## 3 Diffuse Reflectance Spectroscopy: Analyzing Results
### Example Materials  
Diffuse reflectance spectra were measured with different batches of rutile-TiO\({}_{2}\) and YAG:Ce using the white standard _CR30F_ (cf. Figure 7). In addition to a nominally pure TiO\({}_{2}\) powder sample, we also inspected the spectra of a considerably contaminated TiO\({}_{2}\) powder sample. The latter has been  
Figure 6: Comparison of the diffuse reflectance of different aluminum oxide powder pellets with equal thickness and constant excitation intensity. All diffuse reflectance have been scaled by the maximum signal of _CR30F_. prepared following a different synthesis route and, most probably, a contamination appeared due to steel abrasion from one of the powder crucibles and/or the presence of residual oil. This sample will be used to highlight the impact of deviations of the optical quality via direct comparison with the spectra obtained for the nominally pure TiO\({}_{2}\) reference sample. Evidently, measurements are highly reproducible as demonstrated by the three diffuse reflectance spectra of the impure TiO\({}_{2}\) sample which deviate no more than 0.01 in the VIS in relation to a common mean (cf. Figure 7b). In contrast to nominally pure TiO\({}_{2}\), the overall diffuse reflectance is attenuated by approximately 0.25 for VIS wavelengths, concluding the influence of the spectrally flat contaminant. Because the diffuse reflectance is highly sensitive to even small contaminations [1], DRS thus offers a precise tool for detecting such impurities. Furthermore, even small fluctuations in the diffuse reflectance spectrum can point towards notable features. These features can be amplified by taking the first or second derivative of the spectrum [15]. Towards the electronic band gap, the diffuse reflectance drops for wavelengths below 410 nm and approaches a common value of 0.08 for both TiO\({}_{2}\)-samples. This finding is in line with related studies [84; 85; 86; 87] and shows that, even for interband transitions, a fraction of the incoming light is backscattered. In contrast to TiO\({}_{2}\), YAG:Ce possesses a vastly different diffuse reflectance spectrum. The Ce\({}^{3+}\) absorption band at approximately 460 nm induced by its \({}^{2}\)F\({}_{5/2}\to 5d_{1}\) electronic transition [88; 89] dominates the otherwise high diffuse reflectance which rivals that of the used white standard above 550 nm. Even in the center of this absorption band, the diffuse reflectance does not fall below \(\approx\)0.1, once again underlying the material-specific interplay between absorption and scattering. A second absorption dip of the diffuse reflectance in the UV below 370 nm indicates the onset of the \({}^{2}\)F\({}_{5/2}\to 5d_{2}\) transition of Ce\({}^{3+}\)[88; 89]. A common feature for all investigated samples is an increase of noise beyond 800 nm due to an overall weak signal as indicated by the white standard evaluations (cf. Section 3.1, Figure 6). Furthermore, an elevation of the diffuse reflectance at 700 nm is observed in all measurements. Based on additional scans with other substances and white standards, this peak can be attributed to a small absorption of the _CR30F_\(\alpha\)-Al\({}_{2}\)O\({}_{3}\) white standard. Comparative studies using TiO\({}_{2}\) against different white standards clearly reveal a dependence of the local increase of diffuse reflectance at 700 nm on the choice of reference material as evident in Figure 8.  
Figure 7: **(a)** Diffuse reflectance spectra of contaminated and nominally pure TiO\({}_{2}\) as well as YAG:Ce against the white standard _CR30F_. The contaminated sample was scanned three times to highlight the reproducibility of the measurement. Note: The spectral bumps around 700 nm arise from an artifact and will be explained in the accompanying text. **(b)** Absolute deviation of the three contaminated TiO\({}_{2}\) scans from their mean value. As larger grain sizes entail an increased optical path length through the pellet, small residual material absorbances appear more pronounced and thus give rise to a reduced diffuse reflectance.