# Optical Design for Laser Diode Scanner Headlamp with
## 3 Design of Optical Scanner System

Table 2: Specifications of designed prism. In the designed optical scanning system, ray tracing by scanning angle is shown in Figure 5. Figure 5a-e show the ray tracing when the scanning angles were \(12^{\circ}\), \(5^{\circ}\), \(0^{\circ}\), \(-5^{\circ}\), and \(-12^{\circ}\), respectively. As shown in Figure 5c, owing to the prism shape, when the scanning angle was small, the light split into two directions. However, when the scan angle reached an angle that split into two paths, the light appeared outside the area of the effective plane set in this design. In addition, turning off the laser diode when scanning this area while operating the system will remove stray light, which is split into two paths. Figure 6 shows the change in the focusing beam position on the \(x\)-axis (long axis) of the phosphor plane owing to the scanning angle. In the designed scanning optical system, because the light split in the \(-5^{\circ}\)\(\sim\)\(5^{\circ}\) region, the focusing light was designed to deviate from the phosphor's effective area by \(\pm 8\) mm when the scanning angle was between \(-5^{\circ}\) and \(5^{\circ}\). Figure 4: Design of focusing lens using temporary object points. (a) Ray tracing in original optical system layout; (b) ray tracing from temporary object points. \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Specification** & **Value** \\ \hline Surface radius of 1 st surface & \(-154.51\) mm \\ Surface radius of 2 nd surface & \(-12.80\) mm \\ Surface radius of 3 rd surface & \(-26.87\) mm \\ Thickness of 1 st lens & \(10\) mm \\ Thickness of 2 nd lens & \(10\) mm \\ Glass material of 1 st lens & N-BK7 (nd = 1.5168) \\ Glass material of 2 nd lens & SF2 (nd = 1.6447) \\ Back focal length & \(86.46\) mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specifications of designed focusing lens. A general imaging optical system is primarily evaluated by calculating its aberrations. However, in a laser diode scanner headlamp, the designed optical system spreads light evenly across the pixelated phosphor plane. Therefore, considering the role of the scanner system, the performance evaluation of the designed optics only confirmed that the beam spot size was formed to a size suitable for the size of the pixel-rate phosphor. The beam spot size on the phosphor plane considered in this study was 40 \(\upmu\)m, as shown in Table 1.  
Figure 5: Ray tracing according to scanning angle in designed scanning system. (**a**) 12\({}^{\circ}\), (**b**) 5\({}^{\circ}\), (**c**) 0\({}^{\circ}\), (**d**) \(-\)5\({}^{\circ}\), and (**e**) \(-\)12\({}^{\circ}\). Figure 6: Focusing beam position in \(x\)-axis of phosphor plane according to scanning angle. Dashed red lines represent effective area of \(x\)-axis of phosphor plane. Therefore, the focusing lens was designed to maintain a beam spot size of 40 \(\upmu\)m or less in the scanning area. The spot size change according to the scanning angle is shown in Figure 7. The minimum spot size was 5.29 \(\upmu\)m at 11.16\({}^{\circ}\), and the maximum spot size was 23.66 \(\upmu\)m at 8.36\({}^{\circ}\). Therefore, we confirmed that a spot size of less than 40 \(\upmu\)m was maintained in all scan angle ranges.