# A Long-Range Lidar Optical Collimation System Based on a Shaped Laser Source
## 3 Optical Collimation System Design
The specific parameters are set as follows: first, the x axis collimator is set and the front surface radius is set to 30.417. Thickness is set to 3. Material is set to PMMA. Semi-Diameter is set to 2.5. Conic's parameter is set to 0 by default, and the surface type of the rear surface object is selected as polynomial. Thickness is set to 10 and Semi-Diameter is set to 2.5. The quadratic aspheric coefficient Coeff X\({}^{2}\) is set to \(-\)0.073, Coeff X\({}^{4}\) is set to \(-\)1.953 \(\times\) 10\({}^{-3}\), Coeff X\({}^{6}\) is set to \(-\)7.480 \(\times\) 10\({}^{-5}\), Coeff Y\({}^{2}\) is set to \(-\)0.164, Coeff Y\({}^{4}\) is set to \(-\)3.413 \(\times\) 10\({}^{-3}\), and Coeff Y\({}^{6}\) is set to 2.788 \(\times\) 10\({}^{-5}\). Next, the y collimator is set. Thickness is set to 3. Material is also set to PMMA. Semi-Diameter is set to 2.5. The quadratic aspheric coefficient Coeff X\({}^{2}\) is set to \(-\)0.017, Coeff X\({}^{4}\) is set to \(-\)3.404 \(\times\) 10\({}^{-4}\), Coeff X\({}^{6}\) is set to \(-\)5.715 \(\times\) 10\({}^{-6}\), Coeff Y\({}^{2}\) is set to \(-\)0.069, Coeff Y\({}^{4}\) is set to \(-\)2.588 \(\times\) 10\({}^{-3}\), and Coeff Y\({}^{6}\) is set to \(-\)1.015 \(\times\) 10\({}^{-4}\). The rear face Radius is set to \(-\)9.089. The Thickness is set to 100. Clear Semi-Diameter is set to 2.5. Mech Semi-Diameter is set to 2.5. Conic's parameter is set to 0 by default. Based on the information in Table 2, ray tracing simulations are performed, and the layout of light source collimated modelling is shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline
**Lens Surface** & **1** & **2** & **3** & **4** \\ \hline Curvature & 30.417 & & & \(-\)9.089 \\ radius (mm) & & & & \\ Surface & 3 & 10 & 3 & 100 \\ thickness (mm) & PMMA & & PMMA & \\ Net caliber & 2.5 & 2.5 & 2.5 & 2.5 \\  & & Coeff X\({}^{2}\): \(-\)0.073 & Coeff X\({}^{2}\): \(-\)0.017 & \\  & & Coeff X\({}^{4}\): & & \\  & & \(-\)1.953 \(\times\) 10\({}^{-3}\) & \(-\)3.404 \(\times\) 10\({}^{-4}\) & \\  & & Coeff X\({}^{6}\): & Coeff X\({}^{6}\): & \\ Extended & & \(-\)7.480 \(\times\) 10\({}^{-5}\) & \(-\)5.715 \(\times\) 10\({}^{-6}\) & \\ polynomial & & [PERSON] Y\({}^{2}\): \(-\)0.164 & [PERSON] Y\({}^{2}\): \(-\)0.069 & \\  & & [PERSON] Y\({}^{4}\): & [PERSON] Y\({}^{4}\): & \\  & & \(-\)3.413 \(\times\) 10\({}^{-3}\) & \(-\)2.588 \(\times\) 10\({}^{-3}\) & \\  & & [PERSON] Y\({}^{6}\): 2.788 \(\times\) 10\({}^{-5}\) & [PERSON] Y\({}^{6}\): & \\  & & \(-\)1.015 \(\times\) 10\({}^{-4}\) & \\ \hline \end{tabular}
\end{table} 
Table 2: Structural parameters of a pair of optical lens. Figure 10: Optical system scheme for a pair of asymmetric aspherical lenses. (**a**) x–z plane; (**b**) y–z plane. Figure 12 shows spot diagrams at different distances from the lens after collimation. From 100 mm to 10 m, the spot shapes are all close to circular, and although signs of dispersion appear at 30 m, the overall shape can barely be circular. In contrast, a single asymmetric aspherical lens starts to show signs of dispersion at 10 m, and the dispersion effect is larger at 30 m, making it impossible to form a circular shape. Therefore, a pair of asymmetric aspherical lenses can better meet the imaging requirements at long distances compared to a single lens. Moreover, the spot size (long side \(\times\) short side mm) always remains 3.2 mm \(\times\) 3.2 mm, which indicates that this pair of asymmetric aspherical lenses scheme is able to achieve excellent collimation performances. Figure 11: Layout of a pair of lens light source collimation modelling. (**a**) x–z plane; (**b**) y–z plane. Figure 12: Collimation effect of a pair of asymmetric aspherical lenses at different distances. (**a**) At 100 mm; (**b**) at 1 m; (**c**) at 10 m; (**d**) at 30 m.  
In this paper, the front and rear two lenses are used for optical design; the purpose is to collimate the x-axis and y-axis, respectively.