Multipath atmospheric coherence length measurement method and system for satellite-to-ground laser communication

Abstract

The present invention discloses a multi-path atmospheric coherence length measurement method and system for satellite-to-ground laser communication. The system consists of a binocular image acquisition module, a control module, a data processing module, and a storage module. The binocular image acquisition module is used to acquire paired star spot images, the control module is used to control the binocular image acquisition module to effectively acquire images, the data processing module is used to extract the centroid of the star spot from the two frames of synchronously acquired images, and use the differential image motion method to calculate the atmospheric optical turbulence intensity on the path where the spot is located; the storage module saves the data results. In the specific measurement method, the photon flux density method is used to calculate the detection capability of the measurement system; the number of detectable star spots and their probability are determined based on the field of view of the equipment; the optical flow method is used to realize the estimation of pixel motion and the tracking of star point trajectories; the atmospheric coherence length and seeing are calculated based on the variance of the centroid motion of the star spot, revealing the intensity of atmospheric optical turbulence at different positions.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite-to-ground laser communication, and in particular to a multi-path atmospheric coherence length measurement method and system for satellite-to-ground laser communication. Background Art

[0002] Satellite-to-ground laser communication is a key link in the integration of space and ground. In atmospheric optical turbulence, the atmospheric refractive index structure constant is usually used. To characterize turbulence intensity, the distribution of atmospheric turbulence exhibits a vertical structure. In astronomical observations, the atmospheric coherence length (ACL) is often used to describe turbulence intensity along an entire path. In the 1990s, Sarazin and F. Roddier proposed the concept of the Differential Image Motion Monitor (DIMM). Tokovinin further refined this technique in 2002, calculating the Fried parameter, also known as the ACL, from the measured variance of image motion. The DIMM is based on a 250-300mm telescope equipped with two subapertures and a prism, providing two images of the same star. It can capture and analyze the motion of the stellar image caused by atmospheric disturbances and calculate the ACL. Miratlas, a French company, has developed a new device, the C-DIMM, that uses two fixed-spaced, small-field-of-view telescopes to simultaneously capture stellar light spots to measure the ACL. However, this device only observes the path of a single star and is suitable for ground station site selection.

[0003] During satellite-to-ground laser communications, medium and low-orbit satellites will traverse different spaces during their movement, and the performance of the satellite-to-ground laser link will be affected by changes in the intensity of atmospheric optical turbulence along the way. Although the observation results obtained by the single-point observation method of atmospheric optical turbulence are relatively mature, due to the small coverage of traditional atmospheric coherence length observations, it is impossible to obtain multi-path atmospheric coherence length observations. Observations are limited to stellar positions, and the single-point data obtained by observing stars differs from the turbulence intensity at surrounding locations. The actual position of the satellite is offset from the observation point, and the correlation between the atmospheric optical turbulence intensity at different locations at the same time is unclear. Currently, there is a lack of low-cost, high-resolution visible light atmospheric channel transmission condition perception methods with a large field of view. Researchers have not yet proposed a multi-path atmospheric coherence length measurement system for satellite-to-ground laser communications. Therefore, it is necessary to measure multi-path stellar light spots and calculate the atmospheric coherence length to lay the foundation for predicting the satellite laser link communication window.

[0004] Chinese patent application number CN202210996124.4 discloses a method and application for visualizing the spatiotemporal distribution of atmospheric optical turbulence parameters. The application discloses the use of computer software to visualize the atmospheric optical turbulence intensity profile and its integral parameters, obtaining a spatiotemporal distribution map of the atmospheric optical turbulence intensity profile and its integral parameters. However, the spatial resolution accuracy is insufficient, and the local atmospheric channel transmission parameters are not measured. The present invention overcomes this problem. The multipath atmospheric coherence length measurement system can be deployed around ground stations to achieve real-time observation.

[0005] Chinese patent application number CN202410061877.5 discloses a method and system for measuring the atmospheric coherence length of a satellite optical transmission path. The application discloses using a DIMM to aim and track a target satellite to measure the atmospheric turbulence intensity of the satellite's optical transmission path. However, not all transiting low-orbit satellites can provide a light source for tracking. The multi-path atmospheric coherence length measurement system of the present invention obtains the atmospheric coherence length by observing stars along multiple paths, overcoming the limitation that a light source must be provided on the satellite.

[0006] Chinese patent application number CN202411675121.6 discloses a method for measuring whole-layer atmospheric turbulence based on centroid drift and light intensity scintillation. The application discloses the measurement of whole-layer atmospheric turbulence intensity, and the obtained atmospheric turbulence intensity parameter is the equivalent mean value of the atmospheric refractive index structure constant. However, the atmospheric refractive index structure constant has a vertical distribution characteristic. In view of this, the present invention provides a multipath atmospheric coherence length measurement, which can more accurately characterize the impact of atmospheric turbulence on the transmission quality of satellite-to-ground laser communication links. Summary of the Invention

[0007] The purpose of the present invention is to propose a multipath atmospheric coherence length measurement method and system for satellite-to-ground laser communications. This method addresses the limited coverage of existing atmospheric optical turbulence observations and the inability to obtain multipath atmospheric coherence lengths, thereby enabling the measurement of atmospheric turbulence intensity in satellite-to-ground laser communications. The present invention first uses the photon flux density method to calculate the detection capability of the multipath atmospheric coherence length measurement system. Then, a dense constellation within a fixed zenith angle range is selected as the observation area, the angular distances between the stars to be observed are calculated, and the number and probability of detectable star spots are determined based on the field of view of the device. Next, the optical flow method is used to estimate pixel motion and track star point trajectories. Finally, the atmospheric coherence length is calculated based on the center of mass motion variance, revealing the intensity of atmospheric optical turbulence at different locations. The present invention calculates the detection capability using the photon flux density method, selects a dense constellation within a fixed zenith angle range as the observation area, calculates the angular distances between stars, and determines the number and probability of detectable star spots. The optical flow method is used to realize pixel motion estimation and star point trajectory tracking, and the atmospheric coherence length is calculated based on the center of mass motion variance, revealing the intensity changes of atmospheric optical turbulence at different locations, laying the foundation for satellite laser link communication window prediction, optimizing link planning and improving communication reliability. It is crucial for judging the atmospheric channel quality in satellite-to-ground laser communication links, and also provides a scientific basis for link planning in satellite-to-ground laser communication.

[0008] The above purpose is achieved through the following technical solutions:

[0009] The present invention first provides a multi-path atmospheric coherence length measurement system for satellite-to-ground laser communication, which includes: a binocular image acquisition module, a control module, a data processing module, and a storage module, wherein:

[0010] The binocular image acquisition module is used to collect paired star spot images at different positions;

[0011] The control module is used to control the binocular image acquisition module to effectively acquire star spot images; through the preset exposure time, acquisition frequency and signal gain, the binocular image acquisition module is controlled to synchronously acquire star spots according to the selected observation area;

[0012] The data processing module is used to extract the centroid of the star spot from the two synchronously collected images and calculate the centroid of the star spot using the differential image motion method to obtain the atmospheric coherence length and seeing parameters along the path of the star spot.

[0013] The storage module is used to store the collected star spot images and calculated data results;

[0014] The binocular image acquisition module, control module, data processing module and storage module work together; according to the set exposure time, acquisition frame rate and signal gain, a set of images including the centroid of the star spot, atmospheric coherence length and seeing are output at each interval.

[0015] Furthermore, the binocular image acquisition module includes two visible light industrial cameras, lenses, a housing and a high-speed data interface; the visible light industrial cameras are installed inside the housing, and the distance between the two cameras must be greater than or equal to twice the lens aperture, and the cameras have independent image sensors; the housing meets IP67 waterproof requirements and is equipped with a high-speed data interface; the binocular image acquisition module registers a callback function for the data stream of each camera, which is used to process the image data immediately after it is captured.

[0016] The present invention also provides a multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication. The method operates the multi-path atmospheric coherence length measurement system for satellite-to-ground laser communication, and the specific steps include:

[0017] S1. Ensure that the binocular image acquisition module can observe star spots in the field of view of the measurement system at a short exposure time. Record the required short exposure time and the signal gain of the visible light industrial camera in the binocular image acquisition module.

[0018] S2. Select a dense constellation within a fixed zenith angle range as the observation area for the binocular image acquisition module, calculate the angular distance between the stars to be observed, and determine the number and probability of detectable star spots based on the field of view of the binocular image acquisition module;

[0019] S3. The control module sets the exposure time and signal gain parameters of the measurement system based on the short exposure time required to ensure that star spots can be observed in the field of view of the measurement system and the signal gain of the visible light industrial camera in step S1. It also sets the acquisition frame rate of the binocular image acquisition module and the output time parameter values ​​of the data processing module. Within the observation area described in step S2, the control module acquires star spots, estimates the pixel motion of the star spots, and tracks the star point trajectory.

[0020] S4. The data processing module calculates the center-of-mass motion variance based on the star spots collected in step S3, and calculates the atmospheric coherence length and seeing from the center-of-mass motion variance, revealing the intensity of atmospheric optical turbulence at different locations.

[0021] Furthermore, the specific process of step S1 is as follows:

[0022] Adjust the exposure time and signal gain until the binocular image acquisition module can successfully detect the star spot, freeze the atmospheric turbulence under short exposure time, realize the measurement of multi-path atmospheric coherence length, and make the signal-to-noise ratio of the optical signal Able to exceed the detectable signal-to-noise ratio threshold SNR γ , target signal photoelectron number n T and background noise photoelectron number n B for:

[0023]

[0024] Where S area is the receiving area of ​​the multipath atmospheric coherence length measurement system, τ fT and τ fB are the transmittance coefficients of the multipath atmospheric coherence length measurement system for the target signal spectrum and the background noise spectrum, q T and q B are the average quantum efficiencies of the reference signal and background noise, τ0 is the transmittance of the optical system, α u is the spatial solid angle corresponding to a pixel, the relationship between the full pixel spatial solid angle Ω and the zenith angle θ and the field angle φ is dΩ=sinθ·dθ·dφ, t is the exposure time, K T is the number of pixels occupied by star imaging, φ B is the photon flux density of background light per unit solid angle, and the photon flux density of star spot is φ T for:

[0025]

[0026] Where m S is the magnitude, λ is the wavelength, h is the Planck constant, and c is the speed of light. In formula (2), the photon flux density M of the background light per unit solid angle at night is λ (T) is:

[0027]

[0028] Where K is the Boltzmann constant, T temp is the thermodynamic temperature;

[0029] Background light photon flux density φ B for:

[0030]

[0031] Where, I B The background light intensity of the night sky;

[0032] Substituting equations (2), (3) and (4) into equation (1), we can obtain the target signal photoelectron number n: T and background noise photoelectrons n B :

[0033]

[0034] When the signal-to-noise ratio When , the star spots can be detected:

[0035]

[0036] Furthermore, the specific process of step S2 is as follows:

[0037] S2.1 First, it is necessary to clarify the field of view size of the measurement system. The field of view HFOV of the multipath atmospheric coherence length measurement system M-DIMM and focal length f M-DIMM The relationship with the detector's photosensitive area is:

[0038]

[0039] Where, d M-DIMM is the horizontal width of the visible light camera target surface, h M-DIMM is the vertical width of the visible light camera target surface; after the detectable field size is determined, the angular distance between the stars to be measured is calculated to determine the corresponding field of view requirements. Assume that the right ascension and declination coordinates of stars A and B in the celestial coordinate system are (α A , β A )、(α B , β B ), then their corresponding unit direction vectors in the celestial coordinate system are They are:

[0040]

[0041] S2.2 If the angular distance between the observed stars is smaller than the field of view of the observation device, then both stars can be observed simultaneously. Based on the unit direction vector, the angular distance d between stars A and B in the celestial coordinate system can be calculated. c (A, B) is:

[0042]

[0043] The multi-path atmospheric coherence length measurement system is used to conduct synchronous observations at space locations to reflect the influence of atmospheric turbulence on the satellite-to-ground laser link. The average number of stars provided by the star catalogue, N(M v ) and magnitude M v The relationship function is:

[0044]

[0045] The number of detectable stars in the equivalent field of view is:

[0046]

[0047] Where θ FOVis the equivalent field of view, N FOV represents the field of view θ FOV The average number of stars in the corresponding area, N(M Vmax ) is the magnitude of the star in the entire sky less than or equal to M v When setting the resolution, pixel size, focal length, and field angle of the multi-path atmospheric coherence length measurement system, the number of stars with a brightness exceeding third magnitude that can be detected is n mag .

[0048] S2.3 After the detectable limit magnitude, number of stars, and field of view are determined, the probability P of detecting N stars is further clarified. M-DIMM for:

[0049]

[0050] Each star spot represents the spatial location of an observation, and its spatial distribution reflects the estimated distribution of turbulence on that plane.

[0051] Furthermore, the specific process of step S3 is as follows:

[0052] S3.1 Set the exposure time and signal gain parameters of the measurement system based on the short exposure time required to ensure that the star spots can be observed in the field of view of the measurement system and the signal gain of the visible light industrial camera in step S1, and set the acquisition frame rate of the measurement system and the output time parameter of the data processing module;

[0053] S3.2 uses an equatorial mount to precisely point to a selected star cluster, and then uses the optical flow method to track the position changes of star points in continuously collected multi-frame star maps:

[0054] I x u speed +I y v speed +I t =0 (13),

[0055] Where, the optical flow u speed Represents the moving speed in the x direction, optical flow v speed Represents the moving speed in the y direction. In the Cartesian coordinate system, the x-axis and y-axis represent the horizontal and vertical directions on the image plane, and the z-axis represents the change of the grayscale value of the spot in the depth direction; Represents the gradient of the light spot brightness in the x-axis direction in the image plane, Represents the gradient of the light spot brightness in the y-axis direction in the image plane, is the partial derivative on the z-axis;

[0056] S3.3 calculates the optical flow field between adjacent frames, that is, the speed change of pixels; the observation data constitutes the Q matrix, and the optical flow speed vector is x speed, the time gradient of the image is b:

[0057]

[0058] Where, I x (p i ) and I y (p i ) is the pixel p i The brightness gradient of the light spot in the x and y directions, because we need to obtain the star light spot within 6×6 pixels, i=1, 2, ..., 36, I t (p i ) is at pixel p i To track and analyze the light spot, we only need to find a set of velocity parameters [u s v S ], that is, the system of equations The required spot movement speed is to minimize the following expression:

[0059]

[0060] The optical flow problem of spot tracking in S3.4 involves local nonlinear optimization. The least squares solution is obtained by pseudo-inverse method. The value of the point where the derivative is 0 is the optimal value. The symbol T represents the transpose of the matrix. speed =(Q T Q) -1 Q T b finds the partial derivative:

[0061]

[0062] The optical flow method is used to track the position changes of multiple star spots in multiple frames of images. Let the size of the star map be m×n, f(x i ,y j ) is the gray value of the CCD pixel, x i and y j For the horizontal and vertical coordinates corresponding to each pixel, the coordinates of the center of mass of the light spot p are (x, y), and the coordinates of the center of mass of the light spot are updated from p(x, y) to p′(x′, y′):

[0063]

[0064] Save the multipath atmospheric coherence length measurement system camera M DIMM-1 Multi-position data (x1, y1)(x2, y2)...(x m ,y m ), and camera M DIMM-2 At the same time, multiple position data (q1, w1), (q2, w2)... (q m , wm ), the measurement system synchronously collects data at M different times for the calculation of atmospheric coherence length and seeing.

[0065] Furthermore, the specific process of step S4 is as follows:

[0066] S4.1 At the ground receiving end, the focus is on the impact of arrival angle fluctuation on the optical system, ignoring the impact of amplitude; the covariance of the phase can be obtained from the covariance of the arrival angle fluctuation and the phase structure function, and then the motion variance of the two spots in the horizontal and vertical directions can be further calculated, and the wavefront z (x tur ,y tur ) and wavefront phase error φ(x tur ,y tur ), The arrival angle fluctuation component α(x tur ,y tur )for:

[0067]

[0068] Covariance B of arrival angle fluctuation α (ξ,η)=<α <x tur ,y tur ), α(x tur +ξ,y tur +η)>, the phase structure function is introduced as:

[0069] D φ (ξ,η)=2[B φ (0,0)-B φ (ξ,η)] (19),

[0070] Where D φ (ξ, η) represents the phase structure function, which is used to describe the difference between the phase fluctuations at two points (0, 0) and (ξ, η) in space. φ (0, 0) represents the value of the covariance function of the bit fluctuation at the origin, B φ (ξ, η) represents the value of the covariance function of the phase fluctuation at the point (ξ, η), ξ represents the horizontal distance, and η represents the vertical distance;

[0071] S4.2 approximation for Kolmogorov turbulence, the phase structure function is given by Indicates that the covariance B of the phase fluctuation a (ξ,η) is:

[0072]

[0073] Among them, r o represents the atmospheric coherence length, represents the Euclidean distance from the origin. Based on the centroid of the star spot observed by the multipath atmospheric coherence length measurement system, let η = 0 to obtain the longitudinal covariance; let ξ = 0 to obtain the transverse covariance, so as to further calculate the atmospheric coherence length;

[0074] S4.3 The aperture spacing between two cameras in the multipath atmospheric coherence length measurement system is L, the aperture diameter is D, and the ratio of the aperture spacing to the aperture diameter is When S M-DIMM When the S is 6.5 to 7, the consistency is the best. M-DIMM When the value is σ, the consistency will decrease; 2 (L) = 2[B(0) - B(L)] is the variance of the differential image motion. The values ​​in the horizontal and vertical directions can be used to obtain the value of any position (x i , x j ) at atmospheric coherence length r i，j , in centimeters:

[0075]

[0076] Where λ is the wavelength and θ″ is the seeing (FWHM_i，j) By r i，j The value is calculated using the following formula:

[0077]

[0078] The storage module saves the calculation results output by the data processing module at fixed time intervals, with a typical time interval of 1 minute. The calculation results include the coordinates of the center of mass of the light spot, the atmospheric coherence length, and the seeing.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] This method utilizes starlight imaging technology to monitor the transmission characteristics of atmospheric channels in real time, thereby accurately determining the communication window of satellite laser communication links and enhancing the stability and reliability of satellite-to-ground laser communication links. This method overcomes the limitation of traditional differential imaging motion monitors, which can only observe the atmospheric optical turbulence intensity along a single path. Its design is more flexible, eliminating the need for multiple devices to achieve differential imaging and enabling simultaneous observation of multiple stars, ensuring measurement accuracy and enhancing ease of use. The multipath atmospheric coherence length measurement system for satellite-to-ground laser communication utilizes a box-type design, offering enhanced sealing, a simple structure, high cost-effectiveness, and IP67-rated waterproof and dustproof properties, making it particularly suitable for outdoor deployment. This system is not only crucial for acquiring astronomical observation data but also provides a solid foundation for studying the spatial distribution of atmospheric coherence length. Furthermore, the system effectively addresses the discrepancy between the actual satellite position and the observation point, performing spatial interpolation to obtain the atmospheric optical turbulence intensity along different paths. This facilitates link selection for satellite-to-ground laser communication and promotes the realization of efficient and reliable satellite-to-ground laser communication networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a flow chart of the multi-path atmospheric coherence length measurement method based on satellite-to-ground laser communication of the present invention;

[0082] Figure 2 This is a flowchart of the dual-camera SDK of the present invention for synchronous acquisition to calculate measurement parameters;

[0083] Figure 3 A schematic diagram of a method for measuring multi-path atmospheric coherence length in satellite-to-ground laser communications according to the present invention;

[0084] Figure 4 A grayscale schematic diagram of the optical flow method of the present invention for achieving star spot tracking;

[0085] Figure 5 Schematic diagram of realizing multi-frame star tracking using the optical flow method of the present invention: Figure 5 (a) is a schematic diagram of the first group of star point tracking; Figure 5 (b) Schematic diagram of the second set of star point tracking;

[0086] Figure 6 This is a schematic diagram of multiple star acquisition by the multi-path atmospheric coherence length measurement system of the present invention. Figure 6 (a) is a schematic diagram of two stars. Figure 6 (b) is a schematic diagram of three stars. DETAILED DESCRIPTION

[0087] The technical solutions are clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. It should be noted that the embodiments represent only a part of the present invention and are not the entire content. Other embodiments obtained by ordinary technicians based on these embodiments without innovative work are all within the scope of protection of the present invention.

[0088] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0089] Figure 1 A flow chart of a multi-path atmospheric coherence length measurement method for satellite-to-ground laser communications provided by an embodiment of the present invention includes: first, the detection capability of the measurement system is calculated using the photon flux density method through a binocular image acquisition module to determine whether star spots can be observed in the field of view of the measurement system; then, the control module selects a dense constellation within a fixed zenith angle range as the observation area, and determines the number and probability of detectable star spots based on the field of view of the device; then, based on the sky area determined by the equatorial mount pointing, the optical flow method is used to estimate pixel motion and track star point trajectories, and synchronize the acquisition of the multi-path atmospheric coherence length measurement system; the data processing module calculates the center of mass motion variance based on the collected star spots, and calculates the atmospheric coherence length and seeing from the motion variance, revealing the intensity of atmospheric optical turbulence on different paths; finally, the storage module saves the collected star spot images and the calculated data results;

[0090] The present invention provides a multi-path atmospheric coherence length measurement system for satellite-to-ground laser communication, comprising a binocular image acquisition module, a control module, a data processing module, and a storage module, wherein:

[0091] The binocular image acquisition module is used to collect paired star spot images at different positions;

[0092] The control module is used to control the binocular image acquisition module to effectively acquire star spot images; through the preset exposure time, acquisition frequency and signal gain, the binocular image acquisition module is controlled to synchronously acquire star spots according to the selected observation area;

[0093] The data processing module is used to extract the centroid of the star spot from the two synchronously collected images and calculate the centroid of the star spot using the differential image motion method to obtain the atmospheric coherence length and seeing parameters along the path of the star spot.

[0094] The storage module is used to store the collected star spot images and calculated data results;

[0095] The binocular image acquisition module, control module, data processing module and storage module work together; according to the set exposure time, acquisition frame rate and signal gain, a set of images including the centroid of the star spot, atmospheric coherence length and seeing are output at each interval.

[0096] The binocular image acquisition module in this embodiment includes two visible light industrial cameras, lenses, a housing, and a high-speed data interface. The visible light industrial cameras are installed inside the housing, and the distance between the two cameras must be greater than or equal to twice the lens aperture. The cameras have independent image sensors. The housing meets IP67 waterproof requirements and is equipped with a high-speed data interface. The binocular image acquisition module registers a callback function for the data stream of each camera for immediate data processing after image data is captured.

[0097] The present invention provides a multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication, which is run on the multi-path atmospheric coherence length measurement system for satellite-to-ground laser communication. The specific steps include:

[0098] S1. Ensure that the binocular image acquisition module can observe star spots in the field of view of the measurement system at a short exposure time. Record the required short exposure time and the signal gain of the visible light industrial camera in the binocular image acquisition module.

[0099] S2. Select a dense constellation within a fixed zenith angle range as the observation area for the binocular image acquisition module, calculate the angular distance between the stars to be observed, and determine the number and probability of detectable star spots based on the field of view of the binocular image acquisition module;

[0100] S3. The control module sets the exposure time and signal gain parameters of the measurement system based on the short exposure time required to ensure that star spots can be observed in the field of view of the measurement system and the signal gain of the visible light industrial camera in step S1. It also sets the acquisition frame rate of the binocular image acquisition module and the output time parameter values ​​of the data processing module. Within the observation area described in step S2, the control module acquires star spots, estimates the pixel motion of the star spots, and tracks the star point trajectory.

[0101] S4. The data processing module calculates the center-of-mass motion variance based on the star spots collected in step S3, and calculates the atmospheric coherence length and seeing from the center-of-mass motion variance, revealing the intensity of atmospheric optical turbulence at different locations.

[0102] Step S1, specifically implementing the steps include:

[0103] Adjust the exposure time and signal gain until the binocular image acquisition module can successfully detect the star spot, freeze the atmospheric turbulence under short exposure time, realize the measurement of multi-path atmospheric coherence length, and make the signal-to-noise ratio of the optical signal Able to exceed the detectable signal-to-noise ratio threshold SNR γ , target signal photoelectron number n T and background noise photoelectron number n B for:

[0104]

[0105] Where S area is the receiving area of ​​the multipath atmospheric coherence length measurement system, τ fT and τ fB are the transmittance coefficients of the multipath atmospheric coherence length measurement system for the target signal spectrum and the background noise spectrum, q T and q B are the average quantum efficiencies of the reference signal and background noise, τ0 is the transmittance of the optical system, α u is the spatial solid angle corresponding to a pixel, the relationship between the full pixel spatial solid angle Ω and the zenith angle θ and the field angle φ is dΩ=sinθdθdφ, t is the exposure time, K T is the number of pixels occupied by star imaging, φ B is the photon flux density of background light per unit solid angle, and the photon flux density of star spot is φ T for:

[0106]

[0107] Where m S is the magnitude, λ is the wavelength, h is the Planck constant, and c is the speed of light. In formula (2), the photon flux density M of the background light per unit solid angle at night is λ (T) is:

[0108]

[0109] Where K is the Boltzmann constant, T temp is the thermodynamic temperature;

[0110] Background light photon flux density φ B for:

[0111]

[0112] Where, I B The background light intensity of the night sky;

[0113] Substituting equations (2), (3) and (4) into equation (1), we can obtain the target signal photoelectron number n: T and background noise photoelectrons n B :

[0114]

[0115] When the signal-to-noise ratio When , the star spots can be detected:

[0116]

[0117] The multi-path atmospheric coherence length measurement system proposed in the present invention takes spatial position into consideration. On the basis of detecting star spots, it is necessary to further clarify the number of observable star spots within the equivalent field of view to ensure the accuracy and reliability of the measurement results. Table 1 shows the meteorological observation simulation parameter table.

[0118] Table 1 Meteorological observation simulation parameters

[0119]

[0120] Step S2, specifically implementing the steps include:

[0121] S2.1 First, it is necessary to clarify the field of view size of the measurement system. The field of view HFOV of the multipath atmospheric coherence length measurement system M-DIMM and focal length f M-DIMM The relationship with the detector's photosensitive area is:

[0122]

[0123] Where, d M-DIMM is the horizontal width of the visible light camera target surface, h M-DIMM is the vertical width of the visible light camera target surface; after the detectable field size is determined, the angular distance between the stars to be measured is calculated to determine the corresponding field of view requirements. Assume that the right ascension and declination coordinates of stars A and B in the celestial coordinate system are (α A , β A )、(α B , β B ), then their corresponding unit direction vectors in the celestial coordinate system are They are:

[0124]

[0125] S2.2 If the angular distance between the observed stars is smaller than the field of view of the observation device, then both stars can be observed simultaneously. Based on the unit direction vector, the angular distance d between stars A and B in the celestial coordinate system can be calculated. c (A, B) is:

[0126]

[0127] The multi-path atmospheric coherence length measurement system is used to conduct synchronous observations at space locations to reflect the influence of atmospheric turbulence on the satellite-to-ground laser link. The average number of stars provided by the star catalogue, N(M v) and magnitude M v The relationship function is:

[0128]

[0129] The number of detectable stars in the equivalent field of view is:

[0130]

[0131] Where θ FOV is the equivalent field of view, N FOV represents the field of view θ FOV The average number of stars in the corresponding area, N(M Vmax ) is the magnitude of the star in the entire sky less than or equal to M v When setting the resolution, pixel size, focal length, and field angle of the multi-path atmospheric coherence length measurement system, the number of stars with a brightness exceeding third magnitude that can be detected is n mag ;

[0132] S2.3 After the detectable limit magnitude, number of stars, and field of view are determined, the probability P of detecting N stars is further clarified. M-DIMM for:

[0133]

[0134] Each star spot represents the spatial location of an observation, and its spatial distribution reflects the estimated distribution of turbulence on that plane.

[0135] Figure 2 This is a flowchart for the dual-camera SDK synchronous acquisition to calculate measurement parameters. The process begins by obtaining a list of currently connected devices, checking and opening both cameras. Synchronously controlling parameters, including camera exposure time and trigger mode, obtains the camera data streams. An empty list is initialized for each camera to store centroid data. A callback function is registered for each camera's data stream to process the captured image data. The camera acquisition process is initiated, triggering acquisition every 10ms. The centroid data is saved to a file, and the atmospheric coherence length and seeing are calculated, with the calculated values ​​written to the file.

[0136] Each star spot represents the spatial location of an observation, and its spatial distribution reflects the estimated distribution of turbulence on that plane. By using meteorological observation equipment to conduct spatially distributed, synchronous observations of optical turbulence throughout the atmosphere, multiple star observations were performed to reflect the impact of atmospheric turbulence on the satellite-to-ground laser link. It is necessary to calculate the angular resolution of Capella (magnitude 0.24) and Epsilon Aurigae (magnitude 3.14), as well as the angular resolution of Betelgeuse (magnitude 1.68), Bellatrix (magnitude 1.62), and Rigel (magnitude 2.13). Table 2 shows typical stellar parameters, which can be used to further calculate the interstellar angular distances.

[0137] Table 2 Typical star parameters

[0138]

[0139] Step S3, specifically implementing the steps include:

[0140] S3.1 Set the exposure time and signal gain parameters of the measurement system based on the short exposure time required to ensure that the star spots can be observed in the field of view of the measurement system and the signal gain of the visible light industrial camera in step S1, and set the acquisition frame rate of the measurement system and the output time parameter of the data processing module;

[0141] S3.2 uses an equatorial mount to precisely point to a selected star cluster, and then uses the optical flow method to track the position changes of star points in continuously collected multi-frame star maps:

[0142] I x u speed +I y v speed +I t =0(13),

[0143] Where, the optical flow u speed Represents the moving speed in the x direction, optical flow v speed Represents the moving speed in the y direction. In the Cartesian coordinate system, the x-axis and y-axis represent the horizontal and vertical directions on the image plane, and the z-axis represents the change of the grayscale value of the spot in the depth direction; Represents the gradient of the light spot brightness in the x-axis direction in the image plane, Represents the gradient of the light spot brightness in the y-axis direction in the image plane, is the partial derivative on the z-axis;

[0144] S3.3 calculates the optical flow field between adjacent frames, that is, the speed change of pixels; the observation data constitutes the Q matrix, and the optical flow speed vector is x speed , the time gradient of the image is b:

[0145]

[0146] Where, I x (p i ) and I y (p i ) is the pixel p i The brightness gradient of the light spot in the x and y directions, because we need to obtain the star light spot within 6×6 pixels, i=1, 2, ..., 36, I t (p i ) is at pixel p i To track and analyze the light spot, we only need to find a set of velocity parameters [u s v s ], that is, the system of equations The required spot movement speed is to minimize the following expression:

[0147]

[0148] The optical flow problem of spot tracking in S3.4 involves local nonlinear optimization. The least squares solution is obtained by pseudo-inverse method. The value of the point where the derivative is 0 is the optimal value. The symbol T represents the transpose of the matrix. speed =(Q T Q) -1 Q T b finds the partial derivative:

[0149]

[0150] The optical flow method is used to track the position changes of multiple star spots in multiple frames of images. Let the size of the star map be m×n, f(x i ,y j ) is the gray value of the CCD pixel, x i and y j For the horizontal and vertical coordinates corresponding to each pixel, the coordinates of the center of mass of the light spot p are (x, y), and the coordinates of the center of mass of the light spot are updated from p(x, y) to p′(x′, y′):

[0151]

[0152] Save the multipath atmospheric coherence length measurement system camera M DIMM-1 Multi-position data (x1, y1), (x2, y2)... (x m ,y m ), and camera M DIMM-2 At the same time, multiple position data (q1, w1), (q2, w2)... (q m , w m ), the measurement system synchronously collects data at M different times for the calculation of atmospheric coherence length and seeing.

[0153] Figure 3 This paper proposes a multipath atmospheric coherence length measurement method for satellite-to-ground laser communications. A multipath atmospheric coherence length measurement system is deployed near a ground station. This system tracks stellar light spots using the optical flow method. Using short exposure times and high frame rates, the system captures stellar light spot images, analyzes them, and calculates the lateral and longitudinal motion variance of the spot's center of mass. Ultimately, the atmospheric coherence length is calculated based on this calculated motion variance.

[0154] Figure 4 This is a grayscale diagram of the optical flow method used in this invention to track star spots. It is crucial to ensure continuous identification of the same star. The optical flow method accurately tracks star positions by analyzing pixel motion in consecutive frames. Even if some stars are invisible, the identification of other stars is not affected. This helps reduce centroid drift errors and improves star tracking accuracy.

[0155] Figure 5 This is a schematic diagram of the results of the Lucas-Kanade optical flow method used in the present invention to achieve multi-frame star tracking. When tracking stars in multiple frames, it is crucial to ensure that the same star is continuously identified. Figure 5 (a) and (b) in the figure are schematic diagrams of the movement trends of the positions of different star spots in the same star map. By analyzing the pixel movement in consecutive frames, accurate tracking of the star point positions can be achieved.

[0156] Step S4, specifically implementing the steps include:

[0157] S4.1 At the ground receiving end, the focus is on the impact of arrival angle fluctuation on the optical system, ignoring the impact of amplitude; the covariance of the phase can be obtained from the covariance of the arrival angle fluctuation and the phase structure function, and then the motion variance of the two spots in the horizontal and vertical directions can be further calculated, and the wavefront z (x tur ,y tur ) and wavefront phase error φ(x tur ,y tur ), The arrival angle fluctuation component α(x tur ,y tur )for:

[0158]

[0159] Covariance B of arrival angle fluctuation α (ξ,η)=<α(x tur ,y tur ), α(x tur +ξ,y tur +η)>, the phase structure function is introduced as:

[0160] Dφ (ξ,η)=2[B φ (0,0)-B φ (ξ,η)] (19),

[0161] Where D φ (ξ, η) represents the phase structure function, which is used to describe the difference between the phase fluctuations at two points (0, 0) and (ξ, η) in space. φ (0, 0) represents the value of the covariance function of the bit fluctuation at the origin, B φ (ξ, η) represents the value of the covariance function of the phase fluctuation at the point (ξ, n), ξ represents the horizontal distance, and η represents the vertical distance;

[0162] S4.2 approximation for Kolmogorov turbulence, the phase structure function is given by Indicates that the covariance B of the phase fluctuation a (ξ,η) is:

[0163]

[0164] Among them, r o represents the atmospheric coherence length, represents the Euclidean distance from the origin. Based on the centroid of the star spot observed by the multipath atmospheric coherence length measurement system, let η = 0 to obtain the longitudinal covariance; let ξ = 0 to obtain the transverse covariance, so as to further calculate the atmospheric coherence length;

[0165] S4.3 The aperture spacing between two cameras in the multipath atmospheric coherence length measurement system is L, the aperture diameter is D, and the ratio of the aperture spacing to the aperture diameter is When S M-DIMM When the S is 6.5 to 7, the consistency is the best. M-DIMM When the value is σ, the consistency will decrease; 2 (L) = 2[B(0) - B(L)] is the variance of the differential image motion. The values ​​in the horizontal and vertical directions can be used to obtain the value of any position (x i ,y j ) at atmospheric coherence length r i，j , in centimeters:

[0166]

[0167] Where λ is the wavelength and θ″ is the seeing (FWHM_i，j) By r i，j The value is calculated using the following formula:

[0168]

[0169] The storage module saves the calculation results output by the data processing module at fixed time intervals, with a typical time interval of 1 minute. The calculation results include the coordinates of the center of mass of the light spot, the atmospheric coherence length, and the seeing.

[0170] Figure 6 This is a schematic diagram of multiple star acquisition by the multi-path atmospheric coherence length measurement system of the present invention. Multiple stars are observed simultaneously with a 10ms exposure time. Figure 6 The distribution and angular distance of stars are marked in Figure 6 In (a), two stars can be detected. Figure 6 In (b), three stars can be detected. The collected light spot occupies more than 80% of the energy in the 3*3 pixel, which is sufficient to meet the needs of atmospheric turbulence measurement. Based on the differential image motion of the same light spot in the two cameras, the atmospheric coherence length r at different positions is obtained. i，j and seeing.

Claims

1. A multi-path atmospheric coherence length measurement system for satellite-to-ground laser communications, characterized in that: The system includes: a binocular image acquisition module, a control module, a data processing module and a storage module, wherein: The binocular image acquisition module is used to collect paired star spot images at different positions; The control module is used to control the binocular image acquisition module to effectively acquire star spot images. Through the preset exposure time, acquisition frequency and signal gain, the binocular image acquisition module is controlled to synchronously acquire star spots according to the selected observation area. Within the selected observation area, star spots are acquired and the pixel motion of the star spots is estimated and the star point trajectory is tracked. The data processing module is used to extract the centroid of the star spot from the two synchronously collected images, and calculate the centroid of the star spot using the differential image motion method to obtain the atmospheric coherence length and seeing parameter results on the path where the star spot is located; when the aperture spacing between the two cameras in the multi-path atmospheric coherence length measurement system is L, the aperture diameter is D, and the lens focal length is f, the values ​​of the differential image motion variance in the horizontal direction and the differential image motion variance in the vertical direction are used to obtain the atmospheric coherence length at any position (x i , x j ) atmospheric coherence length r i，j , in centimeters: Where λ is the wavelength and θ″ is the seeing (FWHM_i，j) By r i，j The value is calculated using the following formula: The storage module is used to store the collected star spot images and calculated data results; The binocular image acquisition module, control module, data processing module and storage module work together; according to the set exposure time, acquisition frame rate and signal gain, a set of images including the centroid of the star spot, atmospheric coherence length and seeing are output at each interval.

2. The multi-path atmospheric coherence length measurement system for satellite-to-ground laser communication according to claim 1, characterized in that: The binocular image acquisition module includes two visible light industrial cameras, lenses, a housing, and a high-speed data interface. The visible light industrial cameras are installed inside the housing, and the distance between the two cameras must be greater than or equal to twice the lens aperture. The cameras have independent image sensors. The housing meets IP67 waterproof requirements and is equipped with a high-speed data interface. The binocular image acquisition module registers a callback function for the data stream of each camera for immediate data processing after image data is captured.

3. A multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication, the method being operated on the multi-path atmospheric coherence length measurement system for satellite-to-ground laser communication according to any one of claims 1-2, characterized in that: The specific steps include: S1. Ensure that the binocular image acquisition module can observe star spots in the field of view of the measurement system at a short exposure time. Record the required short exposure time and the signal gain of the visible light industrial camera in the binocular image acquisition module. S2. Select a dense constellation within a fixed zenith angle range as the observation area for the binocular image acquisition module, calculate the angular distance between the stars to be observed, and determine the number and probability of detectable star spots based on the field of view of the binocular image acquisition module; S3. The control module sets the exposure time and signal gain parameters of the measurement system based on the short exposure time required to ensure that star spots can be observed in the field of view of the measurement system and the signal gain of the visible light industrial camera in step S1. It also sets the acquisition frame rate of the binocular image acquisition module and the output time parameter values ​​of the data processing module. Within the observation area described in step S2, the control module acquires star spots, estimates the pixel motion of the star spots, and tracks the star point trajectory. S4. The data processing module calculates the center-of-mass motion variance based on the star spots collected in step S3, and calculates the atmospheric coherence length and seeing from the center-of-mass motion variance, revealing the intensity of atmospheric optical turbulence at different locations.

4. The multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication according to claim 3, characterized in that: The specific process of step S1 is as follows: Adjust the exposure time and signal gain until the binocular image acquisition module can successfully detect the star spot, freeze the atmospheric turbulence under short exposure time, realize the measurement of multi-path atmospheric coherence length, and make the signal-to-noise ratio of the optical signal Able to exceed the detectable signal-to-noise ratio threshold SNR γ , target signal photoelectron number n T and background noise photoelectron number n B for: Where S area is the receiving area of ​​the multipath atmospheric coherence length measurement system, τ fT and τ fB are the transmittance coefficients of the multipath atmospheric coherence length measurement system for the target signal spectrum and the background noise spectrum, q T and q B are the average quantum efficiencies of the reference signal and background noise, τ0 is the transmittance of the optical system, α u is the spatial solid angle corresponding to a pixel, the relationship between the full pixel spatial solid angle Ω and the zenith angle θ and the field angle φ is dΩ=sinθ·dθ·dφ, t is the exposure time, K T is the number of pixels occupied by star imaging, φ B is the photon flux density of background light per unit solid angle, and the photon flux density of star spot φ T for: Where m S is the magnitude, λ is the wavelength, h is the Planck constant, and c is the speed of light. In formula (2), the photon flux density M of the background light per unit solid angle at night is λ (T) is: Where K is the Boltzmann constant, T temp is the thermodynamic temperature; Background light photon flux density φ B for: Where, I B The background light intensity of the night sky; Substituting equations (2), (3) and (4) into equation (1), we can obtain the target signal photoelectron number n: T and background noise photoelectrons n B : When the signal-to-noise ratio When , the star spots can be detected:

5. The multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication according to claim 3, characterized in that: The specific process of step S2 is as follows: S2.1 First, it is necessary to clarify the field of view size of the measurement system. The field of view HFOV of the multipath atmospheric coherence length measurement system M-DIMM and focal length f M-DIMM The relationship with the detector's photosensitive area is: Where, d M-DIMM is the horizontal width of the visible light camera target surface, h M-DIMM is the vertical width of the visible light camera target surface; after the detectable field size is determined, the angular distance between the stars to be measured is calculated to determine the corresponding field of view requirements. Assume that the right ascension and declination coordinates of stars A and B in the celestial coordinate system are (α A , β A )、(α B , β B ), then their corresponding unit direction vectors in the celestial coordinate system are They are: S2.2 If the angular distance between the observed stars is smaller than the field of view of the observation device, then both stars can be observed simultaneously. Based on the unit direction vector, the angular distance d between stars A and B in the celestial coordinate system can be calculated. c (A, B) is: The multi-path atmospheric coherence length measurement system is used to conduct synchronous observations at space locations to reflect the influence of atmospheric turbulence on the satellite-to-ground laser link. The average number of stars N (M v ) and magnitude M v The relationship function is: The number of detectable stars in the equivalent field of view is: Where θ FOV is the equivalent field of view, N FOV represents the field of view θ FOV The average number of stars in the corresponding area, N(M Vmax ) is the magnitude of the star in the entire sky less than or equal to M v When setting the resolution, pixel size, focal length, and field angle of the multi-path atmospheric coherence length measurement system, the number of stars with a brightness exceeding third magnitude that can be detected is n mag ; S2.3 After the detectable limit magnitude, number of stars, and field of view are determined, the probability P of detecting N stars is further clarified. M-DIMM for: Each star spot represents the spatial position of an observation value, and its spatial distribution reflects the estimated distribution of turbulence on the plane where the observation angle is located.

6. The multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication according to claim 3, characterized in that: The specific process of step S3 is as follows: S3.1 Set the exposure time and signal gain parameters of the measurement system based on the short exposure time required to ensure that the star spots can be observed in the field of view of the measurement system and the signal gain of the visible light industrial camera in step S1, and set the acquisition frame rate of the measurement system and the output time parameter of the data processing module; S3.2 uses an equatorial mount to precisely point to a selected star cluster, and then uses the optical flow method to track the position changes of star points in continuously collected multi-frame star maps: I x u speed +I y v speed +I t =0(13), Where, the optical flow u speed Represents the moving speed in the x direction, optical flow v speed Represents the moving speed in the y direction. In the Cartesian coordinate system, the x-axis and y-axis represent the horizontal and vertical directions on the image plane, and the z-axis represents the change of the grayscale value of the spot in the depth direction; Represents the gradient of the light spot brightness in the x-axis direction in the image plane, Represents the gradient of the light spot brightness in the y-axis direction in the image plane, is the partial derivative on the z-axis; S3.3 calculates the optical flow field between adjacent frames, that is, the speed change of pixels; the observation data constitutes the Q matrix, and the optical flow speed vector is x speed , the time gradient of the image is b: Where, I x (p i ) and I y (p i ) is the pixel p i The brightness gradient of the light spot in the x and y directions, because we need to obtain the star light spot within 6×6 pixels, i=1,2,...,36,I t (p i ) is at pixel p i To track and analyze the light spot, we only need to find a set of velocity parameters [u s v s ], that is, the system of equations The required spot movement speed is to minimize the following expression: The optical flow problem of spot tracking in S3.4 involves local nonlinear optimization. The least squares solution is obtained by pseudo-inverse method. The value of the point where the derivative is 0 is the optimal value. The symbol T represents the transpose of the matrix. speed =(Q T Q) -1 Q T b finds the partial derivative: The optical flow method is used to track the position changes of multiple star spots in multiple frames of images. Let the size of the star map be m×n, f(x i ,y j ) is the gray value of the CCD pixel, x i and y j For the horizontal and vertical coordinates corresponding to each pixel, the coordinates of the center of mass of the light spot p are (x, y), and the coordinates of the center of mass of the light spot are updated from p(x, y) to p′(x′, y′): Save the multipath atmospheric coherence length measurement system camera M DIMM-1 Multi-position data (x1, y1), (x2, y2)... (x m ,y m ), and camera M DIMM-2 At the same time, multiple position data (q1, w1), (q2, w2)... (q m , w m ), the measurement system synchronously collects data at M different times for the calculation of atmospheric coherence length and seeing.

7. The multi-path atmospheric coherence length measurement method for satellite-to-ground laser communication according to claim 3 is characterized in that Step S4 includes the following process: S4.1 At the ground receiving end, the focus is on the impact of arrival angle fluctuation on the optical system, ignoring the impact of amplitude; the covariance of the phase is obtained from the covariance of the arrival angle fluctuation and the phase structure function, and then the motion variance of the two spots in the horizontal and vertical directions is further calculated, and the wavefront z (x tur ,y tur ) and wavefront phase error φ(x tur ,y tur ), The arrival angle fluctuation component α(x tur ,y tur )for: Covariance B of arrival angle fluctuation α (ξ,η)=<α(x tur ,y tur ), α(x tur +ξ,y tur +η)>, the phase structure function is introduced as: D φ (ξ,η)=2[B φ (0,0)-B φ (ξ,η)](19), Where D φ (ξ, η) represents the phase structure function, which is used to describe the difference between the phase fluctuations at two points (0, 0) and (ξ, η) in space. φ (0, 0) represents the value of the covariance function of the bit fluctuation at the origin, B φ (ξ, η) represents the value of the covariance function of the phase fluctuation at the point (ξ, η), ξ represents the horizontal distance, and η represents the vertical distance; S4.2 approximation for Kolmogorov turbulence, the phase structure function is given by Indicates that the covariance B of the phase fluctuation a ((, η) is: Among them, r o represents the atmospheric coherence length, It represents the Euclidean distance from the origin. According to the centroid of the star spot observed by the multi-path atmospheric coherence length measurement system, let η = 0 to obtain the longitudinal covariance; let ξ = 0 to obtain the transverse covariance, so as to further calculate the atmospheric coherence length and seeing.

Images