Measurement and Spatial Interpolation Method of the Whole-Layer Atmospheric Transmittance for Satellite-Ground Laser Link

Abstract

The present invention discloses a method for measuring the integrated atmospheric transmittance and spatial interpolation of a space-ground laser link, belonging to the technical field of space-ground laser communication. The steps include: constructing an integrated atmospheric transmittance model for the paths where different stars are located according to the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions; using a stellar spot measurement device to observe the stars around the space-ground laser link to obtain the measured stellar spot data; calibrating with the calculation results of the integrated atmospheric transmittance model, processing the images of multiple stars, and calculating the integrated atmospheric transmittance of multiple paths; performing anisotropic semivariogram modeling to describe the variability characteristics of spatial data and analyze the spatial correlation of different data; estimating the integrated atmospheric transmittance of unknown points by weighted summation of known sampling points through spatial interpolation, converting the discrete data in space into continuous surface data, and using the paths between the known stellar positions and the ground station to describe the integrated atmospheric transmittance on the path of the space-ground laser link.

Description

Technical Field

[0001] The present invention relates to the technical field of space - to - ground laser communication, and particularly to a method for measuring the integral atmospheric transmittance of a space - to - ground laser link and spatial interpolation thereof. Background Technique

[0002] In the field of ground - based astronomy, atmospheric optical turbulence can cause fluctuations in the light signals of stars, thereby affecting the observation and research of stars. The absorption effects of gases such as water vapor, carbon dioxide, methane, and ozone on light energy are significant. When light waves propagate in the atmosphere, they cause forced motion of atmospheric molecules, and these gas molecules absorb light energy and convert it into heat energy, resulting in light energy loss. The transmission of light waves in the atmospheric optical channel causes an energy attenuation effect. Different bands of light waves have different absorption capabilities by atmospheric molecules, forming the "atmospheric window effect". To obtain the transmission quality of the atmospheric channel of a space - to - ground laser link, it is necessary to quantitatively analyze the influence of the integral atmospheric transmittance on the transmission result. Different from geostationary satellites, medium - and low - orbit satellites orbit the Earth at a faster speed, more than 12 times a day. Therefore, the laser communication link is significantly affected by the atmosphere. The atmospheric transmittance depends on the position of the star. The closer the star position is to the observation point, the smaller the atmospheric effects such as observation error and atmospheric attenuation. Currently, the spatial characteristics of the integral atmospheric transmittance on different paths have not been analyzed in detail. Therefore, it is crucial to measure the atmospheric transmittance on multiple target observation paths by using the method of ground - based observation of stars.

[0003] Observation data can obtain the integral atmospheric transmittance at known positions. The space - to - ground laser link belongs to points at unknown positions. At this time, it is necessary to estimate the attribute values at unsampled points to generate spatially continuous data. This method is a process of filling the gaps between sample observations to generate a value grid. A major limitation of spatial interpolation methods is the use of geometric distance, rather than statistical distance, to measure the relationship between the sampling position and the interpolation position. This form of interpolation implicitly assumes that the monitored phenomenon has uniform spatial continuity, which is rarely the case in nature. The spatial interpolation of the integral atmospheric transmittance is a promising option. The Kriging method is a stochastic interpolation method that can be used to simulate the integral atmospheric transmittance at any point. Therefore, it is necessary to analyze the spatio - temporal correlation of the integral atmospheric transmittance and measure the integral atmospheric transmittance according to the given time series.

[0004] Chinese Patent Application No. 202310445425.2 discloses a device and method for measuring the integral atmospheric transmittance by using a sunlight sampling array. In this patent application, a beam sampling array is distributed in a 2π solid angle range to measure the solar radiation signal intensity in sub - solid angles. After angle correction and calibration of this signal, the integral atmospheric transmittance can be obtained. Although this atmospheric transmittance measurement method uses a sampling array, it does not analyze the spatial correlation between different sampling points.

[0005] Chinese Patent Application No. 202311507873.7 discloses a method and system for measuring the slant-path integrated atmospheric transmittance. In this patent application, a laser ranging system is used to obtain and count the number of photons per unit time. Based on the functional relationship between the echo photon number N and the slant-path integrated atmospheric transmittance T, the slant-path integrated atmospheric transmittance is obtained through mathematical inversion. However, this method for measuring atmospheric transmittance has the following drawbacks: The target needs to return an echo signal, resulting in limited application scope. Summary of the Invention

[0006] To address the challenge of limited spatial range in measuring the integrated atmospheric transmittance in space-to-ground laser communication, the present invention proposes a method for measuring the integrated atmospheric transmittance and spatial interpolation of a space-to-ground laser link. It processes images of multiple stars, calculates the integrated atmospheric transmittance of multiple paths, conducts anisotropic semivariogram modeling to describe the variation characteristics of spatial data and analyze the spatial correlation of different data, and estimates the integrated atmospheric transmittance of unknown points by weighted summation of known sampling points through spatial interpolation, laying a foundation for the scheduling of ground laser links by low-earth orbit satellites.

[0007] The above objectives are achieved through the following technical solutions:

[0008] The present invention first provides a method for measuring the integrated atmospheric transmittance and spatial interpolation of a space-to-ground laser link. The steps of this method include:

[0009] S1. Considering the attenuation of laser by atmospheric molecules, aerosols, and meteorological conditions, construct an integrated atmospheric transmittance model for the path between the star and the ground station;

[0010] S2. Use a stellar spot measurement device to observe the stars around the space-to-ground laser link and obtain the measured stellar spot data;

[0011] S3. Calibrate using the calculation result of the integrated atmospheric transmittance model constructed in step S1, process images of multiple stars, and calculate the integrated atmospheric transmittance of multiple paths;

[0012] S4. Conduct anisotropic semivariogram modeling to describe the variation characteristics of spatial data in different directions and analyze the spatial correlation of different data;

[0013] S5. Estimate the integrated atmospheric transmittance of unknown points by weighted summation of known sampling points through spatial interpolation, converting the discrete data in space into continuous surface data.

[0014] Furthermore, the specific process of step S1 is as follows:

[0015] S1.1 Attenuation caused by atmospheric molecular absorption Considering water vapor and CO2 gases, it is expressed as:

[0016] T AM (λ)= exp [ - μ H 2 O ⋅ L ⋅ R humidity ⋅ m H 2 O 6.67 - μ C O 2 ⋅ L]= exp [ - μ H 2 O ⋅ e -0.0654 H Start (1- e -0.0654 cos θ ⋅ L ) 0.0654 cos θ ⋅ R humidity ⋅ m H 2 O 6.67 - μ C O 2 ⋅ e -0.19 H Start (1- e -0.19 cos θ ⋅ L ) 0.19 cos θ ] (1),

[0017] wherein, represents the path length of the light beam, is the absorption coefficient of water vapor, is the absorption coefficient of CO2 gas, is the relative humidity, is the mass of water vapor in saturated air, represents the zenith angle of the laser beam, represents the exponential function, and are the starting and ending heights of the laser respectively;

[0018] S1.2 Attenuation Caused by Aerosol Scattering is related to the visibility and is expressed as:

[0019] (2),

[0020] wherein, is an empirical constant related to the atmospheric visibility and V VIS = 3.91[ λ 550 ] -q k e , with the unit of kilometer, represents the extinction coefficient of the aerosol;

[0021] Meteorological Attenuation Transmittance is related to the attenuation coefficient of raindrops to the laser, is the rainfall intensity, with the unit of millimeter per hour:

[0022] (3),

[0023] S1.3 Consider the attenuation of the laser by atmospheric molecules, aerosols, and meteorological conditions. The total atmospheric transmittance , is expressed as:

[0024] (4),

[0025] Substitute equations (1), (2), and (3) into equation (4) to obtain the theoretical value of the integral atmospheric transmittance :

[0026] T theory λ = exp - μ H 2 O ⋅ e -0.0654 H Start 1- e -0.0654 cos θ⋅L 0.0654 cos θ ⋅ R homidity ⋅ m H 2 O 6.67 - μ C O 2 ⋅ e -0.19 H Start 1- e -0.19 cos θ⋅L 0.19 cos θ - 3.192 V VIS ⋅ 0.55 λ q +0.365 J r 0.63 ⋅L] (5),

[0027] The hourly atmospheric transmittance calculated by formula (5) is used as the calibration benchmark to calibrate the measured value of the minute-level atmospheric transmittance.

[0028] Further, the specific process of step S2 is as follows: Monitor the atmospheric transmittance using a starlight spot measurement device. The starlight spot measurement device consists of a visible light camera and a fixed focal length lens. During the observation, first set the exposure time and gain, and then collect the starlight spots at different positions around the space-to-ground laser communication path to obtain the gray value of the star image collected by the ground station .

[0029] Further, the specific process of step S3 is as follows:

[0030] S3.1 Assume that the magnitude of a certain star is , and the radiation intensity it generates outside the atmosphere is . The radiation intensity of other stars at the top of the atmosphere is:

[0031] (6),

[0032] where, is the magnitude difference, is the radiation intensity of the zero magnitude star, and lx is the abbreviation of the unit lux of . The radiation intensity of the star after passing through the entire atmosphere to the ground surface :

[0033] (7),

[0034] In the formula, is the total vertical atmospheric optical thickness, For atmospheric quality:

[0035] (8),

[0036] S3.2 Process the grayscale image of the star to obtain the stellar radiation intensity, and use the atmospheric transmittance calculated by formula (5) in step S1 , and calibrate the grayscale value obtained from the actual collected starlight spot in step S2 and the radiation intensity

[0037] + (9),

[0038] wherein, and are calibration coefficients, and the integral atmospheric transmittance in the vertical direction is:

[0039] T Meas λ = exp [ -τ λ ]= exp ln [ E ground λ ]- ln [ E Tat λ ] m θ (10),

[0040] Substitute equations (7), (8), and (9) into equation (10) to obtain:

[0041] T Meas λ = exp cos πθ 18 0 o +0.15× 93.885 - θ ⋅ ln [ E ground λ ]- ln [ 1 0 0.4×Δm ⋅ E 0 ×1 0 -0.4m ] (11).

[0042] Furthermore, the specific process of step S4 is as follows:

[0043] S4.1 Calculate the integral atmospheric transmittance at the position of the star according to steps S1 to S3, and use the known star position and the integral atmospheric transmittance on the ground station path to characterize the integral atmospheric transmittance on the space-to-ground laser link path. The semivariogram is expressed as:

[0044] (12),

[0045] In the formula, is the number of point pairs for each interval and time lag, , is the interval division of the spatial distance, is the time interval, and are the observed values in space and time, and represent different spatial positions, and represent different time points;

[0046] S4.2 The semivariogram describes the variation characteristics of spatial data in different directions, represents the variance of the data, reflecting the overall variability of the data; is the sill value, representing the nugget effect, reflecting the measurement error of the variable below the minimum sampling scale, ; and are two perpendicular direction components used to describe the lag distance in two-dimensional space; represents the movement speed of the stellar speckle, used to adjust the variation characteristics in different directions; The parametric anisotropic semivariogram is modeled as:

[0047] (13),

[0048] In the formula, is the proportionality constant, used to adjust the scale of the model, ; is the smoothing parameter, used to adjust the smoothness of the model, ; is the shape parameter, used to adjust the shape of the model, ; is used to adjust the weight of the direction vector, ; is used to adjust the attenuation characteristics of the model, ; is used to adjust the attenuation speed of the model, ; is the sill value, is the Dirac function. When the positions of two data points coincide exactly in space, that is, the distance between them is 0, at this time , if the distance between the positions of the two data points is not 0, at this time .

[0049] Furthermore, the specific process of step S5 is as follows:

[0050] S5.1 Use the Kriging method to provide an interpolator for the data collected in step S2, optimize the model parameters by minimizing the sum of squared residuals between the empirical semivariogram and the theoretical semivariogram, and apply the weighted least squares method to calculate the function parameters in formula (13) 、 、 、 、 、 ; Indicates that when = 0, it is the objective function for the least - squares estimation of the semivariogram in the direction; Indicates that when it is the objective function for the least - squares estimation of the semivariogram in the direction; Indicates the objective function for the least - squares estimation of the semivariogram considering both and directions simultaneously; Minimizing , and is:

[0051] (14),

[0052] In the formula, represents the maximum distance in the spatial direction, represents the value of the theoretical semivariogram at the spatial direction and the time direction 0, and the corresponding weight at this time is , is a set of parameters related to the spatial direction. When minimizing the objective function, only the parameters in the parameter set are adjusted; represents the value of the theoretical semivariogram at the spatial direction and the time direction , and the corresponding weight at this time is , is a set of parameters related to the time direction; represents the value of the theoretical semivariogram at the spatial direction and the time direction , and the corresponding weight at this time is , is a set of parameters related to both spatial and time directions; represents the estimated value of the empirical semivariogram at the spatial direction and the time direction 0; represents the estimated value of the empirical semivariogram at the spatial distance and the time direction ; represents the maximum time interval in the time direction; Ensure that the model parameters can accurately reflect the spatial characteristics of the data to estimate the atmospheric transmittance at unknown locations; By finding the point where the semivariogram reaches 95% of its semi - value, obtain the de - correlation relationship between space and time:

[0053] (15),

[0054] In the formula, represents the spatial distance is the semi-variogram value at time direction 0, representing the limiting semi-variogram value in the spatial direction; represents the time interval at which the semi-variogram value is at spatial direction 0, representing the limiting semi-variogram value in the time direction; respectively represent the distances at which the semi-variogram reaches 95% of its semi-value in the spatial direction and the time direction, i.e., the spatial and temporal decorrelation lengths; represents the small-scale variations in the data that are discontinuous;

[0055] S5.2 Use two iterations to obtain more accurate results. In the first iteration, the weight function is:

[0056] (16),

[0057] where is the number of data point pairs at a specific direction and distance , is the number of data point pairs at a specific time and time interval . The denominator is the sum of the number of data point pairs at all possible distances and directions, and normalizes the number of data point pairs at each distance and direction. In the second iteration, the weight function is:

[0058] (17),

[0059] where is the semi-variogram value at a specific direction and distance with parameter , and the denominator is the sum of the reciprocals of the semi-variogram values at all possible distances and directions; is the semi-variogram value at a specific time and time interval ;

[0060] S5.3 Each spot data point in the star chart is the spatial position of an observation value. The stellar spots are equivalent to the spatial sampling of the starry sky. Using the known data, Kriging interpolation is used to obtain the integral atmospheric transmittance at the unknown position :

[0061] (18),

[0062] where is the value of the unknown data, is the observed value of the sampling point, where .

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] By constructing a model of the integral atmospheric transmittance that takes into account atmospheric molecules, aerosols, and meteorological conditions, this method can more comprehensively reflect the attenuation characteristics of the actual atmospheric environment on lasers; by combining the observation data of large-aperture ground-based telescopes and small-aperture observation devices, and using the spot images of multiple stars to calculate the integral atmospheric transmittance of multiple paths, the advantages of different observation devices are effectively integrated, enhancing the reliability and stability of the measurement. Introducing the anisotropic semivariogram modeling can accurately describe the variation characteristics of spatial data in different directions, analyze the spatial correlation of different data, so as to achieve more accurate spatial interpolation, and provide more reliable spatio-temporal distribution information for the measurement of the integral atmospheric transmittance of the space-to-ground laser link. It provides a basis for the dynamic adjustment of the space-to-ground laser communication link and enhances the adaptability and stability of the link in a complex atmospheric environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flow block diagram for the measurement of the integral atmospheric transmittance of the space-to-ground of the present invention;

[0066] Figure 2 is a schematic diagram for the measurement of the integral atmospheric transmittance of the space-to-ground of the present invention;

[0067] Figure 3 is a schematic diagram of the sampling point positions under different gray value thresholds of the present invention: Figure 3 (a) has a gray value threshold of 220; Figure 3 (b) has a gray value threshold of 180; Figure 3 (c) has a gray value threshold of 160;

[0068] Figure 4 is the stellar spot observed by the ground-based telescope of the present invention: Figure 4 (a) is the spot of Alnilam collected at 21:20:02; Figure 4 (b) is the spot of Capella collected at 22:27:00;

[0069] Figure 5 is the measurement result of the integral atmospheric transmittance of multiple paths of the present invention

[0070] Figure 6 is the spatial interpolation result diagram of the integral atmospheric transmittance of the present invention: Figure 6 (a) is a 3D schematic diagram; Figure 6 (b) is a 2D schematic diagram; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0071] By combining the accompanying drawings in the embodiments of the present invention, the technical solutions are clearly and completely described. It should be noted that the embodiments only represent a part of the present invention, not all of the content. According to these embodiments, other embodiments obtained by ordinary technical personnel without creative work are within the protection scope of the present invention.

[0072] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0073] As Figure 1 shown, it is a schematic diagram of the method flow of the embodiment of the present invention. First, according to the attenuation of laser by atmospheric molecules, aerosols, and meteorological conditions, an integral atmospheric transmittance model on the paths where different stellar positions are located is constructed; a large-aperture ground-based telescope and a small-aperture observation device are used to observe the stars around the satellite-ground laser link to obtain the measured starlight spot data; the calculation results of the integral atmospheric transmittance model are used for calibration, the images of multiple stars are processed, and the integral atmospheric transmittance of multiple paths is calculated; an anisotropic semivariogram model is established to describe the variation characteristics of spatial data in different directions and analyze the spatial correlation of different data; based on the spatial sampling of stars, interpolation of the integral atmospheric transmittance is performed, and the weighted sum of known points is used to estimate the value of unknown points. The specific steps include:

[0074] The present invention first provides a method for measuring the integral atmospheric transmittance and spatial interpolation of a satellite-ground laser link, and the steps of this method include:

[0075] S1. Considering the attenuation of laser by atmospheric molecules, aerosols, and meteorological conditions, construct an integral atmospheric transmittance model on the path between the star and the ground station;

[0076] S2. Use a starlight spot measurement device to observe the stars around the satellite-ground laser link to obtain the measured starlight spot data;

[0077] S3. Calibrate with the calculation results of the integral atmospheric transmittance model constructed in step S1, process the images of multiple stars, and calculate the integral atmospheric transmittance of multiple paths;

[0078] S4. Establish an anisotropic semivariogram model to describe the variation characteristics of spatial data in different directions and analyze the spatial correlation of different data;

[0079] S5. Estimate the integral atmospheric transmittance of unknown points by weighted summation of known sampling points through spatial interpolation, and convert the discrete data in space into continuous surface data.

[0080] Further, the specific process of step S1 is as follows:

[0081] S1.1 Attenuation caused by absorption of atmospheric molecules Considering water vapor and CO2 gas, expressed as:

[0082] T AM (λ)= exp [ - μ H 2 O ⋅ L ⋅ R humidity ⋅ m H 2 O 6.67 - μ C O 2 ⋅ L]= exp [ - μ H 2 O ⋅ e -0.0654 H Start (1- e -0.0654 cos θ ⋅ L ) 0.0654 cos θ ⋅ R humidity ⋅ m H 2 O 6.67 - μ C O 2 ⋅ e -0.19 H Start (1- e -0.19 cos θ ⋅ L ) 0.19 cos θ ] (1),

[0083] In the formula, represents the path length of the light beam, is the absorption coefficient of water vapor, is the absorption coefficient of CO2 gas, is the relative humidity, is the mass of water vapor in saturated air, represents the zenith angle of the laser beam, represents the exponential function, and are the starting and ending heights of the laser respectively;

[0084] S1.2 Attenuation caused by aerosol scattering Is related to visibility and expressed as:

[0085] (2),

[0086] In the formula, is an empirical constant related to the atmospheric visibility and V VIS = 3.91[ λ 550 ] -q k e , whose unit is kilometer, represents the extinction coefficient of aerosols;

[0087] Meteorological attenuation transmittance Is related to the attenuation coefficient of raindrops on the laser And is the rainfall intensity, whose unit is millimeters per hour:

[0088] (3),

[0089] S1.3 Consider the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions. The total atmospheric transmittance , is expressed as:

[0090] (4),

[0091] Substitute equations (1), (2) and (3) into equation (4) to obtain the theoretical value of the integral atmospheric transmittance :

[0092] T theory λ = exp - μ H 2 O ⋅ e -0.0654 H Start 1- e -0.0654 cos θ⋅L 0.0654 cos θ ⋅ R homidity ⋅ m H 2 O 6.67 - μ C O 2 ⋅ e -0.19 H Start 1- e -0.19 cos θ⋅L 0.19 cos θ - 3.192 V VIS ⋅ 0.55 λ q +0.365 J r 0.63 ⋅L] (5),

[0093] The hourly atmospheric transmittance calculated by formula (5) is used as the calibration benchmark to calibrate the measured value of the minute-level atmospheric transmittance.

[0094] Furthermore, the specific process of step S2 is as follows: Use the starlight spot measurement device to monitor the atmospheric transmittance. The starlight spot measurement device consists of a visible light camera and a fixed focal length lens. During the observation, first set the exposure time and gain, and then collect the starlight spots at different positions around the satellite-ground laser communication path to obtain the gray value of the star image collected by the ground station .

[0095] In satellite-ground laser communication, for high-orbit satellites, there is no star point light source on their paths, and the description of the surrounding stars has deviations. Therefore, it is necessary to establish the correlation of measurement values at different positions. In the present invention, the atmospheric transmittance is used to characterize the transmission quality of the atmospheric channel; for medium- and low-orbit satellites, within a short period of time when the satellite passes overhead, the transmission quality of the atmospheric channel along the way changes, and the spatial interpolation method is used to obtain the atmospheric transmittance parameter values of the unknown paths along the way;

[0096] In September and October 2024, an experiment on the measurement of the integral atmospheric transmittance was conducted at the laser communication ground station located at longitude 125°24'27.36"E and latitude 43°51'0"N (Changchun). During the experiment, a visible light camera and a high-resolution lens (such as 75 mm) were used to collect star charts. The integral atmospheric transmittance observation equipment was deployed to continuously collect images of the starlight spots during the laser communication process. Specifically, the first-generation Mercury visible light camera, model MER2-230-168U3M / C, with a sensor of IMX252, a resolution of 1900*1200, a receiving target surface of 1 / 1.2 inches, and a pixel size of 5.86μm*5.86μm was used. A C-mount industrial lens of TV LENS with an aperture of F1.4, a diameter of 57.5 mm, and a field of view of 8.6079*6.4615 was adopted. The main observation targets of this experiment included Vega (Lyra constellation) with a magnitude of 0.02 and Deneb (Cygnus constellation) with a magnitude of 1.21.

[0097] In January 2025, an experiment on the measurement of the atmospheric channel transmission parameters based on star observations was conducted at the Yingtian ground station located at longitude 118°50'59.99"E and latitude 32°6'8.28"N (Nanjing). During the experiment, a SkyGuiderPro portable single-axis equatorial mount and the second-generation Mercury visible light camera, model HN-7528-6M-C2 / 3B, with a sensor of IMX174, a resolution of 2048*1536, a receiving target surface of 1 / 1.8 inches, a pixel size of 3.45μm*3.45μm, a lens diameter of 36 mm, an exposure time of 1 second, and a gain setting of 24 were used. The main observations in the experiment were Al Nath (Aries) with a magnitude of 2.17 and Capella (Auriga) with a magnitude of 0.24.

[0098] The observation results (true values) of a single star obtained by the ground station telescope were used to calibrate the integral atmospheric transmittance measurement equipment. The receiving aperture of the ground station telescope system was 500 mm, the receiving field of view was greater than 5 mrad (i.e., ±0.144°), and the single-pixel resolution was in micro-radians (abbreviated as urad). The optical interface was M42. A large-area centroid camera of model AIT-US025KM with a resolution of 5120*5120, a target surface size of 34 mm, a pixel size of 4.5μm*4.5μm, a ROI of a circular area with a diameter of 4900 pixels, and a focal length of 9000 mm was used.

[0099] Figure 2The figure in the middle is a schematic diagram of the experimental observation equipment of the ground station. The left figure shows the laser communication scenario between the satellite and the ground. Atmospheric transmittance observation equipment is deployed around, and the integral atmospheric transmittance data of the positions of the surrounding stars in the communication link are collected synchronously to analyze the spatial characteristics and obtain the integral atmospheric transmittance on the path where the laser link is located. The right figure shows the observation of the stars by the ground station telescope, and at the same time, atmospheric transmittance observation equipment is configured to calibrate the true value of the single-star observation by using the ground station telescope.

[0100] Figure 3 The figure in the middle shows the schematic diagram of the sampling point positions under different gray thresholds. At a fixed exposure time, multiple starlight spots are observed, and different thresholds can be set as needed to screen out the number of spots that meet the analysis requirements. In Figure 3 (a), when the gray value threshold is 220, 5 stars are observed; in Figure 3 (b), when the gray value threshold is 180, 7 stars are observed; in Figure 3 (c), when the gray value threshold is 160, 10 stars are observed.

[0101] Furthermore, the specific process of step S3 is as follows:

[0102] S3.1 Assume that the magnitude of a certain star is , and the radiation intensity it generates outside the atmosphere is , and the radiation intensity of other stars at the top of the atmosphere is:

[0103] (6),

[0104] where, is the magnitude difference, is the radiation intensity of the zero magnitude star, and lx is the abbreviation of the unit lux of . The radiation intensity of the star passing through the entire layer of the atmosphere to the ground surface :

[0105] (7),

[0106] In the formula, is the total vertical atmospheric optical thickness, is the air mass:

[0107] (8),

[0108] S3.2 Process the gray image of the star to obtain the star radiation intensity, and use the atmospheric transmittance calculated by formula (5) in step S1 to the gray value Perform calibration:

[0109] + (9),

[0110] wherein, and are calibration coefficients, and the integral atmospheric transmittance in the vertical direction is:

[0111] T Meas λ = exp [ -τ λ ]= exp ln [ E ground λ ]- ln [ E Tat λ ] m θ (10),

[0112] Substitute equations (7), (8), and (9) into equation (10) to obtain:

[0113] T Meas λ = exp cos πθ 18 0 o +0.15× 93.885 - θ ⋅ ln [ E ground λ ]- ln [ 1 0 0.4×Δm ⋅ E 0 ×1 0 -0.4m ] (11).

[0114] Figure 4 shows a schematic diagram of the stellar light spot observed by the ground station telescope. Figure 4 (a) of Figure 4 shows the light spot of Beta Leonis collected at 21:20:02 on January 16, 2025;

[0115] Figure 5 shows that on September 29, 2024 at 20:00, the atmospheric transmittance was measured in the Changchun area using three different paths. One star map was collected per second, and the results are shown in Figure 5 . In this experiment, we observed that the average atmospheric transmittance at position 1 was 0.470, the average atmospheric transmittance at position 2 was 0.471, and the average atmospheric transmittance at position 3 was 0.464, showing the integral atmospheric transmittance values at different positions.

[0116] Furthermore, the specific process of step S4 is as follows:

[0117] S4.1 Calculate the integral atmospheric transmittance at the position of the star according to steps S1 to S3, and use the known star position and the integral atmospheric transmittance on the ground station path to characterize the integral atmospheric transmittance on the space-ground laser link path. The semivariogram is expressed as:

[0118] (12),

[0119] wherein, is the number of point pairs for each interval and time lag, , is the interval division of the spatial distance, is the time interval, and are the observed values in space and time, and represent different spatial positions, and represent different time points;

[0120] S4.2 The semivariogram describes the variation characteristics of spatial data in different directions, represents the variance of the data, reflecting the overall variability of the data; is the sill value, representing the nugget effect, reflecting the measurement error of the variable below the minimum sampling scale, ; and are the two perpendicular direction components used to describe the lag distance in two-dimensional space; represents the movement speed of the star spot, used to adjust the variation characteristics in different directions; The parametric anisotropic semivariogram is modeled as:

[0121] (13),

[0122] wherein, is the proportionality constant, used to adjust the scale of the model, ; is the smoothing parameter, used to adjust the smoothness of the model, ; is the shape parameter, used to adjust the shape of the model, ; is used to adjust the weight of the direction vector, ; is used to adjust the attenuation characteristics of the model, ; is used to adjust the attenuation speed of the model, ; is the sill value, is the Dirac function. When the positions of two data points coincide exactly in space, i.e., the distance between them is 0, then ; if the distance between the positions of the two data points is not 0, then .

[0123] Furthermore, the specific process of step S5 is as follows:

[0124] S5.1 Use the Kriging method to provide an interpolator for the data collected in step S2, optimize the model parameters by minimizing the sum of squared residuals between the empirical semivariogram and the theoretical semivariogram, and apply the weighted least squares method to calculate the function parameters in Equation (13) 、 、 、 、 、 ; represents the objective function for the least squares estimation of the semivariogram in the = 0 direction; represents the objective function for the least squares estimation of the semivariogram in the direction when ; represents the objective function for the least squares estimation of the semivariogram considering both the and and directions; minimizing 、 and is:

[0125] (14),

[0126] wherein represents the maximum distance in the spatial direction, represents the value of the theoretical semivariogram in the spatial direction and the time direction 0, and the corresponding weight is , is the set of parameters related to the spatial direction. When minimizing the objective function, only the parameters in the parameter set are adjusted; represents the value of the theoretical semivariogram in the spatial direction and the time direction , and the corresponding weight is , is the set of parameters related to the time direction; represents the value of the theoretical semivariogram in the spatial direction and the time direction , and the corresponding weight is , A set of parameters related to spatial and temporal directions; Represents the estimated value of the empirical semivariogram in the spatial direction and at time direction 0; Represents the estimated value of the empirical semivariogram at the spatial distance and at the time direction ; Represents the maximum time interval in the time direction; Ensure that the model parameters can accurately reflect the spatial characteristics of the data to estimate the atmospheric transmittance at unknown locations; By finding the point where the semivariogram reaches 95% of its semi-value, the spatial and temporal decorrelation relationships are obtained:

[0127] (15),

[0128] In the formula, Represents the value of the semivariogram at the spatial distance with time direction 0, Represents the limiting semivariogram value in the spatial direction; Represents the value of the semivariogram at the time interval with spatial direction 0, Represents the limiting semivariogram value in the time direction; Respectively represent the distances at which the semivariogram reaches 95% of its semi-value in the spatial direction and the time direction, that is, the spatial and temporal decorrelation lengths; Represents the small-scale variations in the data that are discontinuous;

[0129] S5.2 Use two iterations to obtain more accurate results. In the first iteration, the weight function is:

[0130] (16),

[0131] In the formula, is the number of data point pairs at a specific direction and distance , is the number of data point pairs at a specific time and time interval . The denominator is the sum of the number of data point pairs at all possible distances and directions, and the number of data point pairs at each distance and direction is normalized. In the second iteration, the weight function is:

[0132] (17),

[0133] where, is the number of data point pairs at a specific direction and distance The semivariogram value at , with parameters , the denominator is the sum of the reciprocals of the semivariogram values ​​at all possible distances and directions; At a specific time and time interval The semivariogram value at ;

[0134] S5.3 Each spot data point in the star map is the spatial position of an observation value. The star spot is equivalent to the spatial sampling of the starry sky. Using the known data, Kriging interpolation is used to obtain the unknown position. The whole layer of atmospheric transmittance above:

[0135] (18),

[0136] In the formula, is the value of the unknown data, is the observed value at the sampling point, where .

[0137] Figure 6 is the spatial interpolation result diagram of the whole-layer atmospheric transmittance of the present invention, Figure 6 (a) is a 3D schematic diagram of Figure 6 (b) is a 2D schematic diagram of . It contains 30 sampling points of star positions, revealing the distribution of this parameter at different coordinate points. In the 3D diagram, the trend of atmospheric transmittance in space is shown, showing the difference between atmospheric transmittance at different positions.

Claims

1. A method for measuring the whole-layer atmospheric transmittance and spatial interpolation of a satellite-to-ground laser link, characterized in that: The method steps include: S1. Considering the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions, a model of the entire atmospheric transmittance on the path between the star and the ground station is constructed; S2. Use star spot measurement equipment to observe the stars around the satellite-to-ground laser link and obtain measured star spot data; S3. Calibrate the calculation results of the whole-layer atmospheric transmittance model constructed in step S1, process the images of multiple stars, and calculate the multi-path whole-layer atmospheric transmittance; S4. Anisotropic semivariogram modeling is used to describe the variation characteristics of spatial data in different directions and analyze the spatial correlation of different data. The specific process is as follows: S4.1 Calculate the transmittance of the entire atmosphere at the position of the star according to steps S1 to S3, and use the transmittance of the entire atmosphere on the known star position and the ground station path to represent the transmittance of the entire atmosphere on the satellite-to-ground laser link path. The semivariogram It is expressed as: Where N(h(d),u) is the number of point pairs per interval and time lag, h(d) is the interval division of spatial distance, u is the time interval, T λ (x i ,t mm ) and T λ (x j ,t nn ) are the observed values ​​in space and time, x i and x j Represents different spatial positions, t mm and t nn Indicates different points in time; S4.2 The semivariogram function describes the variation characteristics of spatial data in different directions, σ 2 represents the variance of the data, reflecting the overall variability of the data; v S is the base value, indicating the nugget effect, reflecting the measurement error of the variable below the minimum sampling scale, 0≤v S ≤1; h1 and h2 are two vertical components used to describe the lag distance in two-dimensional space; v represents the movement speed of the star spot, which is used to adjust the variation characteristics in different directions; the parameter anisotropic semivariogram function is modeled as: In the formula, c is the proportional constant used to adjust the scale of the model, c>0; ζ is the smoothing parameter used to adjust the smoothness of the model, ζ>0; is a shape parameter used to adjust the shape of the model. α is used to adjust the weight of the direction vector, 0≤α≤1; β is used to adjust the attenuation characteristics of the model, 0≤β≤1; δ is used to adjust the attenuation speed of the model, 0≤δ; v S is the sill value, I S＝0 is the Dirac function. When the positions of two data points completely coincide in space, that is, the distance between them is 0, then I S＝0 =1, if the distance between the two data points is not 0, then I S＝0 =0; S5. By performing weighted summation of known sampling points through spatial interpolation, the transmittance of the entire atmospheric layer of unknown points is estimated, and the discrete data in space is converted into continuous surface data. The specific process is as follows: S5.1 uses the Kriging method to provide an interpolator for the data collected in step S2, optimizes the model parameters by minimizing the residual sum of squares between the empirical semivariogram and the theoretical semivariogram, and calculates the function parameters c and v in equation (13) using the weighted least squares method S , α, β, δ; S(ψ1) represents the objective function of the least squares estimation of the semivariogram in the h direction when u=0; S(ψ2) represents the objective function of the least squares estimation of the semivariogram in the u direction when h=0; S(ψ3) represents the objective function of the least squares estimation of the semivariogram in both the h and u directions; minimizing S(ψ1), S(ψ2) and S(ψ3) is: Where D represents the maximum distance in the spatial direction, γ(h(d),0; ψ i ) represents the value of the theoretical semivariogram in the spatial direction h(d) and the time direction 0, and the corresponding weight is w d,0 , ψ1=(v s ,c,ζ) is a set of parameters related to the spatial direction. When minimizing the objective function, only the parameters in the parameter set are adjusted; γ(h(0),u;ψ2) represents the value of the theoretical semivariogram in the spatial direction h(0) and the temporal direction u. The corresponding weight is w 0,u , ψ2=(a s ,α,δ+β) is a set of parameters related to the time direction; γ(h(d),u;ψ3) represents the value of the theoretical semivariogram in the spatial direction h(d) and the time direction u, and the corresponding weight is w d,u , ψ3=(β) is a set of parameters related to the spatial and temporal directions; Represents the estimated value of the empirical semivariogram in the spatial direction h(d) and the time direction 0; represents the estimated value of the empirical semivariogram at spatial distance h(0) and time direction u, and maxt represents the maximum time interval in the time direction; ensure that the model parameters can accurately reflect the spatial characteristics of the data to estimate the atmospheric transmittance at unknown locations; by finding the point where the semivariogram reaches 95% of its half value, the spatial and temporal decorrelation relationship is obtained: In the formula, γ(h Deco ,0) indicates that the space distance h Deco At the time direction, the semivariogram value is 0, γ(h ∞ ,0) represents the limiting semivariogram value in the spatial direction; γ(0,u Deco ) represents the time interval u Deco At the point where the spatial direction is 0, the semivariogram function value, γ(0,u ∞ ) represents the limiting semivariogram value in the time direction; h Deco and u Deco Respectively represent the distance in the spatial direction and the temporal direction when the semivariogram reaches 95% of its half value, that is, the spatial and temporal decorrelation length; c Nugget Represents discontinuous, small-scale variation in the data; S5.2 uses two iterations to obtain more accurate results. In the first iteration, the weight function w l,u for: Where N(h(d),u) is the number of data point pairs at a specific direction u and distance h(d), N(h(k),t) is the number of data point pairs at a specific time t and time interval h(k), the denominator is the sum of all data point pairs, and the number of data point pairs at each distance and direction is normalized. The weight function in the second iteration is: Among them, γ(h(d),u;ψ) is the semivariogram value at a specific direction u and distance h(d), the parameter is ψ, and the denominator is the sum of the reciprocals of all semivariogram values; γ(h(k),t;ψ) is the semivariogram value at a specific time t and time interval h(k); Each spot data point in the S5.3 star map is the spatial position of an observation value. The star spot is equivalent to the spatial sampling of the starry sky. Using the known data, Kriging interpolation is used to obtain the unknown position (x γ ,y γ ) on the whole layer of atmosphere transmittance: Where, T λ_Predicted is the value of the unknown data, T λ_sampling is the observed value at the sampling point, where λ_sampling=1,2,…,n.

2. The method for measuring the whole-layer atmospheric transmittance and spatial interpolation of a satellite-to-ground laser link according to claim 1 is characterized in that The specific process of step S1 is as follows: S1.1 Attenuation caused by absorption of atmospheric molecules T AM (λ) Considering water vapor and CO2 gas, it can be expressed as: Where L is the path length of the light beam, is the absorption coefficient of water vapor, is the absorption coefficient of CO2 gas, R humidit is the relative humidity, is the mass of water vapor in saturated air, θ is the zenith angle of the laser beam, exp[·] represents the exponential function, H Start and H End are the starting and ending heights of the laser respectively; S1.2 Attenuation due to aerosol scattering T AS (λ) is related to visibility and is expressed as: Where q is the atmospheric visibility V VIS The relevant empirical constants are Its unit is kilometer, k e represents the extinction coefficient of aerosol; Meteorological attenuation transmittance T MC (λ) and the attenuation coefficient of raindrops to laser Related, J r is the rainfall intensity in millimeters per hour: S1.3 Considering the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions, the total atmospheric transmittance T theor (λ), expressed as: T theory (λ)=T AM (λ)×T AS (λ)×T MC (l) (4), Substituting equations (1), (2) and (3) into equation (4), we can obtain the whole layer atmospheric transmittance T theor Theoretical value of (λ): The hourly atmospheric transmittance calculated by formula (5) is used as the calibration benchmark to calibrate the measured value of minute-level atmospheric transmittance.

3. The whole-layer atmosphere transmittance measurement and spatial interpolation method of the satellite-to-ground laser link according to claim 1 is characterized in that: The specific process of step S2 is as follows: the atmospheric transmittance is monitored using a star spot measurement device, which consists of a visible light camera and a fixed focal length lens. During the observation process, the exposure time and gain are first set, and then the star spots at different positions around the satellite-to-ground laser communication path are collected to obtain the grayscale value I of the star image collected by the ground station. grounbd (λ).

4. The method for measuring the whole-layer atmospheric transmittance and spatial interpolation of a satellite-to-ground laser link according to claim 1 is characterized in that The specific process of step S3 is as follows: S3.1 Assume that the magnitude of a star is m a , the radiation intensity generated outside the atmosphere is The radiation intensity of other stars at the top of the atmosphere is E Tat (λ) is: E Tat (λ)=10 0.4×Δm ·E a (λ)=10 0.4×Δm (E0×10 -0.4m ) (6), Where Δm is the magnitude difference, E0 = 2.54 × 10 -6 lx is the sporadic radiation intensity, lx is the abbreviation of the unit Lux Lux of E0, and the radiation intensity of the star through the entire atmosphere to the surface of the earth is E ground (λ): E ground (λ)=E Tat (λ)exp[-τ(λ)m(θ)] (7), Where τ(λ) is the total vertical atmospheric optical thickness and m(θ) is the atmospheric mass: S3.2 The grayscale image of the star is processed to obtain the star radiation intensity, and the atmospheric transmittance T is calculated using formula (5) in step S1 theor (λ), the gray value I obtained by actually collecting the star spot in step S2 ground (λ) and radiation intensity E ground (λ) is calibrated: Among them, ∈ and is the calibration coefficient, and the vertical transmittance of the entire layer of atmosphere T is obtained. Meas (λ) is: Substituting equations (7), (8), and (9) into equation (10), we obtain:

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