Because the refractive index for hard x rays is slightly different from unity, the optical phase of a beam is affected by transmission through an object. Phase images can be obtained with extreme instrumental simplicity by simple propagation provided the beam is coherent. But, unlike absorption, the phase is not simply related to image brightness. A holographic reconstruction procedure combining images taken at different distances from the specimen was developed. It results in quantitative phase mapping and, through association with three-dimensional reconstruction, in holotomography, the complete three-dimensional mapping of the density in a sample. This tool in the characterization of materials at the micrometer scale is uniquely suited to samples with low absorption contrast and radiation-sensitive systems.

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Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays.

The crystal structure of the β′ phase in Al–Mg–Si alloys

Low energy electron microscopy (LEEM) is a surface imaging technique in which the surface is illuminated by an approximately parallel electron beam at near normal incidence. The image is formed with those electrons which are elas- tically backscattered into a small angular region around the surface normal. The limitation to a small angular region is necessary because of the large aberrations of the objective lens which produces the primary image. This lens is a so-called cathode lens which not only has imaging properties but at the same time decelerates the fast electrons of the illuminating beam to the desired low energy at the specimen and re-accelerates the backscattered electrons to high energies again. In order to achieve this, the specimen is at a high negative potential which differs from the potential of the emitter of the electron gun of the illumination system by V 0 = E 0/e, where E 0 is the energy of the electrons at the specimen. Typical energy values are E = eV = 15−20 keV for the fast electrons and 0 < E 0 < 50 eV at the specimen. There are three fundamental quantities which are important in LEEM: resolution, intensity and contrast. These will be discussed in Sect. 12.1. Section 12.1 also describes how LEEM can be combined with other surface characterization techniques, such as low energy electron diffraction (LEED), photoemission electron microscopy (PEEM) and other emission microscopies. Section 12.2 illustrates the applications of LEEM and of the associated techniques to the study of clean surfaces, while Sect. 12.3 presents examples of the power of LEEM in the study of surface layers. Section 12.4 gives an outlook for possible future developments. A brief summary (Sect. 12.5) concludes this chapter.

https://iopscience.iop.org/article/10.1088/0034-4885/57/9/002/pdf

Low energy electron microscopy

Since the middle of the 1990s, X-ray phase imaging including phase tomography has been attracting increasing attention. The advantage of X-ray phase imaging is that an extremely high sensitivity is achieved for weak-absorbing materials, such as biological soft tissues, which generate a poor contrast by conventional methods. Medical and biological imaging is the main target of X-ray phase imaging, and several trials using synchrotron radiation sources and laboratory sources have been made. Measuring and controlling the X-ray phase are also significant for X-ray microscopy with a high spatial resolution, and innovative techniques are attracting intense interest. The progress of X-ray phase imaging is supported by the developments in X-ray sources such as third-generation synchrotron radiation sources, optical elements, and image detectors. This article describes the advantages of using X-ray phase information and reviews various techniques studied for X-ray phase imaging.

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Recent Advances in X-ray Phase Imaging

Using an imaging mode based on the adjustment of a negative value of the spherical-aberration coefficient of the objective lens of a transmission electron microscope, we successfully imaged all types of atomic columns in the dielectric SrTiO3 and the superconductor YBa2Cu3O7. In particular, we were able to view the oxygen atoms which, due to their low scattering power, were not previously accessible, and this allowed us to detect local nonstoichiometries or the degree of oxygen-vacancy ordering. This technique offers interesting opportunities for research into oxides, minerals, and ceramics. In particular, this holds for the huge group of perovskite-derived electroceramic materials in which the local oxygen content sensitively controls the electronic properties.

/pdf/atomic-resolution-imaging-of-oxygen-in-perovskite-ceramics-2c75guo3a9.pdf

Atomic-resolution imaging of oxygen in perovskite ceramics.

The use of a coherent field-emission electron source in transmission electron microscopy is combined with phase retrieval by digital processing of a focal image series. For the first time, a dramatic improvement of the high-resolution performance of the electron microscope beyond the usual ``point-to-point'' resolution has been realized: Experiments on a 200-kV microscope with a point resolution of 0.24 nm reveal reconstructed information down to 0.14 nm. Examples are shown in the field of high-${\mathit{T}}_{\mathit{c}}$ superconductors and ferroelectric oxides. The oxygen sublattice in these structures is revealed.

/pdf/phase-retrieval-through-focus-variation-for-ultra-resolution-43ff9pl81p.pdf

Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy.

In this paper we give the proof of principle of a new experimental method to determine the aberrations of an optical system in the field. The measurement is based on the observation of the intensity point spread function of the lens. To analyze and interpret the measurement, use is made of an analytical method, the so-called extended Nijboer-Zernike approach. The new method is applicable to lithographic projection lenses, but also to EUV mirror systems or microscopes such as the objective lens of an optical mask inspection tool. Phase retrieval is demonstrated both analytically and experimentally. Theory and experimental results are given.

Guido C.A.M. Janssen

Papers

Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy.

Characterization of a projection lens using the extended Nijboer-Zernike approach