A method for measuring the coherence length of a horizontal turbulent atmosphere

Abstract

The application discloses a method for measuring horizontal turbulent atmospheric coherence length, and belongs to the technical field of atmospheric coherence length measurement. The method comprises the following steps: converging a reflected light signal and dividing the reflected light signal into a sub-aperture image array; taking an image of a central sub-aperture of the sub-aperture image array as a reference image, and obtaining an accurate offset of each sub-aperture by using a two-stage offset estimation strategy from coarse to fine; calculating a wavefront slope according to the accurate offset, generating Zernike polynomial coefficients of an incident wavefront; and statistically calculating a measured variance value of low-order terms in the Zernike polynomial coefficients, combining a mapping relationship between the variance and the atmospheric coherence length established by Kolmogorov turbulence statistical theory, and inversely calculating the atmospheric coherence length of a horizontal link. The two-stage offset estimation strategy composed of the sum of squared differences criterion and an optical flow algorithm takes into account the calculation efficiency and sub-pixel accuracy, realizes the integration of wavefront measurement and turbulence evaluation, and is suitable for engineering application scenarios such as free space optical communication.

Description

Technical Field

[0001] This application relates to the field of atmospheric coherence length measurement technology, and more specifically to a method for measuring the coherence length of horizontally turbulent atmospheric flow. Background Technology

[0002] In free-space optical communication systems, atmospheric turbulence-induced fluctuations in the refractive index of the medium in vertical and long-distance horizontal communication links severely impact communication reliability and stability. Accurate measurement of atmospheric coherence length—a characteristic scale of how a light beam maintains coherence during atmospheric propagation—provides crucial data for assessing the operating environment of optical systems and the quality of communication links.

[0003] Currently, the widely used method for measuring atmospheric coherence length is the Differential Image Motion Monitor (DIMM) method. This method inverts the atmospheric coherence length by calculating the variance of the arrival angles of the two sub-aperture spots. Its temporal statistical characteristics can effectively suppress interference from non-atmospheric factors such as telescope vibration and temperature effects on the measurement results. However, precisely because this method relies on temporal statistics, the data processing is complex and involves a large amount of image matching and statistical calculations, resulting in a high computational load and placing high demands on system hardware performance. Furthermore, existing methods mostly focus on point targets in vertical communication links and rely on emitted beacon light for auxiliary calibration. These systems are complex in structure and expensive in equipment, and due to their low scattering efficiency, they are difficult to accurately reflect the actual turbulence intensity in measurement scenarios such as the upper atmosphere or long-distance near-ground horizontal links.

[0004] In recent years, researchers have begun to explore wavefront detection methods based on extended targets. For example, a Chinese patent discloses an extended target wavefront detection method based on edge enhancement. This method uses an edge enhancement operator to preprocess the extended target image, then calculates the image offset using a correlation function, ultimately achieving wavefront restoration. Another patent application discloses an extended target Hartmann wavefront detection method based on reference image preprocessing. This method performs preprocessing on the reference image, including grayscale mapping, edge extraction, and image overlay, then calculates the offset using a normalized cross-correlation (NCC) algorithm. Furthermore, related patents propose a fast wavefront restoration method based on kernelized correlation filter (KCF), achieving rapid correlation calculation through frequency domain transformation.

[0005] However, the aforementioned existing technologies have the following shortcomings: First, existing methods mostly stop at wavefront detection or wavefront reconstruction, and their final output is wavefront phase or wavefront aberration coefficients, without involving the measurement of atmospheric coherence length. In application scenarios such as free-space optical communication, the system not only needs wavefront correction, but also needs to evaluate the turbulence intensity of the communication link to guide the selection of coding and modulation methods, which existing methods cannot meet.

[0006] Second, existing methods are mostly designed for vertical links or astronomical observation scenarios, with signal sources being point sources (such as stars) or artificial beacon light. In horizontal communication links, beacon light is difficult to deploy and has low scattering efficiency, making point source methods unsuitable. Although some methods claim to be applicable to extended targets, they essentially treat the extended target as a combination of multiple point sources, failing to truly utilize the spatial structure information of the extended target.

[0007] Third, existing methods generally employ normalized cross-correlation algorithms for image matching. These algorithms involve division and square root operations, resulting in high computational complexity and difficulty in meeting real-time requirements. Although some methods use the Sum of Squared Differences (SSD) criterion, they are not optimized for the characteristics of extended targets, leading to decreased matching accuracy under low signal-to-noise ratio conditions.

[0008] Fourth, existing methods for subpixel offset estimation mostly employ interpolation methods (such as three-point fitting, parabolic interpolation, etc.). This method involves post-processing of the correlation matrix peaks, resulting in limited accuracy. For low signal-to-noise ratio scenarios commonly found in horizontal links, interpolation methods exhibit poor stability.

[0009] Fifth, the preprocessing strategies of existing methods (such as edge enhancement, grayscale mapping, image overlay, etc.) add extra computational burden, and the preprocessing parameters need to be manually adjusted according to the target type, lacking adaptive capability.

[0010] Therefore, how to provide a measurement method that does not require beacon light in horizontal links, has high computational efficiency, strong robustness under low signal-to-noise ratio conditions, and can directly output atmospheric coherence length, and integrate wavefront measurement with turbulence intensity assessment, thereby reducing dependence on additional beacon light emitting devices and independent atmospheric coherence length measurement equipment, and reducing system complexity and hardware costs, is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0011] The purpose of this application is to provide a method for measuring the coherence length of horizontally turbulent atmospheric flow, which can solve at least one of the aforementioned technical problems. The specific solution is as follows: According to a specific embodiment of this application, this application provides a method for measuring the atmospheric coherence length of horizontal turbulence, comprising the following steps: The reflected light signal from the extended target in the horizontal link is acquired, and the reflected light signal is converged and segmented into a sub-aperture image array; Using the image of the central sub-aperture of the sub-aperture image array as a reference image, a two-stage offset estimation strategy from coarse to fine is adopted to obtain the accurate offset of each sub-aperture. The wavefront slope is calculated based on the precise offset, and the wavefront is restored using the Zernik mode method to generate the Zernik polynomial coefficients of the incident wavefront. The measured variance of the lower-order terms in the Zernike polynomial coefficients is statistically analyzed. Combined with the mapping relationship between variance and atmospheric coherence length established by Kolmogorov turbulence statistical theory, the atmospheric coherence length of the horizontal link is obtained by inversion.

[0012] Furthermore, the coarse-to-fine two-stage offset estimation strategy includes: a coarse estimation stage and a fine estimation stage; The coarse estimation stage uses the sum of squared differences criterion to calculate the correlation response between each sub-aperture image and the reference image, and obtains the initial estimate of the offset based on the location of the maximum value of the correlation response. The fine estimation stage uses the initial estimated value of the offset as the initial condition of the optical flow field, constructs the optical flow energy functional, and iteratively solves it using the HS optical flow algorithm to generate the offset correction value. The initial offset estimate is superimposed with the offset correction value to obtain the precise offset of each sub-aperture.

[0013] Furthermore, the extended target is a natural or artificial target with spatial structure information, and the spatial grayscale distribution of the extended target serves as the information source for wavefront detection.

[0014] Furthermore, when calculating the correlation response between each sub-aperture image and the reference image based on the sum of squared differences criterion, a spatially adaptive weighting function based on local gradients is introduced to weight the matching process.

[0015] Furthermore, the spatial adaptive weighting function includes: a first term and a second term; The first item is the local gradient magnitude of the reference image, which is used to enhance the matching contribution of high gradient regions in the reference image; The second term is a Gaussian kernel function multiplied by a balance factor. The Gaussian kernel function takes the geometric center of the reference image as its origin and is used to suppress edge noise. The balance factor is used to balance the weight relationship between the first term and the second term.

[0016] Furthermore, the HS optical flow algorithm includes the following steps: Construct an optical flow energy functional that includes data consistency constraints and smoothness constraints; The Euler-Lagrange equations were derived from the optical flow energy functional using the variational method. The Euler-Lagrange equations are solved iteratively using the Gauss-Seidel iterative method. In each iteration, the optical flow field components of the current iteration are updated using the local neighborhood average of the horizontal component and the local neighborhood average of the vertical component. After iterative convergence, the horizontal and vertical components of the output optical flow field are used as the offset correction values.

[0017] Furthermore, obtaining the precise offset of each sub-aperture includes the following steps: The initial estimate of the offset is taken as an integer pixel-level offset; The offset correction value is used as a sub-pixel level offset; The integer pixel-level offset is superimposed with the sub-pixel-level offset; The output superposition result serves as the precise offset for each sub-aperture.

[0018] Further, the step of calculating the wavefront slope based on the precise offset and reconstructing the wavefront using the Zernike mode method to generate the Zernike polynomial coefficients of the incident wavefront includes the following steps: The precise offset of each sub-aperture is converted into the wavefront slope of that sub-aperture; Collect the wavefront slopes of all sub-apertures to form a wavefront slope vector; The Zernike model method is used to perform wavefront reconstruction with the wavefront slope vector as input data. The restored wavefront phase is expanded into a multinomial Zernik polynomial; Extract the coefficients of each order of Zernike polynomial to generate the Zernike polynomial coefficients of the incident wavefront.

[0019] Furthermore, the measured variance of the lower-order terms in the Zernike polynomial coefficients, combined with the mapping relationship between variance and atmospheric coherence length established by Kolmogorov's statistical theory of turbulence, is used to invert and obtain the atmospheric coherence length of the horizontal link, including the following steps: Extract the coefficients of lower-order terms from the Zernik polynomial coefficients; The lower-order coefficients include the defocused Zernike polynomial coefficients and the astigmatic Zernike polynomial coefficients. The measured variance of the coefficients of the lower-order terms is calculated. Based on Kolmogorov's statistical theory of turbulence, a mapping relationship between the measured variance of Zernike polynomial coefficients and the atmospheric coherence length is established. The mapping relationship is that the measured variance of the Zernike polynomial coefficients is proportional to the negative fifth power of the atmospheric coherence length, and the proportionality coefficient is determined by the sub-aperture diameter of the Shaker-Hartmann wavefront sensor. Substituting the measured variance into the mapping relationship, the atmospheric coherence length of the horizontal link is obtained by inversion calculation.

[0020] Furthermore, the mapping relationship between the measured variance and the atmospheric coherence length established by the Kolmogorov turbulence statistical theory includes at least one of the following: After removing the translation term, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is: ; After removing the translation and tilt terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; After removing the translation, tilt, and defocus terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; After removing translation, tilt, defocus, and astigmatism terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; in, Indicates the diameter of the sub-aperture; Indicates the length of atmospheric coherence; This represents the mean squared error of the wavefront residuals after removing the translation term; This represents the mean squared error of the wavefront residuals after removing translation and tilt. This represents the mean square error of the wavefront residuals after removing translation, tilt, and defocusing. This represents the mean squared error of the wavefront residuals after removing translation, tilt, defocus, and astigmatism.

[0021] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects: 1. This application discloses a method for measuring the coherence length of horizontal turbulent atmosphere. It uses existing extended targets in the horizontal link, such as drones, buildings, and natural landscapes, as direct detection objects. The method acquires the reflected light signals from these extended targets and segments them into a sub-aperture image array. Using the central sub-aperture image as a reference image, a coarse-to-fine two-stage offset estimation strategy is employed to obtain the precise offset of each sub-aperture. Compared to existing technologies that rely on point light sources such as stars or artificial beacon light for auxiliary calibration, this application eliminates the need to deploy beacon light on the horizontal link, solving the technical problems of difficult beacon light deployment and low scattering efficiency in horizontal communication links. This significantly reduces system complexity and hardware costs, making it suitable for practical engineering scenarios such as free-space optical communication.

[0022] 2. This application discloses a method for measuring the coherence length of horizontal turbulent atmospheric conditions, employing a coarse-to-fine two-stage offset estimation strategy: In the coarse estimation stage, the sum of squared differences criterion is used to calculate the correlation response between each sub-aperture image and the reference image. Based on the location of the maximum correlation response, an initial integer-level offset estimate is obtained. The sum of squared differences criterion does not require division or square root operations during calculation and can be directly mapped to hardware multiplication instructions. In the fine estimation stage, the initial integer-level offset estimate is used as the initial condition for the optical flow field. An optical flow energy functional is constructed and iteratively solved using the HS optical flow algorithm to generate a sub-pixel-level offset correction value. The initial integer-level offset estimate is then superimposed with the sub-pixel-level offset correction value to obtain the precise offset of each sub-aperture. This method significantly reduces computational complexity while maintaining sub-pixel-level accuracy and maintains stable offset estimation accuracy even under low signal-to-noise ratio conditions.

[0023] 3. This application discloses a method for measuring the atmospheric coherence length of horizontal turbulent flow. The method calculates the wavefront slope based on the precise offset, performs wavefront reconstruction using the Zernike mode method, and generates Zernike polynomial coefficients for the incident wavefront. The measured variances of the lower-order terms in the Zernike polynomial coefficients, including defocus and astigmatism terms, are statistically analyzed. A mapping relationship between variance and atmospheric coherence length is established using Kolmogorov's turbulence statistical theory. Compared to existing technologies that stop at wavefront detection or reconstruction, ultimately outputting wavefront phase or wavefront aberration coefficients, this application integrates wavefront measurement and atmospheric coherence length measurement, directly outputting the atmospheric coherence length value characterizing turbulence intensity. The measurement results can serve as a communication link quality assessment index for free-space optical communication systems, guiding the selection of adaptive optics correction strategies, coding methods, or modulation methods. This achieves a complete technical closed loop from wavefront detection to turbulence assessment, expanding the engineering application value of the method. Attached Figure Description

[0024] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings: Figure 1 This is a schematic diagram of the method flow of a measurement system for measuring the atmospheric coherence length of horizontal turbulence, as provided in an embodiment of this application.

[0025] Figure 2 This is a schematic diagram of the system structure of a measurement system for a method of measuring atmospheric coherence length in horizontal turbulence provided in an embodiment of this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or device. Without further limitation, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the product or device that includes that element.

[0028] The embodiments of this application are described in detail below with reference to the accompanying drawings.

[0029] This application provides a method for measuring the atmospheric coherence length of horizontal turbulence, such as... Figure 1 As shown, the measurement method is based on an existing measurement system. In this embodiment, the measurement system mainly includes an optical receiving module, a sensing module, and a data processing module, such as... Figure 2 As shown.

[0030] The optical receiving module, consisting of a telescope, receives reflected light signals from extended targets in the horizontal link. These extended targets are natural or man-made objects with spatial structure information, including drones, buildings, or natural landscapes. The optical receiving module then converges the received reflected light signals into the subsequent detection system.

[0031] The core component of the sensing module is the Shaker-Hartmann wavefront sensor, which consists of a microlens array and a photodetector, such as a CCD or CMOS. The microlens array divides the incident wavefront into several sub-apertures, and each sub-aperture focuses the incident light onto the corresponding area of ​​the photodetector, forming an array of light spots.

[0032] The data processing module includes an image acquisition unit, an offset calculation unit, a slope calculation unit, a wavefront reconstruction unit, and an atmospheric coherence length calculation unit. This module receives the spot array image output by the Shaker-Hartmann wavefront sensor, executes the extended target migration algorithm and the wavefront reconstruction algorithm, and finally outputs the atmospheric coherence length measurement result.

[0033] The technical solution of this application provides a method for measuring the atmospheric coherence length of horizontal turbulence. This method involves acquiring the reflected light signal from an extended target, segmenting it into a sub-aperture image array, obtaining accurate offsets through two-stage offset estimation, calculating the wavefront slope, performing wavefront reconstruction using the Zernike model, and statistically analyzing the variance of low-order terms to ultimately invert the atmospheric coherence length. From signal acquisition to final output, this method covers the entire process of measuring the atmospheric coherence length of a horizontal link, forming a complete technical closed loop, which differs from traditional methods for measuring vertical links and point targets.

[0034] This application provides a method for measuring the atmospheric coherence length of horizontal turbulence, comprising the following steps: S1. Acquire the reflected light signal from the extended target in the horizontal link, converge the reflected light signal and divide it into a sub-aperture image array.

[0035] The reflected light signal from the extended target in the horizontal link is acquired, and the reflected light signal is converged by the optical receiving module and segmented into a sub-aperture image array by the Shaker-Hartmann wavefront sensor.

[0036] Using the image of the central sub-aperture of the Shaker-Hartmann wavefront sensor as a reference image, the reference image has a pixel size of M×M, and each sub-aperture image has a pixel size of N×N, where N≥M. The reference image and each sub-aperture image are normalized by dividing the grayscale value of a single pixel by the maximum grayscale value of the entire image, thus mapping the grayscale value range to... Interval.

[0037] The extended targets are natural or artificial targets with spatial structural information, using spatial grayscale distribution as the information source. By limiting the information source to spatial grayscale distribution, distinct from the centroid location of the light spot in point light source methods, the extended targets include existing targets in the scene such as drones, buildings, and natural landscapes. This eliminates the need for artificial beacon lights, reducing system cost and complexity.

[0038] S2. Using the image of the central sub-aperture of the sub-aperture image array as a reference image, a coarse-to-fine two-stage offset estimation strategy is adopted to obtain the accurate offset of each sub-aperture.

[0039] This application provides a preferred technical solution, which includes a coarse-to-fine two-stage offset estimation strategy comprising a coarse estimation stage and a fine estimation stage. The coarse estimation stage employs an improved sum of squared differences criterion method, while the fine estimation stage uses the HS optical flow algorithm. The sum of squared differences criterion method provides reliable initial values, and the HS optical flow algorithm achieves sub-pixel accuracy.

[0040] For extended target wavefront detection, an improved squared difference and correlation algorithm is used as a coarse estimation method for offset. The degree of matching between the reference image and the image to be tested is used as a similarity measure, and the corresponding function definition is as follows: ; in, Representing the squared difference and related response values, the reference image and the sub-aperture image are compared at an offset. The smaller the value, the higher the matching degree; u represents the horizontal offset, which is the horizontal pixel offset between the reference image to be estimated and the sub-aperture image; v represents the vertical offset, which is the vertical pixel offset between the reference image to be estimated and the sub-aperture image. This represents the pixel grayscale value of the sub-aperture image, and the coordinates of the sub-aperture image to be matched. The grayscale value at that location; This represents the grayscale value of a reference image pixel, where the reference image is located in coordinates... The grayscale value at that location is adjusted by offset. Align with sub-aperture image; This represents a spatially adaptive weighting function based on local gradients, used to enhance the matching contribution in high-gradient regions and suppress edge noise; This represents the x and y coordinates of a pixel in the image.

[0041] Spatial adaptive weighting function based on local gradient The expression is: ; in, , These represent reference templates. The geometric center is located at the x and y coordinates of the image; represents the Gaussian kernel parameter, controlling the width of the Gaussian kernel function to suppress edge noise; k represents the balance factor, used to balance the weight relationship between the first term (local gradient magnitude) and the second term (Gaussian kernel function multiplied by the balance factor); in this embodiment, the value of k is 0.7. The value is set to 0.3; This represents the local gradient magnitude of the reference image at pixel (x,y), which reflects the texture intensity or edge information of the pixel. This represents the summation of the local gradient 2-norm over all pixels of the reference image, used to normalize the first term; e represents the base of the exponential function.

[0042] When k is small, the spatial adaptive weighting function relies more on local gradient information, which can enhance the matching contribution of texture-rich regions, but has a weaker ability to suppress edge noise. When k is large, the spatial adaptive weighting function relies more on the spatial weighting of the central region, which has a stronger ability to suppress edge noise, but may weaken the contribution of effective texture information. Experiments have verified that the matching accuracy is optimal when the value is in the range of 0.6 to 0.8 in typical extended target scenarios. In the embodiment of this application, the value of k is 0.7, which achieves a good balance between texture enhancement and noise suppression.

[0043] Gaussian kernel parameters Used to control the spatial decay rate of Gaussian weighting: when When the size is small, the Gaussian kernel window is narrow, with only a small central region having a high weight, which may excessively suppress effective information in the edge regions; when... When the Gaussian kernel window is too large, the spatial selectivity is weaker, and the edge noise suppression effect decreases. The value of is related to the size of the sub-aperture image. Under normalization conditions, Using a value between 0.2 and 0.4 can effectively suppress edge noise while preserving effective texture information. In the embodiments of this application... A value of 0.3 represents a suitable range for spatial attenuation. The values ​​of k and λ can be adjusted within this range based on the image signal-to-noise ratio and sub-aperture size in the specific application scenario. Adaptive adjustments can be made to achieve a matching effect, but this application does not limit the specific implementation of the embodiments.

[0044] Traditional sum-of-squares (SFS) algorithms involve all pixels with equal weight in the matching calculation, failing to adaptively adjust the contribution of each pixel based on image content. This application introduces a spatially adaptive weighting function based on local gradients, building upon the SFS criterion: the magnitude of the local gradient of the reference image and a Gaussian kernel function with the geometric center of the reference image as the origin. The improved SFS correlation algorithm in this application significantly enhances matching accuracy and noise resistance while maintaining the computational simplicity of the SFS.

[0045] Compared to the traditional normalized cross-correlation algorithm, the squared difference and correlation algorithm does not require division and square root operations and can be directly mapped to hardware multiplication instructions. This avoids the overhead of branch prediction, better utilizes the instruction set parallelism of modern central processing units and graphics processing units, and significantly reduces computational complexity.

[0046] After obtaining the initial estimate of the offset through improved related algorithms, the peak value of feature matching is the preliminary offset estimate. , ).

[0047] The fine estimation stage uses the offset as the initial estimate ( , As the initial condition for the optical flow field, an optical flow energy functional is constructed and iteratively solved using the HS optical flow algorithm to generate offset correction values ​​(Δx, Δy).

[0048] The obtained initial estimate ( , As the starting point for the HS optical flow algorithm, the optical flow energy functional is established, and its expression is: ; in, Ω represents the optical flow energy functional, i.e., the total energy of the optical flow estimate, and the optical flow field is solved by minimizing this energy function; Ω represents the image integration region. Represents the horizontal gradient of the image; Represents the gradient in the vertical direction of the image; Represents the gradient in the temporal direction of the image; α This represents the smoothing constraint factor; The gradient squared represents the horizontal optical flow component; This represents the squared gradient of the vertical optical flow component.

[0049] The Euler-Lagrange equation is derived from the optical flow energy functional using the variational method, and its expression is: ; in, Describe the Laplace operator for u; Let v be the Laplace operator.

[0050] The horizontal component u and vertical component v of the optical flow field can be obtained by iteratively solving using the Gauss-Seidel method, and then the offset correction values ​​(Δx, Δy) can be calculated. The expression of the iterative formula is: ; in, and Let u and v represent the local neighborhood averages of the horizontal and vertical components of the optical flow field in the nth iteration, respectively; n represents the iteration number index. , Let u and v represent the values ​​of u and v in the (n+1)th iteration, respectively. , Let u and v represent the local neighborhood averages of the horizontal and vertical components of the optical flow field in the nth iteration, respectively. After the iteration converges, the horizontal and vertical components of the output optical flow field are used as the offset correction values.

[0051] The initial offset estimate is used as the integer pixel-level offset, and the offset correction value is used as the sub-pixel-level offset. The two are then superimposed to output the precise offset of each sub-aperture.

[0052] That is, the initial estimated value of the offset ( , The offset correction value (Δx, Δy) is added together to obtain ( , This serves as the precise offset for each sub-aperture.

[0053] S3. Calculate the wavefront slope based on the precise offset, and perform wavefront reconstruction using the Zernike mode method to generate the Zernike polynomial coefficients of the incident wavefront.

[0054] The wavefront slope of each sub-aperture is measured using a Shaker-Hartmann wavefront sensor, and the precise offset of each sub-aperture is then calculated. , The formula for converting the wavefront slope of the sub-aperture to the wavefront slope of the sub-aperture is as follows: ; ; in, , represents the wavefront slope of the q-th sub-aperture in the x and y directions, respectively; f represents the focal length of the microlens array.

[0055] Collect the wavefront slopes of all sub-apertures to form a wavefront slope vector.

[0056] The Zernike model method is used to perform wavefront reconstruction with the wavefront slope vector as input data.

[0057] In the technical solutions of this application embodiment, the least squares method or singular value decomposition method is used to obtain the Zernike polynomial coefficients.

[0058] The restored wavefront phase is expanded into multiple Zernike polynomials, and the coefficients of each Zernike polynomial are extracted to generate the Zernike polynomial coefficient vector of the incident wavefront.

[0059] S4. Calculate the measured variance of the lower-order terms in the Zernike polynomial coefficients, and invert the atmospheric coherence length of the horizontal link by combining the mapping relationship between variance and atmospheric coherence length established by Kolmogorov turbulence statistical theory.

[0060] If the first J terms of Zenick distortion are compensated by the adaptive optics system, the corrected phase can be expressed as: ; in, Indicates the corrected phase; J represents the number of Zernike polynomial terms; Denotes the Zernike coefficient of the j-th term; Let represent the j-th Zernikal polynomial.

[0061] The remaining phase mean square error can then be expressed as: ; in, This represents the mean square error of the wavefront residuals; Indicates the original wavefront phase; Represents the radial coordinate in the polar coordinate system, the radial distance in the normalized polar coordinates, and its value ranges from [0,1]. Represents the angular coordinates in the polar coordinate system, the angle in polar coordinates, with a value range of [0, 2π].

[0062] The variances of the Zernike coefficients of each order are expressed as follows: ; in, The variance of each Zernike coefficient represents the order of the coefficients; s represents the radial order. The gamma function is represented by D; the sub-aperture diameter is represented by D. It represents the length of atmospheric coherence.

[0063] The lower-order coefficients are extracted from the Zernike polynomial coefficient vector. These lower-order coefficients include the defocus Zernike polynomial coefficients and the astigmatic Zernike polynomial coefficients.

[0064] The measured variance of the lower-order term coefficients is calculated. For multiple consecutively acquired images, the variance of the lower-order term coefficients is calculated.

[0065] Based on Kolmogorov's statistical theory of turbulence, a mapping relationship between the measured variance of the Zernike polynomial coefficients and the atmospheric coherence length is established. The phase residual after correction for the J-term Zernike polynomial given by Fried is shown below: After removing the translation term, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is: ; After removing the translation and tilt terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; After removing the translation, tilt, and defocus terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; After removing translation, tilt, defocus, and astigmatism terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; in, Indicates the diameter of the sub-aperture; Indicates the length of atmospheric coherence; This represents the mean squared error of the wavefront residuals after removing the translation term; This represents the mean squared error of the wavefront residuals after removing translation and tilt. This represents the mean square error of the wavefront residuals after removing translation, tilt, and defocusing. This represents the mean squared error of the wavefront residuals after removing translation, tilt, defocus, and astigmatism.

[0066] Substitute the measured variances of low-order Zernike coefficients obtained from actual measurements, such as the defocus term coefficient, astigmatism term coefficient, and so on, into the residual relationship after removing translation, tilt, and defocus. The atmospheric coherence length can then be obtained by inversion. .

[0067] The atmospheric coherence length obtained by inversion is the atmospheric coherence length value of the horizontal link, which characterizes the turbulence intensity of the horizontal transmission link and can be used as a communication link quality evaluation index for free-space optical communication systems.

[0068] The technical solution of this application abandons the traditional approach of relying on point targets or actively emitting beacon light, and directly uses existing extended targets in the scene as signal sources to measure atmospheric coherence length. The architecture does not require additional auxiliary calibration equipment such as laser guides and atmospheric turbulence profile radar, which significantly reduces system complexity and hardware costs, and improves the system's environmental adaptability.

[0069] The technical solution of this application, in the extended target offset estimation, adopts an improved squared difference and correlation algorithm instead of the traditional normalized cross-correlation algorithm. By introducing a spatially adaptive weight function based on local gradients, the matching contribution of high gradient regions is enhanced and edge noise is suppressed. At the same time, the squared difference operation can be directly mapped to hardware multiplication instructions, avoiding the division and square root operations in the normalized cross-correlation, significantly reducing computational complexity and improving processing efficiency.

[0070] The technical solution of this application adopts a coarse-to-fine offset estimation strategy. First, an initial offset estimate at the integer pixel level is obtained through an improved squared difference and correlation algorithm. Then, using this estimate as the initial value, a sub-pixel fine search is performed using the HS optical flow algorithm to finally obtain a high-precision offset estimation result.

[0071] The technical solution of this application uses a Shaker-Hartmann wavefront sensor as the core detection device. It extracts the wavefront slope within each sub-aperture using an extended target migration algorithm and reconstructs the wavefront phase using the Zernike mode method. The solution utilizes the theoretical relationship between the Zernike coefficient variance and atmospheric coherence length to achieve the inversion calculation of atmospheric coherence length. Compared to the traditional DIMM method, this simplifies the data processing flow and improves measurement efficiency.

[0072] The technical solution of this application embodiment can directly reuse the existing Shak-Hartmann wavefront sensor in the free-space optical communication system to complete the measurement of atmospheric coherence length in parallel without adding additional hardware. This implementation achieves an integrated design of turbulence intensity measurement and wavefront correction functions, avoiding functional overlap and hardware redundancy, and reducing the overall system cost.

[0073] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0074] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for measuring the atmospheric coherence length in horizontal turbulence, characterized in that, Includes the following steps: The reflected light signal from the extended target in the horizontal link is acquired, and the reflected light signal is converged and segmented into a sub-aperture image array; Using the image of the central sub-aperture of the sub-aperture image array as a reference image, a two-stage offset estimation strategy from coarse to fine is adopted to obtain the accurate offset of each sub-aperture. The wavefront slope is calculated based on the precise offset, and the wavefront is restored using the Zernik mode method to generate the Zernik polynomial coefficients of the incident wavefront. The measured variance of the lower-order terms in the Zernike polynomial coefficients is statistically analyzed. Combined with the mapping relationship between variance and atmospheric coherence length established by Kolmogorov turbulence statistical theory, the atmospheric coherence length of the horizontal link is obtained by inversion. The coarse-to-fine two-stage offset estimation strategy includes: a coarse estimation stage and a fine estimation stage; The coarse estimation stage employs an improved sum of squared differences criterion algorithm to calculate the correlation response between each sub-aperture image and the reference image. The feature matching degree is determined based on the sum of squared differences and correlation response values, and the offset corresponding to the feature matching peak is used as the initial estimated value of the offset. The fine estimation stage uses the initial estimated value of the offset as the initial condition of the optical flow field, constructs the optical flow energy functional, and iteratively solves it using the HS optical flow algorithm to generate the offset correction value. The initial offset estimate is superimposed with the offset correction value to obtain the precise offset of each sub-aperture.

2. The measurement method according to claim 1, characterized in that, The extended target is a natural or artificial target with spatial structure information, and the spatial grayscale distribution of the extended target is used as the information source for wavefront detection.

3. The measurement method according to claim 1, characterized in that, Based on the improved sum of squared differences criterion algorithm, when calculating the correlation response between each sub-aperture image and the reference image, a spatially adaptive weighting function based on local gradients is introduced to weight the matching process.

4. The measurement method according to claim 3, characterized in that, The spatial adaptive weighting function includes: a first term and a second term; The first item is the local gradient magnitude of the reference image, which is used to enhance the matching contribution of high gradient regions in the reference image; The second term is a Gaussian kernel function multiplied by a balance factor. The Gaussian kernel function takes the geometric center of the reference image as its origin and is used to suppress edge noise. The balance factor is used to balance the weight relationship between the first term and the second term.

5. The measurement method according to claim 1, characterized in that, The HS optical flow algorithm includes the following steps: Construct an optical flow energy functional that includes data consistency constraints and smoothness constraints; The Euler-Lagrange equations were derived from the optical flow energy functional using the variational method. The Euler-Lagrange equations are solved iteratively using the Gauss-Seidel iterative method. In each iteration, the optical flow field components of the current iteration are updated using the local neighborhood average of the horizontal component and the local neighborhood average of the vertical component. After iterative convergence, the horizontal and vertical components of the output optical flow field are used as the offset correction values.

6. The measurement method according to claim 1, characterized in that, Obtaining the precise offset of each sub-aperture includes the following steps: The initial estimate of the offset is taken as an integer pixel-level offset; The offset correction value is used as a sub-pixel level offset; The integer pixel-level offset is superimposed with the sub-pixel-level offset; The output superposition result serves as the precise offset for each sub-aperture.

7. The measurement method according to claim 1, characterized in that, The step of calculating the wavefront slope based on the precise offset and reconstructing the wavefront using the Zernik model method to generate the Zernik polynomial coefficients of the incident wavefront includes the following steps: The precise offset of each sub-aperture is converted into the wavefront slope of that sub-aperture; Collect the wavefront slopes of all sub-apertures to form a wavefront slope vector; The Zernike model method is used to perform wavefront reconstruction with the wavefront slope vector as input data. The restored wavefront phase is expanded into a multinomial Zernik polynomial; Extract the coefficients of each order of Zernike polynomial to generate the Zernike polynomial coefficients of the incident wavefront.

8. The measurement method according to claim 1, characterized in that, The measured variance of the lower-order terms in the Zernike polynomial coefficients, combined with the mapping relationship between variance and atmospheric coherence length established by Kolmogorov turbulence statistical theory, is used to invert the atmospheric coherence length of the horizontal link, which includes the following steps: Extract the coefficients of lower-order terms from the Zernik polynomial coefficients; The lower-order coefficients include the defocused Zernike polynomial coefficients and the astigmatic Zernike polynomial coefficients. The measured variance of the coefficients of the lower-order terms is calculated. Based on Kolmogorov's statistical theory of turbulence, a mapping relationship between the measured variance of Zernike polynomial coefficients and the atmospheric coherence length is established. The mapping relationship is that the measured variance of the Zernike polynomial coefficients is proportional to the negative fifth power of the atmospheric coherence length, and the proportionality coefficient is determined by the sub-aperture diameter of the Shaker-Hartmann wavefront sensor. Substituting the measured variance into the mapping relationship, the atmospheric coherence length of the horizontal link is obtained by inversion calculation.

9. The measurement method according to claim 8, characterized in that, The mapping relationship between the measured variance and atmospheric coherence length established by the Kolmogorov turbulence statistical theory includes at least one of the following: After removing the translation term, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is: ; After removing the translation and tilt terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; After removing the translation, tilt, and defocus terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; After removing translation, tilt, defocus, and astigmatism terms, the expression for the relationship between the variance of the Zernike polynomial coefficients and the atmospheric coherence length is as follows: ; in, This indicates the sub-aperture diameter of the Shaker-Hartmann wavefront sensor; Indicates the length of atmospheric coherence; This represents the mean squared error of the wavefront residuals after removing the translation term; This represents the mean squared error of the wavefront residuals after removing translation and tilt. This represents the mean square error of the wavefront residuals after removing translation, tilt, and defocusing. This represents the mean square error of the wavefront residuals after removing translation, tilt, defocus, and astigmatism.

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