Method for measuring distance based on petal-shaped Bessel light in hypersonic plasma turbulence

Abstract

The invention relates to the field of electromagnetic calculation, in particular to a petal-shaped Bessel light-based distance measurement method in hypersonic plasma turbulence, which comprises the following steps of: simulating plasma sheath turbulence by establishing a multi-layer random phase screen, calculating diffraction transmission of petal-shaped Bessel light after the petal-shaped Bessel light passes through the turbulence, and capturing intensity distribution of reflected light beams; the rotation angle is determined based on the correlation with the ideal intensity distribution, and high-precision distance measurement is realized by using the linear relation between the rotation angle and the propagation distance. The petal-shaped Bessel light is formed by superposing two Bessel mode light beams with different orbital angular momentum orders, has a spatial structure strongly related to the propagation distance, and can keep higher stability and anti-interference capability in a turbulent environment. By combining the self-focusing and approximately non-diffraction characteristics of the Bessel beam, the target detection and distance measurement precision in hypersonic plasma turbulence is remarkably improved, and reliable technical support is provided for communication and target detection of hypersonic aircrafts.

Description

Technical Field

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

[0002] During the re-entry 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 vortices of varying sizes will appear in the plasma flow field, forming plasma turbulence with electrons and ions. Plasma turbulence will seriously reflect and refract electromagnetic wave signals, and absorb a large amount of signal energy, which seriously damages the stability of communication signals. This interference will not only cause frequent jams and distortions in wireless communications, but in extreme cases, the communication link will even be completely interrupted. Because it interferes with the normal propagation and reception of electromagnetic wave signals, the detection of surrounding targets by the aircraft drops sharply, making it difficult to accurately obtain target information. At present, using laser radar instead of electromagnetic wave radar (time of flight method, pulse method) is a common solution. However, even though the laser band radar has a low attenuation in plasma, it is easily affected by turbulence, causing light 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 turbulent environment, the resolution is limited.

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

[0005] The present invention achieves the above-mentioned purpose through the following technical solutions: The present invention proposes a method for petal-shaped Bessel light ranging in hypersonic plasma turbulence, the method comprising: 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 distance measurement is achieved by utilizing the linear relationship between the propagation distance and the rotation angle.

[0006] Furthermore, 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.

[0007] Furthermore, the establishment of a multi-layer random phase screen for simulating plasma sheath turbulence includes: 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: ; In the formula, is the plasma refractive index variance, is the outer scale of turbulence, and Represents the frequency components along 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: ;

[0008] in, To generate a complex Gaussian random matrix, in the frequency domain it is a standard normal distribution function, is the inverse Fourier transform.

[0009] Furthermore, 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: .

[0010] Furthermore, 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: .

[0011] Further, the 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 includes: 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.

[0012] Furthermore, the propagation distance z and the rotation angle The linear relationship expression between them is: ; in, is the difference in longitudinal wavenumber between two adjacent Bessel modes, , ; is the refractive index of the plasma medium; ; In the formula, is the refractive index of free electrons; is the charge of the electron; is the mass of the electron; is the electron number density; is the speed of light in free space.

[0013] The beneficial effects of the present invention are: Based on the random phase screen theory, the present invention proposes a ranging method based on the space domain. The method studies the unique propagation characteristics of petal-shaped Bessel structured light generated by vortex phase coherent superposition under the plasma flow field, which can improve the detection, tracking and communication of targets.

[0014] The present invention utilizes the relationship between the rotation angle and propagation distance of petal-shaped Bessel light to achieve the purpose of distance measurement, and provides a theoretical basis for studying the propagation problem of vortex laser beams in plasma turbulence, as well as the distance measurement purpose and communication problems in near-Earth space. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is the overall flow chart of the present invention.

[0016] Figure 2 The difference in the order of orbital angular momentum of the petal-shaped Bessel structure light beam in the present invention and its influence on the number of petals, different longitudinal wave numbers ( ) difference in the shape change of the petal-shaped Bessel beam during propagation; where, Figure 2 (a) is a schematic diagram of the difference in the order of orbital angular momentum of the petal-shaped Bessel structure light beam and its influence on the number of petals in the present invention. Figure 2 (b) in the figure is the number of different longitudinal waves ( ) during the propagation of a petal-shaped Bessel beam.

[0017] Figure 3 The conceptual diagram of the petal-shaped Bessel structured light rotating at the z-related angle in the present invention, the difference between the rotation angle of the structured light and the longitudinal wave number Relationship diagram; among them, Figure 3 (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 (b) is the difference between the rotation angle of the structured light and the longitudinal wave number Relationship diagram.

[0018] Figure 4 The present invention is different Schematic diagram of the normalized amplitude distribution of the light field at, and schematic diagram of the multi-layer random phase screen model; Among them, Figure 4 (a) is different from the present invention. Schematic diagram of the normalized amplitude distribution of the light field at Figure 4 (b) is a schematic diagram of the multi-layer random phase screen model in the present invention.

[0019] Figure 5 The petal-shaped Bessel structured light in the present invention has different longitudinal wave number differences at two different propagation distances of z = 0m and z = 0.1m. Graph of light field intensity, phase distribution and angle variation.

[0020] Figure 6 The present invention is different Schematic diagram of the impact on beam intensity distribution and measurement error (MSE) at different propagation distances.

[0021] Figure 7 The petal-shaped Bessel structured light in the present invention is different Schematic diagram of the change of the normalized flicker index (SI) of the petal-shaped Bessel structured light with distance under different values ​​and the change of the flicker index of different light beams with propagation distance.

[0022] Figure 8 The petal-shaped Bessel structured light of the present invention is different Schematic diagram of how the beam diffusion variance of petal-shaped Bessel structured light changes with distance under different values ​​and how the beam diffusion variance of different beams changes with propagation distance. DETAILED DESCRIPTION

[0023] The following description provides specific application scenarios and requirements of this specification, with the purpose of enabling those skilled in the art to make and use the contents of this specification. Various local modifications to the disclosed embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of this specification. Therefore, this specification is not limited to the embodiments shown, but to the widest scope consistent with the claims.

[0024] The terms used herein are only used for the purpose of describing specific example embodiments and are not restrictive. For example, unless the context clearly indicates otherwise, as used herein, the singular forms "a", "an" and "the" may also include plural forms. When used in this specification, the terms "include", "comprise" and / or "contain" 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 that other features, integers, steps, operations, elements, components and / or groups may be added in the system / method.

[0025] In view of the following description, these and other features of the present specification, as well as the operation and function of the related elements of the structure, and the economy of the combination and manufacture of the parts can be significantly improved. Reference is made to the accompanying drawings, all of which form a part of this specification. However, it should be clearly understood that the drawings are for illustration and description purposes only and are not intended to limit the scope of this specification. It should also be understood that the drawings are not drawn to scale.

[0026] 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 of the flowcharts 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.

[0027] like Figure 1 As shown, this embodiment proposes a method for ranging based on petal-shaped Bessel light in hypersonic plasma turbulence, the method comprising: establishing a multi-layer random phase screen for simulating plasma sheath turbulence; calculating the intensity distribution of the reflected light beam transmitted to the receiving surface by the diffraction of the petal-shaped Bessel light through the multi-layer random phase screen; 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; and realizing ranging by using the linear relationship between the propagation distance and the rotation angle.

[0028] In a specific embodiment, petal-shaped Bessel light is emitted by a transmitter, and the petal-shaped Bessel light consists of two Bessel mode beams, and the two Bessel modes have different OAM orders. The spatial interference between the two modes with different OAM orders produces a petal-shaped intensity distribution, and 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: ; ; 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.

[0029] In order to express the rotation angle related to z, the difference in longitudinal wavenumber between two adjacent Bessel modes is introduced: , To achieve a linear z-dependent angular rotation, see Figure 3 .

[0030] In a specific embodiment, a multi-layer random phase screen is established for simulating plasma sheath turbulence. The multi-layer random phase screen is established by a power spectrum inversion method according to a power spectrum function of anisotropic plasma turbulence refractive index fluctuations, specifically including: 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: ; In the formula, is the plasma refractive index variance, is the outer scale of turbulence, and represents the frequency components of the light beam along the x and y directions; 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, it is a standard normal distribution function in the frequency domain. is the disturbance of the phase of the petal-shaped Bessel beam caused by the turbulence in the plasma sheath, see Figure 4 ; is the inverse Fourier transform.

[0031] In a specific embodiment, establishing 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 D-FFT algorithm of Fresnel diffraction integral is used to calculate the light field of the petal-shaped Bessel light after it is transmitted through the plasma sheath turbulence simulated by the multi-layer random phase screens and then transmitted through a free space transmission distance between adjacent random phase screens. , the expression is: .

[0032] In a specific embodiment, calculating the intensity distribution of the reflected light beam transmitted from the receiving surface by the diffraction of the petal-shaped Bessel light through the multi-layer random phase screen includes: Capture the intensity distribution of the reflected beam based on the light field Calculate the intensity distribution of the reflected beam , the calculation formula is: .

[0033] In a specific embodiment, 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 includes: 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, is the measured intensity distribution, is the ideal intensity distribution of a petal-shaped Bessel beam transmitted through free space without plasma turbulence; In one embodiment, the propagation distance z and the rotation angle The linear relationship expression between them is: ; in, is the difference in longitudinal wavenumber between two adjacent Bessel modes, , ; is the refractive index of the plasma medium; ; In the formula, is the refractive index of free electrons; is the charge of the electron; is the mass of the electron; is the electron number density; is the speed of light in free space.

[0034] Based on the random phase screen theory, the present invention proposes a ranging method based on the space domain. The method studies the unique propagation characteristics of petal-shaped Bessel structured light generated by vortex phase coherent superposition under the plasma flow field, which is of great significance for improving target detection, tracking and communication.

[0035] The simulation results of the present invention can be further illustrated by the following experiments: (1) Experimental simulation conditions Based on the plasma sheath turbulence power spectrum, a multi-layer random phase screen is generated, and the transmission characteristics of the multi-layer turbulent phase screen are analyzed by combining the petal-shaped Bessel beam. Among them, the simulated plasma thickness is 0.1m, and a phase screen is generated every 0.01m. The wavelength of the petal-shaped Bessel beam is 1550nm, the orbital angular momentum modes of the two Bessel lights are 1 and -1 respectively, the "truncation" factor a is 0.01, and the cross-sectional scale w is 0.001m.

[0036] (2) Analysis of experimental simulation results Simulation experiment 1: Using the present invention to simulate the intensity and phase distribution of a petal-shaped Bessel beam after passing through plasma turbulence. Select different longitudinal wave number differences , respectively 7.89 , 27.75 and 35.52 , as the propagation distance changes, the rotation angle of the received light beam changes, and the result is as follows Figure 5 shown.

[0037] Figure 5 (a) shows the intensity distribution of the received beam at different propagation distances. The rotation angle of the reflected spatial structure beam depends on the propagation distance. At the same propagation distance, the rotation angle of different transmitted beams in the air is affected by different The impact of value. The size of directly affects the change of the phase difference between the two modes. Under the same propagation distance, different The value results in different accumulated phase differences between the two modes, which causes the rotation angle of the petal-shaped intensity distribution to change. This accumulation of phase difference changes the interference pattern, thus affecting the intensity distribution and rotation characteristics of the beam. Since the interference between different modes produces a petal-shaped intensity distribution, the change in 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.

[0038] Figure 5 (b) shows the rotation angle for a given propagation distance. Follow The three The rotation angle corresponding to the value increases as z increases. The larger the value, the faster the rotation angle increases. This effect may be due to The influence of coupling strength between different Bessel optical modes. The change of coupling strength will affect the energy distribution between different modes. When is small, the coupling between modes is weak and the energy is relatively concentrated in each mode. When is larger, stronger coupling redistributes energy into different modes. This redistribution changes the overall properties of the beam, including its rotation angle. Since the rotation behavior of the beam is closely related to the superposition and interaction of modes, the change in energy distribution changes the modal superposition effect, thereby affecting the rotation of the beam.

[0039] Simulation experiment 2: Using the present invention to simulate the light intensity distribution and ranging error of a petal-shaped Bessel beam after passing through plasma turbulence, the variance of the turbulent refractive index fluctuation is selected. From 10 -14 Increase to 10 -12 The results are as follows Figure 6 shown.

[0040] Figure 6 (a) shows the difference The beam intensity distribution is obtained by measuring the value of the scattering. From 10 -14 Increase to 10 -12 When the propagation distance is the same, the rotation angle of the reflected light beam and the corresponding measurement distance remain basically unchanged. The change in leads to a distortion in the light intensity, which is consistent with our expectations.

[0041] Figure 6 As can be seen from (b) in Figure 1, the measurement error increases with the increase of propagation distance. This is because the longer propagation distance prolongs the time between light and higher The interaction time between the values. Turbulent media increases the possibility of photon scattering and absorption, which leads to the gradual accumulation of measurement errors. In addition, when From 10 -14 Increase to 10 -12 When the refractive index changes, it becomes more obvious. Considering the refractive index fluctuation and The relationship between The higher the value, the stronger the random fluctuation of the refractive index is, and the more complex the aberration is.

[0042] Simulation experiment 3: 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 changes in the beam scintillation coefficient SI and beam broadening variance. The results are as follows Figure 7 shown.

[0043] Flicker 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.

[0044] Beam jitter (beam broadening variance) reflects the statistical characteristics of the lateral size change of the light beam caused by turbulence during transmission.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] like Figure 8 As shown in (b), at the same distance, the beam broadening variance of Petal-BG is the smallest, followed by BG, and the beam broadening variance of Gaussian beam is the largest.

[0050] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. 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 a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosed concept. For example, the above features are replaced with the technical features with similar functions disclosed in the present disclosure (but not limited to) by each other to form a technical solution.

[0051] In addition, although each operation is described in a specific order, this should not be understood as requiring these operations to be performed in the specific order shown or in a sequential order. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although some specific implementation details are included in the above discussion, these should not be interpreted as limiting the scope of the present disclosure. Some features described in the context of a separate embodiment can also be implemented in a single embodiment in combination. On the contrary, the various features described in the context of a single embodiment can also be implemented in multiple embodiments individually or in any suitable sub-combination mode.

[0052] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which 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 distance measurement is achieved by utilizing the linear relationship between the propagation distance and the rotation angle.

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: ； 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.

7. The method for ranging in hypersonic plasma turbulence based on petal-shaped Bessel light according to claim 6, characterized in that: The propagation distance z and the rotation angle The linear relationship expression between them is: ； in, is the difference in longitudinal wavenumber between two adjacent Bessel modes, , ; 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.

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