Summary We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin‐image problem of in‐line holography and is capable of analysing data obtained using X‐ray microscopy, electron microscopy, neutron microscopy or visible‐light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non‐iterative and computationally efficient method is applied to data obtained using an X‐ray phase contrast ultramicroscope.

With controlled nanometre-sized pores and surface areas of thousands of square metres per gram, metal-organic frameworks (MOFs) may have an integral role in future catalysis, filtration and sensing applications. In general, for MOF-based device fabrication, well-organized or patterned MOF growth is required, and thus conventional synthetic routes are not suitable. Moreover, to expand their applicability, the introduction of additional functionality into MOFs is desirable. Here, we explore the use of nanostructured poly-hydrate zinc phosphate (α-hopeite) microparticles as nucleation seeds for MOFs that simultaneously address all these issues. Affording spatial control of nucleation and significantly accelerating MOF growth, these α-hopeite microparticles are found to act as nucleation agents both in solution and on solid surfaces. In addition, the introduction of functional nanoparticles (metallic, semiconducting, polymeric) into these nucleating seeds translates directly to the fabrication of functional MOFs suitable for molecular size-selective applications.

In-line phase contrast enables weakly absorbing specimens to be imaged successfully with x-rays, and greatly enhances the visibility of fine scale structure in more strongly absorbing specimens. This type of phase contrast requires a spatially coherent beam, a condition that can be met by a microfocus x-ray source. We have developed an x-ray microscope, based on such a source, which is capable of high resolution phase-contrast imaging and tomography. Phase retrieval enables quantitative information to be recovered from phase-contrast microscope images of homogeneous samples of known composition and density, and improves the quality of tomographic reconstructions.

SummaryWe outline a new approach to X-ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high-brightness field-emission gun (FEG)-based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 µ m and have demonstrated novel features such as: (i) phase-contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy-resolved imaging to simultaneously produce multiple quasi-monochromatic images using broad-band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude-retrieval algorithms to enable new real-time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object-plane information from intermediate-field images, unlocking the potentially greater contrast and resolution of the intermediatefield regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.