Atmospheric turbulence phase screen generation method based on complex variable matrix space-time interpolation

Abstract

The invention belongs to the technical field of atmospheric optics, and particularly relates to an atmospheric turbulence phase screen generation method based on complex variable matrix space-time interpolation. According to the invention, a complex variable matrix interpolation algorithm is used to simulate the continuous change of the light field intensity and the random phase screen in the propagation process; comprising the following steps: reflecting time continuity of a turbulent phase screen by using a random complex variable matrix according to a frozen flow hypothesis; based on a power spectrum inversion method, an atmospheric turbulence phase screen is generated; performing light field diffraction transmission simulation by using a Fresnel method; and displaying the change of results in different time steps by utilizing visual comparison. According to the invention, the transmission performance of the optical signal in a changing environment can be effectively improved, and the calculation complexity is greatly reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of atmospheric optics, and in particular relates to a method for generating an atmospheric turbulence phase screen based on complex matrix spatiotemporal interpolation. Background Art

[0002] Atmospheric optics is an important part of environmental monitoring and atmospheric science research. It involves the optical properties of atmospheric components and their interaction with light. Existing time-varying turbulence generation methods are usually unable to fully characterize the dynamic changes in the transmission process when simulating the propagation of optical signals, and lack effective observation and parameter recording of intermediate processes. These traditional models are usually based on the fixed turbulence assumption and fail to take into account the random fluctuations of turbulence in time [1], which affects the transmission quality and stability of optical signals in complex environments.

[0003] In 1938, GI Taylor proposed the frozen flow hypothesis, which assumes that under certain conditions, when turbulence flows through a certain area, it can be regarded as "frozen", that is, the spatial changes of the turbulent eddy structure can be ignored, thus converting the turbulence in time into turbulence changes in space. In addition, under the same weather, parameters such as atmospheric coherence length, inner scale and outer scale are constant.

[0004] The existing methods for generating dynamic atmospheric turbulence screens simply merge the coarse-grained and fine-grained phase screens, which cannot ensure that the interpolated atmospheric turbulence phase screen has the same atmospheric structure constants and parameters such as inner and outer scales. In addition, the point-to-point interpolation calculation is highly complex [2]. Although the time-varying atmospheric turbulence algorithm involves spatial light modulation technology, it also ignores the problem of inconsistent structural constants of the atmospheric turbulence phase screen of the time-varying phase screen [3]. Especially in a dynamic turbulent environment, the reliability and stability of the optical signal are severely restricted. Therefore, a new generation method is urgently needed to improve the transmission performance of optical signals in a changing environment. Summary of the invention

[0005] The object of the present invention is to provide an atmospheric turbulence phase screen generation method based on a complex matrix spatiotemporal interpolation algorithm with good transmission performance and low computational complexity.

[0006] The atmospheric turbulence phase screen generation method based on complex matrix spatiotemporal interpolation provided by the present invention uses a complex matrix interpolation algorithm to simulate the continuous change of light field intensity and random phase screen during propagation; including using random complex matrix to reflect the time continuity of turbulence phase screen according to the frozen flow hypothesis; and generating atmospheric turbulence phase screen based on power spectrum inversion method; using Fresnel method to simulate light field diffraction transmission; using visual comparison to show the change of results in different time steps. The specific steps are:

[0007] (1) Using spatial interpolation algorithm to interpolate complex variable matrix;

[0008] According to the random phase screen theory generated by the power spectrum inversion method, the core of the random change of the turbulence phase screen is the random complex variable matrix introduced each time the turbulence is generated. At the same time, according to the "frozen flow" hypothesis, the time change of turbulence in a small range does not change the structural parameters of the turbulence; therefore, the present invention can reflect the time continuity of the turbulence phase screen by controlling the spatial continuity of multiple random complex variable matrices. Specifically:

[0009] First, generate N uncorrelated random complex variable matrix samples h1(x,y),h2(x,y),…,h n (x, y), and a total of T linear interpolations are expected, then the T interpolation points are defined as:

[0010]

[0011] For each interpolation point m j , find the adjacent sample matrix h i and h i+1 , so that:

[0012] i=[m j ·(N-1)],i+1=min(i+1,N-1), (2)

[0013] Then calculate the interpolation ratio α:

[0014] α=m j ·(N-1)-i, (3)

[0015] The interpolated matrix h j (x,y) is:

[0016] h j (x,y)=(1-α)h i (x,y)+αh i+1 (x,y) (4)

[0017] Therefore, the final interpolation matrix is ​​h j (x, y), j = 0, 1, ..., T-1, for a given representation time step T, by changing the number of interpolation points N, the rate of change of the spatial distribution of the complex variable matrix can be controlled.

[0018] (2) Generate atmospheric turbulence phase screen using power spectrum inversion method

[0019] An important parameter of atmospheric turbulence is the power spectrum Φ n, n is the number of samples, which describes the energy distribution of turbulent phenomena on different spatial and temporal scales. In the frequency domain, the power spectrum characterizes the energy ratio of various scales in the turbulent field. For atmospheric turbulence, its power spectrum can usually be described by the Kolmogorov spectrum model. It is a theoretical model for describing fluid turbulence, in which the energy distribution on a large scale obeys a power law relationship, and the relationship between the power spectrum density and the wave number is k -5 / 3 , k is the wave number. This means that atmospheric turbulence has higher energy at smaller scales and gradually decreases at larger scales. The Kolmogorov spectrum model proposed by Kolmogorov is:

[0020]

[0021] Where l and k are the current height and wave number respectively. The relationship between the phase power spectral density and the refractive index fluctuation power spectral density satisfies the following relationship:

[0022]

[0023] Where Δz is the propagation distance of the laser in atmospheric turbulence. The relationship between Δz and the number of phase screens and the transmission distance is:

[0024] z=n z ×Δz (7)

[0025] Among them, n z The number of random phase screens, z is the distance; the coherence length of the atmosphere can be expressed as:

[0026]

[0027] Random phase screen refers to the random change of phase caused by light waves passing through a medium with random phase distribution in an optical system. To represent this random phase screen. The power spectrum of the phase screen Describes the distribution of phase changes in the frequency domain. It is the Fourier transform of the phase function The square of the modulus:

[0028]

[0029] The atmospheric turbulence phase is inverted using the power spectrum inversion method. According to the inversion theorem, given the power spectrum, the spatial distribution of the phase screen can be obtained by inverse Fourier transform:

[0030]

[0031] in, represents the inverse Fourier transform, h(k x ,k y) represents the generation of complex Gaussian random matrices (k x ,k y Represents the wave number on the x-axis and y-axis respectively), which is the standard normal distribution function in the frequency domain and is used to describe the frequency response of the system. is the square root of the phase structure function, indicating the random nature of the phase. Since the phase is a real number, taking the real part of the inverse Fourier transform, the final random phase screen [4] is expressed as:

[0032]

[0033] According to the spatially continuous complex variable matrix sequence obtained in equation (3), the temporal variation of atmospheric turbulence is described, and the temporal continuity atmospheric turbulence phase screen is obtained as follows:

[0034]

[0035] (3) Light field diffraction transmission simulation

[0036] Consider the transmission principle of a light beam in an atmospheric turbulent channel: When studying the diffraction transmission of a light beam, only the electric field component of the light wave field is taken and treated as a scalar. The diffraction integral formula is used to calculate the light field distribution at a straight-line distance in space. When discussing non-infinite transmission, the Fresnel diffraction integral [5] is usually used for calculation. The Fresnel diffraction integral is:

[0037]

[0038] d is the distance from the origin to the observation point, λ is the wavelength, u and v represent the coordinate system, and combined with the theory of random phase shielding, the distribution of the light field after the light beam passes through the single-phase shielding is:

[0039]

[0040] Due to the correlation of time variation, we can estimate the overall trend from a small range of data. To make the algorithm simple and efficient, only one layer of phase screen is used here.

[0041] (4) Visualization results

[0042] First, the random changes of light field intensity are simulated by complex matrix interpolation algorithm, and the temporal continuity of phase screen is reflected by random complex matrix according to the frozen flow hypothesis. Secondly, the atmospheric turbulence phase screen is generated by power spectrum inversion algorithm, and the light field diffraction simulation is performed by Fresnel method. Finally, the result changes of different time steps are displayed by comparing phase screen and power spectrum, so as to clearly present the continuous change process of light field intensity and phase screen, which proves the rationality and effectiveness of the present invention.

[0043] The technical features and performance advantages of the present invention are:

[0044] (1) Interpolation of the complex variable matrix generated by the phase screen, which associates the unrelated complex distributions through interpolation, and replaces the temporal continuity of turbulence changes with the spatial continuity of the complex distribution according to the "frozen flow hypothesis". Although the existing time-varying algorithms involve spatial light modulation technology, they ignore the problem of inconsistent structural constants of the atmospheric turbulence phase screen of the time-varying phase screen;

[0045] (2) The complex matrix space-time interpolation algorithm does not change the structural parameters of atmospheric turbulence, while ensuring the consistency of the spatial structure of the generated turbulence phase screen, it also reflects the temporal continuity of turbulence changes. Traditional models are usually based on the fixed turbulence assumption and fail to take into account the random fluctuations of turbulence in time, thus affecting the transmission quality and stability of optical signals in complex environments;

[0046] (3) The complex matrix spatiotemporal interpolation algorithm starts from the essence of the power spectrum inversion method to generate the atmospheric turbulence phase screen, and controls the core variable of the complex matrix of random phase generation, which greatly reduces the computational complexity. Compared with the algorithm that simply merges the coarse-grained and fine-grained phase screens in the dynamic generation method, it cannot guarantee that the atmospheric turbulence phase screen generated by interpolation has the same atmospheric structure constants and parameters such as inner and outer scales. At the same time, the point-to-point interpolation calculation complexity is high. Especially in a dynamic turbulent environment, the reliability and stability of the optical signal are severely restricted. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a framework diagram of the atmospheric turbulence phase screen generation model of the complex matrix spatiotemporal interpolation algorithm of the present invention.

[0048] Figure 2 The figures are comparative experimental results of the method of the present invention for processing different numbers of interpolation sample points.

[0049] Figure 3 This is a comparison diagram of the random phase screen effects produced by the method of the present invention at each time step under different numbers of interpolation sample points.

[0050] (a) is the result of each time step when Factor=1, (b) is the result of each time step when Factor=3, (c) is the result of each time step when Factor=5, and (d) is the result of each time step when Factor=7.

[0051] Figure 4 This is a graph of light intensity results generated at each time step when the method of the present invention processes a Gaussian beam at different numbers of interpolation sample points.

[0052] Figure 5 This is a graph of light intensity results generated at each time step when the method of the present invention processes the LG light beam under different numbers of interpolation sample points.

[0053] Figure 6This is a comparison chart of the results of processing LG beams with different coherence lengths using the method of the present invention. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with specific simulations and experiments.

[0055] The present invention is applicable to most types of beams. Here, the processing of Gaussian beams and Laguerre-Gaussian (LG) beams is selected for simulation. As one of the most basic beam modes in optics, Gaussian beams have stability and predictability in focusing, diffraction, interference and other phenomena, which makes them widely used in laser physics, optical communications and precision measurement. LG beams have attracted attention because they carry orbital angular momentum (OAM) and have a spiral phase structure. These characteristics make them show great application potential in quantum information processing, optical manipulation and biomedical imaging. In this experiment, the random number factor (Factor) is used to control the number of sample interpolation points. Here, the values ​​are 1, 3, 5 and 7 respectively, and the analysis is performed under the condition that the time step is set to 100 (see Figure 2 ). The results show that, under the premise of keeping the starting and ending conditions similar, as the random number factor value increases, the change trend of atmospheric turbulence becomes more significant. This phenomenon shows that the increase of the random number factor can effectively amplify the impact of turbulence on beam propagation.

[0056] Figure 3 The results of the method of the present invention when processing a Laguerre-Gaussian (LG) beam are also shown. In this case, the number of sample interpolation points is still controlled to be 1, 3, 5 and 7, and the time step is set to 100. In the process of extracting a sample point every 10 time steps, a total of 10 sample points are obtained for comparative analysis of the random phase screen effect. By observing these sample points, the continuity of the turbulent structure in the Taylor frozen flow hypothesis in the time step and its changing trend can be clearly verified.

[0057] Figure 4 The simulation results of the method of the present invention when processing Gaussian beams are shown. The single figure on the left is the result without processing. In this experiment, Figure 4 (a) The number of sample interpolation points is 1, and a sample point is extracted at steps of 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 to obtain the simulation results of the light intensity distribution. The 10 figures are shown in order from left to right and from top to bottom. Figure 4(b) The number of sample interpolation points is 5, and a sample point is drawn at steps of 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 to obtain the simulation results of the light intensity distribution. The 10 figures are shown in order from left to right and from top to bottom. This result shows the effect of random phase on Gaussian beam propagation and provides important information about the change in beam intensity distribution.

[0058] Figure 5 Focus on the simulation of the intensity distribution of Laguerre-Gaussian (LG) beams. The single figure on the left is the result without treatment. In this experiment, Figure 5 (a) The number of sample interpolation points is set to 1, and a sample point is extracted at a step size of 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 to obtain the simulation results of the light intensity distribution. The 10 figures are shown in order from left to right and from top to bottom. Figure 5 (b) The number of sample interpolation points is 5, and a sample point is drawn at a step size of 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 to obtain the simulation results of the light intensity distribution. The 10 figures are shown in order from left to right and from top to bottom. The results in this figure further show the light intensity distribution characteristics of the Laguerre-Gaussian beam and its changes over time under different random number factors, which can be compared with Figure 4 The algorithm is compared with a Gaussian beam, and the same is true for other types of beams. This algorithm is applicable to common optical signal processing.

[0059] at last, Figure 6 The simulation results of the method of the present invention when processing Laguerre-Gaussian (LG) beams with different coherence lengths are compared. In all states, the number of sample interpolation points is set to 3, and a sample point is extracted at a step size of 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 to obtain the simulation results of the light intensity distribution. The 10 figures are shown in order from left to right and from top to bottom. Figure 6 (a) shows the result when the coherence length r0 = 0.01, where obvious artifacts can be observed in the beam shape; Figure 6 (b) shows the result when the coherence length r0 = 0.025, where the beam shape tends to be similar to the original signal; Figure 6 (c) shows the results when the coherence length r0 = 0.05, where the beam shape is almost consistent with the original intensity distribution. These results emphasize the critical influence of the coherence length on the beam propagation characteristics.

[0060] References:

[0061] [1] Zhao Jiantong, Liu Zhi, Yao Haifeng, et al. Research on complex domain simulation method of atmospheric turbulence effect in laser transmission[J]. Laser & Infrared, 2024, 54(06): 878-884.

[0062] [2] Geng Xingning, Liu Zheng, Li Wuzhou, et al. Study on propagation characteristics of laser in dynamic atmospheric turbulence[J]. Laser & Infrared, 2024, 54(01): 40-47.

[0063] [3] Shen Baoliang, Sun Jianfeng, Zhou Yu, et al. Influence of time-varying turbulence on the positioning accuracy of dynamic moving light spot[J]. Chinese Journal of Lasers, 2011, 38(08): 160-165.

[0064] [4] S. Huang and M. Safari, “Free-space optical communication impaired byangular fluctuations,” IEEE Transactions on Wireless Communications, vol.16, no.11, pp.7475–7487, 2017.

[0065] [5] Y.Hu, Z.Wang,

Claims

1. A method for generating an atmospheric turbulence phase screen based on complex matrix spatiotemporal interpolation, characterized in that: Use a complex variable matrix interpolation algorithm to simulate the continuous change of light field intensity and random phase screen during propagation; including, according to the frozen flow hypothesis, using random complex variable matrix to reflect the time continuity of turbulent phase screen; Based on the power spectrum inversion method, the atmospheric turbulence phase screen is generated; the Fresnel method is used to simulate the diffraction transmission of the light field; the changes in the results at different time steps are displayed by visual comparison; the specific steps are as follows: (1) Using spatial interpolation algorithm to interpolate complex variable matrix; According to the random phase screen theory generated by the power spectrum inversion method, the core of the random change of the turbulence phase screen is the random complex variable matrix introduced each time the turbulence is generated. At the same time, according to the "frozen flow" hypothesis, the time variation of turbulence in a small range does not change the structural parameters of the turbulence; therefore, the time continuity of the turbulence phase screen is reflected by controlling the spatial continuity of multiple random complex variable matrices; specifically: First, generate N uncorrelated random complex matrix samples h1(x,y),h2(x,y),…,h n (x, y), a total of T linear interpolation points are performed, then the T interpolation points are defined as: For each interpolation point m j , find the adjacent sample matrix h i and h i+1 , so that: i=[m j ·(N-1)],i+1=min(i+1,N-1), (2) Then calculate the interpolation ratio α: a=m j ·(N-1)-i, (3) The interpolated matrix h j (x,y) is: h j (x,y)=(1-α)h i (x,y)+αh i+1 (x,y) (4) Therefore, the final interpolation matrix is ​​h j (x, y), j = 0, 1, ..., T-1; for a given time step T, by changing the number of interpolation points N, the rate of change of the spatial distribution of the complex variable matrix can be controlled; (2) Generate the atmospheric turbulence phase screen using the power spectrum inversion method; Assume that the power spectrum of atmospheric turbulence is Φ n , n is the number of samples, which describes the energy distribution of turbulent phenomena on different spatial and temporal scales; in the frequency domain, the power spectrum represents the energy proportion of various scales in the turbulent field; the power spectrum is described by the Kolmogorov spectrum model; the energy distribution on large scales obeys a power law relationship, where the relationship between power spectrum density and wave number is k -5 / 3 , k is the wave number; the Kolmogorov spectrum model is: Where l and k are the current height and wave number respectively; the relationship between the phase power spectral density and the refractive index fluctuation power spectral density satisfies the following relationship: Where Δz is the propagation distance of the laser in atmospheric turbulence; the relationship between Δz and the number of phase screens and the transmission distance is: z=n z ×Δz (7) Among them, n z The number of random phase screens, z is the distance; the coherence length of the atmosphere is expressed as: Random phase screen refers to the situation in which the light wave passes through a medium with random phase distribution in the optical system, resulting in random changes in phase. to represent this random phase screen; the power spectrum of the phase screen Describes the distribution of phase changes in the frequency domain, specifically the Fourier transform of the phase function The square of the modulus: The atmospheric turbulence phase is inverted using the power spectrum inversion method. According to the inversion theorem, given the power spectrum, the spatial distribution of the phase screen can be obtained by inverse Fourier transform: in, represents the inverse Fourier transform, h(k x ,k y ) represents the generation of complex Gaussian random matrix, k x ,k y Represents the wave number on the x-axis and y-axis respectively, which is the standard normal distribution function in the frequency domain and is used to describe the frequency response of the system. is the square root of the phase structure function, which indicates the random nature of the phase. Since the phase is a real number, the real part of the inverse Fourier transform is taken to obtain the final random phase screen representation: According to the spatially continuous complex variable matrix sequence obtained in step (1), the temporal variation of atmospheric turbulence is described, and the temporal continuous atmospheric turbulence phase screen is obtained as follows: (3) Light field diffraction transmission simulation Consider the transmission principle of light beams in atmospheric turbulence channels: when studying the diffraction transmission of light beams, only the electric field component of the light wave field is taken and treated as a scalar; the diffraction integral formula is used to calculate the light field distribution at a straight-line distance in space; when discussing the case of non-infinite transmission, the Fresnel diffraction integral is used for calculation, and the Fresnel diffraction integral is: Among them, d is the distance from the origin to the observation point, λ is the wavelength, u and v represent the coordinate system, and combined with the theory of random phase shielding, the distribution of the light field after the light beam passes through the single-phase shielding is: Due to the correlation of time variation, the overall trend can be estimated from small-scale data. To make the algorithm simple and efficient, only one layer of phase screen is used here; (4) Visualize the results; Firstly, the random changes of light field intensity are simulated by complex matrix interpolation algorithm, and the temporal continuity of phase screen is reflected by random complex matrix according to the frozen flow hypothesis. Secondly, the atmospheric turbulence phase screen is generated by power spectrum inversion algorithm, and the light field diffraction simulation is carried out by Fresnel method. Finally, the result changes of different time steps are displayed by comparing the phase screen and power spectrum, so as to clearly present the continuous change process of light field intensity and phase screen.

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