Complex pattern transmission through multimode fiber under diverse light sources

When the light field passes through a strong scattering medium, speckled fields are generally formed at the output surface due to the randomness and anisotropy of the medium that perturbates light in an irregular manner. Researchers have been fighting against this phenomenon since the 1960s, trying to find the propagation law of signal light in the scattering medium.¹ Surprisingly, it was found that imaging through the scattering medium may improve the resolution of the system and reduce the noise.^2,3 Optical fiber, as one of the most important media for modern information delivery, is an exemplary scattering medium. Endeavors have been made to transmit two-dimensional image information directly through fibers, which can greatly improve the throughput.

In 1967, Spitz and Wertz⁴ first proposed a method to transmit images through multimode fibers (MMFs). They utilized phase conjugation to eliminate the image distortion caused by mode dispersion. In recent years, various methods for MMF image transmission have been proposed, such as digital phase conjugation,⁵ transmission matrix (TM),⁶ iterative optimization,⁷ and emerging artificial neural networks.^8,9 Owing to the small size and the capability to simultaneously transmit thousands of modes, MMFs possess the potential to revolutionize traditional cohesive multi-core fiber bundles and to be used to create ultrathin micro-endoscopes.^10,11 Moreover, MMFs can be applied for remote video transmission,¹² encrypted communication,¹³ high-speed detection,¹⁴ and other emerging applications that require fiber image transmission technology as well.

Despite that image transmission via MMFs has a bright development prospect, the system is extremely sensitive during operation.¹⁵ It not only requires stringent management on external perturbation and environmental changes but also demands on its light source stability. In typical applications, light from the source first illuminates the object, then the reflected light carrying the image information is coupled into the fiber for transmission. Therefore, just like diverse imaging¹⁶ and lighting systems, the sources, which play the role of illumination and information carrier in single fiber image transmission systems, are also very vital.

Most of the multimode fiber image transmission techniques are based on speckle fields for image reconstruction. The distribution and contrast of the speckles are closely related to the coherence of the light source. With excellent monochromaticity and high coherence, narrow linewidth lasers (NLL) excel in coherent communication and optical sensing.^17,18 In contrast, amplified spontaneous emission (ASE) sources with low spatial coherence, low temporal coherence, and high power per mode are used for full-field speckle-free imaging.¹⁹ Random lasers have been proven to be a suitable candidate for imaging systems in recent years.²⁰ Due to its random feedback mechanism,²¹ a large number of uneven and highly irregular spatial modes are emitted with uncorrelated phases. Therefore, high spectral density, high output power, and low spatial coherence are simultaneously available. Moreover, random fiber lasers (RFLs) exhibit high stability^22,23 and low noise,^24,25 which makes them suitable for optical communication and sensing. In view of the above outstanding features, the performance of RFL in a single fiber image transmission system is worthy of expectation.

Here, we experimentally demonstrate a single-arm MMF image transmission system and efficiently recover the images by optimizing the inverse transmission matrix (ITM). Different kinds of complex patterns are successfully reconstructed. RFL has been applied to the system for the first time and compared with NLL and ASE. A laser with a common resonant cavity and a narrow-band filtered ASE source are used as the control group. The experimental results show that the system with the RFL and the NLL led to an excellent performance. In addition, light source characteristics affecting the transmission quality are also systematically investigated in terms of spectra, illumination field, output field, and time–domain stability. The light sources with both narrow linewidth and high stability are most suitable for MMF image transmission. The data are also trained using neural networks for comparison, and the results show good consistency. This indicates that our findings are applicative under different transmission methods and similar two-dimensional optical field transmission systems.

The experimental setup and operation principle are illustrated as Fig. 1. The light source illuminates the digital micromirror array device (DMD) through an isolator and a collimator. The training and testing patterns are loaded onto the DMD. The diffracted light from the DMD passes through an objective, which images the patterns on the input facet of a 1.5 m-long MMF (Nufern, MM-S400/440-22A). After the input light field is distorted by MMF, a speckle field is formed by superimposition of modes on the output facet. It is imaged by another objective to an industrial camera. The speckles are recovered to the original images by an optimized approximate ITM or trained neural networks.

We experimentally compare the performance of five kinds of fiber light sources in the system: a broadband ASE fiber source (BASE), an ASE fiber source with narrow linewidth (NASE), a common fiber laser with FBG-based cavity (CFL), a tunable NLL, and an RFL. The specific characteristics and parameters of these lasers are shown in the Results section. Control experiments are designed by changing the light sources while keeping the back-end part fixed. The information of devices and experimental details are presented in the supplementary material.

There exist several methods of single-fiber image transmission currently as mentioned above. Structurally, the conventional dual-arm interferometric measurement method⁶ requires a reference optical path beyond the MMF. The reference light is coherently superimposed with the signal light to obtain the phase information. The interferometric results are inevitably related to the polarization state, stability, and coherence length of the light source, making the relationship between the system performance and the source more complicated.

Therefore, we adopt a simple interference-free structure. It can reconstruct images by only acquiring the amplitude distribution of the output fields to optimize the ITM. This single-arm structure is more conducive to analyzing the impact of source characteristics on the system. The reflective structure is closer to practical application scenarios.

Whether solving the TM in the frequency domain or in the spatial domain, it is necessary to obtain the set of different input responses. The TM can be viewed as a Green’s function that satisfies between an origin array and a response array.²⁶ Specifically, the optical path between the input images and the captured speckles (i.e., from the DMD surface to the sensing surface of the camera in Fig. 1) is viewed as an overall transmission system. The inverse transmission matrix of this system is optimized iteratively so that the product of the output speckle and the ITM can gradually approximates the target image.

We optimize the inverse transmission matrix model²⁷ to achieve better results with shorter run time. Apart from parameter adjustment, we modify the loss function and optimizer. The cosine similarity between the real input image and reconstructed image is used as the loss function L,

where Y_Ri and Y_i are the elements in the reconstructed vector and the real vector, respectively.

The difference between the output value and the true value is fed back to the ITM. We compute the derivatives of the loss function L with respect to the elements of the ITM using adaptive moment estimation (Adam) as the optimizer. It is an extension of the classical stochastic gradient descent (SGD) method and can update the network weights more efficiently. The ITM is optimized iteratively with a specific step size and the loss function converges to a minimum value. The step size of the optimization (i.e., learning rate) also varies adaptively using the loss function as a monitor to enable faster convergence. In our experiment, the acquisition time of training set is 1 h 15 min, the training time is 54 min 35 s, and the average single-step training time is about 31 s.

The ITM after each epoch of optimization is judged by the peak signal-to-noise ratio (PSNR). The PSNR after each epoch is compared with the previous one. The model of this checkpoint is saved if the PSNR increases. The PSNR tends to be stable after several iterations. The ITM method based on dataset training used in this paper is intermediate between the traditional solution of the real TM and the deep learning neural networks with absolutely no assumption for the system. Compared to solving the complete TM, it omits the reference optical path and eliminates the need to collect phase information; and compared to traditional deep learning methods, in this particular physical circumstance, it restrict the function describing the system to the form of a TM, making the network concrete. This results in simple, efficient, and high-quality image transmission.

There are still some limitations of this method for image reconstruction, such as the large amount of training data in the early stage, and the difficulty in recovering three-dimensional information of the input light field. We need to retrain after changing the light source. It is important to ensure the stability and alignment of the fiber system. Deformation of optical fiber will interfere with the comparison between sources. We should try to avoid it, although detection with different bend radii can be achieved by joint learning.²⁸ In addition, in order to evaluate the impact of the image demodulation method on the comparison of light sources, we also apply the neural network approach to training the same database as a benchmark. The processing results of the classical U-net type network verify the experimental conclusions similarly. The specific network structure is shown in Fig. S5, and parameter settings are described in the supplementary material.

Figure 2 shows the structure of the RFL used in this paper. To achieve a stable temporal output from the RFL oscillator, the RFL needs to operate well above the lasing threshold.²⁹ However, too high output power is unsuitable for illumination and image transmission system. Therefore, the RFL adopts a half-open-cavity structure with a 30 km passive fiber (CDSEI, SM-G652D) to decrease the lasing threshold.³⁰ We premeasured the threshold power of the random laser before the experiment to ensure that the RFL operates at a steady state. Specific experimental details are provided in the supplementary material. Random distributed Rayleigh scattering of the 30 km passive fiber and the point-action reflection of the high-reflectivity fiber Bragg grating (HR-FBG, with 0.21 nm bandwidth, core/cladding diameters are 10/125 µm) forms the half-open resonator. An LD (DILAS, 975.6 nm, 25 W, core/cladding diameters are 105/125 µm) serves as the pump source and the pump light is injected into the ytterbium-doped fiber (Nufern, LMA-YDF-10/130-VIII) through a (2 + 1) × 1 combiner. The gain of the ytterbium ions excites a 1064 nm random laser. To reduce feedback, an isolator is inserted before the output and the other pigtail of the HR-FBG is angle cleaved. The output power of the RFL is about 0.8 mW, which is the same as other light sources to ensure the same illumination condition. The structures of the other four sources are shown in Figs. S1–S4 of the supplementary material.

The results recovered by the optimized ITM are shown in Fig. 3. The structural similarity (SSIM), which is a function characterizing the similarity of two images, is used as an evaluation indicator for the quality of image reconstruction.

The RFL and the NLL have the highest transmission quality among light sources, reaching over 0.65. In contrast, the BASE sources can only identify some relative position information for black and white. Images restored by the CFL and the NASE still have some visible blurring, distortion, and noise, whereas the RFL and the NLL perform much better in these aspects. None of the natural scenes shown in Fig. 3 appear in the training set or validation set, so they are completely new to the system. We also selected handwritten digits from the MNIST dataset,³¹ handwritten letters from EMNIST,³² and some simple geometric patterns. These images, whose types are different from the training patterns, also achieve high-quality recovery. More recovery results for the RFL are shown in Fig. S6 of the supplementary material. Some reconstruction is also achieved using a neural network, and the different light source rankings are the same as the above results, which are shown in Fig. S7 of the supplementary material.

Figure 4 shows the resolution limit test for the transmission system with different light sources. We adopt 1951 USAF and stripe patterns with different spatial frequencies. Figure 4(a) shows the 1951 USAF pattern with 19.16 and 21.5 lines/mm, and the recovered results under the 5 sources. In order to more completely measure the image transmission capability and resolution limits of the systems with different light sources, and also to improve the reliability of the experimental data, we test the parallel stripe resolution patterns with frequencies from 8 to 48 lines/mm. We quantitatively assess the identifiability of the stripes using the contrast-to-noise ratio (CNR) as an evaluation indicator,

where $If$ denotes the average intensity of the feature region of interest (e.g., the bar region in the 1951 USAF pattern). $Ib$ denotes the average intensity of the surrounding background. σ_f and σ_b are the standard deviations of the intensity in the two regions, respectively. CNR describes the discrimination of stripe patterns against a given background.³³ The CNR value close to 1 means that the intensity difference is comparable to the intensity fluctuation and the stripes cannot be distinguished.²⁰ 

Figure 4(b) shows the relationship between the CNR of the recovered stripe pattern and the spatial frequency. In our experiments, we tested the CNRs of both horizontal and vertical stripes at the same spatial frequency and took the average of them. Although the CNR under all light sources decreases as the frequency of the stripes increases, the RFL continues to exhibit the highest CNR among all light sources at the same spatial frequency. The CNRs of stripe patterns with different spatial frequencies recovered by the BASE are basically below 1, indicating that they are indistinguishable. The resolution limits of the CFL and the NASE are about 32 lines/mm, while those of the RFL and the NLL are about 38 lines/mm.

The comparison suggests that the RFL and the NLL are more suitable for single MMF transmission, while they are completely different types of lasers. The BASE source also has good operation stability but can hardly be used for ITM-based single-fiber transmission. In contrast, the image transmission quality of the NASE is substantially improved. Therefore, it is not rigorous to directly judge the performance of different types of light sources in the system. In the following, we analyze the factors affecting the transmission quality from the coherence, the output speckle field and the time–domain stability.

For multimode fibers, different phase delays are experienced at the output face of the fiber because the different transmission modes have different phase velocities. The light at any point on the receiving facet of the multimode fiber consists of these modes superimposed together. When the phase delay varies by more than 2π and these light fields are sufficiently coherent, a significant interference phenomenon occurs in the light intensity distribution at the output end of the fiber. Theoretically, different modes within the coherence length of the incident light are involved in the interference. Therefore, the coherence of the incident light is closely related to the formation of the speckle field and can directly affect the quality of image reconstruction.

The speckle contrast C = σ_I/⟨I⟩ (where σ_I is the standard deviation of the intensity, and ⟨I⟩ is the average intensity) is a common index for quantitative measurement of the speckle field. Its expression in the cylindrical coordinate system (r, φ, z) can be written as follows:³⁴ 

where $Ir,φ,z$ and p is a simplified representation of the specific LP_mn mode with modal index pairs (m,n); α_p and E_p(r, φ) are the modal amplitude excitation coefficient and the spatial configuration of mode p, respectively. (τ_p − τ_q) is the group delay time difference between mode p and mode q. γ(t) is the complex degree of temporal coherence of the source field.

The physical meaning of the complex degree of temporal coherence γ(t) in Eq. (3) can be described as the longitudinal coherence properties of a source. The coherence time t_c of the source is defined by the following equation:

From the above analysis, the speckle contrast is closely related to the longitudinal correlation of the light sources. In the training model, the contrast of the output speckle field directly affects the quality of multimode fiber image transmission. In the following, we analyze the coherence of different light sources in terms of spectral characteristics and illumination speckle field.

Figure 5(a) shows the spectra of different light sources. The BASE and the NASE operate at the band around 1030 nm, the NLL at 1060 nm, and the CFL and the RFL at 1064 nm. Even the longest 1064 nm laser has more than 30 000 modes in the MMF used for the experiments. This is much larger than the information load (∼2304) required to transmit an image with 4848 pixels. Therefore, the effect of wavelength on the transmission quality can be neglected in this experiment. Figure 5(b) plots the spectral detail information of the four sources except for the broad-spectrum BASE source. We integrate the detailed figures located in the two different intervals in order to visually compare the line widths of the spectra. It can be seen that the NLL has the narrowest and smoothest spectral lines. The NASE and the CFL have a multi-peak structure, which increases the linewidth and is usually as a sign of low stability.

Since BASE and NASE have the same operation mechanism and similar characteristics, the biggest difference is that the spectrum of NASE is narrowed after filtering. Therefore, the linewidth of the light source is an important factor affecting the quality of MMF image transmission. From the results, the narrower the line width, the better the results. The TM, which characterizes the image transmitting, essentially describes the evolution of the different modes. It can be interpreted in terms of transmission invariant mode theory.³⁵ However, the propagation law of transverse modes varies for different frequencies of light. Thus, a laser with a narrow spectrum is more suitable for characterizing the transfer function of the system with a single complex matrix. The output fields obtained from broad-spectrum sources (such as BASE) can be considered as the superposition of the output fields after the action of the corresponding transmission matrix at different frequencies,

where $Iνi$ is intensity data of a certain frequency of light in a broad-spectrum source. Different frequencies of light correspond to different transmission matrices,

where $Xνi$ is amplitude data of the certain frequency of light. $Tνi$ represents the transmission matrix of the system for the certain frequency optical field. Y_R is the vector of recovered image. These transmission matrices cannot be combined for the same distribution of output images,

For the optimized inverse transmission matrix method, it is impossible to find an inverse transmission matrix that is suitable for all images and optical frequencies. Therefore, the image information cannot be recovered using the BASE.

However, the neural network approach is different. It takes the input–output relationship out of the physical framework described by the transmission matrix. The BASE source can also recover certain information by the U-net (see Fig. S7 of supplementary material).

The light source in a single fiber transmission system plays two main roles: one is as a carrier for image information transmission and the other is as an illumination. Therefore, it is necessary to consider the effect of the illumination fields of different sources on the image transmission.

Figure 6 shows the intensity distributions of the illumination fields and their spatial frequency spectra after the two-dimensional Fourier transform. It can be seen that the BASE source has the evenest illumination field. The spatial frequency spectrogram also shows that the major energy of the BASE source is at the low-frequency area. It is followed by the RFL, while the NASE has contained a distinct high-frequency circular region, and the CFL and the NLL even show intensity distributions at the four high-frequency corners. The uniformity of the illumination field is mainly determined by the coherence of the light source. For the same type of light sources, the narrower the line width, the stronger the coherence. Therefore, the BASE has a more uniform illumination field compared to the NASE; and the CFL compared to the NLL. The ASE and the RFL, which do not have a specific phase, are less coherent due to the special operating mechanisms of spontaneous emission and random feedback, respectively. From the results described above, the images recovered with the NLL, the CFL, and the NASE have noticeable noises. On the one hand, this is due to the deviation of the optimized ITM from the real TM of the system. On the other hand, it is partly due to the additional noises introduced by the speckle illumination fields before the transmission. The signals in the destructive interference region are attenuated, so it will have an unimprovable impact on the image transmission. However, the scattered distribution of the illumination field is relatively fixed during the image transmission process, after the optimization by deep learning, the ITM, as well as the neural network, has basically removed most of the noises introduced in advance by the speckle illumination field. Table I shows the characteristics (especially the coherence) of the different light sources. In order to remove the influence of the black background around the image on the C value, we take a square area with the same size at the center of the illumination fields for the calculation.

The coherence length and the scattering contrast show similar results for the description of the longitudinal coherence of the light sources, and the NLL and the CFL light sources exhibit strong coherence. Among them, the NLL has the strongest longitudinal coherence due to its narrow linewidth, while the NASE and the RFL show weaker coherence. This is partly due to their random luminescence mechanism and the relatively wide spectrum. The BASE source shows the weakest longitudinal coherence.

The transverse modes excited by the signal light carrying the image information also superimpose speckle fields on the output facet of the MMF. Figure 7 shows the intensity distributions and spatial frequency spectra of the output speckle fields. In order to exclude the effect of the transmission pattern on the output field, the fields shown here are results by transmitting the same pattern. The 8-bit grayscale Lena is chosen for the transmitted image because it contains both low-frequency components and high-frequency information. As shown in Fig. 7, except for the output field of the BASE, which is similar to the distribution of the low-order transverse mode, the other four sources show a clear speckled distribution.

Figure 8(a) gives the speckle contrast of the illumination fields and output fields. For the illumination fields, the C value is essentially negatively related to the linewidth of the light source. In terms of illumination, the output fields of light sources are usually speckle fields. Therefore, random light sources and BASE sources with small C values have an advantage. They introduce less additional noise. On the other hand, the signal light as the carrier needs a large C value to increase the information carrying capacity. The speckling of the output field forming by the NLL is most pronounced. We also compared the differentiation between different output fields obtained from different input images. We randomly selected 100 output field images from 20 000 sets of data acquired with the same light source, evaluated the similarity (SSIM and PSNR) between them and the remaining images in turn, and took the average value. The above operation is performed for the data of all 5 light sources. The scatter-plot and box-plot in Fig. 8(b) show the results of these 100 datasets. It represents the degree of difference in the overall output field dataset. A lower similarity (SSIM and PSNR) indicates a higher degree of data discrepancy. Generally higher discrepancy indicates the better training of the ITM and building neural networks. Most of the SSIM and PSNR values of the different speckle fields obtained by the BASE source are distributed at high positions, indicating that varying different input images, the output images are very similar with little effective information. For SSIM, the NLL has the lowest similarity and, therefore, the highest discrepancy of output fields. The BASE, the NASE and the CFL are all above 0.5, while the NLL and the RFL lie below 0.5.

In addition to the above-mentioned factors, the stability of the light source determines the performance of the image transmission system. The time–domain stability of the light source in the fiber imaging system not only refers to the stability of the output power but also the wavelength, the phase, and the intensity distribution of the output field. This is because these characteristics all affect the evolution law of transmission modes. Figure 9 shows the time stability curves of different light sources. We acquire the output fields of the same input image (also the grayscale Lena) continuously while keeping the system fixed. One output field of the MMF is collected every 1 s for a total of 75 min. This is also the acquisition time for the 20 000-group training database in order to ensure that the results can reflect the reliability of the data used for solving the ITM. After that, the similarity [SSIM, mean square error (MSE), PSNR] between the first image acquired at the beginning and each subsequent image is solved to represent the change of the system. If SSIM and PSNR keep high values and MSE keeps low values in the time range with no significant fluctuations, it indicates that the system has good time–domain stability.

As can be seen from Fig. 9, the BASE has the best time–domain stability, with the SSIMs of Lena image acquired at different times reaching above 0.95. It has the lowest coherence and the output field is homogenized by long time detection. It is followed by the RFL, and the SSIM changing curve has a parabolic-like downward trend but decreases slowly. The similarity of most data can maintain above 0.9, while the curve is smooth without obvious fluctuation. The remaining three light sources (NASE, CFL, and NLL) have large fluctuations during the acquisition time. Among them, the NASE has high-frequency fluctuations in every short period of time, and the overall curve has an oscillating downward trend. It could be due to the filter will be affected by the external environment and the variation of the ytterbium gain at different wavelengths. The overall curve of the CFL fluctuates and decreases at a faster rate, which has fallen below 0.6 at the end of the acquisition time period. The CFL uses two fiber gratings to form a resonant cavity with fixed length, which will induce self-pulsing effect and degenerate the temporal stability. Although the NLL has more than half of the SSIMs exceeding 0.9. It is also affected by bandpass filters and self-pulsing effect. So, it is still less stable compared to the BASE and the RFL. The time-varying curves of MSE and PSNR show consistent conclusions.

As can be seen from the above-mentioned analysis, the spectrum and illumination field characteristics of the light source, as well as the output field and comprehensive time–domain stability all have an impact on the quality of image transmission. And these factors are not independent of each other, but have cause-and-effect or mutual constraint relationships. For instance, the narrower the linewidth of the light source, the more suitable the transmission system is for a single TM description. In addition, the stronger the coherence, the higher the speckle contrast of the fiber output field. The speckling will bring discrepancy for different transmission images, which facilitates the training of ITM and neural networks. However, on the other hand, the narrow linewidth also makes the speckle contrast of the illumination field high, and the uneven illumination field will introduce additional noise before the signal light enters the fiber, which is we do not want.

On the whole, with a stable speckle illumination field, the additional noise can basically be removed by the optimized ITM or be “recognized” by the trained neural network. Therefore, we can conclude that a light source with narrow linewidth and high time–domain stability is the most suitable for single MMF image transmission.

Due to the traditional laser mechanism, the cavity length and mode selection are vulnerable to the disturbance of the external environment. Additional methods are needed to further improve the stability of them. The random fiber laser, on the other hand, works with high stability under the effect of homogenization due to the distributed random feedback. It is not as coherent as other lasers because the phase is not fixed, which can alleviate the illumination field speckling caused by narrow linewidth. Moreover, the linewidth of the laser can be further reduced by using a HR-FBG with narrower bandwidth or dispersion-engineered subwavelength meta-structures.^36,37 Further research is needed to establish if the superiority of RFL and NLL holds valid in the general case, and which is its extent. In addition, the conclusions obtained in this work are not only applicable to the present experimental system but also to other similar scenarios. Therefore, it can serve as an instructive guidance for applications such as ultrathin endoscopy, remote high-speed video transmission, and fiber encrypted communication.

In summary, we have experimentally demonstrated a single-arm MMF image transmission system and comprehensively analyzed the results of five different light sources. Original complex images are well recovered based on the optimized ITM. In terms of the reconstruction quality and resolution, random laser slightly outperforms other sources. The average SSIM between the recovered and the original image exceeds 0.65. The coherence of the light source (spectrum, illumination field), the speckle contrast and discrepancy of the output field, and the comprehensive time–domain stability of the system are systematically analyzed and quantitatively compared. The experimental results show that light sources with both narrow linewidth and high time–domain stability are preferred. In order to improve the reliability and generalizability of the results, the same data were benchmarked using conventional neural network for comparison.

See the supplementary material for additional information.

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 62122040, 62075113, and 61875103.

The authors have no conflicts to disclose.

Lele Wang: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Tiancheng Qi: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Methodology (supporting); Writing – original draft (supporting); Writing – review & editing (lead). Zhoutian Liu: Conceptualization (equal); Investigation (lead); Methodology (lead); Validation (equal); Writing – review & editing (equal). Yuan Meng: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (supporting). Dan Li: Funding acquisition (equal); Project administration (equal); Resources (equal). Ping Yan: Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead). Mali Gong: Conceptualization (equal); Funding acquisition (lead); Project administration (lead); Resources (lead). Qirong Xiao: Conceptualization (equal); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – original draft (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.