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Abstract
Reliable laser imaging is crucial to the autonomous driving. In unfavorable weather condition, however, it always suffers from the acute background noise and signal attenuation due to the harmful strong scattering. We demonstrate a noise-tolerant LiDAR with the help of Bessel beam illumination and single-photon detection. After a 31.5-m propagation in thick fog, the Bessel beam employed by our noise-tolerant LiDAR still owns a central spot with the diameter of 1.86 mm, which supports a receiving field of view as small as 60 µrad and a great suppression of the background noise. This noise-tolerant LiDAR simultaneously performs well both in depth and intensity imaging in unfavorable weather, which can be functioned as a reliable imaging sensor in automatic driving.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The light detection and ranging (LiDAR) technique has become an attractive choice for many application scenarios which need three-dimensional (3D) imaging, such as city modeling [1,2], manufacturing [3,4], forestry [5,6], and so on. Especially in recent years, 3D laser imaging is of great importance in autonomous driving [7–9]. In unfavorable weather, some tiny droplets or particles floating in the air will scatter and absorb the laser beam [10], and 15% of the vehicle crashes are blamed on fog, rain, snow, and other visual obstructions [11]. To meet perception requirements, devices like camera, LiDAR, and millimeter-wave (MMW) radar are widely applied in autonomous driving and driving assistance system [12]. Camera can be used to obtain real-time video stream, and provide semantic perception, such as the detection of traffic signs [13]. LiDAR and MMW radar can be employed to get geometrical perception and provide 3D information. MMW radar is capable to work in different weather conditions, but acquiring semantic features is still with technical challenges due to its low resolution [14,15]. On the other hand, LiDAR has high resolution, but its performance deteriorates seriously in bad weather which brings low transmittance and serious backscattering [10]. The single-photon detector can be used to detect the ultra-weak echoes, which has played an important role in remote sensing [16]. To suppress the heavy backscattering light in fog or water, narrow range gate is one of the typical methods, where the detector is time-gated with a short duration to extract the echo photons concentrated around the targets [17,18]. However, the short time-gates limit the measurement into a small dynamic range. Another method is to scan the target synchronously with a collimated laser beam, so that the receiver can use a narrow field of view (FoV). Although the backscattering noise decreases with the square of FoV angle [19], there still be a threshold because the receiving FoV is also restricted by the diffraction. The minimal cross section diameter of the Gaussian laser beam is ∼ (16λL/π)1/2, where λ and L are the laser wavelength and the propagation distance, respectively. The FoV of the Gaussian beam is too large to sufficiently suppress the strong backscattering, especially in the short distance (e.g. the minimal FoV angle of the 532-nm Gaussian laser beam is approximately 0.3 mrad in a 32-m distance). It mat may also be useful for free-space quantum key distribution (QKD) in bad weather condition [20,21] and QKD protocol which need high quality laser transmission [22].
The Bessel beam is impressed due to its feature of non-diffractive [23–29]. In this paper, we propose a noise-tolerant LiDAR with extremely small FoV by using zero-order Bessel beam laser. After propagating 31.5-m away in fog, the Bessel beam sustained well restrained with the central spot diameter was 1.86 mm, while the Gaussian beam would be with the spot diameter 7 times enlarged assumes that under the same conditions. As a result, the receiving FoV in our LiDAR system was achieved as small as 60 µrad offered a significant backscattering noise suppression, and the high-resolution 3D imaging was realized in heavy fog condition with the transmittance of 0.023. This research shows the Bessel-beam single-photon LiDAR could be considered as a potential technique applied to the practical sensing system compatible with autonomous driving in bad weather condition.
2. Bessel beam for small receiving FoV
Bessel beam can be mathematically described by the nth-order Bessel function. At distance L from the transmitter plane, the light field of zero-order Bessel beam (hereinafter referred to as Bessel beam) can be expressed as E(r,ϕ,L)=A0exp(iKLL)J0(krr)exp(±inϕ), where J0 is the zero-order Bessel function, kL and kr are the longitudinal and radial wavevectors with k = (kL2 + kr2)1/2 = 2π/λ, r, φ, and L are the radial, azimuthal and longitudinal components, respectively. The Bessel beam has a bright center lobe surrounded by a series of concentric rings, which are resulted from the interference of plane waves, whose wavevector is derived from a conical surface. During propagating, the central spot does not spread out within a long distance, and the sidelobes makes the light intensity reformed even if the beam is partially obstructed. These characteristics make the Bessel beam to propagate with high quality in a medium filled with scattering particles.
As one kind of diffraction optical element [30], the diffraction axicon can support much smaller physical angle (γ) than the traditional axicon to generate the Bessel beam within much longer non-diffractive distance. Experimentally, a diffraction axicon with the physical angle of 0.36 mrad is employed to manipulate a 532-nm Gaussian beam with a waist radius (ω0) of 8.0 mm to yield the required Bessel beam.
The beam spot is captured by a laser beam profiler (SP620U, Ophir Optronics, Israel). As shown in Fig. 1(a), the diameter of the central spot of the Bessel beam at 4 m is 0.78 mm @ 1/e2. After passing through 31.5-m thick fog with the transmission of 0.017, the intensity distribution of the Bessel beam spot is almost uninfluenced by the backscattering. The diameter of the central spot is measured as 1.86 mm at a distance of 32 m as shown in Fig. 1(b). As illustrated in Fig. 1(c), the central spot of the Bessel beam travels longer than 100 m with a very small divergence angle of ∼31 µrad. The maximum proportion of the central spot to the total spot energy (Rcs) is around 25 m. And the proportion of the central spot is larger than 10% from 10 m to 50 m. The receiving FoV is set to 60 µrad as shown in the red dotted circle in Fig. 1(b) to involve most energy of the central spot. Therefore, based on the Bessel beam, the LiDAR can make full benefits of the very small receiving FoV to greatly reduce the noise of backscattering and background light.
Fig. 1. (a) Intensity distribution of the Bessel beam spot at a 4 m distance; (b) Intensity distributions of the Bessel beam spot after passing through 31.5-m thick fog, the image size is 4.4 mm×4.4 mm; (c) The proportion of the central spot to the total spot energy (blue), and the diameter of the central spot at different distance in clear air (red); (d) The Rcs and its corresponding distance with different physical angle, where the green column is at 532 nm, ω0 = 8.0 mm, and n = 1.46, the red column is at 1550 nm, ω0 = 8.0 mm, and n = 1.445.
The laser energy utilization efficiency of the Bessel-beam LiDAR can be increased with the Rcs. The intensity distribution of zero-order Bessel beam is
3. Bessel-beam single-photon LiDAR system
The experimental setup of the Bessel-Beam single-photon LiDAR is shown in Fig. 2. It is a synchronous scanning imaging system. A collimated 532 nm laser beam with 16.1 mm in diameter is transformed into a Bessel beam by the diffraction axicon. Then, the Bessel beam passes through a polarizing beam splitter, and is scanned by a 2D galvo mirror. The unfavorable weather condition is stimulated by a fog chamber, and the target showed in Fig. 2(c) is placed at a 31.5-m long distance in the fog chamber. The echo light from the target is random polarized, so that half of the echo photons are selected by the PBS and coupled into a fiber to decrease the receiving FoV before being focused into a Si APD based single-photon detector (SPAD). The receiving FoV is 60 µrad, while the focal length of the lens is 150 mm, and the diameter of the fiber core is 9 µm.
Fig. 2. Schematic of the Bessel-beam single-photon LiDAR. Laser: a pulsed laser at 532 nm with the repetition rate of 127 kHz and the pulse width of 1.0 ns; BE: 10× beam expander; DOE: diffraction axicon; HWP: half-wave plate; PBS: polarizing beam splitter; GM: 2D galvo mirror; BPF: bandpass filter at 532 nm; L1, L2: focusing lens, L1 = 150 mm, L2 = 100 mm; M: silver mirror; COL: collimator; SPD: single-photon detector; TDC: time-to-digital converter; FPGA: field-programmable gate array device. Insets (b) and (c) are the photographs of the target and the fog chamber.
To make a clear comparison, the Gaussian-beam laser is also used to function the single-photon LiDAR. The collimate laser beam is expanded with a divergence angle of 0.3 mrad. The diameter of the Gaussian laser beam is 9.8 and 19.5 mm at 0 and 32 m distances, respectively. At last, the echo light is focused into the SPAD directly. The receiving FoV is 0.67 mrad, while the focal length of the lens is 300 mm, and the diameter of active area of the SPAD is 200 µm.
The SPAD is operated in an active quenching and gating mode [31,32], which has a timing jitter of 65 ps with a detection efficiency of 40% at 532 nm. And a time-to-digital converter (TDC) with the resolution of 64 ps is used to record the detection events. The 31.5-m chamber is fully filled with thick fog, and the transmittance at 532 nm is about 0.8%. The background and signal counts are recorded and analyzed for both of the Bessel-beam and Gaussian-beam LiDAR. The histograms recorded by the time-correlated single-photon counting (TCSPC) technique are shown in Fig. 3. In the LiDAR system, small receiving FoV usually leads to suppressed backscattering noise. However, the signal photons suffer great losses due to the small receiving FoV especially in the Gaussian-beam LiDAR. In our experimental setup, the non-diffraction feature of the Bessel beam helps the receiving FoV to involve the beam power 4 times more than the Gaussian beam in the same laser casting condition. Moreover, the energy occupation of the central spot can be further improved by adjusting the laser wavelength or the parameters of the diffraction axicon. For example, with the same parameters, the Rcs will be increased to ∼41.3% at 1550 nm. The signal photon counts are 154 cps and 71 cps of Fig. 3(a) and 3(b), which is basically consistent with the effective laser power in the FoV. As shown in Fig. 3(c), the backscattering noise has saturated the single-photon detector because of the large receiving FoV, which means the Gaussian-beam LiDAR cannot enhance the detection capability in strong scattering medium by increasing casting laser power.
Fig. 3. TCSPC histograms of the detection events with the accumulated time of 5 s and the transmittance of 0.8%.
4. Results
The Bessel beam owns a brighter central spot, which can not only reduce the receiving FoV to suppress the background noise, but also improve the resolution of the scanning imaging. The chamber photos in clear air, or in fog with the transmittance of 0.293, 0.023 and 0.010 are shown in Fig. 4(a) to 4(d). Figure 4(e) to 4(h) are the corresponding depth images with the beam scanning of 100 rows. The background noise was eliminated efficiently by using the spatial coincidence method [33]. Even if under the circumstance of thick fog with a transmittance of 0.023, the LiDAR is still capable to obtain a complete and clear three-dimensional contour. When the transmittance deteriorates even further into 0.01, the target imaging becomes blurry. Even so, the imaging quality in high-loss propagation can be improved by using more intense laser or increasing the aperture of the receiving system.
Fig. 4. Photo of the target in clear air (a), in fog with the transmittance of 0.293 (b), 0.023(c), and 0.010 (d); Depth image of the target in clear air (e), in fog with the transmittance of 0.293 (f), 0.023 (g), and 0.010 (h); Intensity image of the target in clear air (i), in fog with the transmittance of 0.293 (j), 0.023 (k), and 0.010 (l).
The intensity images are illustrated in Fig. 4(i) to 4(l). For each row, the data is segmented into 100 columns. These images are divided into 10000 grids with the width of 1.4 mm and the height of 2.2 mm. The photon counts of each grid are the intensities of each pixel. The mouth and eyes of the target can still be clearly distinguished in Fig. 4(k), which indicates that this noise-tolerance LiDAR also performs well for the intensity imaging in poor transmission condition.
After that, we perform the compared experiment of Gaussian-beam single-photon imaging with the FoV of 670 µrad in clear air and in fog with the transmittance of 0.304 and 0.090, and the corresponding depth images are shown in Fig. 5(a) to 5(c). To avoid photon-counting saturation in clear air, we attenuate the laser power down to 0.113 mW, and the laser power is 87.5 mW imaging in fog. The figures are not as clear as those in the Bessel-beam images. The intensity images are shown in Fig. 5(d) to 5(f). The eyes and mouth are dimly seen in clear air as shown in Fig. 5(d), and the facial expression can hardly be distinguished in foggy obstruction as Fig. 5(e) and 5(f). Compared to Bessel beam, Gaussian beam has a larger divergence angle which needs a bigger receiving FoV. Therefore, the noise-suppression ability and imaging resolution are poor in fog.
Fig. 5. Depth image of the target in clear air (a), in fog with the transmittance of 0.304 (b) and 0.090 (c); Intensity image of the target in clear air (d), in fog with the transmittance of 0.304 (e) and 0.090 (f).
Under the similar transmittance level, the performance of the Gaussian-beam single-photon LiDAR with bigger beam size and bigger FoV, is worse than the Bessel-beam single-photon LiDAR. This experiment verifies that, compared to the Gaussian beam, the Bessel beam has higher light intensity concentration in its central beam spot, so the Bessel-beam single-photon LiDAR has greater imaging performance and superior ability of resisting foggy disturbance in adverse air environment.
5. Conclusion
In summary, we demonstrate a Bessel-beam single-photon LiDAR to achieve the noise-tolerant imaging in thick fog. The well restrained center spot of Bessel beam supports a small receiving FoV of 60 µrad within 100 m, which leads to an effective suppression of the background noise and improvement of the imaging resolution. In the experiment, the noise-tolerant LiDAR obtained high-quality depth and intensity images in thick fog with the transmittance of 0.023. It provides a competitive technique for 3D imaging within the range of 100 meters in bad weather. In the further research, the operation wavelength of the noise-tolerant LiDAR can be optimized to 1.5 µm to take further advantages, such as higher eye safety threshold, stronger penetration in fog, and larger energy proportion of the central spot, to explore its application in autonomous driving in unfavorable weather conditions, and high repetition rate laser pulses can be used to improve the frame rate of LiDAR for the application in high-speed automatic driving.
Funding
National Natural Science Foundation of China (11621404, 11804099, 62075062, 62175067); Research Funds of Happiness Flower ECNU (2021ST2110).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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