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Janos Kirz and Michael Feser contributed to this chapter.
The first x-ray microscopes were one-of-a-kind instruments that were operated by their builders, in a tradition that continues to this day. Although there was a brief phase in the 1950s where commercial point-projection microscopes were available (see Section 6.2, and [Cosslett 1960, Plates IX.B and X]), up until the year 2000 essentially all microscopes were custom-built. These custom-built microscopes are now joined by commercial instruments offering a wide range of capabilities. No matter whether you are using a commercial instrument where you can pop a sample in and push a button to get an image, or a custom instrument, it is useful to understand what “makes it tick.” Hence this chapter. Section 7.1 discusses x-ray sources, while Section 7.2 discusses the optical transport systems and associated equipment needed to bring the x-ray beam to the imaging system. After some brief comments on nanopositioning systems in Section 7.3, the properties of several types of x-ray detectors are covered in Section 7.4. Finally, Section 7.5 provides a short introduction to specimen environments.
The degree of sophistication in modern x-ray microscopes is worth a moment's pause for thanks. It wasn't always so! What is available today makes the home-built system (Fig. 2.4) that the author first encountered look unbelievably crude, and at that point things had already made significant advances from earlier years [Kirz 1980c, Rarback 1980]. An amusing anecdote was presented by Arne Engström in 1980 [Engström 1980] as he looked back on four decades of work in x-ray microscopy:
Another trend in x-ray microscopy and x-ray microanalysis, especially in the field of the biomedical sciences, is the increasing sophistication and complexity of systems and equipment for the collection and treatment of experimental absorption data. However, this trend is not unique to this field of research. In fact, over the last 20 to 30 years there has been such a fantastic development of commercially available instrumentation for research and development that, in retrospect, the immediate post-war conditions seems very primitive indeed. For example, I remember the presentation of an automatic recording optical microabsorptiometer applicable to cellular analysis at an AAAS meeting in Boston in 1951.
Those who cannot remember the past are condemned to repeat it – George Santayana, Reason in Common Sense (Vol. 1 in The Life of Reason), 1905.
Janos Kirz contributed to this chapter.
Röntgen and the discovery of X rays
The words of discovery are rarely those of Archimedes’ legendary shout of “Eureka!” or “I have found it!” as he supposedly leaped naked from his bathtub (good thing there weren't webcams in those days!). Instead, the words of discovery are more likely to be along the lines of “hmm … that's odd.” Such is the case of the discovery of X rays [Glasser 1933, Mould 1993].
At the time of their discovery, many investigators were carrying out experiments with various types of cathode ray tubes, but it was only Wilhelm Conrad Röntgen, Professor and Director of the Physical Institute at the University of Würzburg, who noticed some curious phenomena and decided to investigate further. Röntgen was 50 years old at the time, with a reputation for care in experiments even though his research in the physics of gases and fluids was not particularly cutting-edge. Cathode rays (which we would now call electron beams) were all the rage at the time, so Röntgen decided to investigate whether they would exit thin-walled Hittorf–Crookes tubes. To make it easier to use a phosphor to try to observe this, he surrounded a tube with black paper and worked in a darkened room. While setting up the experiment late on a Friday afternoon (November 8, 1895), he noticed that the phosphor was flickering in synchrony with the fluctuations of the glowing filament in the tube – even though the phosphor was some distance away, and with black paper in between! The odd phenomena immediately captured Röntgen's attention to the point that he did not notice an assistant entering the room later on to retrieve some equipment. When Röntgen's wife Bertha finally succeeded in getting a servant to coax him upstairs to their apartment on the top floor of the Institute, Röntgen ate little of his supper and spoke even less before returning that evening to the puzzle in the lab.
Up until now we have concentrated on two-dimensional (2D) imaging of thin specimens. However, one of the advantages microscopy with X rays offers is great penetrating power. This means that X rays can image much thicker specimens than is possible in, for example, electron microscopy (as discussed in Section 4.10). For this reason, tomography (where one obtains 3D views of 3D objects) plays an important role in x-ray microscopy. There are entire books written on how tomography works [Herman 1980, Kak 1988], and on its application to x-ray microscopy [Stock 2008], so our treatment here will be limited to the essentials. Examples of transmission tomography images are shown in Figs. 12.1, 12.6, and 12.9, while fluorescence tomography is shown in Fig. 12.3.
Our discussion of x-ray tomography will be carried out using several simplifying assumptions:
• We will assume parallel illumination, even though there are reconstruction algorithms [Tuy 1983, Feldkamp 1984] for cone beam tomography where the beam diverges from a point source.
• We will assume that we start with images that provide a linear response to the projected object thickness t(x, y) along each viewing direction. In the case of absorption contrast transmission imaging, this can be done by calculating the optical density D(x, y) = - ln[I(x, y)/I0] = μt(x, y) as given by Eq. 3.83, with μ being the material's linear absorption coefficient (LAC) of Eq. 3.75. In phase contrast imaging, one may have to use phase unwrapping [Goldstein 1988, Volkov 2003] methods to first obtain a projection image which is linear with the projected object thickness since (see Fig. 3.17).
• We will assume that there is no spatial-frequency-dependent reduction in the contrast of image features as seen in a projection image. That is, we will assume that the modulation transfer function (MTF) is 1 at all frequencies u (see Section 4.4.7). One can always approach this condition by doing deconvolution (Section 4.4.8) on individual projection images before tomographic reconstruction, or building in an actual MTF estimate into optimization approaches (Section 8.2.1).
• We will assume that the first Born approximation applies (Section 3.3.4): we can approximate the wavefield that reaches a downstream plane in a 3D object as being essentially the same as the wavefield reaching an upstream plane.
This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.
Written by a pioneer in the field, this text provides a complete introduction to X-ray microscopy, providing all of the technical background required to use, understand and even develop X-ray microscopes. Starting from the basics of X-ray physics and focusing optics, it goes on to cover imaging theory, tomography, chemical and elemental analysis, lensless imaging, computational methods, instrumentation, radiation damage, and cryomicroscopy, and includes a survey of recent scientific applications. Designed as a 'one-stop' text, it provides a unified notation, and shows how computational methods in different areas are linked with one another. Including numerous derivations, and illustrated with dozens of examples throughout, this is an essential text for academics and practitioners across engineering, the physical sciences and the life sciences who use X-ray microscopy to analyze their specimens, as well as those taking courses in X-ray microscopy.