Open Access
Add to BibSonomy
Abstract
Compared to conventional floodlighted imaging systems, a pulsed laser range-gated imaging system can get a real-time high performance underwater image when the distance of target is known. Otherwise, optical properties of the water, mainly the attenuation coefficient of the water, should be obtained to automatically set the parameters of the imaging system. Typically, special instrument is required to measure the attenuation coefficient of the water. In this work, a water attenuation coefficient estimation method is proposed merely with the pulsed laser range-gated imaging system. The imaging model of the backscattered light of the pulsed laser range-gated imaging system is built through the light propagation theory. As a result, the water attenuation coefficient is calculated by nonlinear estimation method. Experiments under different water conditions are designed and carried out to verify the proposed method. Results show that the relative errors between the estimation and the reference are about 1% for the water in the water tank and seawater pool, and about 4% for the towing boat tank, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Light propagated in the water suffers from absorption and scattering severely. Underwater imaging thus degrade heavily with low visibility and contrast. Pulsed laser range-gated imaging (PLRGI) is an effective underwater opto-electronic imaging technique especially in terms of suppressing backscattered light [1–4]. It has a significantly improved viewing performance over conventional camera imaging system, three to five times the range improvement for example [4]. As a result, it has attracted a lot of attention and contributed much to military and civilian underwater applications [5–8]. A PLRGI system contains three key components: a pulsed laser, a receiver containing a gated camera, and a synchronous controller, as shown in Fig. 1. In Fig. 1, a pulse is emitted from the laser to propagate in water, and the receiver is controlled synchronously to the laser with a certain gate delay, which is calculated accurately according to the distance of object. The gated camera of the PLRGI opens its gate for a short time (gate width) as soon as the laser pulse arrives. The opening time for the gate corresponds to the desired depth of view of the object, producing a spatial volume slice called depth of gating (DOG) [9]. The gate is opened merely to capture the diver and closed in other positions. Therefore, it can reject the light scattered and reflected by water beyond the gated time. In other words, it can separate the useful light from the interfering light (mainly the backscattered light) [10], which can contribute to getting a high performance image of the object at the required distance.
Optical properties (absorption, scattering or their combination attenuation, turbidity, etc.) of the water plays a vital role in a PLRGI system. With the knowledge of the attenuation coefficient, the PLRGI system can set and update its operating parameters automatically [8]. However, extra instruments are needed either to measure turbidity or the attenuation of the water. In Ref. [1], in order to characterize the performance of LUCIE-1 in terms of extinction, absorption, and scattering lengths, a narrow forward angle transmissometer-nephelometer (NEARSCAT) is lowered to within 2m of the bottom to take and analyze the absorption and scattering spectra during each dive. The turbidity is monitored with a transmissometer as well in Ref. [11]. For the second generation of LUCIE [2], the NEARSCAT is used as well, along with another instrument (AC-9 plus made by Wetlab Inc.) to measure the absorpotion and attenuation at 9 wavelengths. A turbidity meter (Anaalite 160) is installed near a hybrid underwater camera system (HUC) and measure the turbidity level once per minute. Meanwhile, Secchi disks are used to get an independent estimation of the water attenuation coefficient [3]. An attenuation measurement tool is developed to measure the optical attenuation in different waters for the range-gated system UTOFIA in Ref. [12].
Normally, backscattered light is considered as noise and researches have focused on the removal of this component [13–18]. In fact, we can extract information contained in the backscattered light. In this work, we present a method to calculate the attenuation coefficient of the water from the backscattered light by a PLRGI system. Light propagation theory is utilized to establish the imaging model of the underwater PLRGI system. And the attenuation coefficient of the water is obtained and optimized by nonlinear estimation method. Meanwhile, experiments under different water conditions were carried out to verify the proposed method.
2. Imaging model of the backscattered light of the PLGRI system
With the accurate control of the gate delay, we can obtain the image of backscattered light at certain distances with the PLRGI system. And the water volume in the corresponding DOG is considered. In this section, the imaging model of the backscattered light is presented with the light propagation theory. Firstly, the backscattered light flux received at a certain distance z is calculated and only single scattering is considered in this work. With this knowledge, then the energy of backscattered light received from the water volume in the DOG can be integrated. Finally, the pixel intensity is obtained through multiple photoelectric transforms and the attenuation coefficient is calculated through nonlinear estimation method.
2.1 Backscattered light power received of distance z
Figure 2 depicts the coordinate system of the PLRGI system. The origin of coordinates $O$ and z-axis coincide with the optical center and optical axis of the lens system of the receiver, respectively. The x- and y-axes form a Cartesian coordinate system as shown in Fig. 2. The laser beam has a half divergence angle $\alpha$. The laser is assumed to emit a pulse of energy $E_0$ and its pulse width is $\tau _p$. Speed of the laser in water is $c_w$. Multiple scattering and the influence of ambient light are not considered in this paper. Therefore, the average power of a laser pulse $P_0$ is:
Assuming that the light intensity within the divergence angle is uniformly distributed, then the illumination at distance $z$ can be calculated following the Beer’s law:
where $c$ is the attenuation coefficient that is desired to be estimated in the work. It is assumed that the attenuation coefficient $c$ is approximately constant over the entire path between the laser source and the DOG. Therefore, $c$ is independent to the distance $z$ or the gate delay. Let $S_0$ be the pixel area of the receiver camera, then the image area $S_p$ in the FOV (filed of view) can be obtained: where $f$ is the focal length and subscript $p$ denotes the specified point in the area $S_p$ and its coordinates is $(x,y,z)$. Then the intensity of the backscattered light with a volume of $\Delta V=dxdydz$ from $P$ is: where $\beta$ is the backscattering coefficient of the water.Extensive measuring results of different waters show that the scattering coefficient of the water varies with the water conditions [1]. However, the relative intensity distribution of the backscattering light by the water is similar in space, and the backscattering coefficient is a relatively small value and does not vary much [19]. Therefore, the backscattering coefficients within the area $S_p$ can be considered as equal. The intensity of the backscattered light from $P$ is:
From Eqs. (1),(2),(3),(5), we can get
The backscattered light flux reaching the receiver is:
where $\Delta \Omega \approx \pi D^2/4z^2$, and $D$ is the diameter of the receiver aperture. By substituting Eq. (6) into Eq. (7), we can getTherefore, the backscattered light flux received at a certain distance $z$ is obtained. Then, all of the backscattered light in the DOG have to be considered.
2.2 Backscattered light energy received of the DOG
Once the laser pulse is emitted from the laser of the PLRGI system, the receiver is controlled by the synchronous controller to open its gate with time delay $t_0$. In our work, the descent edge of the laser pulse is regarded as the effective trigger source for the synchronous controller, which means the PLRGI system in our work is a tail-gating system. Therefore, the laser pulse has propagated for a distance of $z_1=c_w t_0/2$ when its backscattered light travels to the gate as soon as it opens at $t_0$. The gate closes after a time interval $\tau$, gate width, which is manually set. At time $t_0+\tau$, the backscattered light at the distance of $z_2=c_w(t_0+\tau )/2$ reaches the gate. Since the system is triggered by the descent edge, we have to consider the pulse width $\tau _p$ further. Depending on whether the pulse is partially or completely entering into the gate, the backscattered light received by the receiver of the PLRGI system can be divided into three parts during the opening of the gate as illustrated in Fig. 3: range $z_1$ to $z_1+0.5z_p (Re1)$, range $z_1+0.5z_p$ to $z_2 (Re2)$ and range $z_2$ to $z_2+0.5z_p (Re3)$, here $z_p=\tau _p \cdot c_w$.
In the part of $Re1$, supporting that the backscattered light originated at distance $z$ approaches the gate of the receiver at time $t_1=2z/c_w$. The time interval of the backscattered light from distance $z$ when the gate is open is :
The energy received of the backscattered light from distance $z$ is $dE_1=d\Phi _s\Delta t_1$. With Eq. (8) and Eq. (10), we can get
By integrating from range $z_1$ to $z_1+0.5z_p$, the energy received of $Re1$ is:
The minimum opening time of the gate that the system can be set is the laser pulse width $\tau _p$. Therefore, the minimum value of $z_2$ is $z_1+0.5z_p$.
For the part of $Re2$, the backscattered light generated by the water is all received by the receiver. The energy of the backscattered light is $dE_2=d\Phi _s\tau _p$. By integrating from range $z_1+0.5z_p$ to $z_2$, the energy received of $Re2$ is:
In $Re3$, the backscattered light at distance $z$ reaches the receiver at $t_2=2z/c_w$. The time interval of the backscattered light from range $z$ before the gate closed is :
The energy received of the backscattered light is $dE_3=d\Phi _s\Delta t_2$. By integrating from range $z_2$ to $z_2+0.5z_p$, the received energy of $Re3$ is:
As a result, all the backscattered light received from the water volume in the DOG is:
In the case that $z_p$ is small. Eqs. 12 and 15 can be reduced to
and respectively. By substituting Eqs. (17) and 18 into Eq. (16), then2.3 Photoelectric conversion of the imaging system
The receiver of the PLRGI system mainly consists of the lens system, the Photocathode, the Microchannel Plate (MCP), fluorescent screen and a CMOS camera as shown in Fig. 4. The light coming into the lens system will finally transfer to a grayscale image by the receiver. The procedure of the transformation is given in Fig. 4 as well. Backscattered light travels through the lens system to the Photocathode, which converts the photons into electrons. Therefore, the amount of electrons generated by the Photocathode is given:
where $\eta _{l}$ is the transmittance of the lens system, $\eta _c$ is the photocathode conversion efficiency, $\upsilon$ is the laser frequency, and $h=6.6\times 10^{-34}J\cdot s$ is the Planck constant. Then the electrons $Q_c$ are magnified by the MCP: where $G$ is the magnification of the MCP. The electrons output from the MCP will continue impact the fluorescent screen and the generated light energy can be written as: where $\eta _s$ is the conversion efficiency of the fluorescent screen. Finally, light emitted from the fluorescent screen will be captured by the CMOS camera. After A/D conversion, the grayscale value of the pixel output is: where $\eta _d$ is the average quantum efficiency of the CMOS, and $n_m$ is the full capacity of a pixel, and $n_b$ is the bit number of the ADC inside the receiver. From Eqs. (19)–23, we can getAs a result, the image of backscattered light of one laser pulse is obtained. For the output of an image frame of the PLGRI system, several or tens or hundreds of pulsed laser image are gathered together to form one image frame. Assuming that the PLGRI system and the water remain steady, thus N pulsed laser image can be considered to be the same. Therefore, Eq. (24) can be modified further when the number of pulsed laser image is considered.
where N denotes the number of pulsed laser image. Consequently, the desired parameters $k$ and $c$ can be solved by nonlinear least squares method in Eq. (27). where M is the number of image frame output by the PLGRI system, i is the i-th image frame and $z_i$ is the corresponding distance where the image frame is obtained.3. Experiment and discussions
3.1 Experimental setup and method
We have built a prototype of the PLRGI system [20] as shown in Fig. 5 and some of its specifications related in this work are listed in Table 1. Gain of the MCP is controlled by a small voltage. When the control voltage increases, the gain of the MCP raises as well. Experiments under different conditions have carried out in water tank, seawater pool and towing boat tank, respectively. The prototype is controlled by a computer to set its working parameters and to show the real-time imaging result.
Table 1. Specifications of our prototype of the PLRGI system
The procedure of the estimation of the attenuation coefficient and result evaluation is illustrated in Fig. 6. Frame rate, control voltage of the MCP, gate delay ($t_0$) and gate width ($\tau$) are set firstly in every experiment. In this work, gate width $\tau$ and frame rate are constantly set as 5 ns and 20 Hz, respectively. The control voltage of the MCP is set with a median value in its adjusting range, so that we can increase and decrease it in two directions conveniently. The initial value of the gate delay $t_0$ is firstly set around 5 ns, with which the contrast of the image of the backscattered light is appropriate not only for the first image but also for the latter images with bigger values of $t_0$ since the contrast will become dark as $t_0$ increases. Once the gate delay is set, the corresponding distance $z_i$ between the starting position of the backscattered light and the PLRGI system is determined as well. Images of the backscattered light are separated from the recorded video and are processed further. As shown in Fig. 7, the image of the backscattered light is a big white circle. In this work, the region of interest (ROI) of the image is chosen according to the boundary of the circle. The centroiding of the ROI, $I_i$, is extracted as the intensity of the backscattered light at distance $z_i$. In order to reduce the effect of noise, 20 frames of image at the same distance $z_i$ from the video are used to calculate the average value of $I_i$. In each experiment, gate delay $t_0$ changes for 10 times with an increment of 0.625ns, the only difference is their initial values of the gate delay. Therefore, the attenuation coefficient $c$ can be estimated with Eq. (27) since $z_i$ and $I_i$ are obtained. Meanwhile, the waters in different experiments are collected as samples, and the attenuation coefficient of the samples are measured in lab based on the principle of double optical path method [21]. The principle is illustrated in Fig. 8. A laser beam is splitted equally and one is propagated through the sampled water while the other is not. They are detected by two power meters which are calibrated in advance. The attenuation coefficient is calculated through the ratio value obtained the computer and it is regarded as a reference. The relative error between the estimation and the reference is calculated in Eq. (28).
where $c'$ is the attenuation coefficient measured by the division of amplitude optical method.
Fig. 7. A frame of pulsed laser image and the region of interest (red square). The center is marked with a plus sign. Here the image is cropped in order to show it better.
3.2 Results and discussions
3.2.1 Experiment in water tank
In order to verify the proposed method, experiment is first carried out in the water tank in the Lab. The size of the water tank is $7m\times 1m\times 0.5m(length\times width \times height)$. Tap water is added into the tank and the Kaolin is mixed into the water to increase the turbidity of the water. The PLGRI system is placed under the turbid water. Figure 9 shows the experiment scene. Gate delay $t_0$ is first set as 5 ns and changed with a step of 0.625 ns until 10 values are used in the experiment. For each image frame, 100 pulsed laser image are gathered together to generate a frame of image for the output of the CMOS camera. The experiment has repeated three times under the same conditions and three groups of results are obtained. A control voltage of the MCP of 2.7V is used and remains unchanged when the experiment is repeated. Estimation results and the relative errors are listed in Table 2.
Table 2. Estimation result with the control voltage of MCP 2.7V in water tank
It can be seen from Table 2 that the variations of the estimation results of the attenuation coefficient in different groups are very small. The same case is for the estimation of the k factor. Compared to the result measured in the Lab., the relative error between the estimation and measurement is smaller than $1\%$. With the estimation result, we can calculate the residual error with Eq. (24). The residual errors are 0.94, 1.23, 0.79 grayscale value (rms, $1\sigma$) for the three repeated experiments, respectively. Considering the steady and the accuracy of the estimation result, therefore the proposed method is verified to be effective.
We have conducted another group of experiment in the water tank to verify the proposed method. In this group of experiment, the attenuation has changed to simulate another type of water. Meanthile, the control voltage of the MCP is changed to obtain images of different SNR. The water is diluted with more tap water added in the tank. As a result, the attenuation coefficient has changed. And the control voltage of the MCP is varied from 2.7V to 2.6V and 2.5V, respectively. The number of pulsed laser image for each frame has changed to 250. Other parameters remain unchanged. The results are given in Table 3. As the control voltage of the MCP increases, the factor $k$ increases as well, which is identical with the derivation in Eq. (25). Estimation of the attenuation coefficient has reduced to $0.431m^{-1}$ since the water in the tank is diluted while the control voltage of the MCP remains 2.7V. And the measured attenuation coefficient is $0.436m^{-1}$. Hence, the estimation result is reliable. The estimation results almost keep the same when the control voltage of the MCP changed to 2.6V and 2.5V, respectively. This is reasonable since there is no change happened for the water during the experiment. The relative error is below $1\%$ for the voltage of 2.5V and 2.6V, but $1.12\%$ for 2.7V. This is caused by the booming of several pixels when the number of pulsed laser image has increased from 100 to 250. As the voltage reduces to 2.6V and 2.5V, the booming of pixels disappears. The residual error for each control voltage are 2.058, 1.04, 1.12 grayscale value (rms, $1\sigma$), respectively.
Table 3. Experiment result under different MCP control voltages in water tank
As a result, the estimation method for the water attenuation coefficient is valid in the water tank of the lab. with different simulated water conditions and different SNR images. In order to verify the proposed method with different medium water, experiments in seawater pool and towing boat tank are implemented as well.
3.2.2 Experiment in seawater pool
Seawater is simulated in our lab in a specific seawater pool. Except for the verification of the proposed method in different medium, different water regions are used here to find out whether the attenuation coefficient is approximately constant in the pool. The pool has a length of 7m, width of 5m and depth of 1m. The PLGRI system is placed under the seawater as shown in Fig. 10. The curtains are closed and the lights are turned off in order to avoid the pollution of the ambient light. Three experiments have designed in the seawater pool. First, the control voltage of the MCP is set to 2.5V and the number of pulsed laser image is 65. The control voltage has changed to 2.6V and the number has reduced to 55 in the second case. Finally, the control voltage and the number of pulsed laser image have increased to 2.7V and 110, respectively. Simultaneously, in order to compare the attenuation coefficient of different water regions, the initial value of the gate delay has changed from 4.375 ns to 6.875 ns, which means that different water regions are taken into consideration. The estimation results are shown in Table 4.
Fig. 10. Experiment in seawater pool. Notice that the lights are turned off while experiments are undergone.
Table 4. Experiment result in the seawater pool
In Table 4, the estimations of attenuation coefficient in the three experiments are slightly different. And the relative errors between the estimations and the measurement of the sample water are about $1\%$. And the residual errors are 2.81, 1.05 and 1.02 grayscale value, respectively. As a result, the experiment in the seawater pool has verified the proposed method further. Take a close look at Table 4, the estimation of k factor decreases when the voltage changes from 2.5V to 2.6V, this is caused by the reduced number of pulsed laser image as given in Eq. (25). The initial value of $t_0$ has set as 4.375 ns first and then 6.875 ns when the voltage is 2.7V. Thus, the region of the water we have taken the image of is not the same as the previous two experiment. The final value of the gate delay is 10 ns for the previous two experiment and 12.5 ns for the last experiment. Therefore, the light path are overlapped for 10 ns between the laser source and the DOG. However, the estimation results are almost the same, which means that the water in the seawater pool is approximately uniform.
3.2.3 Experiment in towing boat tank
Experiments in towing boat tank is carried out in Huazhong university of science and technology. The towing boat tank has a length of 175 m, width of 6m and depth of 4m. The PLRGI system is hanged firmly under the water about 1m by a steel holder as shown in Fig. 11. As listed in Table 5. Initial gate delay $t_0$ has set to 6.875 ns for the Exp.C1 and 13.75 ns for the Exp. C2. The final value of the gate delay is 12 ns for Exp. C1 and 19.375 ns for Exp. C2. Therefore, the water region we have made the experiment on is different for Exp. C1 and C2 and the difference is over 7.375 ns. Since the distance of imaging is different, thus, we have set the number of pulsed laser image to 100 for Exp. C1 and 600 for Exp. C2. In this way, the image of the backscattered light at a long distance will not degrade too much.
Fig. 11. Experiment in the towing boat tank. Notice that the lights are turned off while experiments are undergone.
Table 5. Experiment result in towing boat tank
The estimation result of the attenuation coefficient is 0.249 for Exp. C1 and 0.250 for Exp. C2, respectively. Though a period of 12 ns is overlapped for Exp. C1 and C2 but the measurements of the water samples are 0.26, which means that the water in the towing boat tank is approximately uniform. The relative errors for Exp.s C1 and C2 are $4.23\%$ and $3.85\%$, respectively. The corresponding residual errors are 0.85 and 0.35 grayscale value. Comparing to the results obtained in the water tank and the seawater pool, the relative error acquired in the towing boat tank have increased. The possible reason is that the collected water sample may have varied slightly since we cannot measure it immediately until return to the lab.
4. Conclusions
In this work, we have proposed an estimation method for water attenuation coefficient through the imaging of the backscattered light with the PLRGI system. The imaging model of the backscattered light of the PLRGI system is built through the light propagation theory. With this model, the pixel grayscale value of the backscattered light image can be calculated. Combining the imaging model and the captured image frame of the backscattered light, the water attenuation coefficient in the imaging model is calculated by nonlinear estimation method. Experiments have been designed and carried out in the water tank, seawater pool and towing boat tank, respectively. Different parameters of the PLRGI system have been set and varied to verify the proposed method. The attenuation coefficient of the water samples are measured with a division of amplitude optical method in lab and acts as a referee. Relative error between the estimation and the reference is calculated. Results show that the relative errors are about $1\%$ for the water in the water tank and seawater pool, and about $4\%$ for the towing boat tank, respectively. Consequently, the pulsed laser range-gated imaging system can work independently and automatically. Since the measuring result is an average value over the entire path between the laser source and the DOG, researches and application in much more complex scattering water environment will be carried out and discussed in the future.
Funding
Natural Science Foundation of Naval University of Engineering (435517D43).
Acknowledgments
The authors thank Huazhong university of science and technology for the support of experiment in the towing boat tank. The authors thank Ding Zhichao, Zhang Su, Kai Li and Sun Chunsheng for the help during the experiment.
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. G. R. Fournier, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993). [CrossRef]
2. A. Weidemann, G. R. Fournier, L. Forand, and P. Mathieu, “In harbor underwater threat detection/identification using active imaging,” Proc. SPIE 5780, 59 (2005). [CrossRef]
3. P. Church, W. Hou, G. Fournier, F. Dalgleish, D. Butler, S. Pari, M. Jamieson, and D. Pike, “Overview of a hybrid underwater camera system,” in Spie Sensing Technology + Applications, (2014).
4. P. Mariani, I. Quincoces, K. H. Haugholt, Y. Chardard, A. W. Visser, C. Yates, G. Piccinno, G. Reali, P. Risholm, and J. T. Thielemann, “Range-gated imaging system for underwater monitoring in ocean environment,” Sustainability 11(1), 162 (2018). [CrossRef]
5. K. Yang, L. Yu, M. Xia, T. Xu, and W. Li, “Nonlinear ransac with crossline correction: An algorithm for vision-based curved cable detection system,” Opt. Lasers Eng. 141, 106417 (2021). [CrossRef]
6. X. Liu, X. Wang, P. Ren, Y. Cao, Y. Zhou, and Y. Liu, “Automatic fishing net detection and recognition based on optical gated viewing for underwater obstacle avoidance,” Opt. Eng. 56(08), 1 (2017). [CrossRef]
7. W. Xinwei, L. Youfu, and Z. Yan, “Triangular-range-intensity profile spatial-correlation method for 3d super-resolution range-gated imaging,” Appl. Opt. 52(30), 7399–7406 (2013). [CrossRef]
8. B. L. Ulich, P. Lacovara, S. E. Moran, and M. J. Deweert, “Recent results in imaging lidar,” Proceedings of SPIE - The International Society for Optical Engineering pp. 95–108 (1997).
9. L. D. Dominicis, “Underwater 3d vision, ranging and range gating,” Subsea Optics and Imaging pp. 379–408 (2013).
10. H. Youwei, C. Fengmei, J. Weiqi, and Q. Su, “Underwater pulsed laser range-gated imaging model and its effect on image degradation and restoration,” Opt. Eng. 53(6), 061608 (2013). [CrossRef]
11. E. A. Mclean, H. R. Burris, and M. P. Strand, “Short-pulse range-gated optical imaging in turbid water,” Appl. Opt. 34(21), 4343 (1995). [CrossRef]
12. R. Petter, T. Jostein, J. T. Thielemann, K. Kristin, T. Jon, Y. Chris, S. Chris, A. Igor, A. Jonathan, and H. K. Henrik, “Real-time super-resolved 3d in turbid water using a fast range-gated cmos camera,” Appl. Opt. 57(14), 3927–3937 (2018). [CrossRef]
13. E. Trucco and A. Olmos-Antillon, “Self-tuning underwater image restoration,” IEEE J. Oceanic Eng. 31(2), 511–519 (2006). [CrossRef]
14. C. S. Tan, G. Seet, A. Sluzek, X. Wang, and H. Y. Wong, “Scattering noise estimation of range-gated imaging system in turbid condition,” Opt. Express 18(20), 21147–21154 (2010). [CrossRef]
15. J. Banerjee, R. Ray, S. Vadali, S. N. Shome, and S. Nandy, “Real-time underwater image enhancement: An improved approach for imaging with auv-150,” Sadhana 41(2), 225–238 (2016). [CrossRef]
16. H. Lu, Y. Li, T. Uemura, H. Kim, and S. Serikawa, “Low illumination underwater light field images reconstruction using deep convolutional neural networks,” Futur. Gener. Comput. Syst. 82, 142–148 (2018). [CrossRef]
17. M. Wang, X. Wang, L. Sun, Y. Yang, and Y. Zhou, “Underwater 3d deblurring-gated range-intensity correlation imaging,” Opt. Lett. 45(6), 1455–1458 (2020). [CrossRef]
18. M. Wang, X. Wang, Y. Zhang, L. Sun, and Y. Zhou, “Range-intensity-profile prior dehazing method for underwater range-gated imaging,” Opt. Express 29(5), 7630–7640 (2021). [CrossRef]
19. R. C. Smith, R. W. Austin, and T. J. Petzold, Volume-Scattering Functions in Ocean Waters (Suspended Solids in Water, 1974).
20. B. Peng, D. Jin, C. Ji, C. Pei, and L. Sun, “An underwater laser three-dimensional imaging system,” in Sixth Symposium on Novel Optoelectronic Detection Technology and Applications, vol. 11455J. Chu and H. Jiang, eds., International Society for Optics and Photonics (SPIE, 2020), pp. 437–442.
21. D. Kun, H. Youwei, J. Weiqi, J. Kaijia, and L. Hailan, “Experimental study on the relationship between attenuation coefficient of blue-green laser transmission and the water turbidity,” Infrared Technology 35, 467–471 (2013).
