A method for calculating the refraction angle of non-uniform atmosphere in near space

Abstract

The present invention relates to a method for calculating the refraction angle of a near-space non-uniform atmosphere. The method comprises the following steps: obtaining the deflection angle of light in the atmosphere to obtain a refraction angle model; determining atmospheric density changes to obtain 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 the Boltzmann energy distribution model to obtain the number density of atmospheric molecules at a distance from the center of the earth; determining a variation law of the number density of atmospheric molecules with altitude and atmospheric temperature based on the number density of atmospheric molecules at the distance from the center of the earth; obtaining a transmission path from an observation altitude to the top of the atmosphere, and obtaining the atmospheric temperature and atmospheric pressure at the observation altitude in combination with the variation law of the number density of atmospheric molecules with altitude and atmospheric temperature; inputting the atmospheric temperature and atmospheric pressure at the observation altitude into an Elden refractive index model to obtain a refractive index value under corresponding radiation conditions, and inputting the refractive index value into a refraction angle model to obtain the refraction angle.

Description

Technical Field

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

[0002] The importance of studying atmospheric refraction patterns: The complexity and variability of Earth's atmosphere exhibit distinct spatial characteristics across different layers. When conducting near-space exploration, the deflection of probe light as it passes through the various atmospheric layers is crucial. This deflection can lead to positioning errors. To improve the positioning accuracy of optical detection targets and obtain critical information such as precise deflection angles and propagation trajectories, it is necessary to investigate the distribution of atmospheric refractive index. This is of great significance to fields such as astronomy and meteorology, enabling more accurate observation of celestial positions and prediction of atmospheric optical phenomena.

[0003] Limitations of traditional atmospheric refraction: Due to dynamic atmospheric activity in the Sun-Earth space, conventional atmospheric inhomogeneities exhibit significant cross-scale variations across the globe. This variation is primarily influenced by solar radiation, Earth's primary heat source. The transmission of solar radiation through the atmosphere significantly influences the spatiotemporal distribution of atmospheric refractivity. This leads to significant errors in actual navigation and exploration activities, which not only affect data accuracy but also pose a potential threat to the safety of related operations. Summary of the Invention

[0004] To address the aforementioned issues with existing technologies, this paper proposes a method for calculating the non-uniform atmospheric refraction angle in near-space. This method establishes a non-uniform atmospheric refraction model for near-space that takes solar radiation into account. This model reveals the fundamental laws governing atmospheric refractive index, enhancing the autonomy, controllability, and time-variability of detection activities. Furthermore, this model significantly improves detection accuracy and navigation positioning.

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

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

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

[0008] Determining atmospheric density changes, obtaining a Boltzmann statistical model based on the atmospheric density changes, and obtaining a distribution pattern of atmospheric molecule number density with altitude, i.e., a Boltzmann energy distribution model, based on the Boltzmann statistical model;

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

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

[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, a method for obtaining the deflection angle of the light in the atmosphere is:

[0013]

[0014] Among them, R S is the angle of light deflection 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. The temperature, pressure, and density of the atmosphere in the same layer are all 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 and the radius at the tangent height are:

[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 i-th layer of atmosphere, r iis the height of the i-th layer of atmosphere, R is the refraction angle of light, 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] Where ρ(h) and P(h) are the air density and atmospheric pressure at a height h above sea level, respectively, and g is the acceleration due to gravity.

[0025] Based on the ideal gas state model, the air density at the height h above the sea level is determined. In combination 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 all molecules in a 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 range, and (x,y,z) is the position range.

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

[0032] The method for determining the molecular kinetic energy 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 rate, r e is the radius of the Earth.

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

[0039]

[0040] When the distance from the center of the Earth to the observation position approaches infinite height, determine the total molecular potential energy. If we ignore the variation of gravitational acceleration with height, 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 position, 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, a 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 the 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 and the transmittance condition is set, 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 for near space taking into account solar radiation. The model 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 addresses the problem that the detection light path at different flight altitudes will be refracted in the atmosphere, which leads to an error between the estimated direction of the target detected 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, ensuring the accuracy and reliability of detection data, and is of great significance to astronomical navigation, optical communications, lidar and other fields. 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 following briefly introduces the drawings required for use in the embodiments. 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 any creative work.

[0055] Figure 1 This is a schematic diagram of an embodiment of the present invention showing that when light passes through the Earth's atmosphere in near space, starlight is refracted toward the Earth's center 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 clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts 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] This embodiment discloses a method for calculating the refraction angle of a near-space non-uniform atmosphere, including: obtaining the deflection angle of light in the atmosphere, and obtaining a refraction angle model based on the deflection angle; determining the change in atmospheric density, obtaining a Boltzmann statistical model based on the change in atmospheric density, and obtaining the distribution law of atmospheric molecule number density with altitude, that is, a Boltzmann energy distribution model based on the Boltzmann statistical model; determining molecular kinetic energy and potential energy, substituting the molecular kinetic energy and potential energy into the Boltzmann energy distribution model to obtain the atmospheric molecule number density at a distance from the center of the earth, and determining the change law of the atmospheric molecule number density with altitude and atmospheric temperature based on the atmospheric molecule number density at the distance from the center of the earth; obtaining a transmission path from the observation altitude to the top of the atmosphere, and obtaining the atmospheric temperature and atmospheric pressure at the observation altitude based on the change law of the atmospheric molecule number density with altitude and atmospheric temperature; inputting the atmospheric temperature and atmospheric pressure at the observation altitude into an Elden refractive index model to obtain a refractive index value under 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 the near space of 20km-80km. The atmospheric transmittance is calculated by measuring the solar transmitted 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 theoretical analysis of the multi-layer atmospheric model, the changes in light deflection caused by differences in solar radiation angles under different detection conditions are obtained.

[0062] Using a standard atmospheric model, the effects of atmospheric temperature, pressure, density, and other factors on the atmospheric refractive index, as well as 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 layered 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 stars observed from the spacecraft is shifted upwards compared to the actual position. The principle of light refraction used 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 starlight refraction formula can be used to calculate the deflection angle of light in the atmosphere. Considering that the atmospheric density in near-space varies with altitude, to improve the accuracy of the calculation results, this paper optimizes the starlight refraction model and, based on this, processes the atmospheric stratification to establish a near-space non-uniform atmospheric refraction model. Based on the known altitude, we can call the temperature and pressure data from the standard atmospheric model and substitute them into the Edlen refractive index formula to calculate the refraction angle.

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

[0067] This embodiment discloses the specific process of 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 divided into layers, and it is assumed that light propagates in a straight line within the layer, and that the temperature, pressure, density and other parameters of the atmosphere in the same layer are consistent. If the light is incident at an initial angle α, according to Snell's law, it can be known that:

[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 i-th layer of atmosphere, r i is the height of the i-th atmospheric layer.

[0075] The structure of the Earth's atmosphere is influenced not only 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 and uniform atmospheric stratification, 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 6371.4 km; g0 is the acceleration of gravity at mean sea level, with a value equal to 9.08665 m / s2. The core of the law of atmospheric pressure variation with altitude is the change in atmospheric density, which can be seen from the hydrostatic equation:

[0080]

[0081] Where ρ(h) is the air density at a height h above 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, we can obtain the distribution formula of atmospheric molecular number density with altitude. 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 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 number 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 atmospheric molecular density ρ 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 change of gravity acceleration with height, we can use the substitution formula:

[0096]

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

[0098]

[0099] The law of change of atmospheric molecule number density with altitude and atmospheric temperature was 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 similarly T can be obtained h :

[0107]

[0108] in

[0109] Therefore, we only need to find C in (20) and (21) to get 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 model calculates the refractive index under the corresponding radiation conditions. The refractive index calculation can be used to further derive the refraction angle using numerical integration or superposition summation. This allows for the analysis of complex atmospheric refraction patterns, where the refractive index varies with altitude or other environmental parameters. This improves detection accuracy and provides an important reference for research and applications in the field of optics.

[0114] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined 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 light in the atmosphere, and obtaining a refraction angle model based on the deflection angle; Determining atmospheric density changes, obtaining a Boltzmann statistical model based on the atmospheric density changes, and obtaining a distribution pattern of atmospheric molecule number density with altitude, i.e., a Boltzmann energy distribution model, based on the Boltzmann statistical model; Determine molecular kinetic energy and potential energy, substitute the molecular kinetic energy and potential energy into the Boltzmann energy distribution model to obtain the atmospheric molecular number density at a distance from the center of the earth, and determine how the atmospheric molecular number density changes with altitude and atmospheric temperature based on the atmospheric molecular number density at a distance from the center of the earth; Obtaining the transmission path between the observation altitude and the top of the atmosphere, and combining the variation of the atmospheric molecule number density with the altitude and the atmospheric temperature to obtain the atmospheric temperature and atmospheric pressure at the observation altitude; 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, wherein: 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, wherein: 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. The temperature, pressure, and density of the atmosphere in the same layer are all 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 follows: The refractive index at the tangent height and the radius at the tangent height are: 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 i-th layer of atmosphere, r i is the height of the i-th layer of atmosphere, R is the deflection angle of light in the atmosphere, 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, wherein: Obtaining the Boltzmann statistical model includes: Determine the atmospheric density change: Where ρ(h) and P(h) are the air density and atmospheric pressure at a height h above sea level, respectively, and g is the acceleration due to gravity. Based on the ideal gas state model, the air density at the height h above the sea level is determined. In combination 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, wherein: 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 all molecules in a 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 range, and (x,y,z) is the position range.

6. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 5, wherein: The method to determine the kinetic energy and potential energy of a molecule is: The method for determining the molecular kinetic energy 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 rate, r e is the radius of the Earth.

7. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 4, wherein: 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 center of the earth: When the distance from the center of the Earth to the observation position approaches infinite height, determine the total molecular potential energy. If we ignore the variation of gravitational acceleration with height, it can be simplified to: in, 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, 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, wherein: The method for obtaining the transmission path between the observation altitude and the top of the atmosphere is: in, Solar zenith angle, hObservation altitude, h m Top of the atmosphere.

9. The method for calculating the near-space non-uniform atmospheric refraction angle according to claim 8, wherein: 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 and the transmittance condition is set, 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, 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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