s, it became common to digitally capture holograms by using electron microscope charge-coupled device cameras, film scanners, etc. Phase images, amplitude images and aberration-corrected images were reconstructed on a computer. Lichte et al. [4, 5] examined in detail the hologram-preparation conditions necessary for aberration correction in consideration of digital processing. In the BRITE/EURAM project [6], an aberration-corrected phase image (Fig. 3) of a Si dumbbell structure (0.136 nm) was produced [7]. Kawasaki et al. [8] carried out high-resolution holographic observation of InP with a TEM equipped with a newly developed magnetic-field-superimposed cold FE gun. Focusing on the fact that there is a large difference in the amount of phase change between In and P atoms, the hologram was taken in the direction in which the same type of atoms was arranged in the beam-traveling direction. In the aberration-corrected phase image, In and P atomic columns were distinguishable, and the sample thickness was specified (Fig. 4). Tanji et al. [9] reconstructed the potential distribution on the surface of an MgO crystal by high-resolution electron holography and directly observed that the potential distribution on the (001) surface of MgO extends into the vacuum according to the type of ions facing the vacuum (Fig. 5). To attain high-resolution electron holography, it is necessary to take a hologram with low noise and obtain the aberration function with high accuracy. For the former solution, a mechanically and electrically stable electron microscope equipped with a high-brightness FE gun is used. Because of the latter, it is necessary to accurately determine the imaging conditions of the hologram, especially the amount of defocus and spherical aberration coefficient. To reach a resolution of 0.1 nm, the spherical aberration coefficient and amount of defocus must be determined with an accuracy of several tens of micrometers and several nanometers. Since it is not easy to determine these variables from the hologram in the abovementioned early experiments, they were determined from the minimum contrast condition of the reconstructed amplitude image assuming a phase object. Alternatively, the variables were finely changed within the expected range, and the conditions were determined by comparing this image with a simulation image. With the advent of the spherical-aberration corrector for TEM in 1998, it became possible to measure the details of the aberration coefficients, and this situation improved. However, the spherical-aberration corrector also improved the spatial resolution of the electron microscope. What should we expect from high-resolution holography? It seems important to combine holography with an aberration corrector to correct residual higher-order aberrations and local defocus that cannot be corrected with an aberration corrector and to improve phase resolution. This should contribute to materials science by visualizing minute electric and magnetic fields around atoms. The development of high-resolution holography after introducing an aberration corrector is described in the next section. Fig. 2 Open in new tabDownload slide Optical spherical aberration correction of gold-particle image. (a) Reconstructed image, (b) corrected image and (c) conjugate image of (b) (Reprinted from Fig. 6 of Jpn. J. Appl. Phys (1979) 18, 1373–1377). Fig. 2 Open in new tabDownload slide Optical spherical aberration correction of gold-particle image. (a) Reconstructed image, (b) corrected image and (c) conjugate image of (b) (Reprinted from Fig. 6 of Jpn. J. Appl. Phys (1979) 18, 1373–1377). High-resolution electron holography using aberration corrector In the 1990s, a hardware aberration corrector for an electron microscope was successfully developed by Haider et al. [10] and became available in the early 2000s as an image-aberration corrector for a TEM and probe-aberration corrector for a scanning transmission electron microscope (STEM). For electron holography, the image-aberration corrector is used for removing undesired phase shifts in image waves. A spherical-aberration (Cs)-corrector, which consists of hexapole doublet, adjusts wave aberrations of the image transfer optics in a TEM. By contrast, a chromatic-aberration (Cc)-corrector, which was developed in the TEAM project [11], corrects incoherent aberration due to energy spread of an accelerated electron beam. By using these hardware correctors, structure images of crystalline materials can be easily obtained at an atomic resolution. Sub-50-pm resolution has been achieved [12] in a specially designed TEM. Since the aberration correctors also work for observations of a specimen in a field-free (out of lens) space, high-resolution magnetic-field measurement was achieved. A spatial resolution of a few hundred pm has been reported [13] through Lorentz mode observation. When electron holography is used to detect object waves (i.e. exit waves passing through a specimen to be observed), object waves are transferred into image waves by modifying unnecessary phase shifts. In high-resolution imaging, the relation between the object wave |${{\varphi }}\left( {{{\boldsymbol r}}} \right)$| and image wave |${{\Psi }}\left( {{{\boldsymbol r}}} \right)$| is described by $$\begin{equation}{{\varphi }}\left( {{{\boldsymbol r}}} \right) = {{\Psi }}\left( {{{\boldsymbol r}}} \right) \otimes {\rm{FT}}\left[ {\exp \left[ {{\rm{i\chi }}\left( {{{\boldsymbol q}}} \right)} \right]} \right],\end{equation}$$(1) where |${\rm{\chi }}\left( {{{\boldsymbol q}}} \right)$| is the wave aberration of imaging optics as a function of Fourier space coordinate q. Symbol |$ \otimes $| and FT[ ] denote the convolution operator and Fourier transform, respectively. If a Cs-corrector makes χ(q) disappear, the relation becomes |${{\varphi }}\left( {{{\boldsymbol r}}} \right) = {{\Psi }}\left( {{{\boldsymbol r}}} \right)$|⁠. Therefore, |${{\varphi }}\left( {{{\boldsymbol r}}} \right)$| can be directly accessed through electron holography. In addition, amplitude and phase information of |${{\varphi }}\left( {{{\boldsymbol r}}} \right) $|can be gained at atomic resolution. Of course, as electron holography can give |${{\Psi }}\left( {{{\boldsymbol r}}} \right)$| and χ(q) through a posteriori aberration correction by using Eq. (1), an |${{\varphi }}\left( {{{\boldsymbol r}}} \right) $|may be obtained even without a hardware aberration corrector. However, such a corrector has many benefits regarding high-resolution imaging, which was discussed in detail by Lichte et al. [14]. Improvement of information limit The spatial resolution is finally determined by an information limit of the imaging optics. It cannot be corrected by a posteriori image processing. This means a hardware corrector is indispensable for observation at an extremely high spatial resolution. The envelope function |$E\left( {{{\boldsymbol q}}} \right)$| of the information transfer function is given by $$\begin{equation}E\left( {{{\boldsymbol q}}} \right) = {E_j}\left( {{{\boldsymbol q}}} \right) \cdot {E_D}\left( {{{\boldsymbol q}}} \right),\end{equation}$$(2) where |${E_j}\left( {{{\boldsymbol q}}} \right)$| is the envelope function of spatial coherence, and |${E_D}\left( {{{\boldsymbol q}}} \right)$| is the envelope function of the temporal coherence. These functions are described as follows. $$\begin{equation*}{E_j}\left( {{{\boldsymbol q}}} \right) = {\rm{exp}}\left[ { - {\pi ^2}{{{{\rm{\alpha }}_{\rm{c}}}^2} \over {{\lambda ^2}}}{{\left\{ {{{\partial \chi \left( {{{\boldsymbol q}}} \right)} \over {\partial {{{\boldsymbol q}}}}}} \right\}}^2}} \right], {\rm{and}}\end{equation*}$$ $$\begin{equation*}{E_D}\left( {{{\boldsymbol q}}} \right) = {\rm{ exp}}\left[ { - {1 \over 2}{\pi ^2}{\lambda ^2}{\sigma _{fs}}^2{{{{\boldsymbol q}}}^4}} \right].\end{equation*}$$ Here, |${{\rm{\alpha }}_{\rm{c}}}$| is the illumination beam semi-angle, |$\lambda $| is the wavelength, and |${\sigma _{fs}}$| is the focus spread. In a Cs-corrected TEM, the gradient |$\chi \left( {{{\boldsymbol q}}} \right)$| vanishes by aberration correction, resulting in |${E_j}\left( {{{\boldsymbol q}}} \right) = 1$|⁠. In the case that the information limit is only determined by the temporal coherence, |${E_D}\left( {{{\boldsymbol q}}} \right)$| is characterized by the focus spread |${\sigma _{fs}}$|⁠, $$\begin{equation}{\sigma _{fs}} = {C_c}{\left[ {{{\left( {{f_r}{{\Delta E} \over {e{V_{acc}}}}} \right)}^2} + {{\left( {{f_r}{{\Delta {V_{acc}}} \over {{V_{acc}}}}} \right)}^2} + {{\left( {F{{\Delta {I_{OBJ}}} \over {{I_{OBJ}}}}} \right)}^2}} \right]^{1/2}},\end{equation}$$(3) where |$\Delta E$| is the energy spread of the electron beam, |${V_{acc}}$| is the acceleration voltage, |${I_{OBJ}}$| is the objective lens current, |${f_r}$| is a relativistic correction factor depending on |${V_{acc}}$|⁠, and |$F$| is a constant from 1 to 2 depending on the magnetic saturation of the objective lens. If the Cc-corrector vanishes |${{{C}}_{{c}}}$| constant, |${E_D}\left( {{{\boldsymbol q}}} \right) = 1$| and the information dumping by temporal incoherence disappears. This effect can be also applied in a posteriori processing, but has not yet been experimentally observed. Enhancement of signal When the information limit is extended, the opening of the imaging aperture can be expanded. This means that electrons scattered into larger angles can contribute to Ψ(r). Therefore, a hardware corrector provides the increase in signals regarding the atomic phase shifts in Ψ(r). Fig. 7 Open in new tabDownload slide Detail image of reconstructed amplitude and phase, and simulation image of GaN-foil with thickness 3.2 nm. Phase detail image is from same position as amplitude detail image. (Reprinted from Fig. 20 of Ultramicroscopy (2014) 147, 33). Fig. 7 Open in new tabDownload slide Detail image of reconstructed amplitude and phase, and simulation image of GaN-foil with thickness 3.2 nm. Phase detail image is from same position as amplitude detail image. (Reprinted from Fig. 20 of Ultramicroscopy (2014) 147, 33). Fig. 8 Open in new tabDownload slide TEM image (left, gray scale) and magnetic flux image (right, colored) of CoFeB/Ta multilayer. Magnetic flux displayed by cosine of phase ϕM amplified 600 times (cos600ϕM) with smoothing over length scale of 1.43 nm parallel to CoFeB layer. Constant flux of h/600e flows between adjacent contour lines. Color wheel at bottom-right corner indicates direction of magnetic flux [24]. Fig. 8 Open in new tabDownload slide TEM image (left, gray scale) and magnetic flux image (right, colored) of CoFeB/Ta multilayer. Magnetic flux displayed by cosine of phase ϕM amplified 600 times (cos600ϕM) with smoothing over length scale of 1.43 nm parallel to CoFeB layer. Constant flux of h/600e flows between adjacent contour lines. Color wheel at bottom-right corner indicates direction of magnetic flux [24]. Fig. 9 Open in new tabDownload slide Three-dimensional observation of magnetic vectors in stacked ferromagnetic discs observed by dual-axis 360-degree rotation tomography holder and high voltage electron holography. Upper and lower showed counter clockwise magnetizations. At the center of the discs, the opposite directional vortex cores were observed [25]. Fig. 9 Open in new tabDownload slide Three-dimensional observation of magnetic vectors in stacked ferromagnetic discs observed by dual-axis 360-degree rotation tomography holder and high voltage electron holography. Upper and lower showed counter clockwise magnetizations. At the center of the discs, the opposite directional vortex cores were observed [25]. Enhancement of signal resolution The smallest phase difference |$\delta \varphi $| detectable between two adjacent pixels reconstructed from hologram fringes (i.e. signal resolution) is generally given by $$\begin{equation}\delta \varphi = {{\sqrt 2 snr} \over {C\sqrt N }},\end{equation}$$(4) where |${{C}}$| is the fringe contrast, |$N$| is the number of electrons collected in the hologram per subsequently reconstructed pixel of the reconstructed wave, and snr is a constant value indicating the signal-to-noise ratio at which one wants to measure. A wider imaging aperture available by a hardware corrector increases the number of signals, resulting in reduced |$\delta \varphi $|⁠. If shortening the detection time while maintaining N, C should increase because of the reduction in the vibration of the biprism and external disturbances. This may also reduce |$\delta \varphi $|⁠. Therefore, the signal resolution in electron holography improves using a hardware aberration corrector. Practical atomic-resolution electron holography with an aberration-corrected electron microscope was reported by Linck et al. [15]. A demonstration was carried out on the FEI Titan 80 to 300 TEM equipped with a high-brightness Schottky field emitter (XFEG), and CEOS hexapole corrector. They observed holograms of gold atom columns in a very thin foil. Although the amplitude and phase of |${{\Psi }}\left( {{{\boldsymbol r}}} \right){\rm{s}}$| were reconstructed from an aberration-corrected hologram, residual aberrations from the objective lens and the Cs-corrector were still remained, and they were removed by a posteriori numerical correction, i.e. multiplication of a phase plate in reciprocal space. Finally, the quantitative phase image of gold atom columns with one to five atoms became clearly discernible at one-Angstrom resolution (Fig. 6). As the phase shift did not increase in perfect equi-phase steps due to dynamic interaction, phase intensity of six to seven atoms per column were no longer directly related to the column weight at 300-kV electron energy. For the practical acquisition setup of an atomic-resolution hologram, Genz et al. [16] discussed the optimization of double biprism interferometry, first developed by Harada et al. [17], for significantly reducing biprism-induced artifacts. The biprism vibration, yielding the most stable imaging conditions with lowest over all fringe contrast damping, was estimated. They used the FEI Titan 80 to 300 Berlin Holography Special TEM at an acceleration voltage of 300 kV and showed atomic-resolution images of the amplitude and phase of a GaN foil with a thickness of 3.2 nm (Fig. 7). In comparison with simulations, the amplitude and phase images had the same grey scaling, demonstrating good quantitative match as a consequence of the improved stability. An absolute scale match between experiment and simulation in atomic-resolution electron holography was very important for quantitative analysis. Winkler et al. [18] attempted to obtain unknown experimental parameters determined directly from the recorded electron wave function using an automated numerical algorithm. They showed that the local thickness and tilt of a pristine thin WSe2 flake could be measured uniquely, whereas some electron optical aberrations could not be determined unambiguously for a periodic object. The ability to determine local-specimen and imaging parameters directly from electron wave functions was of great importance for quantitative studies of electrostatic potentials in nanoscale materials. For improving the snr of phase images, an automated hologram acquisition system was recently developed for collecting a vast number of atomic resolution holograms [19]. The 1024 holograms of a gold particle at different positions on a specimen were collected with a slight defocus in about 1 hour (1 sec exposure per image). Particle-size dependency on the mean inner potential was demonstrated with an acceptable snr. In the near future, this technique will be combined with artificial intelligence (AI) technologies for classifying a huge amount of hologram data, automatic image alignment, and averaging of a large number of phase and amplitude images. Magnetic field measurement is another important application of electron holography. An electron microscope with a field-free specimen stage is necessary not to destroy the magnetic remanent state. A specimen is set at out-of-lens position, and the spatial resolution is generally nanometer order [20, 21]. However, with a hardware aberration corrector, the information limit dramatically improves and sub-nm magnetic measurement is possible. Snoeck et al. [22] developed the dedicated Hitachi HF3300C microscope ‘I2TEM’ with a 300-kV cold FEG, a multi-biprism, two specimen stages, and the Cs-corrector ‘B-COR’ from CEOS. One of the two stages is located in a field-free space, at which the spatial resolution of 0.5 nm is attained for Lorentz observation. Using this microscope, Gatel et al. [23] reported the different spin configurations in the vicinity of a single domain/vortex transition in isolated magnetic nanoparticles. They established the ‘magnetic configurations vs. size’ phase diagram of Fe single-crystalline nanocubes and revealed the size range of the transition between single-domain and vortex states for Fe nanocubes. In 2014, Hitachi developed a 1.2-MV atomic-resolution holography electron microscope equipped with a magnetic-field-superimposed cold FE gun, two specimen stages, two objective lenses, a double-biprism interferometer and hardware Cs-corrector from CEOS. The spatial resolution for high-resolution observation reached 43 pm [12]. In the Lorentz observation mode at a field-free position, crossing fringes of 0.235-nm lattice-spacing in gold thin foil were visualized [13], and Tanigaki et al. [24] successfully observed 0.67-nm magnetic information in a CoFeB/Ta multilayer by electron holography (Fig. 8). They observed the magnetic field in each layer by using a pulse magnetization system and analyzed the magnetization reduction due to intermixing between layers. In the magnetic field-free position of this ultra-high voltage electron microscope, a wide space around the sample can be used. This made it possible to observe the magnetic vortex three-dimensionally (Fig. 9) using dual-axial tomography [25]. That research indicated that high-voltage and high-resolution electron holography can be widely applied to pinpoint magnetization analysis with structural and composition information in materials science. Conclusions Electron holography was originally invented by Gabor to improve spatial resolution of electron microscopes. Its capability for analyzing wave-optical properties allows access to electric and magnetic fields in materials. After significant challenges to improve spatial resolution, state-of-the-art high-resolution electron holography has the ability to directly gain amplitude and phase information of materials at atomic resolution. In spite of the fact that coherent aberrations can be corrected by a posteriori image processing of the reconstructed image wave, an aberration corrector in a TEM used for recording the hologram substantially improves the performance of electron holography. By comparison of experimental data with simulation analyses, quantitative atomic information can be accessible with high precision. High-resolution holography will move on to the next step of improving signal resolution by being integrating with AI technologies. 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TI - Holography: application to high-resolution imaging
JF - Microscopy
DO - 10.1093/jmicro/dfaa050
DA - 2021-02-01
UR - https://www.deepdyve.com/lp/oxford-university-press/holography-application-to-high-resolution-imaging-7iUrht0mSC
SP - 39
EP - 46
VL - 70
IS - 1
DP - DeepDyve
ER -