A fast mirror automatic calibration method and system

Abstract

The present application relates to the field of precision optical measurement and automatic control technology, especially to a kind of fast mirror automatic calibration method and system.The method applies symmetrically optimized drive voltage sequence to fast mirror double channel, constructs geometric mapping matrix based on multi-channel sensor displacement measurement data, adopts least square method to fit voltage-angle sensitivity matrix, and synchronously solves rotation center coordinates and sensitivity matrix parameters in an alternating iterative manner, to realize Rx, Ry axis decoupling control from measurement source.The present application adopts a parameter identification method driven by physical model, with the advantages of clear parameter meaning, strong model generalization ability and high calibration efficiency.

Description

Technical Field

[0001] This invention relates to the field of precision optical measurement and automatic control technology, and in particular to an automatic calibration method and system for fast-reflecting mirrors. Background Technology

[0002] In high-precision beam control systems such as photolithography and laser communication, the pointing accuracy of fast reflectors is crucial. However, the measurement center of sensors such as laser interferometers is difficult to perfectly coincide with the physical rotation center (geometric center) of the fast reflector. This deviation can lead to coupling of the Rx and Ry axes of the fast reflector and introduce nonlinear errors.

[0003] Existing technologies can be summarized into the following two main methods. The first method is the offline calibration method based on external high-precision instruments.

[0004] This is a common practice in high-precision systems. The specific process is as follows: the fast-reflecting mirror system is taken out of operation, and a higher-precision external measuring device (such as a laser interferometer or autocollimator) is used to align with the mirror surface. The mirror is driven to perform a grid scan, and the measurement values ​​of the external device and the readings of the internal sensors are recorded to build a large lookup table or fit a compensation model. After calibration, the external device is removed, and the system is put back into operation. The second type of method is the linear / polynomial compensation method based on an ideal geometric model.

[0005] This is a simplified method that defaults to or roughly measures the measurement center and geometric center and assumes that the deviation between them is very small, thus treating the coupling between Rx and Ry as a simple linear or low-order polynomial relationship; by calibrating within a small angular range, a fixed coupling coefficient is obtained, and fixed reverse compensation is performed in the control algorithm.

[0006] Offline calibration methods are cumbersome and inefficient, requiring system shutdown, installation of peripherals, and lengthy scans. Calibration is costly, time-consuming, and cannot be performed frequently. The system state (temperature, stress) during calibration differs from that during actual operation, and cannot compensate for time-varying errors such as mechanical creep and temperature drift that occur during operation. Furthermore, calibration accuracy heavily relies on the absolute accuracy of external equipment and its alignment with the system, introducing additional error factors.

[0007] Ideal model compensation methods suffer from inaccurate models. Simply fitting an inherently nonlinear geometric problem with linear or low-order polynomials results in extremely large residuals over large angular operating ranges or when high precision is required. Furthermore, once the model parameters are fixed, they cannot detect or correct performance degradation that occurs over time and due to environmental factors. Additionally, for asymmetric and cross-coupling errors caused by the rotation center, simple fixed-coefficient compensation has limited effectiveness, restricting the ultimate pointing accuracy achievable by the system.

[0008] Therefore, there is an urgent need for an algorithm that can automatically and online calibrate the rotation center and achieve real-time high-precision decoupling control to improve the system's pointing accuracy, dynamic performance and long-term stability. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art by providing an automatic calibration method and system for fast-reflecting mirrors, thereby improving the closed-loop bandwidth and long-term stability of the system.

[0010] The objective of this invention can be achieved through the following technical solutions.

[0011] In a first aspect, this application provides an automatic calibration method for a fast-reflecting mirror, comprising the following steps: S1. Set the initial value of the rotation center. A sequence of driving voltages is applied to the drive control channel of the fast-reflecting mirror to obtain calibration source data; S2. The sensor displacement change is obtained by solving the calibration source data. S3. Construct a geometric mapping matrix and use the geometric mapping matrix to calculate the decoupled real mirror rotation angle; S4. Fit the sensitivity matrix using the parameter identification method, and calculate the theoretical mirror rotation angle using the sensitivity matrix; S5. Based on the theoretical mirror rotation angle obtained in S4 and the sensor displacement change measured in S2, construct a linear system with the rotation center coordinates as unknowns, and solve for the updated rotation center. S6. Repeat S3~S5 until the estimates of the rotation center and sensitivity matrix converge to the optimal values ​​simultaneously, and then update the final obtained rotation center and sensitivity matrix into the control system.

[0012] The rotation center is the deviation between the measurement center of the laser interferometer and the geometric center of the fast-reflecting mirror.

[0013] The geometric mapping matrix is ​​constructed through the following steps: Define the coordinates of the rotation center of the fast-reflecting mirror as follows: Let the deflection angles of the mirror around the X-axis and Y-axis be Rx and Ry (in radians), respectively. When Rx and Ry are small angles, the displacement change at the i-th sensor position is... The following linear geometric relationship exists between (along the mirror normal) and the center of rotation and the angle of rotation:

[0014] By writing the measurements from all N sensors into vector form, we obtain the geometric mapping matrix H:

[0015] in,

[0016] The H matrix has a dimension of N×2, and each row consists of the currently estimated rotation center coordinates. Position coordinates of the corresponding sensor The calculation yielded the result.

[0017] The decoupled true mirror rotation angle is calculated using the geometric mapping matrix through the following method: Given the center of rotation Given a set of sensor displacement changes ΔS and mirror deflection angles [Rx, Ry], [the following conditions apply]. T This can be obtained by solving the system of equations corresponding to the above linear geometric relationships; since N≥3, the system is overdetermined, and the least squares method is used to solve it.

[0018] Where H + This represents the pseudo-inverse matrix of H. This solution step, used in the iterative process, is to deduce the mirror deflection angle corresponding to each voltage group from the measured sensor data, starting from the currently estimated rotation center.

[0019] The specific form and fitting method of the sensitivity matrix M are described below: Define the driving voltage of the fast-reflecting mirror as and , Corresponding to the Rx axis, Corresponding to the Ry axis, its distance from the central working point (V 20 V 30 The change in ) is:

[0020] Within the small-angle linear operating region, the mirror deflection angle (Rx, Ry) and the voltage change (ΔV2, ΔV3) approximately satisfy a linear relationship:

[0021] The sensitivity matrix M is a 2×2 matrix, and its form is:

[0022] Main diagonal element m 11 m 22 Represent the voltage-angle sensitivity of CH2 to Rx and CH3 to Ry, respectively; off-diagonal elements m 12 m 21 Indicates cross-coupling sensitivity; Fitting method: During the calibration process, given a series of different voltage combinations (ΔV2, ΔV3) and their corresponding mirror deflection angles (Rx, Ry), the sensitivity matrix M can be obtained through least squares fitting; specifically, all P sets of data are organized as follows:

[0023] The least squares solution to M is:

[0024] The least-squares fitting step of the sensitivity matrix is ​​performed alternately in the iterative algorithm: first, (Rx,Ry) of each group is calculated using the currently estimated rotation center and M is fitted; then, (Rx,Ry) is refined again using M and the rotation center is solved again until convergence.

[0025] The method for updating the final obtained rotation center and sensitivity matrix to the control system is as follows: Based on the real-time sensor reading ΔS, through Calculate the true mirror deflection angle; After comparing the target mirror deflection angle with the actual mirror deflection angle, the controller obtains the desired angle increment, which is then converted into the required voltage change (ΔV2, ΔV3) using the inverse matrix of M. .

[0026] Furthermore, the initial value of the rotation center Configure it in the following way: Suppose that N (N≥3) displacement sensors (e.g., three measurement points of a three-channel laser interferometer) are arranged on the surface of the fast-reflecting mirror, and their position coordinates are known. Let i = 1, 2, ..., N. Then the initial value of the rotation center is... It can be taken as the geometric center of all sensor locations, that is: .

[0027] Furthermore, the driving voltage sequence employs dual-channel independent input, and the driving voltage sequence includes: a single-axis symmetric step sequence, a diagonal symmetric step sequence, and a center regression step.

[0028] Furthermore, the single-axis symmetric step sequence includes: changing the voltage of only one channel while keeping the other channel at zero, and exciting multiple sets of amplitudes with positive and negative symmetry.

[0029] Furthermore, the diagonally symmetric step sequence includes: simultaneously changing the voltages of two channels, including one or more combinations of equal amplitude in the same direction, equal amplitude in opposite directions, and unequal amplitude.

[0030] Furthermore, the center return step includes: after each step or group of voltage excitations, the voltage command returns to zero.

[0031] Furthermore, the geometric mapping matrix is ​​constructed using the rotation center and the equivalent focal length from the fast-reflecting mirror to the sensor.

[0032] Furthermore, the parameter identification method is the least squares method.

[0033] Furthermore, in step S6, when the iteration error is less than or equal to the set tolerance, it is determined that the estimation of the rotation center and the sensitivity matrix converges synchronously to the optimal value.

[0034] Furthermore, the sensor is a built-in sensor of the system.

[0035] In a second aspect, this application provides an automatic calibration system for a fast-reflecting mirror, comprising: The drive and control module uses the host computer as the central control core, runs the fast-reflecting mirror automatic calibration method as described in the first aspect, and generates a precise drive voltage signal through the strain adjustment device. The execution and sensing module applies a drive signal to the piezoelectric fast-reflecting mirror, and its micro-displacement is measured in real time and synchronously by a three-channel laser interferometer through a dedicated fiber optic testing fixture. The foundation and environment modules are placed on an air-floating optical vibration isolation platform to actively isolate ground and air vibrations.

[0036] Compared with the prior art, the beneficial effects of the present invention include: 1. This invention adopts a physical model-driven parameter identification method, which has the advantages of clear parameter meaning, strong model generalization ability and high calibration efficiency. Compared with traditional methods, under the same conditions, it can significantly reduce the static coupling error between Rx / Ry axes and improve the closed-loop bandwidth and long-term stability of the system.

[0037] 2. This method does not require an external reference. It can complete high-precision calibration within a few iterations using only the designed driving voltage sequence and feedback from the system's built-in sensors, providing accurate model parameters for real-time decoupled control.

[0038] 3. The optimized driving voltage sequence of this invention fully utilizes the symmetry of piezoelectric ceramics and the characteristics of the system's linear operating region. It can obtain complete information characterizing the independent channel gain, cross-coupling, and nonlinear characteristics of the system with the fewest excitation steps, while effectively suppressing the impact of hysteresis on calibration accuracy, laying the foundation for subsequent high-precision parameter identification. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the automatic calibration method for the fast-reflecting mirror in this embodiment.

[0040] Figure 2 This is a schematic diagram of the core iterative optimization process of the automatic calibration method for fast-reflecting mirrors in the embodiment.

[0041] Figure 3 This is a schematic diagram of the test system structure for the automatic calibration method of the fast-reflecting mirror in the embodiment.

[0042] Figure 4 This is a schematic diagram of the experimental voltage distribution in the example.

[0043] Figure 5 This is a schematic diagram of the convergence calculation process of the calibration method in the embodiment.

[0044] Figure 6 This is a schematic diagram showing the relationship between the calibration method calculation results and the position of the reference sensor in the embodiment. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0046] like Figure 1 As shown, this application proposes an automatic calibration method for fast-reflecting mirrors, comprising the following steps: S1. Set the initial value of the rotation center. A sequence of driving voltages is applied to the drive control channel of the fast-reflecting mirror to obtain calibration source data; S2. The sensor displacement change is obtained by solving the calibration source data. S3. Construct a geometric mapping matrix and use the geometric mapping matrix to calculate the decoupled real mirror rotation angle; S4. Fit the sensitivity matrix using the parameter identification method, and calculate the theoretical mirror rotation angle using the sensitivity matrix; S5. Based on the theoretical mirror rotation angle obtained in S4 and the sensor displacement change measured in S2, construct a linear system with the rotation center coordinates as unknowns, and solve for the updated rotation center. S6. Repeat S3~S5 until the estimates of the rotation center and sensitivity matrix converge to the optimal values ​​simultaneously, and then update the final obtained rotation center and sensitivity matrix into the control system.

[0047] The rotation center is the deviation between the measurement center of the laser interferometer and the geometric center of the fast-reflecting mirror.

[0048] The geometric mapping matrix is ​​constructed through the following steps: Define the coordinates of the rotation center of the fast-reflecting mirror as follows: Let the deflection angles of the mirror around the X-axis and Y-axis be Rx and Ry (in radians), respectively. When Rx and Ry are small angles, the displacement change at the i-th sensor position is... The following linear geometric relationship exists between (along the mirror normal) and the center of rotation and the angle of rotation:

[0049] By writing the measurements from all N sensors into vector form, we obtain the geometric mapping matrix H:

[0050] in,

[0051] The H matrix has a dimension of N×2, and each row consists of the currently estimated rotation center coordinates. Position coordinates of the corresponding sensor The calculation yielded the result.

[0052] The decoupled true mirror rotation angle is calculated using the geometric mapping matrix through the following method: Given the center of rotation Given a set of sensor displacement changes ΔS and mirror deflection angles [Rx, Ry], [the following conditions apply]. T The equations corresponding to the linear geometric relationship can be obtained by solving the system of equations. Since N≥3, the system is overdetermined, and the least squares method is used to solve it.

[0053] Where H + This represents the pseudo-inverse matrix of H. This solution step, used in the iterative process, is to deduce the mirror deflection angle corresponding to each voltage group from the measured sensor data, starting from the currently estimated rotation center.

[0054] The specific form and fitting method of the sensitivity matrix M are described below: Define the driving voltage of the fast-reflecting mirror as and (corresponding to the Rx and Ry axes respectively), its position relative to the central working point (V) 20 V 30 The change in CH

[0055] Within the small-angle linear operating region, the mirror deflection angle (Rx, Ry) and the voltage change (ΔV2, ΔV3) approximately satisfy a linear relationship:

[0056] The sensitivity matrix M is a 2×2 matrix, and its form is:

[0057] Main diagonal element m 11 m 22 Represent the voltage-angle sensitivity of CH2 to Rx and CH3 to Ry, respectively; off-diagonal elements m 12 m 21 Indicates cross-coupling sensitivity; Fitting method: During the calibration process, given a series of different voltage combinations (ΔV2, ΔV3) and their corresponding mirror deflection angles (Rx, Ry), the sensitivity matrix M can be obtained through least squares fitting; specifically, all P sets of data are organized as follows:

[0058] The least squares solution to M is:

[0059] The least-squares fitting step of the sensitivity matrix is ​​performed alternately in the iterative algorithm: first, (Rx,Ry) of each group is calculated using the currently estimated rotation center and M is fitted; then (Rx,Ry) is refined again using M and the rotation center is solved again until convergence.

[0060] The method for decoupling control output is as follows: Based on the real-time sensor reading ΔS, through Calculate the true mirror deflection angle; After comparing the target mirror deflection angle with the actual mirror deflection angle, the controller obtains the desired angle increment, which is then converted into the required voltage change (ΔV2, ΔV3) using the inverse matrix of M. .

[0061] This enables independent, high-precision closed-loop control of the Rx and Ry axes, fundamentally eliminating coupling errors caused by the inconsistency between the measurement center and the geometric center.

[0062] Furthermore, the initial value of the rotation center Configure it in the following way: Suppose that N (N≥3) displacement sensors (e.g., three measurement points of a three-channel laser interferometer) are arranged on the surface of the fast-reflecting mirror, and their position coordinates are known. Let i = 1, 2, ..., N. Then the initial value of the rotation center is... It can be taken as the geometric center of all sensor locations, that is: .

[0063] This initial value ensures that the iterative algorithm starts from a reasonable midpoint and can usually converge to the true value within a few iterations. If prior information indicates a large deviation, other preset values ​​(such as the physical center coordinates of the mirror) can also be used, but the core iterative process of this invention is not sensitive to the initial value and has global convergence.

[0064] The geometric mapping matrix is ​​constructed using the rotation center and the equivalent focal length from the fast-reflecting mirror to the sensor. The parameter identification method in step S4 is specifically the least squares method, which has advantages such as clear principle, stable calculation, high estimation accuracy, and strong resistance to random noise, enabling globally optimal linear estimation of the voltage-angle mapping relationship. The sensor used in this method is a system-built-in sensor.

[0065] Before parameter identification, a pre-optimized drive voltage sequence needs to be applied to the drive control channel of the fast reflector. To efficiently and accurately identify the geometric center and coupling parameters of the fast reflector system, this embodiment designs a drive voltage excitation sequence based on the principle of optimal experimental design. This sequence uses dual-channel independent input and, within the two-dimensional command space composed of dual-channel voltages, presents a structured distribution centered on the system's electrical zero point, exhibiting symmetry, progression, and completeness. Centered on the system zero point (e.g., (50,50)), the sequence comprises three parts: a single-axis symmetric step sequence, a diagonal symmetric step sequence, and a center regression step.

[0066] A single-axis symmetric step sequence includes: changing the voltage of only one channel while keeping the other channel at zero, and exciting it with multiple sets of positive and negative symmetrical amplitudes.

[0067] Diagonally symmetric step sequences include: simultaneously changing the voltage of two channels, including one or more combinations of equal amplitude in the same direction, equal amplitude in opposite directions, and unequal amplitude.

[0068] The center return step includes: after each step or group of voltage excitations, the voltage command returns to zero.

[0069] The driving voltage sequence designed in this embodiment makes full use of the symmetry of piezoelectric ceramics and the characteristics of the system's linear operating region. It can obtain complete information characterizing the independent channel gain, cross-coupling, and nonlinear characteristics of the system with the fewest excitation steps, while effectively suppressing the impact of hysteresis on calibration accuracy, laying the foundation for subsequent high-precision parameter identification.

[0070] In step S6, when the iteration error is less than or equal to the set tolerance, it is determined that the estimation of the rotation center and the sensitivity matrix converges synchronously to the optimal value.

[0071] This method abandons the traditional black-box fitting approach and proposes a multi-parameter synchronous online identification method based on geometric optics principles and iterative least squares. The core of this method lies in identifying the deviation between the measurement center and the geometric center, i.e., the rotation center. Solving for it as an explicit state variable, this approach addresses the iterative optimization problem where the rotation center and rotation angle are interdependent and difficult to solve directly, thereby simultaneously and accurately identifying the rotation center parameters. And the voltage-angle sensitivity matrix M.

[0072] The decoupling control of this method is achieved through a two-stage transformation: First, using the identified center of rotation... A geometric mapping matrix H is constructed to physically reconstruct the interferometer sensor readings, directly calculating the decoupled true mirror rotation angle [Rx, Ry]. Then, a sensitivity matrix M is used to achieve a precise and independent mapping from angle commands to driving voltage. This method eliminates coupling at the measurement source, rather than compensating after coupling occurs.

[0073] like Figure 2 As shown, the online calibration method proposed in this invention is embodied in an iterative parameter estimation process, the core of which lies in a closed optimization loop: starting from an initial guess, the system alternately performs geometric mapping modeling and least squares parameter identification, and continuously feeds the newly estimated rotation center coordinates back to the model building step, thereby improving the accuracy of the rotation center. The estimation of the sensitivity matrix M converges to the optimal value simultaneously. This process requires no external reference and can complete high-precision calibration within a few iterations using only the designed drive voltage sequence and feedback from the system's built-in sensors, providing accurate model parameters for achieving real-time decoupled control.

[0074] To verify the effectiveness and accuracy of this method, this embodiment built a set of... Figure 3 The closed-loop high-precision testing system shown is composed of a drive control module, an execution sensing module, and a vibration isolation and environmental control module. In the drive and control module, a host computer acts as the central control core, running the core calibration method described in this embodiment and generating a precise drive voltage signal through a strain adjustment device.

[0075] In the execution and sensing module, a driving voltage signal is applied to the piezoelectric fast-steering mirror (FSM) of the device under test. The micro-displacement of its mirror surface is measured in real time and synchronously by a three-channel laser interferometer through a dedicated fiber optic testing fixture. This configuration enables high-resolution, in-situ detection of the two-dimensional rotation angles (Rx, Ry) of the mirror surface.

[0076] In the basic and environmental module, the entire system is placed on an air-floating optical vibration isolation platform to actively isolate ground and air vibrations. All experiments are conducted in a cleanroom environment with constant temperature and humidity, which fundamentally suppresses the noise introduced by temperature drift, humidity changes, and environmental vibrations to micro- and nano-scale measurements.

[0077] The above test conditions fully reproduce the actual working scenario of the fast-reflecting mirror in the high-precision beam control system, while ensuring the extreme stability of the measurement reference, providing a reliable guarantee for the objective evaluation of the performance of this method.

[0078] The driving voltage sequence was applied to the CH2 and CH3 channels, with CH1 as the reference voltage. The experimental voltage distribution is as follows: Figure 4 As shown.

[0079] like Figure 5 As shown in the figure, X0 and Y0 represent x0 and y0 in the coordinates of the rotation center. After initial adjustment, the X0 and Y0 parameters quickly reach stable values. This proves that the iterative algorithm proposed in this application can effectively solve the "chicken and egg" problem, achieving parameter synchronization and rapid convergence. The fitting error curve drops sharply in the early stage of iteration and then remains at an extremely low level, which intuitively verifies the stability of the algorithm and shows that the geometric model constructed based on the identified physical parameters can fit the actual measurement data with high accuracy.

[0080] The rotation center coordinates output by the algorithm (e.g.) Figure 6 As shown, the sensitivity matrix M is directly updated to the control system. This reconstructs the independent control channels for Rx and Ry, achieving precise uncoupled angle output.

[0081] This method, employing a physical model-driven parameter identification approach, offers advantages such as clearly defined parameter meanings, strong model generalization ability, and high calibration efficiency (utilizing optimally designed symmetrical voltage points). Compared to traditional methods, under the same conditions, it can significantly reduce the static coupling error between the Rx / Ry axes, thereby improving the system's closed-loop bandwidth and long-term stability.

[0082] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0083] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0084] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0085] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0086] It should be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. When an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0087] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An automatic calibration method for a fast-reflecting mirror, characterized in that, Includes the following steps: S1. Set the initial value of the rotation center. A sequence of driving voltages is applied to the drive control channel of the fast-reflecting mirror to obtain calibration source data; S2. The sensor displacement change is obtained by solving the calibration source data. S3. Construct a geometric mapping matrix and use the geometric mapping matrix to calculate the decoupled real mirror rotation angle; S4. Fit the sensitivity matrix using the parameter identification method, and calculate the theoretical mirror rotation angle using the sensitivity matrix; S5. Based on the theoretical mirror rotation angle obtained in S4 and the sensor displacement change measured in S2, construct a linear system with the rotation center coordinates as unknowns, and solve for the updated rotation center. S6. Repeat S3~S5 until the estimates of the rotation center and sensitivity matrix converge to the optimal values ​​simultaneously, and update the final obtained rotation center and sensitivity matrix into the control system. Wherein, the rotation center is the deviation between the measurement center of the laser interferometer and the geometric center of the fast-reflecting mirror; In step S3, the geometric mapping matrix is ​​constructed through the following steps: Define the coordinates of the rotation center of the fast-reflecting mirror as follows: The deflection angles of the mirror around the X-axis and Y-axis are Rx and Ry, respectively, in radians. When Rx and Ry are small angles, the displacement change along the normal direction of the mirror at the i-th sensor position is... The following linear geometric relationship exists between the rotation center and the rotation angle: ， By writing the measurements from all N sensors into vector form, we obtain the geometric mapping matrix H: ， in, ， The H matrix has a dimension of N×2, and each row consists of the currently estimated rotation center coordinates. Position coordinates of the corresponding sensor Calculated; In step S3, the decoupled true mirror rotation angle is calculated using the geometric mapping matrix through the following method: Given the center of rotation Given a set of sensor displacement changes ΔS and mirror deflection angles [Rx, Ry], [the following conditions apply]. T The equations corresponding to the linear geometric relationship can be obtained by solving the system of equations. Since N≥3, the system is overdetermined, and the least squares method is used to solve it. ， Where H + Let H be the pseudo-inverse matrix. This solution step is used in the iterative process to deduce the mirror deflection angle corresponding to each voltage from the measured sensor data, starting from the currently estimated rotation center.

2. The automatic calibration method for fast-reflecting mirrors as described in claim 1, characterized in that, In step S4, the specific form and fitting method of the sensitivity matrix M are as follows: Define the driving voltage of the fast-reflecting mirror as and , Corresponding to the Rx axis, Corresponding to the Ry axis, its distance from the central working point (V 20 V 30 The change in ) is: ， Within the small-angle linear operating region, the mirror deflection angle (Rx, Ry) and the voltage change (ΔV2, ΔV3) approximately satisfy a linear relationship: ， The sensitivity matrix M is a 2×2 matrix, and its form is: ， Main diagonal element m 11 m 22 Represent the voltage-angle sensitivity of CH2 to Rx and CH3 to Ry, respectively; off-diagonal elements m 12 m 21 Indicates cross-coupling sensitivity; Fitting method: During the calibration process, given a series of different voltage combinations (ΔV2, ΔV3) and their corresponding mirror deflection angles (Rx, Ry), the sensitivity matrix M can be obtained through least squares fitting; specifically, all P sets of data are organized as follows: ， The least squares solution to M is: ， The least-squares fitting step of the sensitivity matrix M is performed alternately in the iterative algorithm: first, (Rx,Ry) of each group is calculated using the currently estimated rotation center and M is fitted; then, (Rx,Ry) is refined again using M and the rotation center is solved again until convergence.

3. The automatic calibration method for fast-reflecting mirrors as described in claim 2, characterized in that, In step S6, the method for updating the final obtained rotation center and sensitivity matrix into the control system is as follows: Based on the real-time sensor reading ΔS, through Calculate the true mirror deflection angle; After comparing the target mirror deflection angle with the actual mirror deflection angle, the controller obtains the desired angle increment, which is then converted into the required voltage change (ΔV2, ΔV3) using the inverse matrix of M. .

4. The automatic calibration method for fast-reflecting mirrors as described in claim 1, characterized in that, The initial value of the rotation center Configure it in the following way: Suppose that N displacement sensors are arranged on the surface of the fast-reflecting mirror, where N≥3, and their position coordinates are known. If i = 1, 2, ..., N, then the initial value of the rotation center is... It can be taken as the geometric center of all sensor locations, that is: .

5. The automatic calibration method for fast-reflecting mirrors as described in claim 1, characterized in that, The driving voltage sequence adopts dual-channel independent input and includes: a single-axis symmetric step sequence, a diagonal symmetric step sequence, and a center regression step. The single-axis symmetric step sequence includes: changing the voltage of only one channel while keeping the other channel at zero, and exciting it with multiple sets of positive and negative symmetric amplitudes; The diagonally symmetric step sequence includes: simultaneously changing the voltage of two channels, including one or more combinations of equal amplitude in the same direction, equal amplitude in opposite directions, and unequal amplitude. The center return step includes: after each step or group of voltage excitations, the voltage command returns to zero.

6. The automatic calibration method for fast-reflecting mirrors as described in claim 1, characterized in that, In step S6, when the iteration error is less than or equal to the set tolerance, it is determined that the estimation of the rotation center and the sensitivity matrix converges synchronously to the optimal value.

7. The automatic calibration method for fast-reflecting mirrors as described in claim 1, characterized in that, The sensor is a built-in sensor of the system.

8. An automatic calibration system for a fast-reflecting mirror, characterized in that, include: The drive and control module uses a host computer as the central control core, runs the automatic calibration method for fast-reflecting mirrors as described in any one of claims 1 to 7, and generates a precise drive voltage signal through a strain adjustment device; The execution and sensing module applies a drive signal to the piezoelectric fast-reflecting mirror, and its micro-displacement is measured in real time and synchronously by a three-channel laser interferometer through a dedicated fiber optic testing fixture. The foundation and environment modules are placed on an air-floating optical vibration isolation platform to actively isolate ground and air vibrations.

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