In this work, we demonstrate a single-photon lidar based on a polarization suppression underwater backscatter method. The system adds polarization modules at the transmitter and receiver, which increases the full width at half-maximum of the system response function by about 5 times, improving the signal-to-background ratio, ranging accuracy, and imaging effect. Meanwhile, we optimize a sparsity adaptive matching pursuit algorithm that achieves the reconstruction of target images with a 7.3 attenuation length between the system and the target. The depth resolution of the system under different scattering conditions is studied. This work provides a new method for underwater imaging.
【AIGC One Sentence Reading】:A single-photon lidar system with polarization suppression enhances underwater imaging, improving signal-to-background ratio and ranging accuracy.
【AIGC Short Abstract】:This work introduces a single-photon lidar system for underwater 3D imaging, utilizing polarization suppression to enhance signal-to-background ratio and ranging accuracy. A sparsity adaptive algorithm improves image reconstruction, and the system's depth resolution is analyzed under various scattering conditions.
Note: This section is automatically generated by AI . The website and platform operators shall not be liable for any commercial or legal consequences arising from your use of AI generated content on this website. Please be aware of this.
Active optical depth imaging has a wide range of applications in scattered underwater environments, including defense[1], archaeology[2,3], and civil engineering[4]. The main limitation of underwater active optical imaging is the absorption and scattering of water bodies (forward and backward)[5], which can cause significant signal attenuation over short propagation distances, while weak echo signals are submerged in backward scattering noise. For the significant signal attenuation caused by laser transmission in water, high-power lasers are usually used to improve the echo signal. However, an increase in laser power also enhances underwater backscattering. Therefore, more and more researchers are choosing to use high-sensitivity detectors to collect weak photons. In recent years, photon-counting lidar has made significant progress in underwater applications due to its uniquely high optical sensitivity and excellent surface-to-surface resolution[6-9]. In 2015 and 2016, Aurora et al.[10-12] studied a high scattering underwater environment depth imaging system based on the time-of-flight (TOF) approach and the time-correlated single-photon counting (TCSPC) technique. The system consists of a pulse supercontinuum laser source, a monostable scanning transceiver, and a silicon single photon avalanche diode (SPAD) for detecting the returned optical signal. In the laboratory, depth images are obtained over distances of up to 8 attenuation length (AL) (one attenuation length being the distance that the light travels before its intensity is reduced to 1/e of its initial value), with a collection time range from 0.5 to 100 ms per pixel and an average optical power range of 0.8 nW to 950 µW. However, the system structure is complex, and the optical path requires high-precision adjustment. In 2023, Aurora et al.[13] demonstrated the fully submerged underwater transceiver system based on single-photon detection. The system operates at the central wavelength of 532 nm and is based on a Si-CMOS SPAD detector array interfaced to a GPU-equipped workstation for real-time, live imaging capabilities. However, the presence of forward and backward scattering may reduce contrast and spatial resolution in the system.
Two universal methods have been proposed to suppress backscattering noise in underwater environment imaging before data acquisition[14,15]. One method is distance-gated imaging[16], where the receiver is time-gated and only allows detection signals related to the expected return of target pulse illumination, thus removing most of the backscattered light while maintaining the complete return signal. This method has been used for imaging with larger attenuation lengths, such as 5 or more attenuation lengths[17]. However, this method requires prior knowledge of the distance information of the target. Another method is synchronous scanning imaging, where a highly collimated source is used to scan the target, and the receiver has a narrow field of view[18]. This method greatly reduces the backscattered light generated by the overlapping volume between the illumination beam and the imaging system field of view, but it requires high system accuracy. In addition, imaging algorithms are often used to process the backscattered noise after data acquisition, achieving depth estimation of underwater targets[19-22]. For example, Sandor et al.[23] proposed a real-time image reconstruction method based on two-step statistics. The first step is to use object detection methods to locate information pixels with target return values, reject information pixels that only contain background counts, and achieve data compression. The second step is to use data statistics and multi-scale information to provide clear depth and reflectance images. However, in high-scattering environments, the algorithm is likely to encounter localization errors in the first step, which can affect the reconstruction effect.
This work presents a single-photon lidar system based on polarization suppression of the underwater backscatter method. The method involves adding a specific rotation polarization module consisting of a linear polarizer and a quarter-wave plate to both the transmitter and receiver of the system so that the transmitter emits right-handed circularly polarized light, while the receiver only receives left-handed circularly polarized light. The polarization effect of circularly polarized light can effectively suppress underwater backscattering. At the same time, a sparsity adaptive matching pursuit (SAMP) algorithm is improved and optimized, which controls the step size by setting multiple thresholds when the signal sparsity is unknown in the scene, and obtains the effective photon range of echo photons, improving the reconstruction quality and imaging speed.
Sign up for Chinese Optics Letters TOC Get the latest issue of Advanced Photonics delivered right to you!Sign up now
2. System and Experimental Description
Figure 1 shows the schematic of the experimental setup. The illumination source used was a supercontinuum laser source (SC-5, YSL PHOTONICS, Wuhan, China) with an output spectral range of 470–2400 nm, a pulse-width of approximately 100 ps, and a repetition rate of 5 MHz. The center wavelength of the 532 nm narrowband filter is (532 ± 10) nm, and the peak transmittance is . The scanning device used (SG7210-B, SINO-GALVO, Jiangsu, China) consists of a scanning head with a reflector, a control board, and a bias source, with a scanning range of and a scanning accuracy of 0.1°. The control board can be adjusted through computer (PC) software, and when the galvanometer is working, the control board will transmit modulation signals to the oscilloscope. The single photon detector (EQR06 11-3030D-S, Novel Device Lab, Beijing, China) used consists of a bias source, a SiPM chip, and a preamplifier, with a detector photosensitive surface of , a photon detection rate of 30% at 420 nm, an effective detection range of 350–600 nm, and a dark counting rate of . The sampling rate of the oscilloscope (HRO 64Zi, LeCroy, American) used is 20 Gs/s, with a bandwidth of 400 MHz and 4 input channels.
Figure 1.Schematic diagram of the underwater depth imaging system.
To reduce the impact of underwater backscattering noise, this system adopts an off-axis optical path[24] and polarization-sensitive method to suppress underwater backscattering[25]. The modulated right-handed circularly polarized light interacts with water particles, and the scattered right-handed circularly polarized light will tend to depolarize, greatly damaging the polarization information carried by the original laser. The light propagating through a more direct path will maintain its initial polarization state[26]. Using this principle, a wave plate combination consisting of a pair of specific rotating linear polarizers (WP25M-VIS, Thorlabs, American) and a quarter-wave plate (WPMQ10M532, Thorlabs, American) is placed at the transmitting and receiving ends of the system to control the polarization state of the laser. For the transmitter, the wave plate combination used is a linear polarizer with a 45-degree angle to the quarter-wave plate, with the linear polarizer in the front and the quarter-wave plate in the back. The emitted laser is modulated into a right-handed circular polarization state. The wave plate combination at the receiver is a quarter-wave plate in front and a linear polarizer in the back. By adjusting its angle, the combination of the receiving wave plates only allows for a left-handed circular polarization state, thereby suppressing backward scattering noise. The laser output is sequentially transmitted through narrowband filters, linear polarizers, and quarter-wave plates to the galvanometer. At the same time, the oscilloscope receives the synchronous pulse signal generated by the laser. The computer software controls the galvanometer to work through a control board, which transmits a modulation signal to the oscilloscope during galvanometer operation. After being emitted by a galvanometer, right-handed circularly polarized light undergoes scattering in water and reflection on the target surface. According to the polarization effect of circularly polarized states, the backscattered light still maintains a right-handed circularly polarized state, which is filtered by the wave plate group in front of the receiver. The photons reflected by the target become left-handed circularly polarized light, which is received by the detector through the wave plate group in front of the receiver and displayed in the oscilloscope through a preamplifier. The oscilloscope calculates TOF data based on synchronous pulse signals and signal pulses received by the detector, and saves the data based on the modulation signal of the control board. The data was copied to the computer, and the program was used to process the data of each pixel into a statistical histogram. The statistical histogram is set to 2000 intervals, each interval is 10 ps, and all pixels are combined into a matrix file as the initial data.
Before each depth profile measurement, the attenuation of the environment was measured using the method and setup described in Ref. [5]. This method allowed us to measure the average optical power of and at a distance of in water. According to Beer Lambert’s law[27], the transmittance of water above half a meter was then calculated as where is the attenuation coefficient of the environment and is the number of AL.
To verify the improvement of the system’s noise resistance after adding a polarization module, we obtained the full width at half-maxima (FWHM) of the system without and with the addition of a polarization module under the condition of 1.9 AL between the system and target. All experiments were conducted in a dark indoor water tank. We placed the Lambertian reference flat target with a nominal reflectance of 99% (Spectralon Diffuse Reflectance Target, Labsphere, North Sutton, NH, USA) at a position of approximately 1.1 m in water, with a laser output power of 3.5 mW. We collected data at different acquisition time of 50, 100, 150, 200, and 250 s, and performed histogram statistics on the data. Gaussian functions were used to fit the histograms to obtain the instrument response function (IRF). Figure 2(a) shows the IRF without the addition of a polarization module. The FWHM of the IRF at different acquisition time is calculated and averaged, resulting in an FWHM of approximately 1280 ps. Figure 2(b) is the IRF when a polarization module is added. After the same operation, the FWHM is calculated to be approximately 255 ps. According to the results, the noise resistance of the system has been improved by about 5 times.
Figure 2.IRF fitting plot. (a) The IRF without polarization module. (b) The IRF with a polarization module added.
Table 1 shows the average target return for each pixel and signal-to-background ratio (SBR) at attenuation lengths of 1.9, 3.6, 4.4, 5.6, 6.7, and 7.4 between the system and target without and with the addition of polarization modules. The SBR is defined as the ratio between the number of counts in the highest bin in the peak and the average background per bin. The acquisition time is 200 ms, and the calculation is performed on approximately 100 pixels containing target information. From the data in the Table 1, as the attenuation length increases, the average target returns of each pixel and SBR decrease, and the experimental results are in line with expectations. Meanwhile, adding a polarization module reduces the average number of target returns per pixel, but the SBR of the system is improved. After 5.6 AL, the difference between the SBR without and with the addition of a polarization module in the system decreases. This may be due to the depolarization effect of the modulated circular polarization state as the length of water attenuation increases, resulting in a decrease in the target signal.
Table 1. The Average Target Returns and SBR of Each Pixel Scanned by the System without and with Polarization Modules at Different Attenuation Lengths
Table 1. The Average Target Returns and SBR of Each Pixel Scanned by the System without and with Polarization Modules at Different Attenuation Lengths
Attenuation length
Average optical power (mW)
Polarization module not added
Add polarization module
Average peak return per pixel
SBR
Average peak return per pixel
SBR
1.9
0.7
9825.3
45.8
6761.5
77.2
3.6
3.5
7447.2
25.7
5553.8
68.7
4.4
3.5
5961.9
16.2
4973.4
55.2
5.6
3.5
4434.5
13.4
2954.4
22.4
6.7
3.5
2933.5
12.1
2148.3
15.2
7.4
3.5
2210.4
10.9
1473.5
12.8
The flange profile was imaged in a 3.6 AL between the receiver and the target using both systems without and with the polarization module added. The acquisition time per pixel was 20 ms, and the laser output power was set to 3.5 mW. The attenuation of the target echo and the influence of backscattering are shown in Fig. 3. The single-pixel histograms of target information under different conditions are as follows: Fig. 3(a) shows the polarization module not added to the system, and Fig. 3(b) shows the polarization module added to the system. When the polarization module is not added to the system, the intensity of the target echo signal severely attenuates. There are many underwater backscattered echo signals in the front end of the system. They have a wider time profile, which may affect the correct depth value in the imaging reconstruction process and cause accuracy errors. When the polarization module is added to the system, the histogram shows a clear single peak returned from the target, indicating that the use of the polarization module can filter out most scattered light with different polarization states. Figure 4 shows the intensity and depth distribution of the flange target obtained using our improved and optimized algorithm (described below) without and with the addition of polarization modules in the system. The first column is the reference image obtained under the condition of collecting 20 ms per pixel in clean water. The second column is the intensity and depth map distribution map when the polarization module is not added to the system. The third column is the intensity and depth map distribution map when the polarization module is added to the system. The comparison results of the second and third columns clearly indicate that the details of the flange plate of the intensity and depth map with the addition of the polarization module are more complete and clearer. This may be because, when the polarization module is not added to the system, more and more backscattered signals are collected, and fewer target signals are returned. The increase in noise during image reconstruction affects the depth estimation of imaging. We also evaluate the imaging quality by calculating the MAE between the estimated depth and the true value, which is defined as where is the number of imaging pixels, is the true value of pixel i, and is the estimate of the pixel . The smaller the MAE value, the better the imaging model. We use the first column of the reference images as the true values. From Fig. 4, the MAE value without the polarization module is 5.4278, while the MAE value with the polarization module is 1.9731. The above results all indicate that adding a polarization module to the system helps to improve the overall imaging effect of the system.
Figure 3.Acquired detection histogram. The attenuation length between the system and the target is 3.6. Collected data of the target to plot timing histograms under different conditions: (a) polarization module is not added to the system; (b) polarization module is added to the system.
Figure 4.The depth and intensity of a flange target at 3.6 AL between the system and the target under different conditions: (a) reference images; (b) polarization module is not added to the system; (c) polarization module is added to the system.
Due to the addition of a polarization module in the system, the number of detected photons decreases, and the photon count distribution can be assumed to follow a Poisson distribution. We assume the background noise matrix and use laser pulses to irradiate the corresponding pixels in the scene, resulting in a luminous flux of where and are the 3D structure and reflectance of the scene that we aim to recover and is the speed of light. Due to the detection efficiency and dark counting of the detector , the total intensity detected within a laser detection period is the final detected intensity, derived from the following equation:
Therefore, the distribution of the photon number after periods of laser pulses can be obtained as
3.2. Reflectivity reconstruction
Based on the Poisson distribution function, we establish its observation model probability density function as
We set as the negative log-likelihood of the reflectance , and log is the natural logarithm. S is the pulse signal waveform of the laser. The grayscale of the reflectance image can be scaled, so the value of S can be set arbitrarily. The algorithm smooths the target through the total variation (TV) norm, solves the regularization optimization problem, and obtains the estimated reflectance of the target. is a regularization parameter, and selecting an appropriate value can minimize the error between the final value and the true value. Thus, the reflectance map of the object can be obtained, and details can be found in Ref. [28],
3.3. Determine the effective photon interval
For depth, the maximum likelihood problem involving dark counting and background noise is not a convex optimization problem, which increases the difficulty of calculation. Therefore, the collected target depth set is denoted as , the detection period is set to 20 ns, is the minimum interval of the histogram, is the total number of time zones, and is denoted as the photon detected in the th time zone of the experiment. Without turning on the laser, turn on the detector, measure the values of the dark count and noise, and subtract them from the target depth set to obtain the denoised target depth set . Therefore, the likelihood estimation problem becomes where is a noisy version of convolved with , is discretized into bins of width , is the discrete convolution operator, is the L0-norm of , and K is the number of non-zero elements in the reconstructed . When reconstructing depth maps, determining the sparsity K of the signal and its corresponding effective photon interval is the problem we need to solve. Therefore, in this paper, the SAMP algorithm is used to estimate the optimal solution. Due to the unknown signal sparsity K, first, we need to estimate the signal sparsity to obtain the initial value of the signal sparsity. If matrix Ø satisfies the restricted isometry property (RIP) property with parameter , if there are Ø holds, then we have , where is the estimated sparsity of the signal and represents the set of indices corresponding to the atoms that best match the residuals in Ø. Based on this, by continuously increasing the value of , the estimated sparsity value and the initial difference can be obtained. By setting a threshold , if is satisfied, where X is the detected discrete signal, the step size is halved; otherwise, iteration continues. Multiple thresholds are set to control the step size, and the step size is halved times based on the value of different thresholds , reducing the number of signal estimations and improving processing speed. Using the above methods, the sparsity of scene K can be estimated from the filtered initial signals, and the effective photon interval corresponding to each sparse signal can be found.
3.4. Depth reconstruction
Similar to reflectivity, we can obtain the probability density function about the time zone:
Measuring the laser pulse shape and applying the left Riemann and approximate integration, we can obtain the negative logarithmic likelihood function, which can be simplified to
Applying spatial smoothness constraints similar to the reflectivity TV norm to depth images, and estimating the depth Z by solving the convex optimization problem within the effective photon interval ,
4. Results and Discussion
The objects imaged in the experiment and their sizes are shown in Fig. 5. The targets used in depth and intensity measurements are shown in Figs. 5(a) and 5(b). The target is a plastic flange with an outer diameter of 17.8 cm and an inner diameter of 8.3 cm, containing 8 small holes with a size of and a depth of 5.5 cm. The depth resolution of the system in different scattering environments was studied using the depth targets shown in Figs. 5(c) and 5(d). The depth target has depth characteristics within the range of 0.25 to 5 cm.
Figure 5.Photographs of the object and its dimensions used in the experiment. (a) Plastic flange, side shown by (b). (c) Depth-resolution object with nine square columns providing ten planes of different heights, shown from the side (d).
4.1. Depth imaging in different underwater scattering environments
The depth imaging capability of the system in various scattering environments was preliminarily studied using the flange shown in Fig. 5(a). To increase the scattering level of water, different scattering environments were simulated by injecting tap water and different weights of spherical powders with a diameter of 1 µm into the water tank. The flange was kept at a distance of 1.80 m in the water. In order to quantitatively describe water quality, the water attenuation coefficient was measured at different concentrations using the method described in Ref. [5].
During the experiment, the laser power was set to 3.5 mW, and the scene size was set to . The collection time per pixel is set to 20 ms, and data are collected in environments with attenuation lengths of 1.9, 3.6, 4.4, 6.7, 7.4, and 8.5 between the system and the target. Our improved and optimized algorithm is used to estimate the reflectivity and depth. The experimental results are shown in Fig. 6. The first column shows the situation of unfiltered tap water, which is equivalent to 1.9 AL between the system and the target. The following columns show an increase in scattering levels in water, with a maximum of 8.5 AL. As the scattering level increases, the depth resolution of the depth profile decreases due to the lower photon return from the target and the higher background level. This may be because the more turbid the water quality, the more times the target echo photons are scattered, resulting in a depolarization effect. Backscattering increases the background count level and reduces signal strength, leading to a deterioration in reconstructed image quality. The results indicate that, in the case of high scattering intensity, the target at 7.3 AL can be detected, but it cannot be distinguished from the background, and the target at 8.5 AL cannot be detected. The system can clearly distinguish targets within 4.4 AL, but as the scattering level further increases, the targets gradually disappear.
Figure 6.Intensity (top row) and depth (bottom row) profiles of the flange target at 1.9, 3.6, 4.4, 6.7, 7.4, and 8.5 attenuation lengths between the system and the target. The acquisition time per pixel is 20 ms.
4.2. Depth imaging at different acquisition time per pixel
The second experiment further investigated the imaging performance of the system at different acquisition time per pixel. The attenuation length between the system and the target in this study is relatively low, around 3.6 AL. Data were collected for pre-pixel at a collection time of 20, 2, 0.2, and 0.02 ms, and our improved and optimized algorithm was used for estimation. The experimental results are shown in Fig. 7. The columns from left to right correspond to data at different collection time, namely 20, 2, 0.2, and 0.02 ms. The first and second rows are the strength and depth profiles of the flange. From the graph, when the acquisition time for pre-pixel is 20 ms, the details of the flange can be well restored. As the acquisition time per pixel decreases, the resolution of the image also decreases accordingly. However, the target can be reconstructed within an acquisition time of 0.2 ms per pixel and can still be detected within an acquisition time of 0.02 ms per pixel. To see the restoration of the flange more intuitively, we removed the background noise and only performed 3D imaging on the pixels of the flange, as shown in the third row of Fig. 7. As the acquisition time per pixel decreases, the 3D imaging effect of the target gradually became less ideal, which may be due to a decrease in the number of collected target signals returned, leading to a deterioration in the quality of the reconstructed image. We also evaluate the imaging quality by calculating the MAE between the estimated depth and the true value. The result is shown in the fourth row of Fig. 7. When the collection time per pixel is 20 ms, the MAE value of the target can be ignored. As the acquisition time per pixel decreases, the MAE value of the image increases, indicating that the depth estimation of the target is affected by the decrease in the number of photons. Finally, we also studied the target reconstruction time of our improved and optimized algorithm at different acquisition time, and the results are shown in Table 2. The algorithm has superiority, with a very fast target reconstruction speed that does not change with the change of the target acquisition time.
Figure 7.Intensity (first row), depth (second row), 3D (third row), and MAE (fourth row) profiles of the flange target at 3.6 AL between the system and the target. The acquisition time per pixel was varied by software from 20 to 0.02 ms.
Table 2. The Processing Time of Our Improved and Optimized Algorithm for Data at Different Acquisition Time per Pixel
Acquisition time per pixel
20 ms
2 ms
0.2 ms
0.02 ms
Processing time of our improved and optimized algorithm
0.1626 s
0.2088 s
0.1990 s
0.2154 s
4.3. Depth resolution
To investigate the achievable depth resolution of the system in different scattering environments, we varied the scattering level in water and imaged the depth target. Figure 8 shows the depth profiles of the deep target in different scattering environments. During the experiment, the laser power was set to 3.5 mW, and the scene size was set to . The acquisition time per pixel was set to 20 ms. The depth target, as shown in Figs. 5(c) and 5(d), has 10 different depths of surfaces, which have the depth characteristics of several millimeters (). From the results in Fig. 8, the depth resolution remains above 2.5 mm at 4.6 AL and begins to decrease at 5.3 AL. At 6.7 AL, depth features on the order of 1 cm can still be retrieved, but at higher scattering levels, the depth structure of the target cannot be identified. At attenuation lengths above 8.2 AL, the target is almost undetectable.
Figure 8.Depth profiles of the deep target at 1.9, 3.1, 4.6, 5.3, 6.7, 7.2, and 8.2 attenuation lengths between the system and the target.
This work demonstrates underwater optical imaging based on polarization suppression backscatter technology. The proposed method incorporates a specific rotational polarization module consisting of a linear polarizer and a quarter-wave plate at both the transmitter and receiver of the system, effectively suppressing underwater backscattering by utilizing the memory polarization effect of circularly polarized light. At the same time, an SAMP algorithm has been improved and optimized based on the system, which is suitable for few-photon imaging. It processes echo photons to obtain effective photon spacing without requiring prior information, improving reconstruction quality and imaging speed. In the experiment, we achieved image reconstruction under the condition of up to 7.3 AL between the system and the target. We studied the millimeter depth resolution of the system, which can reach 4.6 AL, and the centimeter depth resolution, which can reach 6.7 AL. This proves that the system has the potential for deep imaging of underwater environments and provides exploratory value for promoting the application and promotion of photon-counting lidar systems in underwater environments.
In actual underwater detection, this system has certain limitations. First, factors such as the material, roughness, and laser incidence angle of the detected target can cause partial depolarization of the echo light. Second, for outdoor use, it is necessary to modify the optical settings of the receiver to further reduce the background noise. These are all interesting questions worth studying in the future.
[2] B. Foley, D. Mindell. Precision survey and archaeological methodology in deep water. ENALIA: J. Hellenic Institute of Marine Archaeology, 36, 13(2002).
[3] P. J. Sanz, A. Peñalver, J. Sales et al. Multipurpose underwater manipulation for archaeological intervention. Proceedings of the VI International Workshop on Marine Technology, 15(2015).
[4] I. Schjølberg, T. B. Gjersvik, A. A. Transeth et al. Next generation subsea inspection, maintenance and repair operations. Proceedings of the 10th IFAC Conference on Control Applications in Marine Systems (CAMS), 13(2016).
[12] A. Maccarone, A. Halimi, A. McCarthy et al. Underwater three-dimensional imaging using single-photon detection. Conference on Lasers and Electro-Optics (CLEO), SF2M.2(2017).
[21] J. Koo, A. Halimi, A. Maccarone et al. A Bayesian based unrolling approach to single-photon lidar imaging through obscurants. 30th European Signal Processing Conference (EUSIPCO), 872(2022).
Haidong Ye, Rui Xu, Jiafeng Sun, Hang Lü, Yan Shi, Yunfeng Song, Weiwei Liu, "Underwater depth imaging of a single photon lidar system based on polarization suppression," Chin. Opt. Lett. 22, 121101 (2024)