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Abstract
Optical underwater target imaging and detection have been a tough but significant challenge in deep-sea exploration. Distant reflected signals drown in various underwater noises due to strong absorption and scattering, resulting in degraded image contrast and reduced detection range. Single-photon feature operating at the fundamental limit of the classical electromagnetic waves can broaden the realm of quantum technologies. Here we experimentally demonstrate a thresholded single-photon imaging and detection scheme to extract photon signals from the noisy underwater environment. We reconstruct the images obtained in a high-loss underwater environment by using photon-limited computational algorithms. Furthermore, we achieve a capability of underwater detection down to 0.8 photons per pulse at Jerlov type III water up to 50 meters, which is equivalent to more than 9 attenuation lengths. The results break the limits of classical underwater imaging and detection and may lead to many quantum-enhanced applications, like air-to-sea target tracking and deep-sea optical exploration.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past few decades, the interest in air-to-sea optical exploration has rised [1,2] because of its potential scalability to different platforms like aircrafts or artificial satellites, and its wide applications in diverse fields, including underwater target detection [3], seafloor topography and marine science. By adding a laser source to the systems, the imaging methods can significantly improve the reduced image contrast under typical underwater conditions [4]. Moreover, the detrimental effects of scattering can be dramatically suppressed by using spatial, temporal or modulation discrimination techniques [5].
Range-gated imaging technology is an effective spatial-temporal discrimination method to overcome the backscattering of water media, which can improve the working distance and the signal-to-noise ratio [6–11]. The range-gated imaging systems equipped with a high-repetition-frequency laser have gradually become dominant due to its advantages such as small size, low power consumption, and commercially available [12–15]. As the distance increases, the signal photons returned from the object become sparse and submerged in scattered photons, which cannot be effectively extracted. After the accurate time-gate operation, most backscattered photons can be filtered out. However, some scattered photons still randomly enter the camera with a certain probability, which is the critical factor that limits the detection range and further improves the image quality.
Recent advances of sensors are transforming target detection to the single-photon regime, especially in low light conditions [16–24]. At the same time, various emerging imaging principles and computational algorithms enhance the capabilities of reconstructing objects [25–28]. Photon has the unique features of robust to environmental noise, low decoherence properties and low detectable energy level. They play a critical role in quantum computing [29–31], quantum simulation [32–35], quantum communication [36–38], and quantum imaging [39–42]. Experiments with photons have been employed to test the foundations of quantum mechanics and the current developments in quantum optics enable the exploration of many new directions. Especially, we witness the recent progresses in underwater quantum communication [43–46] and quantum state transmission [47]. However, it has been proven that loss eliminates most of the quantum effects in sensing and imaging, which means that the use of quantum states in these applications is invalid [48–51]. Therefore, it is a challenge to realize the potential of quantum technologies and exhibit quantum advantages in underwater conditions.
2. Theory and experiment
Here, we present an experimental demonstration of the quantum-enhanced underwater imaging and detection scheme with the single-photon threshold strategy, which does not detect quantum states directly but separates signals from noises. As is shown in Fig. 1(a), the whole experiment is implemented in a largescale marine test platform with 300 m long, 16 m wide, and 10 m deep, which is the biggest multiple function deep-water towing tank in Asia. The semiopen environment is similar to the natural field situation, which is a benefit to testing the imaging system in a real field condition. The schematic diagram of the experimental setup is shown in Fig. 1(b). The air-to-sea range-gated imaging system contains two sections together located on the same side of the water. We guide photons from the sender section into the water by a cloud stage and collect photons back with the receiver section. A 532 nm pulsed laser beam illuminates the target, provided by a solid-state AOM Q-switched laser operating at a repetition rate of 10 kHz with a tunable average power range of 1-8 W and the full width of half-maximum (FWHM) pulse duration of 50 ns. A small part of the pulse energy ($\sim$ 6 mW) is reflected by the polarization beam splitter onto the Si-PIN photodiode and converted into electrical pulse signals. By comparing the power between the sender and receiver, we can derive the underwater transmission channel loss. The measured attenuation coefficient is about $\alpha$=0.18 $\mathrm {m}^{-1}$, equivalent to an attenuation length of 5.5 m. This attenuation coefficient is also close to the one in coastal seawater Jerlov type III ($\alpha$=0.179 $\mathrm {m}^{-1}$). Our optical setup is a bistatic system in which the separate illuminating and collecting sections can avoid back reflections from the optical components causing damage to the sensitive CCD chip. By the spatial discrimination, a height difference of about 15 cm between the two underwater mirrors can minimize the overlap between the transmitted laser and the field of view of the receiver, which can reduce the effect of backscattering.
Fig. 1. Experimental implementation. A 532 nm pulsed laser beam illuminates the target, which is generated by a Q-switched laser operated at a repetition rate of 10 kHz with the full width of half-maximum pulse duration of 50 ns. A part of the laser output is sent to a linear optical detector to trigger the ICCD camera. The reflected light from the target is gathered by a telescope with an optical aperture of 150 mm. After spectral filtering with a bandpass filter at 532 nm (FWHM $\pm$ 10 nm), photons reflected by the target are focused on the ICCD camera. The focus modulator (FM) is utilized to adjust the size of laser spot by two lens with focal lengths of 30 mm and 75 mm, and the collimation modulator (CM) can guide the laser to illuminate the center of targets. The intensifier is triggered by a Si-PIN detector. (a) Real field-test environment. (b) Sketch of the experimental setup. HWP: half wave plate; QWP: quarter wave plate; PBS: polarization beam splitter; BF: band-pass filter ; ICCD: intensified charge coupled device. (c) Timing diagram of synchronization control signals.
Two timing modes of the ICCD camera are used to optimize signal acquisition in this experiment, as is shown in Fig. 1(c). One is the CCD exposure time, during which a frame of image is formed on the CCD chip, here we set the typical exposure time as 0.01 s. The other is the gate delay and width of the intensifier, here we set the gate width as 50 ns, consistent with the full width at half maximum of the laser pulse. Besides, to improve collection efficiency, the gate can be fired many times during each exposure.
There are two critical factors to achieve the precise triggering delay: the periodic pulse signals and the tunable electronic delay mechanism. The photons per pulse are divided into two parts: some are converted into periodic synchronous electrical signals by the Si-PIN device, which triggers the intensifier and labels the initial time; the rest photons make a round-trip through the high-loss underwater channel, then hit the intensifier. The triggering delay estimation is mainly based on the following considerations: the round-trip time in the free space channel and the underwater channel and the inherent insertion delay time in the camera. By tuning the electronic delay, we can determine the precise delay based on the maximum number of photons captured by the ICCD camera during the same exposure.
Three imaging methods are compared based on the whole system and all of them employ a pulsed laser for illumination. The passive method uses an internal camera pulse generator to randomly activate the image intensifier to capture photons, which is often restricted to a range of only a few meters. The active method employs the optimized time-gates synchronized with the pulsed laser to trigger the image intensifier, which can effectively overcome the underwater backscattered photons. As is shown in Fig. 2(a), the ICCD camera periodically switches between “gate on” and “gate off”. The phosphor screen decay on the image intensifier usually follows a multi-exponential function, where the decay time of the phosphor is about 0.1 ms. Therefore, the laser pulse frequency is 10 kHz, which can effectively avoid the fluorescence crosstalk. If the phosphor decay time and the camera time-gate are matched, the photon events can be detected with the maximum intensity shown in Fig. 2(b). In other cases, such as the “late gate”, “early gate” and “no gate” in Fig. 2(c), the intensity of stochastic backscattered photons is lower than that of signal photons. However, the classical intensity integration based on both methods cannot effectively distinguish between signal and backscattered photons.
Fig. 2. Photon threshold strategy. After optimizing the precise activated time-gate, we can obtain the strongest signal photons, while a fraction of the blink responding to backscattered photons appears for the integration period, and therefore the A/D counts are averaged out with the background. (a) Timing of the image intensifier on the ICCD camera. The time intervals of “gate on” and “gate off” have been scaled for better visibility. (b) The integral results corresponding signal photons. (c) The integral results corresponding backscattered photons. “late gate”: the photons hit the intensifier before the activated time gate. “early gate”: the photons hit the intensifier after the activated time gate. “no gate”: the photons hit the intensifier outside the activated time gate. (d) The photon threshold strategy procedure. (i) A sample image including signal photons and noises. The cluster covering an area of 3 pixels $\times$ 3 pixels can avoid the interference of hot pixels. (ii) A distribution of A/D counts on each pixels of the sample image. (iii)-(v) Images obtained for different threshold values of (iii) 560, (iv) 580 and (v) 600. The influence of noise gradually weakens as the threshold value increases, but setting a threshold too high will cause discarding some real photon events. The optimum threshold value in this experiment is 580.
Based on the active system, we implement and optimize the photon threshold strategy by the statistics of signals and noises, as is shown in Fig. 2(d). It consists of the differences in A/D counts from individual pixels, including signal photons (i). As the distance increases, the number of returned photons per pulse becomes sparse, so there are only a few signal photons on each frame image. As mentioned before, the response intensity of signal photons on the camera is higher than that of scattered photons and camera noise, and this difference is truly recorded on the camera. To characterize this difference, we collect the A/D counts per pixel from 1017 frames and analyze the distribution of the outputs on each pixel (ii). This distribution can be determined a threshold, counts over which and covering an area of 3 pixels $\times$ 3 pixels are considered as an amplifying electron cluster corresponding to a real signal photon event. Therefore, each original image has a binary outcome. We combine all binary frames to create the final image, the intensity of which is proportional to the probability of successfully hitting the detector from signal photons. Typical integral images for a different threshold of 560, 580 and 600 are shown in (iii)-(v). A low threshold means that more backscattered photons are recognized as signal photons in the final integration, which makes the acquired images noisier. While a high threshold value removes some valuable signals. Therefore, a reasonable threshold is necessary to avoid discarding real signal photons in the final image.
3. Results
We compare the results obtained by the three imaging schemes at the range of 18 m, 24 m, 30 m, 36 m and 42 m respectively, as is shown in Fig. 3. The intensity of the passive and the active methods represents the electronic A/D counts, while the intensity of the thresholded method represents the number of thresholded photons. As the distance increases, the field of view of the target on the camera shrinks. The image quality becomes worse due to the huge spatial geometric loss and the strong backward scattering. The passive method is strongly affected by the backscattering of the laser source and therefore can only image the target in a limited distance (see Fig. 3(a)). However, in the active imaging method, short gate-width can filter out most scattered light noise and get clear images at relatively long distances (see Fig. 3(b)). Interestingly, Fig. 3(c) shows that the photon threshold strategy gives a better performance at the single-photon level and reaches a longer distance. A concentric-ring board is chosen as the test target in this experiment, as is shown in Fig. 3(d), and a laser beam illuminates only the section marked in orange.
Fig. 3. Experimental results for different field-test distances. Three types of imaging strategies are shown in (a)-(c) for different distance (18 m, 24 m, 30 m, 36 m, 42 m). (a) shows that passive method is strongly affected by the backscattering of laser source and can only image the target in a very limited distance. (b) shows that short gate-width is beneficial to filter the scattered light noise and can get clear images at relative long distances. (c) shows that photon threshold strategy gives a better performance in underwater optical imaging. (d) shows the test target and orange section is the imaging area illuminated by the laser beam.
In the same conditions, the classical intensity methods integrate all A/D counts in the final image, which is inevitably affected by the multiplication noise. In contrast, the single-photon threshold strategy can register the existence of every single photon. After a succession of exposures, we accumulate these individual binary images into the final image. This methodology means that the signal intensity is proportional to the probability of photons successfully hitting the detector, which is not affected by the multiplication noise. Thus, it is beneficial to extract and optimize weak signals in the underwater environment, compared to a single integral image with the same overall exposure time.
The peak signal-to-noise ratio (PSNR) is usually used to compare image compression quality. To further compare the performance of the above three imaging schemes, we compare the PSNR shown in Table 1. Active intensity imaging can provide a better image quality than passive one; in the long-range, where the ICCD camera collects only a few single photons, active and passive imaging based on intensity accumulation cannot obtain the target information. In the limited-photon condition, the single-photon threshold strategy with area-array pixels has the fast-tracking ability and good robustness to the noisy environment.
Table 1. The PSNR for all imaging schemes
Since the image data determined by photon threshold strategy is a collection of discrete photons hitting a detector. The measurement results are strongly affected by shot noise due to the inherent nature of coherent light at a low light level. According to prior knowledge, the number of photons in a pulsed laser beam is subject to Poisson statistical distribution [52–54]. Combined with the practical measurement process, it can be written the modified format as follows
Poisson statistical distribution can be optimized to reconstruct salient features of targets from these noisy measurements as accurately as possible. It can be rewritten as a negative Poisson log-likelihood form
The term $\ln \left (n_{(i,j)} !\right )$ can be neglected since it is constant with respect to $I_{(i,j)}$, which does not impact the global optimization. The image data is modified within the bounds set by Poisson statistics of the original data. The optimization process for $I_{(i,j)}$ is based on minimizing a convex function, $\Phi$, as follows [55]
The first term is the negative Poisson log-likelihood function of the measured image, which facilitates the subsequent optimization process. The second term is a total variation (TV) seminorm regularization, which often converts the image denoising process into a well-posed problem through ensuring the existence and uniqueness of the optimized image. $\tau$ is a balance factor that satisfies the measured data and the sparsity condition constraints. When $\tau$ is at a low level, the reconstructed image is underfitting. In contrast, when $\tau$ is at a very high level, the reconstructed image corresponds to an overfitting result.
We reconstruct the target images of a submarine model and a concentric ring placed in 36 m and 42 m respectively in Fig. 4(a). The original measurements and images for a low value, optimized value and high value of $\tau$ are shown in Fig. 4(b)-(e). These results highlight the trade-off by changing the balance factor $\tau$ between two modified terms in Eq. (3). When $\tau$ is zero, the reconstructed images correspond to the initial measured data in Fig. 4(b). For small values of $\tau$ in Fig. 4(c), the reconstructed images are still noisy in the spatial frequency domain due to undersmoothing. As $\tau$ increases, the images become smoother since the TV seminorm regularization term dominates the final image data, thus the resolution gets degraded for high values of $\tau$. For high values of $\tau$ in Fig. 4(e), the intensity estimate has overfitting distortions. As is shown in Fig. 4(d), the regularization parameters for the central values of $\tau$ give the best-optimized images.
Fig. 4. Regularized image results. (a) Original test objects. (b) Raw measurements captured by the ICCD camera. Reconstructed images for increasing values of $\tau$ in columns (c)-(e). (c) The reconstructed images weighted towards maximizing the log likelihood. (e) The reconstructed images obtained when the optimization algorithm is overly weighted towards increasing the sparsity. (d) The reconstructed images with $\tau$ adjusted to give subjectively the best images.
In addition to underwater imaging, single-photon threshold strategy is also sensitive to detect targets by reflected photon statistics. We choose a 2.56 m $\times$ 2.56 m scene area corresponding to 1024 pixels $\times$ 1024 pixels of the ICCD camera with the target about 0.2 m $\times$ 0.2 m at the center of the scene. The target is 50 meters away from the camera, which means the loss is more than 9 attenuation lengths.
We perform the basic calculation about the number of photons per pulse. The maximum energy of a single laser pulse is 300 $\mu$J/pulse. By measuring the power between the sender section and receiver section, we estimate the underwater channel loss is about 40 dB at a distance of 50 meters. The loss wound be double due to the round-trip distance that the laser travels in water. The spatial geometric loss is about 60 dB in the reflection channel. Besides, in the imaging system, the effective quantum efficiency of the ICCD camera is about 10 $\%$, and the reflectivity of mirrors on the cloud stage is about 90 $\%$. Half of the area of targets can return photons. Considering all the above loss, we can calculate about 0.8 photons per pulse on average. In such a photon-limited case, traditional active intensity imaging has been unable to obtain the location information about the target, as is shown in Fig. 5(a). However, the existence of the target will cause the statistical change of the number of reflected photons, which can help us determine whether there are objects by the single-photon threshold strategy.
Fig. 5. The photon threshold strategy for identifying the targets at an ultimately high loss. (a) The reflected photons captured by the ICCD camera at a distance of 50 m away from the scene. (a) The camera can cover an area of 2.56 m $\times$ 2.56 m, a 0.2 m $\times$ 0.2 m target is placed in a center of the scene. After thousands of frames acquisition, signals and background noise in different areas are analyzed and shown in (c)-(f). The number of reflected photons are slightly higher than the surrounding areas. Based on above result, we can lock the location of targets even in a very high-loss scenario.
To illustrate this capability, we divide 400 pixels $\times$ 400 pixels into 25 subareas on average, where the target covers an area of 80 pixels $\times$ 80 pixels in the center, as is shown in Fig. 5(b). We add up the total number of photons in these subareas for statistics, respectively. When the number of photons is sparse, the signal is submerged in the fluctuations of noise. The peak area is random so that it is difficult to determine the location of a target shown in Fig. 5(c)-(d). As frames increase, the statistical results change in each subarea as is shown in Fig. 5(e)-(f). Signal photons exceed the fluctuation of environmental noise, and the peak area is locked in the center and no longer changes. Surprisingly, an ultimately high loss may induce a failure of imaging, it is still possible to identify the existence of the target by photon statistics. The photon threshold strategy ensures that the target information can still be obtained even though the signal photons are incredibly sparse, where the classical methods fail to meet the challenge.
4. Conclusion
In summary, we experimentally demonstrate quantum-enhanced underwater imaging and detection using the single-photon threshold method. This strategy does not detect quantum states directly but filters out low counts representing backscattered photons, which is a unique way to break through the classical limits and exhibit quantum-enhanced properties. We verify the unique advantage by analyzing the enhancement on the PSNR of underwater sensing, imaging and other light-detection applications. The method always improves the PSNR in principle in the high-noise regime and can transform underwater optical imaging to the single-photon regime. Besides, we show that the statistical change of the number of reflected photons can identify the existence of targets. The scheme of thresholded single-photon underwater imaging and detection, together with our field test in the longest-ever distance, suggests a promising route for air-to-sea and deep-sea exploration.
Funding
National Key Research and Development Program of China (2017YFA0303700, 2019YFA0308700, 2019YFA0706302); National Natural Science Foundation of China (11690033, 11761141014, 11904229, 61734005); Shanghai Municipal Science and Technology Major Project (2019SHZDZX01); Shanghai Municipal Education Commission (2017-01-07-00-02-E00049); Science and Technology Commission of Shanghai Municipality (17JC1400403).
Acknowledgments
The authors thank Jian-Wei Pan for helpful discussions. X.-M. J. acknowledges additional support from a Shanghai Talent Program and support from Zhiyuan Innovative Research Center of Shanghai Jiao Tong University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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