Method for calculating non-uniform atmospheric refraction angle of near space

Abstract

The invention relates to a near space non-uniform atmospheric refraction angle calculation method, which comprises the following steps: acquiring a deflection angle of light in the atmosphere, and obtaining a refraction angle model; determining atmospheric density change, obtaining a Boltzmann statistical model, and further obtaining a Boltzmann energy distribution model; determining molecular kinetic energy and potential energy, substituting the molecular kinetic energy and potential energy into a Boltzmann energy distribution model to obtain the atmospheric molecular number density away from the geocenter, and determining the change rule of the atmospheric molecular number density along with the altitude and the atmospheric temperature according to the atmospheric molecular number density away from the geocenter; acquiring a transmission path from the observation height to the top of the atmospheric layer, and acquiring the atmospheric temperature and atmospheric pressure at the observation height by combining the change rule of the atmospheric molecular number density along with the altitude and the atmospheric temperature; and inputting the atmospheric temperature and the atmospheric pressure at the observation height into an Elden refractive index model to obtain a refractive index value under a corresponding radiation condition, and inputting the refractive index value into a refraction angle model to obtain a refraction angle.

Description

Technical Field

[0001] The invention relates to the technical field of near-space atmospheric optics, and in particular to a method for calculating a near-space non-uniform atmospheric refraction angle. Background Art

[0002] Importance of studying atmospheric refraction laws: The complexity and variability of the Earth's atmosphere show significant spatial characteristics in different spheres. When conducting near-space detection activities, the deflection of detection light when passing through various atmospheric layers cannot be ignored. This deflection phenomenon may lead to positioning errors. If you want to improve the positioning accuracy of optical detection targets and obtain key information such as accurate deflection angles and propagation trajectories, it is necessary to explore the distribution law of atmospheric refractive index. It is of great significance to fields such as astronomy and meteorology, and can help us observe the positions of celestial bodies more accurately, predict atmospheric optical phenomena, etc.

[0003] Limitations of traditional atmospheric refraction: Due to the dynamic atmospheric activities in the Sun-Earth space, the atmospheric inhomogeneity around the world shows significant cross-scale changes. This change is mainly affected by solar radiation. As the main heat source of the earth, the transmission process of solar radiation in the atmosphere has a significant impact on the temporal and spatial distribution of atmospheric refractive index. This leads to considerable errors in actual navigation and detection activities. These errors not only affect the accuracy of the data, but also pose a potential threat to the safety of related operations. Summary of the invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the present invention proposes a method for calculating the non-uniform atmospheric refraction angle in near space, and establishes a non-uniform atmospheric refraction model in near space considering solar radiation. The model can reveal the basic law of atmospheric refractive index and improve the autonomy, controllability and time-varying nature of detection activities. In addition, this model can also significantly improve the detection accuracy and the accuracy of navigation positioning.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for calculating the refraction angle of non-uniform atmosphere in near space, comprising:

[0007] Obtaining the deflection angle of the light in the atmosphere, and obtaining a refraction angle model according to the deflection angle;

[0008] Determine the change of atmospheric density, obtain a Boltzmann statistical model according to the change of atmospheric density, and obtain the distribution law of atmospheric molecule number density with altitude based on the Boltzmann statistical model, that is, the Boltzmann energy distribution model;

[0009] Determine the molecular kinetic energy and potential energy, substitute the molecular kinetic energy and potential energy into the Boltzmann energy distribution model, obtain the number density of atmospheric molecules at a distance from the center of the earth, and determine the law of change of the number density of atmospheric molecules with altitude and atmospheric temperature according to the number density of atmospheric molecules at a distance from the center of the earth;

[0010] Obtain the transmission path from the observation altitude to the top of the atmosphere, and obtain the atmospheric temperature and atmospheric pressure at the observation altitude by combining the variation law of the atmospheric molecule number density with the altitude and the atmospheric temperature;

[0011] The atmospheric temperature and atmospheric pressure at the observation height are input into the Elden refractive index model to obtain the refractive index value under the corresponding radiation conditions, and the refractive index value is input into the refraction angle model to obtain the refraction angle.

[0012] Optionally, the method for obtaining the deflection angle of the light in the atmosphere is:

[0013]

[0014] Among them, R S is the deflection angle of light in the atmosphere, R L is the radius of curvature of the light, n is the refractive index of any layer, r is the height of the corresponding atmospheric layer, n T The zenith angle of the light is The refractive index at the tangent height, r T is the tangent height radius, and θ is the refraction angle.

[0015] Optionally, the method for obtaining the refraction angle model is:

[0016] The near-space atmosphere is layered, and the light in each layer is set to propagate in a straight line, and the temperature, pressure, and density of the atmosphere in the same layer are consistent. If the light is incident at an initial angle α, the zenith angle of the light is determined according to Snell's law as The refractive index at the tangent height is related to the radius at the tangent height:

[0017] n0r0 sinα=n T r T

[0018] According to the zenith angle of the light The refractive index at the tangent height and the tangent height radius are combined with the deflection angle to obtain the refraction angle model:

[0019]

[0020] Among them, α is the initial angle, Δn is the difference in refractive index between the two layers of atmosphere, and n i is the refractive index of the ith layer of atmosphere, r iis the height of the ith layer of atmosphere, R is the light refraction angle, n0 is the atmospheric refractive index at the initial detection position, and r0 is the initial detection height.

[0021] Optionally, obtaining the Boltzmann statistical model includes:

[0022] Determine the atmospheric density change:

[0023]

[0024] Among them, ρ(h) and P(h) are the air density and atmospheric pressure at a height h from sea level, respectively, and g is the gravitational acceleration;

[0025] Based on the ideal gas state model, the air density at the height h from the sea level is determined: combined with the atmospheric density change, the Boltzmann statistical model is obtained:

[0026]

[0027] Where m is the molecular mass, κ is the Boltzmann constant, and T(h) is the atmospheric temperature at a height h above sea level.

[0028] Optionally, obtaining the Boltzmann energy distribution model includes:

[0029]

[0030] in, is the number of molecules distributed in the velocity interval and position interval, ρ0 is the potential energy ε p is the number of molecules per unit volume at 0, T is the thermodynamic temperature, ε k is the molecular kinetic energy, κ is the Boltzmann constant, (v x ,v y ,v z ) is the speed interval, and (x,y,z) is the position interval.

[0031] Optionally, the method for determining the molecular kinetic energy and potential energy is:

[0032] The method for determining the kinetic energy of the molecule is:

[0033]

[0034] The method for determining the molecular potential energy is:

[0035]

[0036] Where r is the distance from the center of the earth to the observation position, m is the molecular mass, G is the gravitational constant, M is the gravitational mass, ρ is the molecular density, and v x 、vy 、v z is the molecular velocity, r e is the radius of the Earth.

[0037] Optionally, obtaining the atmospheric molecule number density at the distance from the center of the earth includes:

[0038] Substitute the molecular kinetic energy and potential energy into the Boltzmann energy distribution model to obtain the number density of atmospheric molecules at the distance from the center of the earth:

[0039]

[0040] When the distance from the center of the earth to the observation position approaches infinite height, the total molecular potential energy is determined. If the variation of gravitational acceleration with height is ignored, it can be simplified to:

[0041]

[0042] in, is the molecular density at sea level, r is the distance from the center of the earth to the observation location, h is the altitude, m is the molecular mass, and v x 、v y 、v z is the molecular velocity, G is the gravitational constant, m is the gravitational mass, r e is the radius of the Earth.

[0043] Optionally, the method for obtaining the transmission path from the observation altitude to the top of the atmosphere is:

[0044]

[0045] in, Solar zenith angle, hObservation altitude, h m Top of atmosphere.

[0046] Optionally, obtaining the atmospheric temperature and atmospheric pressure at the observation height includes:

[0047] Integrate the transmission path from the observation height to the top of the atmosphere. When the top of the atmosphere is infinite, set the transmittance condition and obtain the atmospheric temperature and atmospheric pressure at the observation height:

[0048]

[0049] Where κ is the Boltzmann constant, m is the molecular mass, k is the dispersion coefficient, ρ0 is the sea level atmospheric density, T0 is the sea level atmospheric temperature, g is the intermediate gravitational acceleration, is the solar zenith angle, T h B(h) is the temperature-related action, C is the pressure-related action, and P0 is the atmospheric pressure at sea level.

[0050] The beneficial effects of the present invention are:

[0051] The present invention establishes a non-uniform atmospheric refraction model in near space taking into account solar radiation, which can reveal the basic laws of atmospheric refractive index and improve the autonomy, controllability and time-varying nature of detection activities.

[0052] The present invention aims to solve the problem that the detection light path at different flight altitudes will be refracted in the atmosphere, which will lead to an error between the estimated direction of the target detected and extracted and the actual direction. Based on the star light refraction navigation model, the present invention uses the atmospheric layered structure, comprehensively considers the relationship between the solar radiation angle and the atmospheric refractive index, deeply analyzes the changing law of the atmospheric refractive index and constructs a refraction model.

[0053] The present invention helps to accurately predict the propagation direction and propagation path of optical signals in the atmosphere, which can ensure the accuracy and reliability of detection data and is of great significance to the fields of astronomical navigation, optical communication, lidar, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0055] Figure 1 This is a schematic diagram of an embodiment of the present invention in which when light passes through the Earth's atmosphere in near space, starlight is refracted toward the center of the Earth due to uneven atmospheric density;

[0056] Figure 2 A flow chart of establishing a near-space non-uniform atmospheric refraction model according to an embodiment of the present invention;

[0057] Figure 3 This is a flow chart of a near-space non-uniform atmospheric refraction model under solar radiation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] 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.

[0060] The present embodiment discloses a method for calculating the refraction angle of a non-uniform atmosphere in near space, including: obtaining the deflection angle of light in the atmosphere, and obtaining a refraction angle model according to the deflection angle; determining the change of atmospheric density, and obtaining a Boltzmann statistical model according to the change of atmospheric density, and obtaining the distribution law of the number density of atmospheric molecules with altitude based on the Boltzmann statistical model, that is, the Boltzmann energy distribution model; determining the molecular kinetic energy and potential energy, substituting the molecular kinetic energy and potential energy into the Boltzmann energy distribution model, obtaining the number density of atmospheric molecules at a distance from the center of the earth, and determining the change law of the number density of atmospheric molecules with altitude and atmospheric temperature according to the number density of atmospheric molecules at the distance from the center of the earth; obtaining the transmission path from the observation height to the top of the atmosphere, and obtaining the atmospheric temperature and atmospheric pressure at the observation height in combination with the change law of the number density of atmospheric molecules with altitude and atmospheric temperature; inputting the atmospheric temperature and atmospheric pressure at the observation height into the Elden refractive index model, obtaining the refractive index value under the corresponding radiation conditions, and inputting the refractive index value into the refraction angle model to obtain the refraction angle.

[0061] Specifically, the atmosphere is divided into continuous and uniform concentric layers, and it is assumed that the atmospheric composition and physical-optical parameters in the same layer of atmosphere are approximately the same, thereby establishing a non-uniform atmospheric refraction model in near space of 20km-80km. The atmospheric transmittance is calculated by the solar transmission irradiance at different solar zenith angles at altitudes of 20km-80km, and the atmospheric temperature and atmospheric pressure at the corresponding altitude are obtained. Finally, through the theoretical analysis of the multi-layer atmospheric model, the changes in light deflection caused by the differences in solar radiation angles under different detection conditions are obtained.

[0062] Using the standard atmospheric model, the effects of atmospheric temperature, pressure, density and other factors on the atmospheric refractive index and the spatial distribution of the refractive index are studied at a 1km layered scale.

[0063] The atmospheric transmittance is calculated by the transmitted irradiance and the incident irradiance, the atmospheric temperature and atmospheric pressure at the corresponding height are calculated using the Boltzmann distribution law, and the refractive index of different stratified areas is calculated using the Edlen refractive index theory.

[0064] Due to the uneven density of the atmosphere, starlight will be refracted toward the center of the earth. Therefore, the apparent position of the star observed from the spacecraft is shifted upward compared to the actual position. The principle of light refraction for high-precision positioning in the inhomogeneous atmosphere is as follows: Figure 1 shown.

[0065] like Figure 2As shown, based on the known tangent height of the light, the deflection angle of the light in the atmospheric propagation can be calculated using the starlight refraction formula. Considering that the atmospheric density in the near space changes with the height, in order to improve the accuracy of the calculation results, the present invention optimizes the starlight refraction model, and on this basis, the atmospheric stratification is processed to establish a near space non-uniform atmospheric refraction model. Based on the known altitude, we can call the temperature and pressure data in the standard atmospheric model, and substitute it into the Edlen refractive index formula to calculate the refraction angle.

[0066] like Figure 3 As shown in the figure, firstly, by applying Snell's Law and the principle of light refraction, we can model the propagation path of light between regions with different refractive indices. Then, using MODTRAN atmospheric radiation software to calculate the solar spectrum transmittance can help us more accurately analyze the propagation of light at different solar altitudes, and can also analyze the molecular absorption spectrum and scattering process under specific atmospheric conditions, so as to invert the atmospheric temperature and atmospheric pressure. h and T h Substitute it into the Elden refractive index model formula and calculate the refractive index value under the corresponding radiation conditions according to the model. Through the calculation of the refractive index, the numerical integration or superposition summation method can be used to further obtain the value of the refraction angle.

[0067] This embodiment discloses a specific process for establishing a near-space non-uniform atmospheric refraction model:

[0068] According to the basic law of atmospheric refraction, the deflection angle of light in the atmosphere can be expressed as:

[0069]

[0070] The near-space atmosphere is layered, and it is assumed that the light in the layer propagates in a straight line, and the temperature, pressure, density and other parameters of the same layer of atmosphere are consistent. If the light is incident at an initial angle α, according to Snell's law:

[0071] n0r0 sinα=n T r T , (2)

[0072] Then formula (1) can be written as:

[0073]

[0074] Where Δn is the difference in refractive index between the two layers of atmosphere, n i is the refractive index of the ith layer of atmosphere, r i is the height of the ith atmospheric layer.

[0075] The structure of the Earth's atmosphere is not only affected by the Earth's gravity, but also by factors such as solar radiation and the Earth's own rotation. These factors work together to form a complex and orderly atmospheric environment. Under the assumption of fluid dynamics equilibrium, the atmosphere is evenly layered, and the differential of air pressure with respect to altitude h is:

[0076]

[0077] According to the inverse square law of gravity, the acceleration due to gravity is related to the altitude and can be expressed as follows:

[0078]

[0079] where r e is the radius of the earth, with an average value of 6371.4km; g0 is the gravitational acceleration at the average sea level, with a value equal to 9.08665m / s2. The core of the law of atmospheric pressure changing with altitude is the change in atmospheric density, which can be known from the hydrostatic equation:

[0080]

[0081] In the formula, ρ(h) is the air density at a height h from sea level. From the ideal gas state equation, we know that:

[0082]

[0083] In the above formula, m is the molecular mass; κ is the Boltzmann constant, which is 1.38×10 -23 J / K. Combining equations (8) and (9):

[0084]

[0085] Next, according to the Boltzmann statistical law, the distribution formula of atmospheric molecular density with altitude is obtained. The Boltzmann energy distribution expression is:

[0086]

[0087] In the formula is the number of molecules distributed in the velocity interval and position interval; ρ0 is the potential energy ε p is the number of all molecules per unit volume at 0; T is the thermodynamic temperature in K; ε k is the molecular kinetic energy, expressed as:

[0088]

[0089] For the Earth's atmosphere, if sea level is taken as the zero potential energy surface, then the molecular density at sea level is ρ r0It is numerically equal to ρ0. The molecular potential energy expression can be obtained from the law of universal gravitation:

[0090]

[0091] In the above formula, r is the distance from the center of the earth to the observation position, r = r e +h, substitute equations (12) and (13) into equation (11) and integrate the velocity to obtain the number density of atmospheric molecules at a distance r from the center of the earth: r :

[0092]

[0093] When r approaches infinite height, that is, the top of the atmosphere, the altitude h<<re, and the total molecular potential energy is approximately:

[0094] ε p ≈mgh, (15)

[0095] If we ignore the variation of gravitational acceleration with height, we can use the substitution formula:

[0096]

[0097] Then equation (14) can be simplified to

[0098]

[0099] The law of how the number density of atmospheric molecules changes with altitude and atmospheric temperature is obtained.

[0100] In actual observation, due to the existence of the solar zenith angle Therefore, the observation height h to the top of the atmosphere h m The transmission path is approximately:

[0101]

[0102] Substitute (17) into the transmission equation and integrate it:

[0103]

[0104] Since the top of the atmosphere is h m →∞, so equation (19) can be written as:

[0105]

[0106] In the formula is the zenith angle. Under the condition of known transmittance τ, C can be obtained, then P h can be obtained, and T can be obtained by the same logic h :

[0107]

[0108] in

[0109] Therefore, we only need to solve C in equations (20) and (21) to obtain P at the observation height h. h ,T h .

[0110] We will find P h and T h Substitute into the Elden refractive index model formula:

[0111] (n-1) s ×10 8 =8342.13+2406030(130-v 2 ) -1 +15997(38.9-v 2 ) -1 , (twenty two)

[0112]

[0113] The refractive index value under the corresponding radiation conditions is calculated according to the model. Through the calculation of the refractive index, the numerical integration or superposition summation method can be used to further obtain the value of the refraction angle. The complex atmospheric refraction law is realized when the refractive index changes with the height or other environmental parameters. The detection accuracy is improved, providing an important reference for research and application in the field of optics.

[0114] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for calculating the refraction angle of non-uniform atmosphere in near space, characterized in that: include: Obtaining the deflection angle of the light in the atmosphere, and obtaining a refraction angle model according to the deflection angle; Determine the change of atmospheric density, obtain a Boltzmann statistical model according to the change of atmospheric density, and obtain the distribution law of atmospheric molecule number density with altitude based on the Boltzmann statistical model, that is, the Boltzmann energy distribution model; Determine the molecular kinetic energy and potential energy, substitute the molecular kinetic energy and potential energy into the Boltzmann energy distribution model, obtain the number density of atmospheric molecules at a distance from the center of the earth, and determine the law of change of the number density of atmospheric molecules with altitude and atmospheric temperature according to the number density of atmospheric molecules at a distance from the center of the earth; Obtain the transmission path from the observation altitude to the top of the atmosphere, and obtain the atmospheric temperature and atmospheric pressure at the observation altitude by combining the variation law of the atmospheric molecule number density with the altitude and the atmospheric temperature; The atmospheric temperature and atmospheric pressure at the observation height are input into the Elden refractive index model to obtain the refractive index value under the corresponding radiation conditions, and the refractive index value is input into the refraction angle model to obtain the refraction angle.

2. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 1, characterized in that: The method for obtaining the deflection angle of the light in the atmosphere is: Among them, R is the deflection angle of light in the atmosphere, R L is the radius of curvature of the light, n is the refractive index of any layer, r is the height of the corresponding atmospheric layer, n T The zenith angle of the light is The refractive index at the tangent height, r T is the tangent height radius, and θ is the refraction angle.

3. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 2, characterized in that: The method for obtaining the refraction angle model is: The near-space atmosphere is layered, and the light in each layer is set to propagate in a straight line, and the temperature, pressure, and density of the atmosphere in the same layer are consistent. If the light is incident at an initial angle α, the zenith angle of the light is determined according to Snell's law as The refractive index at the tangent height is related to the radius at the tangent height: n0r0sinα=n T r T According to the zenith angle of the light The refractive index at the tangent height and the tangent height radius are combined with the deflection angle to obtain the refraction angle model: Among them, α is the initial angle, Δn is the difference in refractive index between the two layers of atmosphere, and n i is the refractive index of the ith layer of atmosphere, r i is the height of the ith layer of atmosphere, R is the light refraction angle, n0 is the atmospheric refractive index at the initial detection position, and r0 is the initial detection height.

4. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 1, characterized in that: Obtaining the Boltzmann statistical model includes: Determine the atmospheric density change: Among them, ρ(h) and P(h) are the air density and atmospheric pressure at a height h from sea level, respectively, and g is the gravitational acceleration; Based on the ideal gas state model, the air density at the height h from the sea level is determined: combined with the atmospheric density change, the Boltzmann statistical model is obtained: Where m is the molecular mass, κ is the Boltzmann constant, and T(h) is the atmospheric temperature at a height h above sea level.

5. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 1, characterized in that: Obtaining the Boltzmann energy distribution model includes: in, is the number of molecules distributed in the velocity interval and position interval, ρ0 is the potential energy ε p is the number of molecules per unit volume at 0, T is the thermodynamic temperature, ε k is the molecular kinetic energy, κ is the Boltzmann constant, (v x ,v y ,v z ) is the speed interval, and (x,y,z) is the position interval.

6. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 5, characterized in that: The method to determine the kinetic energy and potential energy of a molecule is: The method for determining the kinetic energy of the molecule is: The method for determining the molecular potential energy is: Where r is the distance from the center of the earth to the observation position, m is the molecular mass, G is the gravitational constant, M is the gravitational mass, ρ is the molecular density, and v x 、v y 、v z is the molecular velocity, r e is the radius of the Earth.

7. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 1, characterized in that: Obtaining the atmospheric molecule number density at the distance from the center of the earth includes: Substitute the molecular kinetic energy and potential energy into the Boltzmann energy distribution model to obtain the number density of atmospheric molecules at the distance from the center of the earth: When the distance from the center of the earth to the observation position approaches infinite height, the total molecular potential energy is determined. If the variation of gravitational acceleration with height is ignored, it can be simplified to: Among them, ρ r0 is the molecular density at sea level, r is the distance from the center of the earth to the observation position, h is the altitude, m is the molecular mass, G is the gravitational constant, m is the gravitational mass, and r e is the radius of the Earth.

8. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 1, characterized in that: The method for obtaining the transmission path from the observation altitude to the top of the atmosphere is: in, Solar zenith angle, hObservation altitude, h m Top of atmosphere.

9. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 1, characterized in that: Obtaining the atmospheric temperature and atmospheric pressure at the observation height includes: Integrate the transmission path from the observation height to the top of the atmosphere. When the top of the atmosphere is infinite, set the transmittance condition and obtain the atmospheric temperature and atmospheric pressure at the observation height: Where κ is the Boltzmann constant, m is the molecular mass, k is the dispersion coefficient, ρ0 is the sea level atmospheric density, T0 is the sea level atmospheric temperature, g is the intermediate gravitational acceleration, is the solar zenith angle, T h B(h) is the temperature-related action, C is the pressure-related action, and P0 is the atmospheric pressure at sea level.

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