A high-fidelity dynamic atmospheric-turbulence phase screen generation method

Abstract

The application discloses a high-fidelity dynamic atmospheric turbulence phase screen generation method, relates to the field of atmospheric optics, and particularly relates to a simulation method of an atmospheric turbulence phase screen. The core problem that full spatial frequency fidelity and calculation efficiency cannot be considered in the prior art dynamic atmospheric turbulence phase screen generation method is solved. The method comprises the following steps: constructing an atmospheric turbulence power spectrum model, wherein the power spectrum model adopts a modified von Karman power spectrum model; applying Karhunen-Loeve transformation to Zernike polynomials through a Zernike polynomial method, and combining a Taylor frozen flow hypothesis to generate a low-frequency phase screen; calculating a residual spectrum between the von Karman power spectrum model and the ensemble average power spectrum of the low-frequency phase screen, and synthesizing a high-frequency phase screen according to the residual spectrum; and linearly superimposing the low-frequency phase screen and the high-frequency phase screen in a spatial domain to obtain a high-fidelity dynamic atmospheric turbulence phase screen. The atmospheric turbulence phase screen can be directly used as the input of a spatial light modulator in a laboratory turbulence simulation setup.

Description

Technical Field

[0001] This invention relates to the field of atmospheric optics, and more specifically to a simulation method for an atmospheric turbulence phase screen. Background Technology

[0002] Atmospheric turbulence is a core factor limiting the performance of high-resolution astronomical imaging and free-space laser communication systems. The wavefront distortion it causes directly degrades image quality and communication reliability. Adaptive optics (AO) technology, through real-time detection and compensation of wavefront distortion, has become a core means of suppressing turbulence effects. However, turbulence experiments in real atmospheric environments are costly, time-consuming, and difficult to reproduce. Therefore, conducting related research based on laboratory-controlled turbulence simulation is a technical approach that is both economical and reproducible.

[0003] Current laboratory turbulence simulation research mostly employs physical simulation schemes, such as hot-plate turbulence cavities, hot-air optical turbulence generators, and natural water convection devices. However, these physical simulation methods have inherent limitations: on the one hand, they cannot accurately control the full-space frequency domain characteristics of turbulence; on the other hand, they are difficult to flexibly reproduce atmospheric turbulence conditions of different intensities and scenarios. In recent years, liquid crystal spatial light modulators (LC-SLMs), with their advantages of high refresh rate and high resolution, have provided a new technical path for the accurate reproduction of realistic atmospheric turbulence. The technique of constructing turbulence simulation units based on spatial light modulators is called the "phase screen method," in which the phase screen data loaded onto the modulator directly determines the realism and reliability of the turbulence simulation.

[0004] Numerical generation of phase screens is mainly based on statistical turbulence physics models. Currently, mainstream numerical generation methods for phase screens can be divided into two categories: one is based on Fourier transform, which can quickly generate the phase screen by performing a Fast Fourier Transform (FFT) on the turbulence power spectrum. However, this method suffers from the problem of missing low-frequency components, and can only be partially corrected through complex subharmonic compensation, with limited compensation effect; the other is the Zernike polynomial method, which uses orthogonal basis functions adapted to the wavefront description for modeling. This method has excellent low-frequency characteristics, but its efficiency is extremely low when modeling high-frequency components, requiring thousands of high-order terms to ensure accuracy, and the computational cost increases exponentially with the required accuracy.

[0005] Simulating the dynamic temporal evolution of turbulence further increases the technical difficulty, and existing dynamic modeling methods all have significant limitations: the infinitely long phase screen translation method based on FFT inevitably introduces spatial periodic artifacts; although the sparse spectrum sampling model can avoid the periodicity problem, the non-uniform sampling mechanism sacrifices the computational efficiency advantage of the FFT method; the fractal method relies on the Kolmogorov turbulence statistical model, which is prone to information loss during the phase screen generation process; although the coefficient evolution method based on the Zernike polynomial time spectrum has high accuracy, it requires a large number of high-order Zernike terms, resulting in huge computational overhead and making it difficult to support large-scale time series simulations.

[0006] Chinese patent document CN116011353A discloses a hybrid method for simulating atmospheric turbulence phase screens, which uses Zernike polynomials to generate the low-frequency component and power spectrum inversion to generate the high-frequency component, and then superimposes them. However, this method has the following shortcomings: First, the high-frequency component directly uses the power spectrum inversion result without high-pass filtering, resulting in overlap between the low-frequency and high-frequency bands, affecting the accuracy of power spectrum statistics; second, this method only generates a static phase screen, which cannot reflect the temporal evolution characteristics of atmospheric turbulence, making it difficult to meet the needs of dynamic simulation and data-driven algorithm training in adaptive optics systems; third, this method uses the Kolmogorov spectral model and does not consider the internal scale dissipation effect, resulting in limited accuracy in the high-frequency region. Summary of the Invention

[0007] This invention solves the core problem in existing methods for generating dynamic atmospheric turbulence phase screens that cannot simultaneously achieve both full-space frequency fidelity and computational efficiency.

[0008] The technical solution provided by this invention: Option 1: A method for generating a high-fidelity dynamic atmospheric turbulence phase screen, comprising the following steps: S1: Construct an atmospheric turbulence power spectrum model, which adopts a modified von Kármán power spectrum model; S2: Based on the aforementioned von Kármán power spectrum model, the Karhunen-Loève transform is applied to the Zernike polynomial using the Zernike polynomial method, and a low-frequency phase screen PS is generated by combining it with Taylor's frozen flow assumption. L ; S3: Calculate the von Kármán power spectrum model and the low-frequency phase screen PS. L The residual spectrum between the ensemble average power spectra is used to synthesize a high-frequency phase screen PS. H ; S4: The low-frequency phase screen PS L With the high-frequency phase screen PS HLinear superposition in the spatial domain yields a high-fidelity dynamic atmospheric turbulence phase screen (PS).

[0009] In a further preferred embodiment, the modified von Kármán power spectrum model in step S1 is: , Where k is the spatial frequency modulus, k0 is the cutoff spatial frequency determined by the outer scale L0, and km is the cutoff spatial frequency determined by the inner scale l0, k0 = 1 / L0, k m =5.92 / (2πl0), where L0 is the external scale of atmospheric turbulence, l0 is the internal scale of atmospheric turbulence, and r0 is the Fried parameter.

[0010] In a further preferred embodiment, in step S2, the polar coordinates of the Zernike polynomial are: , in, As the normalization factor, Let n be the radial function, n be the radial order, and m be the angular frequency. Let be the normalized radial coordinates, and 0 ≤ ≤1, Let be the azimuth angle, and 0 ≤ ≤2π; Normalization factor for: , Where, δ m0 For the Kronecker operator, and when m≠0, δ m0 =0; when m=0, δ m0 =1; The radial function is: , Where s is the summation index, This is a factorial operation.

[0011] In a further preferred embodiment, in step S2, the low-frequency phase screen PS L for: , In the formula, Z represents the polynomial Zernike. j The row vector formed; A t G is the time coefficient of the Zernike polynomial. a,i (t) forms a vector; K is a row vector formed by the Karhunen-Loève transformation, B t G is the time coefficient of the Karhunen-Loève transform. b,i(t) vector; j is the Zernike polynomial index, i is the Karhunen-Loève transformation index, t is time, and U is the transformation matrix.

[0012] In a further preferred embodiment, in step S3, the residual spectrum is: , In the formula, S(k,kc,Δk) is a smooth activation function centered at kc, and Δk is the transition band width. This is the ensemble average power spectrum.

[0013] In a further preferred embodiment, in step S3, the high-frequency phase screen PS H for: , Where ρ is the aperture. Let be the aperture mask function. For inverse Fourier transform, This represents the ensemble-average power spectral density. It is a Hermitian symmetric complex Gaussian random field.

[0014] In a further preferred embodiment, in step S4, the high-fidelity dynamic atmospheric turbulence phase screen PS is: .

[0015] Option 2: A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of any of the methods described in this invention.

[0016] Option 3: A computer-readable storage medium storing a computer program thereon, characterized in that the computer program, when executed by a processor, implements the steps of any of the methods described in this invention.

[0017] Option 4: A computer program product, comprising computer instructions, characterized in that, when executed by a processor, the computer instructions implement the steps of any of the methods described in this invention.

[0018] The present invention provides a high-fidelity dynamic atmospheric turbulence phase screen generation method that combines the Zernike polynomial method and FFT to generate a high-fidelity dynamic atmospheric turbulence phase screen PS with real time characteristics. This solves the core problem in existing dynamic atmospheric turbulence phase screen generation methods that cannot simultaneously achieve full-space frequency fidelity and computational efficiency.

[0019] The specific benefits compared to existing technologies are as follows: 1. This invention utilizes the Zernike polynomial method combined with Taylor's frozen flow hypothesis to generate a low-frequency phase screen PS. L , and the high-frequency phase screen PS synthesized based on the residual spectrum H Linear superposition in the spatial domain effectively overcomes the problems of low-frequency loss, anisotropic artifacts introduced by subharmonic compensation, and exponential growth of high-frequency modeling computation in the single FFT method, achieving a balance between high fidelity and high computational efficiency across the entire spatial frequency domain.

[0020] 2. This invention calculates the von Kármán power spectrum model and the low-frequency phase screen PS. L The residual spectrum between the ensemble average power spectrum and the low-frequency components are suppressed by a smooth activation function, and the high-frequency contribution is gradually activated in the transition band. At the same time, the negative values ​​are clipped to zero, avoiding the energy duplication or loss caused by frequency band overlap, so that the two-dimensional power spectrum of the hybrid phase screen is consistent with the theoretical model in the transition region from low frequency to high frequency.

[0021] 3. Compared to the traditional Zernike polynomial method, which requires thousands of terms to approximate high-frequency components, this invention synthesizes high-frequency phase screens (PS) using residual spectra. H It requires only a few orders to make the structure function closely match the theoretical curve, which greatly reduces the computational overhead in dynamic simulation and facilitates engineering deployment and long-term sequence generation.

[0022] The atmospheric turbulence phase screen generated by this invention can be directly used as the input of a spatial light modulator in a laboratory turbulence simulation setup. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating a method for generating a high-fidelity dynamic atmospheric turbulence phase screen.

[0024] Figure 2 This is a dynamic atmospheric turbulence phase screen under different turbulence intensities.

[0025] Figure 3 Two-dimensional power spectra of phase screens generated using different methods are given, where (a) is the theoretical value of the two-dimensional power spectrum of the phase screen, (b) is the two-dimensional power spectrum of the phase screen generated using the FFT+subharmonic compensation method, (c) is the two-dimensional power spectrum of the phase screen generated using the Zernike method, and (d) is the two-dimensional power spectrum of the phase screen generated using a hybrid method.

[0026] Figure 4 This is a schematic diagram of the phase screen structure function curve for the hybrid method.

[0027] Figure 5The diagram shows the energy envelope distribution of a low-order Zernike polynomial. (a) is the first peak estimate, and (b) is the peak estimate with cutoff frequency. k c A filter centered on [the target element].

[0028] Figure 6 This is a schematic diagram illustrating the principle of the phase screen method.

[0029] Figure 7 This is a schematic diagram of the intensity distribution of different components of the PS (photometer) in a high-fidelity dynamic atmospheric turbulence phase screen. Detailed Implementation

[0030] To facilitate understanding of the technical solutions claimed in this invention, the following specific embodiments are provided in conjunction with the accompanying drawings. These embodiments are merely used to explain the technical principles of the embodiments of this application and are not intended to limit the scope of protection of this application. Those skilled in the art can make reasonable adjustments to the embodiments given in the following specific embodiments based on their general knowledge in the art to adapt to specific application scenarios. It should also be noted that, for ease of description, only the parts related to this invention are shown in the accompanying drawings, not the entire structure.

[0031] Implementation Method 1, see [link] Figure 1 This embodiment describes a method for generating a high-fidelity dynamic atmospheric turbulence phase screen, which includes the following steps: S1: Construct an atmospheric turbulence power spectrum model, which adopts a modified von Kármán power spectrum model; S2: Based on the aforementioned von Kármán power spectrum model, the Karhunen-Loève transform is applied to the Zernike polynomial using the Zernike polynomial method, and a low-frequency phase screen PS is generated by combining it with Taylor's frozen flow assumption. L ; S3: Calculate the von Kármán power spectrum model and the low-frequency phase screen PS. L The residual spectrum between the ensemble average power spectra is used to synthesize a high-frequency phase screen PS. H ; S4: The low-frequency phase screen PS L With the high-frequency phase screen PS H Linear superposition in the spatial domain yields a high-fidelity dynamic atmospheric turbulence phase screen (PS).

[0032] In this embodiment, the modified von Kármán power spectrum model in step S1 is: , Where k is the spatial frequency modulus, k0 is the cutoff spatial frequency determined by the outer scale L0, and km is the cutoff spatial frequency determined by the inner scale l0, k0 = 1 / L0, k m =5.92 / (2πl0), where L0 is the outer scale of atmospheric turbulence, l0 is the inner scale of atmospheric turbulence, and r0 is the Fried parameter, used to characterize the equivalent turbulence intensity along the propagation path.

[0033] For plane wave propagation, r0 can be expressed as: , In the formula, λ is the wavelength of light; Cn 2 denoted by , where is the refractive index structure constant; L is the propagation distance. The refractive index structure constant Cn 2 The intensity of refractive index fluctuations in a turbulent medium is characterized, but it is usually difficult to measure directly in real-world scenarios. Therefore, this implementation uses the Fried parameter r0 to characterize the turbulence intensity along the propagation path.

[0034] For low-frequency phase screen PS L Based on the preset radial order n of the Zernike polynomial, a corresponding low-order Zernike polynomial Z is selected within the unit circular aperture. j Since the Zernike polynomial is defined on the unit circle, describing it in polar coordinates will yield the product of the radial and angular functions.

[0035] In this embodiment, the polar coordinates of the Zernike polynomial in step S2 are: , in, As the normalization factor, Let n be the radial function, n be the radial order, m be the angular frequency, ρ be the normalized radial coordinate, and 0 ≤ ρ ≤ 1, and θ be the azimuth angle, and 0 ≤ θ ≤ 2π. Normalization factor for: , Where, δ m0 For the Kronecker operator, and when m≠0, δ m0 =0; when m=0, δ m0 =1; The radial function is: , Where s is the summation index, This is a factorial operation.

[0036] For low-frequency phase screen PS LThe Zernike polynomial method can be used to characterize the low-frequency component of a high-fidelity dynamic atmospheric turbulence phase screen (PS). It can be expressed in two ways: first, by multiplying the coefficients of a statistically correlated stochastic Zernike polynomial with the corresponding Zernike polynomial; second, by converting the Zernike polynomial mode into a Karhunen-Loève function mode through the Karhunen-Loève transform and multiplying it with statistically independent stochastic Karhunen-Loève transform coefficients.

[0037] In this embodiment, in step S2, the low-frequency phase screen PS L for: , In the formula, Z represents the component Znike polynomial. j The row vector formed; A t G is the time coefficient of the Zernike polynomial. a,i (t) forms a vector; K is a row vector formed by the Karhunen-Loève transformation, B t G is the time coefficient of the Karhunen-Loève transform. b,i (t) vector; j is the Zernike polynomial index, i is the Karhunen-Loève transformation index, t is time, and U is the transformation matrix.

[0038] The transformation matrix U is obtained by performing Cholesky decomposition on the covariance matrix C of the Zernike polynomial coefficients, such that C = UU. T G a,j (t) represents the time-evolutionary random function corresponding to the coefficients aj of the j-th Zernike polynomial, with a mean of zero and a variance determined by the statistical energy of the corresponding mode. Its time statistical characteristics are given by the time power spectrum w. a,j (ν) Description. Based on Taylor's freezing flow assumption, under plane wave propagation conditions, if the wind direction is assumed to be along the x-axis, then the time power spectrum w a,j (ν) can be represented as: , Where v represents the time frequency relative to the time variable t, with units of s⁻¹. Under the von Kármán power spectral model... for: , In the formula, The two-dimensional Fourier transform of an orthogonal Zernike polynomial defined on the unit circle is expressed as: , In the formula, Jn+1(·) is the first-order Bessel function of order n+1.

[0039] To generate the time-dependent coefficient sequence Ga,j(t), phase-independent and uniformly distributed complex random samples with unit amplitudes in the [0, 2π) domain are generated and weighted by the square root of the von Kármán power spectral density; subsequently, they are transformed to the time domain using an inverse Fourier transform. The resulting initial independent random sequence is used as the Karhunen-Loève transform coefficient sequence and further normalized to:

[0040] Normalized sequence G b,i (t) has zero mean and unit variance, and is used to represent the time correlation coefficient of the i-th KL pattern. Its covariance can be expressed as: , It should be noted that finite-order Zernike polynomials are not ideal low-pass basis functions in the spatial frequency domain; their spectrum still contains certain high-frequency sidelobes. Therefore, if the low-frequency phase screen PS is directly applied... L With high-frequency phase screen PS after high-pass filtering H Superposition can easily lead to energy repetition or energy loss in the transition frequency band. To improve the spectral consistency of the high-fidelity dynamic atmospheric turbulence phase screen PS, this implementation is based on the von Kármán power spectrum model and the low-frequency phase screen PS. L The residual spectrum between the ensemble average power spectra is synthesized based on the high-frequency phase screen PS after high-pass filtering. H Low-frequency phase screen PS L The ensemble average power spectrum is estimated as follows: , In this embodiment, the residual spectrum is: , In the formula, S(k,kc,Δk) is a smooth activation function centered at kc, and Δk is the transition band width. This function is used in high-frequency phase screen PS H Suppressing low-frequency phase screen PS during generation L The low-frequency components are already included, and the FFT-based residual contribution is gradually activated within the crossband. Before random spectrum synthesis, negative values ​​in the residual spectrum are pruned to zero to ensure the non-negativity of the ensemble average power spectrum.

[0041] To synthesize the residual spectral components, a Hermitian-symmetric complex Gaussian random field h(k) with zero mean and one variance is generated on a discrete spatial frequency grid. Hermitian symmetry is used to guarantee the high-frequency phase screen PS obtained after the inverse Fourier transform.H The value is real. Then, h(k) is weighted by the square root of the ensemble average power spectral density and subjected to inverse FFT to obtain the high-frequency phase screen PS. H .

[0042] In this embodiment, in step S3, the high-frequency phase screen PS H for: , Where ρ is the aperture. Let be the aperture mask function. For inverse Fourier transform, This represents the ensemble-average power spectral density. It is a Hermitian symmetric complex Gaussian random field.

[0043] The high-frequency phase screen PS is obtained by clipping along a predefined path using the aperture mask function W(ρ,t). H The preset path center coordinates can be defined as c(x) t ,y t ): , Where V is the wind speed vector, f s To correspond to the sampling frequency, the smallest unit that moves within the preset path is =D / N, where D is the actual size of the corresponding aperture and N represents the grid resolution.

[0044] The cutoff frequency in this embodiment is explained below. The method for determining the low-frequency phase screen PS. L The energy envelope at different spatial frequencies can be expressed as: , As the radial order n increases, J n+1 (·) main response area and I n The dominant energy distribution of (k) gradually shifts towards higher spatial frequencies. Due to the sidelobes in the spectrum of the Zernike polynomial, the first major low-frequency peak is only used to establish an approximate correspondence between the mode order and spatial frequency, and is not suitable as a strict spectral separation boundary. Let x = 2πRk, then the nominal cutoff frequency can be expressed as: , As can be seen from the energy envelope of the low-order Zernike polynomial, the first response peak gradually shifts to higher spatial frequencies as n increases, indicating that higher-order Zernike polynomials can represent finer phase structures. See also Figure 5 For example, when n=10, the nominal cutoff frequency k can be obtained. c =3.98m-1 In the process of residual spectrum synthesis, k c The center position of the finite transition band is defined by Δk, which controls the width of the transition band, ensuring that the residual spectrum is smoothly activated within the transition frequency band, rather than at k. c A sudden change occurs at this point. By statistically subtracting the energy of low-order modes before FFT synthesis, the energy repetition caused by frequency band overlap can be reduced, and the consistency between the power spectrum of the mixed phase screen and the target power spectrum can be improved.

[0045] Due to high frequency phase screen PS H With low-frequency phase screen PS L All are generated based on the same von Kármán power spectrum model to ensure the continuity of statistical characteristics across the entire frequency band. Therefore, a linear superposition method is used to construct a hybrid phase screen. Finally, the complete PS is obtained by linearly superimposing the corresponding PSL and PSH components frame by frame. .

[0046] Implementation Method 2, see below Figure 3 , Figure 4 and Figure 5 This embodiment will be explained in detail. This embodiment is a result analysis of the high-fidelity dynamic atmospheric turbulence phase screen generation method described in Embodiment 1.

[0047] For the entire propagation path L, the atmospheric coherence length r0 is the Friedel-Crafts constant used to characterize vision, and its magnitude directly determines the resolution of the optical system. r0 can be expressed as: , When the propagation distance L is set to 2 km, and the simulation parameters are: λ = 1064 nm, L0 = 100 m, l0 = 0.01 m, Nx × Ny = 512 × 512, D = 1 m, n = 10, the dynamic atmospheric turbulence phase results for different turbulence intensities are obtained by calculating using the above formula. Figure 2 Figures (a1), (b1), and (c1) show the three-dimensional PS distributions for r0=0.01, r0=0.05, and r0=0.1, respectively. Under different turbulence intensities, the phase screen generated by the hybrid method not only retains the smooth global variation characteristics of the low-frequency components captured by the Zernike polynomial method, but also retains the typical local detail fluctuations of the high-frequency components provided by the FFT-based method. Figure 2 Figures (a2), (b2), and (c2) show the time evolution of the phase screen under different turbulence intensities, f s =50Hz, Δt=0.1s, displayed every five frames. Clearly, the amplitude of the phase fluctuation is inversely proportional to r0. These results confirm that the mixing method effectively reproduces the time-varying characteristics of atmospheric turbulence within the turbulence intensity range.

[0048] To evaluate the power spectrum characteristics of phase screens generated by different methods, simulation parameters were used: r0=0.1, λ=1064nm, L0=100m, l0=0.01m, L=2km, Nx×Ny=512×512. Four methods (theoretical value, FFT+subharmonic compensation method, Zernike method and hybrid method) were used to generate the Fourier transform of random phase screens to obtain two-dimensional power spectra.

[0049] like Figure 3 (a) shows the theoretical value, and the theoretical power spectrum exhibits symmetry and uniformity.

[0050] Figure 3 (b) shows the two-dimensional power spectrum of the phase screen generated using the FFT + subharmonic compensation method. Since the traditional FFT method suffers from insufficient low-frequency response, this is usually mitigated by subharmonic compensation. Therefore, the FFT method combined with subharmonic compensation is used to obtain the power spectrum of the phase screen. Figure 3 (b) It can be determined that the low-frequency energy after subharmonic compensation is close to the theoretical value. However, there are obvious cross-shaped creases along the axes in the power spectrum. This is because the grid sampling of the low-frequency part of the power spectrum is not isotropic during the subharmonic compensation process. Specifically, the sampling intervals along the x and y axes are the smallest.

[0051] Figure 3 (b) shows the two-dimensional power spectrum of the phase screen generated using the Zernike method. In contrast, when using the Zernike mode expansion alone, as... Figure 3 As shown in (c), the low-frequency region matches the theoretical value. However, due to the limited ability of low-order Zernike basis functions to represent high-frequency details, the typical value for the high-frequency portion is approximately 10. -4 ,and Figure 3 The value of (a) is approximately 10. Although increasing the number of Zernike terms can alleviate this high-frequency deficiency, the computational cost of dynamic phase screen simulation becomes quite high. The power spectrum produced by the hybrid phase screen is as follows: Figure 3 As shown in (d), it maintains symmetry, and although the high-frequency regions overlap due to the superposition of phase screens at the corners, the overall transition from high to low frequencies is consistent. The transition region from low to high frequencies is consistent with the theoretical value. This indicates that the hybrid method effectively compensates for the limitations of the two methods and significantly improves the statistical fidelity of the simulated phase screen.

[0052] Figure 3(d) shows the two-dimensional power spectrum of the phase screen generated using the hybrid method (the method described in this invention). Based on this figure, it can be determined that the phase screen generated by the Zernike polynomial still carries a small amount of high-frequency information. In the hybrid method, this high-frequency information is superimposed with the PSH. Since the high-frequency components of the FFT method in the PSH far exceed those of the Zernike method, the latter's contribution to the statistical properties of the final phase screen is negligible. To quantitatively evaluate the accuracy of the phase screen generated by the hybrid method, we introduce the wavefront structure function (WSF) as a key indicator describing the spatial statistical properties of the phase screen, defined as follows: , in, This represents the ensemble average.

[0053] The theoretical expression for WSF is given by the following formula: , in, It is a modified Bessel function of the second kind. It is the Gamma function.

[0054] Since the relative error of the structure function is a function of the spatial interval r, directly using the error of local feature points as the evaluation function cannot fully reflect the overall accuracy of the model. Therefore, this study uses uniform sampling to calculate the average relative error of each point, which is defined as a quantitative evaluation standard for model accuracy. , See Figure 4 The following is a diagram. Figure 3 The calculation results of the hybrid method are shown under the same simulation parameters. When n=5, the low-frequency components are significantly insufficient, resulting in poor consistency with the theoretical curve. This is because the low-frequency part consists only of PSL, so it is necessary to ensure that the structure function of the PSL generated by the Zernike method is consistent with the theoretical value in the low-frequency part. When n≥10, the low-frequency and high-frequency parts can approach the theoretical curve. When n=10, the full-frequency error value is only 2.08% according to the quantitative evaluation standard formula for model accuracy. As the Zernike order increases, the hybrid method can continuously optimize the modeling accuracy. Although the implementation of a low-order hybrid framework may lead to insufficient low-frequency components, the hybrid method has significant advantages because it requires only a fewer Zernike order to achieve high-precision phase screen simulation compared to traditional methods.

[0055] In practical applications, high-fidelity PS is used to simulate the effect of atmospheric turbulence on beam propagation. For example... Figure 6The diagram shows the principle of the phase screen method, which uses a single phase screen (PS) to model the cumulative atmospheric turbulence disturbance along the propagation path. After passing through the initial point of the single-layer phase screen (the location of the incident light spot in the figure), the plane wave undergoes wavefront degradation, resulting in a significant difference between the incident and outgoing light spots.

[0056] In practical applications, numerically generated PS often exhibits a performance far exceeding the maximum phase modulation range of the phase modulation device. To address this full-scale mismatch, continuous phase values ​​are first constrained within the (0, 2π) interval using a 2π phase envelope. These enclosed phases are then linearly mapped to an 8-bit grayscale range

[0255] to generate a phase bitmap compatible with SLM. Figure 7 The image shows the result of light waves passing through a phase screen with simulated parameters λ=1064nm, L0=100m, l0=0.01m, Nx×Ny=512×512, D=1m, n=10, r0=0.05m. Specifically, Figure 7 In (b), the low-frequency components primarily induce a time-series shift in the centroid of the continuous beam, while maintaining a relatively compact original spot profile. In contrast, Figure 7 The high-frequency residual components in (c) cause significant beam spread and severe speckle debris in each frame, while exhibiting minimal centroid drift over time. Figure 7 The mixing method shown in (a) combines low-frequency components and high-frequency residual components in the time series; therefore, the original spot simultaneously exhibits centroid drift across consecutive frames and spot fragmentation within each individual frame.

[0057] This invention proposes a novel simulation method for dynamic atmospheric turbulence phase screens (PS). This method combines the low-frequency components of the Zernike polynomial method with the high-frequency components of the FFT method, while simultaneously removing the low-frequency components of the FFT using a high-pass filter. Results show that the wavefront structure function of the PS simulated by this hybrid method is in high agreement with the von Kármán theoretical model. Furthermore, compared to the traditional Zernike method, it requires only a small number of Zernike orders to achieve high-precision phase screen simulation, thus improving computational efficiency. The dynamic atmospheric turbulence phase screen PS generated by this method can provide large-scale continuous time-series phase screen data for training data-driven adaptive optics algorithms.

Claims

1. A method for generating a high-fidelity dynamic atmospheric turbulence phase screen, characterized in that, Includes the following steps: S1: Construct an atmospheric turbulence power spectrum model, which adopts a modified von Kármán power spectrum model; S2: Based on the aforementioned von Kármán power spectrum model, the Karhunen-Loève transform is applied to the Zernike polynomial using the Zernike polynomial method, and a low-frequency phase screen PS is generated by combining it with Taylor's frozen flow assumption. L ; S3: Calculate the von Kármán power spectrum model and the low-frequency phase screen PS. L The residual spectrum between the ensemble average power spectra is used to synthesize a high-frequency phase screen PS. H ; S4: The low-frequency phase screen PS L With the high-frequency phase screen PS H Linear superposition in the spatial domain yields a high-fidelity dynamic atmospheric turbulence phase screen (PS). In step S2, the polar coordinates of the Zernike polynomial are: ， in, As the normalization factor, Let n be the radial function, n be the radial order, and m be the angular frequency. Let be the normalized radial coordinates, and 0 ≤ ≤1, Let be the azimuth angle, and 0 ≤ ≤2π; Normalization factor for: ， Where, δ m0 For the Kronecker operator, and when m≠0, δ m0 =0; when m=0, δ m0 =1; The radial function is: ， Where s is the summation index, For factorial operation; In step S2, the low-frequency phase screen PS L for: ， In the formula, Z represents the polynomial Zernike. j The row vector formed; A t G is the time coefficient of the Zernike polynomial. a,i (t) forms a vector; K is a row vector formed by the Karhunen-Loève transformation, B t G is the time coefficient of the Karhunen-Loève transform. b,i (t) vector; j is the Zernike polynomial index, i is the Karhunen-Loève transformation index, t is time, and U is the transformation matrix; In step S3, the residual spectrum is: ， In the formula, S(k,kc,Δk) is a smooth activation function centered at kc, and Δk is the transition band width. The spectrum is the ensemble average power spectrum, and kc is the nominal cutoff frequency. For the modified von Kármán power spectrum model; In step S3, the high-frequency phase screen PS H for: ， Where ρ is the aperture. For the aperture mask function, This is the inverse Fourier transform. This represents the ensemble average power spectral density. It is a Hermitian symmetric complex Gaussian random field.

2. The method for generating a high-fidelity dynamic atmospheric turbulence phase screen according to claim 1, characterized in that, In step S1, the modified von Kármán power spectrum model is as follows: ， Where k is the spatial frequency modulus, k0 is the cutoff spatial frequency determined by the outer scale L0, and km is the cutoff spatial frequency determined by the inner scale l0, k0 = 1 / L0, k m =5.92 / (2πl0), where L0 is the external scale of atmospheric turbulence, l0 is the internal scale of atmospheric turbulence, and r0 is the Fried parameter.

3. The method for generating a high-fidelity dynamic atmospheric turbulence phase screen according to claim 1, characterized in that, In step S4, the high-fidelity dynamic atmospheric turbulence phase screen PS is: 。 4. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes a computer program to implement the steps of the method according to any one of claims 1-3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-3.

6. A computer program product comprising computer instructions, characterized in that, When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1-3.

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