Underwater optical imaging has been intensively investigated recently to determine the scalability of its potential applications, which include marine science, underwater rescue, mineral exploration, and seafloor topography^[1,2]. However, the ranging distances and imaging quality are limited by the huge channel loss of propagated light, due to the strong absorption and scattering from underwater media^[3]. To improve the ranging distance and imaging quality, two categories of technologies have been developed^[4]. The first one is imaging enhancement by optimized algorithms and specific hardware, including histogram equalization^[5], homomorphic filtering^[6], Retinex algorithm^[7], and wavelet transformation^[8], as well as their fusions^[9]. The other one is signal light enhancement based on physical properties of scattering, including range-gated imaging^[10], laser synchronous scanning^[11], polarization imaging^[12], and spectral imaging^[13]. The comparison between these technologies can be found in a recently published review^[4].

With the increase of the underwater distance, the scattering light from the target becomes sparse, or even the detected signal is much less than one photon per pulse^[14]. In this case, single-photon detectors (SPDs), such as silicon single-photon avalanche diodes or SPD arrays, have infinitely expanded their detection distance, where high-quality underwater optical imaging with dozens of attenuation lengths has been achieved^[15–17]. However, to a certain degree, the extreme sensitivity of SPD hinders underwater optical imaging under natural conditions, such as sunshine or other natural lights, which may bring massive noise. This external noise will dramatically degrade the imaging contrast or even cause the failure of the target reorganization. To overcome this shortcoming, Maccarone et al. proposed a thresholded single-photon underwater imaging scheme to extract signals from the noisy environment, and a capability of underwater detection down to 0.8 photons per pulse with Jerlov III water up to 50 m has been achieved^[17]. Other typical progress with high-contrast imaging and long detection distance is ghost imaging, which is also known as correlation imaging or second-order correlation imaging^[18,19]. This scheme manifests the advantage of being turbulence-free, robustness against scattering, and a wider range of views^[4]. Nevertheless, the low reconstruction efficiency is also present in correlation imaging, due to the imaging quality depending on the fluctuations in the detected signal and the corresponding correlated photons rather than the absolute value of intensity. Notwithstanding, the commonly employed coherent lasers or pseudothermal lights show a relatively low probability of correlated photons, particularly with the detected photons per pulse much less than one^[20,21]. The nonclassical light sources, such as spontaneous parametric down conversion with entangled biphotons^[22,23], can improve the correlation probability. However, the utilization of the nonclassical sources for underwater optical imaging is still limited by their low generation rates and complex structures^[24].

Here, we generated a nonclassical laser with giant second-order correlations and extremely high-bundle N-photon emission. Compared to a coherent laser with Poissonian distribution, the generation of bundle N-photons of the super-bunching laser can be enhanced by one or several orders of magnitude, which proves a much higher probability for underwater correlated biphotons. To prove our proposal, we performed underwater correlated biphoton imaging (CPI) in a glass tank with a length of 10 m under huge noise-to-signal ratios (NSRs) and extremely weak detected signal (mean photon per pulse less than 0.012, i.e., ⟨n⟩≤0.012). We have experimentally demonstrated that underwater optical imaging with reasonably good contrast can be determined with ⟨n⟩ down to 0.002 and NSR up to 150. Our results offer a new non-classical light source to enhance underwater optical imaging contrast in noisy environments.

The detailed optical scheme for the realization of the super-bunching laser has been described in a previous work^[25]. Briefly, the super-bunching laser was generated by the stochastic nonlinear interactions between a picosecond pulsed laser (with the wavelength of 1064 nm) and an optimized photonic crystal fiber (PCF), as shown in Fig. 1(a). The repetition frequency of the pulsed laser was 5 MHz. The structure of the PCF was composed of five layers of periodically arranged air holes, forming a ring-shaped configuration within the fiber, as shown in the insert in Fig. 1(a). By changing the pumping power of the pulsed laser, both the output power and the corresponding wavelength ranges can be optimized, which are distributed from visible to near-infrared regions. Considering that the absorption and scattering coefficients of water at the blue-green spectral region (generally with a wavelength of 450–570 nm) are both small^[1], we selected a wavelength of 532 nm with a bandwidth of 10 nm through a band filter (BF) to perform underwater optical imaging. To characterize the feature of the super-bunching laser, we used four SPDs to perform second-order correlations and photon number probability distribution measurements under different mean photon numbers per pulse, ⟨n⟩, which was controlled by an attenuation (Att). The information of each photon was determined by a multi-channel event timer with a time-correlated single-photon counting (TCSPC) unit.

The critical characteristics of the super-bunching laser are the giant second-order correlation, g2(τ), and extreme multi-photon events. To show the advantage of the super-bunching effect, we compared these two values with a conventional picosecond laser (PicoQuant, LDH-D-TA-530). The results are shown in Figs. 1(b)–1(e). Generally, the normalized second-order correlation of a coherent laser at zero delay, g2(0), is equal to 1^[26,27], exactly in agreement with our experimental results, as shown in Fig. 1(b). In contrast, the super-bunching laser manifests giant values of g2(0), which are much larger than the coherent laser [g2(0)=1] and thermal light [g2(0)=2]. Figure 1(c) presents a result with g2(0)=340, under ⟨n⟩=0.068. Typically, the smaller the ⟨n⟩, the larger the g2(0). The giant g2(0) indicates the existence of correlated photons or a multi-photon bundle emission and suggests extreme photon-number fluctuations stronger than those of thermal light. To prove these conclusions, we performed photon number probability distribution measurements of the coherent laser and super-bunching laser under different ⟨n⟩ values, as shown in Fig. 1(d). The probability distributions of the coherent laser (the hollow symbols) are very consistent with the Poissonian distribution, whereas those of the super-bunching laser are significantly deviated from the Poissonian distribution. Specifically, the probabilities of the one-photon event, P(1), are slightly lower than the Poissonian distribution. In contrast, these two- to four-photon events [P(2), P(3), and P(4)] are much larger than the coherent laser. Figure 1(e) illustrates the ratios of the probability between the super-bunching and coherent lasers, ζ(N), under different ⟨n⟩. ζ(N) can be varied from a few to huge values^[25]. The larger values of ζ(N≥2) are beneficial to CPI.

Here, we present an experimental demonstration of underwater CPI through the super-bunching laser. As shown in Fig. 2(a), the whole experiment is implemented in a glass tank (10.0m×0.6m×0.5m), which is similar to a natural field situation, and it is beneficial to test the imaging system in an actual field condition. The sender and receiver of CPI were located on the same side of the glass tank, and the target was placed in the water and stuck on the end of the glass tank. The super-bunching laser was first split by a beam splitter (BS) with a ratio of 1:99, where the weaker beam was decayed by attenuation and detected by an SPD (SPDr). This photon was identified as one of the biphotons, and the electric response was used as the reference. The stronger beam was guided to the glass tank, expanded by a soft lens (L2, f2=500mm), and then illuminated the target. The diameter of the laser beam was close to 200 mm, which could fully cover the target. The scattered light was collected by a telescope system (L3 and L4) and then collimated to another SPD (SPDs) by a galvo mirror (GM). The detected photon was identified as another photon of the correlated biphoton, named the signal. The underwater imaging was achieved by scanning the GM pixel-by-pixel. Both the reference and signal were guided to the TCSPC and calculated by a personal computer (PC). During the imaging, the noise originated from the natural light (NL), the intensity of which can be controlled by removing the light-blocking fabrics covering the glass tank. The attenuation coefficient of the water (α) was controlled by salt with different concentrations. The value of α in the region of 0.062–0.176m−1 was calibrated by a home-built multi-pass cell.

The principle of noise-resistant CPI can be understood from the schematic shown in Fig. 2(b). Considering that the reference arm can be maintained in a dark environment, the noise from the natural light can be removed. Although the dark noise from SPDr is still present, the counting rates per second are at least three orders of magnitude smaller than that of the detected photons. Thus, the influence of dark noise can also be ignored in our current technology. In contrast, the noise from the natural light would be much stronger than the scattering light from the target. Benefiting from the strong time-correlated feature of the super-bunching laser, most of the noise can be removed by counting the correlated biphoton events, which is defined as that the difference of the arriving time of photons between the reference and signal arms is less than a finite time (Δt). In this experiment, the time interval between pulses (T) was 200 ns (the repetition frequency of the super-bunching laser was 5 MHz), and Δt was set as 1 ns. After calibrating the time delay between the reference and signal arms through their second-order correlation, only the scattering light from the target and some of the noise will be regarded as the signal. In this case, most of the noise will be removed, and thus, CPI manifests dramatic noise-resistant features.

To optimize the light intensity of the reference arm and confirm the noise-resistant feature of our current scheme, we measured the counting rates of the correlated biphotons under different conditions before performing underwater CPI. Figure 2(c) illustrates the coincidence rates of biphotons (cps) as functions of light intensities of the reference beam. Note that under a certain intensity of the signal beam (such as Ns=7kcps), the coincidence rates (Nc) almost linearly increase with the rise of the reference intensity (Nr) when Nr≤Ns. As the intensity of the reference beam further increases, the coincidence rates tend to saturate. On the other hand, when the intensities of the signal beam are much larger than the reference beam, such as Ns=375kcps or 1200 kcps and also Ns≥Nr, the coincidence rates show similar values. These results indicate that the maximum coincidence rate is about 5%–10% of the signal intensity (without external noise). The extremely high probability of the correlated biphoton events originated from the bundle emission feature of the super-bunching laser. Taking Nr=Ns≈7kcps as an example [the dashed circle shown in Fig. 2(c)], the coincidence rate is 922 cps, and thus, the ratio between the number of the correlated biphotons and all detected photons is close to 6.59% (922 cps/14 kcps), under ⟨n⟩ close to 0.0028 (14 kcps/5 MHz). However, for a coherent laser with a Poisson distribution, this ratio is about 0.14%. Thus, compared to a coherent laser under the identical ⟨n⟩, the rate of correlated biphotons for the super-bunching laser can be enhanced by 47-fold. Furthermore, we also investigated the rates of correlated biphotons under a certain signal intensity but varied reference and noise intensities, as shown in Fig. 2(d). Note that with the increase of the noise intensity (Nn), the difference in the coincidence rates can almost be ignored, indicating the strong noise-resistant feature of our scheme. However, when both Nr≥10Ns and Nn≥10Ns, the coincidence rate still increases with the rise of the reference intensity [insert in Fig. 2(d)], indicating the contribution to the correlated biphoton from the noise light. Therefore, in the later experiments, the intensities of the reference beam were set to 10 times the signal beam, which can not only guarantee the maximum correlated biphotons between the reference and the signal beams but also remove the occasional correlated biphotons between the reference and the noisy lights as long as possible.

Before performing the underwater imaging, we first conducted CPI under different noise levels without any water. The results are shown in Fig. 3. Here, a black cross was used as a target. The averaged intensities of reference and signal were about 600 and 60 kcps, respectively, corresponding to ⟨n⟩ of about 0.012 for the received signal. The integral time for each pixel was set to 0.5 s. For comparison, we also performed single-photon imaging (SPI) by counting the photon number of SPDs. Without any noise from the natural light, the target can be clearly visualized, as presented in Fig. 3(a). However, when NSR was larger than 3 (i.e., the intensity of the external noise was three times or even stronger than the signal intensity), the target was almost wholly submerged in the noise and could not be demonstrated, as shown in Figs. 3(b)–3(d). In contrast, CPI exhibits strong noise-resistant features, as presented in Figs. 3(f)–3(h). Note that although the average counts per pixel of CPI without noise are much smaller than SPI, the CPI also presents a good contrast. Furthermore, the counts of CPI manifest an insignificant increase when the external noise was detected by SPDs (such as NSR=3). This result further indicates that the random noise showcases an ignorable influence on CPI; even when the noise was two orders of magnitude stronger than the signal, the target still can be demonstrated, as illustrated in Fig. 3(g) (NSR=100). When the NSR rises to 1000, the contrast becomes poor, but the target still can be roughly estimated, as presented in Fig. 3(h). To show the advantage of the super-bunching laser, we also performed CPI by a coherent laser (PicoQuant); the results are shown in Figs. 3(i)–3(l). Apparently, the counts of the correlated biphoton from a coherent laser are much smaller than those of the super-bunching laser, as shown in the comparison between Figs. 3(e) and 3(i). In this case, with the increase of the noise, the contrast of CPI decays much faster than the super-bunching laser. To compare these results further, we used the contrast-to-noise ratios (CNRs) to quantifiably describe the image quality, which can be expressed as^[28]CNR=|I1¯−I2¯|σ12+σ22,(1)where I1 and I2 are the intensities of the target and the background, I1¯ and I2¯ are the corresponding mean values, and σ1 and σ2 are the standard deviation of I1 and I2, respectively. The calculated CNRs varying as NSRs are listed in Fig. 3(m). Note that although CNR for SPI without noise shows the biggest value (4.50), it decays very quickly with the increase of NSR and is almost close to zero (0.153) when NSR exceeds 10. On the contrary, CNR for CPI via the super-bunching laser presents a very slow decay behavior before NSR reaches 10³. Although CNR for CPI via a coherent laser shows a similar tendency to that via the super-bunching laser, the corresponding values are much smaller. We also defined the enhancement between these CNR values, as illustrated in Fig. 3(n). Under different noise levels, the enhancements of CNR between CPI via the super-bunching laser and SPI are between 4.4 and 61, indicating the strong noise-resistant feature of our CPI blueprint. Furthermore, the enhancements of CNR for CPI between the super-bunching laser and a coherent laser are also between 1.5 and 47, which also declares the advantages of the super-bunching laser for the CPI scheme.

Later, we performed underwater SPI and CPI using tap water with an attenuation coefficient of about 0.062m−1 (i.e., α=0.062m−1), corresponding to 0.62 attenuation lengths. The results are presented in Fig. 4. Due to the underwater transmission channel loss, the numbers of detected single photons without external noise show a decrease, as the comparison between Figs. 3(a) and 4(a). Clearly, with the increase of the natural light noise, the contrast of underwater SPI fast decays and cannot be demonstrated, as shown in Figs. 4(b)–4(d). In contrast, the reduction of the correlated biphoton numbers is relatively slight compared to that of the detected single photons, as shown in the comparison between Figs. 3(a) and 3(b) and 4(a) and 4(b), respectively, indicating that the correlated biphoton of the super-bunching laser manifests anti-attenuation characteristics, which is also counterintuitive to conventional coherent lasers. Furthermore, with the increase of the natural noise, the noise-resistant feature still remains for underwater CPI; even when NSR reaches 100, the target can still be obviously visualized, as presented in Fig. 4(g). The calculated CNR declares that even when NSR is up to 300, the value of CNR is yet larger than one [1.14 as illustrated in Fig. 4(i)], and the maximum enhancement between underwater CPI and SPI can reach 30, as presented in Fig. 4(j).

To illustrate the noise-resistant feature of CPI in different conditions, we further performed underwater CPI with different attenuation coefficients, which were varied by adding salt with various concentrations. Figures 5(a)–5(d) present CPI without external noise under attenuation coefficients ranging from 0.062 to 0.176m−1. Obviously, the counts of correlated biphotons decreased with the increase of the attenuation coefficients, due to the rise in underwater channel loss of the transition and scattering light. On the other hand, the imaging contrast of underwater CPI presents a slight reduction with the increase of the external noise, as shown in Figs. 5(e)–5(h) (with NSR equaling 30) and Figs. 5(i)–5(l) (with NSR equaling 150), benefiting from the anti-noise feature of our current CPI scheme. Taking α=0.176m-1 (close to the one in coastal seawater Jerlov type III, α=0.179m-1^[14]) and NSR=150 as an example [Fig. 5(l)], the received signal (⟨n⟩) was about 0.002 in this case; the target still can be roughly visualized, and the profile of the target can be well recognized after limited smoothing, as shown in Fig. 5(m). The corresponding CNRs as functions of NSRs have been illustrated in Fig. 5(n); although the values of CNR decayed with the increase of NSR, the relatively good imaging contrast (CNR=1) can be determined under conditions where the intensity of the external noise is two orders of magnitude stronger than that of the correlated biphoton (NSR=150). On the other hand, with the increase of attenuation coefficients, the variations of CNR among different conditions become soft. We also plotted CNR varying as attenuation coefficients with and without external noise, as presented in Fig. 5(o). Note that under both conditions, the variations can be well fit by linear functions, indicating that the imaging contrast decays linearly with the increase in the attenuation coefficients, rather than exponential decay behavior. This result also reveals that our current blueprint may apply underwater imaging with significant attenuation coefficients or very long underwater channel distances.

In summary, we have experimentally demonstrated noise-resistant underwater CPI based on a home-built super-bunching laser with extreme multi-photon events. The fundamental features of the super-bunching laser, including the second-order correlations and photon number probability distribution, have been studied and compared with conventional coherent lasers. The underwater optical imaging was implemented with a 10 m glass tank with Jerlov type III water. The imaging contrast of CPI and SPI varied as NSR and attenuation coefficients have been investigated to disclose their capacity. Finally, CPI with reasonably good contrast has been achieved under the conditions of NSR=1000 and ⟨n⟩=0.012, as well as NSR=150 and ⟨n⟩=0.002. These results indicate that our CPI blueprint has promising applications under noisy environments with extremely weak received light signal, thus suitable for large attenuation and long-distance underwater imaging. In future work, we will aim to improve the emission power of the super-bunching laser and further enhance its multi-photon generation probability, which can both improve the imaging distance and shorten the integral time.