# A Study of High-Efficiency Laser Headlight Design Using Gradient-Index Lens and Liquid Lens
## 3 Simulation and Analysis of the Headlight Optical System  
Due to the complexity of the optical system, the output light pattern from the laser source to the freeform lens requires a large number of calculations. Therefore, geometric optical theory was used to design the preliminary light propagation framework. However, the details must be verified using a finite element method. This study used LightTools(r) optical simulation software to perform the necessary simulations and analysis to verify the accuracy of the optical model results. First, a three-dimensional (3D) digital model of each optical device was developed, with various parameters being assigned to the digital model, according to its optical characteristics. The optical devices were further combined into a 3D digital system based on the optical architecture that was designed in this experiment. There are two lighting modules available in this proposed system: a left and right headlight set. Each light source module was a combination of eight 1 W white diode lasers in a 4 \(\times\) 2 array. There was a total of 16 laser sources; therefore, the total power of the laser source was 16 W. All laser sources were numbered (see Figure 6). \begin{table}
\begin{tabular}{c c c} \hline \hline \begin{tabular}{c} **Test Point** \\ **(Right Side Driver)** \\ \end{tabular} & \
\begin{tabular}{c} **Position** \\ **(Units: m)** \\ \end{tabular} &
\begin{tabular}{c} **Illuminance** \\ **Value, Type B** \\ **(Units: lux)** \\ \end{tabular} \\ \hline Point: HV & (0,0) & \(\geq\)48 \\
2.5 R & (0,1.125) & \(\geq\)24 \\
2.5 L & (0,\(-\)1.125) & \(\geq\)24 \\
5 L & (0,\(-\)2.25) & \(\geq\)6 \\
5 R & (0,2.25) & \(\geq\)6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: ECE R-112 high-beam test specification. \begin{table}
\begin{tabular}{c c c} \hline \hline \begin{tabular}{c} **Test Point** \\ **(Right Side Driver)** \\ \end{tabular} & \
\begin{tabular}{c} **Position** \\ **(Units: m)** \\ \end{tabular} &
\begin{tabular}{c} **Illuminance** \\ **Value, Type B** \\ **(Units: lux)** \\ \end{tabular} \\ \hline Point: & & & \\
50 L & (\(-\)1.5,0.25) & \(\leq\)0.4 \\
75 R & (0.5,\(-\)0.25) & \(\geq\)3 \\
75 L & (1.5,\(-\)0.25) & \(\leq\)12 \\
50 L & (\(-\)1.5,\(-\)0.375) & \(\leq\)15 \\
50 R & (0.75,\(-\)0.375) & \(\geq\)12 \\
50 & (0,0.375) & \(\geq\)6 \\
25 L & (\(-\)3.96,\(-\)0.75) & \(\geq\)2 \\
25 R & (3.96,\(-\)0.75) & \(\geq\)2 \\ Zone I & & \(\leq\)20 \\ Zone III & & \(\leq\)0.7 \\ Zone IV & & \(\geq\)3 \\ \hline Point & & \\ \(1+2+3\geq 0.3\) lux & & \(0.7\geq 7\geq 0.1\) lux \\ \(4+5+6\geq 0.6\) lux & & \(0.7\geq 8\geq 0.2\) lux \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ECE R-112 low-beam test specification. The ray trace analysis of the optical system is shown in Figure 7A. Each chart below shows the different light source distribution on each image plane after simulation to achieve light efficiency [24; 25]. The laser is a Gaussian light source, and the light intensity at the middle point is the strongest. The Gaussian distribution of light intensity in X and Y directions is different (Figure 7B). Laser transmission through the optical fiber significantly improved laser polarization. Figure 7C shows the light pattern simulation of the fiber exit side, which indicates the effectiveness of improving polarized light. The intensity of the laser light output from the optical fiber was still concentrated; however, the polarization of the laser beam was eliminated after it entered the ROD, which performed an optical adjustment. In addition, the light intensity was uniformly diffused. Figure 7D shows the light pattern on the ROD exit side, indicating the results of the homogenization of laser diffusion and the elimination of polarization. After the periphery of the light beam output from the ROD was adjusted using the light shaper, eliminating stray light and shaping the beam, the light beam entered the GRIN lens for diffusion. Show in Figure 7E. Firstly, in this experiment, we find the right laser diode and its LightTools file from LightTools database.