A method for analyzing thermal blooming aberration of different truncation factors based on Zernike polynomials

Abstract

The application discloses a method for analyzing thermal blooming aberration with different truncation factors based on Zernike polynomials, and belongs to the technical field of high-energy laser atmospheric transmission and thermal blooming correction. Firstly, a thermal blooming wavefront phase distribution of a Gaussian beam after atmospheric transmission is acquired, and normalization processing is performed; then, mode decomposition is performed on the normalized wavefront by using Zernike polynomials, and Zernike coefficients of each order under different truncation factors are extracted; further, the evolution law of the structure characteristics and aberration components of the thermal blooming wavefront distortion with the truncation factor is quantitatively analyzed; based on a point spread function, a Strehl ratio is calculated, and a source energy transmittance is introduced to construct a target light intensity evaluation index, and the optimal truncation factor balancing the transmission efficiency and aberration suppression is determined through extreme value optimization; finally, the optimal truncation factor is converted into a hardware control instruction to drive a variable beam expander telescope or a dynamic diaphragm to perform physical adjustment. The application can effectively improve the peak target light intensity of the system under typical thermal blooming conditions.

Description

Technical Field

[0001] This invention belongs to the field of high-energy laser atmospheric transmission and thermal corona correction technology, specifically involving a method for analyzing thermal corona aberrations with different cutoff factors based on Zernike polynomial analysis. Background Technology

[0002] When high-energy lasers are transmitted over long distances in a real atmospheric environment, the atmosphere absorbs the laser energy, generating a non-uniform temperature field. This leads to a spatial gradient in the refractive index, ultimately superimposing a phase distortion similar to a "thermal lens" onto the laser beam, known as the "thermal coma effect." The thermal coma effect causes severe deflection, divergence, and wavefront distortion of the laser beam, posing a significant nonlinear physical bottleneck that severely limits the effective long-distance energy transmission of systems such as high-energy laser weapons and free-space optical communications.

[0003] In practical high-energy laser emission systems, the emission aperture must be hard-truncated at the edges of the Gaussian beam due to limitations in the physical aperture size. The truncation factor, as a core parameter of the emitting beam, directly determines the spatial intensity distribution of the initial light field. In traditional high-energy laser engineering, based on free-space diffraction theory, a large truncation factor (e.g., above 1.2) is typically used to obtain extremely high source emission transmittance. However, facing the complex atmospheric thermal halo environment, traditional system design and existing aberration assessment and correction techniques reveal the following serious theoretical lags and engineering bottlenecks:

[0004] First, existing research on thermal halo severely lacks precise quantitative analysis of wavefront aberration structures. Although there are numerous studies on the thermal halo effects of Gaussian beams or novel structured beams, they generally focus on macroscopic phenomenological characterizations such as beam broadening, centroid drift, and Strelby ratio (SR). Unlike atmospheric turbulence research, where Zernike polynomial decomposition has long been used as a standard tool, the Zernike structure and evolutionary characteristics of thermal halo aberrations have rarely been systematically quantified. This lack of a quantitative "structural model" directly prevents researchers from accurately revealing the deep physical influence of the "truncation effect" on the distribution of high- and low-order aberration components.

[0005] Second, the complex high-frequency aberrations caused by large cutoff factors overwhelm adaptive optics (AO) systems. Traditional designs, blindly pursuing high transmittance, produce Gaussian beams with large cutoff factors and steep intensity gradients, which evolve into complex high-frequency phase distortions due to multimode superposition during transmission. Currently, mainstream closed-loop AO systems (relying on wavefront sensors) face high hardware costs and limited bandwidth, while wavefront-sensorless AO systems are limited by convergence speed. Faced with such strong high-frequency distortions, low-order AO systems have limited correction capabilities, leading to severe far-field beam fragmentation.

[0006] Third, existing technologies lack a comprehensive evaluation system that breaks down the barriers between "maximizing emission energy" and "minimizing thermal corona distortion." An ideal strategy for suppressing thermal corona should be "preventing it at the source and simplifying downstream correction," that is, through active beam shaping (e.g., finding the optimal cutoff factor to actively shape a flat-top beam), the thermal corona wavefront should exhibit a predominantly low-order structure, thereby greatly reducing the correction burden on the downstream adaptive optics (AO) system. However, existing system designs often treat the energy transmittance at the emitter and the beam degradation at the target surface in isolation, lacking a dual-constraint evaluation mechanism that tightly couples the two. This results in the system being unable to extract the optimal cutoff factor that balances transmission efficiency and aberration suppression in complex thermal corona environments.

[0007] In summary, existing technologies lack an effective means to accurately and quantitatively analyze the thermal halo aberration structure under different cutoff factors, making it difficult to theoretically guide the selection of parameters between emission energy transmittance and thermal halo aberration suppression. Due to the lack of a corresponding evaluation system, existing systems struggle to balance energy transmission efficiency and target-reaching beam intensity performance in complex atmospheric environments, thus limiting the improvement of far-field beam quality and target-reaching power in high-energy laser systems to some extent. Summary of the Invention

[0008] To address the problem of beam quality degradation caused by thermal coma during high-energy laser atmospheric transmission, and the lack of effective thermal coma wavefront analysis methods in existing technologies, making quantitative control of this effect at its source difficult, this invention provides a method based on Zernike polynomial analysis of thermal coma aberrations under different truncation factors. This method achieves quantitative characterization of wavefront distortion structure under different truncation factors by performing mode decomposition on the thermal coma wavefront, thereby revealing the influence of the truncation factor on the distribution of thermal coma aberrations. Based on this, an evaluation index that balances transmission efficiency and aberration suppression is constructed to optimize the truncation factor, obtaining an optimized truncation factor corresponding to the thermal coma environment. By adjusting the initial beam spatial intensity distribution, it is beneficial to suppress the generation of complex high-frequency thermal coma aberrations and reduce the correction burden on downstream adaptive optics systems, thereby improving the overall target-reaching efficiency of the high-energy laser system.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for analyzing thermal halo aberrations with different cutoff factors based on Zernike polynomials includes the following steps:

[0011] Step 1: Obtain the phase distribution of the thermal halo wavefront generated after the Gaussian beam passes through the atmosphere, and normalize the phase distribution of the thermal halo wavefront to obtain the normalized thermal halo wavefront phase distortion corresponding to different cutoff factors.

[0012] Step 2: Use Zernike polynomials to perform mode decomposition on the normalized thermal halo wavefront phase distortion and extract the Zernike coefficients of each order corresponding to different cutoff factors.

[0013] Step 3: Based on the extracted Zernike coefficients, quantitatively analyze the structural characteristics and evolution of aberration components of the thermal wavefront phase distortion under different cutoff factors;

[0014] Step 4: Based on the wavefront phase distortion of thermal halos under different cutoff factors, the Strell ratio (SR) corresponding to different cutoff factors is calculated using the point spread function (PSF). The source energy transmittance is introduced into the target light intensity evaluation index. By optimizing the extreme value of this index, the optimal cutoff factor that balances transmission efficiency and aberration suppression is determined. ;

[0015] Step 5: Apply the obtained optimal cutoff factor The commands are converted into hardware control instructions to drive the variable beam expander or shrinker telescope or dynamic aperture in the high-energy laser emission system to perform physical adjustments. By actively reshaping the spatial intensity distribution of the initial beam, the overall target-reaching efficiency of the high-energy laser in a thermal coma environment is improved.

[0016] The beneficial effects of this invention are as follows:

[0017] (1) Quantitative analysis: The Zernike polynomial is cleverly introduced to transform the complex thermal halo phase distortion into intuitive aberration coefficients of each order, thus realizing accurate quantitative analysis of thermal halo aberration structure.

[0018] (2) Source suppression and global optimization: The mapping relationship between source energy loss caused by the cutoff effect and far-field thermal halo distortion was established, which effectively alleviated the technical bias of blindly pursuing static high energy transmittance in traditional high-energy laser engineering and realized the dynamic optimization of the optimal cutoff factor.

[0019] (3) This method not only provides a solid theoretical basis for the beam shaping strategy of “reshaping aberrations from the source and simplifying correction”, but also significantly improves the overall peak light intensity of the high-energy laser system in the actual thermal oscillation range. Attached Figure Description

[0020] Figure 1 A flowchart illustrating the overall steps of a method for analyzing thermal halo aberrations with different cutoff factors based on Zernike polynomial analysis, provided in this embodiment of the invention.

[0021] Figure 2 This is a graph showing the relationship between the normalization coefficients of the first 35 Zernike aberrations and the truncation factor in an embodiment of the present invention.

[0022] Figure 3This is a comparison of the normalized three-dimensional phase distribution of the thermal halo wavefront under representative cutoff factors (T=0.5, 1.5, 4.0) in an embodiment of the present invention.

[0023] Figure 4 The image shows a comparison of the far-field point spread function (PSF) spot intensity distribution under different cutoff factors (T=0.5, 1.5, 4.0) obtained from simulations in this embodiment of the invention.

[0024] Figure 5 This is a graph showing the relationship between the comprehensive evaluation indicators, such as the target peak light intensity factor, and the cutoff factor in this embodiment of the invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of the invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, the invention adopts the following technical solutions.

[0026] In this embodiment, the numerical simulation environment for high-energy laser atmospheric transmission is set as follows: laser wavelength. =1064 nm, diameter of the hard-edge aperture of the emission system =0.125 m, transmission distance The numerical computation space grid is set to... This is to satisfy the sampling theorem requirements of the Fast Fourier Transform (FFT).

[0027] like Figure 1 As shown, this invention proposes a method for analyzing thermal halo aberrations with different cutoff factors based on Zernike polynomials, specifically including the following steps:

[0028] Step 1: Obtain and normalize the phase distortion of the thermal halo wavefront.

[0029] 1.1 Obtaining the phase distortion of the thermal corona wavefront generated after the collimated Gaussian beam passes through the atmosphere:

[0030] Under the weak thermal coma approximation—that is, neglecting the intensity change during beam propagation—the steady-state thermal coma wavefront phase distortion can be calculated from the initial intensity distribution at the exit surface. For a collimated Gaussian beam with uniform transverse wind, the phase change of the light wave along the uniform propagation path (ignoring energy attenuation due to absorption) caused by the thermal coma effect can be obtained from the steady-state solution of the density change during thermal coma. for:

[0031] (1)

[0032] in, The intensity radius is 1 / e of the beam. Let be the error function, and be the maximum phase distortion. ,in This is a dimensionless thermal distortion parameter.

[0033] 1.2 Obtaining the normalized thermal halo wavefront phase distortion Gaussian beam with different cutoff factors passing through a radius of... When the aperture is a circular, hard aperture, the initial field strength distribution changes from a smooth Gaussian function to a truncated distribution. Let the initial beam waist radius be w, and the truncation factor is typically defined as... .

[0034] To analyze aberrations at a uniform scale, a spatial coordinate normalization transformation is performed: Let =x / R and =y / R, Equation (1) is transformed into a normalized wavefront defined on the unit circle. .

[0035] (2)

[0036] Equation (2) maps the phase distortion of the wavefront of the thermal halo with different cutoff factors onto a unified unit circle, laying the foundation for subsequent quantitative comparison of their aberration structures.

[0037] Step 2: Perform wavefront mode decomposition using Zernike polynomials.

[0038] To analyze the internal structure of aberrations in depth, this step employs a mode decomposition-based method.

[0039] 2.1 Constructing the Zernike expansion model:

[0040] Any wavefront defined on the unit circle All of these can be expanded into a linear combination of Zernike polynomials. Therefore, the normalized thermal halo wavefront phase distortion established in step 1.2 can be used to... Expanded in this normalized coordinate system, it is as follows:

[0041] (3)

[0042] In equation (3), Let i be the standard Zernike polynomial of order i defined on the unit circle domain; Indicates the first Phase amplitude of a certain aberration mode (such as tilt, defocus, etc.) under the current truncation factor.

[0043] 2.2 Determine the theoretical inner product solution formula:

[0044] Utilizing the orthogonality of standard Zernike polynomials in the unit circle, the expansion coefficients of each order... It can be obtained by calculating the inner product of continuous spaces:

[0045] (4)

[0046] 2.3 Numerical Solution Implementation (Numerical Integration of Continuous Inner Products):

[0047] Since it is difficult to obtain a closed-loop analytical integral solution for the thermal corona wavefront expression containing error functions, this embodiment employs a continuous inner product numerical integration method based on polynomial orthogonality for high-precision solution. The specific process is as follows: for each order of Zernike coefficients to be determined... In the numerical calculation program, a continuous two-dimensional integrand is constructed according to equation (4). Subsequently, a high-precision two-dimensional numerical integration algorithm (such as the adaptive double quadrature algorithm) is called to strictly limit the integration domain to the normalized unit circle (i.e., This method performs numerical integration operations in continuous space. It adaptively approximates the true integral area, thereby accurately calculating the aberration coefficients corresponding to different cutoff factors. .

[0048] Step 3: Quantitatively analyze the evolution of thermal halo aberration with the cutoff factor.

[0049] After obtaining different cutoff factors After obtaining the thermal halo wavefront aberration coefficients, this step quantitatively reveals the deep physical impact of beam edge truncation on the thermal halo distortion structure by extracting aberration feature terms and plotting evolution curves. The specific implementation process is as follows:

[0050] 3.1 Normalization and Unified Comparison Benchmark:

[0051] According to the steady-state thermal corona analytical model in step 1, the thermal corona wavefront phase distortion and thermal distortion parameters are... They exhibit a strictly proportional relationship, therefore the Zernike coefficients of each order obtained from the model decomposition... and It is also directly proportional. In order to eliminate To mitigate interference from aberration structure evolution analysis, this step normalizes the extracted coefficients of each order. The coefficients to be obtained are... Unified division by thermal distortion parameter Thus, the relative aberration coefficient amplitude under unit thermal distortion parameter is obtained. / Furthermore, to facilitate subsequent intuitive engineering evaluation in conjunction with the attached diagrams, the original radian value of this amplitude was further divided by... , converted into wavelength Normalized aberration coefficients in units of 1.

[0052] 3.2 Mode decomposition of phase distortion in thermal wavefront:

[0053] To address the issue of high-frequency spatial fluctuations in thermal halo wavefronts under large cutoff factors, and to accurately analyze the multi-scale spatial structure of the wavefront, this step extends the expansion order of the Zernike mode decomposition to the first 35 orders. (After removing translation terms), two types of aberration components are obtained: one is a low-order aberration component used to characterize the overall defocusing of thermal halos and beam deflection; the other is a high-order complex aberration component used to characterize wavefront edge distortion and high spatial frequency fluctuations.

[0054] 3.3 Quantitative analysis of aberration evolution laws:

[0055] like Figure 2 As shown, this step plots the normalized aberration coefficients for the first 35 Zernike aberrations (unit: wavelength). The evolution curves of aberration structure with truncation factor T (0.5 ≤ T ≤ 4.0) are shown. Comparative observation reveals that the change process of aberration structure exhibits extremely obvious stage-like characteristics:

[0056] Phase 1 (Region of Rapid Accumulation of Aberrations) ):

[0057] along with As the intensity gradient gradually increases from 0, the waist of the Gaussian beam gradually contracts towards the aperture stop, and the effective intensity distribution within the pupil rapidly evolves from an initial "flat-top shape" to a "complete Gaussian shape." This rapidly increasing intensity gradient induces a strong temperature gradient along the transmission path, rapidly enhancing the thermal halo effect. Simultaneously, the crosswind effect causes wavefront distortion to exhibit extremely significant direction selectivity (i.e., under the aforementioned model assumptions, aberrations are concentrated in the y-direction parallel to the wind field, while the x-direction aberration component approaches zero). Within this range, the absolute amplitudes of both low-order and high-order aberrations in the y-direction show a synchronous increasing trend. Notably, low-order aberrations exhibit a asynchronous arrival of their extreme points: Inclined component in It was the first to reach its amplitude extreme. Defocus and Like scattered components Reaching the extreme value; and The coma component lags relatively, until... The amplitude reaches its maximum point in the vicinity. The process of the aforementioned low-order aberration components successively reaching their amplitude extremes and then falling back constitutes the main characteristic of thermal halo wavefront distortion in this stage.

[0058] The second stage (the region of high and low aberration differentiation) ):

[0059] With cutoff factor As the beam increases further, the beam energy becomes highly concentrated towards the center of the pupil, and the wavefront distortion evolves into a localized high-frequency phase abrupt change confined to a small central region.

[0060] At this point, the Zernike aberration coefficients exhibit a significant "high-low order differentiation" characteristic: on the one hand, low-order aberration components (such as...) Defocus, Like scattered After passing the amplitude extreme point, coma and other aberrations show a gradual decline trend; on the other hand, high-frequency and high-order aberration components increase significantly.

[0061] The aforementioned high- and low-order aberration differentiation characteristics indicate that, under large cutoff factor conditions, most of the thermal corona distortion energy has shifted to the high-frequency spatial domain. In this case, conventional correction of only low-order aberrations will not effectively suppress the dominant high-frequency distortion, severely limiting the actual beam correction effect.

[0062] To more intuitively illustrate the physical morphological evolution behind the differentiation between high and low order aberrations, Figure 3 Normalized three-dimensional phase distribution maps of the thermal halo wavefront are presented under cutoff factors (T=0.5, 1.5, 4.0) corresponding to the stage boundary characteristics. Figure 3 As shown in (a), in the low-order, gradual accumulation region at T=0.5, the light spot exhibits a flat-top distribution, and the wavefront distortion is relatively gentle; as Figure 3 As shown in (b), when the core inflection point of evolution T≈1.5 is reached, that is, when entering the low-order distortion peak region, low-order aberrations (such as coma and astigmatism) reach their peak state; while as Figure 3 As shown in (c), when entering the region of deep aberration differentiation (T=4.0), the phase of the vast peripheral region of the pupil tends to flatten, the distortion energy is highly contracted, and it evolves into a sharp high-frequency phase abrupt change at the center of the pupil. This three-dimensional aberration evolution characteristic verifies the physical mechanism of thermal halo distortion energy transfer to the high-frequency spatial domain under a large cutoff factor as described in this invention.

[0063] Step 4: Determination of the optimal cutoff factor for suppressing thermal corona based on the target light intensity evaluation index.

[0064] This step establishes an evaluation system centered on the target peak intensity factor by simulating the diffraction and aberration coupling effects during the long-distance propagation of a light beam in free space. This allows for the precise extraction of the optimal cutoff factor to suppress thermal corona effects. The specific implementation process is as follows:

[0065] 4.1 Constructing a complex amplitude field on the pupil surface with truncation properties and free-space divergence:

[0066] Taking into account the modulation effect of the truncation factor T on the initial amplitude of the aligned Gaussian beam, the thermal corona phase distortion generated along the transmission path, and the inherent wavefront divergence effect of long-distance transmission, a complex amplitude field defined on the emission pupil plane is constructed. :

[0067] (5)

[0068] In equation (5), The physical space coordinates of the pupil plane; This is the aperture function of the hard-edge aperture (1 inside the pupil, 0 outside the pupil); = The initial beam amplitude distributions are for different cutoff factors, where Where is the aperture radius; The thermal halo wavefront phase distortion obtained from step 1.2 is calculated by normalizing the wavefront defined on the unit circle. It is obtained by directly mapping back to the physical space coordinate system, that is... = The third term on the right side of the equation is the Fresnel quadratic phase factor, where... For wave number, The wavelength of the laser. The transmission distance to the target surface is 30km in this embodiment.

[0069] 4.2 Fresnel diffraction simulation solution of far-field point spread function (PSF):

[0070] The process of the light beam propagating in free space to the far-field target surface satisfies the Fresnel diffraction condition. This step calculates the actual light intensity distribution on the target surface, including the effects of thermal halo aberration, by performing a two-dimensional Fast Fourier Transform (FFT) on the complex amplitude field of the pupil surface established in step 4.1. This is the actual point spread function. :

[0071] (6)

[0072] in, This represents the two-dimensional Fourier transform operation. These are the physical space coordinates on the far-field target surface.

[0073] like Figure 4 Figures (a), (b), and (c) show the actual far-field target surface spot intensity (PSF) distribution under different cutoff factors obtained from simulation. These figures visually demonstrate that a large cutoff factor leads to severe fragmentation of the far-field spot, while a smaller cutoff factor maintains the integrity of the main spot.

[0074] 4.3 Quantitative Calculation of Strell's Ratio (SR) under Dynamic Comparison Benchmark:

[0075] To scientifically evaluate beam quality under different cutoff factors, the cutoff factor must be eliminated. The impact of changes in total emitted energy and diffraction limit caused by the alteration on the evaluation results.

[0076] First, for the current cutoff factor T, calculate the corresponding aberration-free ideal reference field (i.e., set Φ=0), and then obtain the ideal point spread function using the same algorithm. Subsequently, the peak light intensity of the actual light spot was extracted by strictly using the total energy (full-field integral value) of both the actual and ideal light spots as the normalized denominator. Peak light intensity of the ideal reference spot The strict definition for calculating the Strelby ratio (SR) is:

[0077] (7)

[0078] Since the thermal corona effect is a pure phase distortion, it does not change the total transmitted energy of the beam, thus satisfying the energy conservation condition. Therefore, equation (7) can be directly simplified to the following equivalent equation in numerical calculation:

[0079] (8)

[0080] This calculation method and simplification process ensure that the SR value only reflects the degree of spot fragmentation caused by wavefront phase distortion (thermal halo effect), and is independent of the initial total energy.

[0081] 4.4 Optimal Truncation Factor Optimization Based on Dual Constraints of Beam Quality and Transmission Efficiency:

[0082] Although the distribution of the beam within the pupil approaches a flat-top shape under a very small cutoff factor, resulting in extremely gentle thermal phase distortion and a very high Strell ratio (SR), a large amount of beam energy is blocked by the hard-edge aperture of the emission system, and the actual energy transmittance of the system is extremely low, which cannot meet the actual engineering requirements of high-energy lasers for absolute target power.

[0083] Therefore, in order to accurately reflect the impact of the cutoff factor on the actual destructive effect, this step introduces the "target peak intensity factor" (…). This is used as the final optimization index. This index couples the "source energy loss" caused by the truncation effect with the "far-field spot degradation" caused by the thermal halo effect. Its calculation model is as follows:

[0084] (9)

[0085] In equation (9), Let be the energy transmittance of a Gaussian beam through a hard-edged aperture, expressed as: ; The Strelby obtained in step 4.3.

[0086] With a certain step size (e.g.) By iterating through the cutoff factor parameters within a given range, the corresponding transmittance and Strell ratio are calculated respectively, and finally the peak intensity factor to the target is plotted. The relationship curve of the cutoff factor evolution, such as Figure 5 As shown.

[0087] Extract the corresponding curve Obtain the x-coordinate of the global maximum value; this value represents the atmospheric transport environment (thermal distortion parameter) under the current conditions. Under these conditions, the optimal cutoff factor that balances "beam transmission efficiency" and "thermal corona distortion suppression" is determined. .

[0088] Step 5: Hardware dynamic control strategy based on the evolution law of target surface performance.

[0089] Based on the above comprehensive evaluation system and as follows Figure 5 The different thermal distortion parameters shown ( The evolution curves under these conditions can be used to extract dynamic control strategies to guide the actual emission of high-energy lasers.

[0090] In a heat haze environment, if we follow the traditional experience of using a large cutoff factor (such as...) Blindly pursuing high transmittance at the transmitter can actually cause severe high-frequency phase distortion, leading to far-field beam fragmentation and a significant decrease in target surface intensity; while appropriately reducing the cutoff factor... This will affect the target peak light intensity factor The curve exhibits extreme value characteristics. Extract the optimal cutoff factor corresponding to this peak value. This means that the system, at the cost of sacrificing some of the source emission energy (actively shaping a flat-top beam), greatly suppresses thermal distortion, thereby achieving a leap in the final destructive force on the target surface.

[0091] Evolutionary laws reveal It is not a fixed constant, but varies with atmospheric thermal distortion. The exacerbation of this will cause a significant shift towards smaller values. Therefore, in practical engineering applications, the system can determine the appropriate values ​​based on real-time detected atmospheric parameters. Dynamic locking This allows for adaptive adjustment of the variable beam expander or aperture of the transmission system, effectively alleviating the engineering limitations of static parameter settings and ensuring the system's global adaptive optimality under complex thermal conditions.

Claims

1. A method for analyzing thermal halo aberrations with different cutoff factors based on Zernike polynomial analysis, characterized in that, Includes the following steps: Step 1: Obtain the phase distribution of the thermal halo wavefront generated after the Gaussian beam passes through the atmosphere, and normalize the phase distribution of the thermal halo wavefront to obtain the normalized thermal halo wavefront phase distortion corresponding to different cutoff factors. Step 2: Use Zernike polynomials to perform mode decomposition on the normalized thermal halo wavefront phase distortion and extract the Zernike coefficients of each order corresponding to different cutoff factors. Step 3: Based on the extracted Zernike coefficients, quantitatively analyze the structural characteristics and evolution of aberration components of the thermal wavefront phase distortion under different cutoff factors; Step 4: Based on the wavefront phase distortion of thermal halos under different cutoff factors, the Strell ratio (SR) corresponding to different cutoff factors is calculated using the point spread function (PSF). Source energy transmittance is then introduced into the target light intensity evaluation index. By optimizing the extreme values ​​of this index, the optimal cutoff factor that balances transmission efficiency and aberration suppression is determined. ; Step 5: Apply the obtained optimal cutoff factor The commands are converted into hardware control instructions to drive the variable beam expander or shrinker telescope or dynamic aperture in the high-energy laser emission system to perform physical adjustments. By actively reshaping the spatial intensity distribution of the initial beam, the overall target-reaching efficiency of the high-energy laser in a thermal coma environment is improved.

2. The method according to claim 1, characterized in that, The normalization process described in step 1 specifically includes: mapping the thermal halo wavefront phase distortion under different cutoff factors to a unified unit circle through spatial coordinate normalization transformation.

3. The method according to claim 1, characterized in that, The mode decomposition described in step 2 specifically includes: utilizing the orthogonality of Zernike polynomials in the unit circle domain, calculating the Zernike coefficients of each order through the inner product of continuous space.

4. The method according to claim 3, characterized in that, The continuous spatial inner product calculation in step 2 adopts the continuous inner product numerical integration method based on polynomial orthogonality, and performs numerical product calculation within the normalized unit circle.

5. The method according to claim 1, characterized in that, The quantitative analysis described in step 3 further includes: dividing the extracted Zernike coefficients of each order by the thermal distortion parameter. The relative aberration coefficient amplitude under unit thermal distortion parameter is obtained and converted into normalized aberration coefficient in wavelength unit.

6. The method according to claim 5, characterized in that, The quantitative analysis described in step 3 specifically includes: expanding the expansion order of the Zernike model decomposition to the first 35 orders, obtaining low-order aberration components and high-order complex aberration components, and plotting the curve of the normalized aberration coefficient evolving with the truncation factor to identify the region of rapid aberration accumulation and the region of differentiation between high and low order aberrations.

7. The method according to claim 1, characterized in that, The Strelby SR mentioned in step 4 is calculated as follows: for the current cutoff factor Calculate the ideal point spread function of an aberration-free ideal reference field. The Strell ratio is defined as the ratio of the peak intensity of the actual light spot to the peak intensity of the ideal reference light spot. .

8. The method according to claim 7, characterized in that, The target-reaching light intensity evaluation index mentioned in step 4 is specifically the target-reaching peak light intensity factor. Its calculation model is as follows: ； in, Let be the energy transmittance of a Gaussian beam through a hard-edged aperture, expressed as: .

9. The method according to claim 8, characterized in that, The extreme value optimization described in step 4 specifically includes: traversing the cutoff factor parameters within a given range with a certain step size, calculating the corresponding energy transmittance and Strell ratio respectively, plotting the relationship curve of the target peak light intensity factor as a function of the cutoff factor, and extracting the abscissa of the maximum value on the curve as the optimal cutoff factor. .

10. The method according to claim 9, characterized in that, The hardware control instructions in step 5 further include: based on the real-time detected atmospheric thermal distortion parameters. Dynamically locking the optimal cutoff factor It can adaptively adjust the variable beam expansion device or the physical aperture of the aperture of the emission system to achieve adaptive adjustment under different thermal corona environments.

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