A Long-Range Lidar Optical Collimation System Based on a Shaped Laser Source

Abstract

Semiconductor near-infrared lasers have been widely used in lidar systems. However, various source types have different shapes and divergence angles, causing more difficulties for long-distance detection. In this paper, an optical collimation system is designed for a long-range lidar system with a shaped laser source (the wavelength is 905 nm, the emitted spot size is 50 µm long by 10 µm wide, and the divergence angles are 33°and 15°, respectively, which are unconventional). On the basis of the traditional method of aspheric lens setting, a pair of asymmetric aspherical lenses were designed using an extended polynomial. The simulation results show that the spot shapes are all close to circular from 100 mm to 30 m and the spot size always remains the same value. The corrected optical system is put into the designed lidar system for verification. It results show that the average divergence angles in the long and short axis directions are 0.06°and 0.07°, which satisfy the project requirements. This optical system designed provides a collimation scheme and expands the application of vehicle-mounted lidar in the field of long-range detection.

1. Introduction

Light detection and ranging (lidar) is an active modern optical device that uses lasers as the emitting signal. Taking laser as the signal source, the pulsed laser emitted by the laser hits the target object, causing scattering, and a part of the light wave is reflected to the receiver of the lidar, and after comparing the detected signal with the received signal and making appropriate processing, the relevant information of the target can be obtained [1]. Given the rapid development of lidar technology over the last few decades, it has broad application prospects in the fields of resource exploration [2,3,4,5], urban planning [6,7,8,9], environmental monitoring [10,11,12,13], and traffic communication [14,15,16,17]. Especially in the era of driverless technology and navigation intelligence technology, it is becoming more and more important to realize better recognition of elements of the road using lidar, making people pay more attention to research on lidar in road detection. Chen et al. introduced a novel lidar adaptive-assisted road detection (PLARD) method, which combines lidar information with visual image-based road detection in order to improve detection performances [18]. Lei et al. used a lidar-based method to detect obstacles in front of the vehicle by clustering the lidar data using an improved curing method. This method could calculate the width and length of the obstacles and identify the vehicle more accurately [19]. Garcia et al. describe the use of lidar to detect moving obstacles in a road environment. According to an object’s shape and motion, lidar provides information to classify and detect velocity, acceleration, and motion without being limited to shape [20].

Currently, conventional lidar optical systems [21,22] are designed to meet the detection needs of roads, but as the distance increases, is it not only difficult to ensure the compression and collimation effect of the beam [23,24,25], but the requirements for the imaging system also become more stringent. Zhang et al. designed a lightweight, compact and non-thermalized four-piece all-glass telephoto lens, combining the telephoto lens with a line-array detector, to significantly improve the detection resolution of lidar systems through local image-level imaging and satisfy the temperature adaptability of vehicle-mounted lidar in complex environments [26]. Zhu et al. designed a four-element, three-group, tenside-type vehicle lens to meet the requirements of intelligent vehicles in terms of recognition accuracy and imaging quality for close-range targets in front of them by varying the distance and curvature of the lens [27]. Xu et al. proposed a method of optical design parameter optimization to design a matching aspherical surface shape structure to improve the laser echo signal detection capability. The contradiction between the optical system size and the collimation and focusing effect was solved for the near-field conditions and the on-board state interference [28]. All of the above studies can prove that the optical design system of vehicle-mounted lidar at close range has good imaging capability and image quality, but there are still relatively few studies on the imaging system at long range.

For example, Figure 1 shows the display of the lidar signal on the main control screen of an existing car from a car manufacturer for autonomous driving. It is observed that in the application of the actual scene, the distant target vehicle outline at the opposite lane is incomplete and the imaging effect is not ideal. This proves that the overall performance in long-range imaging needs to be further improved.

This paper presents a long-range lidar optical collimation system based on shaped lasers. The shaped laser refers to the compression of the light source in two different directions, x and y, in the design of the optical system. The laser parameter used in this manuscript is a 905 nm infrared pulsed laser diode, which has different divergence angles of 33 degrees and 15 degrees in the x and y directions, respectively. A pair of asymmetric aspherical lenses, utilizing an extended polynomial, is used to collimate the light source. Both the simulation and experimental results show that the designed lens could realize relatively good collimation performance and meet the requirements of imaging research on obstacles. This work can be widely used in the field of long-range lidar detection.

2. Lidar Detection Principle and System Design

2.1. Lidar Detection Principle

Lidar could measure the range by emitting laser pulses to the target object and processing the laser echo received from the reflective surface. The distance between the target and the lidar is set to be $R$, the divergence angle of the emitted laser beam is set to be ${\theta }_t$, the stereo angle is set to be ${\Omega }_t$, the transmittance of the emitting optical system is set to be ${\eta }_t$, the transmittance of the receiving optical system is set to be ${\eta }_r$, and the transmittance of the laser pulse in the atmosphere is set to be ${\eta }_a$. The effective area of the target at the cross-section of the laser beam is $A_t$, the steric angle is ${\Omega }_r$, the cross-sectional area of the laser beam at the target position is $A_l$, the normal direction of the target is ON, the angle between the optical axis of the launching optical system and the target normal direction ON is ${\theta }_{\mathrm{target}}$, and $A_r$ is the area of the detector’s photosensitive area. The laser emission process is shown in Figure 2.

If the laser emission power is $P_t$, then the total laser power that passes through the atmosphere to reach the target is ${\eta }_a{P}_t$, assuming that the power distribution of the laser beam is the same everywhere, where, according to the formula for the stereo angle, $A_t$ can be expressed as:

$${\Omega }_t={\displaystyle \frac{A_l}{R^2}},$$

(1)

Then, the radiant flux of the part of the target irradiated by the laser pulse is:

$${\theta }_{\mathrm{target}}={\displaystyle \frac{{\eta }_t{\eta }_a{P}_t{A}_t}{A_l}}={\displaystyle \frac{{\eta }_t{\eta }_a{P}_t{A}_t}{{\Omega }_t{R}^2}},$$

(2)

The laser reception process is shown in Figure 3. Assume that the reflectivity of the target is ${\rho }_t$; then, after diffuse reflection from the target, combined with the transmittance of the receiving system, and after another pass through the atmosphere, the power of the laser pulse received by the receiving system is:

$$P_{\mathrm{receive}}={\theta }_{\mathrm{target}}{\rho }_t{\eta }_r{\eta }_a{\displaystyle \frac{A_r}{{\Omega }_r{R}^2}}={\displaystyle \frac{{\eta }_t{\eta }_a{P}_t{A}_t}{{\Omega }_t{R}^2}}{\rho }_t{\eta }_r{\eta }_a{\displaystyle \frac{A_r}{{\Omega }_r{R}^2}},$$

(3)

where ${\Omega }_t$ can be expressed by solid angle, ${\Omega }_r$ is in accordance with diffuse reflection, solid angle takes $2\pi$ or $\pi$, and in this paper, $\pi$ is taken. Then, the laser pulse power received by the receiving system can be expressed as:

$$P_{\mathrm{receive}}={\displaystyle \frac{4{\eta }_t{\eta }_a{P}_t{A}_t}{\pi R^2{\theta }_t^2}}{\rho }_t{\eta }_r{\eta }_a{\displaystyle \frac{A_r}{\pi R^2}}={\displaystyle \frac{4{\eta }_t{\eta }_a}{\pi R^2{\theta }_t^2}}{A}_t{\rho }_t{\displaystyle \frac{{\eta }_r{\eta }_a{A}_r}{\pi R^2}}{P}_t,$$

(4)

Assume the pulse width of the laser is $P_w$. Then, the energy obtained by the receiving system is combined with the energy of a single photon and quantum efficiency ${\eta }_q$. The average number of photons generated by the detector can be obtained:

$$\overline{N}={\displaystyle \frac{{\eta }_q{P}_w{P}_{\mathrm{receive}}}{hv}}={\displaystyle \frac{{\eta }_q}{hv}}{\displaystyle \frac{4{\eta }_t{\eta }_a}{\pi R^2{\theta }_t^2}}{A}_t{\rho }_t{\displaystyle \frac{{\eta }_r{\eta }_a{A}_r}{\pi R^2}}{P}_t{P}_w,$$

(5)

Equations (1)–(5) are for laser emission beams that are larger than the effective receiving area of the target object. At this point, the target object can be considered as a point target. When the effective receiving area of the target object is greater than or equal to the emission area of the laser emission beam, the target object is considered to be a surface target.

When the target object is a surface target, the laser pulse power received by the receiving system can be expressed as Equation (6).

$$P_{receive}={\eta }_t{\eta }_a{P}_t{\rho }_t{\eta }_r{\eta }_a{\displaystyle \frac{A_r}{\pi R^2}}={\eta }_t{\eta }_a{\rho }_t{\displaystyle \frac{{\eta }_r{\eta }_a{A}_r}{\pi R^2}}{P}_t,$$

(6)

In this case, the average number of photons produced by the detector can be obtained and expressed as Equation (7).

$$\overline{N}={\displaystyle \frac{{\eta }_q{P}_w{P}_{receive}}{hv}}={\displaystyle \frac{{\eta }_q}{hv}}{\eta }_t{\eta }_a{\rho }_t{\displaystyle \frac{{\eta }_r{\eta }_a{A}_r}{\pi R^2}}{P}_t{P}_w,$$

(7)

The lidar equations are thus derived.

2.2. Lidar System Design

Based on the principles of Section 2.1 and project requirements, a lidar system for application on a vehicle has been designed, as shown in Figure 4. It can be seen that the optical system is placed on the top. The laser selected in the system has a wavelength of 905 nm and an output power of 25 W, with a x-direction spot size of 10 µm and a divergence angle of 15°, and a y-direction spot size of 50 µm and a divergence angle of 33°. Due to the emission angle of the light source being asymmetrical, the beam needs to be strictly collimated in order to achieve accurate measurements. This means the laser spot should be converted into a circular spot with symmetrical long and short axes (close to a circle at different positions within 30 m). Therefore, according to the requirement of the system structure, a collimated lens should be designed and placed in the lens design space shown in Figure 4.

Figure 5 shows the normalized optical energy distribution of the laser. The red and blue curves represent the energy distribution of the light source in different directions. The red curve is the x-direction spot size of 10 µm, and the blue curve is the y-direction spot size of 50 µm.

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:

The specific parameter settings for the main lens are shown in

Table 1. Structural parameters of a single optical lens.

Lens Surface	1	2
Surface thickness (mm)	8	100
Lens material	PMMA
Net caliber	2.5	2.5
Extended polynomial	$\mathrm{Coeff} {\mathrm{X}}^2$: −0.051 $\mathrm{Coeff} {\mathrm{X}}^4$$:-5.803 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{X}}^6$$: 1.005 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{Y}}^2$: 0.173 $\mathrm{Coeff} {\mathrm{Y}}^4$$:-1.681 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{Y}}^6$$: 5.699 \times {10}^{-5}$	$\mathrm{Coeff} {\mathrm{X}}^2$: −0.106 $\mathrm{Coeff} {\mathrm{X}}^4$$:-8.725 \times {10}^{-4}$ $\mathrm{Coeff} {\mathrm{X}}^6$$:-5.579 \times {10}^{-6}$ $\mathrm{Coeff} {\mathrm{Y}}^2$: −0.020 $\mathrm{Coeff} {\mathrm{Y}}^4$$: 4.055 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{Y}}^6$$: 2.322 \times {10}^{-4}$

.

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 ${\mathrm{X}}^2$ is set to −0.051, Coeff ${\mathrm{X}}^4$ is set to −5.803 × ${10}^{-3}$, Coeff ${\mathrm{X}}^6$ is set to 1.005 × ${10}^{-3}$, Coeff ${\mathrm{Y}}^2$ is set to 0.173, Coeff ${\mathrm{Y}}^4$ is set to −1.681 × ${10}^{-3}$, and Coeff ${\mathrm{Y}}^6$ is set to 5.699 × ${10}^{-5}$. The rear surface thickness is set to 100. Semi-Diameter is set to 2.5. The quadratic aspheric coefficient Coeff ${\mathrm{X}}^2$ is set to −0.106, Coeff ${\mathrm{X}}^4$ is set to −8.725 × ${10}^{-4}$, Coeff ${\mathrm{X}}^6$ is set to −5.579 × ${10}^{-6}$, Coeff ${\mathrm{Y}}^2$ is set to −0.02, Coeff ${\mathrm{Y}}^4$ is set to 4.055 × ${10}^{-3}$, and Coeff ${\mathrm{Y}}^6$ is set to 2.322 × ${10}^{-4}$.

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 µm, width of 10 µm, and divergence angles of 33° and 15°, respectively. Figure 8 shows the shape of the outgoing spot. The design requirement is to change an oval spot into a circular 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.

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. Structural parameters of a pair of optical lens.

Lens Surface	1	2	3	4
Curvature radius (mm)	30.417			−9.089
Surface thickness (mm)	3	10	3	100
Lens material	PMMA		PMMA
Net caliber	2.5	2.5	2.5	2.5
Extended polynomial		$\mathrm{Coeff} {\mathrm{X}}^2$: −0.073 $\mathrm{Coeff} {\mathrm{X}}^4$$:-1.953 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{X}}^6$$:-7.480 \times {10}^{-5}$ $\mathrm{Coeff} {\mathrm{Y}}^2$: −0.164 $\mathrm{Coeff} {\mathrm{Y}}^4$$:-3.413 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{Y}}^6$$: 2.788 \times {10}^{-5}$	$\mathrm{Coeff} {\mathrm{X}}^2$: −0.017 $\mathrm{Coeff} {\mathrm{X}}^4$$:-3.404 \times {10}^{-4}$ $\mathrm{Coeff} {\mathrm{X}}^6$$:-5.715 \times {10}^{-6}$ $\mathrm{Coeff} {\mathrm{Y}}^2$: −0.069 $\mathrm{Coeff} {\mathrm{Y}}^4$$:-2.588 \times {10}^{-3}$ $\mathrm{Coeff} {\mathrm{Y}}^6$$:-1.015 \times {10}^{-4}$

.

Both the x and y axis collimators use polynomials. 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 ${\mathrm{X}}^2$ is set to −0.073, Coeff ${\mathrm{X}}^4$ is set to −1.953 × ${10}^{-3}$, Coeff ${\mathrm{X}}^6$ is set to −7.480 × ${10}^{-5}$, Coeff ${\mathrm{Y}}^2$ is set to −0.164, Coeff ${\mathrm{Y}}^4$ is set to −3.413 × ${10}^{-3}$, and Coeff ${\mathrm{Y}}^6$ is set to 2.788 × ${10}^{-5}$.

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 ${\mathrm{X}}^2$ is set to −0.017, Coeff ${\mathrm{X}}^4$ is set to −3.404 × ${10}^{-4}$, Coeff ${\mathrm{X}}^6$ is set to −5.715 × ${10}^{-6}$, Coeff ${\mathrm{Y}}^2$ is set to −0.069, Coeff ${\mathrm{Y}}^4$ is set to −2.588 × ${10}^{-3}$, and Coeff ${\mathrm{Y}}^6$ is set to −1.015 × ${10}^{-4}$. 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.

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 × short side mm) always remains 3.2 mm × 3.2 mm, which indicates that this pair of asymmetric aspherical lenses scheme is able to achieve excellent collimation performances.

Beam collimation plays an important role in the optical lidar system, and its purpose is to collimate and shape the beam emitted by the light source with poor image quality and a large divergence angle, so as to improve the beam quality of the lidar system.

In this paper, two schemes are compared, of which Figure 6 uses a single lens, and after simulating the ray tracing, the spot diagram shows that spot shapes have become dispersed on the image plane at a distance of 30 m. Therefore, on the basis of Figure 6, the lens is optimized and a system with two lenses is adopted; after simulating ray tracing, the spot shape is basically circular on the image plane. Compared to a single lens, a pair of lenses can better achieve the imaging requirements at a long distance.

4. Experiments and Data Analysis

The corrected optical lenses are applied to the lidar system in Figure 4 for verification. Firstly, the position of the ground glass is adjusted so that it is 500 mm away from the center of the lidar. The laser shoots pulsed lasers to irradiate the ground glass for a period of time, and after the light spot displayed on the ground glass is stabilized, the spot shape is photographed and recorded, as displayed in Figure 13a. The results show that the size of the spot size (long side × short side mm) in Figure 13a is 9 × 6 mm. In this case, the position of Figure 13a is used as a reference point. Then, the position of the ground glass is adjusted so that the ground glass moves back 3000 mm from the center of the lidar, which means an increase in the detection distance. The position of the ground glass is adjusted every two meters and the above steps are repeated so that values at different positions are recorded. The experimental data are shown in Figure 13 and

Table 3. Spot size data.

Ground Glass to Lidar Distance (m)	Spot Shape and Size (Long Side × Short Side mm)	Ground Glass to Lidar Distance (m)	Spot Shape and Size (Long Side × Short Side mm)
0.5	9 × 6	3	13 × 12
5	19 × 16	7	22 × 21
10	30 × 29

.

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. The divergence angle is first compressed, followed by beam and collimation processing, ultimately resulting in a highly collimated homogeneous beam with a divergence angle reaching the milliradian level.

Figure 13 shows the spot imaging at different distances from the lidar. From the experimental results shown in Figure 13, it can be seen that during the propagation of the beam from 0.5 m to 10 m, the spot on the image plane changes gradually from oval to round until it is basically in a round shape at the end. Therefore, the beam collimation lens designed in this paper has a very good effect.

Table 3 shows the spot size data. It can be seen that as the distance increases, the ratio of long and short size gets closer to 1. Based on the spot size of any two different positions, the average divergence angles in the long and short axis directions are calculated as 0.06°and 0.07°, which satisfy the project requirements.

5. Conclusions

This paper describes a long-range lidar optical collimation system based on a shaped laser, which could achieve a good spot shape and small divergence angles at 30 m. Firstly, a single asymmetric aspherical lens scheme is used, but the collimation effect is not ideal at long distances. Then, it is optimized using a pair of asymmetric aspherical lenses, which are designed using an extended polynomial. The simulation results show that the designed optical system can achieve near-infrared laser collimation between 100 mm and 30,000 mm from the last lens surface. The corrected optical system is put into the lidar system for verification. The experimental results show that the spot size on the ground glass at 10 m away is almost circular and the average divergence angles on the long and short axis directions are 0.06°and 0.07°, respectively. In summary, the lidar optical collimation system designed in this paper greatly improves the collimation effect of the laser and has wide application value in the field of optical research based on shaped laser.