## 2 Materials and Method
### Lateral and Axial Resolution
To study the influence of the confocal hole on the depth resolution, 13 hyperspectral Raman images of a fired CaO-SiO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\) ceramic (T\({}_{\text{max}}\) 1097 \({}^{\circ}\)C) were recorded at RT at the same location with a different confocal pinhole (100 to 1300 \(\upmu\)m). With decreasing pinhole, the depth resolution increases, but at the price of intensity loss (cf. Figures 5b and 9). Small rutile grains (purple) are clearly distinguishable within the Raman images recorded with a confocal hole of up to 400 \(\upmu\)m, whereas they appear to have \"grown\" together in images recorded with a larger confocal aperture (Figure 9). Furthermore, due to the overall lower intensity of the images recorded with a confocal hole smaller than 300 \(\upmu\)m most of the grain boundaries are blurry. As already shown in Figure 5b, the intensity decrease with decreasing confocal hole is linear over a large range with a slight kink at a confocal hole of 300 \(\upmu\)m. For our Raman system and the chosen instrumental settings, a confocal hole of 300 \(\upmu\)m appears to be the best compromise between sufficient intensity and spatial resolution. It is important to note that the axial resolution at the surface also depends on the absorption properties of the material investigated. To study this dependence, a series of hyperspectral Raman images of a fired ceramic (Kln\({}_{60}\)Qtz\({}_{15}\)Cal\({}_{25}\), T\({}_{\text{max}}\) 1097 \(\pm\) 5 \({}^{\circ}\)C) were recorded at different nominal depth (\(z\) drive) to investigate the effect of the laser focus on the quality and details of the image (inset of Figure 10). As expected, the intensity of the Raman bands of the individual phases decreases with increasing nominal depth (Figure 10). A Raman intensity loss of 20% to 40% is observed within the first ten micrometers, whereas within the first 20 \(\upmu\)m, which is a typical grain diameter, already about half of the intensity of the Raman bands is lost. At a depth of about 50 \(\upmu\)m, Raman signals from any of the analyzed phases are hardly detectable anymore due to strong absorption of the incident and scattered light. This is also reflected by the observation that the Raman images recorded at different nominal depths from the surface (\(z=0\)\(\upmu\)m) to a depth of \(z=-15\)\(\upmu\)m are very similar (Figure 11). As a matter of fact, the statistical variations of the average mineral fractions, obtained from all 16 images, are in the same order of magnitude of those that were estimated from multiple images that were recorded from the same area (volume) with identical focus (cf. Section 2.6.3). It follows that slight variations of the focus among different images (e.g., due to failing autofocus, shrinking or expansion of the sample during image acquisition) do not significantly affect the recorded mineral fractions and morphological details (e.g., the location of grain boundaries). Figure 10: Normalized intensities of the main Raman band of the respective phase at six x-y positions as a function of nominal depth (\(z=0\), focus at the sample surface). The data was extracted from 50 hyperspectral Raman images of a fired ceramic that were recorded at RT at a focal depth between 0 and \(-50\) μm (\(z\)-axis) with a step size of 1 μm (inset diagram) and a confocal hole of 300 μm. Figure 9: RT hyperspectral Raman images of a fired CaO-SiO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\) ceramic recorded with a different confocal pinhole. Note that images acquired with a pinhole smaller than 300 μm show the worst quality due to significantly lower band intensities, whereas with larger confocal pinholes morphological details get lost. For instance, the small rutile grains (purple) that are clearly distinguishable in those images recorded with a pinhole smaller than 400 μm are increasingly “grown” together and appear to be one single grain in the images recorded with a confocal pinhole larger than about 800 μm.