Noise-tolerant correlated coincidence imaging based on supercorrelated light at 1550 nm

Abstract

Single photon–level imaging at 1550 nanometers is a key driver for crucial advancements in the next-generation laser detection technology. This cutting-edge approach plays a vital role in space ranging, target recognition, and three-dimensional remote sensing. However, it has faced severe challenges such as insufficient noise-tolerant performance. Here, we introduced noise-tolerant correlated coincidence imaging (CCI) based on supercorrelated light (SCL). The light source, generated through nonlinear interaction between a pulsed laser and a photonic crystal fiber, exhibits a broader power-law photon number probability distribution and extremely strong photon correlation [with second-order correlation function g⁽²⁾(0) up to 18,166]. Our noise-tolerant CCI can resist random environmental noise up to 100,000 times stronger than the echo signal photons. SCL offers an exceptionally strong noise tolerance for single photon–level imaging in extreme environments with intense noise, paving the way for the future development of extremely sensitive light detection.

Super-correlated light source with g⁽²⁾(0) of 18,166 is used for high-quality correlated imaging under intense noise.

INTRODUCTION

Active imaging technology operating at a wavelength of 1550 nm combines the dual advantages of low transmission loss and human eye safety (1–3), serving as a core driver in advancing frontier fields such as target recognition, biomedical imaging, and safety monitoring (4–7). High-power lasers are commonly used for target object illumination in conventional imaging systems, while traditional photodetectors are used to capture echo signals (8, 9). Single photon–level imaging technology overcomes the limitations of traditional systems by enabling robust detection under illumination conditions that are far below the threshold of conventional imaging systems (10, 11).

Despite single-photon imaging technology having achieved outstanding performance, it still faces a frontier question: noise interference (12, 13). The simultaneous influence of environmental noise and dark counts from detectors dramatically compromises both the signal-to-noise ratio and image contrast, resulting in the masking of accurate target information by substantial noise. Currently, optical modulation and computing algorithms are used as an effective strategy to suppress a large amount of noise interference (14–19). Recent advances in correlated coincidence imaging (CCI) have proposed schemes based on exploiting bright squeezed vacuum light and entangled photon sources, substantially enhancing image quality (20–28). Key properties enabling these improvements include photon correlations in entangled photon pairs and bright squeezed vacuum light. For instance, Zhang (22) demonstrated that CCI, achieved through spatial correlation between photon pairs, exhibits a 25-fold greater noise tolerance than conventional imaging. Similarly, in (23), spatial-momentum entanglement is used to extract biphoton coincidence counts in CCI using a covariance algorithm, effectively eliminating uncorrelated noise. This method is capable of withstanding environmental noise up to 155 times stronger than the classical signal. Notably, this inherent photon correlation property provides a natural advantage in suppressing environmental noise. For photon pairs, the coincidence-to-accidental ratio (CAR) and the coincidence count rate are two key indicators. In correlated imaging, a high CAR grants the strong noise resistance of imaging systems. Meanwhile, a high coincidence count rate means that it can tolerate a degree of external attenuation and allows for image reconstruction over short measurement times. Although photon pairs with high CAR have been reported, achieving a balance between the CAR and the coincidence count rate remains a challenge (29, 30). Consequently, developing a correlated light with strong correlations and dramatic multiphoton coincidence count rates is a key strategy for fundamentally resisting noise.

Strong photon correlation can not only be achieved through the entanglement process with phase matching but also via the generation of intense photon number fluctuations. Recent studies have demonstrated that the bright squeezed vacuum light is a nonclassical light source [with second-order correlation function g⁽²⁾(0) > 2] exhibiting strong photon correlations (31). This strong correlation arises from dramatic photon number fluctuations, which result in nonclassical statistical behavior that deviates markedly from the Poisson distribution, giving rise to a substantially higher probability of multiphoton emission (32, 33). In general, enhancing photon number fluctuation and multiphoton emission probability have been achieved in both linear and nonlinear optical systems. In linear systems, modulation of photon number probability distribution and photon correlations can be achieved through optical scattering systems (such as rotating ground glasses) or optical modulators (34, 35). On the other hand, strong photon correlation properties have been observed in various nonlinear optical systems, including those involving nonlinear optical crystals (36), cold atom systems (37, 38), quantum dots (39–42), and two-dimensional materials (43). Furthermore, studies demonstrate that the nonlinear interaction between bright squeezed vacuum light and single-mode fiber generates enhanced photon correlation, enhancing the correlation properties of the light field. The second-order correlation function g⁽²⁾(0) has reached the current maximum reported value of 170. It also declared that this kind of light source with strong fluctuations in the photon number can be highly beneficial in correlated imaging, and the imaging contrast is determined by g⁽²⁾(0) (44).

In this work, we propose a noise-tolerant CCI system based on a supercorrelated light (SCL) source at 1550 nm. The SCL sources that exhibit unprecedented photon correlations are achieved through complex nonlinear effects between pulsed lasers and engineered photonic crystal fibers (PCFs). The measured intensity correlation function g⁽²⁾(0) reached 18,166. This supercorrelation arises from the utmost multiphoton bundled emissions and a broader photon number distribution than classical light. Our imaging scheme uses biphoton coincidence detection from the source’s dual output paths. The system maintains imaging capability under environmental noise 100,000 times stronger than signal photons. The results demonstrated that CCI can resist random environmental noise up to 100,000 times stronger than signal photons. Compared to the most advanced CCI schemes using other nonclassical light sources, the noise-tolerant ability of our CCI scheme has improved by three orders of magnitude (20–23). When the noise photon counts reach 50,000 and 20,000 times that of the signal photons, respectively, the peak signal-to-noise ratio (PSNR = 13.68 dB) and contrast-to-noise ratio (CNR = 4.46) of our CCI are comparable to those of traditional photon-counting imaging (PCI) without external noise. SCL sources exhibit stronger photon correlations, which translates to unparalleled noise tolerance, thereby enabling single photon–level correlated imaging.

RESULTS

Principle of noise-tolerant CCI

We introduced a noise-tolerant CCI technique based on a pulsed SCL source with high g⁽²⁾(0). For CCI, one path of the SCL source is used to illuminate the target object, and scattered light from the object is used as the detection light (CH1, Fig. 1A). The other path serves as reference light (CH2), remaining locally, which is combined with detection photons for coincidence measurements. The arrival pattern of photons is shown in Fig. 1A, where the red and blue balls represent the correlated photons and noise photons, respectively. The arrival times of noise photons are distributed randomly across all pulses. In contrast, correlated photons from a single pulse arrive simultaneously within their pulse width. Therefore, coincidence counts from SCL can only be measured if both photons arrive within the coincidence window t_gate (t_gate ≪ T, where T is the pulse period) of the same pulse. Noise photons can be effectively suppressed through coincidence measurements between the detection and reference paths with a limited time window.

Fig. 1. Principle of noise-tolerant CCI by SCL.

(A) Schematic diagram of CCI through the coincidence counts from the dual channels. Red and blue balls represent the photons detected from the SCL source and noise. (B) The simulated CNR for CCI and PCI as a function of R across g⁽²⁾(0). (C) The simulated CNR as a function of g⁽²⁾(0) across different R.

To quantify CCI quality, we can determine that the coincidence count per second of the object area C_o is $C_{\mathrm{o}}=\left[g^{\left(2\right)}\left(0\right)\cdot \right.$$\left.N_{\mathrm{r}}{N}_{\mathrm{s}}+N_{\mathrm{r}}(t_{\text{gate}}/T)N_{\mathrm{n}}\right]\times T$, and that of the background area C_b is $C_{\mathrm{b}}=N_{\mathrm{r}}(t_{\text{gate}}/T)N_{\mathrm{n}}\cdot T$, where N_r, N_s, and N_n denote the reference, signal, and noise photon count per second, respectively (see derivation in note S1). Consequently, the difference between the coincidence counts per second of the object area and the background area can be expressed as $C_{\mathrm{o}}-C_{\mathrm{b}}=g^{\left(2\right)}\left(0\right)\cdot N_{\mathrm{r}}{N}_{\mathrm{s}}T$, exhibiting a positive correlation with g⁽²⁾(0). Under identical conditions, higher g⁽²⁾(0) values lead to greater differences, thereby enhancing imaging contrast.

Here, we used the CNR to evaluate the noise tolerance of CCI based on SCL sources with high g⁽²⁾(0) in an intense noise environment. The CNR of the reconstructed image can be expressed as (note S1)

$$\begin{array}{c}\mathit{CNR}=\frac{\mid C_{\mathrm{o}}-C_{\mathrm{b}}\mid }{\sqrt{{\mathrm{\sigma }}_{C_{\mathrm{o}}}^2+{\mathrm{\sigma }}_{C_{\mathrm{b}}}^2}}=\hfill \\ \frac{g^{\left(2\right)}\left(0\right)N_r{N}_s}{\sqrt{{\left[g^{\left(2\right)}\left(0\right)\right]}^2\cdot {\left(N_{\mathrm{r}}{N}_{\mathrm{s}}\right)}^2(\frac{1}{N_{\mathrm{r}}}+\frac{1}{N_{\mathrm{s}}})+2{\left(N_{\mathrm{r}}\frac{t_{\text{gate}}}{T}{N}_{\mathrm{n}}\right)}^2(\frac{1}{N_{\mathrm{r}}}+\frac{T}{t_{\text{gate}} \times N_{\mathrm{n}}})}}\hfill \end{array}$$ (1)

where ${\mathrm{\sigma }}_{C_{\mathrm{o}}}$and ${\mathrm{\sigma }}_{C_{\mathrm{b}}}$ represent the standard deviations of the coincidences of the object and background areas. For comparison, we also present the results of conventional single-photon imaging (i.e., PCI), where the value of each pixel corresponds to the number of detected photons. The corresponding CNR calculation method is detailed in note S1. To quantitatively analyze the influence of g⁽²⁾(0) value and noise photons on the imaging CNR, we assume that N_r = N_s, and define the ratio of total photons to signal photons, R, as follows

$$R=\frac{N_{\mathrm{n}}+N_{\mathrm{s}}}{N_{\mathrm{s}}}$$ (2)

The simulation results of the CNR of CCI and PCI are shown in Fig. 1 (B and C). For CCI, where g⁽²⁾(0) remains constant, with R gradually increasing from 10⁰, CNR maintains good stability across a wide range of R values. Only when R reaches extremely high values does the CNR begin to decline gradually. Comparing the simulations with different photon correlation, we find that a high g⁽²⁾(0) value has a strong resistance to intense noise. For instance, when g⁽²⁾(0) = 10⁴, CNR exhibits excellent robustness across the range of R = 10⁰ to 10⁴. As R increases to 10⁵, CNR gradually degrades. In contrast, the dotted line represents the traditional PCI, which exhibits dramatically degraded CNR as R increases. Figure 1C shows the CNR variation as a function of g⁽²⁾(0) values across different R conditions. The CNR exhibits progressive enhancement with increasing g⁽²⁾(0). Notably, at R = 10⁵ and g⁽²⁾(0) = 10⁴, the CNR can reach 9.4, demonstrating that the SCL source with a high g⁽²⁾(0) can substantially enhance image quality. Therefore, SCL sources with high g⁽²⁾(0) exhibit excellent noise resistance in CCI. Consequently, developing a light source with a high g⁽²⁾(0) value is crucial for advancing noise-resistant correlation imaging.

Generation and characterization of SCL

To develop a nonclassical light source with giant g⁽²⁾(0) values for CCI applications, we proposed the generation of SCL source through nonlinear interaction between a pulse laser and optimized PCF (44–47). The details have been reported in our recent work (33).

We first generated an SCL source at 1550 nm by using a picosecond pulse laser at 1064 nm to pump an optimized PCF. Additional details are provided in Materials and Methods and the Supplementary Materials (note S3 and figs. S2 and S3). Subsequent characterization revealed the unique properties of this SCL source. The pump power can substantially alter the dominant nonlinear effects, thereby altering both the photon emission rate and the second-order correlation function g⁽²⁾(0) of the SCL source (48, 49). When the power of the pump pulse reaches the generation threshold of 190 mW for the 1550-nm spectrum (inset of Fig. 2A), a large number of photons emit from the PCF, leading to a sharp increase in the photon count rates, as shown in Fig. 2A. As the pump power exceeds 340 mW, the growth of photon counts slows down because of the gradual emergence of other spectral components. To confirm its supercorrelation characteristics, we measured the second-order correlation function g⁽²⁾(0) of the generated SCL source based on the Hanbury Brown-Twiss (HBT) system (Fig. 2B, the HBT device is shown in fig. S2). The g⁽²⁾(0) value increases sharply as the pump power approaches the threshold of SCL source, which can be considered as the proportion of generated correlation photons increases dramatically. With a further increase in pump power, the g⁽²⁾(0) value shows a decreasing trend due to a large number of uncorrelated photons generated as the gain continues to increase. When the pump power exceeds 450 mW, g⁽²⁾(0) gradually decreases to 1, attributed to the increasing dominance of coherent (CL) and thermal light (TL) components. It is in good agreement with the theoretical prediction (fig. S1). Therefore, the maximum g⁽²⁾(0) can be determined under optimal conditions. For example, at a pump power of 260 mW, g⁽²⁾(0) reaches its maximum, with a value of 18,166 (Fig. 2C). We further characterized the g⁽²⁾(0) at different mean photon numbers $\langle n\rangle$ from 3.9 × 10⁻³ to 6.1 × 10⁻⁵, achieved by attenuation with a neutral density filter (Fig. 2D). The measured g⁽²⁾(0) values exhibit a dramatic increase from 210 to 10,738. Contrary to the traditional understanding that second-order correlations are insensitive to the variation of $\langle n\rangle$, g⁽²⁾(0) of the SCL source increases substantially as the $\langle n\rangle$ decreases. This unusual behavior is attributed to the presence of a large number of multiphoton pulses in the SCL source. As the attenuation ratio increases, single- and two-photon pulses (N ≤ 2) are suppressed, resulting in an increase in photon sparsity in the time domain, which leads to a higher proportion of multiphoton pulses. This increase, in turn, substantially enhances g⁽²⁾(0) (note S4 and fig. S4). Compared to CL and TL, the g⁽²⁾(0) of the SCL source is improved by at least four orders of magnitude (39, 50, 51). In addition, we compared the CAR and coincidence count generation rate of the SCL source with those of previously reported photon pairs (fig. S5) (29, 30, 52–55). The comparison shows that when the second-order correlation function g⁽²⁾(0) of our SCL source is at the same order of magnitude as the CAR of the photon pairs, the coincidence count rate of the SCL source is more than two orders of magnitude higher than that of the photon pairs. Furthermore, we measured the coincidence counts per second and g⁽²⁾(0) over varying measurement times while maintaining a constant pump power of 260 mW. As measurement time increases, the deviations of coincidence counts per second and g⁽²⁾(0) are substantially reduced (Fig. 2E). This phenomenon clearly indicates that the stability of the photon correlation of the light source varies over time. In practical applications, the measurement time needs to be optimized to achieve the required stability.

Fig. 2. Characterization of supercorrelated features.

(A) Photon counts per second of SCL as a function of pump power. The inset shows the filtered spectrum centered at 1550 nm. (B) Measured g⁽²⁾(0) as a function of pump power. (C) Second-order correlation function g⁽²⁾(τ) as a function of the time delay τ, observed bunching and normalization peaks at τ = NT, where T = 1/f = 41.06 ns and N are integer values. (D) Comparison of g⁽²⁾(0) as a function of the mean photon number per pulse $\langle n\rangle$ for SCL and CL. (E) The coincidence counts (coin-counts) and second-order correlation function g⁽²⁾(0) corresponding to different measurement times.

To verify the multiphoton characteristics of the SCL source, the photon number probability distribution was measured and compared with that of CL and TL, which satisfied the Poisson and Bose-Einstein distributions, respectively (notes S5 and S6 and fig. S6). Figure 3A shows the photon number probability distribution at different pump powers. As expected, the mean photon number and the photon emission probability increased intuitively with the increase in the pump power. SCL source exhibits a broader photon number probability distribution compared with CL and TL, revealing a substantial enhancement of multiphoton events. The unique photon number probability distribution of the SCL source, which follows a power-law distribution, can be expressed as $P\left(N\right)\propto N^{-k}$ (44). Thus, we performed a power-law fit on the photon number distribution in Fig. 3A. This distribution arises from the huge multiphoton events in the SCL source, which leads to a much higher multiphoton probability than that of CL (Poisson distribution) and TL (Bose-Einstein distribution) (fig. S7).

Fig. 3. Measurement of photon number probability distribution of the generated SCL source.

(A) Photon emission probability of 1550 nm under different pump powers with fixed attenuation. The triangle and circle symbols represent the simulated photon number probability distributions at $\langle n\rangle =1.3\times {10}^{-1}$ for TL and CL, respectively. The ratio of the multiphoton emission probabilities of SCL to CL (B) and TL (C) under different pump powers. (D) Photon emission probability for varying mean photon numbers per pulse $\langle n\rangle$ at the same pump power. The triangle and circle symbols represent the simulated photon number probability distributions at $\langle n\rangle =2.8\times {10}^{-4}$ for TL and CL, respectively. The ratio of the multiphoton emission probabilities of SCL to CL (E) and TL (F) under the same pump power and different $\langle n\rangle$ values.

To quantify the deviation of the multiphoton emission probability, we define the ratio ${\mathrm{\xi }}_{\text{SCL}/\text{ML}}$ as

$${\mathrm{\xi }}_{\text{SCL}/\mathrm{M}L}=\frac{P_{\text{SCL}}\left(N\right)}{P_{\text{ML}}\left(N\right)}$$ (3)

where $P_{\text{SCL}}\left(N\right)$ and $P_{\text{ML}}\left(N\right)$ represent the N-photon bundled emission probabilities of SCL and other light [CL as $P_{\mathrm{CL}}\left(N\right)$ and TL as $P_{\mathrm{TL}}\left(N\right)$], respectively. For instance, at the pump powers of 230, 260, and 290 mW (corresponding to $\langle n\rangle =1.1\times {10}^{-2},4.4\times {10}^{-2}, \text{and} 1.3\times {10}^{-1}$), the multiphoton emission probabilities are all dramatically enhanced relative to those of CL and TL. In particular, the emission probabilities for 16 photons increased by 36, 29, and 23 orders of magnitude relative to CL (Fig. 3B) and by 23, 16, and 10 orders of magnitude relative to TL (Fig. 3C), respectively. In other words, the lower pump powers the smaller mean photon numbers and the greater the enhancement of multiphoton events. These results demonstrate a large number of extreme multiphoton events, which substantially deviate from both the Poisson distribution and the Bose-Einstein distribution. We also confirm that these enhancements can be further expanded by attenuating the mean photon number $\langle n\rangle$ while holding the pumping power. As shown in Fig. 3D, the pump power is maintained at 260 mW, and as the mean photon number drops to $\langle n\rangle =2.8\times {10}^{-4}$, the probability of detecting 16 photons reaches as high as 4.9 × 10⁻¹⁰, representing the enhancement of 60 and 47 orders of magnitude compared to CL and TL, respectively (Fig. 3, E and F). Therefore, as the mean photon number $\langle n\rangle$ decreases, single- and two-photon pulses (N ≤ 2) are annihilated, while the probability of multiphoton emission increases relatively. This result is intrinsically related to the increase of g⁽²⁾(0) with the decrease of $\langle n\rangle$, as shown in Fig. 2D. These supercorrelation properties and extreme multiphoton events offer an approach to noise-tolerant CCI under extremely weak light conditions, where weaker light intensity corresponds to higher photon correlation g⁽²⁾(0).

Noise-tolerant CCI based on the SCL

Note that the SCL source reaches its maximum g⁽²⁾(0) value at a pump power of 260 mW (Fig. 2C). Therefore, we performed noise-tolerant CCI under this pump power condition. The imaging scheme is shown in Fig. 4A. The SCL source is divided into two beams by the fiber beam splitter 1 (FBS1). One beam is stored locally as the reference light, which is free from external noise and connected to the superconducting nanowire single-photon detector (SNSPD), with its mean photon number adjustable via a variable optical attenuator (VOA). Another beam forms the detection path, being collimated by a collimator (COL) and then incident on a dual-axis galvanometer scanner (two-axis galvo) via a 45° perforating mirror (PERM) to scan the target object. The scattered photons from the target object are collected by the lens and coupled to the high-transmission port (99% port) of the FBS (FBS2). Environmental noise photons are injected through the low-transmission port (1% port) of the FBS2, where it is mixed with the detected signal photons and transmitted to the SNSPD. For comparison, we evaluated the results of PCI under the same noise conditions.

Fig. 4. Experiments of CCI and analysis.

(A) Schematic diagram of the imaging system. FBS, fiber beam splitter; VOA, variable optical attenuator; COL, collimator; PERM, 45° perforating mirror; two-axis galvo, dual-axis galvanometer scanner. (B to E) Reconstructed images of CCI at different R, ranging from 1 to 100,000. The color bar indicates the coincidence count (coin-counts) values. (F to I) Reconstructed images of PCI at different R, ranging from 1 to 100,000. The color bar indicates the photon count values. (J and K) The PSNR and CNR of CCI and PCI under different R. (L) The visibility (V) of average coincidence counts per pixel of CCI and average photon counts per pixel of PCI in object and background areas, respectively.

To evaluate the distinguishability of the target object, the reconstructed image obtained with high photon counts (under noise-free conditions) and long measurement time serves as the true (reference) image, as shown in fig. S8, compared this reference imaging with CCI and PCI under different noise conditions (R = 1, 100, 1000, and 100,000) to calculate PSNR and CNR. The calculation workflows for PSNR and CNR are shown in Materials and Methods. The color bars represent the coincidence counts and photon counts per pixel, respectively. Under noise-free conditions (i.e., R = 1), CCI achieves better imaging performance (PSNR = 28.32 dB, CNR = 8.02) than PCI (PSNR = 13.68 dB, CNR = 4.46), allowing for more distinct target identification. Even with R increasing by three orders of magnitude (from 1 to 1000), the target object and background regions can still be well distinguished for CCI (Fig. 4, B to D). For instance, at R = 1000, the system exhibits excellent robustness, with a PSNR of 24.91 dB and a CNR of 6.14. Until R = 100,000, there is partial blurring between the target object and the background area (Fig. 4E). During the gradual increase in noise photons, both PSNR and CNR showed a slow decline (Fig. 4, J and K). The noise tolerance limit is reached when the accidental coincidence counts from the background area become comparable to the coincidence counts of the object area. However, for PCI, as the R values increased, the signal photon of the target object was rapidly submerged in the background noise (Fig. 4, F to I), resulting in dramatic reductions in both PSNR and CNR (Fig. 4, J and K). Furthermore, as shown in Fig. 4 (J and K), CCI achieves PSNR and CNR values comparable to noise-free PCI even at extremely high R of 50,000 and 20,000 respectively. This result demonstrates the exceptional robustness of the SCL source, as its strong photon correlation properties enable high-quality CCI even in intense noise environments. Furthermore, we compared the noise tolerance of imaging systems based on our SCL source and conventional photon pairs. The SCL source exhibits noise tolerance that is three orders of magnitude greater than that of previously reported light sources (fig. S10) (20–23).

To elucidate the noise-tolerant mechanism of CCI over PCI, we performed an analysis by sampling 16 pixels from both object and background areas. For each area, we systematically evaluated the visibility ($V=\frac{\mid I_1-I_2\mid }{\mid I_1+I_2\mid }$) of average coincidence counts and photon counts per pixel at different R values (Fig. 4L). Here, I₁ represents the average coincidence counts per pixel or average photon counts per pixel of the object area, and I₂ represents the average coincidence counts per pixel or average photon counts per pixel of the background area. For PCI, when R exceeds 100, the PCI visibility drops below 0.1, demonstrating that signal photons are overwhelmed by noise photons. In contrast, the visibility of CCI is 0.99. Even when the R increases to 100,000, it remains 0.24. Thus, CCI achieves superior noise tolerance relative to PCI.

Moreover, we evaluated the image capability of the SCL source at different integration times per pixel (10, 20, 50, 100, 200, 300, 400, and 500 ms). We compared the minimum integration time per pixel required to resolve the object from the background between our method and the reported quantum imaging scheme (9, 22, 56–59). When the integration time per pixel of the SCL source is 20 ms, each pixel in the object and the background area of the reconstructed image can still be distinguished, which is an order of magnitude improvement over the current reports (fig. S11). This pronounced advantage establishes a promising framework for developing robust optical systems capable of maintaining a high signal-to-noise ratio in single-photon level imaging under extreme environments.

DISCUSSION

We demonstrate noise-tolerant CCI based on SCL sources, aiming to enhance noise tolerance in extreme environments by leveraging the unique properties of these light sources. The environmental noise is suppressed by detecting the coincidence counts of correlated photons with time correlation (60). Compared with PCI, coincidence count rate and noise resistance have been substantially improved because of its extremely high g⁽²⁾(0) value. These improvements can dramatically enhance the imaging quality in practical applications (61, 62). It offers a solution for single photon–level imaging in complex environments. Next, for tiny mean number of photons per pulse $\langle n\rangle$, the exceptionally high probability of N-photon emission by the SCL source enables us to image the target by statistically counting the coincidences between multiple channels even if the echo pulses are extremely weak. This characteristic may be helpful for quantum imaging in environments where the signal photons are dramatically attenuated but with intense background light and noise (63). Last, another advantage of the SCL source is its full fiberization, which can be integrated into subsequent work and offers stable environmental robustness. This advantage considerably reduces system complexity, making it highly valuable for further expanding the applications of SCL sources.

In summary, we have developed an SCL source and demonstrated its capability for high-contrast imaging under extreme noise conditions. By leveraging the nonlinear interaction between pulsed lasers and optimized PCF, SCL sources with powerful second-order correlation functions and extreme multiphoton events have been generated. The g⁽²⁾(0) is as high as 18,166, which is two orders of magnitude higher than the current optimal report. When the mean photon number is $\langle n\rangle =2.8\times {10}^{-4}$, the emission probability of 16 photons is increased by 60 and 47 orders of magnitude, respectively, compared with CL and TL. At the single-photon level, CCI based on strong photon correlation can resist random environmental noise exceeding 100,000 times, which is three orders of magnitude more robust than the most advanced nonclassical light source correlation imaging schemes. When the noise photons exceeded signal photons by 50,000 and 20,000-fold, respectively, the PSNR (13.68 dB) and CNR (4.46) of CCI reached the levels of PCI without external noise interference, indicating its excellent robustness. Each pixel of the reconstructed image is generated at the single-photon level, which enables the target to be identified even in extremely weak light environments. Moreover, by adjusting the pump power and filtering range, SCL source across the C + L band can be generated. This capability offers solutions for parallel single-photon light detection and ranging systems and quantum random number generation (64, 65), highlighting the versatility and potential of SCL source in advanced photonic technologies. Notably, when the biphoton coincidence counts reach the noise tolerance limit, the SCL source can leverage its inherent multiphoton emission probability to construct higher-order correlations, achieving superior noise resistance. Optical imaging systems based on SCL have opened up avenues for target recognition in extreme environments.

MATERIALS AND METHODS

Experimental design

The schematic diagram of the SCL-generating device is shown in fig. S2. The seed light is a mode-locked laser based on semiconductor saturable absorption mirror (SESAM, SAM-1064-21-3 ps, BATOP). The laser system comprises the following key components: a SESAM, a semiconductor laser (LD1, VLSS-976-B-600-FA, CONNET), a wavelength division multiplexer (WDM, MCWDM-9764-00-H1-10-L-FA, DK Photonics), a fiber Bragg grating (FBG, MCFBG-1064-300-H1-0.3-10-FA, DK Photonics), a fiber isolator (ISO, MCI-1064-00-P-S-H1-10-N-FA, DK photonics), and a 0.6-m-long single-mode ytterbium-doped fiber (YDF, Yb/1200, LIEKKI) as the gain medium. The LD1 has a central wavelength of 976 nm and a maximum output power of 600 mW. The SESAM exhibits a modulation depth of 14% and a reflectance of 78% at 1064 nm. The FBG has a reflectance of 10% at 1064 nm and a spectral bandwidth of 0.3 nm. The ISO1 features an isolation bandwidth of ±5 nm and an isolation ratio of 30 dB. When the pumping power of LD1 reaches 120 mW, the seed laser achieves mode-locking, with an output center wavelength of 1064 nm, a pulse width of approximately 100 ps, a repetition rate of 24.35 MHz, and an average power of 35 mW. Then, the power of the pulsed laser is amplified. It consists of a semiconductor laser (LD2, VLSM-976-B-5, CONNET) with a maximum output power of 5 W, a fiber combiner (MCMPL-976/20-105/125/22/H1-1064/10-10/125D-08-2, DK Photonics), a 3-m-long double-clad YDF (LMA-YDF-10/125, Nufern), and fiber isolators (ISO2, MCHI-1064-30-P-50-S-10/125 DC-10-B-N, DK Photonics), all of which combine to form a pulsed laser with an average power of 1 W. The output pigtail of the pulsed laser is coupled to a mode field adapter (MCMFA-1064-B-20-10/125 DC-H1-08-P2, DK Photonics) to convert the mode field area and then fused with the PCF (SC-PRO, YSL Photonics). The output light is collimated by an optical COL (MCCOL-1550-50-2-10-S2-08-L-S, DK Photonics) and then passed sequentially through an acousto-optic tunable filter (AOTF-PRO2, YSL Photonics) and neutral density filters (Att, COFV2-40M, JCOPTIX). The filtered signal is subsequently coupled into a dense WDM (MCDWDM-1-C34-00-S2-08-L-FA, DK Photonics) operating at a center wavelength of 1550 nm with a channel bandwidth of 0.8 nm. The spectrum is measured using a fiber optic spectrometer (AQ6370, Yokogawa). The FBS (MCFBT-12-1550-50-00-16-S2-08-L-FA, DK Photonics) evenly splits the light and is connected to a 16-channel superconducting nanowire SNSPD (P-SPD-16S, PHOTEC). The detected signal is recorded and processed using time-correlated single-photon counting (TCSPC, MT16, SIMINICS). On the basis of the recorded photon time series, photons detected by the same pulse at the same time are counted as coincidence counts. In contrast, photons detected by adjacent pulses are counted as accidental coincidence counts. The multichannel photon count rates and coincidence count rates obtained from the measurements are used to calculate the photon number probability distribution and the second-order correlation function g⁽²⁾(0).

Detection of the photon number probability distribution

In this experiment, each photon is detected by the SNSPD, and the arrival time of the photons is recorded via TCSPC. The multibody coincidence function in TCSPC enables the measurement of simultaneous multiphoton events detected within a defined time window. First, the photon arrival times of all SNSPD channels were aligned by TCSPC, and then all the detected multiphoton events were classified and counted. In this work, the repetition frequency of 24.35 MHz corresponds to a time window of 41.06 ns.

Noise-tolerant CCI based on an SCL

Noise-noise CCI is performed at a pump power of 260 mW, resulting in a relatively high second-order correlation function, g⁽²⁾(0). The reference path and the detection path are separated by FBS1 (MCFBT-12-1550-50-00-2-S2-08-L-FA, DK Photonics). A 45° PERM and two-axis galvo (GVS012/M, Thorlabs) are used to transmit signal light and scan target objects. The signal photons and noise photons are mixed by FBS2 (MCFBT-12-1550-01-00-2-S2-08-L-FA, DK Photonics) and transmitted to SNSPD. A white light-emitting diode (LED, M1550L4, Thorlabs) powered by an LED driver (DC2200, Thorlabs) was used to generate random noise photons during imaging. The number of noise photons can be adjusted via a VOA (MCVOA-1550-00-S2-10-L-FA, DK Photonics). To achieve higher image quality, the measurement time for each pixel is 500 ms.

PSNR and CNR

PSNR and CNR are used to quantify the imaging results. It can be described as

$$\mathit{\text{PSNR}}=10{\text{log}}_{10}\left[\frac{{\left({\mathit{\text{MAX}}}_{\text{pixel}}\right)}^2}{MSE}\right]$$ (4)

where MAX_pixel is the maximum pixel value, and MSE is the mean square error.

$$\mathit{CNR}=\frac{\mid {\mathrm{\mu }}_{\mathrm{o}}-{\mathrm{\mu }}_{\mathrm{b}}\mid }{\sqrt{{\mathrm{\sigma }}_{\mathrm{o}}^2+{\mathrm{\sigma }}_{\mathrm{b}}^2}}$$ (5)

where ${\mathrm{\mu }}_{\mathrm{o}}$ and ${\mathrm{\mu }}_{\mathrm{b}}$ represent the mean values of the pixel values of the object area and the background area, respectively. For PCI imaging, it is the photon count value; For CCI imaging, it is in accordance with the count value. ${\mathrm{\sigma }}_{\mathrm{o}}$and ${\mathrm{\sigma }}_b$ represent the standard deviations of the pixel values of the object area and the background area, respectively.

Supplementary Materials

This PDF file includes:

Notes S1 to S6

Figs. S1 to S11