A two-dimensional galvanometer visual axis pointing coupling correction method

Abstract

The application discloses a two-dimensional galvanometer visual axis pointing coupling correction method, and mainly solves the problem that the visual axis pointing error calculated by the prior art is in the order of milliradians, and it is difficult to meet the high-precision correction requirement.The method comprises the following steps: step 1, establishing a visual axis pointing model for a two-dimensional galvanometer to be corrected; step 2, acquiring a linear model between the rotation angle of the two-dimensional galvanometer and the visual axis pointing angle of a two-stage stable pointing system based on the visual axis pointing model by using a linear approximation method; acquiring a pointing error based on the visual axis pointing model and the linear model; performing nonlinear correction on the pointing error by using a Volterra series to acquire a nonlinear correction relationship; step 3, acquiring a corrected pointing error by using the nonlinear correction relationship; and step 4, acquiring the control angle of the two-dimensional galvanometer based on the corrected pointing error.The application can reduce the visual axis pointing error from the order of milliradians to the order of microradians, the pointing calculation precision is improved by about 75 times, and the visual axis pointing calculation precision is significantly improved.

Description

Technical Field

[0001] This invention relates to a method for correcting the orientation of an optical device, specifically a method for coupling and correcting the orientation of a two-dimensional galvanometer. Background Technology

[0002] Two-dimensional galvanometers (FSMs) are an important component of two-stage stabilization systems, offering advantages such as fast response, high accuracy, and high resolution. They have been widely used and researched in areas such as precise beam pointing and stable tracking. Existing FSMs typically employ piezoelectric ceramics as the driving mechanism, flexible hinges as the support elements, and strain gauges as the measurement feedback element. Since a two-dimensional galvanometer is a dual-input-output (MIMO) system, shaft and The coupling phenomenon between axes leads to a decrease in the deflection and positioning accuracy of the secondary stabilization system, as well as a reduction in the system's anti-interference capability. Therefore, establishing the relationship between the rotation angle of the two-dimensional galvanometer and the pointing angle of the line of sight of the secondary stabilization system to reduce the coupling between the two axes is one of the challenges in the study of two-dimensional galvanometer systems, and it is of great significance for improving the pointing and stabilization accuracy of the line of sight of the secondary stabilization system.

[0003] Satyam Satyarthi summarized the formulas for the rotation angle and rate compensation of frame-type scanning mirrors with different structural forms. See {Satyam S. Optical line-of-sight steering using gimbaled mirrors[J]. IJK Controls LLC (United States); Rockwell Collins, Inc. (United States); UTC Aerospace Systems (United States); USNaval Research Lab. (United States); Exelis Inc. (United States); Raytheon Intelligence & Information Systems (United States), 2014, 907690760E-90760E-8.DOI: 10.1117 / 12.2050637}. Wu Fan et al. analyzed the imaging and scanning characteristics of two-dimensional pointing mirrors, pointing out that the rotation of the two-dimensional pointing mirror causes image rotation, resulting in image distortion and nonlinearity in the visual axis scanning trajectory. See {Wu Fan, Wang Dapeng. Analysis of scanning characteristics of localized scanning mode of two-dimensional pointing mirror [J]. Optoelectronic Technology Application, 2009, 24(04): 16-20}. The above scholars all analyzed large-angle frame-type scanning mirrors, but lacked analysis of the visual axis pointing kinematic equations of small-angle flexible shaftless galvanometers.

[0004] JMHilkert, Peng Shuping, Li Hongguang, et al. derived the kinematic equations for the line-of-sight pointing of small-angle flexible axisless galvanometers and analyzed the line-of-sight pointing error under linear approximation. See {JMHilkert, Gavin K, KK Line-of-sight kinematics and corrections for fast-steering mirrors used in precisionpointing and tracking systems[J]. Univ. of Texas at Dallas (United States); Lockheed Martin Missiles and Fire Control (United States); Rockwell Collins, Inc. (United States); UTC Aerospace Systems (United States); USNaval ResearchLab. (United States); Exelis Inc. (United States); Raytheon Intelligence & Information Systems (United States)} States), 2014, 907690760F-90760F-15.DOI: 10.1117 / 12.2049857}, {Peng Shuping, Chen Tao, Liu Tingxia, et al. Light reflection process of fast reflector in laser emission system[J]. Optics and Precision Engineering, 2015, 23(02): 378-386}, {Li Hongguang, Ji Ming, Shou Shaojun, et al. Composite axis stabilization mechanism of top reflector optoelectronic system[J]. Infrared and Laser Engineering, 2016, 45(07): 285-291}. However, the line-of-sight pointing error calculated by this equation is on the order of milliradians, which is difficult to meet the requirements of high-precision correction. Summary of the Invention

[0005] The purpose of this invention is to solve the technical problem that the line-of-sight pointing error calculated by existing technology is on the order of milliradians, which is difficult to meet the requirements of high-precision correction, and to provide a two-dimensional galvanometer line-of-sight pointing coupling correction method.

[0006] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0007] A two-dimensional galvanometer line-of-sight coupling correction method, characterized by the following steps:

[0008] Step 1: Establish a line-of-sight pointing model for the two-dimensional galvanometer to be calibrated;

[0009] Step 2: Using a linear approximation method based on the line-of-sight pointing model, obtain a linear model between the rotation angle of the two-dimensional galvanometer and the line-of-sight pointing angle of the secondary stabilization system;

[0010] Based on the eye axis pointing model and the linear model, obtain Axis pointing error and Axis pointing error Using Volterra series pairs Axis pointing error and Axis pointing error After performing nonlinear corrections, the following nonlinear correction equations are obtained:

[0011] ;

[0012] In the formula: for Axis correction for pointing error; for Axis correction for pointing error; For the outgoing ray vector at Representation below the axis; For the outgoing ray vector at Representation below the axis; For the outgoing ray vector at Representation below the axis; For two-dimensional galvanometers Axis rotation angle; For two-dimensional galvanometers Axis rotation angle; Angle of incidence;

[0013] Step 3: Calculate the desired eye axis pointing angle using a linear model. and Using this as an initial value, we substitute it into the inversion equation system composed of the nonlinear correction relation to obtain the numerical solution. and ;

[0014] Step 4, based on and Correcting the pointing angle and And using a linear model with the corrected eye axis pointing angle and Calculate the corrected and This angle is used as the control angle of the two-dimensional galvanometer to achieve line-of-sight pointing coupling correction.

[0015] Further, step 1 specifically involves using Snell's law of reflection to establish the following line-of-sight pointing model for the two-dimensional galvanometer to be corrected:

[0016] ;

[0017] In the formula: For two-dimensional galvanometers Axis pointing angle; For two-dimensional galvanometers Axis pointing angle.

[0018] Furthermore, in step 2, the expression for the linear model is as follows:

[0019] .

[0020] Furthermore, in step 2, Axis pointing error for: , Axis pointing error for: .

[0021] Compared with the prior art, the present invention has the following beneficial technical effects:

[0022] 1. This invention proposes a two-dimensional galvanometer line-of-sight coupling correction method. By introducing a Volterra series for nonlinear correction, high-precision inversion of the line-of-sight direction calculation is achieved. This method is applicable when the two-dimensional galvanometer travel is ±20... Under the condition of an incident angle of 45°, the line-of-sight pointing error is reduced from the milliarthroat level to the microarthroat level, and the pointing calculation accuracy is improved by about 75 times, significantly improving the line-of-sight pointing calculation accuracy.

[0023] 2. This invention proposes a two-dimensional galvanometer line-of-sight pointing coupling correction method. Based on the vector form of Snell's reflection law, a line-of-sight pointing model is established to establish the nonlinear kinematic relationship between the rotation angle of the two-dimensional galvanometer and the line-of-sight pointing angle of the two-stage stabilization system. This achieves high-precision modeling of the line-of-sight pointing relationship of the two-dimensional galvanometer, providing a reliable mathematical basis for subsequent high-precision control. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the coordinate system of the two-dimensional galvanometer in an embodiment of the present invention;

[0025] Figure 2 As described in the embodiments of the present invention Axis pointing error A schematic diagram of the calculation results;

[0026] Figure 3 As described in the embodiments of the present invention Axis pointing error A schematic diagram of the calculation results;

[0027] Figure 4 As described in the embodiments of the present invention Axis correction pointing error A schematic diagram of the calculation results;

[0028] Figure 5 As described in the embodiments of the present invention Axis correction pointing error A schematic diagram of the calculation results;

[0029] Figure 6 This is a schematic diagram showing the calculation results of the nonlinear correction relationship under different incident angles in an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0031] This embodiment provides a two-dimensional galvanometer line-of-sight coupling correction method, which is implemented using the following steps:

[0032] Step 1: Establish a line-of-sight pointing model based on nonlinear kinematic relationships.

[0033] Based on the two-dimensional galvanometer currently under development, a line-of-sight pointing model for the rotation of the two-dimensional galvanometer is established according to Snell's law of reflection, and the coupling characteristics caused by the deflection of the two axes are analyzed.

[0034] Establish such as Figure 1 The coordinate system shown is a two-dimensional galvanometer, where the x-axis and y-axis are the rotation axes of the two-dimensional galvanometer, and the corresponding rotation angles are respectively... , . , Let be the incident ray vector and the outgoing ray vector, and let be the corresponding incident angle and outgoing angle, respectively. , . Let be the normal vector of the two-dimensional galvanometer. When the two-dimensional galvanometer is not rotating, the normal vector is perpendicular to . Collinear axes.

[0035] for In a two-dimensional galvanometer coordinate system, it is represented as:

[0036] (1)

[0037] After the two-dimensional galvanometer is rotated by a certain angle It becomes:

[0038] (2)

[0039] in:

[0040]

[0041]

[0042] Depend on arrive Transformation matrix for:

[0043]

[0044] According to Snell's law of reflection, we can obtain The representation in the two-dimensional galvanometer coordinate system is:

[0045]

[0046] Will Transformed to the line-of-sight coordinate system, it can be represented as:

[0047]

[0048] After sorting and calculating, we get The representation in the line-of-sight coordinate system is:

[0049] (8)

[0050] The calculated pointing angle of the line of sight is:

[0051] (9)

[0052] (10)

[0053] In the formula: For two-dimensional galvanometers Axis pointing angle; For two-dimensional galvanometers Axis pointing angle; For the outgoing ray vector at Representation below the axis; For the outgoing ray vector at Representation below the axis; For the outgoing ray vector at Representation below the axis.

[0054] As can be seen from the above formula, the line-of-sight pointing angle is a nonlinear function of the rotation angle of the two axes of the two-dimensional galvanometer. At the same time, there is a coupling phenomenon between the two axes. In order to accurately control the line-of-sight pointing and obtain the rotation angle of the two-dimensional galvanometer, it is necessary to decouple the two axes kinematics.

[0055] Step 2: Obtain the linear model and nonlinear correction formula.

[0056] Because the stroke of a two-dimensional galvanometer is relatively small, typically around 20... Therefore, firstly, for the line-of-sight pointing model composed of equations (9) and (10), a linear approximation is adopted, and the relationship between the rotation angle of the two-dimensional galvanometer and the line-of-sight pointing angle of the two-stage stabilization system is obtained as follows:

[0057] (11)

[0058] (12)

[0059] Formulas (11) and (12) are combined to form a linear model.

[0060] When using a linear model to calculate the line-of-sight pointing angle, there is a significant line-of-sight pointing error, the magnitude of which is:

[0061] (13)

[0062] (14)

[0063] To obtain more accurate results for calculating the line-of-sight pointing angle, a higher-order approximation is used for the line-of-sight pointing model composed of equations (9) and (10). Since it exhibits weak nonlinearity under small-angle conditions, using Volterra series for higher-order approximation of the nonlinear terms has significant advantages. This method can explicitly decompose the nonlinear effect into static bias, equivalent linear gain, and higher-order disturbance terms while maintaining the linear control framework, thus clearly revealing the generation mechanism of the harmonic and intermodulation components, providing good theoretical support for the performance evaluation of the two-dimensional galvanometer. At this point, the relationship between the rotation angle of the two-dimensional galvanometer and the line-of-sight pointing angle of the secondary stabilization system is:

[0064] (15)

[0065] (16)

[0066] The line-of-sight pointing error after nonlinear correction is:

[0067] (17)

[0068] (18)

[0069] In the formula: for Axis correction for pointing error; for Axis correction pointing error.

[0070] Formulas (17) and (18) constitute the aforementioned nonlinear correction relationship.

[0071] Step 3: Nonlinear Inversion

[0072] The input to the secondary stabilized aiming system is the desired line-of-sight pointing angle. and The goal is to calculate, based on this expected value, the force that should be applied to the two-dimensional galvanometer. axis, The high-precision rotation angle of the shaft, i.e. and .

[0073] Calculated using a linear model and Using this as the initial value for iteration, we substitute it into the inversion equation system composed of the nonlinear correction relation for numerical solution to obtain... and .

[0074] Step 4, based on and Correcting the pointing angle and And using a linear model with the corrected eye axis pointing angle and Calculate the corrected and This angle is used as the control angle of the two-dimensional galvanometer to achieve line-of-sight pointing coupling correction.

[0075] Based on the schedule of research in the laboratory Taking a two-dimensional galvanometer as an example, the simulation analysis was performed using Matlab. When the angle is 45°, the linear approximation of the line of sight pointing error is as follows: Figure 2 and Figure 3 As shown, the maximum line-of-sight pointing error is 0.6. For high-precision two-stage stabilization systems, linear approximation is no longer sufficient to meet the requirements.

[0076] Nonlinear simulation results are as follows Figure 4 As shown. Less than 8 , Less than 4 Compared to linear approximation, the accuracy of the eye axis pointing calculation is improved by 75 times, meeting the requirements. High-precision two-stage stabilization system.

[0077] Taking a two-dimensional galvanometer with the same stroke as an example, the following analysis was conducted. The line-of-sight pointing error at 45° is shown in the simulation results. Figure 5 As shown. Less than 8 , Less than 4 Compared to linear approximation, the accuracy of the eye axis pointing calculation is improved by 75 times, meeting the requirements. High-precision two-stage stabilization system.

[0078] The above only applies to Analyzing the line-of-sight pointing error at 45°, according to formulas (17) and (18), the line-of-sight pointing error is: The nonlinear function is analyzed below. The following analysis considers a two-dimensional galvanometer with a mirror tilt angle of 10°. Under the premise of 0°~90° The line-of-sight pointing errors after higher-order Volterra series corrections are shown in the analysis results. Figure 6 As shown, At different times, the line-of-sight pointing error will also be different. The line-of-sight pointing error is minimized at a 45° angle.

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A two-dimensional galvanometer line-of-sight coupling correction method, characterized in that, Includes the following steps: Step 1: Establish a line-of-sight pointing model for the two-dimensional galvanometer to be calibrated; Step 2: Using a linear approximation method based on the line-of-sight pointing model, obtain a linear model between the rotation angle of the two-dimensional galvanometer and the line-of-sight pointing angle of the two-stage stabilization system; Based on the eye axis pointing model and the linear model, obtain Axis pointing error and Axis pointing error Using Volterra series pairs Axis pointing error and Axis pointing error Nonlinear corrections were performed separately, and the following nonlinear correction equations were obtained: ； In the formula: for Axis correction for pointing error; for Axis correction for pointing error; For the outgoing ray vector at Representation below the axis; For the outgoing ray vector at Representation below the axis; For the outgoing ray vector at Representation below the axis; For two-dimensional galvanometers Axis rotation angle; For two-dimensional galvanometers Axis rotation angle; Angle of incidence; Step 3: Calculate the desired eye axis pointing angle using a linear model. and Using this as an initial value, we substitute it into the inversion equation system composed of the nonlinear correction relation to obtain the numerical solution. and ; Step 4, based on and Correcting the pointing angle and And using a linear model with the corrected eye axis pointing angle and Calculate the corrected and This angle is used as the control angle of the two-dimensional galvanometer to achieve line-of-sight pointing coupling correction.

2. The two-dimensional galvanometer sight axis pointing coupling correction method according to claim 1, characterized in that, Step 1 specifically involves using Snell's law of reflection to establish the following line-of-sight pointing model for the two-dimensional galvanometer to be corrected: ； In the formula: For two-dimensional galvanometers Axis pointing angle; For two-dimensional galvanometers Axis pointing angle.

3. A two-dimensional galvanometer sight axis pointing coupling correction method according to claim 1 or 2, characterized in that, In step 2, the expression for the linear model is as follows: 。 4. The two-dimensional galvanometer sight axis pointing coupling correction method according to claim 3, characterized in that: In step 2, Axis pointing error for: , Axis pointing error for: .

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