Wavefront aberration compensation method based on nonlinear response cascade model

Abstract

The present invention discloses a wavefront aberration compensation method based on a nonlinear response cascade model, which uses the frequency reconstruction technology in the process of establishing a Bouc-Wen hysteresis model of a fast steering mirror (FSM). The frequency reconstruction technology can overcome the zero-point drift characteristics of piezoelectric ceramic materials and improve the accuracy and robustness of Bouc-Wen hysteresis modeling. Subsequently, the present invention uses the hysteresis model of FSM for a wavefront corrector with a cascade structure of FSM and a deformable mirror (DM), and proposes a wavefront closed-loop compensation method based on absolute phase distortion based on the model structure of the nonlinear response cascade of the wavefront corrector. Taking absolute phase distortion as the fitting target avoids the accumulation of model errors and hardware noise, so that the wavefront corrector of the FSM and DM cascade can complete the correction of the wavefront with only one closed-loop feedback, thereby improving the compensation capability range, accuracy and efficiency.

Description

Technical Field

[0001] The present invention relates to the fields of free space optical communication (FSOC), vision correction, astronomical observation, and more specifically to a modeling and compensation method for a cascaded wavefront corrector comprising a fast steering mirror (FSM) and a deformable mirror (DM) in an adaptive optics (AO) module used for atmospheric turbulence correction in a free space laser communication system. Background Art

[0002] FSOC occupies untapped carrier frequency bands and can effectively address the spectrum resource shortages currently facing wireless communications. FSOC also offers the advantages of high communication speeds and high security. However, during signal transmission using the atmosphere as a physical channel, laser signals are significantly affected by atmospheric turbulence, resulting in severe phase disturbances that degrade communication quality and stability.

[0003] AO technology corrects optical signals disrupted by atmospheric turbulence by constructing a nonlinear, time-varying system. In engineering, the AO module consists of a wavefront sensor, a wavefront controller, and a wavefront corrector, deployed at the FSOC receiver. The wavefront sensor captures phase information, the wavefront controller performs logical operations, and the wavefront corrector adjusts the spatial phase. The modeling and compensation methods of the wavefront corrector determine the robustness and real-time performance of the AO system's atmospheric turbulence correction.

[0004] The combination of a DM and a Shack-Hartmann wavefront sensor (SHWS) forms the optical path of a common AO system. The introduction of an FSM further enhances the wavefront corrector's correction capability and efficiency. Ideally, incident light passes through a microlens array and is focused onto the camera's photosensitive surface, forming a two-dimensional array of light spots. The coordinates of the light spots at that moment are recorded as reference positions, as shown in Figure 2(a). When an optical signal affected by atmospheric turbulence enters the system, each light spot shifts relative to the reference position, as shown in Figure 2(b). The resulting offset in the x and y directions represents the wavefront aberration captured by the SHWS. To compensate for this aberration, the system drives the wavefront corrector to create equal and opposite offsets, counteracting the spot offset caused by atmospheric turbulence. The extent to which the wavefront-corrected two-dimensional light spot array can approach the reference position and the response frequency at which it can handle wavefront distortion determine the robustness and real-time performance of the laser communication system. Therefore, establishing an accurate and reliable model for the wavefront corrector and providing a compensation method with low time complexity and high correction efficiency play a vital role in the practical application of AO systems. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings of the prior art and provide a wavefront aberration compensation method based on a nonlinear response cascade model. Based on a wavefront corrector with a FSM and DM cascade structure, the present invention addresses the phenomenon of zero-point drift interference in hysteresis modeling of piezoelectric ceramic materials in the FSM by proposing a Bouc-Wen hysteresis modeling method based on frequency reconstruction for the FSM. Furthermore, a closed-loop compensation method based on absolute phase distortion is proposed to address the nonlinear cascade model of the wavefront corrector.

[0006] The specific technical solutions adopted in the present invention are as follows:

[0007] The present invention provides a wavefront aberration compensation method based on a nonlinear response cascade model, comprising the following steps:

[0008] S1. Establish the Bouc-Wen hysteresis model for the fast mirror using frequency reconstruction technology;

[0009] S2. Performing closed-loop wavefront compensation based on absolute phase distortion around a nonlinear response cascade model of a wavefront corrector; the nonlinear response cascade model of the wavefront corrector is composed of a cascade of a complete second-order response model of a deformable mirror and a Bouc-Wen hysteresis model of a fast-reflection mirror obtained in step S1.

[0010] Preferably, the step S1 is specifically as follows:

[0011] A Bouc-Wen hysteresis model with the following form is established for the x-direction offset of the sub-spot captured by the i-th aperture of the Shack-Hartmann wavefront sensor with respect to the fast mirror control signal:

[0012] D x，i [n] = k x，i ×s x [n]+c x，i +h x，i [n]

[0013] h x，i [n]-h x，i [n-1]=α x，i (s x [n]-s x [n-1])-β x，i (s x [n]-s x [n-1])|h x，i [n-1]|-γ x，i |s x [n]-s x [n-1]|h x，i [n-1]

[0014] Among them, D x，i [n] represents the output of the wavefront corrector; n represents the data corresponding to the nth input; represents the modeling input signal, N is the modeling input signal period, and in order to use the least squares method to model, theoretically at least three periods of modeling signal acquisition sample data are required; h x，i [n] describes the hysteresis part of the hysteresis model; k x，i , c x，i , α x，i , β x，i , γ x，i represents the model coefficient;

[0015] The following two intermediate variable sequences are obtained during the modeling process:

[0016] [(s x [1]-s x [0])|h x，i [0]|,(s x [2]-s x [1])|h x，i [1]|,…,(s x [L]-s x [L-1])|h x，i [L-1]|]

[0017] [|s x [1]-s x [0]|hx，i [0],|s x [2]-s x [1]|h x，i [1],…,|s x [L]-s x [L-1]|h x，i [L-1]]

[0018] Where L is an integer multiple of N, representing the amount of data involved in estimating the hysteresis coefficients. The frequency points of the above two intermediate variable sequences are reconstructed separately. Subsequently, the same method is used to establish a Bouc-Wen hysteresis model for the y-direction offset of the sub-spot captured by the i-th aperture of the Shack-Hartmann wavefront sensor with respect to the fast mirror control signal.

[0019] Furthermore, the frequency reconstruction technology is specifically as follows:

[0020] S11. Perform L-point fast Fourier transform on the intermediate variable sequence to obtain L-point discrete spectrum;

[0021] S12, the front of the spectrum obtained from step S11 Extract Positive integer multiples of the frequency and Extract the frequency points corresponding to the high frequency, and put the extracted results into the position corresponding to the subscript of the L-point length zero vector to obtain the extracted spectrum;

[0022] S13, performing L-point inverse fast Fourier transform on the spectrum obtained in S12 to obtain a sequence after frequency point reconstruction;

[0023] The two reconstructed sequences are used to obtain the nonlinear response cascade model of the wavefront corrector through least squares modeling.

[0024] Preferably, the method for performing the wavefront closed-loop compensation based on the absolute phase distortion in step S2 is to correct the phase change value D generated by the wavefront aberration corrector last time by model The additional phase change value required by the wavefront corrector to correct this wavefront aberration is -D residual To calculate the fitting target of this correction; the fitting target D target Expressed as:

[0025] D target =D model --D residual

[0026] Among them, D target , D model , D residualThey are all vectors of length 2P, where P represents the number of light spots captured by the Shack-Hartmann wavefront sensor, and each element represents the x or y direction offset of a certain aperture sub-spot of the Shack-Hartmann wavefront sensor.

[0027] Furthermore, the D model The nonlinear response cascade model of the wavefront corrector is f(·)=[f x，i , f x，2 (·),…,f x，P (·), f y，1 , f y，2 (·),…,f y，P (·)] combined with the current control signal S of the wavefront corrector crt =[s crt，1 , s crt，2 ,…,s crt，M ]Calculated:

[0028] D model =f(S crt )

[0029] Where M represents the number of control signals that the wavefront corrector can accept.

[0030] Furthermore, the D residual is the relative aberration produced by the outside world captured on the Shack-Hartmann wavefront sensor. The wavefront corrector should produce -D residual aberrations to eliminate the captured aberrations.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) The FSM hysteresis modeling method based on frequency reconstruction can overcome the influence of the zero-point drift characteristics of piezoelectric ceramic materials on the robustness and accuracy of the Bouc-Wen hysteresis model.

[0033] (2) Compared with the single DM structure wavefront corrector, the FSM and DM cascade structures as wavefront correctors have a wider correction capability range.

[0034] (3) The compensation method improves the compensation efficiency and reduces the necessary number of closed-loop feedbacks to 1, which helps to improve the response frequency of the AO system.

[0035] (4) Compared with most compensation methods, the root mean square error (RMSE) of the phase plane after compensation is reduced to wavelength, the compensation method of the present invention reduces the RMSE of the phase plane after compensation to wavelength.

[0036] (5) The FSM modeling adopts the calibration method. Each time the modeling is done, data is collected from the experimental platform, so that the model has the ability to describe the FSM usage status and usage environment, thereby enhancing the environmental adaptability of the AO system. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the internal structure of the AO system.

[0038] Figure 2(a) shows the distribution of the two-dimensional array of light spots on the SHWS under ideal input.

[0039] Figure 2(b) shows the distribution of the two-dimensional array of light spots on the SHWS under disturbed input.

[0040] Figure 3 This is a diagram of the hysteresis effect.

[0041] Figure 4 Simulation performance diagram for compensation method. DETAILED DESCRIPTION

[0042] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention may be combined accordingly, provided that there is no conflict between them.

[0043] The present invention focuses on a wavefront corrector with a cascade structure of FSM and DM, and proposes a wavefront aberration compensation method based on a nonlinear response cascade model, which includes the following two parts:

[0044] (1) Bouc-Wen hysteresis modeling method based on frequency reconstruction of FSM.

[0045] Since the modeling principles and processes of the wavefront sensor control signal for the x- and y-direction spot offsets are the same, the modeling process of the x-direction spot offset is introduced below.

[0046] The Bouc-Wen hysteresis model with the following form is established for the x-direction offset of the sub-spot captured by the i-th aperture of the SHWS with respect to the FSM control signal:

[0047] D x，i [n] = k x，i ×s x [n]+c x，i +h x，i [n]

[0048] h x，i [n]-h x，i [n-1]=α x，i (s x [n]-s x [n-1])-β x，i (sx [n]-s x [n-1])|h x，i [n-1]|-γ x，i |s x [n]-s x [n-1]|h x，i [n-1]

[0049] Among them, n represents the data corresponding to the nth input; In order to use the least squares method to model the model, theoretically at least three cycles of modeling voltage acquisition sample data are required; N is the modeling input signal period; h x，i [n] describes the hysteresis part of the hysteresis model; k x，i , c x，i , α x，i , β x，i , γ x，i Represents the model coefficients.

[0050] First estimate the non-hysteresis coefficient k for FSM modeling x，i , c x，i , and then estimate the hysteresis coefficient α x，i , β x，i , γ x，i Therefore, when estimating the hysteresis coefficient, the non-hysteresis coefficient is considered to be a known quantity. The principle used in modeling is the linear least squares principle, and the fitting process is:

[0051]

[0052] Among them, h x，i [n] = D x，i [n]-k x，i ×s x [n]-c x，i From the fitting process, we can see from the second and third columns of the matrix that the modeling involves the following two intermediate variable sequences:

[0053] [(s x [1]-s x [0])|h x，i [0]|,(s x [2]-s x [1])|h x，i [1]|,…,(s x [L]-s x [L-1])|h x，i [L-1]|]

[0054] [|s x [1]-s x [0]|h x，i[0],|s x [2]-s x [1]|h x，i [1],…,|s x [L]-s x [L-1]|h x，i [L-1]]

[0055] Where L is an integer multiple of N, indicating the amount of data involved in estimating the hysteresis coefficient. The frequency reconstruction technique is performed on the above two sequences respectively.

[0056] Frequency reconstruction technology includes the following three steps:

[0057] S1. Perform L-point fast Fourier transform on the sequence to obtain L-point discrete spectrum.

[0058] S2, from the spectrum Extract Positive integer multiples of the frequency and The frequency points corresponding to the high frequency are extracted, and the extracted results are placed at the position corresponding to the subscript of the L-point length zero vector to obtain the extracted spectrum.

[0059] S3. Perform an L-point inverse fast Fourier transform on the spectrum after frequency extraction to obtain a sequence after frequency reconstruction.

[0060] The two sequences after frequency point reconstruction are used to complete the modeling.

[0061] (2) A closed-loop compensation method based on absolute phase distortion is proposed for the nonlinear cascade model of wavefront corrector.

[0062] Regarding the DM in the wavefront corrector, a full second-order response model is adopted. The Bouc-Wen hysteresis model of the FSM and the full second-order response model of the DM are cascaded to form a nonlinear response cascade model.

[0063] It is known that the wavefront corrector control signal used to correct the previous wavefront distortion is S crt =[s crt，1 , s crt，2 ,…,s crt，M ], wavefront corrector nonlinear response cascade model f(·)=[f x，i , f x，2 (·),…,f x，P (·), f y，1 , f y，2 (·),…,f y，P (·)], it can be calculated that under the current control signal S crt The spot offset actively generated by the lower wavefront corrector is:

[0064] D model =f(Scrt )

[0065] The control signal of the wavefront corrector is S crt In the state, SHWS still captures D residual Therefore, the wavefront corrector has generated D model The offset needs to be additionally generated based on D residual Equal and opposite offsets - D residual To offset the wavefront aberration. Therefore, the fitting target of this round of wavefront corrector is:

[0066] D target =D model -D residual

[0067] Among them, D target , D model , D residual It is a vector of length 2P (P represents the number of spots captured by SHWS), and each element represents the x or y direction offset of a certain aperture sub-spot of SHWS. residual D is the relative wavefront distortion generated by the outside world relative to the current state of the wavefront corrector captured by SHWS; target is the absolute wavefront distortion of the current wavefront distortion relative to the reference plane.

[0068] D target The fitting objective of the nonlinear response cascade model can be summarized as the following nonlinear least squares problem:

[0069]

[0070] ste=D target.i -f(S nxt )

[0071] The above nonlinear least squares problems can be solved by Newton's method, Gauss-Newton method, Levenberg-Marquardt method and trust region reflection method.

[0072] Example 1

[0073] The internal structure diagram of the AO system built in this embodiment is shown in Figure 1 .

[0074] Figure 1 The Fine Tracing Camera (Fine Tracing Camera) is not used in the modeling and compensation process.

[0075] Figure 1The FSM uses a deformable mirror provided by Shanghai Nanomotion Displacement Technology Co., Ltd. and accepts two control channels. Each channel accepts an analog input voltage range of 0 to 10V, corresponding to a digital voltage of 0 to 4095. To enable bidirectional movement of the FSM, the present invention defines a reference plane corresponding to a digital voltage of 2048. To accommodate the DM reflective surface radius and SHWS camera frame, the FSM's input digital voltage range is limited to ±400 of the reference plane voltage, i.e., a digital voltage range of 1648 to 2448.

[0076] Considering that the gradient descent method is used in the subsequent compensation design, in order to ensure the speed of gradient descent in finding the optimal solution, the control signal of the wavefront corrector needs to be normalized in advance according to the following formula:

[0077]

[0078] Among them, v x [n] is the FSM control signal affecting the sub-spot's x-direction motion, expressed as a digital voltage. The y-direction control signal is normalized in the same way.

[0079] When modeling FSM, input 10 cycles of x and y control channels in turn. Signal, where N=40, thus 400 sets of modeling sample data can be obtained.

[0080] First estimate the non-hysteresis coefficient k for FSM modeling x，i , c x，i , and then estimate the hysteresis coefficient α x，i , β x，i , γ x，i Therefore, when estimating the hysteresis coefficient, the non-hysteresis coefficient is considered to be a known quantity. The principle used in modeling is the linear least squares principle, and the fitting process is:

[0081]

[0082] Among them, h x，i [n] = D x，i [n]-k x，i ×s x [n]-c x，i The second and third columns of the matrix involve the following two sequences of modeling intermediate variables:

[0083] [(s x [1]-s x [0])|h x，i [0]},(s x [2]-s x [1])|h x，i [1]|,…,(s x

[400] -sx

[399] )|h x，i

[399] ]]

[0084] [|s x [1]-s x [0]|h x，i [0],|s x [2]-s x [1]|h x，i [1],…,|s x

[400] -s x

[399] |h x，i

[399] ]

[0085] In the above formula, L = 400. The frequency reconstruction technique is performed on the above two sequences according to the following three steps:

[0086] Step 1: Perform a 400-point FFT transform on the sequence to obtain a 400-point discrete spectrum with frequency subscripts ranging from 0 to 399.

[0087] Step 2: For frequency points with subscripts between 1 and 200, extract the frequency points with subscripts of 10k, k∈Z; for frequency points with subscripts between 201 and 399, extract the frequency points with subscripts of 400-10k, k∈Z. Store the extracted frequency points in a 400-point zero vector according to their original subscripts as the extracted frequency spectrum.

[0088] Step 3: Perform a 400-point ifft transform on the spectrum after frequency extraction to obtain a sequence after frequency reconstruction.

[0089] The two sequences after frequency reconstruction are used for calculation, and the second and third columns of the modeling matrix are:

[0090]

[0091] and

[0092]

[0093] Figure 3 The model curves showing the hysteresis effect of FSM and model reconstruction.

[0094] Example 2

[0095] After the Bouc-Wen hysteresis model of the FSM is established, a complete second-order response model is established for the DM in the wavefront corrector. The Bouc-Wen hysteresis model of the FSM and the complete second-order response model of the DM are cascaded to form a nonlinear response cascade model of the wavefront corrector.

[0096] It is known that the wavefront corrector control signal used to correct the previous wavefront distortion is S crt =[scrt，1 , s crt，2 ,…,s crt，M ], wavefront corrector nonlinear response cascade model f(·)=[f x，i , f x，2 (·),…,f x，P (·), f y，1 , f y，2 (·),…,f y，P (·)], it can be calculated that under the current control signal S crt The spot offset actively generated by the lower wavefront corrector is:

[0097] D model =f(S crt )

[0098] The control signal of the wavefront corrector is S crt In the state, SHWS still captures D residual Therefore, the wavefront corrector has generated D model The offset needs to be additionally generated based on D residual Equal and opposite offsets - D residual To offset the wavefront aberration. Therefore, the fitting target of this round of wavefront corrector is:

[0099] D target =D model -D residual

[0100] Among them, D target , D model , D residual It is a vector of length 2P (P represents the number of spots captured by SHWS), and each element represents the x or y direction offset of a certain aperture sub-spot of SHWS. residual is the relative wavefront distortion captured by SHWS relative to the current state of the wavefront corrector; D target is the absolute wavefront distortion of the current wavefront distortion relative to the reference plane.

[0101] D target The fitting objective of the nonlinear response cascade model can be summarized as the following nonlinear least squares problem:

[0102]

[0103] ste=D target.i -f(S nxt )

[0104] This example uses the Gauss-Newton method to solve the above nonlinear least squares problem.

[0105] To evaluate the effectiveness of this invention, the phase root mean square error (RMSE) is introduced as an evaluation metric for the input and output phase planes of the AO system. This metric uses the Zernike method to reconstruct the input and output phase planes with the number of SHWS effective apertures as the resolution. The phase RMSE is expressed as follows:

[0106]

[0107] Among them, φ j represents the phase value reconstructed by the Zemike method in the j-th aperture of the SHWS.

[0108] Figure 4 In the simulation environment, a trend chart of 1000 groups of inputs and the corresponding outputs of each group is presented. Figure 4 It shows that for RMSE between The input optical signal with a wavelength and an average wavelength of 0.47 is compensated by the AO system. Except for some 2nd and 3rd order Zernike modes with a large proportion of input, the RMSE of 95% of the output optical signals is between wavelength.

[0109] Finally, simulation shows that the compensation algorithm proposed in the present invention can obtain a convergent correction result after one closed-loop feedback.

[0110] The above examples demonstrate the effectiveness and reliability of the wavefront aberration compensation method based on the nonlinear response cascade model of the present invention.

[0111] It can be seen that the method of the present invention uses the technology of frequency reconstruction in the process of establishing the Bouc-Wen hysteresis model of FSM. The frequency reconstruction technology can overcome the zero-point drift characteristics of piezoelectric ceramic materials and improve the accuracy and robustness of Bouc-Wen hysteresis modeling. Subsequently, the present invention uses the hysteresis model of FSM for the wavefront corrector of FSM and DM cascade structure, and proposes a wavefront closed-loop compensation method based on absolute phase distortion based on the model structure of the nonlinear response cascade of the wavefront corrector. Taking absolute phase distortion as the fitting target avoids the accumulation of model errors and hardware noise, so that the wavefront corrector of the FSM and DM cascade can complete the correction of the wavefront with only one closed-loop feedback, thereby improving the compensation capability range, accuracy and efficiency.

[0112] The embodiment described above is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Persons skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent substitution or equivalent transformation falls within the scope of protection of the present invention.

Claims

1. A wavefront aberration compensation method based on a nonlinear response cascade model, characterized in that: The following steps are involved: S1. Establish the Bouc-Wen hysteresis model for the fast mirror using frequency reconstruction technology; S2. Performing closed-loop wavefront compensation based on absolute phase distortion around a nonlinear response cascade model of a wavefront corrector; the nonlinear response cascade model of the wavefront corrector is composed of a cascade of a complete second-order response model of the deformable mirror and a Bouc-Wen hysteresis model of the fast-reflection mirror obtained in step S1; The frequency reconstruction technology is specifically as follows: S11. Perform L-point fast Fourier transform on the intermediate variable sequence to obtain L-point discrete spectrum; S12, the front of the spectrum obtained from step S11 Extract Positive integer multiples of the frequency and Extract the frequency points corresponding to the high frequency, and put the extracted results into the position corresponding to the subscript of the L-point length zero vector to obtain the extracted spectrum; S13, performing L-point inverse fast Fourier transform on the spectrum obtained in S12 to obtain a sequence after frequency point reconstruction; The two reconstructed sequences are used to obtain the nonlinear response cascade model of the wavefront corrector through least squares modeling; The method for performing wavefront closed-loop compensation based on absolute phase distortion in step S2 is to correct the phase change value D generated by the wavefront aberration corrector last time by model The additional phase change value required by the wavefront corrector to correct this wavefront aberration is -D residual To calculate the fitting target of this correction; the fitting target D target Expressed as: D target =D model -D residual Among them, D target ,D model ,D residual They are all vectors of length 2P, where P represents the number of light spots captured by the Shack-Hartmann wavefront sensor, and each element represents the x or y direction offset of a certain aperture sub-spot of the Shack-Hartmann wavefront sensor.

2. The wavefront aberration compensation method based on the nonlinear response cascade model according to claim 1, characterized in that: The step S1 is specifically as follows: A Bouc-Wen hysteresis model with the following form is established for the x-direction offset of the sub-spot captured by the i-th aperture of the Shack-Hartmann wavefront sensor with respect to the fast mirror control signal: D x,i [n]=k x,i ×s x [n]+c x,i +h x,i [n] h x,i [n]-h x,i [n-1]=α x,i (s x [n]-s x [n-1]) -b x,i (s x [n]-s x [n-1])|h x,i [n-1]| -γ x,i |s x [n]-s x [n-1]|h x,i [n-1] Among them, D x,i [n] represents the output of the wavefront corrector; n represents the data corresponding to the nth input; represents the modeling input signal, N is the modeling input signal period, and in order to use the least squares method to model, theoretically at least three cycles of modeling signal acquisition sample data are required; h x,i [n] describes the hysteresis part of the hysteresis model; k x,i ,c x,i ,α x,i ,β x,i ,γ x,i represents the model coefficient; The following two intermediate variable sequences are obtained during the modeling process: [(s x [1]-s x [0])|h x,i [0]|,(s x [2]-s x [1])|h x,i [1]|,…,(s x [L]-s x [L-1])|h x,i [L-1]|] [|s x [1]-s x [0]|h x,i [0],|s x [2]-s x [1]|h x,i [1],…,|s x [L]-s x [L-1]|h x,i [L-1]] Where L is an integer multiple of N, representing the amount of data involved in estimating the hysteresis coefficients. The frequency points of the above two intermediate variable sequences are reconstructed separately. Subsequently, the same method is used to establish a Bouc-Wen hysteresis model for the y-direction offset of the sub-spot captured by the i-th aperture of the Shack-Hartmann wavefront sensor with respect to the fast mirror control signal.

3. The wavefront aberration compensation method based on the nonlinear response cascade model according to claim 1, characterized in that: The D model The nonlinear response cascade model of the wavefront corrector is f(·)=[f x,1 ,f x,2 (·),…,f x,P (·),f y,1 ,f y,2 (·),…,f y,[ (·)] combined with the current control signal S of the wavefront corrector crt =[s crt,1 ,s crt,2 ,…,s crt,m ]Calculated: D model =f(S crt ) Where M represents the number of control signals that the wavefront corrector can accept.

4. The wavefront aberration compensation method based on the nonlinear response cascade model according to claim 1, characterized in that: The D residual is the relative aberration produced by the outside world captured on the Shack-Hartmann wavefront sensor. The wavefront corrector should produce -D residual aberrations to eliminate the captured aberrations.

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