# Mail Inspection Based on Terahertz Time-Domain Spectroscopy
## 2 System Design
### Suppression of Multiple Reflections  
Considering realistic mail inspection scenarios, multiple reflections at paper sheets have to be considered. Mail envelopes and contents are mainly paper of various thicknesses, densities, and distributions. Therefore, no constant, but alternating contributions can be considered. One attempt to overcome this problem is to vary the angle of incidence and evaluate the sample's response in dependence on the angle of incidence [36; 37]. As the material intrinsic response (absorption) is independent of the angle of incidence, the contributions of multiple reflections are not: they base on angle-of-incidence-dependent reflectivity and interferences which themselves depend on optical path lengths, varying with the angle of incidence. Therefore, one can discriminate the constant contribution of the hidden substance and the varying contribution of multiple reflections [38; 39].  
As the enclosure is most commonly of the same material (paper or cardboard), one can assume that its refractive index is more or less defined. Considering the polarization-dependent reflectivity at various angles of incidence, a much more elegant solution can be applied to the problem of multiple reflections: angle of incidence at Brewster's angle [40]  
\[\alpha_{Brewster}=\arctan(n), \tag{2}\]  
with the refractive index of the enclosure material \(n\) and assuming the measurement in air environment (\(n_{\text{air}}=1\)), which will be the case for all mail scanning systems.  
Assuming a mean refractive index of \(n\sim\) 1.5, the angle of incidence has to be chosen to be approximately \(56^{\circ}\). A comparison of substances embedded in paper stacks at normal incidence and [PERSON]'s angle can be seen in Figure 9, where the spectra at normal incidence are vertically shifted for better readability. The results show that at normal incidence multiple reflections lead to additional spectral features that cover those of PABA. This is significantly suppressed when using an incidence at [PERSON]'s angle, where the spectral features of the substance are unaffected as the multiple reflections are physically prevented.  
To investigate the influence of the angle of incidence change on the detection performance, a plethora of measurements on negative samples (paper stacks and mail without substances) were made with both incident angles and compared to positive measurements (with substances). Depending on the correlation threshold of the detection algorithm (sharpness of detection), one can find the true positive and false positive rate. The farther they are apart, the better. Figure 10 shows the results of these measurements and demonstrates the benefit of measuring at Brewster's angle. At a correlation threshold of 0.2, the false positive rate was suppressed in our exemplary measurement set by a factor of about 14 and 10 for PABA and \(\alpha\)-Lactose mh., respectively. In practice, a certain correlation threshold has to be set for each substance. Depending on the acceptable false positive rate, one can then gain a true positive rate and vice versa. When applying the Brewster'sconfiguration, the resulting true positive rate is enhanced for a desired acceptable false positive rate [41].