Whole-layer atmospheric transmittance measurement and spatial interpolation method of satellite-ground laser link

Abstract

The invention discloses a whole atmosphere transmittance measurement and spatial interpolation method of a satellite-ground laser link, and belongs to the technical field of satellite-ground laser communication. The method comprises the following steps: according to attenuation of atmospheric molecules, aerosol and meteorological conditions to laser, constructing a whole-layer atmospheric transmittance model on paths where different fixed stars are located; the method comprises the following steps: observing fixed stars around a satellite-ground laser link by using fixed star light spot measuring equipment to obtain actually measured fixed star light spot data; calibration is carried out according to the calculation result of the whole atmosphere transmittance model, images of multiple fixed stars are processed, and the whole atmosphere transmittance of multiple paths is calculated; carrying out anisotropic semi-variable function modeling, describing variation characteristics of spatial data, and analyzing spatial correlation of different data; weighted summation is carried out on known sampling points through spatial interpolation, the whole atmospheric transmittance of an unknown point is estimated, discrete data in space is converted into continuous curved surface data, and the whole atmospheric transmittance on a satellite-ground laser link path is described by using the known fixed star position and the path of a ground station.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite-to-ground laser communication, and in particular to a whole-layer atmosphere transmittance measurement and spatial interpolation method for a satellite-to-ground laser link. Background Art

[0002] In the field of ground-based astronomy, atmospheric optical turbulence can cause fluctuations in stellar light signals, which in turn affects the observation and research of stellar bodies. Gases such as water vapor, carbon dioxide, methane, and ozone have significant absorption effects on light energy. Because when light waves propagate in the atmosphere, atmospheric molecules are forced to move. 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 will cause energy attenuation effects. Light waves in different bands have different absorption capacities by atmospheric molecules, forming an "atmospheric window effect". In order to obtain the atmospheric channel transmission quality of the satellite-to-ground laser link, it is necessary to quantitatively analyze the impact of the entire atmospheric transmittance on the transmission results. Unlike high-orbit synchronous satellites, medium- and low-orbit satellites orbit the earth faster, more than 12 times a day, so laser communication links are significantly affected by the atmosphere. Atmospheric transmittance depends on the position of the star. The closer the position of the star is to the observation point, the less atmospheric effects such as observation errors and atmospheric attenuation will be. At present, the spatial characteristics of the entire atmospheric transmittance on different paths have not been analyzed in detail. Therefore, it is critical to use ground-based star observation methods to measure and obtain the atmospheric transmittance on multi-target observation paths.

[0003] Observational data can obtain the transmittance of the entire atmosphere at known locations. The satellite-to-ground laser link belongs to a point at an unknown location. At this time, it is necessary to estimate the attribute values ​​at the unsampled points to generate spatially continuous data. This method is the process of filling the gaps between sample observations to generate a value grid. A major limitation of spatial interpolation methods is that geometric distances, rather than statistical distances, are used to measure the relationship between sampling locations and interpolation locations. This form of interpolation implicitly assumes that the monitored phenomenon has uniform spatial continuity, which is rarely the case in nature. Spatial interpolation of the transmittance of the entire atmosphere is a promising option. Kriging is a random interpolation method that can be used to simulate the transmittance of the entire atmosphere at any point. Therefore, it is necessary to analyze the spatiotemporal correlation of the transmittance of the entire atmosphere and measure the transmittance of the entire atmosphere based on a given time series.

[0004] The Chinese patent application with application number 202310445425.2 discloses a device and method for measuring the transmittance of the entire atmosphere using a sunlight sampling array. In this patent application, a beam sampling array is distributed and arranged within a 2π solid angle range to measure the intensity of the solar radiation signal in solid angles. After the signal is angle-corrected and calibrated, the transmittance of the entire atmosphere 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] The Chinese patent application with application number 202311507873.7 discloses a method and system for measuring the transmittance of the entire layer of the atmosphere at an oblique distance. In the patent application, a laser ranging system is used to obtain and count the number of photons per unit time, and the transmittance of the entire layer of the atmosphere at an oblique distance is obtained through mathematical inversion based on the functional relationship between the number of echo photons N and the transmittance T of the entire layer of the atmosphere at an oblique distance. The atmospheric transmittance measurement method has the following shortcomings: the target needs to return an echo signal, and the scope of use is limited. Summary of the invention

[0006] In order to cope with the challenge of limited spatial range of whole-layer atmospheric transmittance measurement in satellite-to-ground laser communication, the present invention proposes a whole-layer atmospheric transmittance measurement and spatial interpolation method for satellite-to-ground laser links, processes images of multiple stars, and calculates the whole-layer atmospheric transmittance of multiple paths; performs anisotropic semivariable function modeling to describe the variation characteristics of spatial data and analyze the spatial correlation of different data; and estimates the whole-layer atmospheric transmittance of unknown points by weighted summation of known sampling points through spatial interpolation, laying a foundation for scheduling of low-orbit satellites to ground laser links.

[0007] The above purpose is achieved through the following technical solutions:

[0008] The present invention first provides a method for measuring the whole-layer atmospheric transmittance and spatial interpolation of a satellite-to-ground laser link, the method comprising the following steps:

[0009] 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;

[0010] S2. Use star spot measurement equipment to observe the stars around the satellite-to-ground laser link and obtain measured star spot data;

[0011] 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 atmospheric transmittance of the whole layer;

[0012] S4. Anisotropic semivariogram modeling, describing the variation characteristics of spatial data in different directions and analyzing the spatial correlation of different data;

[0013] S5. By performing weighted summation of known sampling points through spatial interpolation, the transmittance of the entire atmospheric layer at unknown points is estimated, and the discrete data in space is converted into continuous surface data.

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

[0015] S1.1 Attenuation due to absorption by atmospheric molecules Considering water vapor and CO2 gas, it can be expressed as: T AM (λ)= exp [ - m H 2 O ⋅ L ⋅ R humidity ⋅ m H 2 O 6.67 - m C O 2 ⋅ L]= exp [ - m H 2 O ⋅ e -0.0654 H Start (1- e -0.0654 cos i ⋅ L ) 0.0654 cos i ⋅ R humidity ⋅ m H 2 O 6.67 - m C O 2 ⋅ e -0.19 H Start (1- e -0.19 cos i ⋅ L ) 0.19 cos i ] (1) 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;

[0016] S1.2 Attenuation due to aerosol scattering Related to visibility, expressed as: (2) In the formula, For atmospheric visibility The relevant empirical constants are V VIS = 3.91[ l 550 ] -q k e , whose unit is kilometers, represents the extinction coefficient of aerosol;

[0017] Meteorological attenuation transmittance Attenuation coefficient of laser light by raindrops Related, is the rainfall intensity in millimeters per hour: (3)

[0018] S1.3 Considering the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions, the total atmospheric transmittance , expressed as: (4)

[0019] Substituting equations (1), (2) and (3) into equation (4), we can obtain the whole layer atmospheric transmittance: Theoretical value: T theory l = exp - m H 2 O ⋅ e -0.0654 H Start 1- e -0.0654 cos θ⋅L 0.0654 cos i ⋅ R humidity ⋅ m H 2 O 6.67 - m C O 2 ⋅ e -0.19 H Start 1- e -0.19 cos θ⋅L 0.19 cos i - 3.192 V VIS ⋅ 0.55 l q +0.365 J r 0.63 ⋅L] (5)

[0020] The hourly atmospheric transmittance calculated by formula (5) is used as the calibration benchmark to calibrate the measured value of minute-level atmospheric transmittance.

[0021] Furthermore, the specific process of step S2 is as follows: the atmospheric transmittance is monitored using a star spot measurement device, which is composed 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 of the star image collected by the ground station. .

[0022] Furthermore, the specific process of step S3 is as follows:

[0023] S3.1 Assume that the magnitude of a star is , the radiation intensity generated outside the atmosphere is , the radiation intensity of other stars at the top of the atmosphere for: (6) in, is the magnitude difference, is the sporadic radiation intensity, lx is Lux is the abbreviation of Lux, which is the radiation intensity of the star through the entire atmosphere to the surface of the earth. : (7) In the formula, is the total vertical atmospheric optical depth, For air quality: (8)

[0024] S3.2 processes the grayscale image of the star to obtain the star radiation intensity, and uses the atmospheric transmittance calculated by formula (5) in step S1 , the gray value of the star spot actually collected in step S2 and radiation intensity To perform calibration: + (9) in, and is the calibration coefficient, and the vertical transmittance of the entire atmospheric layer is obtained. for: T Meas l = exp [ -t l ]= exp ln [ E ground l ]- ln [ E Tat l ] m i (10)

[0025] Substituting equations (7), (8), and (9) into equation (10), we obtain: T Meas l = exp cos pt 18 0 o +0.15× 93.885-θ ⋅ ln [ E ground l ]- ln [ 1 0 0.4×Δm ⋅ E 0 ×1 0 -0.4m ] (11).

[0026] Furthermore, the specific process of step S4 is as follows:

[0027] S4.1 Calculate the transmittance of the entire atmosphere at the position of the star according to steps S1 to S3, and use the known star position and the transmittance of the entire atmosphere on the ground station path to characterize the transmittance of the entire atmosphere on the satellite-to-ground laser link path. The semivariogram It is expressed as: (12), In the formula, is the number of point pairs per bin and time lag, , is the interval division of spatial distance, is the time interval, and are observations in space and time, and Represents different spatial locations. and Indicates different points in time;

[0028] S4.2 Semivariogram function describes the variation characteristics of spatial data in different directions. It represents the variance of the data, reflecting the overall variability of the data; is the base value, which represents the nugget effect and reflects the measurement error of the variable below the minimum sampling scale. ; and are two perpendicular components used to describe the lag distance in two-dimensional space; 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: (13), In the formula, is a proportional constant used to adjust the scale of the model, ; is a smoothing parameter used to adjust the smoothness of the model. ; is a shape parameter used to adjust the shape of the model. ; Used to adjust the weight of the direction vector, ; Used to adjust the attenuation characteristics of the model, ; Used to adjust the decay speed of the model. ; is the sill value, is the Dirac function. When the positions of two data points completely coincide in space, that is, the distance between them is 0, then , if the distance between the two data points is not 0, then .

[0029] Furthermore, the specific process of step S5 is as follows:

[0030] S5.1 uses the kriging method to provide an interpolator for the data collected in step S2, and optimizes the model parameters by minimizing the residual sum of squares between the empirical semivariogram and the theoretical semivariogram. The weighted least squares method is used to calculate the function parameters in equation (13): , , , , , ; Indicated in =0, The objective function of the least squares estimation of the directional semivariogram; Indicated in When, yes The objective function of the least squares estimation of the directional semivariogram; Considering at the same time and The objective function for the least squares estimation of the directional semivariogram; minimize , and for: (14), In the formula, represents the maximum distance in the spatial direction, Represents the theoretical semivariogram in the spatial direction and the value at 0 in the time direction, the corresponding weight is , It 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 theoretical semivariogram in the spatial direction and time direction The corresponding weight is , is a set of parameters related to the time direction; Represents the theoretical semivariogram in the spatial direction and time direction The corresponding weight is , It is a set of parameters related to spatial and temporal directions; Represents the empirical semivariogram in the spatial direction and the estimated value at time 0; Represents the empirical semivariogram in spatial distance and time direction The estimated value at Represents the maximum time interval in the time direction; ensures that the model parameters can accurately reflect the spatial characteristics of the data to estimate the atmospheric transmittance at unknown locations; and obtains the spatial and temporal decorrelation by finding the point where the semivariogram reaches 95% of its half value: (15), In the formula, Indicates the distance in space At , the semivariogram value when the time direction is 0, Represents the limiting semivariogram value in the spatial direction; Indicates the time interval At , the semivariogram value when the spatial direction is 0, represents the limiting semivariogram value in the time direction; 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; Represents discontinuous, small-scale variation in the data;

[0031] S5.2 uses two iterations to obtain more accurate results. In the first iteration, the weight function for: (16), In the formula, In a specific direction and distance The number of data point pairs at At a specific time and time interval The number of data point pairs at 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. The weight function in the second iteration is: (17), in, In 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 ;

[0032] 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: (18), In the formula, is the value of the unknown data, is the observed value at the sampling point, where .

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] This method can more comprehensively reflect the attenuation characteristics of the actual atmospheric environment to the laser by constructing a whole-layer atmospheric transmittance model that takes into account atmospheric molecules, aerosols and meteorological conditions; combined with the observation data of large-aperture ground station telescopes and small-aperture observation equipment, the spot images of multiple stars are used to calculate the multi-path whole-layer atmospheric transmittance, which effectively integrates the advantages of different observation equipment and enhances the reliability and stability of the measurement. The introduction of anisotropic semivariable function modeling can accurately describe the variation characteristics of spatial data in different directions, analyze the spatial correlation of different data, and thus achieve more accurate spatial interpolation, providing more reliable spatiotemporal distribution information for the whole-layer atmospheric transmittance measurement of satellite-to-ground laser links. It provides a basis for the dynamic adjustment of satellite-to-ground laser communication links and enhances the adaptability and stability of links in complex atmospheric environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The flowchart of the present invention is a flow chart of measuring the transmittance of the entire layer of atmosphere between the satellite and the earth;

[0036] Figure 2 It is a schematic diagram of measuring the transmittance of the entire layer of atmosphere of the satellite and the earth according to the present invention;

[0037] Figure 3 Schematic diagram of sampling point positions under different grayscale thresholds of the present invention: Figure 3 The gray value threshold of (a) is 220; Figure 3 The gray value threshold of (b) is 180; Figure 3 The gray value threshold of (c) is 160;

[0038] Figure 4 The star spots observed by the ground station telescope of the present invention are: Figure 4 (a) is the Lousu III light spot collected at 21:20:02; Figure 4 (b) is the Capella light spot collected at 22:27:00;

[0039] Figure 5 The multi-path whole-layer atmospheric transmittance measurement result of the present invention is

[0040] Figure 6 This 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; DETAILED DESCRIPTION

[0041] By combining the drawings in the embodiments of the present invention, the technical scheme is clearly and completely described. It should be pointed out that the embodiments only represent a part of the present invention, not all of it. According to these embodiments, other embodiments obtained by ordinary technicians without innovative work are all within the scope of protection of the present invention.

[0042] 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.

[0043] like Figure 1The figure is a schematic flow chart of the method of an embodiment of the present invention. First, according to the attenuation of the laser by atmospheric molecules, aerosols and meteorological conditions, a whole-layer atmospheric transmittance model on the path where different star positions are located is constructed; a large-aperture ground station telescope and a small-aperture observation equipment are used to observe the stars around the satellite-to-ground laser link to obtain measured star spot data; the calculation results of the whole-layer atmospheric transmittance model are used for calibration, and the images of multiple stars are processed to calculate the whole-layer atmospheric transmittance of multiple paths; anisotropic semivariable function modeling is used to describe the variation characteristics of spatial data in different directions and analyze the spatial correlation of different data; based on stellar space sampling, the whole-layer atmospheric transmittance is interpolated, and the weighted sum of known points is performed to estimate the values ​​of unknown points. The specific steps include:

[0044] The present invention first provides a method for measuring the whole-layer atmospheric transmittance and spatial interpolation of a satellite-to-ground laser link, the method comprising the following steps:

[0045] 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;

[0046] S2. Use star spot measurement equipment to observe the stars around the satellite-to-ground laser link and obtain measured star spot data;

[0047] 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 atmospheric transmittance of the whole layer;

[0048] S4. Anisotropic semivariogram modeling, describing the variation characteristics of spatial data in different directions and analyzing the spatial correlation of different data;

[0049] S5. By performing weighted summation of known sampling points through spatial interpolation, the transmittance of the entire atmospheric layer at unknown points is estimated, and the discrete data in space is converted into continuous surface data.

[0050] Furthermore, the specific process of step S1 is as follows:

[0051] S1.1 Attenuation due to absorption by atmospheric molecules Considering water vapor and CO2 gas, it can be expressed as: T AM (λ)= exp [ - m H 2 O ⋅ L ⋅ R humidity ⋅ m H 2 O 6.67 - m C O 2 ⋅ L]= exp [ - m H 2 O ⋅ e -0.0654 H Start (1- e -0.0654 cos i ⋅ L ) 0.0654 cos i ⋅ R humidity ⋅ m H 2 O 6.67 - m C O 2 ⋅ e -0.19 H Start (1- e -0.19 cos i ⋅ L ) 0.19 cos i ] (1) 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;

[0052] S1.2 Attenuation due to aerosol scattering Related to visibility, expressed as: (2) In the formula, For atmospheric visibility The relevant empirical constants are V VIS = 3.91[ l 550 ] -q k e , whose unit is kilometers, represents the extinction coefficient of aerosol;

[0053] Meteorological attenuation transmittance Attenuation coefficient of laser light by raindrops Related, is the rainfall intensity in millimeters per hour: (3)

[0054] S1.3 Considering the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions, the total atmospheric transmittance , expressed as: (4)

[0055] Substituting equations (1), (2) and (3) into equation (4), we can obtain the whole layer atmospheric transmittance: Theoretical value: T theory l = exp - m H 2 O ⋅ e -0.0654 H Start 1- e -0.0654 cos θ⋅L 0.0654 cos i ⋅ R humidity ⋅ m H 2 O 6.67 - m C O 2 ⋅ e -0.19 H Start 1- e -0.19 cos θ⋅L 0.19 cos i - 3.192 V VIS ⋅ 0.55 l q +0.365 J r 0.63 ⋅L] (5)

[0056] The hourly atmospheric transmittance calculated by formula (5) is used as the calibration benchmark to calibrate the measured value of minute-level atmospheric transmittance.

[0057] Furthermore, the specific process of step S2 is as follows: the atmospheric transmittance is monitored using a star spot measurement device, which is composed 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 of the star image collected by the ground station. .

[0058] In satellite-to-ground laser communication, if it is a high-orbit satellite, there is no stellar point light source on its path, and the surrounding stars have deviations in describing it, so it is necessary to establish the correlation of measurement values ​​at different positions. In the present invention, atmospheric transmittance is used to characterize the transmission quality of the atmospheric channel; if it is a medium or low-orbit satellite, the transmission quality of the atmospheric channel along the way changes in a short time when the satellite passes overhead, and the spatial interpolation method is used to obtain the atmospheric transmittance parameter value of the unknown path along the way;

[0059] In September and October 2024, a whole-layer atmospheric transmittance measurement experiment was carried out at the laser communication ground station at longitude 125°24'27.36"E, latitude 43°51'0"N (Changchun). In the experiment, a visible light camera and a high-resolution lens (such as 75mm) were used to collect star maps. Deploy whole-layer atmospheric transmittance observation equipment to continuously collect images of star spots during laser communication. Specifically, the first-generation Mercury visible light camera was used, model MER2-230-168U3M / C, sensor IMX252, resolution 1900*1200, receiving target surface 1 / 1.2 inches, pixel size 5.86μm*5.86μm. TV LENS C-mount industrial lens with an aperture of F1.4, a diameter of 57.5mm, and a field of view angle of The main observation objects of this experiment include Vega (Lyra), whose magnitude is 0.02, and Deneb (Cygnus), whose magnitude is 1.21.

[0060] In January 2025, an atmospheric channel transmission parameter measurement experiment based on star observation was conducted at the Yingtian ground station at longitude 118°50'59.99"E, latitude 32°6'8.28"N (Nanjing). The experiment used a SkyGuiderPro portable single-axis equatorial mount and a second-generation Mercury visible light camera, model HN-7528-6M-C2 / 3B, sensor IMX174, resolution 2048*1536, receiving target surface 1 / 1.8 inches, pixel size 3.45μm*3.45μm, lens diameter 36mm, exposure time 1 second, and gain setting 24. The experiment mainly observed Aries (Aries), with a magnitude of 2.17, and Capella (Auriga), with a magnitude of 0.24.

[0061] The observation results (true value) of a single star by a ground-based telescope are used to calibrate the whole-layer atmospheric transmittance measurement equipment. The receiving aperture of the ground-based telescope system is 500mm, the receiving field of view is greater than 5mrad (i.e. ±0.144°), and the single-pixel resolution is micro-radians (abbreviated as urad). The optical interface is M42, the model is the AIT-US025KM large-array centroid camera, the resolution is 5120*5120, the target size is 34mm, the pixel size is 4.5μm*4.5μm, the ROI is a circular area with a diameter of 4900 pixels, and the focal length is 9000mm.

[0062] Figure 2 The figure in the middle is a schematic diagram of the experimental observation equipment of the ground station. The left figure shows the laser communication scene between the satellite and the ground. Atmospheric transmittance observation equipment is deployed around it to synchronously collect the transmittance data of the entire layer of atmosphere around the star position of the communication link, analyze the spatial characteristics and obtain the transmittance of the entire layer of atmosphere on the path of the laser link. The figure on the right shows the observation of stars by the ground station telescope. At the same time, the atmospheric transmittance observation equipment is configured to use the ground station telescope to calibrate the real value of single star observation.

[0063] Figure 3 The schematic diagram of the sampling point position under different grayscale thresholds is shown in . Under a fixed exposure time, when multiple star spots are observed, different thresholds can be set as needed to filter out the number of spots that meet the analysis requirements. Figure 3 In (a), when the gray value threshold is 220, 5 stars are observed; Figure 3 In (b), when the grayscale value threshold is 180, 7 stars are observed; Figure 3 In (c), when the grayscale value threshold is 160, 10 stars are observed.

[0064] Furthermore, the specific process of step S3 is as follows:

[0065] S3.1 Assume that the magnitude of a star is , the radiation intensity generated outside the atmosphere is , the radiation intensity of other stars at the top of the atmosphere for: (6) in, is the magnitude difference, is the sporadic radiation intensity, lx is Lux is the abbreviation of Lux, which is the radiation intensity of the star through the entire atmosphere to the surface of the earth. : (7) In the formula, is the total vertical atmospheric optical depth, For air quality: (8)

[0066] S3.2 processes the grayscale image of the star to obtain the star radiation intensity, and uses the atmospheric transmittance calculated by formula (5) in step S1 , the gray value of the star spot actually collected in step S2 and radiation intensity To perform calibration: + (9) in, and is the calibration coefficient, and the vertical transmittance of the entire atmospheric layer is obtained. for: T Meas l = exp [ -t l ]= exp ln [ E ground l ]- ln [ E Tat l ] m i (10)

[0067] Substituting equations (7), (8), and (9) into equation (10), we obtain: T Meas l = exp cos pt 18 0 o +0.15× 93.885-θ ⋅ ln [ E ground l ]- ln [ 1 0 0.4×Δm ⋅ E 0 ×1 0 -0.4m ] (11).

[0068] Figure 4 The figure shows a schematic diagram of star spots observed by ground-based telescopes. Figure 4 (a) shows the light spot of Lousu III collected at 21:20:02 on January 16, 2025; Figure 4(b) shows the Capella light spot collected at 22:27:00 on January 16, 2025. As the magnitude increases, the number of pixels covered by the observed light spot increases, which can be used as a relative true value. By comparing these light spot data with the whole-layer atmospheric transmittance obtained from multipath observations, correlation is established and other observation equipment is calibrated.

[0069] Figure 5 The results show that at 20:00 on September 29, 2024, atmospheric transmittance was measured in Changchun, using three different paths. A star map is collected every 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 transmittance values ​​of the entire atmosphere at different positions.

[0070] Furthermore, the specific process of step S4 is as follows:

[0071] S4.1 Calculate the transmittance of the entire atmosphere at the position of the star according to steps S1 to S3, and use the known star position and the transmittance of the entire atmosphere on the ground station path to characterize the transmittance of the entire atmosphere on the satellite-to-ground laser link path. The semivariogram It is expressed as: (12), In the formula, is the number of point pairs per bin and time lag, , is the interval division of spatial distance, is the time interval, and are observations in space and time, and Indicates different spatial locations. and Indicates different points in time;

[0072] S4.2 Semivariogram function describes the variation characteristics of spatial data in different directions. It represents the variance of the data, reflecting the overall variability of the data; is the base value, which represents the nugget effect and reflects the measurement error of the variable below the minimum sampling scale. ; and are two perpendicular components used to describe the lag distance in two-dimensional space; 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: (13), In the formula, is a proportional constant used to adjust the scale of the model, ; is a smoothing parameter used to adjust the smoothness of the model. ; is a shape parameter used to adjust the shape of the model. ; Used to adjust the weight of the direction vector, ; Used to adjust the attenuation characteristics of the model, ; Used to adjust the decay speed of the model. ; is the sill value, is the Dirac function. When the positions of two data points completely coincide in space, that is, the distance between them is 0, then , if the distance between the two data points is not 0, then .

[0073] Furthermore, the specific process of step S5 is as follows:

[0074] S5.1 uses the kriging method to provide an interpolator for the data collected in step S2, and optimizes the model parameters by minimizing the residual sum of squares between the empirical semivariogram and the theoretical semivariogram. The weighted least squares method is used to calculate the function parameters in equation (13): , , , , , ; Indicated in =0, The objective function of the least squares estimation of the directional semivariogram; Indicated in When, yes The objective function of the least squares estimation of the directional semivariogram; Considering at the same time and The objective function for the least squares estimation of the directional semivariogram; minimize , and for: (14), In the formula, represents the maximum distance in the spatial direction, Represents the theoretical semivariogram in the spatial direction and the value at 0 in the time direction, the corresponding weight is , It 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 theoretical semivariogram in the spatial direction and time direction The corresponding weight is , is a set of parameters related to the time direction; Represents the theoretical semivariogram in the spatial direction and time direction The corresponding weight is , It is a set of parameters related to spatial and temporal directions; Represents the empirical semivariogram in the spatial direction and the estimated value at time 0; Represents the empirical semivariogram over spatial distance and time direction The estimated value at Represents the maximum time interval in the time direction; ensures that the model parameters can accurately reflect the spatial characteristics of the data to estimate the atmospheric transmittance at unknown locations; and obtains the spatial and temporal decorrelation by finding the point where the semivariogram reaches 95% of its half value: (15), In the formula, Indicates the distance in space At , the semivariogram value when the time direction is 0, Represents the limiting semivariogram value in the spatial direction; Indicates the time interval At , the semivariogram value when the spatial direction is 0, represents the limiting semivariogram value in the time direction; 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; Represents discontinuous, small-scale variation in the data;

[0075] S5.2 uses two iterations to obtain more accurate results. In the first iteration, the weight function for: (16), In the formula, In a specific direction and distance The number of data point pairs at At a specific time and time interval The number of data point pairs at 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. The weight function in the second iteration is: (17), in, In 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 ;

[0076] 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: (18), In the formula, is the value of the unknown data, is the observed value at the sampling point, where .

[0077] 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 atmospheric transmittance of the whole layer; S4. Anisotropic semivariogram modeling, describing the variation characteristics of spatial data in different directions and analyzing the spatial correlation of different data; S5. By performing weighted summation of known sampling points through spatial interpolation, the transmittance of the entire atmospheric layer at unknown points is estimated, and the discrete data in space is converted into continuous surface data.

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 due to absorption by atmospheric molecules Considering water vapor and CO2 gas, it can be expressed as: (1)， 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; S1.2 Attenuation due to aerosol scattering Related to visibility, expressed as: (2)， In the formula, For atmospheric visibility The relevant empirical constants are , whose unit is kilometers, represents the extinction coefficient of aerosol; Meteorological attenuation transmittance Attenuation coefficient of laser light by raindrops Related, is the rainfall intensity in millimeters per hour: (3)， S1.3 Considering the attenuation of laser by atmospheric molecules, aerosols and meteorological conditions, the total atmospheric transmittance , expressed as: (4)， Substituting equations (1), (2) and (3) into equation (4), we can obtain the whole layer atmospheric transmittance: Theoretical value: (5)， 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 of the star image collected by the ground station. .

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 , the radiation intensity generated outside the atmosphere is , the radiation intensity of other stars at the top of the atmosphere for: (6)， in, is the magnitude difference, is the sporadic radiation intensity, lx is Lux is the abbreviation of Lux, which is the radiation intensity of the star through the entire atmosphere to the surface of the earth. : (7)， In the formula, is the total vertical atmospheric optical depth, For air quality: (8)， S3.2 processes the grayscale image of the star to obtain the star radiation intensity, and uses the atmospheric transmittance calculated by formula (5) in step S1 , the gray value of the star spot actually collected in step S2 and radiation intensity To perform calibration: + (9)， in, and is the calibration coefficient, and the vertical transmittance of the entire atmospheric layer is obtained. for: (10)， Substituting equations (7), (8), and (9) into equation (10), we obtain: (11)。 5. 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 S4 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 known star position and the transmittance of the entire atmosphere on the ground station path to characterize the transmittance of the entire atmosphere on the satellite-to-ground laser link path. The semivariogram It is expressed as: （12）， In the formula, is the number of point pairs per bin and time lag, , is the interval division of spatial distance, is the time interval, and are observations in space and time, and Indicates different spatial locations. and Indicates different points in time; S4.2 Semivariogram function describes the variation characteristics of spatial data in different directions. It represents the variance of the data, reflecting the overall variability of the data; is the base value, which represents the nugget effect and reflects the measurement error of the variable below the minimum sampling scale. ; and are two perpendicular components used to describe the lag distance in two-dimensional space; 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: （13）， In the formula, is a proportional constant used to adjust the scale of the model, ; is a smoothing parameter used to adjust the smoothness of the model. ; is a shape parameter used to adjust the shape of the model. ; Used to adjust the weight of the direction vector, ; Used to adjust the attenuation characteristics of the model, ; Used to adjust the decay speed of the model. ; is the sill value, is the Dirac function. When the positions of two data points completely coincide in space, that is, the distance between them is 0, then , if the distance between the two data points is not 0, then .

6. 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 S5 is as follows: S5.1 uses the kriging method to provide an interpolator for the data collected in step S2, and optimizes the model parameters by minimizing the residual sum of squares between the empirical semivariogram and the theoretical semivariogram. The weighted least squares method is used to calculate the function parameters in equation (13): , , , , , ; Indicated in =0, The objective function of the least squares estimation of the directional semivariogram; Indicated in When, yes The objective function of the least squares estimation of the directional semivariogram; Considering at the same time and The objective function for the least squares estimation of the directional semivariogram; minimize , and for: （14）， In the formula, represents the maximum distance in the spatial direction, Represents the theoretical semivariogram in the spatial direction and the value at 0 in the time direction, the corresponding weight is , It 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 theoretical semivariogram in the spatial direction and time direction The corresponding weight is , is a set of parameters related to the time direction; Represents the theoretical semivariogram in the spatial direction and time direction The corresponding weight is , It is a set of parameters related to spatial and temporal directions; Represents the empirical semivariogram in the spatial direction and the estimated value at time 0; Represents the empirical semivariogram in spatial distance and time direction The estimated value at Represents the maximum time interval in the time direction; ensures that the model parameters can accurately reflect the spatial characteristics of the data to estimate the atmospheric transmittance at unknown locations; and obtains the spatial and temporal decorrelation by finding the point where the semivariogram reaches 95% of its half value: （15）， In the formula, Indicates the distance in space At , the semivariogram value when the time direction is 0, Represents the limiting semivariogram value in the spatial direction; Indicates the time interval At , the semivariogram value when the spatial direction is 0, represents the limiting semivariogram value in the time direction; 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; 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 for: （16）， In the formula, In a specific direction and distance The number of data point pairs at At a specific time and time interval The number of data point pairs at the denominator is the sum of the number 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: （17）， in, In a specific direction and distance The semivariogram value at , with parameters , the denominator is the sum of the reciprocals of all semivariogram values; At a specific time and time interval The semivariogram value at ; 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: （18）， In the formula, is the value of the unknown data, is the observed value at the sampling point, where .

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