## 3 Diffuse Reflectance Spectroscopy: Analyzing Results
### Pitfalls and Artifacts
#### 3.3.1 Higher Order Diffraction  
Owing to potential higher order diffraction in gratings, e.g., the second order at half the center wavelength, the diffuse reflectance may be severely affected. Consequentially, appropriate spectral filtering is essential to minimize the influence of spurious wavelengths by such higher orders. Figure 9a exemplary shows the broadband spectrum after transmission through a monochromator before and after spectral filtering. Besides the desired signal at 700 nm, an additional peak at 350 nm can be clearly resolved. This disruptive peak can be eliminated via long-pass (LP) filters, yielding an unperturbed monochromatic spectrum.  
Even though the spurious signals are comparably low in relation to the desired wavelength, their effect on the diffuse reflectance can be dramatic. Figure 9b displays the diffuse reflectance of the same rutile-TiO\({}_{2}\) sample (against the same _CR30F_ white standard) with and without proper filtering after the excitation monochromator (cf. Figure 3).  
Apart from the band gap absorption below 410 nm, rutile shows a relatively homogeneous diffuse reflectance through the VIS up into the near infrared wavelength range. However, for excitation wavelengths above 680 nm, additional higher order diffraction signals impinge sample and standard alike when the LP filter is not inserted which yield a notable decrease of the measured diffuse reflectance. This loss can be attributed to the significant UV-absorption of TiO\({}_{2}\): For wavelengths \(\lambda>680\) nm the impinging spectrum contains a considerable UV component at half its nominal wavelength. This portion is strongly absorbed by TiO\({}_{2}\), and as such only weakly remitted, compared to the _CR30F_ white standard resulting in considerable attenuation of \(R_{\infty}\). For wavelengths exceeding 820 nm, the second-order diffracted light is beyond the band edge of TiO\({}_{2}\) at \(\lambda/2>410\) nm, such that additional absorption is significantly reduced and the diffuse reflectance becomes comparable to spectrally filtered measurements.  
Apart from the evident diffuse reflectance characteristics of the individual sample, this effect can be further enhanced or reduced depending on the spectrometer. The most important influences stem from the excitation spectrum of the light source and the spectral detector response. For example, if the spectral intensity of the excitation lamp at wavelength \(\lambda_{1}\) is considerably lower than at its half wavelength \(\lambda_{2}=\lambda_{1}/2\), the second-order diffracted line at \(\lambda_{2}\) will appear strongly reinforced, thereby increasing the portion of stray radiation onto the sample. Depending on the spectral sensitivity of the detector \(\eta(\lambda)\), this effect may become even further pronounced when \(\eta(\lambda_{2})>\eta(\lambda_{1})\).  
For reference, both excitation lamp spectrum and spectral detector quantum efficiency curve for the components used within the present studies have been plotted in Figure 10.  
Figure 9: **(a)** Evidence of higher order diffraction for a center wavelength of 700 nm, when no additional spectral filters are engaged (red) and removal of undesired wavelengths using a long-pass (LP) filter transmitting wavelengths greater than 680 nm (blue). **(b)** Diffuse reflectance of a rutile-TiO\({}_{2}\) sample against _CR30F_ without (red) and with (blue) spectral filtering after the excitation monochromator.  
In the end, the measured intensity is a product of several additional spectral response functions that include, besides excitation light source and detection unit, any intermediary optics such as filters, lenses or monochromators.