Identification method of piezoelectric ceramic deformed mirror surface shape response nonlinear model

Abstract

The invention discloses an identification method of a piezoelectric ceramic deformed mirror surface shape response nonlinear model, and belongs to the technical field of adaptive optics. The method comprises the following steps: firstly, transmitting calibration light to a Shack-Hartmann wavefront sensor through a piezoelectric ceramic deformable mirror and a relay optical system; then grouping the piezoelectric ceramic drivers, sequentially applying continuous step, variable period square wave and reduced amplitude triangular wave voltage signals, and synchronously collecting slope data output by a wavefront sensor; extracting the slope of the nearest sub-aperture surrounding area of the driver, calculating the slope in the x / y direction, and synthesizing the slope into a total slope; and finally, the creep characteristic of the surface shape response is fitted through the transfer function model, the resonance characteristic of the surface shape response is fitted through the multi-order resonance model, and the hysteresis characteristic of the surface shape response is fitted through the KP hysteresis model, so that nonlinear characteristic high-precision identification is realized. According to the invention, the open-loop control precision and stability of the piezoelectric ceramic deformable mirror can be improved, and the method can be used for open-loop control of a multi-target adaptive optical deformable mirror.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of adaptive optics, and particularly relates to a piezoelectric ceramic deformable mirror surface shape response nonlinear model identification method, which is suitable for high-precision open-loop control of a piezoelectric ceramic deformable mirror. BACKGROUND

[0002] A deformable mirror is a core component of adaptive optics technology, which has been successfully applied in the fields of astronomical observation, laser beam purification, and medical ophthalmic imaging. Piezoelectric ceramic drivers are widely used in deformable mirrors due to their large stroke, high precision, and high density. In large telescopes, large-aperture piezoelectric deformable secondary mirrors can significantly improve system integration and light energy utilization. Compared with voice coil deformable secondary mirrors, piezoelectric deformable secondary mirrors have the advantages of compact structure, no need for additional displacement sensors or cooling systems, etc.

[0003] Multi-objective adaptive optics is an advanced adaptive optics technology that aims to correct atmospheric turbulence for multiple scientific objectives or in multiple field-of-view directions simultaneously, and is suitable for wide-field observation. Multi-objective adaptive optics usually uses open-loop control, which directly drives the deformable mirror based on prediction or model without relying on real-time feedback. Since there is no feedback loop, open-loop control can respond quickly and has a higher control bandwidth than closed-loop control. However, due to the inherent nonlinear characteristics of piezoelectric ceramic drivers of deformable mirrors, such as creep and hysteresis, the open-loop control accuracy of the system is severely affected, so high-precision open-loop control has great research significance. To improve the closed-loop control bandwidth and achieve high-precision open-loop control, the nonlinear model of the deformable mirror surface shape response needs to be identified, and then the model is used for open-loop compensation.

[0004] Existing technologies usually only detect the nonlinearity of a single driver, i.e., by directly measuring the displacement output of a single driver using a displacement sensor to calibrate the nonlinearity. For example, on each driver of a two-axis piezoelectric ceramic fast steering mirror, a strain sensor is arranged to measure the strain of the driver, thereby obtaining the deflection angle of the fast steering mirror for nonlinearity identification. However, this method has obvious shortcomings in large-aperture, multi-driver deformable mirror systems: configuring a sensor for each driver significantly increases system complexity and cost, and it is difficult to simultaneously measure and solve the nonlinearity of multiple drivers, increasing the detection and solving time and complexity. SUMMARY

[0005] The technical problem solved by the present application is: how to obtain a nonlinear model of a deformed mirror surface shape response without adding an additional sensor to an adaptive optical system, so as to improve the control accuracy and control bandwidth of the deformed mirror. Since a Shack-Hartmann wavefront sensor is usually provided in the adaptive optical system to detect a wavefront, and the influence function of the deformed mirror driver needs to be measured by using the wavefront sensor, the slope output of the deformed mirror when the driver is driven by a specific voltage can be detected by directly using the Shack-Hartmann wavefront sensor, so that fast and efficient nonlinear characteristic identification can be realized. By obtaining the nonlinear model of the piezoelectric ceramic deformed mirror surface shape response, feedforward compensation can be performed, which has important practical significance and application value for improving the open-loop control accuracy and control bandwidth of the deformed mirror.

[0006] Therefore, the present application provides a piezoelectric ceramic deformed mirror surface shape response nonlinear model identification method based on a Shack-Hartmann wavefront sensor. By using multi-signal excitation and sub-area slope processing, high-precision identification of the creep, resonance and hysteresis characteristics of the piezoelectric ceramic deformed mirror can be realized, so that the control accuracy and control bandwidth of the deformed mirror can be significantly improved.

[0007] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0008] The present application provides a piezoelectric ceramic deformed mirror surface shape response nonlinear model identification method, which comprises:

[0009] Step 1: calibrate parallel light and transmit it to a Shack-Hartmann wavefront sensor through a multi-unit piezoelectric ceramic deformed mirror reflection and a relay optical system in sequence; the multi-unit piezoelectric ceramic deformed mirror comprises a plurality of piezoelectric ceramic drivers and a reflective mirror surface;

[0010] Step 2: group the piezoelectric ceramic drivers to ensure that the mechanical coupling error between the drivers in the group is less than a preset threshold;

[0011] Step 3: apply a continuous step voltage signal, a variable period square wave voltage signal and a descending amplitude triangular wave voltage signal to each group of drivers in sequence, and synchronously collect slope data output by the wavefront sensor;

[0012] Step 4: process the slope data by a sub-aperture slope synthesis method;

[0013] Step 5: based on the processed slope data, fit the nonlinear characteristics of the surface shape response of the multi-unit piezoelectric ceramic deformed mirror; the nonlinear characteristics include creep characteristics, resonance characteristics and hysteresis characteristics.

[0014] The present application has the following beneficial effects:

[0015] (1) The present application directly utilizes a Shack-Hartmann wavefront sensor in an adaptive optical system, without increasing hardware, significantly simplifies the system architecture, and reduces cost and complexity.

[0016] (2) The present application supports parallel detection of multiple drivers, realizes efficient parallel identification of the nonlinear characteristics of multiple drivers through driver grouping and wavefront slope synchronous acquisition, greatly shortens the detection time, and improves efficiency.

[0017] (3) The present application is compatible with the working process of an adaptive optical system, and is based on wavefront sensor slope calculation, seamlessly connects with the influence function measurement process of a deformable mirror, meets the actual engineering needs, and has strong practicality.

[0018] (4) The present application can effectively reduce the influence of environmental disturbance and noise through an m x m sub-aperture slope synthesis method and multiple signal excitation (continuous step voltage signal, variable period square wave voltage signal, and descending amplitude triangular wave voltage signal), and accurately fits creep, resonance, hysteresis and other nonlinear characteristics through decoupling, thereby providing a high-precision model for open-loop control compensation.

[0019] (5) The present application uses a 2-5 order transfer function to fit the creep, uses multiple series second-order models to fit the resonance, and uses a KP (Krasnosel'skii-Pokrovskii) model to fit the hysteresis, so that the model has few parameters, high fitting precision, and a relatively simple control algorithm, and is easy to implement in engineering.

[0020] (6) The nonlinear model identified by the present application can be used for feedforward compensation, which can significantly improve the open-loop control precision and control bandwidth of the deformable mirror, and solve the control precision problem caused by nonlinear errors in the traditional control method. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 It is a flowchart of the piezoelectric ceramic deformable mirror surface shape response nonlinear model identification method of the present application.

[0022] Figure 2 It is a test optical path schematic diagram of the present application; the meaning of the reference signs in the figure is as follows: 1 is a collimator, 2 is a piezoelectric ceramic deformable mirror, 3 is a secondary mirror, 4 is a lens, and 5 is a Shack-Hartmann wavefront sensor.

[0023] Figure 3 It is a schematic diagram of the resonance identification sampling point reorganization method in the present application.

[0024] Figure 4 It is a schematic diagram of the descending amplitude triangular wave voltage signal used for hysteresis identification in the present application.

[0025] Figure 5 It is a simulation effect diagram of using different numbers of sub-apertures of a wavefront sensor to calculate slopes in the present application. DETAILED DESCRIPTION

[0026] The application will be further described below in conjunction with the accompanying drawings and examples.

[0027] The term "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations.

[0028] The terms "first", "second", and the like, do not denote any ordinal, sequential, or passable relationship. It is possible that implementations are distinguished by these terms and can be identical to some other implementations.

[0029] The term "comprises" or any other similar term are intended to encompass non-exclusive inclusion such that processes, methods, articles, or apparatuses / apparatuses that comprise a list of elements do not necessarily include only those elements in the list, but can include other elements not expressly listed or inherent to such processes, methods, articles, or apparatuses / apparatuses.

[0030] In addition, for the purpose of clarity and a concise description, numerous specific details are set forth in the following detailed description. It should be understood that the application can be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been described in detail in order to avoid obscuring the application.

[0031] Figure 1 A flow chart of the method for identifying the piezoelectric ceramic deformable mirror surface shape response nonlinear model of the application is shown in FIG. 1, which comprises the following steps: Figure 1

[0032] Step 1, system configuration: calibrate parallel light is reflected by a plurality of piezoelectric ceramic deformable mirrors and transmitted to a Shack-Hartmann wavefront sensor by a relay optical system; the plurality of piezoelectric ceramic deformable mirrors comprise a plurality of piezoelectric ceramic drivers and a mirror surface.

[0033] Exemplarily, the calibration parallel light is generated by a calibration light source, which comprises a collimator; the relay optical system comprises a secondary mirror and a lens.

[0034] Step 2, grouping the plurality of piezoelectric ceramic drivers to ensure that the mechanical coupling error between the drivers in the group is less than a preset threshold.

[0035] Step 3, signal loading and data acquisition: a continuous step voltage signal, a variable period square wave voltage signal, and a descending amplitude triangular wave voltage signal are sequentially applied to each group of drivers, and the slope data output by the wavefront sensor is synchronously collected.

[0036] ​Exemplarily, the loading duration of the sustained step voltage signal is greater than or equal to the loading duration of the variable period square wave voltage signal and the loading duration of the decreasing amplitude triangular wave voltage signal; the wave front sensor sampling frequency corresponding to the sustained step voltage signal is less than or equal to the wave front sensor sampling frequency corresponding to the variable period square wave voltage signal and the wave front sensor sampling frequency corresponding to the decreasing amplitude triangular wave voltage signal. The loading duration refers to the duration of applying the voltage signal to the driver; the wave front sensor sampling frequency refers to the frequency of collecting the slope data output by the wave front sensor when the voltage signal is applied to the driver.

[0037] Exemplarily, the loading time of the sustained step voltage signal is relatively long, and the corresponding wave front sensor sampling frequency is relatively low, which is used for creep characteristic identification.

[0038] Exemplarily, the variable period square wave voltage signal contains n square wave periods with the same high level duration and decreasing low level duration, and the loading frequency (i.e. the frequency of applying the voltage signal to the driver) of the variable period square wave voltage signal is n times of the corresponding wave front sensor sampling frequency. The wave front sensor sampling frequency corresponding to the variable period square wave voltage signal can be relatively high, which is used for resonance characteristic identification. The calculation formula of the low level duration in the kth period of the variable period square wave voltage signal is as follows:

[0039]

[0040] wherein, represents the high level duration in each period of the variable period square wave voltage signal, represents the wave front sensor sampling frequency corresponding to the variable period square wave voltage signal.

[0041] Exemplarily, the voltage range of the piezoelectric ceramic driver is -V max / 2~V max / 2 (i.e. the full stroke voltage is V max ), the decreasing amplitude triangular wave voltage signal starts from the middle point 0V of the voltage range of the piezoelectric ceramic driver, the amplitude of the first period is the full stroke voltage V max (i.e. -V max / 2~V max / 2), the amplitude of each subsequent period decreases by 2 / L of the full stroke voltage V max , L is an even number, and the amplitude is zero after L / 2 periods (i.e. the number of periods of the decreasing amplitude triangular wave voltage signal is L / 2), and the voltage signal returns to the starting position 0V. The wave front sensor sampling frequency corresponding to the decreasing amplitude triangular wave voltage signal can be relatively high, which is used for hysteresis characteristic identification.

[0042] ​​Exemplarily, the collected slope data includes a first slope signal, a second slope signal and a third slope signal; wherein the first slope signal is the slope data collected when a continuous step voltage signal is applied to each group of drivers; the second slope signal is the slope data collected when a variable period square wave voltage signal is applied to each group of drivers; and the third slope signal is the slope data collected when a descending amplitude triangular wave voltage signal is applied to each group of drivers.

[0043] Step 4, slope signal processing: processing the slope data by a sub-aperture slope synthesis method.

[0044] Exemplarily, step 4 specifically includes:

[0045] (1) For each driver, extracting the sub-aperture slope in the m x m sub-aperture region around the nearest sub-aperture from the collected slope data, m > 1.

[0046] (2) According to the sub-aperture slope, calculating the x-direction slope and the y-direction slope of each driver, and synthesizing the total slope of each driver.

[0047] The x-direction slope and the y-direction slope can be calculated by average difference, and the total slope is synthesized, and the calculation formulas are respectively:

[0048] ;

[0049] ;

[0050] ;

[0051] wherein m represents the number of rows and columns of the taken sub-aperture region, represents the x-direction slope of the i-th row and j-th column sub-aperture, represents the y-direction slope of the i-th row and j-th column sub-aperture.

[0052] Step 5, nonlinear model identification: fitting the nonlinear characteristics of the multi-unit piezoelectric ceramic deformable mirror surface shape response based on the processed slope data; the nonlinear characteristics include creep characteristics, resonance characteristics and hysteresis characteristics.

[0053] Exemplarily, step 5 specifically includes:

[0054] (1) Based on the processed first slope signal, fitting the creep characteristics by a transfer function.

[0055] As an example, the first slope signal processed by step 4 can be fitted by a 2~5 order transfer function to obtain the creep characteristic of the piezoelectric ceramic deformable mirror surface shape response.

[0056] (2) Based on the processed second slope signal, the resonance characteristic is fitted by a multi-order resonance model.

[0057] As an example, the last 2~n period sampling points of the second slope signal can be filled to the first period (i.e. resonance identification sampling point reorganization), forming equivalent high sampling rate data, and then the equivalent high sampling rate data is processed by step 4, and the processed equivalent high sampling rate data is fitted by a plurality of second-order resonance models in series to obtain the resonance characteristic of the piezoelectric ceramic deformable mirror surface shape response; n is the number of periods of the variable period square wave voltage signal.

[0058] (3) Based on the processed third slope signal, the hysteresis characteristic is fitted by a KP hysteresis model.

[0059] As an example, the third slope signal processed by step 4 can be fitted by an L-order KP hysteresis model to obtain the hysteresis characteristic of the piezoelectric ceramic deformable mirror surface shape response; L is twice the number of periods of the amplitude-reducing triangular wave voltage signal.

[0060] The principle and working process of the application are as follows: when the optical system is working, the light beam emitted by the calibration light source is reflected by the piezoelectric ceramic deformable mirror and transmitted to the Shack-Hartmann wavefront sensor through the relay optical system, and the dynamic response of the deformable mirror surface shape is obtained by using the inherent wavefront detection function. First, the deformable mirror driver (i.e. piezoelectric ceramic driver) is grouped to ensure the independence between the drivers; then three specially designed voltage signals are applied in turn: the continuous step voltage signal is used to excite and measure the creep characteristic, the variable period square wave voltage signal is used to capture the resonance characteristic, and the amplitude-reducing triangular wave voltage signal is used to represent the hysteresis characteristic, while the slope data output by the wavefront sensor is collected synchronously at an optimized sampling frequency. For each driver, the wavefront slope in the surrounding sub-aperture region affected by the driver is extracted, and the average differential slope in the x and y directions is calculated to effectively suppress noise interference, and finally the total slope signal is synthesized to improve the signal-to-noise ratio. Finally, the 2~5 order transfer function is used to fit the creep characteristic, the signal is reorganized and the second-order resonance model is used to analyze the resonance characteristic, and the KP hysteresis model is used to analyze the hysteresis characteristic, thereby establishing a complete nonlinear mathematical model. The model can be directly embedded in the control algorithm of the adaptive optical system, and through the feedforward compensation of the control voltage, the problem of insufficient precision caused by nonlinear error in the traditional control method is effectively overcome, and the control precision and response bandwidth of the deformable mirror are significantly improved.

[0061] The application realizes a high-efficiency piezoelectric ceramic deforming mirror surface shape response nonlinear model identification method based on a Shack-Hartmann wavefront sensor, and through a carefully designed multi-mode voltage excitation signal and a wavefront slope processing technology, the creep, resonance and hysteresis characteristics of the deforming mirror are accurately modeled without increasing additional hardware, and the control accuracy and control bandwidth of the deforming mirror are significantly improved.

[0062] The piezoelectric ceramic deforming mirror surface shape response nonlinear model identification method of the application will be described in detail below with reference to the accompanying drawings and embodiments.

[0063] In the embodiment of the application, first, a test optical path composed of a calibration light source (including a collimator 1), a piezoelectric ceramic deforming mirror 2, a relay optical system (including a secondary mirror 3 and a lens 4), a Shack-Hartmann wavefront sensor 5 and a controller is built as shown in the figure. Figure 2 The controller is used to generate a voltage signal of the piezoelectric ceramic driver of the deforming mirror, and collect a slope signal output by the Shack-Hartmann wavefront sensor 5. In the optical system initialization stage, the piezoelectric ceramic drivers are grouped according to the mechanical coupling characteristics between the piezoelectric ceramic drivers, the interval between the drivers in each group is greater than 3 times the interval between the adjacent drivers, and the coupling error of each group of drivers is less than 5%.

[0064] During the test, three specially designed voltage signals are applied to each group of drivers in turn: a continuous step voltage signal, a variable period square wave voltage signal and a descending amplitude triangular wave voltage signal.

[0065] The continuous step voltage signal applied for more than 10 minutes is used to stimulate the creep characteristics, and the slope data output by the wavefront sensor is collected at a low sampling frequency of not more than 1 Hz.

[0066] The variable period square wave voltage signal is designed by decreasing the interval time, and the wavefront sensor sampling frequency is greater than or equal to 10 Hz to capture the resonance characteristics, and the method of filling the data from the later period to the former period is used to reorganize the equivalent high sampling rate data. Figure 3 The reorganization mode of the sampling points in the resonance identification in the application is shown in the figure, Figure 3 The (a) in the figure shows the variable period square wave voltage signal, the resonance output signal and the misaligned sampling points before reorganization, Figure 3(b) in FIG. 1 shows the square wave signal after recombination of sampling points, the resonant output signal, and the equivalent sampling points; wherein n=5, the wavefront sensor sampling frequency corresponding to the variable period square wave voltage signal is 50Hz, the charging frequency (i.e. loading frequency) corresponding to the variable period square wave voltage signal is 250Hz, and the simulated resonant frequency is 40Hz; the first square wave low level duration is 0.496s, the second square wave low level duration is 0.492s, and so on, and the fifth square wave low level duration is 0.48s. Due to the fixed sampling frequency, this charging method makes a complete resonant output be misaligned sampling, fills the last 4 period sampling points into the first period, obtains equivalent high sampling rate data, and the equivalent high sampling rate data has an equivalent sampling frequency of 250Hz, thereby satisfying the Nyquist sampling theorem and being able to identify the resonant frequency of 40Hz.

[0067] Figure 4 FIG. 1 shows a schematic diagram of a triangular wave voltage signal with a decreasing amplitude used for hysteresis identification in the application, as shown in Figure 4 As shown in FIG. 1, the normalized voltage range is -1V~1V (i.e. the full stroke voltage is 2V), L=10, that is, the triangular wave voltage signal with a decreasing amplitude decreases the amplitude by 20% (i.e. the positive and negative voltages each decrease the full stroke voltage by 10% per period, that is, the positive and negative voltages each decrease by 0.2V per period), and the amplitude is zero after 5 periods. Sampling is performed once every interval 1 / L for charging, which is used to record the formation process of the hysteresis loop completely.

[0068] In the data processing stage, a 3x3 sub-aperture region corresponding to each driver is selected, and noise interference is suppressed by excluding the central sub-aperture and calculating the average differential slope of the peripheral sub-aperture. Figure 5 FIG. 1 shows a simulation effect diagram of slope calculation using different numbers of sub-apertures by a wavefront sensor in the application, and the detection errors (RMS) of 1x1 to 6x6 sub-aperture schemes are simulated respectively by introducing environmental noise, atmospheric disturbance and test nonlinearity, as shown in Figure 5 As shown in FIG. 1, the detection error of the 3x3 sub-aperture region is the smallest under the simulation conditions, which is the optimal scheme. This method significantly improves the signal-to-noise ratio while ensuring spatial resolution. Based on the processed slope data, the creep characteristic model is obtained by fitting the creep characteristic with a 2-3 order transfer function, the resonant characteristic model is obtained by analyzing the resonant characteristic through a series of second-order resonant models, and the hysteresis characteristic model is obtained by matching the nonlinear response under the triangular wave excitation using the KP hysteresis model. Finally, the three types of models are integrated into a complete nonlinear feedforward compensator, which can be directly embedded into the control loop of the adaptive optical system.

[0069] The contents not described in detail in the specification of the application belong to the prior art known to those skilled in the art.

[0070] The above-described specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above-described specific embodiments are merely examples of the present application and are not intended to limit the present application. The above description is exemplary and is not exhaustive, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for identifying the nonlinear model of the shape response of a piezoelectric ceramic deformable mirror, characterized in that, include: Step 1: The calibration parallel light is sequentially reflected by a multi-unit piezoelectric ceramic deformable mirror and transmitted to the Shaker-Hartmann wavefront sensor via a relay optical system; The multi-unit piezoelectric ceramic deformable mirror includes multiple piezoelectric ceramic actuators and a reflective mirror surface; Step 2: Group the multiple piezoelectric ceramic actuators to ensure that the mechanical coupling error between the actuators in the group is less than a preset threshold; Step 3: Apply a continuous step voltage signal, a variable period square wave voltage signal, and a reduced amplitude triangular wave voltage signal sequentially to each group of drivers, and simultaneously acquire the slope data output by the wavefront sensor. Step 4: Process the slope data using the sub-aperture slope synthesis method; Step 5: Based on the processed slope data, fit the nonlinear characteristics of the multi-unit piezoelectric ceramic deformable mirror surface response; the nonlinear characteristics include creep characteristics, resonance characteristics, and hysteresis characteristics.

2. The method according to claim 1, characterized in that, The calibration parallel light is generated by a calibration light source; the calibration light source includes a collimator. The relay optical system includes a secondary mirror and a lens.

3. The method according to claim 1, characterized in that, In step 3, the loading duration of the continuous step voltage signal is greater than or equal to the loading duration of the variable period square wave voltage signal and the loading duration of the amplitude-reduced triangular wave voltage signal. The sampling frequency of the wavefront sensor corresponding to the continuous step voltage signal is less than or equal to the sampling frequency of the wavefront sensor corresponding to the variable period square wave voltage signal and the sampling frequency of the wavefront sensor corresponding to the amplitude-drop triangular wave voltage signal.

4. The method according to claim 1, characterized in that, In step 3, the variable-period square wave voltage signal comprises n square wave periods with the same high-level duration and decreasing low-level duration, and the loading frequency of the variable-period square wave voltage signal is n times the sampling frequency of its corresponding wavefront sensor; the low-level duration in the k-th period of the variable-period square wave voltage signal... The calculation formula is: ； in, This indicates the duration of the high level in each cycle of a variable-period square wave voltage signal. This indicates the sampling frequency of the wavefront sensor corresponding to the variable-period square wave voltage signal.

5. The method according to claim 1, characterized in that, In step 3, the amplitude-reduced triangular wave voltage signal starts from the midpoint of the voltage range of the piezoelectric ceramic driver. The amplitude of the first cycle is the full-stroke voltage of the piezoelectric ceramic driver. The amplitude of each subsequent cycle decreases by 2 / L of the full-stroke voltage, where L is an even number. After a total of L / 2 cycles, the amplitude returns to zero, and the voltage signal returns to the starting position.

6. The method according to claim 1, characterized in that, Step 4 specifically includes: For each driver, extract the sub-aperture slope within the m×m sub-aperture region surrounding its nearest sub-aperture, where m>1; Based on the sub-aperture slope, calculate the x-direction slope corresponding to each actuator. and slope in the y direction And synthesize the total slope corresponding to each driver. .

7. The method according to claim 6, characterized in that, slope in the x direction y-slope and total slope The calculation formulas are as follows: ； ； ； Where m represents the number of rows and columns of the selected sub-aperture region. This represents the slope in the x-direction of the sub-aperture in the i-th row and j-th column. This represents the y-direction slope of the sub-aperture in the i-th row and j-th column.

8. The method according to claim 1, characterized in that, The slope data includes a first slope signal, a second slope signal, and a third slope signal; wherein, the first slope signal is the slope data collected when a continuous step voltage signal is applied to each group of drivers; the second slope signal is the slope data collected when a variable period square wave voltage signal is applied to each group of drivers; and the third slope signal is the slope data collected when a reduced amplitude triangular wave voltage signal is applied to each group of drivers.

9. The method according to claim 8, characterized in that, Step 5 specifically includes: Based on the processed first slope signal, creep characteristics are fitted using a transfer function. Based on the processed second slope signal, the resonance characteristics are fitted by a multi-order resonance model. Based on the processed third slope signal, the hysteresis characteristics are fitted using the KP hysteresis model.

10. The method according to claim 9, characterized in that, In step 5, the creep characteristics are fitted using 2nd to 5th order transfer functions; the resonance characteristics are formed by filling the last 2 to n period sampling points of the second slope signal into the first period to form equivalent high sampling rate data, and fitted using multiple second-order resonance models in series; the hysteresis characteristics are fitted using an L-order KP hysteresis model; where n is the number of periods of the variable period square wave voltage signal; and L is twice the number of periods of the amplitude-reduced triangular wave voltage signal.

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