# Total Internal Reflection Lens for Optical Wireless Receivers
## 4 Discussion  
### Performance  
The measurement from Figure 5b shows a high concentration ratio of 44.7 (16.5 dB) despite the small form factor of the lens. The eye diagram measurements and the BERT prove that the optical concentration improves the data transmission drastically. In our tests, the TIR lens increased the eye opening, thereby improving the BER. The eye opening is not directly proportional to the optical concentration ratio due to adjusted APD gain. The range measurements were limited by our optical bench to a maximum distance of 150 cm. At a first approximation, a concentration ratio of 44.7 corresponds to a range improvement by a factor of approximately \(\sqrt{44.7}\approx 6.7\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration** & **TIR Lens** & \(Z_{\text{o}}\) & **BER** \\ \hline a & no & 50 cm & \textless{}10^{-12}\) \\ b & no & 100 cm & \(3\times 10^{-4}\) \\ c & no & 150 cm & \(3\times 10^{-2}\) \\ d & yes & 50 cm & \textless{}10^{-12}\) \\ e & yes & 100 cm & \textless{}10^{-12}\) \\ f & yes & 150 cm & \textless{}10^{-12}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Numerical results of the BERT.  
Figure 7: Eye diagrams for PRBS-7 signals with a bit rate of 1.289 Gbit/s. (**a**) No lens (\(Z_{\text{o}}\) = 50 cm), (**b**) no lens (\(Z_{\text{o}}\) = 100 cm), (**c**) no lens (\(Z_{\text{o}}\) = 150 cm), (**d**) with lens (\(Z_{\text{o}}\) = 50 cm), (**e**) with lens (\(Z_{\text{o}}\) = 100 cm), (**f**) with lens (\(Z_{\text{o}}\) = 150 cm). The observed bandwidth is 3 GHz.  
Nevertheless, the measured values are well below the simulation values according to Figure 5b. The shift of the profile and the fact that the mounting structures did not fit perfectly indicate that there is a misalignment between the lens and the PD chip. Because the gain falls slower outside the FOV than simulated, it is likely that the focus point of the lens is larger than intended, which could be caused by an additional z-displacement between lens and PD. A part of those deviations is caused by the finite shape accuracy of the tooling process and roundings at the edges of the surfaces. A precise analysis is challenging and costly, especially for the inner surfaces of the cavity. Therefore, such analyses are out of the scope of this work. A rework of the mounting structures is one way to reduce the position tolerances. However, the final position accuracy also depends on the spatial tolerances of the SMD packages. Those are typically in the range of a few hundredths of \(\upmu\)m due to the sawing process that is used for device separation. Active positioning is another possibility to address the mechanical tolerances. However, this makes the fabrication more complex and thus is not desired for mass fabrication.  
A significant drawback of our setup is the flat surface of the SMD package. In contrast to a package with an integrated convex lens, the optical concentration ratio is reduced, because the flat surface reduces the angular acceptance region and the TIR lens cannot fully profit from the higher refractive index \(n_{2}\) of the PD package surrounding the active chip according to Equation (1). Moreover, an integrated lens would further reduce the influence of a displacement between the lens and the PD chip.