Abstract: By combining statistical parameter estimation and model-order selection using a Bayesian framework, the maximum a posteriori (MAP) probability rule is proposed in this chapter as an objective and quantitative method to detect atom columns from high-resolution scanning transmission electron microscopy (HRSTEM) images. The validity and usefulness of this approach is demonstrated to both simulated and experimental annular dark-field (ADF) STEM images, but also to simultaneously acquired annular bright-field (ABF) and ADF STEM image data.

Abstract: An efficient model-based estimation algorithm is introduced to quantify the atomic column positions and intensities from atomic-resolution (scanning) transmission electron microscopy ((S)TEM) images. This algorithm uses the least squares estimator on image segments containing individual columns fully accounting for overlap between neighboring columns, enabling the analysis of a large field of view. To provide end-users with this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license. In this chapter, this efficient algorithm is applied to three different nanostructures for which the analysis of a large field of view is required.

Abstract: The maximum a posteriori (MAP) probability rule for atom column detection can also be used as a tool to evaluate the relation between scanning transmission electron microscopy (STEM) image quality and atom detectability. In this chapter, a new image-quality measure is proposed that correlates well with atom detectability, namely the integrated contrast-to-noise ratio (ICNR). Furthermore, the working principle of the MAP probability rule is described in detail showing a close relation to the principles of model-selection methods.

Abstract: In this chapter, the principles of detection theory are used to quantify the probability of error for atom counting from high-resolution scanning transmission electron microscopy (HRSTEM) images. Binary and multiple hypothesis testing have been investigated in order to determine the limits to the precision with which the number of atoms in a projected atomic column can be estimated. The probability of error has been calculated when using STEM images, scattering cross-sections or peak intensities as a criterion to count atoms. Based on this analysis, we conclude that scattering cross-sections perform almost equally well as images and perform better than peak intensities. Furthermore, the optimal STEM detector design can be derived for atom counting using the expression of the probability of error. We show that for very thin objects the low-angle annular dark-field (LAADF) regime is optimal and that for thicker objects the optimal inner detector angle increases.

Abstract: Recent studies in which X-ray beams of macroscopic to (sub) microscopic dimensions were used for non-destructive analysis and characterization of pigments, paint micro samples and/or entire paintings by Vincent van Gogh are concisely reviewed. The overview presented encompasses the use of laboratory and synchrotron radiation-based instrumentation and deals with the use of several variants of X-ray fluorescence (XRF) as a method of elemental analysis and imaging as well as with the combined use of X-ray diffraction (XRD) and X-ray absorption spectroscopy (XAS). Microscopic and macroscopic XRF are variants of the method that are well suited to visualize the elemental distribution of key elements, mostly metals, present in paint multi layers, either on the length scale from 1–100 μm inside micro samples taken from paintings or on the 1–100 cm length scale when the (subsurface) distribution of specific pigments in entire paintings is concerned. In the context of the characterization of van Gogh's pigments subject to natural degradation, the use of methods limited to elemental analysis or imaging usually is not sufficient to elucidate the chemical transformations that have taken place. However, at synchrotron facilities, combinations of μ-XRF with related methods such as μ-XAS and μ-XRD have proven themselves to be very suitable for such studies. Their use is often combined with microscopic Fourier transform infra-red (μ-FTIR) spectroscopy since this method delivers complementary information at more or less the same length scale as the X-ray microprobe techniques. Also in the context of macroscopic imaging of works of art, the complementary use of X-ray based and infra-red based imaging appears very promising; some recent developments are discussed.

Abstract: Historical glass, especially non-durable mediaeval glass, can undergo corrosion. This sometimes results in the formation of dark-coloured manganese-rich inclusions or stains that reduce the transparency of the glass. A conservation treatment with reducing or chelating agents may be considered with the aim of improving the transparency. In this paper, high-resolution desktop microcomputed tomography (µCT) is used in combination with element-specific twodimensional imaging methods for in situ monitoring of manganese removal by hydroxylamine hydrochloride from an archaeological stained-glass sample suffering from manganese browning and from artificially corroded model glass samples. µCT also proved itself useful for the study of the (re-)penetration of manganese into the gel layer during artificial corrosion of a model glass.