A Method for Ranging Based on Petal-shaped Bessel Light in Hypersonic Plasma Turbulence

Abstract

The present invention relates to the field of electromagnetic calculations, and specifically relates to a method for ranging based on petal-shaped Bessel light in hypersonic plasma turbulence. This method simulates plasma sheath turbulence by establishing a multi-layer random phase screen, calculates the diffraction transmission of petal-shaped Bessel light through the turbulence, captures the intensity distribution of the reflected light beam, and determines the rotation angle based on its correlation with the ideal intensity distribution. The high-precision ranging is achieved by using the linear relationship between the rotation angle and the propagation distance. The petal-shaped Bessel light is formed by superimposing two Bessel mode beams with different orbital angular momentum orders, and has a spatial structure strongly correlated with the propagation distance, capable of maintaining high stability and anti-interference ability in a turbulent environment. By combining the self-focusing and approximately non-diffracting characteristics of the Bessel beam, the present invention significantly improves the target detection and ranging accuracy in hypersonic plasma turbulence, providing reliable technical support for the communication and target detection of hypersonic vehicles.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic calculations, and particularly to a method for ranging based on petal-shaped Bessel light in hypersonic plasma turbulence. Background Art

[0002] During the reentry of a hypersonic vehicle into the atmosphere, the vehicle rubs violently against the air, causing a plasma sheath to form around it. In addition, affected by the aerodynamic shape and flight attitude of the vehicle, multiple turbulent vortices of different sizes will appear in the plasma flow field, forming plasma turbulence with electrons and ions. Plasma turbulence will severely reflect and refract electromagnetic wave signals, and at the same time absorb a large amount of signal energy, seriously damaging the stability of communication signals. This interference will not only cause frequent lags and distortions in wireless communication, but in extreme cases, the communication link will even be completely interrupted. Since it interferes with the normal propagation and reception of electromagnetic wave signals, the detection of surrounding targets by the vehicle drops sharply, and it is difficult to accurately obtain target information. Currently, using lidar instead of electromagnetic wave radar (time-of-flight method, pulse method) is a common solution. However, even though lidar in the laser band has a lower attenuation in plasma, it is easily affected by turbulence, causing optical path drift and spot distortion; at the same time, as the turbulence intensity increases and the propagation distance increases, the beam distortion and spot dispersion become more serious, and the stability is poor; and in a strong turbulence environment, the resolution is limited.

[0003] Although Bessel structured light has self-focusing and approximately non-diffracting characteristics due to its unique intensity distribution and phase structure, and has a certain robustness in a turbulent environment, its performance in a strong turbulent environment is still limited. In hypersonic plasma turbulence, the beam of existing lidar technology is easily affected by turbulence, resulting in optical path drift and spot distortion, and as the propagation distance increases, the beam distortion and spot dispersion become more serious, and the stability is poor. In addition, existing ranging methods are mainly based on the time domain, and the amplitude and phase space distribution of the beam have a low tolerance for highly scattering media, making it difficult to achieve high-precision target detection and ranging in a complex plasma turbulence environment. Therefore, there is an urgent need for a new beam propagation and ranging method that can stably transmit and achieve high-precision ranging in hypersonic plasma turbulence. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for ranging based on petal-shaped Bessel light in hypersonic plasma turbulence, so as to solve the problems of beam distortion, spot dispersion, and insufficient ranging accuracy of lidar caused by turbulence in the prior art.

[0005] The present invention achieves the above purpose through the following technical solutions:

[0006] The present invention proposes a method for ranging based on petal-shaped Bessel light in hypersonic plasma turbulence, and the method includes:

[0007] Establishing a multi-layer random phase screen to simulate plasma sheath turbulence;

[0008] Calculating the intensity distribution of the reflected light beam of the petal-shaped Bessel light diffracted through the multi-layer random phase screen to the receiving surface;

[0009] Based on the maximum correlation between the intensity distribution of the reflected light beam and the ideal intensity distribution, determining the rotation angle of the reflected light beam;

[0010] Utilizing the linear relationship between the propagation distance and the rotation angle to achieve ranging.

[0011] Furthermore, the petal-shaped Bessel light is composed of two Bessel mode light beams, and the expression is:

[0012] ;

[0013] ;

[0014] In the formula represents in the cylindrical coordinate system; is the OAM order of the i-th Bessel mode, is the longitudinal wave number of the i-th Bessel mode; is the corresponding radial wave number; is the wave number of the light beam, ; is the Bessel function of the first kind of order ; is the light beam wavelength.

[0015] Furthermore, the establishment of the multi-layer random phase screen for simulating plasma sheath turbulence includes:

[0016] According to the flow field law of hypersonic vehicles, determining the refractive index fluctuation power spectral density function in the anisotropic plasma sheath turbulence, and the expression is:

[0017] ;

[0018] In the formula, is the plasma refractive index variance, is the turbulence outer scale, and represent the frequency components along the horizontal and vertical directions in the frequency domain;

[0019] Obtaining the phase spectrum , the expression is: ; where is the spatial wave number;

[0020] The expression for the standard deviation of the phase spectrum is: , where, is the spacing between two adjacent phase screens, N is the number of samples, is the grid interval;

[0021] Calculate the diffraction transmission of petal-shaped Bessel light through multiple phase screens, simulate the transmission characteristics of the beam in the plasma sheath turbulence, and use the power spectrum inversion method to obtain random phase screens for the power spectral density function of the plasma sheath turbulence , the expression is:

[0022] ;

[0023] where, is to generate a complex Gaussian random matrix, which is a standard normal distribution function in the frequency domain, is the inverse Fourier transform.

[0024] Furthermore, the establishment of multiple random phase screens for simulating plasma sheath turbulence further includes:

[0025] According to the crosstalk caused by the flow field of the hypersonic vehicle, the optical field after turbulent perturbation is expressed as:

[0026] ;

[0027] Use the D-FFT algorithm of the Fresnel diffraction integral to calculate the transmission through a certain free space distance to reach the second phase screen, and repeat the cycle to obtain the transmitted optical field , the expression is:

[0028] .

[0029] Furthermore, the calculation of the intensity distribution of the reflected beam of the petal-shaped Bessel light diffracted and transmitted through the multiple random phase screens to the receiving surface includes:

[0030] Capture the intensity distribution of the reflected beam, specifically based on the optical field Calculate the intensity distribution of the reflected beam , the calculation formula is:

[0031] .

[0032] Furthermore, determining the rotation angle of the reflected beam based on the maximum correlation between the intensity distribution of the reflected beam and the ideal intensity distribution includes:

[0033] The rotation angle of the contour is obtained from the reflected beam image, and the rotation angle is estimated using an angle detection algorithm , and the expression is:

[0034] ;

[0035] wherein, is the measured intensity distribution, is the ideal intensity distribution of the petal-shaped Bessel beam transmitted through free space without plasma turbulence.

[0036] Furthermore, the linear relationship expression between the propagation distance z and the rotation angle is:

[0037] ;

[0038] wherein, is the difference in longitudinal wave number between two adjacent Bessel modes, , ;

[0039] is the refractive index of the plasma medium;

[0040] ;

[0041] In the formula, is the refractive index of free electrons; is the electron charge; is the electron mass; is the electron number density; is the speed of light in free space.

[0042] The beneficial effects of the present invention are as follows:

[0043] Based on the random phase screen theory, the present invention proposes a ranging method based on the spatial domain. This method studies the unique propagation characteristics of the petal-shaped Bessel structured light generated by the coherent superposition of vortex phases in the plasma flow field, and can improve the detection, tracking, and communication of targets.

[0044] The present invention utilizes the relationship between the rotation angle of the petal-shaped Bessel light and the propagation distance to achieve the purpose of ranging, providing a theoretical basis for studying the propagation problem of vortex laser beams in plasma turbulence, the ranging purpose, and the communication problem in near-earth space. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is the overall flowchart of the present invention.

[0046] Figure 2The difference in the orbital angular momentum order of the petal-shaped Bessel-structured beam in the present invention, as well as the difference in the number of petals it affects and the difference in different longitudinal wave numbers ( ) is a schematic diagram of the morphological changes during the propagation of the petal-shaped Bessel beam; among them, Figure 2 In (a) is a schematic diagram of the difference in the orbital angular momentum order of the petal-shaped Bessel-structured beam in the present invention and the number of petals it affects, Figure 2 In (b) is a schematic diagram of the morphological changes during the propagation of the petal-shaped Bessel beam due to the difference in different longitudinal wave numbers ( ).

[0047] Figure 3 is a conceptual schematic diagram of the petal-shaped Bessel-structured light rotating at a z-related angle in the present invention, and a schematic diagram of the relationship between the rotation angle of the structured light and the difference in longitudinal wave numbers ; among them, Figure 3 In (a) is a conceptual schematic diagram of the petal-shaped Bessel-structured light rotating at a z-related angle in the present invention, Figure 3 In (b) is a schematic diagram of the relationship between the rotation angle of the structured light and the difference in longitudinal wave numbers .

[0048] Figure 4 is a schematic diagram of the normalized amplitude distribution of the light field at different in the present invention, and a schematic diagram of the multi-layer random phase screen model; among them, Figure 4 In (a) is a schematic diagram of the normalized amplitude distribution of the light field at different in the present invention, Figure 4 In (b) is a schematic diagram of the multi-layer random phase screen model in the present invention.

[0049] Figure 5 is a diagram of the light field intensity, phase distribution, and angle change of the petal-shaped Bessel-structured light at two different propagation distances of z = 0m and z = 0.1m, with different differences in longitudinal wave numbers .

[0050] Figure 6 is a schematic diagram of the influence of different on the beam intensity distribution and measurement error (MSE) at different propagation distances.

[0051] Figure 7 is a schematic diagram of the change of the normalized scintillation index (SI) of the petal-shaped Bessel-structured light with distance at different values of the petal-shaped Bessel-structured light in the present invention, and the change of the scintillation index of different beams with propagation distance.

[0052] Figure 8 is the petal-shaped Bessel-structured light in the present invention at different Schematic diagram of the change of the beam diffusion variance of petal-shaped Bessel structured light with distance at a certain value and the change of the beam diffusion variance of different beams with propagation distance. Detailed implementation mode

[0053] The following description provides specific application scenarios and requirements of this specification, aiming to enable those skilled in the art to manufacture and use the content in this specification. For those skilled in the art, various local modifications to the disclosed embodiments are obvious, and without departing from the spirit and scope of this specification, the general principles defined here can be applied to other embodiments and applications. Therefore, this specification is not limited to the shown embodiments, but has the widest scope consistent with the claims.

[0054] The terms used here are only for the purpose of describing specific example embodiments and are not restrictive. For example, unless otherwise clearly specified in the context, the singular forms "a", "an", and "the" used here may also include the plural forms. When used in this specification, the terms "comprising", "including", and / or "containing" mean that the associated integers, steps, operations, elements, and / or components exist, but do not exclude the existence of one or more other features, integers, steps, operations, elements, components, and / or groups, or the addition of other features, integers, steps, operations, elements, components, and / or groups in the system / method.

[0055] Considering the following description, these features of this specification and other features, as well as the operations and functions of the related elements of the structure, and the economy of the combination and manufacture of components can be significantly improved. Referring to the accompanying drawings, all of these form a part of this specification. However, it should be clearly understood that the drawings are only for the purpose of illustration and description and are not intended to limit the scope of this specification. It should also be understood that the drawings are not drawn to scale.

[0056] The flowcharts used in this specification illustrate the operations implemented by the system according to some embodiments in this specification. It should be clearly understood that the operations in the flowchart may not be implemented in sequence. On the contrary, the operations may be implemented in reverse order or simultaneously. In addition, one or more other operations may be added to the flowchart. One or more operations may be removed from the flowchart.

[0057] As Figure 1 shown, this embodiment proposes a method for ranging based on petal-shaped Bessel light in hypersonic plasma turbulence. The method includes: establishing a multi-layer random phase screen to simulate plasma sheath turbulence; calculating the intensity distribution of the reflected beam of petal-shaped Bessel light diffracted through the multi-layer random phase screen and transmitted to the receiving surface; determining the rotation angle of the reflected beam based on the maximum correlation between the intensity distribution of the reflected beam and the ideal intensity distribution; and realizing ranging by using the linear relationship between the propagation distance and the rotation angle.

[0058] In a specific embodiment, petal-shaped Bessel light is emitted by a transmitter. The petal-shaped Bessel light is composed of two Bessel mode beams. The two Bessel modes have different OAM orders. The spatial interference between the two modes with different OAM orders generates a petal-shaped intensity distribution. The petal-shaped angular distribution gradually changes along the propagation distance z. The angular rotation of the petal is linearly proportional to the relative phase between the two modes. See Figure 2 . The petal-shaped Bessel light is composed of two Bessel mode beams, and the expression is:

[0059] ;

[0060] ;

[0061] where represents the cylindrical coordinate system; is the OAM order of the i-th Bessel mode, is the longitudinal wave number of the i-th Bessel mode; is the corresponding radial wave number; is the wave number of the beam, ; is the Bessel function of the first kind of order ; is the beam wavelength.

[0062] To represent the rotation angle related to z, the difference in longitudinal wave numbers between two adjacent Bessel modes is introduced, to achieve a linearly z-related angular rotation. See Figure 3 .

[0063] In a specific embodiment, a multi-layer random phase screen is established to simulate plasma sheath turbulence. The multi-layer random phase screen is established by the power spectrum inversion method according to the anisotropic plasma turbulence refractive index fluctuation power spectrum function. Specifically, it includes:

[0064] According to the flow field law of hypersonic vehicles, the refractive index fluctuation power spectral density function in anisotropic plasma sheath turbulence is determined. The expression is:

[0065] ;

[0066] where is the plasma refractive index variance, is the outer scale of turbulence, and represent the frequency components of the beam along the x and y directions;

[0067] The phase spectrum is obtained from the relationship between the refractive index spectrum and the power spectral density of the phase. , and the expression is: ; where is the spatial wave number;

[0068] The standard deviation expression of the phase spectrum is: , where is the spacing between two adjacent phase screens, N is the number of samples, is the grid interval;

[0069] Calculate the diffraction transmission of the petal-shaped Bessel light through multiple phase screens, simulate the transmission characteristics of the beam in the plasma sheath turbulence, and use the power spectrum inversion method to obtain random phase screens for the power spectral density function of the plasma sheath turbulence , and the expression is:

[0070] ;

[0071] where is to generate a complex Gaussian random matrix, which is a standard normal distribution function in the frequency domain. is the perturbation of the petal-shaped Bessel beam phase caused by the turbulence in the plasma sheath, see Figure 4 ; is the inverse Fourier transform.

[0072] In a specific embodiment, establishing multiple random phase screens for simulating plasma sheath turbulence further includes:

[0073] According to the crosstalk caused by the hypersonic vehicle flow field, the optical field after turbulence perturbation is expressed as:

[0074] ;

[0075] Using the D-FFT algorithm of the Fresnel diffraction integral, calculate the optical field of the beam after the petal-shaped Bessel light is transmitted through the plasma sheath turbulence simulated by the multiple random phase screens in sequence and then transmitted through a free space transmission distance between adjacent random phase screens , and the expression is:

[0076] .

[0077] In a specific embodiment, calculating the intensity distribution of the reflected beam when the petal-shaped Bessel light is diffracted and transmitted through multiple random phase screens to the receiving surface includes:

[0078] Capture the intensity distribution of the reflected beam, specifically calculate the intensity distribution of the reflected beam based on the optical field , and the calculation formula is: ​

[0079] 。

[0080] In a specific embodiment, based on the maximum correlation between the intensity distribution of the reflected beam and the ideal intensity distribution, the rotation angle of the reflected beam is determined, including:

[0081] Obtaining the rotation angle of the contour from the reflected beam image and estimating the rotation angle using an angle detection algorithm , the expression is:

[0082] ;

[0083] where, is the measured intensity distribution, is the ideal intensity distribution of the petal-shaped Bessel beam transmitted through free space without plasma turbulence;

[0084] In a specific embodiment, the linear relationship expression between the propagation distance z and the rotation angle is:

[0085] ;

[0086] where, is the difference in longitudinal wave numbers between two adjacent Bessel modes, , ; is the refractive index of the plasma medium;

[0087] ;

[0088] In the formula, is the refractive index of free electrons; is the electron charge; is the electron mass; is the electron number density; is the speed of light in free space.

[0089] Based on the random phase screen theory, the present invention proposes a ranging method based on the spatial domain, which studies the unique propagation characteristics of the petal-shaped Bessel structured light generated by the coherent superposition of vortex phases in the plasma flow field, and is of great significance for improving the detection, tracking, and communication of targets.

[0090] The simulation results of the present invention can be further illustrated by the following experiments:

[0091] (1) Experimental simulation conditions

[0092] Generate multi-layer random phase screens based on the plasma sheath turbulence power spectrum, and analyze the propagation characteristics of petal-shaped Bessel beams passing through multi-layer turbulent phase screens. Among them, the simulated plasma thickness is 0.1 m, and a phase screen is generated every 0.01 m. The wavelength of the petal-shaped Bessel beam is 1550 nm. The orbital angular momentum modes of the two Bessel beams are 1 and -1 respectively, the "apodization" factor a is 0.01, and the cross-sectional scale w is 0.001 m.

[0093] (2)Analysis of experimental simulation results

[0094] Simulation experiment 1: Use the present invention to simulate the intensity and phase distributions of petal-shaped Bessel beams after passing through plasma turbulence. Select different differences in longitudinal wave numbers , which are 7.89 , 27.75 and 35.52 respectively. As the propagation distance changes, the rotation angle of the received beam changes, and the results are as shown in Figure 5 .

[0095] Figure 5 (a) in shows the intensity distributions of the received beam at different propagation distances. The rotation angle of the reflected spatial structured beam depends on the propagation distance. At the same propagation distance, the rotation angles of different emitted beams in air are affected by different values. directly affects the change of the phase difference between the two modes. At the same propagation distance, different values result in different cumulative phase differences between the two modes, thus causing changes in the rotation angle of the petal-shaped intensity distribution. This accumulation of phase difference changes the interference pattern, thereby affecting the intensity distribution and rotation characteristics of the beam. Since the interference between different modes generates a petal-shaped intensity distribution, the change of the phase difference directly affects the shape and direction of the interference fringes. Therefore, the rotation angle of the beam can be controlled by adjusting the phase accumulation.

[0096] Figure 5 (b) in shows the rotation angle changing with different values at a given propagation distance. The rotation angles corresponding to the three values increase as z increases, and the larger the value, the faster the rotation angle increases. This effect may be due to the influence of on the coupling strength between different Bessel light modes. The change of the coupling strength affects the energy distribution between different modes. When is small, the coupling between modes is weak, and the energy is relatively concentrated within each mode. On the contrary, when When it is large, the strong coupling redistributes the energy into different modes. This redistribution changes the overall characteristics of the light beam, including its rotation angle. Since the rotation behavior of the light beam is closely related to the superposition and interaction of modes, the change in the energy distribution changes the mode superposition effect, thus affecting the rotation of the light beam.

[0097] Simulation Experiment 2: Using the present invention to simulate the light intensity distribution and ranging error of the petal-shaped Bessel beam after passing through plasma turbulence, and selecting the variance of the refractive index fluctuation of the turbulence from 10 -14 to 10 -12 . The results are as Figure 6 shown.

[0098] Figure 6 In (a) of shows the beam intensity distribution measured by scattering at different values. When -14 increases from 10 -12 to 10 for the same propagation distance, the rotation angle of the reflected beam and the corresponding measured distance remain basically unchanged.

[0099] Figure 6 In (b) of it can be seen that as the propagation distance increases, the measurement error shows an upward trend. This is because the longer propagation distance prolongs the interaction time between light and higher values. The turbulent medium increases the possibility of photon scattering and absorption, resulting in the gradual accumulation of measurement errors. In addition, when -14 increases from 10 -12 to 10 the change in the refractive index becomes more obvious. Considering the relationship between the refractive index fluctuation and the higher the

[0100] value, the stronger the random fluctuation of the refractive index, and the more complex the aberration caused. is 10 -12 , 10 -13 , 10 -14 , and observe the changes in the scintillation coefficient SI and the beam broadening variance of the beam. The results are as Figure 7 shown.

[0101] Scintillation coefficient It describes the relative fluctuation of light intensity. The larger the flicker coefficient value, the more drastic the fluctuation of light intensity. When light is propagating and affected by turbulence, the light intensity will fluctuate. The flicker coefficient is the quantification of the magnitude of this fluctuation.

[0102] Beam jitter (beam broadening variance) reflects the statistical characteristics of the lateral size change of the light beam caused by turbulence during transmission.

[0103] Figure 7 As can be seen from (a) in Figure 2, under the same propagation distance, as As the propagation distance increases, the SI also increases. Stronger turbulence leads to more pronounced refractive index changes and enhanced light-turbulence interactions, resulting in larger intensity fluctuations. In addition, as the propagation distance increases, the interaction time between light and the turbulent medium is prolonged, resulting in the accumulation of intensity fluctuations. This SI trend is more pronounced at high More obvious.

[0104] Figure 7 As can be seen in (b), in PST (Plasma sheath turbulence), the petal-shaped Bessel beam (Petal-BG) proposed in this paper has a lower SI than traditional beams such as Gaussian light (Gauss) and ordinary Bessel beam (BG). This shows that the petal-shaped Bessel light exhibits smaller intensity fluctuations and maintains greater intensity stability. Turbulence causes wavefront distortion and changes the intensity distribution; however, the structural characteristics of the Bessel beam make it less sensitive to wavefront distortion, thereby reducing intensity fluctuations and enhancing anti-turbulence.

[0105] Simulation experiment 4: Comparison of the transmission performance of the petal-shaped Bessel beam of the present invention, Gaussian beam and ordinary Bessel beam in plasma turbulence, respectively selecting the refractive index fluctuation variance For 10 -12 , 10 -13 , 10 -14 , observe the change of beam broadening variance, the result is as follows Figure 8 shown.

[0106] Figure 8 (a) in the table is different Figure 3. Variation of the beam broadening variance of Petal-BG with propagation distance at 100 Å. The beam drift effect weakens with the increase of spot size. Although its initial non-diffraction property suppresses the beam jitter to a certain extent, the cumulative effect of turbulence causes the beam broadening variance to gradually increase with the increase of propagation distance. However, at the same transmission distance, Petal-BG exhibits a smaller beam broadening variance compared with Gaussian beams and ordinary Bessel beams (BG) due to its initial structural characteristics.

[0107] As shown Figure 8 in (b) of [reference], at the same distance, the beam broadening variance of Petal - BG is the smallest, that of BG is the second, and that of Gaussian beam is the largest.

[0108] The above description is only a preferred embodiment of the present disclosure and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of disclosure involved in the present disclosure is not limited to the technical solutions formed by the specific combination of the above - mentioned technical features. At the same time, it should also cover other technical solutions formed by any combination of the above - mentioned technical features or their equivalent features without departing from the above - mentioned disclosure concept. For example, the technical solutions formed by mutually replacing the above - mentioned features with the technical features (but not limited to) having similar functions disclosed in the present disclosure.

[0109] In addition, although the operations are depicted in a particular order, this should not be construed as requiring that the operations be performed in the particular order shown or in sequential order. In certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although a number of specific implementation details are included in the above discussion, these should not be construed as limiting the scope of the present disclosure. Certain features described in the context of separate embodiments may also be implemented combinatorially in a single embodiment. Conversely, the various features described in the context of a single embodiment may also be implemented separately or in any suitable sub - combination in multiple embodiments.

[0110] The above - described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as limiting the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A method for petal-shaped Bessel light ranging in hypersonic plasma turbulence, characterized in that: The method comprises: A multi-layer random phase screen is established to simulate plasma sheath turbulence; Calculating the intensity distribution of the reflected light beam transmitted from the receiving surface by the petal-shaped Bessel light through the diffraction of the multi-layer random phase screen; determining a rotation angle of the reflected light beam based on a maximum correlation between an intensity distribution of the reflected light beam and an ideal intensity distribution; The linear relationship between the propagation distance and the rotation angle is used to achieve distance measurement; Propagation distance z and rotation angle The linear relationship expression between them is: ； in, is the difference in longitudinal wavenumber between two adjacent Bessel modes, ; n is the refractive index of the plasma medium; ; In the formula, is the refractive index of free electrons; is the electron charge; is the mass of the electron; is the electron number density; is the speed of light in free space.

2. The method for ranging in hypersonic plasma turbulence based on petal-shaped Bessel light according to claim 1, characterized in that: The petal-shaped Bessel light is composed of two Bessel mode beams, and the expression is: ， ， In the formula Expressed in cylindrical coordinate system; is the OAM order of the ith Bessel mode, is the longitudinal wave number of the i-th Bessel mode; is the corresponding radial wave number; is the wave number of the beam, ; The order is Bessel functions of the first kind; is the wavelength of the light beam.

3. The method for petal-shaped Bessel light ranging in hypersonic plasma turbulence according to claim 1, characterized in that: The method of establishing a multi-layer random phase screen for simulating plasma sheath turbulence comprises: According to the flow field law of hypersonic vehicle, the power spectrum density function of refractive index fluctuation in anisotropic plasma sheath turbulence is determined , the expression is: á ñ ; In the formula, is the plasma refractive index variance, is the outer scale of turbulence, and Represents the frequency components in the horizontal and vertical directions in the frequency domain; The phase spectrum is obtained from the relationship between the refractive index spectrum and the power spectrum density of the phase , the expression is: ;in is the spatial wave number; The standard deviation expression of the phase spectrum is: ,in, is the distance between two adjacent phase screens, N is the number of samples, is the grid spacing; Calculate the diffraction transmission of petal-shaped Bessel light through a multi-layer phase screen, simulate the transmission characteristics of the light beam in the plasma sheath turbulence, and use the power spectrum inversion method to obtain the random phase screen for the power spectrum density function of the plasma sheath turbulence , the expression is: ； in, To generate a complex Gaussian random matrix, in the frequency domain it is a standard normal distribution function, is the inverse Fourier transform.

4. The method for petal-shaped Bessel light ranging in hypersonic plasma turbulence according to claim 2, characterized in that: The establishment of a multi-layer random phase screen for simulating plasma sheath turbulence also includes: According to the crosstalk caused by the flow field of hypersonic aircraft, the light field after turbulence disturbance It is expressed as: ； The Fresnel diffraction integral D-FFT algorithm is used to calculate the light field after a period of free space transmission and reaching the second phase screen. , the expression is: ； In the formula is the inverse Fourier transform, is the Fourier transform, and Represents the frequency components in the horizontal and vertical directions in the frequency domain.

5. The method for ranging in hypersonic plasma turbulence based on petal-shaped Bessel light according to claim 4, characterized in that: The step of calculating the intensity distribution of the light beam reflected from the receiving surface by the diffraction of the petal-shaped Bessel light through the multi-layer random phase screen comprises: Capturing the intensity distribution of the reflected beam, based on the light field Calculate the intensity distribution of the reflected beam , the calculation formula is: 。 6. The method for ranging in hypersonic plasma turbulence based on petal-shaped Bessel light according to claim 5, characterized in that: The step of determining the rotation angle of the reflected light beam based on the maximum correlation between the intensity distribution of the reflected light beam and the ideal intensity distribution comprises: The rotation angle of the contour is obtained by the reflected beam image, and the rotation angle is estimated using the angle detection algorithm , the expression is: ； in, To measure the intensity distribution, This is the ideal intensity distribution of a petal-shaped Bessel beam transmitted through free space without plasma turbulence.

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