Coherent detection lidar, a pivotal optical sensing technology, is widely used in various fields, including meteorological forecasting, wind energy generation, and other fields. However, the performance of coherent-detection lidar is significantly affected by atmospheric turbulence in practical applications. Turbulence induces random variations in the optical path, resulting in wavefront distortion that adversely affects the quality of the received beam. Wavefront distortion correction, achieved through adaptive optics technology, has been proved to be an effective solution. The core of this method involves the use of optimization algorithms to control a deformable mirror, generating a phase that is conjugate to the wavefront distortion, thereby compensating for wavefront aberrations. The stochastic parallel-gradient descent (SPGD) algorithm is widely used for this purpose. However, because of the introduction of random perturbations, it exhibits a slow convergence speed. The particle swarm optimization (PSO) algorithm, proposed by Kennedy and Eberhart, is favored owing to its rapid convergence, simplicity, independence from derivative information, and parallel computation capabilities. However, both algorithms are susceptible to becoming trapped in local optima, particularly when addressing large and complex problem spaces. To address this challenge, we propose an improved PSO algorithm for distortion spot correction.

The improved PSO algorithm introduces the Metropolis criterion to probabilistically accept solutions with relatively low performance, which aids in escaping local optima, thereby achieving a higher convergence limit. The application of this algorithm to wavefront distortion correction further enhances the correction capabilities. First, we simulated the laser transmission through atmospheric turbulence based on the multi-phase screen propagation principle, resulting in the generation of distorted spots. Subsequently, we optimized the inertial parameters in both the PSO and improved PSO algorithms as well as the gain coefficients and perturbation amplitudes in the SPGD algorithm. This is because different parameter values can significantly influence the optimization performance. Hence, these parameters were adjusted to ensure that the algorithms operated at their peak efficiencies. Finally, we conducted a comprehensive comparative analysis of the correction results achieved by the SPGD, PSO, and improved PSO algorithms under medium and strong turbulence conditions, using the Strehl ratio (SR) as the evaluation function.

The improved PSO algorithm exhibited remarkable insensitivity to the inertial parameters (Fig. 9), indicating its superior robustness. All three algorithms were employed to correct the distorted spots under medium and strong turbulence conditions (Figs. 10 and 11). Based on the correction results, the convergence speed and limit were analyzed. Table 2 lists the convergence iterations and the time required by each of the three algorithms to achieve convergence. Under similar conditions, SPGD converges the slowest, followed by PSO, and the improved PSO converges the fastest. The reason for this discrepancy is the pronounced stochasticity of the SPGD algorithm during the optimization process, resulting in a longer convergence time. Additionally, the improved PSO algorithm concentrated the energy of the corrected distorted spot and achieved a higher SR because it increased the probability of accepting bad solutions (Fig. 12). Under strong turbulence conditions, the SPGD, PSO, and improved PSO algorithms contributed to SR improvements of 1.2, 2.6, and 3.2 times, respectively. Strong turbulence can result in severe spot distortion. When local optima are present during optimization, the advantages of the improved PSO algorithm become particularly prominent, enabling it to attain a higher convergence limit. This is advantageous for enhancing the system coupling efficiency, thereby effectively improving the performance of coherent detection lidar.

Coherent detection lidar is affected by atmospheric turbulence. Turbulence results in spot distortion, which reduces the detection performance. AO technology is an effective method for mitigating this distortion, and the selection of an intelligent optimization algorithm is crucial in this process. The SPGD algorithm exhibits parallel processing capabilities; its incorporation of random voltage perturbations results in slow convergence, whereas the PSO algorithm not only offers parallel processing and simplicity but also achieves rapid convergence without the need for derivative information. Nonetheless, both algorithms easily fall into the local optima. To address this problem, this study proposes an improved PSO algorithm that introduces the Metropolis criterion to escape local optima and reach a higher convergence limit. This algorithm is insensitive to the inertial parameters and exhibits better robustness. In comparison with the SPGD and PSO algorithms, the improved PSO algorithm enhances the convergence speed and convergence limit. In summary, the improved PSO algorithm demonstrates a more advantageous capacity for improving the performance of coherent detection lidar, particularly for strong turbulence.

Optical synthetic aperture is an effective technical approach for developing large aperture telescopes. The key to achieving diffraction limit for the actual resolution of synthetic aperture based opto-electronic telescopes lies in the real-time sensing and correction of piston error between sub-apertures. Among the traditional methods, the specific optics-based methods measure piston errors from the pupil information modulated by specially designed hardware, which inevitably increases the system complexity. The image-based methods can measure piston errors directly from the intensity image, which simplifies the system. However, it does need a large amount of iterative optimization calculation, thus failing to realize instant correction. Recently, deep learning method has contributed to many areas with piston sensing included, which is capable of achieving end-to-end piston sensing by fitting the mapping relationship between piston error and intensity image. Although many efforts have been made to improve the piston sensing performance of the deep learning model, most of the studies still stay in the simulation stage. In the few experimental studies, only piston sensing is implemented while co-phasing closed-loop correction has never been worked out. In the present study, we establish an optical synthetic aperture imaging experimental platform and implement co-phasing closed-loop experiment using deep learning approach. We hope that our research could be helpful for promoting the practical process of deep learning based co-phasing technology.

Real-time closed-loop piston error correction is achieved for two-aperture system and three-aperture system, respectively. First, the experimental platform is built, where broadband light is utilized to remove 2π ambiguity and sequence piston errors are loaded to the sub-apertures to generate corresponding training images. Then, a lightweight MobileNet convolutional neural network (CNN) is established to learn the nonlinear mapping relationship between broadband point spread function (PSF) and piston error. By converting standard convolution module into depthwise separable convolution module, MobileNet effectively reduces model parameters and computational complexity while ensuring the overall performance of network, thus realizing fast inferring. When the loss function converges to the minimum stably, the training process is completed and the testing dataset is used to evaluate the performance of the network. In the next step, the well-trained model, which is capable of inferring the piston errors directly from the intensity images, is deployed on an embedded computing platform. When implementing the closed-loop correction, the image captured by charge-coupled device (CCD) is transferred to the computing platform and the instant piston error is obtained through forward inference of model in real time. Finally, piston error correction is carried out by controlling the piezo steering mirror based on the predicted output.

The experimental results show that the lightweight MobileNet deep learning model realizes high-precision piston sensing and a large capture range of ±6λ₀ (λ₀=600 nm) is achieved by using 550?650 nm broadband light. For the two-aperture imaging system, the average value of the root mean square error (RMSE) between testing outputs of the network and true piston error values is about 18 nm (Fig.6). Besides, the predicted values are very close to the true values in the whole capture range. In the process of closed-loop correction, the residual curve converges to the zero line rapidly and stably. The initial piston error is 2.3λ₀ and the average residual after closed-loop correction is about 0.043λ₀. In addition, the PSF image with closed-loop correction is almost the same as the ideal image (Fig.7). Each piston prediction takes about 3 ms for the lightweight MobileNet, while the time is 10 ms for the VGG-19 model. It is evident that our method has significant advantage in real-time performance. Then another experiment is implemented in the three-aperture system, where the average value of RMSE between testing outputs of the network and true piston values is about 30 nm (Fig.9). The average residual after closed-loop correction is about 0.063λ₀, which shows a reduced accuracy compared with the correction results of two-aperture system. This is because increasing sub-aperture number will complexify the mapping relationship between the PSF and the piston error. Correspondingly, the training data needed and the difficulty in training will greatly increase. Nevertheless, our study shows that there is little difference in the piston sensing time between the two-aperture system and the three-aperture system, which means the increase of sub-apertures to be measured has little effect on the real-time performance.

In the present study, deep learning based co-phasing closed-loop experiment of optical synthetic aperture is successfully implemented. This technology uses a single lightweight MobileNet CNN to extract piston information from focused PSF image, thus greatly reducing optical complexity of the system. At the same time, the end-to-end mode further simplifies the sensing process and achieves rapid and robust piston error estimation. Under the experimental conditions established in our study, it takes about 3 ms to complete each detection, which means good real-time performance is achieved. Fine co-phasing control with high sensing accuracy is realized for two-aperture system as well as three-aperture system. In summary, the reliability and superiority of deep learning co-phasing technology in engineering application have been preliminarily verified through the co-phasing closed-loop experiments.

The thermal effects and mechanical deformation of high-power lasers impede the output performance of laser systems. Compact laser systems, such as solid lasers, increasingly rely on adaptive optics (AO) featuring simpler structured wavefront sensors to improve beam quality. Unlike the traditional methods that retrieve wavefront from intensity distribution, deep learning, which is well-suited for nonlinear mapping, holds significant potential in this regard. In this article, we present a deep learning wavefront sensor (DLWFS) and demonstrate its applications in AO wavefront corrections. We use conditional generative adversarial networks (cGAN) to extract high-level features from the entire input intensity and retrieve wavefront from the intensity distribution. In other words, we view this intensity-to-wavefront nonlinear mapping as an image-translating problem. To overcome the compression of the wavefront information due to the diversity of coordinates during focusing propagation with a converged beam, the DLWFS relies on acquiring intensity from both the focal spot and the spot just before the focus, also called “double spots”, as input intensity distribution. By comparing the wavefront reconstruction results of DLWFS with those of commercial Shack-Hartmann wavefront sensor (SHWFS), and applying DLWFS in AO closed-loop of wavefront correction, the practicability of DLWFS can be proved.

We simulated the propagation of random initial wavefront through physical diffraction to obtain the intensity of spots on focus and defocus (0.98 times focal length) as training data and testing data of DLWFS. Network model cGAN was constructed by a generator (G) and discriminator (D). G had a U-Net structure comprising encoder-decoder convolutional neural networks (CNNs). It was trained to generate wavefront G(x) from input intensity distribution x(x1,x2), considering both on focus (x1) and defocus (x2) intensity data. The discriminator with a U-Net structure of encoder-decoder was trained to distinguish between tuple (G(x),x) of generated results G(x) with condition x as fake, and tuple (y,x) of real wavefront y with condition x as real. The training of the generator was considered completed when G was able to successfully fool D. The concept is shown in Fig.2 and is expressed mathematically in Eqs. (2)‒(5). We built an experimental platform of deformable mirrors (DM) for disturbing and correcting, and referencing SHWFS for comparison, as shown in Fig.7. DLWFS exhibits superior resolution compared to SHWFS, and SHWFS, in turn, offers higher resolution than DM for the purpose of wavefront correction. The laser beam was split 50/50 into SHWFS and DLWFS separately, to compare the wavefront results. Furthermore, by computing the wavefront response function of the DM, the closed-loop of AO used the wavefront generated from DLWFS for wavefront correction. Therefore, these experiments can serve to demonstrate the practicability of DLWFS as a wavefront sensor in AO systems.

DLWFS is capable of retrieving wavefront data with a root mean square (RMS) residual error of less than 0.3 μm at best, as shown in Fig.4. When comparing the wavefront results of DLWFS with those from SHWFS experiments, as shown in Fig.6, it becomes clear that the DLWFS generated wavefront results are smoother than referencing SHWFS, but both results have similar magnitude and shape of distribution. The RMS residual error is approximately 0.0965‒0.1531 μm in this comparison. The most noticeable disparities are observed near edges, with a significant reduction in disparity toward central areas. We conduct multiple AO wavefront correction experiments through controlling parameters and utilizing different 3D-printed apertures inducing circle and square shapes of beams. The correction results obtained by utilizing DLWFS as the wavefront sensor closely resemble the results obtained from SHWFS, as shown in Fig.9. The results of utilizing DLWFS in the correction of wavefront distortion induced by DM1 are shown in Fig.10. The first two rows depict the results with and without AO correction of the 50 mm diameter circular beam, while the last two rows depict the results of the 50 mm×50 mm square beam. We improve the circle beam quality from β=8.18 without AO to β=2.40 with AO, while we improve the square beam quality from β=10.83 without AO to β=3.61 with AO. These results demonstrate the practicability of using DLWFS in AO. Based on the experimental results mentioned earlier, we find that in retrieving wavefronts, the DLWFS shows a certain degree of deviation when compared to SHWFS. The primary causes of this deviation can be attributed to the sensitivity of DLWFS in these aspects: the parametric sensitivity of focal point position when acquiring spots, SNR of the wavefront with high frequency or small stroke aberrations, nonuniform distributed near-field intensity, and irregularly shaped beams. Hence, the performance of DLWFS can be improved by using the real data acquired by experiments conducted using an improved model.

Compact wavefront sensor is highly suitable for improving the beam quality of compact solid lasers in AO systems. In this article, we introduce DLWFS as a new method of nonlinear mapping from intensity distribution of focus and defocus spots into wavefront. The model is trained using simulated data. By using cGAN-based generator to retrieve wavefront from input focus and defocus spots, we compare wavefront results of DLWFS with those of SHWFS. The residual error falls in the range of 0.0965‒0.1531 μm. We also apply DLWFS for AO wavefront correction and correct square and circle beams with beam quality β=3.61 and β=2.40 separately. Although there is a noticeable deviation in wavefront results compared with the reference wavefront, the wavefront correction results demonstrate the practicability of DLWFS. We believe that future improvements in the model structure and the utilization of experimentally acquired training data will enhance the performance of DLWFS in future studies.

With the development of optical technology, the application fields of optical elements and optical systems are becoming increasingly extensive; however, localized microscopic defects on the surface of optics affect the corresponding system performance. Therefore, it is necessary to detect defects on the optical surface. With the development of machine vision technology, the microscopic scattering dark-field imaging method of noncontact detection has become an important method for automated surface defect detection. However, in large-aperture fine optics, there are fewer defects on the surface and a large number of sub-aperture images. When using defect images for sub-aperture stitching, the amount of data used for image storage and processing is high and increases with the size of the detection aperture, which requires a significant amount of time for detection. Accordingly, a surface defect stitching method is proposed based on a sub-aperture feature dataset, which uses the constructed sub-aperture feature dataset to realize full-aperture defect stitching, thereby reducing the amount of data stored and processed during the stitching procedure.

To perform full-aperture defect stitching, the defect feature data (defect number, type, shape feature, relative position feature, and sparse matrix data) in the binarized sub-aperture image and its overlapping area image were extracted and the sub-aperture feature dataset could be constructed. Then, based on the constructed feature dataset, for the sub-apertures containing defects in the overlapping areas, the overlapping area matching relationship and the offset parameters between the matched overlapping areas were solved and combined with the initial position calculated from the number of scanning steps of the sub-apertures to obtain an accurate positional relationship between the sub-apertures. For sub-apertures without defects in the overlapping areas, the stitching position was determined based on the theoretical position. Finally, the defect sparse matrix data of each sub-aperture were transformed to the corresponding position using coordinates to realize full-aperture defect stitching. As described herein, the sub-aperture feature dataset was constructed based on the feature data extracted from the images captured using the microscopic scattering dark-field imaging device. Full aperture defect stitching was completed based on the dataset, and then compared with the full-aperture stitching results based on the template matching method to analyze and validate the effectiveness of the proposed research method.

The constructed sub-aperture feature dataset (Table 1) was adopted to calculate the overlapping area matching relationship and the corresponding offset parameter, and compared with the offset calculation results obtained using the template matching method (Table 3). The offset calculation results of this study are basically consistent with those of the template matching method. During the offset calculation in the proposed method, the feature data of all the defective areas extracted from the overlapping areas are used to calculate the offset parameter without the need for comparison between unrelated regions, thereby simplifying the calculation process and improving the corresponding efficiency. Meanwhile, some sub-aperture areas were selected for matching and stitching and compared with the results of the direct stitching method (Fig. 5), showing that the method in this study improves the positional deviation that exists in the defective part of the results of the direct stitching method. Thus, this method can effectively realize the accurate matching of sub-aperture areas. Finally, the full-aperture defect images were obtained using the full-aperture defect stitching method based on the feature dataset and the full-aperture stitching method based on the template matching method (Fig. 6). The number and type of defects and some of the scratch size data in the full-aperture image were detected using the connected component labeling algorithm and the minimum enclosing rectangle algorithm (Fig. 8, Table 4). The defect detection results of the full-aperture images obtained using the two methods are basically consistent. In addition, in the process of full-aperture stitching, when stitching images using the template matching method, the data volume of a single processed sub-aperture image is 1.17 MB, and the corresponding processing and storage data volume increases with each completed image stitching, the data volume of the final full-aperture stitching result image is 9.24 MB. However, the method in this study is based on the feature dataset to complete the full-aperture defect stitching; the data volume of the constructed feature dataset is 3.26 MB, and the final data volume of the full-aperture defect image converted from the full-aperture defect data is 20.9 kB. Thus, the proposed method can effectively obtain full-aperture defects, and the volume of stored and processed data in the stitching process is less than that of the image-based stitching method.

In this study, we extracted the feature data in a defect image to construct a sub-aperture feature dataset and complete full-aperture defect stitching. This was compared with the full-aperture image stitching method based on the template matching method. The results of the defects detected in the full-aperture images corresponding to the two methods are basically consistent. During the full-aperture stitching process, the proposed method uses the feature dataset to determine the relative positional relationship of the sub-aperture and to complete the stitching of full-aperture defects, effectively reducing the volume of processed and stored data in the stitching process compared with the image stitching method based on the template matching method.

The miniaturization and integration of multispectral detectors have become one of the development directions for infrared detectors. This paper proposes a component structure that integrates a lens and window with airtight packaging, focusing on the characteristics of integrating low-temperature optical lenses for multispectral detectors. Various aspects are investigated, including high-precision optical alignment for different focal planes of the same component multispectral detector, low deformation filter support structure, and suppression of optical crosstalk and stray light. These studies address a series of issues related to high-precision alignment, low deformation filter support, prevention of optical crosstalk, and suppression of stray light in the miniaturization and integration packaging of multispectral detectors. The developed component has been successfully applied in a spectral imaging instrument for a specific project.

A component structure for a multispectral infrared detector with an integrated lens has been designed (Fig.3). The airtight packaging component structure of the multispectral infrared detector with an integrated lens includes a component housing, cover plate, lens, primary aperture, filter holder, filter, chip module, electrode plate, and filter holder support. Before packaging, the entire component is evacuated, followed by filling with inert gas, and finally sealed using parallel seam welding. The airtightness meets the long-term requirements of the payload.

By designing a three-layer laminated low-deformation multispectral filter holder assembly, multiple small filter pieces are adhered to the low-stress filter holder structure. This structure can also be used for the assembly of multiple mid-wave and long-wave filter pieces with the detector. It overcomes the problems of size interference and complex integration process with low yield associated with traditional bonding methods. It achieves the coupling of low-deformation multispectral filters with the detector (Fig.4).

This study employs the micro-adjustment technique for different focal planes of the multispectral infrared detector and the coaxial lens adjustment technique. It achieves a precision deviation of less than ±5 μm between different focal planes and the filter assembly for a three-band detector within the same component. The lens-to-detector alignment precision within ±15 μm is achieved (Table 1). Spectral tests are performed using the infrared detector component with an integrated lens, and the results indicate no significant optical crosstalk among channels (Fig.6).

Through the design of a three-layer laminated structure with low deformation, multiple small filters have been successfully bonded to the low deformation stress filter frame. The maximum low-temperature deformation of the 1.64 μm filter at 130 K is 0.9278 μm, while the maximum low-temperature deformation of the 2.13 μm and 1.38 μm filters at 130 K is 0.2292 μm (Fig.5). By using micro-adjustment techniques for different focal planes of the multi-band infrared detectors and coaxial lens adjustment techniques, the deviation in the alignment between different focal planes of the three-band detectors and the filters within the same component is better than ±5 μm, and the alignment precision between the lens and the detectors is better than ±15 μm. Spectral testing is conducted using the integrated lens infrared detector component. The results of the spectral testing indicate that there is no significant optical crosstalk among channels. A series of low-stress design and process improvements are applied to the low-temperature lens, and the results show that the band detection rate is greater than 1.5×10¹¹ cm·Hz^1/2·W^-1 (130 K). The maximum absolute variation in band response rate before and after rigorous environmental testing is 8.5% (Fig.9). The high-performance multi-spectral integrated infrared detector component is obtained, and the experimental results confirm that the detector functions properly and the component performs well (Table 2).

This article focuses on solving the packaging technology of multi-channel integrated infrared detector components, proposes a multi-band infrared detector airtightness packaging component with integrated lenses, and emphasizes the key technologies such as jointing of different focal planes for different bands and coaxial lens adjustment technology for the same component, high reliability support structure for multi-filter narrow seam splicing, and stray light suppression, solving the high-precision alignment of multi-channel integrated infrared detector components, low stress control, low optical crosstalk, low power consumption, and high reliability of the detector. A high-performance multi-band infrared detector component with integrated lenses has been obtained.

With the rapid expansion of oil and gas pipelines in China and the growing implementation of urban gas pipelines, pipeline leakages have garnered significant attention. These leakages directly affect the safety of human lives and property. Consequently, pipeline leakages have emerged as a prominent research area. Volatile gases released during oil and gas leaks consist not only of methane but also of characteristic gases such as propane and butane. Precisely measuring the volume fractions of these gases can help in addressing the limitations of isolated measurements of methane. This comprehensive approach has significant value in terms of safety and environmental protection.

Because the stretching vibration of C—H chemical bonds in alkane macromolecules can cause the superposition of absorption spectra in the near-infrared region, it is difficult to achieve accurate measurements of propane and butane using traditional tunable diode laser absorption spectroscopy technique. In this study, a traditional tunable diode laser absorption spectroscopy technique was combined with a stoichiometric algorithm. Direct absorption signals and second harmonic signals within the range of 1685.9?1686.8 nm were recorded using a tunable diode laser absorption spectroscopy technique platform. The quantification of the two gas components was then achieved through the application of a partial least squares regression algorithm, which effectively addresses the challenges posed by overlapping absorption spectra. The study shows that this approach significantly enhances the accuracy and sensitivity of the quantitative analysis model.

Initially, a regression relationship between the volume fractions of elementary propane and butane gas and the second-harmonic signal was established using partial least squares analysis. This relationship enabled the prediction of unknown gas volume fractions below 2000×10^-6. The experimental results demonstrate that the maximum prediction error for propane is 14×10^-6, whereas for butane, it is 41×10^-6. The correlation coefficients R² are 0.9999 and 0.9995 for propane and butane (Fig.6), respectively. These findings serve as preliminary evidence for the partial least squares algorithm and its ability to accurately demodulate wide-spectrum absorption gas lines. Next, based on the mixture of propane and butane, the study observed that the amplitude of the second-harmonic signal demodulated from propane and butane at the same volume fraction differs by two orders of magnitude (Fig.7). This difference does not pose an issue for the inversion of their respective volume fractions in the presence of elementary gases. However, in the case of mixed gas, the butane signal with a smaller amplitude is submerged within significant variations in the propane signal. Consequently, the amplitude of the second-harmonic signal at the absorption center of propane is significantly reduced. Thus, modeling the second harmonic signal alone results in unacceptable errors. To address this challenge, the characteristic absorption information represented by the second harmonic signal was combined with the spectral band absorption information represented by the direct absorption signal. Both signals were collected and used as independent variables to train the regression model for gas mixtures. This approach ensures a more comprehensive and accurate analysis of the volume fractions of mixed gases. The developed model is capable of detecting low volume fraction gas mixtures, including propane and butane at volume fractions of 0.8% and 0.9%, respectively, of the lower explosive limit. The maximum prediction errors in the low volume fraction group, ranging from 100×10^-6 to 800×10^-6, are found to be propane at 34×10^-6 and butane at 51×10^-6 (Fig.8). Similarly, the maximum prediction errors in the high volume fraction group, ranging from 2000×10^-6 to 10000×10^-6, are found to be propane at 64×10^-6 and butane at 148×10^-6 (Fig.9). Importantly, all the prediction errors remain below 3% of the lower explosion limit, which aligns with the safety requirements of the petroleum industry. This methodology caters to the specific safety requirements of the petroleum industry by enabling the precise and sensitive detection of low volume fraction gas mixtures and ensuring production safety and hazard prevention. To further validate the dynamic reliability of the model during continuous operation, two continuous tests were conducted at low (Fig.10) and high (Fig.11) volume fractions. These tests successfully confirmed the stability and reliability of the partial least squares regression model in predicting the volume fraction of each component in the propane and butane mixtures throughout the dynamic process.

This study relies on a tunable diode laser absorption spectroscopy technique and leverages multiple measurement signals that represent gas absorption within a narrower scanning range. This approach enables the quantitative analysis of the overlapping spectral lines of propane and butane. Consequently, it offers a practical solution for accurately measuring the volume fractions of various volatile oils and gases. This solution is particularly well suited for addressing the specific needs encountered at oil and gas storage sites. The approach exhibits tremendous potential for expanding its applications and will undergo further validation in the field of oil and gas pipeline leakages.