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Abstract
Mono-static system benefits from its more flexible field of view and simplified structure, however, the backreflection photons from mono-static system lead to count loss for target detection. Counting loss engender range-blind, impeding the accurate acquisition of target depth. In this paper, count loss is reduced by introducing a polarization-based underwater mono-static single-photon imaging method, and hence reduced blind range. The proposed method exploits the polarization characteristic of light to effectively reduce the count loss of the target, thus improving the target detection efficiency. Experiments demonstrate that the target profile can be visually identified under our method, while the unpolarization system can not. Moreover, the ranging precision of system reaches millimeter-level. Finally, the target profile is reconstructed using non-local pixel correlations algorithm.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Underwater optical imaging holds great potential for marine science and underwater detection [1,2]. However, conventional Light Detection and Ranging (LiDAR) technique suffers from strong absorption and scattering effects in water, resulting in reduced imaging performance in underwater environments [3]. The rapidly evolving Single-Photon Avalanche Diode (SPAD) [4,5] and the Time-Correlated Single Photon Counting (TCSPC) technique has been widely employed in LiDAR, which has remarkably improved its ability to detect targets in environments with limited luminosity. Hence, this technique promotes extensive application in underwater detection. [6–11].
Underwater single-photon imaging system utilizes the time-of-flight (ToF) method, applying both TCSPC technique and SPAD to capture depth profiles of objects. TCSPC technique involves measuring the time delay between the input pulse and the photon detection event from the SPAD, and the discrete waveform is formed by accumulating a large number of reflected photons which allows the acquisition of information regarding the depth of the target. Finally, by repeating the above measurements for each pixel, 3D information of the target can be obtained. The transceiver system can be designed in either a mono-static or a bi-static configuration. Compared with the bi-static system, the mono-static system presents flexible field of view and simple structure [12]. However, the backreflection photons (BRP) from mono-static system lead to count loss and thus a range-blind for target detection. According to the TCSPC technique, after recording the first arriving photon, the detector triggers dead time during which time echo photons can not be recorded, and thus fails to detect target in blind range (detector’s dead-time equivalent distance). The BRP is detected by the SPAD before the target signal, and the target signal is much lower in energy than the BRP because it has been transmitted through the water, thus resulting in a loss of counts, which leads to blind ranging of the target. This problem is even challenging in underwater environments where the BRP surpasses that of the underwater target [13,14].
Pawlikowska et al. adopted high-speed electronic range-gated technique to alleviate system noise in single-photon imaging systems by regulating the opening time of SPAD, where the SPAD only works within the user defined time gate [15]. However, the range-gated technique requires fast electronics and prior knowledge of the target’s distance [16]. Consequently, despite the theoretical maturity of range-gated, range-gated technique apply to underwater single-photon imaging remains challenging.
Moreover, to address the strong noise which is common in highly scattering attenuation environment, Rapp et al. underscored the unmixing of contributions from signal and noise sources [17–19]. Halimi et al. adopted a Bayesian approach, where the Poisson distributed observations are combined with prior distributions regarding to the parameters of interest,and hence joint posterior distribution [20–22]. Peng et al. analyzed the non-local features, and achieved high-quality reconstruction under extreme conditions [23]. These methods primarily concentrate on post-processing. Better results can be achieved by improved system design and tailored photon efficient algorithm.
Researchers from photonics community have developed underwater polarization imaging techniques from the polarization characteristics of the optical field. Guan et al. used the polarization difference to effectively separate the target signal from the background scattering, thus realizing clear imaging of underwater targets [24–27].
To best of our knowledge, current research on polarized single-photon imaging system mainly focus on the transmission in air. Preliminary experiments in [28–30] have verified that polarized single-photon detection technology can effectively improve the signal-to-noise ratio. Therefore, this technology can be considered as a promising solution in underwater blind range detection.
This paper proposes a method that improves the detection efficiency of the target by using polarization. Our methodology aims to mitigate the loss of photon counts, thereby elevating the efficiency of target detection [31]. This is achieved by decreasing the probability of BRP triggering the detector’s dead time, and capture the target signal with a highly sensitive SPAD, thus increasing the efficiency of target detection within the underwater blind range. Since the underwater environment and polarization characteristics lead to a scarcity of signal photons, efficient reconstruction algorithm is applied to further optimize the reconstruction results. The proposed method is validated through imaging experiments, and the results indicate that the algorithm significantly improves the target detection efficiency.
2. Theoretical analysis
2.1 Model description
Due to the response characteristics of the SPAD and the TCSPC technique, the response state of the detector can be described by Markov chains. Markov chains are a type of stochastic process whose future state only depends on the current state. It can be used to model and analyze the response of single-photon detectors within two adjacent detection periods in underwater environment.
In this paper, the state $(z,h)$ is used to denote the response state of the detector during a detection period, with $z$ representing the response state of the BRP detection and $h$ representing the response state of the target detection, where "1" stands for response and "0" means no response. Thus, state A(0,0) represents the absence of both BRP and the target, while state D(1,1) represents the detection of both BRP and the target in a single detection period. Similarly, state B(0,1) and state C(1,0) mean that target is detected and BRP are detected in one detection period, respectively.
Note that it is assumed that other noise are not considered, either BRP or the target would be responded in each detection period, and that BRP and the target would not be responded simultaneously, in other words, states A and D would not consider. Accordingly, the detector response in two adjacent detection periods should be either state B or state C. Based on the above assumption, we could express the state transfer matrix as
2.2 Principle analysis of detection efficiency
Figure 1 is a schematic diagram of the detection efficiency of target based on polarization enhancement. The laser emits a partially polarized pulsed laser, which generates pulsed laser with vertical linear polarization through a linear polarizer, and pulsed laser is transmitted to the target, it is partially reflected by the smooth surface of water tank (i.e., BRP), which maintains a vertical linear polarization state. Meanwhile, the other part is transmitted into the water and to the target, which has a strong depolarization characteristic when the target surface is relatively rough, so that the diffusely reflected light from the target contains both the horizontal component P and the vertical component S of polarization concomitantly. When the BRP pass through the Polarization Beam Splitter (PBS), the polarization properties of the light are utilized to prevent the BRP from penetrating the PBS, while the horizontal component of the target’s polarized light transmits the receiving optical system through the PBS and is transmitted to the SPAD through the optical fiber, where the absorbing material is used to absorb the reflected light from the PBS. The linear polarizer acting in conjunction with the PBS in the system can play the role of polarization to enhance the detection efficiency of the target, so this paper describes above a systems as a polarization-based imaging system versus a unpolarization imaging system, with the difference between them being the presence or absence of a PBS.
$\eta _{s}$ denotes the reflectance of the PBS to the vertically polarized light S; $\eta _{p}$ represents the transmittance of the PBS to the horizontally polarized light P; $\phi _{p}$ stands for the percentage of the horizontally polarized component of target. In the case of a fixed counting rate, the state transfer matrix becomes:
Figure 2 shows the single-pixel waveform comparison schematic diagram between polarization system and unpolarization system; Fig. 2(a) and 2(b) illustrate the single-pixel reflected photons detected by the unpolarization system and the polarization-based system, respectively; Fig. 2(c) and 2(d) show the breakdown of Fig. 2(a) and 2(b) into BRP and target reflected photons, respectively, with the red waveform indicating the target signal and the blue waveform indicating the BRP. When the detection is based on the unpolarization imaging system, the target cannot be distinguished from the reflected photons at all, whereas the intensity of BRP decreases significantly in the detection based on the polarization imaging system, and the target outline is clearly visible from the return photons.
Fig. 2. Schematic comparison of single-pixel return photons detected w. and w./o. polarization system. (a) and (b) Show the single-pixel detection return photons of the same location of the underwater target w. and w./o. the polarization-based system, respectively. (c) and (d) Show the signal decomposition map of a and b, respectively, where the blue color indicates the return waveform of return photons from the device export (BRP) and the red color indicates the return waveform of target signal.
2.3 Reconstruction algorithm
In this paper, the following algorithms are investigated to address the issue of sparse reconstruction of underwater target signals, which process the 3D information of the target to derive depth and reflectivity information.
1. Peak algorithm is based on the concept that the peak time delay of the photon counting histogram is regarded as the time when the SPAD detects the returned photons. According to the large number theorem, the photon count at the peak should be considerably higher than that at other positions, and the peak position is relatively stable, as in Eq. (3).
2. Cross-Correlation algorithm is based on the cross-correlation between the reflected signal and Instrument Response Function (IRF) to obtain the time delay information of the target, thus acquiring the depth information of the target. The algorithm is also known as the matched filtering algorithm [32–34].
3. Optimization based Non-local 3D Restoration (OPN3DR) [35]. This algorithm is based on learning non-local spatial correlations between pixels/patches and statistical estimation of the images of interest. The approach uses multiresolution to obtain robust results, non-uniform sampling to reduce the computational cost, and an ADMM algorithm to achieve fast estimation.
3. Experiment setup
In the experimental system shown in Fig. 3, the pulse signal was engendered by a FL-532-PICO CJ10963 laser from Changchun New Industries (CNI), the SPAD employed was an Excelitas DTS_SPCMAQRH-16, the TCSPC counter was a PicoQuant PicoHarp 300, and the Ophir PD300-3w served as the optical power meter for attenuation coefficient calibration. Additionally, the GCC-402023, produced by Daheng Optics, was utilized as the PBS. The control unit was an Intel Core i7-9700 CPU based computer. The main parameters of the system are given in Table 1.
Fig. 3. Experimental system setup. (a) The underwater polarization mono-static single-photon imaging system. (b) Imaging system without polarization. In (a) and (b), the green line indicates the transmitting optical path and the red line represents the receiving optical path.
Table 1. Main parameters of the system
To reduce the probability of the detector triggering dead time, a polarizer was placed before the perforated reflector to generate S-state polarized light, and the PBS was placed in front of the detector. As the linear polarizer and PBS work in conjunction to suppress BRP by polarization, two systems were built w. and w./o. PBS, as shown in Fig. 3.
4. Experimental analysis
The experiments were conducted by building an underwater single-photon imaging system based on polarization and an unpolarization single-photon imaging system, to analyse the recorded data to validate the detection of underwater targets.
4.1 Attenuation coefficient calibration
To simulate the transmission characteristics of laser in underwater environment, a 0.35 m water tank was deployed in the laboratory environment, as shown in Fig. 4(a), and the photons reflected from the tank wall are BRP. In this paper, the water tank wall is used to simulate the optical export of an underwater single-photon detection device.
Fig. 4. Attenuation coefficient calibration. (a) The experimental water tank. (b) A schematic diagram of the attenuation coefficient calibration method.
The attenuation coefficient calibration method was implemented as follows: An optical power meter was operated to measure the optical power before and after passing through the water tank. To simulate the highly attenuating and scattering underwater environment, milk was injected into unfiltered tap water to imitate underwater environments. Meanwhile, to eliminate the influence of tank on the light, the average light power was measured in front of and behind the empty water tank as $132\mathrm{\mu}$W and $95\mathrm{\mu}$W respectively, therefore 72% of the light could pass through the water tank without water. The average optical power in front of and behind the water tank in milk environment was $132\mathrm{\mu}$W and 270nW, respectively. The attenuation coefficient calibration method is shown in Fig. 4(b). Since the light range in air was very short, the attenuation in air is ignored here, and the optical power was averaged from multiple measurements.
According to Beer Lambert’s law, the attenuation coefficient is
where $P_b$ represents the power of the laser out of the water tank; $P_f$ denotes the power of the laser in front of the water tank; $d$ is the length of the water tank (i.e., the range of laser transmission in the water); the turbidity attenuation coefficient $\alpha _m$ of milk is 16.8, as calculated in Eq. (5).4.2 Ranging experiments
4.2.1 Comparative experiments
The target (a brick made by clay) was placed in the glass water tank, as shown in Fig. 5, and the tank wall was simulated as the optical export of the sealed unit during underwater detection, where Fig. 5(a) and Fig. 5(b) are the actual images of the target, respectively. The attenuation coefficient $\alpha _m$ measured in the method described in subsection 4.1 is 17.7. Since the dead time of SPAD utilized in this paper was 22 ns, which corresponds to 2.48 m of light transmission in water, and the length of the tank was 0.35 m, the entire water tank was in the range-blind area of the system. Hence, the target could be fixed at any location of the tank to simulate underwater range-blind target detection.
Fig. 5. Test scene. (a) and (b) are captured using ordinary camera. (c) The schematic diagram of two points A and B, where point B is positioned 10 cm behind point A.
Figure 5(c) includes the schematic diagram of the target location, where Point A was 15 cm from the front wall of the tank and Point B was the location where the target was moved a depth $L$ (in this case is 10 cm) backward from Point A. In this section, the comparative experiment of detection w. and w./o. polarization was first conducted for the target at point A. The single pixel acquisition time was set to 10s, enough acquisition time to effectively acquire the reflected signal and avoid the effect of sparse reflected photons on the target reconstruction, so as to validate the effectiveness of the polarization system to extract the target signal.
The target detection results at point A are shown in Fig. 6, with Fig. 6(a) and Fig. 6(b) showing the detection results of the underwater system without polarization at point A and that of the system based on polarization. In Fig. 6(a), the (1) waveform is the reflected photons from the perforated reflector in the system, corresponding to the green waveform of (1) in Fig. 6(b). The highest peak in Fig. 6(a) was the BRP, corresponding to the blue peak in Fig. 6(b). The (2) waveform in Fig. 6(a) is the trailing BRP, while the red waveform in (2) in Fig. 6(b) indicates the overlap of the trailing BRP and the target when the target contour can be clearly distinguished from the BRP. Figure 6(a) reveals that the target cannot be identified without polarization detection results as it can be clearly distinguished based on the polarization detection results in Fig. 6(b).
Fig. 6. Comparison of detection results of point A under single pixel acquisition time of 10s. (a) Shows the detection results without the polarization system. (b) Indicates the detection results based on the polarization system.
Compared with the detection result in Fig. 6(a) without polarization, the peak BRP in the detection result Fig. 6(b) based on polarization decreases from 80703 to 821. This intensity reduction of 99% is in accordance with the theoretical analysis and the target outline can be clearly seen in the reflected waveform, indicating that the method based on polarized light has an obvious effect in suppressing the BRP and reducing the count loss of the target. In order to further verify the general applicability of the proposed method, comparative experiments with single-pixel acquisition time of 100 ms, 1 s, and 5 s were conducted under the same experimental conditions.
Figure 7 shows the comparative experimental results of detection w. and w./o. polarization system for different acquisition time at point A. In Fig. 7, (a), (c), and (e) represent the detection results without polarization for acquisition time of 100 ms, 1 s, and 5 s, respectively, and (b), (d), and (f) are the results of detection based on polarization for acquisition time of 100 ms, 1 s, and 5 s, respectively. It is clear from the comparison that for the detection without polarization system, only BRP can be seen in the reflected waveform without identifying the target signal, and the target signal cannot be detected by increasing the acquisition time. In fact, the acquisition of high-quality target information is typically achieved by extending the cumulative acquisition time. However, after introducing of polarization, the BRP peak photon count is greatly reduced, and the target signal can be identified from the reflected waveform. Even in the case of a single pixel acquisition time of 100 ms, the target signal can be identified obviously. The detectability of the target signal is proportional to the acquisition time. The above analysis is based on the visualization of the reflected waveform and the target profile, and the following statistical analysis aims to verify the benefit of polarization on the BRP and target detection in terms of the reflected photon counts.
Fig. 7. Comparison of detection results at point A with different acquisition time. (a), (c), and (e) Show the detection results of point A without a polarization system when the single pixel acquisition time is 100 ms, 1 s, and 5 s, respectively. (b), (d), and (f) Show the detection results of point A based on polarization in the same acquisition time periods.
Table 2 shows the statistical analysis of the peak and total photon counts of the BRP and the target, where peak indicates the peak photon count and total represents the total photon counts. From the statistical results, it can be seen that the number of BRP reflected photons dropped significantly after introducing polarization. For different acquisition periods of 100 ms, 1 s, 5 s, and 10 s, the peak BRP photon count dropped by 98.3%, 98.7%, 99%, and 99%, respectively, at an average decline of 98.8%; the total BRP photon counts was down by 98.2%, 98.1%, 98.3%, and 98.3%, respectively, at an average reduction of 98.2%. Since the target is in the range-blind area of the system, the target cannot be identified without polarization, while the target signal can be clearly detected in polarization-based detection, although polarization reduction in target intensity, the count loss of the target is significantly reduced. In this section, the comparative experiment w. and w./o. polarization was conducted under the premise of sufficient acquisition time to verify the effectiveness of polarization. Based on that, the acquisition time was shortened for target detection of point A in comparison, which fully verifies the detection efficiency of the target in the range-blind area by using the polarization property of light proposed in this paper. Finally, the target signal can be distinguished from the reflected waveform, which further validates the universal adaptability of the system.
Table 2. BRP photon counts and target photon counts
4.2.2 Ranging performance
For further verification on the ranging performance of the proposed method, the target at point B was detected based on the polarization system in the same experimental environment, using the same acquisition time for ranging experiments, with the same cumulative time of 100 ms, 1 s, 5 s, and 10 s.
The detection results of point B are shown in Fig. 8, in which (a), (b), (c), and d indicate the acquisition periods of 100 ms, 1 s, 5 s, and 10 s for the reflected waveforms, respectively. The results show that the target signal at point B can be clearly distinguished in the detected reflected waveform based on the polarization system, which further verifies the applicability of the system for targets at different depth.
Fig. 8. Target detection results based on the polarization system at point B. (a)-(d) Show the detection results in single-pixel acquisition time of 100 ms, 1 s, 5 s, and 10 s, respectively
The depth information of two points A and B was calculated using the Peak algorithm. Table 3 indicates the ToF and the measured depth of the target at the two points, where the bin width was 4 ps; the transmission depth in water was 0.045 cm; measure depth (MD) was the distance between the two points calculated through the different in ToF bins. The experimental results show that the ranging error of the system is on the millimeter level, and the mean Percentage Error (PE) of 2.4% validates the ranging accuracy of the system. The error is reduced with the increase of the single pixel acquisition time. Among them
Table 3. The time of flight (ToF) and ranging accuracy between the points A and B. The depth information is given by bins and the speed of light.
4.3 Imaging experiments
4.3.1 Comparative imaging experiments
The single-pixel ranging experiment has verified the feasibility of the polarization-based method. In order to visualize the effect of the polarization-based system more clearly, a comparative scanning experiment based on two systems for underwater target (Puppy model) detection is carried out in this section. The actual scene is shown in Fig. 9. The target was placed in the vicinity of the glass wall; the scanning pixels were $64\times 64$; the size of the scene was $8cm\times 8cm$; the single-pixel acquisition time was 100 ms; the water attenuation coefficient $\alpha _p$ was 16.8; the average transmitting power was $132\mathrm{\mu}$W.
Figure 10 shows the comparative reconstruction reflectivity map of the cross-correlation algorithm for the reflected data w. and w./o. the polarization system, where the results of processing unpolarization reflected data are shown in the first row and the those of the polarization-based reflected data are shown in the second row. The results show that the target cannot be recognized from the reconstruction results of unpolarization system, while it can be clearly observed from the reconstruction results of the polarization-based system, with distinct contours, and target can be identified. In Fig. 11, the reconstruction results of the three algorithms described in Section 2.3 for the reflected data of the two systems are presented, in which the reconstruction results of the algorithm for unpolarization reflected data are shown in rows 1, 3, and 5, and those of the algorithm for the polarization-based reflected data are in rows 2, 4, and 6. From the results of Fig. 10 and 11, the target signal is not visually identifiable in unpolarization system, while the target signal can be clearly recognized in the polarization-based system. This section is designed to discuss the role of polarization from image level analysis. Compared with the analysis from the perspective of signal in Section 4.2, the approach adopted in this section is more direct and effective. It verifies that the proposed method is effective in underwater single-photon detection to improve the detection efficiency of targets in range blind areas.
Although the peak algorithm and the cross-correlation algorithm in Fig. 11 can both reconstruct the target 3D information and reveal the target information contour, their reconstruction results were unsatisfactory. Moreover, the introduction of polarization reduces the reflected intensity of the target, despite the improvement of detection efficiency of the target. In response, the results of the OPN3DR algorithm to introduce the non-local correlation characteristics are significantly better than the two former approaches, and the reconstruction results are the best with the most distinct target contour. The chosen of parameters are detailed in [35]. In addition, it is still impossible to obtain the target 3D information from the reflected data without polarization, regardless of the algorithms applied for processing. Figure 12 showed the 3D point cloud of both polarization and unpolariztion results that given by OPN3DR.
4.3.2 Evaluation metrics
For an objective evaluation of the results in Fig. 11, where the target is known to be a smooth object, the following evaluation metrics can be applied to evaluate the reconstructed image.
1. The Gray-scale Mean Gradient (GMG), as an image reference indicator of depth, can describe the smoothness of the image. A smaller value indicates that the smoother the image to be evaluated is, the better the quality of the results obtained by the restoration approach, as calculated below:
2. The Equivalent Number of Looks (ENL) can be used to evaluate the denoising effect in the smooth area of the image, and the greater the value, the better the suppression effect of the noise in the smooth area, which is calculated as
where $\mu$, $\sigma$ denote the mean and standard deviation of the flat areas in the image.3. The Singular Value Decomposition Global Features (SVD-G). SVD is widely used in image analysis [36,37] to evaluate images based on the singular eigenvalue coefficients of the images. The SVD of a matrix $B$ sized $q\times g$ is expressed as
where $\boldsymbol {U}=[U_{1},U_{2},\ldots,U_{q}]$, $\boldsymbol {V}=[V_{1},V_{2},\ldots,V_{q}]$, and $\boldsymbol {S}=diag(S_{1},S_{2},\ldots,S_{r},0,\ldots,0)$. Among them, $r$ is the rank of matrix $\boldsymbol {B}$. In this section, a global feature based on SVD is proposed. Specifically, it is assumed that the proportion of the sum of the first $l$ singular values to the sum of the singular values of the whole image is $K$, i.e., $\frac {S_1+S_2+\cdots +S_l}{S_1+S_2+\cdots +S_r}\geq K$. The smaller the value of $l$, the more concentrated the image features are proven and the better the image quality. SVD-G is defined as follows:In this section, the ratio K was set at 90% based on experience.
With the above metrics, the reconstructed images were calculated for the data of quality metrics as shown in Table 4. Since the target cannot be identified from the reconstruction results without polarization return waveform, these images are not involved comparisons.
Table 4. The evaluation metrics of different algorithms and acquisition time for depth images
Table 4 shows the comparison of GMG, ENL, and SVD-G results for different acquisition time. Based on the result, it can be concluded that the OPN3DR approach outperforms the peak algorithm and the cross-correlation algorithm. The peak algorithm and the cross-correlation algorithm are simple in computation, but the reconstructed results contain more noise, while OPN3DR takes into account the spatial correlation of non-neighboring domains to iteratively update the spatial relationship of non-local and reconstructed results, which can be better adapted to the underwater single-photon detection environment.
As the experimental results suggest, the OPN3DR algorithm yields the optimal reconstruction results. The reconstruction results of OPN3DR at a single pixel acquisition time of 50 ms were selected for comparative analysis with the peak algorithm and the mutual correlation algorithm. The GMG was improved by 6.5 fold and 2.1 fold, ENL by 100% and 10%, and SVD-G by 5 fold and 2.8 fold, respectively, which is close to subjective evaluation.
5. Conclusion
This paper proposes a single-photon imaging approach based on polarization to reduce the blind range of the target. This method combines the advantages of single-photon detection technology and the properties of polarization to filter out most of the BRP through polarization and reduce the probability of the BRP triggering the detector, thus increasing the efficiency of target detection within the underwater blind range. And effective reconstruction algorithms are applied to solve the signal sparsity issue due to the underwater environment and polarization characteristics. Experiment shows that the proposed method reduces the BRP intensity by 98.2% on average, the target profile can be visibly identified from return photons, and the ranging precision of the system can reach the millimeter level. This method is proved to be effective for range-blind underwater targets where the detection resources of the system are limited.
The results are further optimized through efficient reconstruction algorithms. Among them, the OPN3DR algorithm can effectively overcome the problem of sparse reflected data as it fully considers the spatial correlation of the target, improving GMG 6.5 fold and 2.1 fold, ENL by 100% and 10%, and the SVD-G by 5 fold and 2.8 fold, respectively, compared with the peak algorithm and the cross-correlation algorithm at the single-pixel acquisition time period of 50 ms. The proposed method apply suitable algorithms to optimize it to obtain reconstructed targets with higher quality. In addition, the quality of the reconstructed image is also related to some key factors, such as single pixel acquisition time, laser power and beam quality, as well as advanced reconstruction algorithms. This paper has exploited some of the properties of polarization to solve the problem of target detection in the blind range, and our future work will be to investigate polarization for target detection in long-range underwater imaging, and to explore underwater target imaging in more extreme environments.
Funding
China Postdoctoral Science Foundation (2020M683600); the Open Research Fund for development of high-end scientific instruments and core components of the Center for Shared Technologies and Facilities (E32931Q101).
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.
References
1. J. S. Jaffe, “Underwater optical imaging: the past, the present, and the prospects,” IEEE J. Oceanic Eng. 40(3), 683–700 (2015). [CrossRef]
2. J. Ma, T. Lu, Y. He, Z. Jiang, C. Hou, K. Li, F. Liu, X. Zhu, and W. Chen, “Compact dual-wavelength blue-green laser for airborne ocean detection lidar,” Appl. Opt. 59(10), C87–C91 (2020). [CrossRef]
3. P. Risholm, J. Thorstensen, J. T. Thielemann, K. Kaspersen, J. Tschudi, C. Yates, C. Softley, I. Abrosimov, J. Alexander, and K. H. Haugholt, “Real-time super-resolved 3D in turbid water using a fast range-gated CMOS camera,” Appl. Opt. 57(14), 3927–3937 (2018). [CrossRef]
4. S. Donati and T. Tambosso, “Single-photon detectors: From traditional PMT to solid-state SPAD-based technology,” IEEE J. Sel. Top. Quantum Electron. 20(6), 204–211 (2014). [CrossRef]
5. D. Bronzi, F. Villa, S. Tisa, A. Tosi, and F. Zappa, “SPAD figures of merit for photon-counting, photon-timing, and imaging applications: a review,” IEEE Sens. J. 16(1), 3–12 (2016). [CrossRef]
6. A. Maccarone, A. McCarthy, X. Ren, R. E. Warburton, A. M. Wallace, J. Moffat, Y. Petillot, and G. S. Buller, “Underwater depth imaging using time-correlated single-photon counting,” Opt. Express 23(26), 33911–33926 (2015). [CrossRef]
7. A. Maccarone, A. Halimi, A. McCarthy, R. Tobin, S. McLaughlin, Y. Petillot, and G. S. Buller, “Underwater three-dimensional imaging using single-photon detection,” in CLEO: Science and Innovations, (Optica Publishing Group, 2017), pp. SF2M–2.
8. A. Maccarone, F. M. Della Rocca, A. McCarthy, R. Henderson, and G. S. Buller, “Three-dimensional imaging of stationary and moving targets in turbid underwater environments using a single-photon detector array,” Opt. Express 27(20), 28437–28456 (2019). [CrossRef]
9. A. Maccarone, G. Acconcia, U. Steinlehner, I. Labanca, I. Rech, and G. S. Buller, “Underwater time of flight depth imaging using an asynchronous linear single photon avalanche diode detector array,” in Emerging Imaging and Sensing Technologies for Security and Defence V; and Advanced Manufacturing Technologies for Micro-and Nanosystems in Security and Defence III, vol. 11540 (SPIE, 2020), pp. 102–108.
10. H. Shi, H. Qi, G. Shen, Z. Li, and G. Wu, “High-Resolution Underwater Single-Photon Imaging With Bessel Beam Illumination,” IEEE J. Sel. Top. Quantum Electron. 28(5: Lidars and Photonic Radars), 1–6 (2022). [CrossRef]
11. A. Maccarone, K. Drummond, A. McCarthy, U. K. Steinlehner, Y. R. Petillot, R. K. Henderson, Y. Altmann, and G. S. Buller, “Real-time underwater single-photon three-dimensional imaging,” in Emerging Imaging and Sensing Technologies for Security and Defence VII, vol. 12274 (SPIE, 2022), p. 1227403.
12. K. Hua, B. Liu, L. Fang, H. Wang, Z. Chen, and Y. Yu, “Detection efficiency for underwater coaxial photon-counting lidar,” Appl. Opt. 59(9), 2797–2809 (2020). [CrossRef]
13. J. Rapp, Y. Ma, R. M. Dawson, and V. K. Goyal, “Dead time compensation for high-flux ranging,” IEEE Trans. Signal Process. 67(13), 3471–3486 (2019). [CrossRef]
14. W. Becker, Advanced time-correlated single photon counting techniques, vol. 81 (Springer Science & Business Media, 2005).
15. A. M. Pawlikowska, A. Halimi, R. A. Lamb, and G. S. Buller, “Single-photon three-dimensional imaging at up to 10 kilometers range,” Opt. Express 25(10), 11919–11931 (2017). [CrossRef]
16. Y. Kang, “Research on single photon counting lidar 3D imaging technology with a few echo photons,” Ph.D. thesis, University of Chinese Academy of Sciences (2019).
17. J. Rapp and V. K. Goyal, “A few photons among many: Unmixing signal and noise for photon-efficient active imaging,” IEEE Trans. Comput. Imaging 3(3), 445–459 (2017). [CrossRef]
18. K. Hua, B. Liu, Z. Chen, L. Fang, and H. Wang, “Efficient and Noise Robust Photon-Counting Imaging with First Signal Photon Unit Method,” in Photonics, vol. 8 (MDPI, 2021), p. 229.
19. Z. Chen, B. Liu, G. Guo, and C. He, “Single photon imaging with multi-scale time resolution,” Opt. Express 30(10), 15895–15904 (2022). [CrossRef]
20. A. Halimi, A. Maccarone, A. McCarthy, S. McLaughlin, and G. S. Buller, “Object depth profile and reflectivity restoration from sparse single-photon data acquired in underwater environments,” IEEE Trans. Comput. Imaging 3(3), 472–484 (2017). [CrossRef]
21. R. Tobin, A. Halimi, A. McCarthy, M. Laurenzis, F. Christnacher, and G. S. Buller, “Three-dimensional single-photon imaging through obscurants,” Opt. Express 27(4), 4590–4611 (2019). [CrossRef]
22. A. Halimi, A. Maccarone, R. A. Lamb, G. S. Buller, and S. McLaughlin, “Robust and guided bayesian reconstruction of single-photon 3d lidar data: Application to multispectral and underwater imaging,” IEEE Trans. Comput. Imaging 7, 961–974 (2021). [CrossRef]
23. J. Peng, Z. Xiong, X. Huang, Z.-P. Li, D. Liu, and F. Xu, “Photon-Efficient 3D Imaging with A Non-local Neural Network,” in Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part VI 16, (Springer, 2020), pp. 225–241.
24. J. Guan, W. Ren, and Y. Cheng, “Stokes vector based interpolation method to improve the efficiency of bio-inspired polarization-difference imaging in turbid media,” J. Phys. D: Appl. Phys. 51(14), 145402 (2018). [CrossRef]
25. F. Liu, P. Han, Y. Wei, K. Yang, S. Huang, X. Li, G. Zhang, L. Bai, and X. Shao, “Deeply seeing through highly turbid water by active polarization imaging,” Opt. Lett. 43(20), 4903–4906 (2018). [CrossRef]
26. K. O. Amer, M. Elbouz, A. Alfalou, C. Brosseau, and J. Hajjami, “Enhancing underwater optical imaging by using a low-pass polarization filter,” Opt. Express 27(2), 621–643 (2019). [CrossRef]
27. F. Liu, Y. Wei, P. Han, K. Yang, L. Bai, and X. Shao, “Polarization-based exploration for clear underwater vision in natural illumination,” Opt. Express 27(3), 3629–3641 (2019). [CrossRef]
28. R. Liu, X. Tian, F. He, and J. Ma, “Multi-depth photon-counting imaging based on polarisation modulation,” Opt. Express 29(24), 39362–39375 (2021). [CrossRef]
29. R. Liu, X. Tian, and S. Li, “Polarisation-modulated photon-counting 3d imaging based on a negative parabolic pulse model,” Opt. Express 29(13), 20577–20589 (2021). [CrossRef]
30. S.-H. Baek and F. Heide, “All-photon polarimetric time-of-flight imaging,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, (2022), pp. 17876–17885.
31. J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express 16(2), 1196–1207 (2008). [CrossRef]
32. M. A. Richards, Fundamentals of radar signal processing (McGraw-Hill Education, 2014).
33. D. B. Lindell, M. O’Toole, and G. Wetzstein, “Single-photon 3d imaging with deep sensor fusion,” ACM Trans. Graph. 37(4), 1–12 (2018). [CrossRef]
34. Z. Zhang, S. Chen, J. Wang, C. Ma, and X. Su, “Precision improvement of underwater single photon imaging based on model matching,” IEEE Photonics Technol. Lett. 35(5), 253–256 (2023). [CrossRef]
35. S. Chen, A. Halimi, X. Ren, A. McCarthy, X. Su, S. McLaughlin, and G. S. Buller, “Learning non-local spatial correlations to restore sparse 3d single-photon data,” IEEE Trans. on Image Process. 29, 3119–3131 (2020). [CrossRef]
36. Q. Guo, C. Zhang, Y. Zhang, and H. Liu, “An efficient svd-based method for image denoising,” IEEE Trans. Circuits Syst. Video Technol. 26(5), 868–880 (2016). [CrossRef]
37. A. Shnayderman, A. Gusev, and A. M. Eskicioglu, “An svd-based grayscale image quality measure for local and global assessment,” IEEE Trans. on Image Process. 15(2), 422–429 (2006). [CrossRef]
