Make it connected! 2D close-packed layers of inorganic nanoparticles are interconnected by organic fibrils of oleic acid as clearly visualized by electron holography. These fibrils can be mineralised by PbS to transform an organic-inorganic framework to a completely interconnected inorganic semiconducting 2D array.

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Off-axis electron holography provides access to the complete complex image wave hence opens up the opportunity for numerical aberration correction [1]. This allowed "aberration-free imaging" several years before Cs-correctors became commonly accessible for atomic resolution analysis. However, especially at high lateral resolution, the limited signal resolution in the holographically reconstructed wave was not sufficient to apply holography to materials science questions. It was the Cs-corrector that pushed the atomic resolution holography performance beyond hitherto existing limits [2]. Nowadays, off-axis holography, applied in a state-of-the-art aberration-corrected TEM, offers an amazing signal resolution at lateral atomic resolution: Recently, from a single hologram a phase detection limit of 2π/300 was reported, which is close to the phase shift of a single hydrogen atom [3]. The improvement of the holographic performance with respect to lateral resolution and signal resolution is not the Cs-corrector's only benefit to electron holography: The attainable lateral resolution given by the spacing of the hologram fringes and the field of view determined by the hologram width cannot be selected independently, since they are inversely connected with each other by the biprism optics hence have to fulfill several requirements. Therefore, the range of holographic setups within a single TEM is strictly limited. In particular, the sampling of the interference fringes puts very severe constraints on the total magnification of the TEM, so that a wide range of magnifications cannot be used for the holographic recording. This can be solved by the aberrationcorrector: As an electron optical add-on with additional lenses, the Cs-corrector opens up a variety of new holographic setups. In our Cs-corrected Tecnai F20-TEM, we achieved a series of holographic setups ranging from fields of view of only a few nanometers at atomic resolution up to even a few microns at corresponding lower resolution. The milestone therein is a continuous magnification series of holographic setups. As an additional highlight, the Cs-corrector is used as an aberration-corrected "pseudo Lorentz Lens" within a part of this series. This allows investigating magnetic specimens without the magnetic field related to the high-resolution objective lens, and furthermore without the giant spherical aberration of the conventional Lorentz Lens. All in all, the aberration corrector enables a comprehensive holographic analysis at nearly all magnifications within one single TEM column. As an example, Fig. 1 shows a partial magnification series of holographically reconstructed object waves of a carbon grid with Gold-shaded latex spheres. The different holographic setups range from a field of view of microns down to few nanometers with atomic resolution. References[1] M.

The phase loss encountered in conventional (S)TEM means a substantial loss of object information, because essential structure components, e.g. electric and magnetic fields, mainly modulate the image phase hence are virtually invisible in a conventional micrograph. This presents a huge obstacle for a thorough understanding of modern functional materials e.g. in semiconductors and nano-magnetism. Phases can only be determined by interference of the image wave with a reference wave. Gabor's bright idea of holography was to use the interference pattern (hologram) as a diffraction grating, where one of the diffracted waves turns out a replica of the image wave. This replica wave is reconstructed from the hologram allowing subsequent quantitative evaluation of both amplitude and phase separately.Holography needs coherence between the image wave and the reference wave for recording the hologram. In electron holography, alas, the coherent current given by the brightness of the electron beam is severely restricted, and hence the intensity in a coherently illuminated area gives rise to signal/noise-problems. Furthermore, the hologram should be recorded in the object plane or a conjugate image plane, because otherwise the waves diffracted into larger angles hence carrying the information about fine details, end outside the coherent area, and hence are missing in the reconstructed wave. Up to now, Image Plane off-axis Electron Holography is the most powerful holographic method in electron microscopy.After improving the method´s performance, an increasing spectrum of applications has been reported from an increasing number of groups. The high quality allows investigating subtle details of the solid state such as the magnetization in nanoparticles, basics of superconductivity, electric fields and dopant distribution in semiconductors as well as the behavior of the charge carriers; at atomic resolution including a-posteriori aberration correction and fine-tuning, using an aberration-corrected TEM allows measuring atomic fields of single atoms, enabling to identify different atom species.Resolution comprises both lateral resolution and signal resolution; signal resolution means the smallest phase difference distinguishable between two adjacent reconstructed pixels. Both parts of resolution are in principle limited by the Quantum Noise found at certain degree of coherence, i.e., at the corresponding contrast of the hologram fringes. It turns out that lateral resolution and signal resolution are concatenated by means of the figure of merit InfoCont given by the quality of the TEM and the disturbance level in the lab. Concatenation is simply given as n rec  φ = InfoCont, with n rec the number of reconstructed pixels across the width w of the wave; by n rec = 2q res w, it links field of view w with lateral resolution q res . n φ is the number of phase steps distinguishable in the phase range of 2π; the phase detection limit follows as δφ lim = 2π/n φ . For example, at our FEI Tecnai F20 Cs-corr TEM operated in the Triebenberg-Lab, ...