# A Long-Range Lidar Optical Collimation System Based on a Shaped Laser Source
## 3 Optical Collimation System Design  
Based on the above system requirements, a single asymmetric aspherical lens scheme is first adopted for collimation. The optical system is obtained as shown in Figure 6:  
Figure 4: Space limitation of lens and laser position. Figure 5: Normalized luminous energy distribution of lasers. The red curve is the x-direction spot size of 10 \(\upmu\)m, and the blue curve is the y-direction spot size of 50 \(\upmu\)m.  
The specific parameter settings for the main lens are shown in Table 1.  
A single lens uses a polynomial, with the specific parameters set as follows: the front surface thickness is set to 8. Material is set to PMMA. Semi-Diameter is set to 2.5. The quadratic aspheric coefficient Coeff \(X^{2}\) is set to \(-0.051\), Coeff \(X^{4}\) is set to \(-5.803\times 10^{-3}\), Coeff \(X^{6}\) is set to 1.005 \(\times\)\(10^{-3}\), Coeff \(Y^{2}\) is set to 0.173, Coeff \(Y^{4}\) is set to \(-1.681\times 10^{-3}\), and Coeff \(Y^{6}\) is set to 5.699 \(\times\)\(10^{-5}\). The rear surface thickness is set to 100. Semi-Diameter is set to 2.5. The quadratic aspheric coefficient Coeff \(X^{2}\) is set to \(-0.106\), Coeff \(X^{4}\) is set to \(-8.725\times 10^{-4}\), Coeff \(X^{6}\) is set to \(-5.579\times 10^{-6}\), Coeff \(Y^{2}\) is set to \(-0.02\), Coeff \(Y^{4}\) is set to \(4.055\times 10^{-3}\), and Coeff \(Y^{6}\) is set to \(2.322\times 10^{-4}\). Based on the information in Table 1, ray tracing simulations are performed, and the layout of light source collimated modelling is shown in Figure 7.  
Here, we use a laser source with a wavelength of 905 nm, emitted light length of 50 \(\upmu\)m, width of 10 \(\upmu\)m, and divergence angles of 33\({}^{\circ}\) and 15\({}^{\circ}\), respectively. Figure 8 shows the shape of the outgoing spot. The design requirement is to change an oval spot into a circular \begin{table}
\begin{tabular}{c c c} \hline
**Lens Surface** & **1** & **2** \\ \hline Surface thickness (mm) & 8 & 100 \\ Lens material & PMMA & \\ Net caliber & 2.5 & 2.5 \\ Coeff \(X^{2}\): \(-0.051\) & Coeff \(X^{2}\): \(-0.106\) \\ Coeff \(X^{4}\): \(-5.803\times\ 10^{-3}\) & Coeff \(X^{4}\): \(-8.725\times\ 10^{-4}\) \\ Extended polynomial & Coeff \(X^{6}\): \(1.005\times\ 10^{-3}\) & Coeff \(X^{6}\): \(-5.579\times\ 10^{-6}\) \\ [PERSON] \(Y^{2}\): \(0.173\) & Coeff \(Y^{2}\): \(-0.020\) \\ [PERSON] \(Y^{4}\): \(-1.681\times\ 10^{-3}\) & Coeff \(Y^{4}\): \(4.055\times\ 10^{-3}\) \\ [PERSON] \(Y^{6}\): \(5.699\times\ 10^{-5}\) & Coeff \(Y^{6}\): \(2.322\times\ 10^{-4}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Structural parameters of a single optical lens. Figure 6: Scheme of a single asymmetric aspheric lens optical system: (**a**) x–z plane; (**b**) y–z plane. Figure 7: Layout of a single lens light source collimation modelling. (**a**) x–z plane; (**b**) y–z plane. spot with symmetrical long and short axes after the lens collimation. Figure 9 shows the spot diagrams at different distances from the lens using the single asymmetric aspherical lens scheme above. It can be seen from Figure 9 that the spot shapes are all close to circular from 100 mm to 10 m, but at 30 m, the spot diagram shows that the effects have become more dispersed and can no longer be barely circular in shape. Figure 8: Outgoing spot shape. Figure 9: Collimation effect of single asymmetric aspherical lens at different distances. (**a**) At 100 mm; (**b**) at 1 m; (**c**) at 10 m; (**d**) at 30 m.  
In order to shape the emitted spot into a circular spot at a further distance, a scheme using a pair of asymmetric aspherical lenses is adopted to optimize the collimation effects. The optical system is obtained as shown in Figure 10.  
The first face of the first lens is a sphere, and the second face is a polynomial free-form surface; the first face of the second lens is a polynomial free-form surface, and the second face is a sphere. The specific parameter settings for the main lens are shown in Table 2.  
Both the x and y axis collimators use polynomials.