In high resolution electron off-axis holography, the complete information about amplitude and phase of the complex electron image wave is captured in a single hologram, fed to a computer, numerically reconstructed, and analyzed using methods of wave optical image processing. Specifically, the blurring effect due to the aberration of the objective lens of the electron microscope is corrected under reconstruction.The presented first results, achieved with a Philips CM30FEG electron microscope specially developed for the needs of high resolution electron holography, reveal that the point resolution of modern electron microscopes is significantly improved.PACS numbers: 42.30.Rx, In contrast to the light optical case, in electron microscopy the lateral resolution is not limited by the diffraction error, i.e. , by the wavelength of the electrons, but instead is governed by the spherical aberration of the objective lens. As shown by Scherzer [1] already in 1936, this error cannot be avoided as long as common rotational symmetric lens designs are used. For example, in the case of the Philips CM30FEG high resolution electron microscope applied in this work, the best point resolution is 0.198 nm, about 2 orders of magnitude worse than the diffraction limit of the A = 1.98 pm wavelength, 300 keV electrons.In electron microscopy we deal with a complex electron wave o(r) = a(r) exp[i'(r)] modulated in both amplitude and phase due to the interaction with the object. During the imaging process from this object wave to the recordable image wave, the aberrations of the objective lens lead to a blurring of the available information.The backpropagation from the aberration-corrupted image wave b(r) = A(r) exp[i@(r)] to the level of the object is possible following the wave laws given by the Kirchhoff diffraction integral. Prerequisites are the registration of the image wave amplitude and phase as well as a sufhcient knowledge of the lens aberrations. This approachcalled holography -was proposed by Gabor already in 1948 [2] but it took nearly 50 years until electron holography finally achieved this goal. From the various forms of electron holography [3] under investigation, the off-axis technique has proven to be most promising [4]. Using a Moellenstedt biprism, the image wave is coherently superimposed with a plane reference wave, and the resulting interference pattern -the hologram -reveals a cosinusoidal intensity distribution, I(r) = 1 + A(r) + 2A(r) cos(2rrq, . r + &b(r)). (1)

It is demonstrated that energy-filtered transmission electron microscope enables following of in situ changes of the Ca-L2,3 edge which can originate from variations in both local symmetry and bond lengths. Low accelerating voltages of 20 and 40 kV slow down radiation damage effects and enable study of the start and finish of phase transformations. We observed electron beam-induced phase transformation of single crystalline calcite (CaCO3) to polycrystalline calcium oxide (CaO) which occurs in different stages. The coordination of Ca in calcite is close to an octahedral one streched along the <111> direction. Changes during phase transformation to an octahedral coordination of Ca in CaO go along with a bond length increase by 5 pm, where oxygen is preserved as a binding partner. Electron loss near-edge structure of the Ca-L2,3 edge show four separated peaks, which all shift toward lower energies during phase transformation at the same time the energy level splitting increases. We suggest that these changes can be mainly addressed to the change of the bond length on the order of picometers. An important pre-condition for such studies is stability of the energy drift in the range of meV over at least 1 h, which is achieved with the sub-Ångström low-voltage transmission electron microscope I prototype microscope.

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