CN110954903A - Atmospheric turbulence detection method and system based on vortex electromagnetic waves - Google Patents

Atmospheric turbulence detection method and system based on vortex electromagnetic waves Download PDF

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CN110954903A
CN110954903A CN201911323840.0A CN201911323840A CN110954903A CN 110954903 A CN110954903 A CN 110954903A CN 201911323840 A CN201911323840 A CN 201911323840A CN 110954903 A CN110954903 A CN 110954903A
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electromagnetic waves
atmospheric turbulence
turbulence
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CN110954903B (en
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周晨
王翔
周欣
赵正予
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Wuhan University WHU
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    • G—PHYSICS
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G01S13/95—Radar or analogous systems specially adapted for specific applications for meteorological use
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G01S13/95—Radar or analogous systems specially adapted for specific applications for meteorological use
    • G—PHYSICS
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract

The invention discloses an atmospheric turbulence detection method and system based on vortex electromagnetic waves, belonging to the field of atmospheric detection, and the realization of the method comprises the following steps: transmitting OAM electromagnetic waves to a region to be detected; receiving the backward scattering electromagnetic waves aiming at the region to be detected, identifying a wave field distribution function of the backward scattering electromagnetic waves, and solving a multiphase interference factor of the atmospheric turbulence according to the wave field distribution function of the backward scattering electromagnetic waves and the wave field distribution function of the OAM electromagnetic waves under the condition of no turbulence; solving a phase factor corresponding to the atmospheric turbulence according to a wave field distribution function of the back scattering electromagnetic wave and the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction, and representing the atmospheric turbulence state by using a complex phase interference factor and the phase factor. The invention can effectively detect the long-distance atmospheric turbulence.

Description

Atmospheric turbulence detection method and system based on vortex electromagnetic waves
Technical Field
The invention belongs to the technical field of atmospheric detection, and particularly relates to an atmospheric turbulence detection method and system based on vortex electromagnetic waves.
Background
Since the discovery of turbulent flow phenomena by Reynolds in 1883, research on the mechanisms by which turbulence occurs, the structure of turbulence, and the fundamental laws of turbulent flow has been a topic of interest to hydromechanics and heat transfer scientists for over a hundred years. Turbulence is a spatially irregular and temporally disorganized non-linear fluid motion of the atmosphere that exhibits a highly complex three-dimensional unsteady, rotating irregular flow regime. Atmospheric turbulence can cause the real-time structure of the atmosphere to change, can simultaneously generate certain interference effect on the propagation of light waves, sound waves and electromagnetic waves in the atmosphere, and has great influence on the flight performance, the structural load and the flight safety of an aircraft. Therefore, it is necessary to detect atmospheric turbulence.
Currently, doppler sodar and doppler lidar are mainly used in the prior art, wherein although the accuracy of doppler sodar is high, the sound is greatly attenuated in the atmosphere, resulting in a limited detection range of doppler sodar. The doppler laser radar uses laser as a detection medium, and utilizes the atmospheric turbulence to realize turbulence detection on scattering and refraction signals of the laser, however, the action distance of the doppler laser radar is generally within 10 kilometers, and therefore, the doppler laser radar has a limited effect.
Therefore, the prior art has the technical problem that the long-distance atmospheric turbulence cannot be effectively detected.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides an atmospheric turbulence detection method and system based on vortex electromagnetic waves, so that the technical problem that the prior art cannot effectively detect the long-distance atmospheric turbulence is solved.
To achieve the above object, according to one aspect of the present invention, there is provided an atmospheric turbulence detection method based on vortex electromagnetic waves, including:
transmitting OAM electromagnetic waves to a region to be detected;
receiving backward scattering electromagnetic waves aiming at the region to be detected, identifying a wave field distribution function of the backward scattering electromagnetic waves, and solving a complex phase interference factor of atmospheric turbulence according to the wave field distribution function of the backward scattering electromagnetic waves and the wave field distribution function of the OAM electromagnetic waves under the condition of no turbulence;
solving a phase factor corresponding to the atmospheric turbulence according to the wave field distribution function of the back scattering electromagnetic wave and the probability density distribution of the orbital angular momentum mode of the super-geometry Gaussian beam in the radial direction, and using the complex phase interference factor and the phase factor to represent the atmospheric turbulence state.
Preferably, the transmitting the OAM electromagnetic wave to the region to be detected includes:
taking a ternary yagi antenna as an array element, uniformly arranging N array elements at equal intervals on a circumference with the radius of lambda to form a ring-shaped phased array, wherein N is an integer larger than 2;
by
Figure BDA0002327846840000021
Obtaining a phase difference between two adjacent array elements on the annular phased array, wherein l is a modal value generated by OAM, N is the number of the array elements of the annular phased array antenna, and
Figure BDA0002327846840000022
and adjusting each array element on the annular phased array to feed the same signal at intervals of the phase difference in a counterclockwise or clockwise direction.
Preferably, the solving of the complex phase interference factor of the atmospheric turbulence according to the wave field distribution function of the backscattered electromagnetic waves and the wave field distribution function of the OAM electromagnetic waves under the turbulence-free condition includes:
by
Figure BDA0002327846840000023
Obtaining a wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence;
wherein the content of the first and second substances,
Figure BDA0002327846840000031
the wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence;
Figure BDA0002327846840000035
is a normalization constant; z is the propagation distance of the OAM electromagnetic wave; z is a radical ofRIs a Rayleigh distance, and zR＝kw0 2K k ═ 2 π/λ denotes the wavevector, λ denotes the wavelength; i is an imaginary unit; m is0Is the topological charge of the OAM electromagnetic wave; p is a hollow parameter of the super-geometric Gaussian beam; r is a spatial position vector; exp () is an exponential function with a natural constant as the base; phi is the phase of the OAM electromagnetic wave;1F1is a confluent hyper-geometric function; w is a0Is the girdling;
by
Figure BDA0002327846840000032
Obtaining a multiphase interference factor of the atmospheric turbulence, wherein psi (r, phi, z) is the multiphase interference factor of the atmospheric turbulence; ln is a logarithmic function with a natural constant as a base; ep(r, phi, z) is a wave field distribution function of the backscattered electromagnetic waves.
Preferably, the solving of the phase factor corresponding to the atmospheric turbulence according to the wave field distribution function of the backscattered electromagnetic wave and the probability density distribution of the orbital angular momentum mode of the hyper-geometric gaussian beam in the radial direction includes:
by
Figure BDA0002327846840000033
Obtaining the spatial coherence radius of spherical waves in non-Kolmogorov weak fluctuation turbulence, wherein rho0The space coherence radius of spherical waves in the non-Kolmogorov weak fluctuation turbulent flow, α the non-Kolmogorov turbulent flow parameter, k the wave vector;
Figure BDA0002327846840000034
n represents the atmospheric refractive index as a generalized refractive index structural parameter;
according to the spatial coherence radius of spherical waves in non-Kolmogorov weak fluctuation turbulence
Figure BDA0002327846840000041
Obtaining the probability of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial directionDensity distribution of β whereinm(r, z) is the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction; gamma-shaped2() Is a Gamma function; | m0I is the mode of the topological charge of the OAM electromagnetic wave;
Figure BDA0002327846840000042
is a constant integral sign; phi' is the phase of the conjugate wave mode of the OAM electromagnetic wave; m is a topological charge;1F1is a confluent hyper-geometric function;
according to the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction
Figure BDA0002327846840000043
Solving a phase factor corresponding to the atmospheric turbulence, wherein exp (-im phi) is the phase factor corresponding to the atmospheric turbulence;
Figure BDA0002327846840000044
is a summation function.
Preferably, the method further comprises:
to pair
Figure BDA0002327846840000045
The modes are solved to obtain the atmospheric turbulence vortex spectrum.
According to another aspect of the present invention, there is provided an atmospheric turbulence detection system based on a vortical electromagnetic wave, comprising: the system comprises an antenna, a transmitting subsystem, a receiving subsystem and a signal processing subsystem;
the antenna is an annular phased array formed by uniformly arranging N ternary yagi antennas serving as array elements on a circumference with the radius of lambda at equal intervals, and N is an integer larger than 2;
the transmitting subsystem is used for amplifying the radio frequency excitation signal from the frequency source, amplifying the radio frequency excitation signal again by the power divider and radiating the radio frequency excitation signal by each antenna array element;
the receiving subsystem is used for receiving the backscattering signals, performing digital sampling on the backscattering signals and outputting I/Q data to the signal processing subsystem;
the signal processing subsystem for performing the atmospheric turbulence detection method as claimed in any one of claims 1 to 4.
Preferably, each array element is connected with a radio frequency switch, the radio frequency switch is used for sequentially electrifying eight array elements in the array antenna, and the feeding phases among the array elements are sequentially increased or decreased
Figure BDA0002327846840000051
Wherein l is a mode value generated by OAM, N is the number of array elements of the annular phased array antenna, and
Figure BDA0002327846840000052
φmand m is topological charge.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the invention utilizes the interaction of vortex electromagnetic waves and neutral atmospheric turbulence, and carries out characterization on the atmospheric turbulence according to characterization parameters calculated by the wave field distribution function of back scattering electromagnetic waves, the corresponding wave field distribution function of OAM electromagnetic waves under the condition of no turbulence and the probability density distribution of the orbital angular momentum mode of super-geometric Gaussian beams in the radial direction.
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FIG. 1 is a schematic flow chart of a method for detecting atmospheric turbulence based on vortex electromagnetic waves according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an array of eight-element yagi antennas used in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention;
FIG. 4 is a three-dimensional radiation diagram of an eight-element yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention;
FIG. 5 is a directional diagram of an eight-element yagi antenna used in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an array of twenty-element yagi antennas for use in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention;
FIG. 7 is a three-dimensional radiation diagram of a twenty-element yagi antenna used in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention;
fig. 8 is a directional diagram of a twenty-element yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
When a vortex electromagnetic wave is transmitted in the atmosphere, phase distortion caused by atmospheric turbulence has an interfering effect on the complex amplitude of the electromagnetic wave.
In the weak fluctuation region of the atmospheric turbulence, when the electromagnetic wave propagates along the positive propagation direction z > 0, the super-geometric gaussian beam can be represented as:
Figure BDA0002327846840000061
wherein the content of the first and second substances,
Figure BDA0002327846840000062
is free of turbulenceA wave field distribution function of the OAM electromagnetic waves under streaming conditions;
Figure BDA0002327846840000063
a multiple phase interference factor for atmospheric turbulence; exp () is an exponential function with a natural constant as the base;
under the condition of the paraxial approximation,
Figure BDA0002327846840000064
can be expressed as:
Figure BDA0002327846840000065
wherein the content of the first and second substances,
Figure BDA0002327846840000066
is a normalization constant; z is the propagation distance of the OAM electromagnetic wave; z is a radical ofRIs a Rayleigh distance, and zR＝kw0 2(ii) a k is 2 pi/lambda represents wave vector, lambda represents wavelength, and i is an imaginary unit; m is0Is the topological charge of the OAM electromagnetic wave; p is a hollow parameter of the super-geometric Gaussian beam; r is a spatial position vector; | m0I is the mode of the topological charge of the OAM electromagnetic wave;
the refractive index fluctuation of the atmospheric turbulence has an interference effect on the electromagnetic wave transmitted by the atmospheric turbulence, so that the orbital angular momentum mode can not keep the original quantum state, but jumps to the adjacent orbital angular momentum mode under the action of the turbulence to form modal change, which is also called crosstalk.
Thus, the wavefield at reception may be rewritten to carry the phase factor
Figure BDA0002327846840000071
Superposition mode of helical harmonics of (1):
Figure BDA0002327846840000072
coefficient of equation βm(r, z) can be expressed as:
Figure BDA0002327846840000073
when the super-geometric Gaussian beam carries orbital angular momentum modes to be transmitted in non-Kolmogorov weak fluctuation turbulence, the probability density distribution of the orbital angular momentum modes of the super-geometric Gaussian beam in the radial direction is as follows:
Figure BDA0002327846840000074
in the formula, ρ0The spatial coherence radius of a spherical wave in non-kolmogorov weak fluctuating turbulence can be expressed as:
Figure BDA0002327846840000081
wherein α is a non-kolmogorov turbulence parameter,
Figure BDA0002327846840000082
is a generalized refractive index structural parameter in m3-αWhen is coming into contact with
Figure BDA0002327846840000083
When the temperature of the water is higher than the set temperature,
Figure BDA0002327846840000084
will degrade into refractive index structure constant
Figure BDA0002327846840000085
Non-kolmogorov turbulence is converted into kolmogorov turbulence.
Based on the above analysis process, fig. 1 is a schematic flow chart of an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention, as shown in fig. 1, the method includes:
s101: transmitting OAM electromagnetic waves to a region to be detected;
there are two main mechanisms of influence of atmospheric turbulence in the troposphere on the propagation of electromagnetic waves. One is refraction of electromagnetic waves caused by non-uniformity of the atmospheric background, so that the direction of radio waves propagating therein deviates from the original direction and the propagation speed is lower than the speed of light, a phenomenon called atmospheric refraction effect, and atmospheric electrical parameters related to the background atmosphere are refractive index N and refractive index N. The other is the scattering of electromagnetic waves by atmospheric turbulence. Because tropospheric atmospheres are often turbulent, the large number of different sized and shaped inhomogeneities dispersed in the atmosphere, whether temperature, humidity or pressure, differ from the surrounding air and thus also in their refractive index. When the radio waves propagate through the troposphere, they may be re-radiated in all directions by such inhomogeneities, in addition to being refracted along the way, so-called troposphere scattering.
The wave front of the OAM vortex electromagnetic wave is not a traditional plane or spherical surface, but a vortex-shaped structure with a column symmetry characteristic. The phase wavefront of a vortex beam appears helical, having its wave vector with an azimuthal term that rotates around the vortex center, causing the beam to carry rotational angular momentum. Based on the special structure of vortex electromagnetic waves, atmospheric turbulence can influence the spatial structure of the vortex electromagnetic waves more obviously, so that a new method and new parameters for detecting the atmospheric turbulence based on the vortex electromagnetic waves can be found by researching the influence.
Therefore, in the embodiment of the invention, the ternary yagi antenna is used as an array element, N array elements are uniformly arranged on the circumference with the radius of λ at equal intervals to form a ring-shaped phased array, and N is an integer greater than 2.
Fig. 2 is a schematic structural diagram of a yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention, and as shown in fig. 2, the array element antenna structure is a director, an effective array, and a reflector from top to bottom, respectively. The length of the guider is 2.644m from top to bottom; an effective array with the length of 2.710 m; a reflector having a length of 2.836 m. The effective array is 3m away from the ground, the director and the reflector are 1.5m away from the effective array and 1.5m away from the effective array respectively, and the feed element is positioned at the central point of the effective array. In the array antenna, the distance between adjacent array element antennas is 4.6 m.
By means of the formula (I) and (II),
Figure BDA0002327846840000091
calculating the phase difference between two adjacent array elements on the annular phased array, wherein l is the mode value generated by OAM, N is the number of the array elements of the annular phased array antenna, and
Figure BDA0002327846840000092
and adjusting each array element on the annular phased array to feed the same signal at intervals of the phase difference according to the anticlockwise direction or the clockwise direction. For an 8-element yagi antenna array, an initial phase is set to 0, and when l is equal to 1, the phases of adjacent elements are increased
Figure BDA0002327846840000093
When l is 2, the phase of adjacent array elements is increased
Figure BDA0002327846840000094
When l is 3, the phase of adjacent array elements is increased
Figure BDA0002327846840000095
The yagi antenna array with 20 array elements, when l is 1, the phase of the adjacent array element of the inner circle antenna is increased
Figure BDA0002327846840000096
Phase increase of adjacent array elements of outer ring antenna
Figure BDA0002327846840000097
When l is 2, the phase of the adjacent array element of the inner ring antenna is increased
Figure BDA0002327846840000098
Phase increase of adjacent array elements of outer ring antenna
Figure BDA0002327846840000099
When l is 3, the phase of the adjacent array element of the inner ring antenna is increased
Figure BDA00023278468400000910
Outer ring skyPhase increase of adjacent array elements
Figure BDA00023278468400000911
For an N-element OAM circular array antenna, all the array elements are fed with signals with the same phase shift increment or decrement, the electromagnetic wave rotates around the central axis for one circle, the phase is increased by 2 pi l, and therefore OAM electromagnetic waves can be generated.
The array antenna array elements designed by the embodiment of the invention respectively adopt eight array elements and twenty array elements, in order to realize the switching of the same array antenna among different modes, the eight array elements in the array antenna are sequentially electrified through a radio frequency switch, the feeding phases among the array elements are sequentially increased or reduced, and different feeding phases can generate different OAM modes. When l is 0, 1, 2, 3, the corresponding phase delays are 0, 45, 90, 135. Simulations were performed using FEKO electromagnetic simulation software to set the center frequency to 50 Mhz.
The embodiment of the invention designs a circular three-array-element Yagi array antenna, which realizes that electromagnetic waves carrying orbital angular momentum are generated at 50MHz, and vortex electromagnetic waves generated by eight-array-element and twenty-array-element array antennas are analyzed, so that the gain of the vortex electromagnetic wave array antenna is obtained, and the vortex electromagnetic waves generated by the two array antennas are compared. The eight-array element array antenna and the twenty-array element array antenna can obtain vortex electromagnetic waves.
FIG. 3 is a schematic diagram of an array of eight-element yagi antennas used in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention; fig. 4 is a three-dimensional radiation diagram of an eight-element yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention; fig. 5 is a directional diagram of an eight-element yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention; as shown in fig. 3-5, when l is 0, the main lobe direction is perpendicular to the antenna front, electromagnetic energy is mainly radiated in the axial direction of the antenna array, and the gain is maximum, about 67.5 dB.
In order to reduce main lobe holes that may exist in the main lobe, an array of twenty array elements is used in a further technical solution of the embodiments of the present invention. FIG. 6 is a schematic diagram of an array of twenty-element yagi antennas used in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention; FIG. 7 is a three-dimensional radiation diagram of a twenty-element yagi antenna used in a vortex electromagnetic wave-based atmospheric turbulence detection method according to an embodiment of the present invention; fig. 8 is a directional diagram of a twenty-element yagi antenna used in an atmospheric turbulence detection method based on vortex electromagnetic waves according to an embodiment of the present invention; 3-8, compared with the simulation of the twenty-element and eight-element array antennas, the increase of the number of the elements can strengthen the gain of the antenna; and the cavities in the axial direction of the radiation pattern have the same modal value, and the more the array elements are, the smaller the cavities are.
S102: receiving the backward scattering electromagnetic waves aiming at the region to be detected, identifying a wave field distribution function of the backward scattering electromagnetic waves, and solving a multiphase interference factor of the atmospheric turbulence according to the wave field distribution function of the backward scattering electromagnetic waves and the wave field distribution function of the OAM electromagnetic waves under the condition of no turbulence;
it is possible to use a formula of,
Figure BDA0002327846840000111
calculating a wave field distribution function of the OAM electromagnetic waves under turbulence free conditions, wherein,
Figure BDA0002327846840000112
the wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence;
Figure BDA0002327846840000113
is a normalization constant; z is the propagation distance of the OAM electromagnetic wave; z is a radical ofRIs a Rayleigh distance, and zR＝kw0 2(ii) a i is an imaginary unit; m is0Is the topological charge of the OAM electromagnetic wave; p is a hollow parameter of the super-geometric Gaussian beam; r is; exp () is an exponential function with a natural constant as the base; phi is the phase of the OAM electromagnetic wave; f1For confluence to exceedA geometric function; w is a0Is the girdling;
the formula is solved and the solution is carried out,
Figure BDA0002327846840000114
obtaining a multiphase interference factor of the atmospheric turbulence, wherein psi (r, phi, z) is the multiphase interference factor of the atmospheric turbulence; ln is a logarithmic function with a natural constant as a base; ep(r, phi, z) is the wave field distribution function of the backscattered electromagnetic wave.
S103: solving a phase factor corresponding to the atmospheric turbulence according to a wave field distribution function of the back scattering electromagnetic wave and the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction, and using the complex phase interference factor and the phase factor to represent the atmospheric turbulence state.
Using the formula:
Figure BDA0002327846840000115
obtaining the spatial coherence radius of spherical waves in non-Kolmogorov weak fluctuation turbulence, wherein rho0The spatial coherence radius of a spherical wave in the non-Kolmogorov weak fluctuation turbulent flow, α a non-Kolmogorov turbulent flow parameter, k;
Figure BDA0002327846840000121
is a generalized refractive index structural parameter;
according to the spatial coherence radius of spherical waves in non-Kolmogorov weak fluctuation turbulence, utilizing a formula:
Figure BDA0002327846840000122
calculating the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction, wherein βm(r, z) is the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction; gamma-shaped2() Is a Gamma function; | m0I is the mode of the topological charge of the OAM electromagnetic wave;
Figure BDA0002327846840000123
is a constant integral sign; m is the topological charge number;1F1is a confluent hyper-geometric function;
according to the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction, by using a formula,
Figure BDA0002327846840000124
solving a phase factor corresponding to the atmospheric turbulence, wherein exp (-im phi) is the phase factor corresponding to the atmospheric turbulence;
Figure BDA0002327846840000125
is a summation function.
By applying the embodiment of the invention, the atmospheric turbulence is represented according to the wave field distribution function of the back scattering electromagnetic wave, the corresponding wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence and the characterization parameters calculated according to the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction by utilizing the interaction of the vortex electromagnetic wave and the neutral atmospheric turbulence, and the long-distance atmospheric turbulence detection can be displayed because the propagation distance of the vortex electromagnetic wave is farther than that of the sound wave and the light wave in the prior art.
The embodiment of the invention can also improve the time and density of high-altitude detection, and has the capability of continuously detecting the wind field structure, so that the wind field detection capability of the middle-layer atmosphere is obviously enhanced, the specific distribution of vertical speed and divergence is obtained, and the information is helpful for forecasters to improve weather forecast.
Further, based on the integral formula:
Figure BDA0002327846840000131
in the formula In(η) is a second class of nth order Bessel functions Using the above integration equation, the probability density of the orbital angular momentum signal mode in the z-plane becomes:
Figure BDA0002327846840000132
thus, the normalized power of the spiral spectrum carrying the topological charge m can be expressed in the paraxial channel as:
Figure BDA0002327846840000133
received power of orbital angular momentum mode
Figure BDA0002327846840000134
Defined as the topological charge m of the received signal at the receiving plane0Normalized power of (i.e., m ═ m)0)。PΔmCross-talk power being orbital angular momentum, i.e. the topological load of the received signal at the receiving plane is m ═ m0Normalized power of + Δ m. Thus, by comparing the resulting signal PmThe atmospheric turbulence vortex spectrum can be obtained by solving the modes of (1).
By applying the embodiment of the invention, the atmospheric turbulence vortex spectrum can be obtained.
Corresponding to the above embodiments of the present invention, the present invention further provides an atmospheric turbulence detection system based on vortex electromagnetic waves, the system comprising: an antenna, a transmitting subsystem, a receiving subsystem and a signal processing subsystem,
the antenna is as follows: n ternary yagi antennas are used as array elements and evenly arranged on a circumference with the radius of lambda at equal intervals to form an annular phased array, and N is an integer larger than 2;
the transmitting subsystem is used for amplifying the radio frequency excitation signal from the frequency source, amplifying the radio frequency excitation signal again by the power divider and radiating the radio frequency excitation signal by each antenna array element;
the receiving subsystem is used for receiving the backscattering signal, performing digital sampling on the backscattering signal, and outputting I/Q data to the signal processing subsystem;
the signal processing subsystem is used to perform the atmospheric turbulence detection method as described above.
The radar system of the embodiment of the invention has the following overall parameter design:
1. the working frequency is as follows: 50MHz (λ ═ 6 m);
2. pulse width: 1-10 mus;
3. pulse repetition period: 80-800 mus;
4. emission peak power: 172.8KW (300W × 576);
5. average power: 34.56KW (maximum duty cycle: 20%);
6. antenna array area: 6831m2；
7. Power aperture product: 2.36X 108Wm2；
8. Antenna array:
rectangular active phased antenna array formed by 24 x 24 pairs of three-array element yagi antennas
(1) Beam width of antenna array: not more than 4 degree
(2) Antenna beam pointing: fixed 5-beam pointing, Doppler scanning
(zenith plumb, N, E, W, S direction each 15 degree from zenith)
(3) Antenna gain: 34.4dB
9. Radar power synthesis:
all-solid-state transmitter, all-distributed
10. The total power consumption of the system: less than or equal to 200KW
The radar system full-solid full-coherent pulse Doppler system used in the embodiment of the invention mainly comprises an antenna system, a feeder system, a full-solid transmitting system, a digital receiving system, a beam control system, a signal processing system, a data processing and product generating system, a user terminal and the like. The technology applies new technologies and processes such as a high-reliability all-solid-state transmitter, a low-noise large-dynamic-range digital receiver, an active phased array antenna, digital signal processing, a real-time image terminal and the like, and has the characteristics of high sensitivity, large dynamic, high reliability, convenience in use and maintenance and the like. The system can continuously and automatically observe, process data, monitor operation and calibrate in all weather. The PD system design enables the radar to measure the distribution characteristics of the atmospheric turbulence echo in the ground clutter background, and simultaneously, the radial speed and the speed spectrum width of the scatterer can be measured. Compared with the pulse system radar of general time domain detection, the PD radar is frequency domain detection, carries out spectrum analysis on an echo pulse sequence, and has the outstanding advantage of fundamentally solving the clutter suppression problem.
The radar includes a pulsed doppler radar operating in the 50MHz range and associated hardware and software. When the radar works, a high-frequency detection pulse signal is generated under the control of a main control computer, the signal is subjected to phase shift amplification in a T/R assembly and then radiated out through a feeder system, power synthesis is carried out in space, and energy is concentrated to a certain beam direction of the antenna. Electromagnetic wave signals are scattered and returned after encountering atmospheric turbulence, echo signals received by the radar antenna are amplified, phase-shifted and synthesized in the T/R assembly and then transmitted to the digital intermediate frequency receiver, then the digital intermediate frequency receiver carries out filtering, amplification, quadrature phase detection and data extraction, and finally the signal processor carries out FFT calculation to form a turbulence echo signal power spectrum. The power spectrum is analyzed by data processing and inverted into an atmospheric wind field.
The probe pulse width determines the closest range and range resolution. Narrow pulses are needed to meet the requirements of the nearest action distance and the distance resolution; the pulse width is increased, and the requirements of the maximum detection distance and the distance resolution can be met simultaneously by adopting a pulse compression technology.
The radar designs three pulse widths, and the combination parameters of various forms are shown in table 1.
TABLE 1 three modes of operation of the radar
Mode of operation Pulse width Repetition period Pulse width after compression Duty cycle Resolution ratio
Low mode 8μs 80μs 1μs 10％ 150m
Middle mode 32μs 160μs 4μs 20％ 600m
High mode 160μs 800μs 10μs 20％ 1500m
In consideration of eliminating secondary return distance ambiguity, improving anti-interference performance and reducing atmospheric turbulence body target distance side lobes caused by pulse compression, the radar is realized by adopting a binary pseudo-random sequence phase coding technology of a complementary sequence.
The eight-bit complementary code element is:
A＝{-1,1,-1,-1,1,-1,-1,-1}
B＝{1,-1,1,1,1,-1,-1,-1}。
in a first aspect, the antenna used in the embodiment of the present invention is formed by a three-element Yagi antenna unit of 50 MHz. Through the control of the wave control subsystem, five wave beams of zenith, east 15 degrees, west 15 degrees, south 15 degrees and north 15 degrees are swept in an antenna scanning period, and echo signals are amplified through a receiving channel and then transmitted to a receiver and a signal processing subsystem.
The technical indexes are as follows:
(1) wavelength: λ ═ 6m
(2) Array element spacing: dx is less than or equal to 0.7 lambda, dy is less than or equal to 0.7 lambda
(3) The length of the array element is as follows: x is 24 multiplied by 0.7 lambda and is less than or equal to 100m
(4) Polarization: horizontal linear polarization
(5) Normal beam width: not more than 4.5 degree
(6) Beam pointing: zenith, east 15 degrees, west 15 degrees, south 15 degrees and north 15 degrees
(7) Receive side lobe (in scan direction):
a first secondary lobe: not more than-20 dB
Distal flap: less than or equal to-30 dB (other than 45 degrees)
(8) Standing wave coefficient: less than or equal to 1.3
(9) Impedance: 50 omega
(10) Beam control: intelligent distributed type
(11) Polarization conversion: an electrically controlled electronic switch.
2.4m long main pole of the antenna, 50mm caliber of outer diameter, galvanized iron pipe and plastic spraying treatment. Antenna level cumulative error: less than or equal to 10 mm; antenna positioning error: less than or equal to 10 mm.
In a second aspect, the launch system of embodiments of the invention generally comprises a launch front stage and a T/R assembly, wherein,
the main function of the emission front stage is to amplify a radio frequency excitation signal from a frequency source to 300W, and the radio frequency excitation signal is radiated by 576 antenna units after being amplified by a power divider. The transmitting front extension set consists of a front RF amplifier, a protection detection board, a PIN modulator, a radio frequency fault detection circuit and a transmitting power supply part. The technical indexes of the emission front stage are as follows:
(1) transmitter type: preceding-stage distributed TR component power amplifier module
(2) The working ratio is as follows: 20% (maximum)
(3) Emission preceding stage input signal power: 10mW +/-3 mW
(4) Emission preceding stage output signal power:
Figure BDA0002327846840000171
(5)VSWR≯1.5；
(6) characteristic impedance: 50 omega;
(7) the phase noise degradation is < 3 dB.
The transmitting system uses two kinds of T/R components, one is a large T/R component containing a phase shifter and a low noise amplifier, and the total number of the T/R components is 24, and the other is a small T/R component containing a power amplifier, and the total number of the T/R components is 576. The large T/R component is a module for completing power amplification and echo signal amplification and is a core device of the active phased array. The T/R component consists of a circulator, a phase shifter, a power amplifier, a low noise amplifier, a circulator, a directional coupler, an electronic switch, a beam control unit and the like. The small T/R component is a module for completing power amplification and is a power amplification system of the radar.
The technical indexes of the T/R component are as follows:
(1) emission power: the peak value is more than or equal to 300W, and the average power is more than or equal to 60W (the maximum duty ratio is 20%);
(2) emission pulse width: 8 μ s, 32 μ s, 160 μ s;
(3) scanning form: 5-bit digital phase scanning;
(4) receive branch gain (large T/R component): g is more than or equal to 20dB (normal temperature);
(5) receive noise figure (large T/R component): n is a radical offLess than or equal to 2.5dB (room temperature);
(6)1dB compression point level (large T/R component): 10 dBm;
(7) the amplitude inconsistency of the receiving branch of the T/R component is within +/-1.0 dB (large T/R component);
(8) detecting the transmitting power and indicating the power state;
(9) and detecting the working state of the phase shifter, and returning to the state of the phase shifter (large T/R component) through the wave control system.
The phase shift system adopts a 5-bit digital phase shifter to improve the phase shift precision and ensure that the adjustment of the beam direction is more accurate. The transmitting power and the phase shifter state of the T/R component are detected by the wave control system, the work of an antenna system can be monitored in real time, the system reliability is improved, and the system maintenance is facilitated. As the work ratio reaches up to 20%, forced air cooling is adopted for the T/R assembly to ensure long-term stable and reliable operation.
In a third aspect, a receiving subsystem of an embodiment of the invention is configured to receive backscattered echoes.
Because the received backscattering signal is very weak, most of the echo signal is under noise, so the requirements on various indexes of the receiver are very high. The radar of the embodiment of the invention adopts direct digital sampling, and the signal phase detection is carried out on a digital domain, so that good phase orthogonality and amplitude consistency can be obtained. The inconsistency of I, Q amplitude and phase directly affects the detection performance of the radar target and the loss of energy. The inconsistency of I, Q amplitude and phase is processed by FFT to generate mirror image spectrum in addition to the main spectrum of the required echo in the frequency domain, thus causing false target and energy loss and bringing trouble to signal processing, therefore, the requirement for the inconsistency of I, Q amplitude and phase must be provided. The sampling is carried out on the intermediate frequency, the input signal is a single-path signal, and the orthogonal double-path signal is formed in a digital domain, so that the signal phase detection performance can be well controlled under a certain condition, the amplitude consistency and the phase orthogonality of the two paths can be improved by more than one magnitude, and the problem of output null shift is greatly improved.
The receiver is also provided with a fault detection device, a frequency synthesizer in the fault detection device generates a test signal, and the test signal is sent to a receiving system through a directional coupler before field amplification and a high-frequency selection switch. The selection of the test source is controlled by a control instruction issued by the signal processor. Most of the indicators of the receiver and the signal processor can be detected by using the test signal. When the system has a fault, the fault point can be isolated by using the test signal.
The technical indexes of the receiving subsystem are as follows:
(1) dynamic range: not less than 65 dB;
(2) single sideband phase noise of frequency synthesizer: less than or equal to-80 dBc/Hz/10 Hz;
(3) the excitation source outputs pulse peak power: not less than 11.35 dBm;
(4) A/D bit number: 14 bit;
(5) sampling frequency: 80 MHz;
(6) i, Q output amplitude imbalance: less than or equal to 0.05 dB;
(7) i, Q output orthogonality imbalance: is less than or equal to 0.1 degree.
In a fourth aspect, a signal processing subsystem in the embodiment of the present invention employs a dedicated DSP chip to complete processing such as coded pulse pressure, coherent averaging, FFT processing, clutter suppression, and spectrum averaging in real time; the system is responsible for the state detection and function control of the whole radar, and is responsible for processing the input control of a user and returning various calculation results and state information of the radar.
The technical indexes of the signal processing subsystem are as follows:
(1) i, Q data input maximum rate: 1 MHz;
(2) i, Q number of input bits: 16 bits;
(3) number of range gates (bin number): less than or equal to 200;
(4) height resolution (library length): 150m, 600m, 1500 m;
(5) time domain accumulation: 1-256 (continuous integer variable);
(6) the number of FFT points: 2048, 128-;
(7) mean number of spectra: 100 or less (continuous integer is variable);
(8) the structural form is as follows: and (4) a standard PC/PCI expansion board card.
By applying the embodiment of the invention, the atmospheric turbulence is represented according to the wave field distribution function of the back scattering electromagnetic wave, the corresponding wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence and the characterization parameters calculated according to the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction by utilizing the interaction of the vortex electromagnetic wave and the neutral atmospheric turbulence, and the long-distance atmospheric turbulence detection can be displayed because the propagation distance of the vortex electromagnetic wave is farther than that of the sound wave and the light wave in the prior art.
In a specific implementation manner of the embodiment of the present invention, each array element is connected to a radio frequency switch, the radio frequency switches are used for sequentially energizing the array elements in the array antenna, and feeding phases between the array elements are sequentially increased or decreased
Figure BDA0002327846840000201
It should be noted that, according to the implementation requirement, each step/component described in the present application can be divided into more steps/components, and two or more steps/components or partial operations of the steps/components can be combined into new steps/components to achieve the purpose of the present invention.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (7)

1. An atmospheric turbulence detection method based on vortex electromagnetic waves is characterized by comprising the following steps:
transmitting OAM electromagnetic waves to a region to be detected;
receiving backward scattering electromagnetic waves aiming at the region to be detected, identifying a wave field distribution function of the backward scattering electromagnetic waves, and solving a complex phase interference factor of atmospheric turbulence according to the wave field distribution function of the backward scattering electromagnetic waves and the wave field distribution function of the OAM electromagnetic waves under the condition of no turbulence;
solving a phase factor corresponding to the atmospheric turbulence according to the wave field distribution function of the back scattering electromagnetic wave and the probability density distribution of the orbital angular momentum mode of the super-geometry Gaussian beam in the radial direction, and using the complex phase interference factor and the phase factor to represent the atmospheric turbulence state.
2. The method according to claim 1, wherein the transmitting OAM electromagnetic waves to the area to be probed comprises:
taking a ternary yagi antenna as an array element, uniformly arranging N array elements at equal intervals on a circumference with the radius of lambda to form a ring-shaped phased array, wherein N is an integer larger than 2;
by
Figure FDA0002327846830000011
Obtaining a phase difference between two adjacent array elements on the annular phased array, wherein l is a modal value generated by OAM, N is the number of the array elements of the annular phased array antenna, and
Figure FDA0002327846830000012
and adjusting each array element on the annular phased array to feed the same signal at intervals of the phase difference in a counterclockwise or clockwise direction.
3. The method according to claim 1 or 2, wherein the solving of the complex phase interference factor of the atmospheric turbulence from the wave field distribution function of the backscattered electromagnetic waves and the wave field distribution function of the OAM electromagnetic waves under turbulence-free conditions comprises:
by
Figure FDA0002327846830000021
Obtaining a wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence;
wherein the content of the first and second substances,
Figure FDA0002327846830000022
the wave field distribution function of the OAM electromagnetic wave under the condition of no turbulence;
Figure FDA0002327846830000023
is a normalization constant; z is the propagation distance of the OAM electromagnetic wave; z is a radical ofRIs a Rayleigh distance, and zR＝kw0 2K 2 pi/λ represents a wavevector, λ represents a wavelength; i is an imaginary unit; m is0Is the topological charge of the OAM electromagnetic wave; p is a hollow parameter of the super-geometric Gaussian beam; r is a spatial position vector; exp () is an exponential function with a natural constant as the base; phi is the phase of the OAM electromagnetic wave;1F1is a confluent hyper-geometric function; w is a0Is the girdling;
by
Figure FDA0002327846830000024
Obtaining a multiphase interference factor of the atmospheric turbulence, wherein psi (r, phi, z) is the multiphase interference factor of the atmospheric turbulence; ln is a logarithmic function with a natural constant as a base; ep(r, phi, z) is a wave field distribution function of the backscattered electromagnetic waves.
4. The method according to claim 3, wherein solving the phase factor corresponding to the atmospheric turbulence according to the wave field distribution function of the backscattered electromagnetic wave and the probability density distribution of the orbital angular momentum mode of the hyper-geometric Gaussian beam in the radial direction comprises:
by
Figure FDA0002327846830000025
Obtaining the spatial coherence radius of spherical waves in non-Kolmogorov weak fluctuation turbulence, wherein rho0The space coherence radius of spherical waves in the non-Kolmogorov weak fluctuation turbulent flow, α the non-Kolmogorov turbulent flow parameter, k the wave vector;
Figure FDA0002327846830000026
n represents the atmospheric refractive index as a generalized refractive index structural parameter;
according to the spatial coherence radius of spherical waves in non-Kolmogorov weak fluctuation turbulence
Figure FDA0002327846830000031
Obtaining the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction, wherein βm(r, z) is the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction; gamma-shaped2() Is a Gamma function; | m0I is the mode of the topological charge of the OAM electromagnetic wave;
Figure FDA0002327846830000032
is a constant integralA symbol; phi' is the phase of the conjugate wave mode of the OAM electromagnetic wave; m is a topological charge;1F1is a confluent hyper-geometric function;
according to the probability density distribution of the orbital angular momentum mode of the super-geometric Gaussian beam in the radial direction
Figure FDA0002327846830000033
Solving a phase factor corresponding to the atmospheric turbulence, wherein exp (-im phi) is the phase factor corresponding to the atmospheric turbulence;
Figure FDA0002327846830000034
is a summation function.
5. The method of claim 4, further comprising:
to pair
Figure FDA0002327846830000035
The modes are solved to obtain the atmospheric turbulence vortex spectrum.
6. An atmospheric turbulence detection system based on vortex electromagnetic waves, comprising: the system comprises an antenna, a transmitting subsystem, a receiving subsystem and a signal processing subsystem;
the antenna is an annular phased array formed by uniformly arranging N ternary yagi antennas serving as array elements on a circumference with the radius of lambda at equal intervals, and N is an integer larger than 2;
the transmitting subsystem is used for amplifying the radio frequency excitation signal from the frequency source, amplifying the radio frequency excitation signal again by the power divider and radiating the radio frequency excitation signal by each antenna array element;
the receiving subsystem is used for receiving the backscattering signals, performing digital sampling on the backscattering signals and outputting I/Q data to the signal processing subsystem;
the signal processing subsystem for performing the atmospheric turbulence detection method as claimed in any one of claims 1 to 4.
7. The system of claim 6, wherein each array element is connected with a radio frequency switch, the radio frequency switch is used for sequentially electrifying the array elements in the annular phased array antenna, and the feeding phases between the array elements are sequentially increased or decreased
Figure FDA0002327846830000041
Wherein l is a mode value generated by OAM, N is the number of array elements of the annular phased array antenna, and
Figure FDA0002327846830000042
φmand m is topological charge.
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