Composite aberration construction method based on beta distribution

Abstract

The invention discloses a beta distribution-based composite aberration construction method, which relates to the technical field of laser optics and comprises the following steps of: constructing a non-ideal laser initial light field; generating a Zernike polynomial weight coefficient based on a beta distribution model; substituting the weight coefficient into the phase expression to form a composite aberration mode, and substituting the composite aberration mode into the non-ideal laser initial light field to obtain a non-ideal laser initial light field with composite aberration; repeating the steps, generating N groups of different weight coefficient combinations corresponding to N composite aberration scenes, simulating transmission evolution of laser in atmospheric turbulence by adopting a multi-layer phase screen method for each group of aberrations, and performing simulation calculation; a simulation result change rule is observed by changing parameters of the beta distribution model, and a parameter-light spot quality mapping relation is established. According to the method, the beta distribution model is introduced, a brand new technical path is provided for flexible construction and high-precision simulation of the composite aberration, and the reliability and efficiency of laser optical system design can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of laser optics technology, and in particular to a composite aberration construction method based on beta distribution. Background Art

[0002] In the field of laser optical system design and transmission simulation, accurate modeling of composite aberrations is crucial for evaluating the impact of different aberrations on beam quality. Existing techniques use Zernike polynomials as a standard tool for aberration decomposition. The distribution of their weight coefficients is typically modeled using a normal distribution approach, characterizing the aberration distribution through its mean and variance. However, this approach has significant limitations: 1. Single distribution: The normal distribution can only describe aberrations with a symmetrical bell-shaped distribution, and cannot characterize the skewed distribution (such as the high-order aberration weights caused by strong turbulence concentrated in a certain range) or multimodal distribution (such as the composite aberrations introduced by hybrid optical elements) that are widely present in real scenes. 2. Limited parameter adjustment: The normal distribution relies on fixed second-order moments (mean and variance), making it difficult to dynamically adapt to the diverse requirements of aberration weight distribution under different laser transmission conditions (such as atmospheric turbulence intensity and optical component processing errors); 3. Insufficient simulation accuracy: In high-power laser transmission or long-distance atmospheric transmission scenarios, the non-Gaussian characteristics of composite aberrations can cause the simulation results of the normal distribution model to deviate significantly from the actual transmission effect (for example, the spot splitting phenomenon cannot be effectively predicted).

[0003] In laser transmission simulation, the distribution of Zernike polynomial weight coefficients directly determines the shape and transmission characteristics of composite aberrations. For example, in atmospheric turbulence simulations, the weight coefficients of higher-order aberrations often exhibit a right-skewed distribution (with a high proportion of small values and sparse large values). The Beta distribution, a two-parameter probability distribution (with adjustable parameters α and β), can flexibly fit a variety of distribution forms, including symmetric, skewed, and U-shaped, by adjusting its shape parameters. It is also naturally suitable for modeling normalized weights within the interval [0,1]. In comparison, its ability to characterize complex aberration distributions significantly outperforms traditional normal distribution methods. Currently, there are no publicly available technical solutions for applying the Beta distribution to fitting Zernike polynomial aberration weight coefficients. Existing literature and patents are limited to the normal distribution or simple deformations, which cannot meet the requirements for accurately modeling the diverse distributions of composite aberrations in laser transmission simulation. Summary of the Invention

[0004] In order to overcome the above problems existing in the prior art, the present invention proposes a composite aberration construction method based on beta distribution.

[0005] The technical solution adopted by the present invention to solve the technical problem is: a composite aberration construction method based on beta distribution, comprising the following steps: Step 1, constructing a non-ideal laser initial light field; Step 2: Generate Zernike polynomial weight coefficients based on the Beta distribution model; Step 3: Substitute the weight coefficient generated in step 2 into the phase expression to form a composite aberration pattern, and then substitute it into the non-ideal laser initial light field in step 1 to obtain a non-ideal laser initial light field with composite aberration; Step 4: Repeat steps 2-3 to generate N groups of different weight coefficient combinations, corresponding to N composite aberration scenarios. For each group of aberrations, use the multi-layer phase screen method to simulate the transmission evolution of the laser in atmospheric turbulence and perform simulation calculations. Step 5: By changing the parameters of the Beta distribution model and observing the change pattern of the simulation results, a parameter-spot quality mapping relationship is established.

[0006] The above-mentioned composite aberration construction method based on Beta distribution, in step 1, uses orthogonal Zernike polynomials in the unit circle domain to simulate system aberrations, and R In the exit pupil, the light wave front is expressed as: , where: ρ, θ are variables in polar coordinates, used to describe the position of a point on the wavefront, a i is the Zernike polynomial i The weight of the order term, Z i is the Zernike polynomial i The order term, the corresponding phase is expressed as: ,in S i To introduce the i The corresponding phase change is when the order aberration is k =2π / λ is the wave number.

[0007] In the above-mentioned composite aberration construction method based on beta distribution, the step 2 is specifically as follows: setting four pairs of shape parameters and The values satisfy right-skewed, left-skewed, U-shaped and symmetric distributions respectively. 36 random numbers are generated for each pair. The coefficient range is controlled between [0, 0.45] by scaling, and the sum of the weight coefficients in each distribution is set equal.

[0008] The above-mentioned composite aberration construction method based on Beta distribution, the shape parameter and Value, when The time distribution is symmetrical; Left deviation; When the right side; , It shows a U-shaped distribution.

[0009] In the above-mentioned composite aberration construction method based on Beta distribution, the weight coefficients of the first three terms of the Zernike polynomial in step 2 are all 0.

[0010] In the above-mentioned composite aberration construction method based on beta distribution, the expression of the non-ideal laser initial light field with composite aberration in step 3 is: Among them, Si is introduced alone i The corresponding phase change is when the order aberration is represents the initial light field after aberration modulation, represents the original emitted light field, represents the radial coordinate, i.e. the polar diameter; represents the angular coordinate, i.e. the polar angle; Z represents the laser transmission distance.

[0011] In the above-mentioned composite aberration construction method based on beta distribution, the indicators for evaluating the transmission quality of laser in atmospheric turbulence in step 4 are one or more of beam expansion, spot drift, and light intensity scintillation index.

[0012] The present invention has the beneficial effect of accurately fitting arbitrary aberration weight distributions through the tunability of the beta distribution's two parameters (α, β), simulating real optical systems more accurately than the traditional normal distribution. By introducing the beta distribution model, the present invention provides a new technical approach for the flexible construction and high-precision simulation of composite aberrations, effectively improving the reliability and efficiency of laser optical system design. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 Schematic diagram of the variation of the light intensity scintillation index of groups 1-3 with the turbulence intensity in an embodiment of the present invention; Figure 3 Schematic diagram of the variation of the light intensity scintillation index of groups 4-6 with the turbulence intensity in an embodiment of the present invention; Figure 4 2 is a schematic diagram showing the variation of the light intensity flicker index of groups 7 to 9 with the turbulence intensity in an embodiment of the present invention; Figure 5 10-12 is a schematic diagram of the variation of the light intensity flicker index with turbulence intensity in the embodiment of the present invention. DETAILED DESCRIPTION

[0014] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0015] like Figure 1 As shown, this embodiment discloses a composite aberration construction method based on beta distribution, which specifically includes the following steps: 1. Constructing a non-ideal laser initial light field Orthogonal Zernike polynomials in the unit circle domain are used to simulate system aberrations. R In the exit pupil, the light wave front can be expressed as: , where: ρ, θ are variables in polar coordinates, used to describe the position of a point on the wavefront, a i is the Zernike polynomial i The weight of the order term, Z i is the Zernike polynomial i By setting different a i The different aberrations and aberration combinations of the system pupil can be obtained by using the value of the aberration weight. a i , this embodiment sets its range as: 0< a i <0.46; Z i is the Zernike polynomial i The order term, the corresponding phase can be expressed as: ,in S i To introduce the i The corresponding phase change is when the order aberration is k =2π / λ is the wave number.

[0016] 2. Generate Zernike polynomial weight coefficients based on Beta distribution The Beta distribution is a continuous probability distribution defined on the interval [0,1] and is often used to describe the distribution of probabilities. Its name comes from the Beta function, and its probability density distribution is: in and is the shape parameter, is the beta function, is the gamma function.

[0017] The shape of the distribution is given by and Joint decision: When When the distribution is symmetrical, left-biased (peak close to 1), is right-biased (peak close to 0), and , In order to make the generated random numbers suitable for Zernike polynomial weight coefficients, four pairs of and The values satisfy right-skewed, left-skewed, U-shaped and symmetric distributions respectively. 36 random numbers are generated for each pair. The coefficient range is controlled between [0, 0.45] by scaling, and the sum of the weight coefficients in each distribution is set equal.

[0018] In the Zernike polynomials, the first term is the piston term and is usually not considered. The second and third terms are the tilted x and y terms, which can generally be corrected and are therefore set to 0 here.

[0019] 3. Generating diverse composite aberrations and evaluating their impact on laser transmission characteristics Substitute the 36 weight coefficients generated in step 2 into the phase expression in step 1 to form a set of composite aberration patterns. Substitute them into the non-ideal laser initial light field to obtain a non-ideal laser initial light field containing composite aberrations.

[0020] The non-ideal initial light field expression after the introduction of composite aberrations is: .

[0021] Among them, when Si introduces the i-th order aberration alone, the corresponding phase change is, represents the initial light field after aberration modulation, represents the original emitted light field, represents the radial coordinate, i.e. the polar diameter; represents the angular coordinate, i.e. the polar angle; Z represents the laser transmission distance.

[0022] Transmission simulation iteration: Repeat steps 2 and 3 to generate N groups of different weight coefficient combinations, corresponding to N composite aberration scenarios; for each group of aberrations, use the multi-layer phase screen method to simulate the transmission evolution of the laser in atmospheric turbulence.

[0023] Performance evaluation indicators: beam expansion, spot drift, and light intensity flicker index.

[0024] 4. Beta distribution parameter optimization and adaptive adjustment By changing the parameters of the Beta distribution model and observing the changing pattern of the simulation results, a parameter-spot quality mapping relationship is established.

[0025] Based on the above method, this embodiment conducts an experimental design with the following research objectives: to construct four different forms of composite aberrations through beta distribution, to deeply explore their influence on the spot scintillation index when the laser is transmitted in atmospheric turbulence, and to provide a theoretical basis and practical guidance for the design and optimization of laser transmission systems.

[0026] Aberration model: The first 36 Zernike polynomials are used to characterize the composite aberration, where the weight coefficients of the first three are set to 0 and the weight coefficients are expressed as Indicates that models with different aberration combinations are constructed.

[0027] Simulation method: Atmospheric turbulence is simulated based on the multi-layer phase screen method to provide a reliable turbulent environment for ocean-atmosphere laser transmission simulation.

[0028] Parameter configuration: Four beta distributions are designed for the Zernike coefficient: left-skewed distribution (dominated by low-order aberrations), right-skewed distribution (dominated by high-order aberrations), U-shaped distribution (bipolar value), and symmetric distribution (normal distribution). Each distribution is assigned a corresponding group number, such as the left-skewed distribution corresponds to group numbers 1, 2, and 3, as shown in Table 1.

[0029] Table 1 Parameter configuration and corresponding group number Random number generation and scaling: Generate random numbers of the required distribution by setting appropriate parameters. Calculate the sum of the random numbers for each distribution and perform normalization to ensure that the sum of the random number weight coefficients for each distribution is equal and the value is between [0-0.45], which is in line with the general selection range of the aberration weight coefficient.

[0030] Laser parameters: wavelength of 532 nm, initial beam diameter of 80 mm, emission aperture of 200 mm, curvature radius R of 1100 m, emission light power of 1 W, zenith angle of 90°, and horizontal transmission distance L of 1100 m.

[0031] Atmospheric turbulence simulation parameters: the number of transmissions is set to 200, 22 phase screens are arranged in the transmission path, the grid size of each phase screen is 512×512, and the grid spacing is 1 mm.

[0032] Transmission calculation: The generated weight coefficient is substituted into the phase function, and the laser transmission is simulated and calculated in combination with the multi-layer phase screen method. The light intensity scintillation index is calculated through the light intensity distribution on the receiving surface, thereby obtaining the light intensity fluctuation characteristics of the laser when it is transmitted in atmospheric turbulence.

[0033] For the calculation of light intensity flicker index, when evaluating the transmission quality of laser in the atmosphere, the light intensity flicker index It is one of the important indicators for evaluating the transmission quality of laser beams in the atmosphere. Its physical meaning is to quantify the random fluctuation characteristics of the light intensity at the receiving end, which is crucial for a deep understanding of the transmission characteristics of lasers in the atmosphere. Its mathematical expression is the ratio of the light intensity variance to the square of the average light intensity on the receiving plane: in represents the square mean of the light intensity on the receiving plane, The square of the mean light intensity on the receiving plane is shown in Figure 1. The light intensity scintillation index of groups 1-10 varies with the turbulence intensity. Figure 2-5 shown.

[0034] right The average flicker index is calculated and the results are shown in Table 2.

[0035] Table 2 Calculation results of average flicker index From Table 2 and Figure 2-5 It can be seen that in When the turbulence intensity is weak, the difference in scintillation index between different composite aberrations is small. Except for the composite aberration of group G8, the relative change rates of the composite aberrations of the other groups are all less than 0, that is, the scintillation index is less than that of no aberration.

[0036] As the turbulence intensity gradually increases to , the scintillation index value increases with the increase of turbulence intensity. When the flicker index of the 8th, 9th, and 10th group composite aberrations is less than that of the aberration-free group The remaining composite aberration groups all contribute to a higher axial flicker index than the aberration-free state. This is because the interaction between aberrations and turbulence becomes complex in moderately turbulent environments. The unique combination of aberrations in composite aberration groups 8, 9, and 10 may somewhat weaken the effect of turbulence on light intensity, resulting in a lower flicker index than the aberration-free state. The composite aberrations in other groups interact with turbulence, exacerbating light intensity fluctuations and leading to an increase in the flicker index.

[0037] In summary, in the actual design of laser transmission systems, the combined effects of composite aberrations and turbulence intensity must be fully considered to accurately predict and optimize laser transmission performance.

[0038] Advantages of the beta distribution: It can flexibly control the statistical properties of complex aberrations, simulating real optical systems more accurately than the traditional normal distribution. It can also be combined with adaptive optics systems to dynamically adjust correction strategies based on beta distribution parameters, improving system performance.

[0039] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art may make various modifications or equivalent substitutions to the present invention within the spirit and scope of protection of the present invention, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present invention.

Claims

1. A composite aberration construction method based on beta distribution, characterized in that: The steps include: Step 1, constructing a non-ideal laser initial light field; Step 2: Generate Zernike polynomial weight coefficients based on the Beta distribution model; Step 3: Substitute the weight coefficient generated in step 2 into the phase expression to form a composite aberration pattern, and then substitute it into the non-ideal laser initial light field in step 1 to obtain a non-ideal laser initial light field with composite aberration; Step 4: Repeat steps 2-3 to generate N groups of different weight coefficient combinations, corresponding to N composite aberration scenarios. For each group of aberrations, use the multi-layer phase screen method to simulate the transmission evolution of the laser in atmospheric turbulence and perform simulation calculations. Step 5: By changing the parameters of the Beta distribution model and observing the change pattern of the simulation results, a parameter-spot quality mapping relationship is established.

2. A composite aberration construction method based on beta distribution according to claim 1, characterized in that: In step 1, the orthogonal Zernike polynomials in the unit circle domain are used to simulate the system aberration. R In the exit pupil, the light wave front is expressed as: , Among them: ρ, θ are variables in polar coordinates, used to describe the position of the point on the wavefront, a i is the Zernike polynomial i The weight of the order term, Z i is the Zernike polynomial i The order term, the corresponding phase is expressed as: ,in S i To introduce the i The corresponding phase change is when the order aberration is k =2π / λ is the wave number.

3. The composite aberration construction method based on beta distribution according to claim 1, characterized in that: The step 2 is specifically as follows: setting four pairs of shape parameters and The values satisfy right-skewed, left-skewed, U-shaped and symmetric distributions respectively. 36 random numbers are generated for each pair. The coefficient range is controlled between [0, 0.45] by scaling, and the sum of the weight coefficients in each distribution is set equal.

4. A composite aberration construction method based on beta distribution according to claim 3, characterized in that: The shape parameters and Value, when The time distribution is symmetrical; Left deviation; When the right side; , It shows a U-shaped distribution.

5. The composite aberration construction method based on beta distribution according to claim 1, characterized in that: In step 2, the weight coefficients of the first three terms of the Zernike polynomial are all 0.

6. The method for constructing a composite aberration based on beta distribution according to claim 2, wherein: The expression of the non-ideal laser initial light field with composite aberration in step 3 is: Among them, when Si introduces the i-th order aberration alone, the corresponding phase change is, represents the initial light field after aberration modulation, represents the original emitted light field, represents the radial coordinate, i.e. the polar diameter; represents the angular coordinate, i.e. the polar angle; Z represents the laser transmission distance.

7. The method for constructing a composite aberration based on beta distribution according to claim 1, wherein: In step 4, the indicators for evaluating the transmission quality of the laser in atmospheric turbulence are one or more of beam expansion, spot drift, and light intensity scintillation index.

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