Abstract: Recent studies in which X-ray beams of (sub)micrometre to millimetre dimensions have been used for non-destructive analysis and characterization of pigments, minute paint samples and/or entire paintings from fifteenth to twentieth century artists are discussed. 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 with X-ray diffraction (XRD). Microscopic XRF (μ-XRF) is a variant of the XRF method able to visualize the elemental distribution of key elements, mostly metals, on the scale from 1 μm to 100 μm present inside multi-layered micro samples taken from paintings. In the context of the characterization of artists’ pigments subjected to natural degradation, in many cases the use of methods limited to elemental analysis or imaging does not suffice to elucidate the chemical transformations that have taken place. However, at synchrotron facilities, combinations of μ-XRF with related methods such as μ-XAS (microscopic X-ray absorption spectroscopy) and μ-XRD have proven themselves to be very suitable for such studies. Since microscopic investigation of a relatively limited number of minute paint samples may not yield representative information about the complete artefact they were taken from, several methods for macroscopic, non-invasive imaging have recently been developed. Combined macroscopic XRF/XRD scanning is able to provide a fairly complete overview of the inorganic pigments employed to create a work of art, to answer questions about ongoing degradation phenomena and about its authenticity. As such these newly developed non-invasive and highly specific imaging methods are of interest for many cultural heritage stakeholders.

Abstract: An approach using optical data to simulate both the bremsstrahlung continuum and characteristic K and L X-ray lines generated by low energy electrons (cfr. electron microscopy) in solids is discussed in this paper. The necessary analytical expressions together with the data to calculate the relevant cross sections for elastic and inelastic interactions at these energies along with variance reduction techniques are given. The results of the Monte Carlo simulation are compared to experimental data measured with a JEOL 6300 electron microscope.

Abstract: A new method to estimate case specific prediction uncertainty for univariate trilinear partial least squares (tri-PLS1) regression is introduced. This method is, from a theoretical point of view, the most exact finite sample approximation to true prediction uncertainty that has been reported up till now. Using the new method, different error sources can be propagated, which is an advantage that cannot be offered by data driven approaches such as the bootstrap. In a concise example, it is illustrated how the method can be applied. In the Appendix, efficient algorithms are presented to compute the estimates required.