Peter Robert Miller

Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object

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.

X-ray phase-contrast microscopy and microtomography

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.

Quantitative X‐ray projection microscopy: phase‐contrast and multi‐spectral imaging

We 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 µm 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 intermediate‐field 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.

Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging

Simple analytical expressions are derived for the spatial resolution, contrast and signal-to-noise in X-ray projection images of a generic phase edge. The obtained expressions take into account the maximum phase shift generated by the sample and the sharpness of the edge, as well as such parameters of the imaging set-up as the wavelength spectrum and the size of the incoherent source, the source-to-object and object-to-detector distances and the detector resolution. Different asymptotic behavior of the expressions in the cases of large and small Fresnel numbers is demonstrated. The analytical expressions are compared with the results of numerical simulations using Kirchhoff diffraction theory, as well as with experimental X-ray measurements.

Generation and absorption of characteristic X-rays under dynamical electron diffraction conditions

Abstract The theory for formation of incoherent channelling patterns (ICPs), produced by variations in characteristic X-ray emission in response to a systematic scan in the direction of the incident electron beam for orientations near a zone axis, is extended to account for absorption of X-rays within the specimen. This is achieved by calculating the probability of X-ray generation as a function of depth within a crystal prior to the inclusion of an absorptive term which is dependent on the geometry of the X-ray detector relative to the crystal as well as the absorption characteristics of the specimen for the particular X-ray energy. ICPs from three major zones of the L1 0 phase in Ti Al and Ti Ga alloys are compared and effects of different absorption due to variation of goniometer tilt with respect to the X-ray detector are calculated. Although fast electron quantum states that are peaked on Ti atomic sites have similar eigenvalues (binding energies) in both alloys, it is shown that differences in complex eigenvalues (including absorption) occur between states that are localized on Al or Ga, and that this results in substantially different contrast between the two alloys in ICPs from Al and Ga characteristics X-rays.

Software image alignment for X-ray microtomography with submicrometre resolution using a SEM-based X-ray microscope.

Improved X‐ray sources and optics now enable X‐ray imaging resolution down to ∼50 nm for laboratory‐based X‐ray microscopy systems. This offers the potential for submicrometre resolution in tomography; however, achieving this resolution presents challenges due to system stability. We describe the use of software methods to enable submicrometre resolution of approximately 560 nm. This is a very high resolution for a modest laboratory‐based point‐projection X‐ray tomography system. The hardware is based on a scanning electron microscope, and benefits from inline X‐ray phase contrast to improve visibility of fine features. Improving the resolution achievable with the system enables it to be used to address a greater range of samples.

X-ray ultramicroscopy using integrated sample cells.

The X-ray ultramicroscope (XuM), based on using a scanning electron microscope as host, provides a new approach to X-ray projection microscopy. The right-angle-type integrated sample cells described here expand the capabilities of the XuM technique. The integrated sample cell combines a target, a spacer, a sample chamber, and an exit window in one physical unit, thereby simplifying the instrumentation and providing increased mechanical stability. The XuM imaging results presented here, obtained using such right-angle integrated sample cells, clearly demonstrate the ability to characterize very small features in objects, down to of order 100nm, including their use for dry, wet and even liquid samples.

Laboratory-based x-ray micro-tomography with submicron resolution

X-ray Microtomography bridges the 3D analysis gap between conventional x-ray tomography and TEM tomography. The use of a laboratory-based microfocus source opens up the opportunity to gain additional benefits from in-line phase contrast for enhancing the visibility of fine features, cracks, voids and boundaries in individual views. Coupled with phase retrieval methods, such images can be used as input to conventional reconstruction algorithms for three dimensional visualization. Working at high resolution brings challenges of physical stability of the system. Software approaches to overcoming these difficulties have enabled submicron resolution 3D reconstructions.