A method for generating a turbulent phase screen based on a hybrid profile and simulating image degradation

Abstract

The application discloses a method for generating a turbulent phase screen and simulating image degradation based on a mixed spectrum, comprising the following steps: constructing a mixed spectrum adaptive to weak-strong turbulent conditions; the mixed spectrum fuses the advantages of a classical Kolmogorov spectrum and a non-Kolmogorov spectrum, reflects large-scale turbulent structure in a low-frequency band, and retains small-scale disturbance characteristics in a high-frequency band; a low-frequency structure function in a generated phase screen is compensated through an 8-order Zernike polynomial, and a high-precision phase screen is generated; the compensated high-precision phase screen is taken as an input parameter, a corresponding point spread function (PSF) is calculated by using a Fresnel diffraction propagation model, and the PSF is applied to convolution operation of an ideal image, so that a real reproduction of a turbulent degradation effect is realized. According to the application, the simulation result of the turbulent degradation image under different turbulent conditions is significantly better than a single-spectrum baseline, and the image degradation process in an actual atmospheric turbulent environment can be better simulated.

Description

Technical Field

[0001] This invention relates to the technical field of optical imaging and atmospheric turbulence simulation, and particularly to a method for generating turbulent phase screens and simulating image degradation based on mixed spectral types. Background Technology

[0002] Atmospheric turbulence, a common random flow phenomenon in the near-surface layer, is dominated by refractive index fluctuations induced by temperature gradients and surface thermal convection, leading to wavefront distortion, spatial coherence degradation, and anomalous energy distribution in light wave propagation. This effect is particularly pronounced in astronomical observation, military reconnaissance, and free-space optical communication, often causing image geometric distortion, loss of high-frequency details, and contrast degradation, resulting in a 30%-70% reduction in resolution and severely limiting target identification and signal transmission reliability. To characterize turbulence intensity, the atmospheric refractive index structure constant C_n is used. 2 The coherence length r0 of Fried is widely used, but obtaining real-time profile data remains challenging.

[0003] In existing technologies, early turbulence simulations relied on single-spectral phase screens, such as the Kolmogorov spectrum (suitable for isotropic weak turbulence) or the Von Karman spectrum (introducing internal and external scale corrections). However, these methods suffer from energy loss in low-frequency large-scale structures and poor high-frequency realism under strong turbulence, failing to capture fractal nonlinear effects. In recent years, Zernike polynomial expansions have been used for low-order aberration compensation, such as the Noll-Tokovinin relation quantifying mode variance, but higher orders are prone to introducing overfitting noise. Some studies have attempted hybrid models, such as Bachmann's "Hybrid Phase Screen" empirical stitching or Wu's team's multivariate optical field transmission framework, which have improved the accuracy of weak turbulence simulations, but lack a unified intensity partitioning index, and the switching threshold is subjective, resulting in poor generalization across intensity levels. Furthermore, image degradation assessments are mostly limited to MSE / PSNR, neglecting structural fidelity. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types. This method addresses the problems of existing turbulent phase screen generation methods being limited to a single spectral type, leading to low-frequency / high-frequency distortion and an inability to accurately simulate the full-spectrum degradation mechanism of weak-to-strong turbulence; and the limitations of existing image evaluation metrics, which make it difficult to quantify detail preservation and information attenuation, thus hindering optical system design and restoration algorithm development. The invention also proposes for the first time a method using J = L is a tanh-weighted hybrid spectral type with a single index, achieving continuous adaptive spectral type; combined with 8th-order Zernike compensation to solve low-frequency defects, it provides high-fidelity simulation across the entire intensity range (r0=0.01-1.5 m); compared with existing methods, it has smaller relative error, improved computational efficiency, fills the simulation gap in turbulence mechanism analysis, and has significant industrial applicability. To achieve the above-mentioned objectives and other advantages of this invention, a method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types is provided, comprising: Using the turbulence intensity index J as the sole partitioning threshold, adaptive continuous switching between Kolmogorov, Von Karman, and fractal power spectra is achieved. An 8th-order Zernike polynomial is introduced to compensate for the low-frequency structure function, generating a high-precision phase screen. The point spread function (PSF) is calculated using Fresnel propagation to simulate turbulence degradation. Fresnel propagation is used to calculate the PSF, achieving I... deg =I clear *PSF convolution supports full-spectrum simulation with r0=0.01-1.5 m. Based on the changing characteristics of actual atmospheric turbulence environments, a hybrid spectral model expression is constructed that can adaptively match the range from weak to strong turbulence. This hybrid spectral model combines the advantages of classical Kolmogorov and non-Kolmogorov spectra, reflecting large-scale turbulence structures in the low-frequency range and preserving small-scale perturbation features in the high-frequency range, thereby improving the model's versatility and accuracy under different turbulence intensities.

[0005] Preferably, it is proposed for the first time that J = L is a tanh-weighted hybrid spectrum with a single index, achieving continuous adaptive spectrum; combined with 8th-order Zernike compensation to solve low-frequency defects, it provides high-fidelity simulation across the entire intensity range (r0=0.01-1.5 m); compared with existing methods, it has smaller relative error and improved computational efficiency, filling the simulation gap in turbulence mechanism analysis and has significant industrial applicability.

[0006] Preferably, the low-frequency components in the generated phase screen are compensated by structure function using an 8th-order Zernike polynomial. This effectively suppresses low-frequency distortion caused by finite sampling or truncation errors, enhances the spatial continuity and statistical stability of the phase screen, and provides a basic guarantee for the subsequent generation of high-quality degraded images.

[0007] Preferably, the mixed spectral weights threshold , To ensure continuous switching.

[0008] Preferably, the Zernike compensation coefficient Following the Noll-Tokovinin relationship The size of the phase screen is D=3m.

[0009] This invention is particularly suitable for quantifying the degradation effects of weak to strong turbulence on optical systems, providing a full-link solution from phase perturbation modeling to degradation assessment, applicable to complex environments such as remote imaging, satellite communication, and UAV monitoring.

[0010] Preferably, the image degradation simulation employs block convolution technology, and the specific steps include: Input image I clear Divide into blocks of w=256 pixels; Execute I independently for each block clear *PSF convolution operation; Spatial correlation of atmospheric turbulence was simulated by multi-screen overlay (Δz=100 m); The SSIM structural similarity, PSNR peak signal-to-noise ratio, and MSE mean square error of the degraded images were evaluated to ensure that the relative error was <2% in order to verify the simulation accuracy.

[0011] Preferably, the hybrid spectrum is specifically defined by using the turbulence intensity index J as the unique partition threshold to achieve adaptive continuous switching between Kolmogorov, Von Karman, and fractal power spectra.

[0012] Compared with the prior art, the advantages and positive effects of the present invention are: (1) Improved accuracy: The relative error between the simulated and real turbulent SSIM / PSNR / MSE is smaller, which is better than the single-spectrum model. (2) Full spectrum coverage: r0=0.01-1.5 m adaptive, and the low-frequency structure function matches the theoretical value. (3) Application expansion: Quantization of D / L / Cn 2 / r0 has an impact and supports the training of the recovery algorithm. Attached Figure Description

[0013] Figure 1 This is a schematic diagram illustrating optical transmission under simulated atmospheric turbulence conditions using the method for generating turbulent phase screens and simulating image degradation based on mixed spectral types according to the present invention. Figure 2 The figures show the phases of the mixed-spectrum turbulence model under three turbulence intensities according to the method of generating a turbulent phase screen and simulating image degradation based on mixed-spectrum turbulence according to the present invention: (A) r0 = 1.5m (B) r0 = 0.15m (C) r0 = 0.01m. Figure 3Figure 1 shows the Zernike polynomial low-frequency compensated phase screen under three turbulence intensities according to the method of generating and simulating image degradation of turbulent phase screen based on mixed spectrum according to the present invention: (A) r0 = 1.5 m (B) r0 = 0.15 m (C) r0 = 0.01 m. Figure 4 The figures show Zernike polynomial low-frequency compensated phase screens with different phase screen spacings under moderate turbulence according to the method of generating turbulent phase screens based on mixed spectrum and simulating image degradation according to the present invention: (A) Δz = 50 m (B) Δz = 100 m (C) Δz = 200 m. Figure 5 The following diagrams illustrate the method for generating and simulating image degradation of turbulent phase screens based on mixed-spectrum turbulence according to the present invention: (A) Phase screen of low-frequency compensated mixed-spectrum turbulence models of different orders with moderate turbulence intensity; (B) Mixed-spectrum turbulence model; (C) 8th-order Zernike polynomial; and (D) 38th-order Zernike polynomial diagram. Figure 6 The image shows the phase structure function of the hybrid spectral model after Zernike polynomial low-frequency compensation, based on the method for generating turbulent phase screens and simulating image degradation according to the present invention. Figure 7 This is a comparison chart of real turbulence images and simulated turbulence images based on the method of generating turbulence phase screens and simulating image degradation according to the present invention; Figure 8 The figures show simulation results of different phase screen sizes for the method of generating turbulent phase screens and simulating image degradation based on mixed spectral types according to the present invention. Figure 9 The figures show simulation results for different propagation distances of the method for generating turbulent phase screens and simulating image degradation based on mixed spectral types according to the present invention. Figure 10 The figure shows the simulation results of different turbulent refractive index structure constants of the method for generating turbulent phase screens and simulating image degradation based on mixed spectra according to the present invention. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] Reference Figure 1 A method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types includes: Example 1: Generation of Hybrid Spectral Phase Screens and Zernike Compensation As shown in Table 1, the wavelength λ = 0.532 μm, propagation distance z = 1000 m, grid N = 1000 × 1000 (Δx = 3 mm), and internal scale were selected. =0.01 m, external dimensions =1 m. Intensity threshold. (Weak-Medium Switching) Smoothing factor α = 4. Generation process: Calculate Determine the weights , , Power spectrum inversion ; 8th-order Zernike expansion Synthetic φ total The result is as follows Figure 2 The simulation results show phase screens with intensities of r0 = 1.5, 0, 15, and 0.01 m. As can be seen from the figures, with the decrease of the atmospheric coherence length r0 (i.e., the increase of turbulence intensity), the phase fluctuations of the phase screens significantly increase, the high-frequency spot density increases significantly, and the wavefront undulations become larger. Especially when r0 = 0.01 m, the turbulence intensity is high, and the phase fluctuations are particularly pronounced. When using Zernike polynomials for low-frequency compensation, the simulation parameters are the same as the mixed spectral model, but an 8th-order Zernike polynomial is used in the compensation process. The simulation results are shown in Figure 3. After Zernike polynomial compensation, the phase screens exhibit smoother fluctuations. By adjusting the phase screen spacing to 50 m, 100 m, and 200 m, we simulated the low-frequency compensation effect of Zernike polynomials at different spacings. The simulation results are shown in Figure 4. At Δz = 50 m, the multi-screen superposition is smoother, and the proportion of low frequencies is higher. As the spacing between the phase screens increases, the phase ripple of the phase screens gradually intensifies. At Δz = 200, high-frequency energy is slightly aliased, indicating that the spacing between the phase screens has a significant impact on the phase ripple. The changes in the phase screens were observed by increasing the order of the Zernike polynomial from 8th to 38th. The simulation results are shown in Figure 5. The 8th-order Zernike polynomial provides smooth and rich low-frequency components, while higher-order Zernike polynomials, although enhancing high-frequency components, result in less smooth phase ripple.

[0016] Example 2: Image Degradation Simulation and Parameter Analysis Input clear image I clear (512×512, grayscale [0,255]), PSF calculation: Degeneration .

[0017] A hybrid model was used to simulate atmospheric turbulence degradation images. The parameters were set as follows: phase screen length and width 3m, transmission distance 1000m, phase screen spacing Δz = 100m, and atmospheric coherence length r0 = 0.15. The simulation results were compared with real turbulence, and the results are as follows. Figure 7 As shown, it can be seen that the degraded image affected by the mixed spectral turbulence is very close to the degraded image acquired from real turbulence.

[0018] For the phase screen size D, propagation distance L, atmospheric coherence length r0, and refractive index structure constant Different values ​​of the parameters were used to simulate atmospheric turbulence degradation using a hybrid spectral turbulence degradation model, and the results were compared to analyze the impact of parameter changes on imaging quality, so as to more accurately predict atmospheric turbulence degradation images under different conditions.

[0019] 1) The simulation results when the transmission distance L=1000m, r0=0.15, and D takes values ​​of 1, 2, and 3m are as follows: Figure 8 As shown. From Figure 8 It is clearly visible that as the size of the phase screen increases, the image distortion becomes more severe, and the loss of detail becomes significant. Especially with larger phase screens, the image geometry becomes distorted, and details are almost unrecognizable. This indicates that as the phase screen size increases, the effect of turbulence on the beam intensifies, leading to a significant deterioration in image quality.

[0020] 2) When D=1, r0=0.15, the transmission distance L is changed to 1000, 2000, and 3000 m. The simulated images of turbulence degradation at different propagation distances are as follows: Figure 9 As shown, image distortion gradually worsens with increasing propagation distance. This is because the probability of light refraction and scattering increases with the propagation distance, leading to a greater degree of turbulence affecting the imaging system. The image geometry becomes more blurred, and the loss of detail is more severe.

[0021] 3) When D=1 and L=1000 m, change the turbulent refractive index structure constant. Structure constants with different refractive indices =9.47×10 -17 4.40×10 -15 4.02×10 -13 The simulation results of turbulent degradation are as follows Figure 10 As shown, the turbulent refractive structure constant can be seen. As the refractive index structure constant increases, the image quality deteriorates significantly, especially under strong turbulent conditions (when the refractive index structure constant is large), where the loss of image geometry and detail becomes more severe. This indicates that the intensity of turbulence directly affects the degree of image degradation, and an increase in the refractive index structure constant leads to a significant reduction in image distortion and contrast.

[0022] Table 1 Parameter Settings

[0023] The number of devices and processing scale described herein are for simplification purposes. Applications, modifications, and variations of this invention will be readily apparent to those skilled in the art. Although embodiments of the invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for this invention, and further modifications can be readily implemented by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, this invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types, characterized in that, Includes the following steps: A hybrid spectrum model is constructed to adapt to weak-strong turbulence conditions. The hybrid spectrum model combines the advantages of classical Kolmogorov spectrum and non-Kolmogorov spectrum, reflecting large-scale turbulence structure in the low-frequency range and retaining small-scale perturbation characteristics in the high-frequency range. A high-precision phase screen is generated by compensating the low-frequency structure function in the generated phase screen using an 8th-order Zernike polynomial. Using the compensated high-precision phase screen as input parameters, the Fresnel diffraction propagation model is used to calculate its corresponding point spread function (PSF), which is then applied to the convolution operation of the ideal image to achieve a realistic reproduction of the turbulence degradation effect.

2. The method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types as described in claim 1, characterized in that, The hybrid spectrum specifically uses the turbulence intensity index J as the unique partition threshold to achieve adaptive and continuous switching between Kolmogorov, Von Karman, and fractal power spectra.

3. The method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types as described in claim 2, characterized in that, The turbulence intensity index J is specifically... Furthermore, a tanh weighting function is used to combine Kolmogorov, Von Karman, and fractal spectral types.

4. The method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types as described in claim 1, characterized in that, Weights of the mixed spectrum It consists of the following components: ， Among them, the middle threshold , This is used to achieve a mixed spectrum in weakly turbulent flow (J≤J w ) and strong turbulence (J≥J s Smooth transition between ( ).

5. The method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types as described in claim 1, characterized in that, The compensation coefficient of the 8th order Zernike polynomial Follows a normal distribution And variance Following the Noll-Tokovinin relation: Where the phase screen size D = 3m, and r0 is the atmospheric coherence length. Let be the order of the Zernike polynomial.

6. The method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types as described in claim 1, characterized in that, The calculation of the point spread function (PSF) through Fresnel propagation to simulate turbulence degradation images specifically involves calculating the PSF based on Fresnel propagation theory and performing convolution operations. deg =I clear *PSF generates degraded images and supports full-spectrum simulation of turbulence intensity with atmospheric coherence length r0 = 0.01-1.5 m.

7. The method for generating turbulent phase screens and simulating image degradation based on hybrid spectral types as described in claim 6, characterized in that, The image degradation simulation employs a block convolution technique, with specific steps including: Input image I clear Divide into blocks of w=256 pixels; Execute I independently for each block clear *PSF convolution operation; Spatial correlation of atmospheric turbulence was simulated by multi-screen overlay (Δz=100 m); The SSIM structural similarity, PSNR peak signal-to-noise ratio, and MSE mean square error of the degraded images were evaluated to ensure that the relative error was <2% in order to verify the simulation accuracy.

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