Wavefront distortion correction method based on dynamic adaptive MESSA algorithm and coherent free space optical communication system

Abstract

The invention discloses a wavefront distortion correction method based on a dynamic adaptive MESSA algorithm and a coherent free space optical communication system. The problems that an existing method is prone to falling into a local optimal solution, the correction effect is poor under dynamic turbulence, and the adaptive capacity is weak are solved. According to the method, an individual position is initialized through a Circle chaotic mapping method, iterative optimization is carried out in combination with a Levy flight strategy and a variable spiral search strategy, and a step size control parameter, a safety threshold, spiral strength and a spiral adjustment coefficient are dynamically adjusted through a double-discrimination dynamic adaptive parameter adjustor. And reducing the population scale according to a nonlinear population reduction strategy, finally outputting an optimal individual position, and driving the deformable mirror to perform wavefront correction according to a control voltage vector corresponding to the optimal individual position. According to the invention, the dynamic adjustment of the algorithm parameters and the population structure is realized, and the adaptability, convergence speed and stability of the wavefront distortion correction method in the dynamic turbulence environment are enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical communication technology, in particular to a wavefront distortion correction method based on a dynamic adaptive MESSA algorithm and a coherent free space optical communication system. BACKGROUND

[0002] Free space optical communication (FSOC) is a wireless communication method that uses laser as information carrier and atmosphere as transmission medium. Compared with traditional wireless communication technology, FSOC has higher confidentiality, stronger anti-electromagnetic interference ability, higher channel utilization rate and faster transmission rate, so it has become one of the important research directions in the field of wireless communication. In the military and civilian fields, FSOC technology has been widely used in satellite-to-ground communication, inter-satellite communication, border and coastal defense, "last kilometer" communication and emergency rescue communication, etc.

[0003] At present, compared with the traditional intensity modulation / direct detection (IM / DD) method, coherent free space optical communication (CFSOC) has become one of the core technologies of FSOC research and application due to its flexibility in modulation method, improvement of detection sensitivity and excellent channel selectivity. However, due to the influence of atmospheric turbulence, CFSOC system will face problems such as light intensity flicker, beam drift and angle of arrival fluctuation, which will seriously affect the beam quality and lead to the increase of system bit error rate (BER), thereby reducing the communication quality and stability. Therefore, how to efficiently compensate for channel distortion and improve the performance of CFSOC system is the focus of current research.

[0004] Adaptive optics (AO) technology is considered to be an effective solution for FSOC channel compensation. This technology suppresses the influence of atmospheric turbulence on the performance of CFSOC system through real-time measurement and closed-loop correction. AO system is usually divided into traditional AO system and sensor-less adaptive optics (SLAO). In the traditional AO system, Shack-Hartmann (S-H) wavefront sensor is widely used to measure wavefront aberration, and its measurement performance is stable and mature. However, S-H wavefront sensor also has many shortcomings, such as high equipment cost, low light energy utilization rate (due to multiple light splitting leading to energy loss) and complex deployment in some specific scenarios.

[0005] To solve the above-mentioned limitations, researchers have developed a wavefront AO system that replaces the wavefront sensor with a charge-coupled device (CCD) and combines an adaptive optimization algorithm to complete the wavefront correction. This way not only saves the space occupied by the wavefront sensor, but also reduces the energy loss caused by beam splitting. Since the performance of the wavefront AO system depends entirely on the performance of the optimization algorithm, compared with the traditional S-H wavefront sensor, SLAO shows potential advantages and application value in strong turbulent environments.

[0006] In the SLAO system, the most commonly used optimization algorithm is the Stochastic Parallel Gradient Descent (SPGD). Based on the simultaneous perturbation stochastic approximation theory, SPGD algorithm is widely used in wavefront AO system due to its simple structure, good correction performance and easy engineering implementation. However, SPGD algorithm also has some shortcomings, such as being easy to fall into local optimal solution in complex optimization problems, and being unable to effectively correct wavefront distortion in strong turbulent conditions, which limits its application performance in high dynamic and severe atmospheric disturbance scenes. SUMMARY

[0007] In order to overcome the problems that the existing SPGD algorithm is easy to fall into local optimal solution in SLAO system, the correction effect is not good in strong turbulent flow, and the adaptive ability is weak when dealing with complex dynamic wavefront distortion, the present application provides a wavefront distortion correction method based on dynamic adaptive MESSA algorithm and a coherent free space optical communication system.

[0008] In order to solve the above technical problems, the present application provides the following technical solutions:

[0009] A wavefront distortion correction method based on dynamic adaptive MESSA algorithm, the method is applied to a wavefrontless adaptive optical system, and the method comprises the following steps:

[0010] Step 1: initialize sparrow population parameters, including total population, number of discoverers PD, number of alarmers, maximum number of iterations and safety threshold, the position of each individual in the sparrow population in the search space corresponds to a control voltage vector composed of a group of voltage values applied to all drivers of the deformable mirror in the wavefrontless adaptive optical system, and the dimension of the control voltage vector is the same as the number of the drivers;

[0011] Step 2: use the Circle chaotic mapping method to generate the initial position corresponding to each individual;

[0012] Step 3: calculate the fitness value of each individual , and according to the fitness value Sort all individuals and find the maximum fitness value And the minimum fitness value ;

[0013] Step 4: select the PD individuals with fitness as the discoverers, introduce the Levy flight strategy in the discoverer position updating process, update the position of the discoverer by using the discoverer position updating formula combined with the Levy flight strategy, and in the discoverer position updating formula, the step length control parameter and the safety threshold of the Levy flight strategy are dynamically adjusted by the double-discriminant dynamic adaptive parameter adjuster according to the acceptance rate and the population diversity;

[0014] Step 5: introduce the variable spiral search strategy in the follower position updating process, update the position of the follower based on the position of the discoverer according to the follower position updating formula combined with the variable spiral search strategy, and in the follower position updating formula, the spiral strength and the spiral adjustment coefficient of the variable spiral search strategy are dynamically adjusted by the double-discriminant dynamic adaptive parameter adjuster according to the acceptance rate and the population diversity;

[0015] Step 6: for each sentry individual, judge whether its fitness value is equal to the current global optimal fitness value, if equal, update its position according to the original sentry position updating formula; otherwise, introduce the dynamic refraction reverse learning strategy, and update the position of the sentry according to the sentry position updating formula combined with the dynamic refraction reverse learning strategy;

[0016] Step 7: after completing an iteration, recalculate the fitness value of each individual , and update the maximum fitness value , the minimum fitness value ;

[0017] Step 8: reduce the population size according to the nonlinear population reduction strategy;

[0018] Step 9: judge whether the iteration termination condition is met, if yes, output the optimal individual position, and output the control voltage vector corresponding to the optimal individual position as a control signal to the driver in the deformable mirror, drive the deformable mirror to perform wavefront correction; otherwise, return to step 3 and continue iteration.

[0019] Meanwhile, the application also provides a coherent free space optical communication system, which comprises a wavefront adaptive optical system, and the wavefront adaptive optical system adopts the wavefront distortion correction method as described above to perform wavefront distortion correction.

[0020] Compared with the prior art, the application has the following beneficial effects:

[0021] Compared with the traditional SPGD algorithm, the dynamic adaptive MESSA algorithm is obtained by improving the traditional sparrow search algorithm, the Circle chaos mapping method is used to enhance the diversity of the initial distribution of the population, the risk of early convergence is avoided, the Levy flight strategy is introduced to improve the global search ability, the algorithm is helped to jump out of the local optimal solution, the variable spiral search strategy is used to enhance the flexibility of local development, so that the algorithm can perform more fine local search on the basis of global optimization, and three mechanisms of double-discriminating dynamic adaptive parameter regulator, dynamic refraction reverse learning strategy and nonlinear population reduction strategy are introduced, the search scale and population structure are adjusted on demand, the calculation efficiency of the wavefront distortion correction method is improved, and the adaptability, stability and convergence efficiency in the dynamic aberration field are improved, and the wavefront distortion correction performance, the convergence speed and the stability are better in weak turbulence and strong turbulence conditions. Especially for the dynamically changing wavefront aberration, the method has stronger adaptability and robustness, the dynamic parameter adjustment mechanism can effectively cope with the time-varying uncertainty of the aberration, avoid the premature convergence or low search efficiency caused by fixed parameters, and the correction effect is more stable and converges faster in the dynamic turbulence environment.

[0022] The dynamic adaptive MESSA algorithm is combined with the wavefront adaptive optics system, a high-efficiency, stable and adaptive wavefront distortion correction solution is provided for the coherent free space optical communication system, and the communication quality and reliability of the coherent free space optical communication system are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 The flowchart of the wavefront distortion correction method based on the dynamic adaptive MESSA algorithm described in the embodiment of the application is shown in the figure.

[0024] Figure 2 The path schematic diagram of the spiral search is shown in the figure.

[0025] Figure 3 The lens refraction reverse learning principle diagram is shown in the figure.

[0026] Figure 4 The strong turbulence simulation data graph is shown in the figure.

[0027] Figure 5 The correction effect graphs of different iteration numbers in the dynamic strong turbulence environment are shown in the figures.

[0028] Figure 6 The curve graphs of ME of the MESSA algorithm and the DA-MESSA algorithm changing with iteration numbers in the dynamic turbulence condition are shown in the figures.

[0029] Figure 7 The curve graphs of BER of the MESSA algorithm and the DA-MESSA algorithm changing with iteration numbers are shown in the figures.

[0030] Figure 8 RMS value and ME value of MESSA algorithm and DA-MESSA algorithm;

[0031] Figure 9 A curve graph of population number changing with iteration number;

[0032] Figure 10 A comparison graph of RMS value before and after correction when iteration number is 20;

[0033] Figure 11 A comparison graph of RMS value before and after correction when iteration number is 50. DETAILED DESCRIPTION

[0034] The technical solutions of the present application will be described in detail below with reference to the accompanying drawings and preferred embodiments.

[0035] As shown in the figure, the embodiment provides a wavefront distortion correction method based on dynamic adaptive MESSA algorithm, which can be applied to a wavefront adaptive optical system to correct wavefront distortion. Specifically, the method comprises the following steps: Figure 1 Step 1: initialize sparrow population parameters, including total population number PD, number of scouts SD, maximum iteration number and safety threshold, the position of each individual in the search space in the sparrow population corresponds to a group of Zernike coefficients, the group of Zernike coefficients corresponds to a control voltage vector, the control voltage vector is composed of a group of voltage values applied to all drivers in the deformable mirror in the wavefront adaptive optical system, the control voltage vector uniquely defines a group of voltage values applied to all drivers, and the dimension of the control voltage vector is the same as the number of drivers in the deformable mirror;

[0036] Step 2: use Circle chaotic mapping method to generate the initial position corresponding to each individual to ensure the initial diversity of the population;

[0037] Step 3: calculate the fitness value of each individual , and sort all individuals according to the fitness value

[0038] , and find the maximum fitness value and the minimum fitness value ;

[0039] ​​Step 4: Select the top PD individuals as discoverers, introduce Levy flight strategy in the discoverer position updating process, update the position of the discoverer using the discoverer position updating formula combined with the Levy flight strategy, and in the discoverer position updating formula, the step length control parameter and the safety threshold of the Levy flight strategy are dynamically adjusted by the double-discriminant dynamic adaptive tuner according to the acceptance rate and population diversity;

[0040] Step 5: Introduce variable spiral search strategy in the follower position updating process, update the position of the follower based on the position of the discoverer according to the follower position updating formula combined with the variable spiral search strategy, continue global and local search, and in the follower position updating formula, the spiral strength and spiral adjustment coefficient of the variable spiral search strategy are dynamically adjusted by the double-discriminant dynamic adaptive tuner according to the acceptance rate and population diversity;

[0041] Step 6: For each sentry individual, determine whether its fitness value is equal to the current global optimal fitness value, if equal, update its position according to the original sentry position updating formula; otherwise, introduce dynamic refraction reverse learning strategy, update the position of the sentry according to the sentry position updating formula combined with the dynamic refraction reverse learning strategy;

[0042] Step 7: After completing one iteration, recalculate the fitness value of each individual , update the maximum fitness value , the minimum fitness value ;

[0043] Step 8: Reduce the population size according to the nonlinear population reduction strategy to reduce the calculation resources;

[0044] Step 9: Determine whether the iteration termination condition (such as the maximum number of iterations or the preset precision) is met, if yes, output the optimal individual position, and output the control voltage vector corresponding to the optimal individual position as the control signal to the driver in the deformable mirror, drive the deformable mirror to perform wavefront correction; otherwise, return to step 3 and continue iteration.

[0045] The wavefront distortion correction method of the embodiment is applied in the SLAO system, which mainly consists of three components: a deformable mirror (DM), a charge coupled device (CCD), and a wavefront controller. Among them, the CCD is responsible for capturing the wavefront distortion information of the laser beam and transmitting these information to the wavefront controller. The wavefront controller adjusts the DM in real time according to the received wavefront data to correct the wavefront aberration, thereby ensuring the accurate recovery of the optical signal.

[0046] During operation, the actual optical path length changes in different sections of the beam due to the curved shape of the DM (Diverterless Damping Mesh), resulting in a corresponding change in the beam phase. This phase change forms a phase conjugate relationship with the phase distortion caused by atmospheric turbulence, thus offsetting the effect of atmospheric turbulence on beam quality. To simulate the phase compensation effect of the DM, a Gaussian mathematical model is typically used, where the compensated phase generated by a single driver can be expressed as:

[0047] (1)

[0048] In formula (1), Representing the The compensation phase generated by the driver This represents the crosslinking value between adjacent drivers in the DM. The normalized pitch representing the driver, and Representing the The coordinates of each driver in the DM Represents the coefficients of the Gaussian function.

[0049] Under the influence of the driving voltage, DM will generate the following phase compensation under the action of each driver:

[0050] (2)

[0051] In formula (2), This represents the phase compensation generated by DM. Representing the The control voltage corresponding to each driver, where M represents the number of driver units in DM.

[0052] In the CFSOC system, Zernike polynomials are widely used to represent wavefront aberrations. A Zernike polynomial is a polynomial defined on the unit circle with a root mean square value of 1. Different orders correspond to different phase characteristics and can be represented in either polar or rectangular coordinates. Table 1 shows the coordinate representations and physical meanings of the first 15 Zernike polynomials.

[0053] Table 1. Coordinate representation and physical meaning of the first 15 Zernike polynomials

[0054]

[0055] The corresponding distorted wavefront can be obtained by weighting multiple Zernike polynomials, and its expression is as follows:

[0056] (3)

[0057] In formula (3), is the distortion wavefront, is the th Zernike polynomial, is the coefficient corresponding to the th Zernike polynomial, the larger the value of is, the more delicate the image represented by the

[0058] th Zernike coefficient is,

[0059] SSA algorithm is a new swarm intelligence optimization algorithm, whose core idea is derived from the foraging behavior and anti-predation behavior of sparrows. This algorithm simulates the group dynamics and information dissemination mechanism of sparrows when they are searching for food. In a sparrow population, individuals usually play three roles: discoverer (or producer, leader), follower, and alarmist (or early warning sparrow). Through the interaction of these three roles and the reaction mechanism of sparrows when they face danger, the algorithm achieves a balance between global search and local development. The discoverer is responsible for exploring new food resources (solutions), which is equivalent to searching for potential global optimal solutions in the parameter space. During the search process, the discoverer will preferentially obtain food (i.e., better solutions) and provide foraging areas and directions for other sparrows. The position update strategy of the discoverer takes into account the global search capability, ensuring that the algorithm can explore the entire search space. In the SSA algorithm, the position update formula of the discoverer is as follows:

[0060] (4)

[0061] where and represent the current iteration number and the maximum iteration number, respectively; represents the th sparrow's position at the current iteration number, represents the dimension; and are random numbers between 0 and 1 (excluding 0), where is an important parameter that controls the flight behavior of individuals; is a safety threshold that measures whether the discoverer's position is safe, and its value range is [0.5, 1]; is a 1 × D matrix with all elements being 1; is a random number following a normal distribution. If , it means that the current position is temporarily safe, and there is no predator in the surrounding environment, so the discoverer can search for food in a larger area. If which means that the traces of predators are found at the current position, and the finder needs to go to other safe areas for foraging activities. In the wavefront correction, the behavior of the finder can be understood as a large adjustment of the deformable mirror parameters to find the globally optimal correction method.

[0062] The follower follows the finder foraging to increase the exploration depth of the local area. The position update strategy of the follower relies on the information near the current optimal position to make local optimization based on the current solution. Through local search, the follower can further improve the accuracy and convergence of the solution. The role of the follower is equivalent to further refining and adjusting the state of each driver after a relatively good correction is found initially, ensuring that the distortion compensation is more accurate. The position update formula of the follower is:

[0063] (5)

[0064] wherein, represents the optimal position occupied by the finder in the th iteration so far. represents the worst position occupied by the group in the th iteration. is a 1 × D matrix, the elements of the matrix are randomly assigned as 1 or -1, and . is the population size. If , it means that the current follower is at the edge of the entire population and has no food. At this time, the follower needs to go to other places to find food, otherwise the follower will follow the finder's pace to forage.

[0065] The alarm is responsible for monitoring the surrounding environment and issuing an alarm signal to avoid falling into a local optimal solution. When the sparrow population realizes the danger, the alarm will trigger an anti-predation behavior, such as calling for help and quickly flying away from the dangerous area, as shown in formula (6). This helps the algorithm jump out of the local optimum and continue to search for a better solution in the entire search space. This mechanism of jumping out of the local optimum helps to find a better correction solution in a complex distortion scenario.

[0066] (6)

[0067] In formula (6), is the current global optimal position; is a step control parameter, which is a normal distribution of random numbers with a mean of 0 and a variance of 1; is also a step control coefficient, which is a random number of ; is the fitness value of the current sparrow; and are the best fitness value (also known as the maximum fitness value) and the worst fitness value (also known as the minimum fitness value) of the current iteration number, respectively; is the minimum constant to avoid zero-division error. represents the position of the population center, around which it is safe. If , it indicates that the individual is on the edge of the population and is easily preyed upon by natural enemies. If , it means that the individual is located in the center of the population. At this time, the sparrow needs to be close to other individuals to reduce the possibility of being captured. The fitness value in this embodiment is calculated using the evaluation index of mixing efficiency (ME).

[0068] The SSA algorithm is a swarm intelligence-based optimization algorithm that performs global and local search by simulating the dynamic behavior of sparrow groups in the search space. This algorithm has strong global search capability and can help the searcher jump out of the local optimal solution, while also being able to fine-tune the solution through local search. In the CFSOC system, the control voltage needs to find a balance between global optimization and local optimization. The use of the SSA algorithm can effectively improve the precision of voltage control and the effect of wavefront distortion correction, while avoiding falling into a local optimum. The SSA algorithm has strong adaptability and can handle various types of optimization problems. It does not rely on gradient information, so it performs well in complex nonlinear optimization problems such as the CFSOC system. In the process of wavefront distortion correction, the update process of the control voltage usually involves complex nonlinear relationships. The SSA algorithm, through the natural selection mechanism, can adaptively optimize according to the complexity of the problem, thereby improving the control efficiency and the quality of the solution. Therefore, the introduction of SSA as the control algorithm of the CFSOC system not only improves the global optimization capability of the system, but also maintains high precision, efficiency and robustness when solving the voltage optimization problem in wavefront distortion correction. Through the adaptive, global and local search capabilities of the SSA algorithm, local optimal solutions can be effectively avoided, the control voltage of the deformable mirror can be optimized, and the overall performance of the system can be improved.

[0069] II. Multi-strategy enhanced sparrow search (MESSA) algorithm

[0070] To enhance the adaptability of the algorithm in strong atmospheric turbulence, the present invention improves the SSA algorithm by introducing the Circle chaotic mapping method, Levy flight strategy and variable spiral search strategy. The improved algorithm exhibits stronger global search capability and local development capability in high-dimensional and complex optimization problems. These improvements make the algorithm more suitable for complex environments such as atmospheric turbulence, improve the precision of wavefront distortion correction, enhance the robustness and calibration performance of the system, and significantly improve the ability to optimize signals and reduce bit error rate.

[0071] (1) Circle chaotic mapping method:

[0072] In the SSA algorithm, the initialization of the population is crucial to the performance of the algorithm. The traditional SSA algorithm uses random initialization of the population, but this randomness is strong, which may lead to a lack of diversity in the population initialization, affecting the convergence speed and global search ability of the algorithm. Therefore, in order to improve the diversity of the initialized population and the controllability of the algorithm, the Circle chaotic mapping method is introduced to improve the population initialization of SSA. Circle chaotic mapping is a chaotic mapping based on trigonometric functions, which can generate stable and ordered sequences, and has good periodicity. By introducing Circle chaotic mapping into the SSA algorithm, the diversity of population initialization can be effectively improved, thereby improving the performance of the algorithm. The Circle chaotic mapping method is used to generate the initial position of each individual, and the specific process includes the following steps:

[0073] Step 2.1, initialization: randomly generate chaotic values with initial value and ensure .

[0074] Step 2.2, iteration: iterate the initial value using the mapping formula to generate new chaotic values ; wherein the mapping formula is as follows:

[0075] (7)

[0076] wherein is the chaotic value obtained by the th iteration, and the initial value satisfies is the core part of generating chaotic sequences, which realizes periodic mapping through trigonometric functions; is a random number, taking value in the range of [0, 1], used to increase randomness; is a scaling factor, used to control the weight of the trigonometric function term and the random term in the mapping function.

[0077] Step 2.3, stopping condition: when the number of iterations reaches the preset maximum number of iterations, stop the iteration generation process, and record the generated chaotic values to obtain the chaotic sequence.

[0078] Step 2.4, store sequence: store the generated , that is, the chaotic sequence, and use the generated chaotic sequence as the basis for population initialization in the algorithm, each in the chaotic sequence corresponds to the position of an individual.

[0079] (2) Levy flight strategy:

[0080] In the SSA algorithm, the update mechanism of the population has certain limitations. The individual update formula of the same role is the same, which may cause multiple individuals to stay in the same optimal position. The high repetition rate of solutions will reduce the efficiency of the algorithm, which is not conducive to the optimization process. In order to solve this problem, Levy flight strategy is introduced to increase the randomness of solutions and enrich the diversity of population positions. This helps to avoid the premature convergence of the population to local optimal solutions, thereby improving the global search ability and optimization efficiency of the algorithm.

[0081] Levy flight follows the principle of Levy distribution, which has the characteristics of long and short range random steps, and can explore the solution space in a larger range. After adding the Levy flight strategy, the position formula of individuals in the population is as follows:

[0082] (8)

[0083] where, represents the position of the th individual at the th iteration; represents the position of the th individual at the th iteration after adding Levy flight; is a dot product symbol, representing point-to-point multiplication; is a step length control parameter, which is obtained by the following formula:

[0084] (9)

[0085] where, is a randomly selected individual position; is a path following distribution, representing the introduced flight strategy, which satisfies the following conditions:

[0086] (10)

[0087] where, is a normally distributed random number.

[0088] By introducing the Levy flight strategy, the algorithm can search in a wider solution space, thereby effectively improving the population diversity and enhancing the global search ability, ultimately improving the optimization efficiency of the algorithm. Because the Levy distribution is very complex, the Mantegna algorithm is usually used to simulate it. The introduction of Levy flight strategy makes the searcher more flexible in this stage and can guide other individuals to find better positions and get rid of the constraints of local extrema. After introducing the Levy flight strategy, the position update formula of the finder is:

[0089] (11)

[0090] (3) Variable spiral search strategy:

[0091] In traditional search mechanisms, followers update their positions based on the positions of discoverers, which can lead to a lack of diversity in search patterns, easily falling into local optimal solutions. To solve this problem, inspired by the rotation operation in the whale algorithm, a variable spiral search strategy is introduced, which enhances the flexibility of follower position updates, allowing it to develop diverse search paths, thereby balancing the global and local search of the algorithm. Figure 2 The path of spiral search is shown.

[0092] In the process of updating the position of the follower, the spiral strength should be kept fixed shape, but the fixed shape will lead to a single search mode, increasing the possibility of falling into local optimal solutions, thereby weakening the search ability of the algorithm. To solve this problem, an adaptive variable is designed to dynamically adjust the spiral shape of the follower search. This adjustment can help the follower explore unknown areas more effectively, improving search efficiency and global search performance of the algorithm. After introducing the variable spiral search strategy, the position update formula of the follower is as follows:

[0093] (12)

[0094] wherein, is a random number, taking values in the range [-1, 1]; is the position of the worst individual in the current iteration; is the position of the discoverer in the optimal position in the current population at the th iteration; is the maximum number of iterations; is the spiral strength; is the spiral adjustment coefficient; is the population size.

[0095] In this formula, the spiral strength is dynamically updated according to the number of iterations and adjusted based on the exponential function. The size and amplitude of the spiral are affected by the characteristics of the cosine function. The spiral adjustment coefficient is set to 3 under static aberration correction, optimizing the search range of the algorithm. As the follower's position updates from large to small, the strategy helps to find more high-quality solutions in the early stage, while reducing invalid work in the later iterations, thereby improving the global optimization performance. At the same time, the spiral characteristics also improve the optimization accuracy of the algorithm.

[0096] In practical applications, the key control parameters of the MESSA algorithm are set as follows: the initial population size = 30, PD = 0.2 , SD = 0.2 , ST = 0.8; initial value in Circle chaotic mapping ∈ [0, 1]; scaling factor = 0.5; a parameter affecting the shape of Levy distribution = 1.5; spiral adjustment coefficient k = 3 in variable spiral search strategy, perturbation term L' ∈ [-1, 1].

[0097] When the MESSA algorithm is applied as an optimization algorithm in the SLAO system, the surface morphology of the DM is changed by adjusting the voltage applied to the DM to achieve wavefront correction. The MESSA algorithm is used as a control algorithm to adjust the voltage of each actuator in the DM, and the target variable of the algorithm is U, where U represents the control voltage of the DM actuator. In order to correct the wavefront distortion, U is continuously updated to adjust the shape of the DM. Mixing Efficiency (ME) can be used as an adaptive evaluation index, and the goal is to optimize ME to the desired value. The optimal ME is determined by the MESSA algorithm, and the optimal voltage signal of the CFSOC system is calculated.

[0098] In the MESSA algorithm, each individual position corresponds to a set of Zernike coefficients, which is then mapped to a set of control voltage values of the DM, which is one-to-one mapped to the actual voltage values of each actuator of the DM. Assuming that the entire population has 30 individuals, there are 30 sets of voltage candidate solutions simultaneously optimized in the search space. The MESSA algorithm continuously updates the position of each individual by finding the global optimal voltage combination, fine-tuning the local adjustment, triggering the anti-local fall mechanism, and optimizing the wavefront correction performance of the DM. In each iteration, the individual position is updated → voltage mapping → DM wavefront response → fitness calculation, forming a closed-loop optimization to ensure that the algorithm output closely corresponds to the physical DM system.

[0099] The MESSA algorithm has the following advantages:

[0100] Stronger global search capability: With the introduction of Circle chaotic mapping and Levy flight strategy, the global search capability of MESSA algorithm has been significantly improved, and the distribution of sparrows in the solution space is more uniform, which can avoid the premature convergence or local optimal situation in traditional algorithms;

[0101] More flexible local development capability: By introducing the variable spiral search strategy, MESSA algorithm not only can globally explore, but also can quickly and effectively search locally in areas that need fine adjustment, which makes the algorithm quickly adapt and optimize the solution in dynamic environments such as atmospheric turbulence;

[0102] Stronger robustness and adaptability: MESSA algorithm can adaptively adjust the search strategy according to the characteristics of the solution space, improve the performance in complex environment (strong atmospheric turbulence), especially in high-dimensional complex system, MESSA algorithm can effectively avoid the common premature convergence and local extremum problem, improve the calibration performance and robustness;

[0103] Improve the bit error rate (BER) and system performance: theoretical analysis and simulation results show that MESSA algorithm not only improves the performance in calibration, but also effectively reduces the BER, in the environment of atmospheric turbulence with large interference, the algorithm adjusts the control voltage dynamically, significantly improves the system performance and optimization efficiency.

[0104] In the present application, in order to verify the feasibility of the algorithm, the wavefront controller is used to serially traverse all individuals to perform the optimization process. When using SSA algorithm and MESSA algorithm, in order to reduce the operation time, the control voltage vector matrix can be mapped to the Zernike coefficient matrix, so as to reduce the search dimension and guarantee the algorithm performance.

[0105] Three, dynamic adaptive MESSA (DA-MESSA) algorithm.

[0106] Atmospheric turbulence experiences real-time fluctuations, so it is necessary to consider the wavefront correction ability of the optimization algorithm under dynamic changes, so as to realize the consistency with the actual conditions. Under the dynamic change of aberration, the adjustment ability of the algorithm is required to be high, and the fixed parameters of MESSA algorithm and the parameters with too regular change are easy to appear insufficient exploration leading to early convergence, or excessive exploration weakening local search precision when dealing with time-varying and uncertainty of aberration. Therefore, the present application proposes a dynamic adaptive MESSA algorithm. DA-MESSA algorithm has three improvements compared with MESSA algorithm:

[0107] (1) A dual-indicator dynamic adaptive regulator (DiDAR) is proposed, which uses acceptance rate and diversity as discriminant signals to adjust the dynamic step control parameters in Levy flight strategy , dynamic spiral strength and dynamic safety threshold , dynamically balance global exploration and local development search, and have stronger robustness;

[0108] (2) A dynamic refraction reverse learning strategy is introduced to enhance the ability of the guard to jump out of the local optimum, improve the global search, significantly improve the population diversity and exploration radius, and improve the overall convergence quality;

[0109] (3) The nonlinear population reduction strategy is adopted to improve the development efficiency of the late iteration. The individuals with poor potential are reduced based on the role ranking, which reduces the computational overhead while ensuring the correction performance, saves the computing resources, and speeds up the algorithm correction speed.

[0110] The above improvements significantly enhance the adaptability and stability of the algorithm in the dynamic aberration scene while maintaining the simplicity of the MESSA algorithm structure.

[0111] (1) Double-discriminating dynamic adaptive tuner:

[0112] The double-discriminating dynamic adaptive tuner is used to adjust the dynamic step control parameter , dynamic spiral strength , and dynamic safety threshold in real time with acceptance rate and diversity as the discriminant signals, dynamically balance global exploration and local development search, avoid premature convergence or invalid diffusion, quickly match the appropriate search scale, reduce the time domain mismatch of fixed parameters and the burden of manual parameter tuning, and have stronger robustness.

[0113] The acceptance rate is the proportion of individuals with improved fitness value to the total number of individuals in each iteration. When the acceptance rate is too small, it means that few individuals perform better in the update. This situation is prone to occur in a dynamically changing environment, and the effect of a certain iteration will show that the acceptance rate is small, indicating that the corresponding strategy should be changed to immediately explore better positions to achieve rapid response. The calculation formula of the acceptance rate is as follows:

[0114] (13)

[0115] Wherein, is an indicator function, and its value is 1 when the condition “ ” is true, otherwise it is 0; is a numerical tolerance, for example , only when the fitness value increases by more than is considered to be a progressive individual; is the population size; is the fitness value function.

[0116] (14)

[0117] Wherein, is a measure of the change in the current acceptance rate compared to the given baseline acceptance rate . In this embodiment, the baseline acceptance rate = 0.25. When When the current acceptance rate is low and the overall optimization is partial, the algorithm should be adjusted to favor global search and strengthen exploration. When the number of individuals increases, it indicates that the current optimization direction is correct, and the solution should be more local to find the optimal solution.

[0118] Diversity The pair-wise average distance of the population is the Euclidean distance between all non-repeated individual pairs, normalized and averaged. This provides overall position information for the entire population, i.e., population position diversity. The population position diversity is the diversity criterion for the present invention, The greater the diversity, the more dispersed the population, and the smaller the diversity, the more concentrated the population, which , if , it is considered too concentrated, and exploration is triggered, with corresponding dynamic adjustment of parameters, if , the diversity meets the standard, and no additional changes are triggered. The population position diversity is calculated as follows:

[0119] (15)

[0120] where and represent the lower and upper bounds of each dimension of the optimization variable, respectively.

[0121] The double-discriminating dynamic self-adaptive parameter tuner adjusts the step size control parameter spiral strength and safety threshold based on the results of the above criteria, and outputs the dynamic step size control parameter , dynamic spiral strength , and dynamic safety threshold .

[0122] Here, the step size control parameter is changed to the dynamic step size control parameter , which is calculated as follows:

[0123] (16)

[0124] (17)

[0125] where , are the dynamic adjustment coefficients at the th and th iterations, with an initial value of 0.01; is a randomly selected individual position; and This is an adjustment coefficient, and it must be a positive number. It is used to control the strength of the influence of acceptance rate and diversity on the step size. and All values ​​should be small, ranging from (0.01 to 0.3), to avoid oscillations. Let the minimum acceptable Euclidean distance be denoted as... This indicates a positive effect when diversity is insufficient. Utilizing dynamic adjustment... The size of the step size is used to control the levy distribution step size control parameter, and the step size is dynamically adjusted to cope with the uncertainties brought about by the dynamic changes in the environment. The larger the value, the greater the exploration intensity, effectively utilizing the ability to escape local search when trapped in local convergence, thus enhancing algorithm performance.

[0126] Dynamic spiral strength and dynamic spiral adjustment coefficient The formulas are respectively

[0127] (18)

[0128] (19)

[0129] in, This is the dynamic screw adjustment coefficient, with an initial value of 3; This represents the maximum number of iterations. and All are adjustment coefficients, with values ​​ranging from (0.01 to 0.3), used to control the influence of acceptance rate and population location diversity on spiral strength.

[0130] The spiral adjustment coefficient in the spiral search It is set to be dynamically variable, and the size of the spiral is adjusted adaptively according to equation (19). Represents the spiral intensity, which can be dynamically adjusted by scaling up or down. Scale-up will favor a large-scale search to enhance exploration, while scaling down will favor a local search to find the optimal solution.

[0131] Dynamic security threshold The formula is:

[0132] (20)

[0133] in, This is a modulating factor used to control the strength of the impact of the acceptance rate on the safety threshold.

[0134] This invention will use the safety threshold It is also adjusted to change dynamically, when the acceptance rate When the value is too low, the safe range should be appropriately reduced to make it easier for individual discoverers to step outside the safe zone to explore, thereby accelerating the optimization process and improving search accuracy.

[0135] In summary, the position updating formula of the discoverer combined with the Levy flight strategy is:

[0136] (21)

[0137] Wherein, Updated by formula (16) and formula (17), Updated by formula (20).

[0138] The position updating formula of the follower combined with the Levy flight strategy is:

[0139] (22)

[0140] Wherein, Updated by formula (19).

[0141] The double-discriminating dynamic adaptive parameter adjuster proposed in the application can effectively deal with the poor adjustment ability and easy-to-trap-in-local-convergence problem of the MESSA algorithm under dynamic aberration, improve the algorithm accuracy and convergence speed, and the simulation results show that the introduction of the dynamic adjustment method greatly enhances the robustness of the algorithm.

[0142] (2) Dynamic refraction reverse learning strategy:

[0143] The forewarners in the SSA algorithm are often in poor positions, and it is often difficult to achieve ideal results when avoiding predators, and they cannot complete the warning task well, therefore, the DA-MESSA algorithm adds a dynamic refraction reverse learning strategy to solve this problem, and the forewarners will move reversely when avoiding predators, so that the improved forewarners are easy to jump out of the local optimal solution, and the ability of the algorithm to search for the global optimal solution is enhanced.

[0144] The principle of the dynamic refraction reverse learning strategy is shown in the lens refraction reverse learning principle diagram shown in Figure 3 In a two-dimensional coordinate system, the horizontal axis of the search interval is , and the vertical axis is regarded as the position of a convex lens. Let the horizontal projection of the object point B be , and the height be ; the image point B* obtained by imaging through the lens has a horizontal projection of and a height of . Based on the geometric similarity relationship, the ratio of the horizontal distance of the object and image relative to the midpoint of the interval is equal to the ratio of the vertical height, so there is:

[0145] (23)

[0146] From equation (23), the explicit expression of the reverse position can be solved.

[0147] (24)

[0148] wherein, with may be understood as the search boundary of the dimension; The scaling ratio of the reverse distance from the relative midpoint is described, In the actual algorithm, the dynamic quantity is set to change with the iteration, which is used to adjust smoothly between the exploration of the far side and the fine-tuning of the near side. The greater the value is, the shorter the reverse distance is, and vice versa, The smaller the value is, the farther the reverse distance is, so in order to jump far in the early stage and jump near in the later stage, It is set to linearly increase from small to large, and its formula is as follows:

[0149] (25)

[0150] wherein, is the current iteration number, is the maximum iteration number, is the minimum value of , and is the maximum value of . Optionally, , .

[0151] Then the position update formula of the guard after combining the dynamic refraction reverse learning strategy is:

[0152] (26)

[0153] wherein, is the fitness value of the current sparrow; is a dynamic quantity that changes with the iteration number.

[0154] The introduction of the dynamic refraction reverse learning strategy effectively enhances the ability of the guard in the DA-MESSA algorithm to easily jump out of the local optimal solution. With the increase of the iteration number, the distance of the reverse jump is dynamically changed, which enhances the stability of the algorithm.

[0155] (3) Nonlinear population reduction strategy:

[0156] Based on the theory that large population is beneficial to global exploration and small population is helpful to local development, the application adopts larger population size in early stage to fully cover the solution space; then implements faster size reduction in middle stage to create conditions for small population focusing development and accelerating convergence in later stage. Considering that size reduction may weaken diversity and induce premature convergence to local optimum, the application introduces a role division mechanism (discoverer, follower, and sentinel) to eliminate individuals by role: it is more capable of maintaining structural diversity while maintaining algorithm performance by preferentially eliminating weaker individuals from each role than unified deletion for the whole population. Further, when determining the number of deletions for each role, the ranking of the optimal individual in the whole population is weighted, and the earlier the ranking, the greater the potential, which corresponds to fewer deletions and more individuals and computing resources, thereby continuously strengthening the development of potential optimal regions.

[0157] The nonlinear population reduction strategy introduced by the application can realize the maintenance of large population for sufficient exploration in early stage, fast reduction in middle stage, and maintenance of small population for enhanced development to accelerate convergence in later stage. The nonlinear population reduction strategy specifically includes the following steps:

[0158] a) determining the population size of the current generation, the formula is as follows:

[0159] (27)

[0160] wherein, is the population size of the current generation; are the upper and lower bounds of the population, respectively; is the maximum number of iterations; is used to round the number of individuals to an integer, ensuring that the population size of the current generation is an integer. b) determining the population size of the current generation by formula (27)

[0161] After that, the ranking of the optimal individual in the whole population of the current generation is weighted by role, and the number of individual reductions for each role is allocated according to the weighted ranking, which is represented by formula:

[0162] (28) In formula (28),

[0163] indicates the number of individual reductions for each role, correspond to the three roles of discoverer, follower, and sentinel, respectively; and are the total population numbers of the last iteration (the th iteration) and the current iteration (the th iteration), respectively; indicates the ranking of the optimal individual in the whole population of the current generation, and are the number of deletions for the discoverer and the follower, respectively.In the next iteration, the role The best individual Ranking within the entire population of this generation. Optional, It is 30. The value is set to 12 to ensure that some individuals are optimized for search later, rather than reducing the number entirely.

[0164] As can be seen from formula (28), the better individual in each role is ranked higher in the overall ranking, the greater the potential, and the more computing resources should be retained for that role, so its reduction share should be relatively smaller; conversely, roles ranked lower should be deleted more appropriately to compress invalid overhead.

[0165] c) After determining the reduction quota for each role, i.e. the number of individuals to be reduced, within each role, individuals corresponding to the number of individuals to be reduced are randomly deleted using a roulette wheel method based on their fitness values. This can protect overall diversity on the one hand, and eliminate low-potential individuals with a higher probability on the other.

[0166] In summary, the uncertainty caused by aberration fluctuations over time means that some fixed or conventionally evolving parameters in the MESSA algorithm often either lead to premature convergence due to insufficient exploration or excessive exploration at the expense of local refinement in dynamic scenarios. To address this, the DA-MESSA algorithm proposed in this invention, without altering the basic MESSA operator structure, addresses three core issues: when to focus on the global perspective, when to focus on the local perspective, and how to escape local limitations more quickly. It proposes three mechanisms: a dual-discriminator dynamic adaptive parameter tuner, a dynamic refraction back-learning strategy, and a nonlinear population reduction mechanism. These mechanisms enable on-demand adjustment of the search scale and population structure, enhancing computational efficiency and improving adaptability, stability, and convergence efficiency in dynamic aberration scenarios. Compared to the traditional SPGD algorithm, the DA-MESSA algorithm proposed in this invention has better real-time correction capabilities and greater stability in solving dynamic aberration problems compared to the MESSA algorithm.

[0167] To verify the correction performance of the proposed DA-MESSA algorithm under dynamic turbulent conditions, this invention uses the MATLAB software platform for simulation analysis and compares it with the classic SPGD algorithm, the traditional SSA algorithm, and the static parameter MESSA algorithm.

[0168] First, the key control parameters for the DA-MESSA algorithm are set as follows: initial population size. =30, PD=0.2 SD=0.2 The initial value of ST is also 0.8. (Initial value in the Circle chaotic mapping) ∈[0,1], scaling factor =0.5, which affects the morphology of the Levy distribution. =1.5; in the variable spiral search strategy, the spiral adjustment coefficient The initial value is 3, and the perturbation term L' is in [-1, 1]. In the simulation process, it is assumed that the laser wavelength is 532 nm, the ratio of the diameter to the focal length of the optical lens is 1, the number of photons in a single bit is 10, the Airy pattern radius is , the quantum efficiency of the detector is 1, 32-unit adaptive DM is used as a wavefront corrector, and the parameter D / r0 is used to measure the strength of atmospheric turbulence, wherein D is the aperture size of the receiving system, and r0 represents the atmospheric coherence length. To further study the influence of the parameter, the application adjusts the value range of D / r0 to generate different Zernike polynomials. The application sets D / r0 to 15 to simulate strong turbulence conditions. In the simulation process, the application randomly generates the coefficients of the 4th to 15th components of the Zernike polynomial to describe the initial aberration wavefront of strong turbulence. Figure 4 (a), (b), (c) in the figure respectively show the set of Zernike polynomials, the corresponding original wavefront and the point spread function (PSF) plane. In order to verify the correction ability of the algorithm in the case of real fluctuation of atmospheric turbulence, the frequency is set to 120HZ, and the Zernike polynomial is randomly disturbed to simulate the change of atmospheric turbulence. Single disturbance randomly selects second-order or third-order aberration, so that the change range is between 75% and 130% of the initial value, which is more realistic for the fluctuation effect of atmospheric turbulence.

[0169] For Figure 4 strong turbulence, after adding random disturbance and wavefront dynamic change, the experiment is repeated 50 times, and the maximum iteration number is set to 50. The DA-MESSA algorithm is used as the control algorithm of the wavefront controller. After the iterative correction of the AO system, the aberration of the light beam is well suppressed. Figure 5 The phase aberration of the corrected light beam and the PSF in the dynamic strong turbulence environment are shown. In order to show the correction ability of the correction system to the light beam, the application randomly selects a group of experiments, and selectively intercepts the results of the algorithm at the 20th and 50th iterations. It can be easily seen that the algorithm shows excellent performance in correcting the phase aberration of the light beam.

[0170] In Figure 5In the middle, Fig. (a) and Fig. (c) show the phase aberration plane of the light beam after 20 and 50 iterations of the algorithm in strong turbulence environment, while Fig. (b) and Fig. (d) show the point spread function of the corresponding aberration of Fig. (a) and Fig. (c). It can be seen from the figure that the distortion of the light beam is basically compensated by the system after 20 iterations of the DA-MESSA algorithm. Therefore, the DA-MESSA algorithm meets the requirements of the system for light beam correction. In the following experiment, in order to avoid contingency, the present application is independently repeated 50 times in strong turbulence and weak turbulence environments respectively. Figure 6 The curves of ME changing with the number of iterations of MESSA algorithm and DA-MESSA algorithm in dynamic turbulence are shown. The horizontal coordinate Iteration represents the number of iterations. Figure 7 The curves of BER changing with the number of iterations of MESSA algorithm and DA-MESSA algorithm are shown. Figure 6 And Figure 7 In the middle, the black curve corresponds to a single independent repeated experiment curve, and the red curve corresponds to the mean curve of 50 repeated simulation data.

[0171] In the middle, Figure 6 Fig. (a) is the ME value change of MESSA algorithm under dynamic aberration. The dynamic aberration causes the ideal solution position to change constantly. It can be seen that the overall convergence curve is relatively scattered, and there are more local convergence situations, more delayed convergence situations, and the overall performance is slightly poor, and the performance is relatively unstable. The minimum number of iterations for the ME value to exceed 0.8 is 12 times, but in the worst case, the ME value reaches 0.808 after 42 iterations, and the average is 20 iterations. More curves have ME values that do not reach 0.9 after 50 iterations, and the average is 30 iterations. Fig. (b) is the ME value change of DA-MESSA algorithm under dynamic aberration. The maximum number of iterations for the ME value to exceed 0.8 is 18 times, and the average is 12 times. The minimum ME value after 50 iterations is 0.9819, and the average value reaches 0.9948. It can be seen from Figure 6 that the ME value converges more stably, and the local convergence and convergence delay are rare, and the overall has strong applicability to solve dynamic aberration correction due to the strong ability of DA-MESSA algorithm to adjust its strategy according to the dynamic changes of the environment.

[0172] Correspondingly, Figure 7Figure (a) in the figure is the change of BER value of 50 repeated experiments of MESSA algorithm, figure (b) is the change of BER value of 50 repeated experiments of DA-MESSA algorithm, compared with MESSA algorithm, DA-MESSA algorithm has obvious convergence speed improvement and precision improvement, and is more stable, and the convergence hysteresis is less, the application can see that DA-MESSA algorithm as the optimization algorithm of SLAO can more effectively reduce the wavefront distortion caused by atmospheric turbulence, realize real-time wavefront correction, and improve communication performance. Figure 8 It is the RMS value and ME value average comparison of MESSA algorithm and DA-MESSA algorithm, which can more obviously compare the convergence accuracy of the two algorithms, DA-MESSA algorithm is more stable than MESSA algorithm, and has better convergence accuracy, and the convergence speed of DA-MESSA algorithm is also significantly improved compared with MESSA algorithm.

[0173] Figure 9 The change of the number of population individuals with the number of iterations is shown, and the main role of the nonlinear population reduction strategy in the DA-MESSA algorithm is to reduce the complexity of the algorithm and save the computing resources, and in the later period, the algorithm speed can be effectively improved. Because a large number of individuals are needed in the early stage of global search to ensure the global convergence of the algorithm, and a small number of individuals are needed in the later stage of local search to ensure the local search performance of the algorithm, therefore, by adding the nonlinear population reduction strategy, the number of population gradually reduces from 30 to 12, effectively reducing the computing resources required by the algorithm and reducing the complexity of the algorithm.

[0174] In order to avoid the particularity of the initial aberration, 20 groups of Zernike polynomials of strong atmospheric turbulence are randomly collected, and are corrected by DA-MESSA algorithm and MESSA algorithm respectively by using dynamic random disturbance coefficient, and the change of their RMS values is recorded, and the results of iteration 20 times and 50 times are selectively intercepted. Figure 10 It is the RMS value comparison when the iteration number is 20, Figure 11 It is the RMS value comparison when the iteration number is 50, which can more obviously show that DA-MESSA algorithm can achieve better accuracy with fewer iteration times. From the 20 iteration results, it can be seen that DA-MESSA algorithm has faster convergence speed, and from the 50 iteration results, it can be seen that DA-MESSA algorithm has better convergence accuracy. The simulation results further show that DA-MESSA algorithm has better correction effect when facing dynamic aberration change, and the calculation efficiency, adaptability, stability and convergence efficiency of DA-MESSA algorithm are enhanced compared with MESSA algorithm. It is shown that DA-MESSA algorithm is more suitable for the case of obvious atmospheric turbulence fluctuation when facing dynamic aberration change.

[0175] The simulation experiment verifies the feasibility of the DA-MESSA algorithm, and the simulation results show that the DA-MESSA algorithm has strong dynamic self-adaptation capability, can effectively correct the wavefront distortion in the dynamic environment, and shows strong stability when facing random disturbance. The DA-MESSA algorithm has significant performance advantage when facing complex atmospheric turbulence, and is more suitable for real-time application of the CFSOC system, and can effectively improve the communication quality and reliability of the CFSOC system.

[0176] In another embodiment, the application provides a coherent free space optical communication system, which mainly comprises a sending end and a receiving end, at the receiving end, the distorted optical signal is corrected by a wavefront distortion correction method, and the wavefront distortion correction method is the wavefront distortion correction method described in the foregoing embodiments.

[0177] The embodiment combines the dynamic adaptive MESSA algorithm with the wavefront distortion correction method, and provides a high-efficiency, stable and adaptive wavefront distortion correction solution for the coherent free space optical communication system, and significantly improves the communication quality and reliability of the coherent free space optical communication system.

[0178] The technical features of the above-described embodiments can be combined arbitrarily, and to make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, however, as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present application.

[0179] The above-described embodiments only express several implementation manners of the application, and the description is more specific and detailed, but it should not be understood as the limitation of the patent scope of the application. It should be pointed out that, for ordinary skilled in the art, without departing from the concept of the application, a number of modifications and improvements can be made, which all belong to the protection scope of the application. Therefore, the patent protection scope of the application should be subject to the appended claims.

Claims

1. A wavefront distortion correction method based on a dynamic adaptive MESSA algorithm, characterized in that, The method is applied to a wavefront-free adaptive optical system, and comprises the following steps: Step 1: initializing sparrow population parameters, including total population size, number of discoverers PD, number of sentinels, maximum iteration number and safety threshold, wherein the position of each individual in the sparrow population in a search space corresponds to a control voltage vector composed of a group of voltage values applied to all drivers of a deformable mirror in the wavefront-free adaptive optical system, and the dimension of the control voltage vector is the same as the number of the drivers; Step 2: generating an initial position corresponding to each individual by using a Circle chaotic mapping method; Step 3: Calculate fitness value for each individual And according to fitness value Sort all individuals and find the maximum fitness value And the minimum fitness value ; Step 4: selecting the first PD individuals as discoverers, introducing a Levy flight strategy in the discoverer position updating process, updating the positions of the discoverers by using a discoverer position updating formula combined with the Levy flight strategy, and dynamically adjusting the step length control parameter of the Levy flight strategy and the safety threshold in the discoverer position updating formula by a double-judgment dynamic adaptive parameter adjuster according to an acceptance rate and population diversity; Step 5: introducing a variable spiral search strategy in the follower position updating process, updating the positions of the followers according to a follower position updating formula combined with the variable spiral search strategy based on the positions of the discoverers, and dynamically adjusting the spiral strength and spiral adjustment coefficient of the variable spiral search strategy in the follower position updating formula by the double-judgment dynamic adaptive parameter adjuster according to the acceptance rate and population diversity; Step 6: for each sentinel individual, judging whether the fitness value thereof is equal to a current global optimal fitness value, if yes, updating the position thereof according to an original sentinel position updating formula, and if not, introducing a dynamic refraction reverse learning strategy, and updating the position of the sentinel according to a sentinel position updating formula combined with the dynamic refraction reverse learning strategy; Step 7: After completion of one iteration, recalculate the fitness value of each individual and update the maximum fitness value , minimum fitness value ; Step 8: reducing the population size according to a nonlinear population reduction strategy; Step 9: judging whether an iteration termination condition is met, if yes, outputting an optimal individual position, outputting a control voltage vector corresponding to the optimal individual position as a control signal to the drivers in the deformable mirror, and driving the deformable mirror to perform wavefront correction, and if not, returning to step 3 and continuing iteration.

2. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 1, characterized in that, In step 2, the process of generating the initial position by using the Circle chaotic mapping method comprises the following steps: Step 2.1: Randomly generating chaotic values of the initial values , and ; Step 2.2: Using a mapping formula on the initial value iterating to generate new chaotic values, the mapping formula being as follows: （7）； wherein, is the chaotic value obtained in the th iteration is the core part of generating chaotic sequence, which realizes periodic mapping through trigonometric functions; is a random number, with a value range of [0, 1]; is a scaling factor; Step 2.3: when the iteration number reaches a preset maximum iteration number, stopping the iteration process, and recording the generated chaotic value to obtain a chaotic sequence; Step 2.4: storing the generated chaotic sequence, each chaotic value in the chaotic sequence corresponding to a position of an individual.

3. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 1, characterized in that, The discoverer position updating formula combined with the Levy flight strategy is: （21）； where, , are the first and second iteration, respectively, the first and second iteration, respectively, the first only sparrow position, represent the dimensions; are random numbers between 0 and 1; and are random numbers between 0 and 1; is the maximum number of iterations; is a 1 x D matrix with all elements equal to 1; is a random number following a normal distribution; is a path following a Levy distribution; The dynamic step size control parameter output by the double-discriminative dynamic adaptive parameter tuner has a formula as follows: （16）； （17）； wherein, , are the dynamic adjustment coefficients at the first and second iterations, respectively; is a randomly selected individual position; , is the acceptance rate, is the baseline acceptance rate; and are adjustment coefficients for controlling the strength of the influence of the acceptance rate and diversity on the step size, and are both positive; is the minimum Euclidean distance acceptable, noted , indicates a positive term in case of lack of diversity; is the population position diversity; The dynamic safety threshold output by the double-discriminative dynamic adaptive parameter tuner has a formula as follows: （20）； wherein, , the dynamically adjusted safety threshold at the first and second iterations, respectively; is a regulation factor for controlling the influence strength of the acceptance rate on the safety threshold.​ 4. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 3, characterized in that, The follower position updating formula combined with the variable spiral search strategy is: （22）； wherein, is a random number with a value range of [-1, 1]; is the position of the worst individual in the current population at the th iteration; is the position of the best individual in the current population at the th iteration; A is a 1 x D matrix, the elements in the matrix are randomly assigned as 1 or -1, and ; , are the dynamic spiral strength and dynamic spiral adjustment coefficient output by the double-discriminant dynamic adaptive parameter tuner respectively, and their formulas are respectively: （18）； （19）； wherein and are adjustment factors for controlling the strength of the effect of acceptance rate and population position diversity on the strength of the spiral.

5. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 3 or 4, characterized in that, Acceptance rate The formula for calculating the acceptance rate is as follows: （13）； wherein, is an indicator function, which has a value of 1 if the condition is true, and 0 otherwise; is a numerical tolerance; is a population size, is a fitness value function.

6. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 3 or 4, characterized in that, Population position diversity The formula for calculating the population position diversity is as follows: （15）； wherein and respectively represent lower and upper bounds of each dimension of the optimization variable.

7. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 4, characterized in that, The sentinel position updating formula combined with the dynamic refraction reverse learning strategy is: （26）； wherein, is the fitness value of the current sparrow; ∈ [-1, 1] is a random number; is a dynamic quantity that varies with the number of iterations.

8. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 1, characterized in that, The nonlinear population reduction strategy comprises the following steps: a) determining the population size of the current generation; b) weighting the ranking of the optimal individual in each role in the entire population of the current generation according to the role, and distributing the individual reduction number of each role according to the weighted ranking; c) respectively in each role, deleting individuals in a roulette wheel manner according to the individual fitness value, and the number of the deleted individuals is the individual reduction number corresponding to the role.

9. The wavefront distortion correction method based on dynamic adaptive MESSA algorithm according to claim 8, characterized in that, The size of the present population The formula for the calculation is as follows: （27）； wherein, is the number of generations; is the population size of the current generation; are the upper and lower bounds of the population, respectively; is the maximum number of iterations; is the number of individuals rounded to an integer, ensuring that the population size of the current generation is an integer; The calculation formula of the individual reduction number of each role is as follows: （28）； wherein, denotes the individual reduction number of each role, respectively correspond to the discoverer, follower and guard three roles; and respectively are the total population number of the last iteration and the current iteration; In the first iteration, the role of the optimal individual in the whole population of this generation.

10. A coherent free space optical communication system, characterized by The wavefront distortion correction method according to any one of claims 1 to 9 is used for wavefront distortion correction of a wavefront-free adaptive optical system.

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