# Optical Design for Laser Diode Scanner Headlamp with
## 3 Design of Optical Scanner System  
To achieve an efficient optical power distribution, the laser diode scanner system was designed to direct the optical flux to the edge of the phosphor plane when the scanning angle is small. It was designed to direct the optical flux to the center of the phosphor plane at a relatively slow maximum scanning angle. Hence, the optical system was designed by including a prism with a specific angle based on the specifications shown in Table 1 below to apply the pixelated phosphor system, as shown in Figure 1. The diameter of the collimated beam was 2 mm, and the designed wavelength was 450 nm. Considering the size of the pixelated phosphor, the size was less than 40 \(\upmu\)m when light was concentrated on the phosphor surface, and it was designed such that no large deviations appeared in the spot size over the entire area of the phosphor surface. The tilt angle generated by the scanning mirror was designed to be \(\pm 12^{\circ}\). The specifications shown in Table 1 were specified for experimental verification. The design concept presented herein can yield an efficient light distribution, which is the main purpose of this study, even when using scanning mirrors with different scan angles, and phosphor planes with different areas. Figure 3: Schematic diagram of proposed optical system for laser diode scanner headlamp. Table 2 lists the specifications of the designed prism. The prism's apex angle was 140\({}^{\circ}\). The smaller the prism's apex angle, the larger is the deflection angle of the beam through the prism. Therefore, the optical scanner system can be miniaturized, but the focusing lens must be designed to have a larger refractive power. The prism was also designed with a flat short axis for ease of fabrication and alignment of optical components. If the length of the short axis of the phosphor is relatively long, and if one wishes to control the light distribution along the short axis, a prism shape can be achieved by creating a square pyramid shape using the design method proposed herein. The beam deflected by the prism can be assumed as offset to a certain height in the optical axis. The offset amount can be calculated as shown in Equation (1). \[x=d\times\tan(\sin^{-1}(\sin(\theta)/n)), \tag{1}\]  
where \(x\), \(d\), \(\theta\), and n are the offset position along the \(x\)-axis, the distance between the galvanometer and prism, the angle of one side of the prism (\(\theta=(180-\) apex angle of prism)/2), and the refractive index of the prism, respectively, as shown in Figure 4a. The scanning mirror was placed at position \(x\) and calculated using Equation (1), as shown in Figure 4b. The focusing lens was optimized by setting the light beam to pass through the scanning mirror at the offset position and enter the focusing lens. In addition, the position in the \(z\)-axis direction of the scanning mirror was adjusted by the optical path difference that occurred when light passed through the prism. In this study, the distance between the galvanometer and prism was 20 mm, \(\theta\) was 20\({}^{\circ}\), and n was 1.525; hence, \(x\) was 4.6 mm. Table 3 lists the specifications of the focusing lens optimized for virtual objects. The focusing lens was designed as a doublet, and the glass used was N-BK7, SF2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Specification** & **Value** \\ \hline Collimated beam diameter & 2 mm \\ Designed wavelength & 450 nm \\ Beam spot size at phosphor plane & \textless{}40 μm \\ Scanning range at phosphor plane & 16 mm (x axis) \(\times\) 4 mm (y axis) \\ Scanning angle & \(\pm\)12\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optical specification considered in design of laser diode scanner headlamp. \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Specification** & **Value** \\ \hline Apex angle & 140\({}^{\circ}\) \\ Surface radius of \(y\)-axis & Infinity (flat) \\ Thickness & 10 mm \\ Glass material & N-BK7 (nd = 1.5168) \\ \hline \hline \end{tabular}
\end{table}