Two-degree-of-freedom large-stroke reflector high-precision optical axis pointing resolving method

Abstract

The invention provides a high-precision optical axis direction resolving method for a two-degree-of-freedom large-stroke reflecting mirror. The method comprises the following steps: firstly, determining an incident angle of the reflecting mirror at an initial zero position according to the mounting position of the two-degree-of-freedom large-stroke reflecting mirror; secondly, an analytical expression of the relation between the two rotation angles of the reflector and the change angle of the direction of the optical axis of the reflected light is established; dispersing the change angle of the visual axis direction of the reflected light within a limited range to obtain a plurality of groups of angle combinations of the reflected light; for each combination, calculating according to an analytical expression to obtain a reflector rotation angle, and constructing a relational database between the reflector rotation angle and a reflected light visual axis pointing change angle; and finally, carrying out model fitting on the database, and carrying out accurate control on the visual axis pointing of the two-degree-of-freedom large-stroke fast reflector by utilizing the model. According to the invention, polynomial fitting decoupling of the resolving relation between the rotation angle of the two-degree-of-freedom large-stroke fast reflector and the change angle of the direction of the optical axis of the reflected light is realized.

Description

Technical Field

[0001] The invention relates to the technical field of reflectors, and in particular to a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector. Background Art

[0002] The fast reflector is an electromechanical device used to precisely control the direction of a light beam. It has the advantages of high precision, high bandwidth, and fast response. It is widely used in the fields of enhancing photoelectric imaging, improving image stabilization, and assisting in guidance and pointing. The fast reflector system uses a voice coil motor or a piezoelectric ceramic driver as a driving mechanism to drive the reflector surface to rotate precisely to the required angle. It combines a variety of advanced technical theories such as high-precision angle measurement technology, micro-displacement drive technology, and advanced control theory. Since the moment of inertia of the reflector is much smaller than that of the traditional frame servo stabilization structure, it can significantly improve the bandwidth and angular resolution of the pointing control accuracy of the optical system.

[0003] The two-degree-of-freedom fast reflector can deflect the reflected light in two directions, which corresponds to the two dimensions in the plane coordinate system of the photoelectric detector's sight line, thereby realizing the functions of stabilization, pointing and tracking of the optoelectronic system. Since the rotation angle of the two-degree-of-freedom fast reflector in the two degrees of freedom is coupled with the change in the angle of the visual axis pointing of the reflected light, it is impossible to directly solve the rotation angle of the reflector according to the required reflected light pointing. The use of numerical calculation methods such as iteration is time-consuming and cannot meet the requirements of high bandwidth, and is not suitable for embedded systems. In actual engineering applications, linear approximation methods are currently used for decoupling calculations. However, the linear approximation method is effective when the travel of the fast reflector is relatively small. When the rotation angle of the reflector is large, the error caused by the linear approximation is large, which is difficult to meet the requirements of the optoelectronic system. Therefore, it is necessary to study a method that can accurately decouple the rotation angle of the reflector and the visual axis pointing of the reflected light in real time. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention proposes a high-precision axis pointing solution method for a two-degree-of-freedom large-stroke reflector, which realizes the polynomial fitting decoupling of the solution relationship between the rotation angle of the two-degree-of-freedom large-stroke fast reflector and the change angle of the axis pointing of the reflected light.

[0005] The technical solution of the present invention is:

[0006] A high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector comprises the following steps:

[0007] Step 1: Determine the incident angle of the reflector at the initial zero position according to the installation position of the two-degree-of-freedom large-stroke reflector;

[0008] Step 2: Establish the coordinate system of the reflector body, and obtain the analytical expression of the relationship between the two rotation angles of the reflector and the change angle of the reflected light axis direction according to the incident direction of the reflector, the incident angle at the initial zero position, and the rotation direction;

[0009] Step 3: According to the actual application scenario, the change angle of the reflected light axis direction is discretized in a fine manner within its limit range to obtain several groups of reflected light angle combinations; for each group of reflected light angle combinations, the corresponding reflector rotation angle is calculated according to the analytical expression obtained in step 2, and a database of the relationship between the discrete reflector rotation angle and the change angle of the reflected light axis direction is constructed;

[0010] Step 4: Perform model fitting on the database obtained in step 3 to obtain a fitting model between the rotation angle of the reflector and the change angle of the reflected light axis direction;

[0011] Step 5: Use the model established in step 4 to accurately control the visual axis pointing of the two-degree-of-freedom large-stroke fast reflector.

[0012] Further preferably, in step 2, the analytical expression obtained is:

[0013]

[0014] where ψ x and ψ y Respectively represent the change angle of the reflected light in the X and Y directions in the visual axis sight line coordinate system, θ x and θ y is the rotation angle of the reflector in the X and Y directions of the reflector body coordinate system, β i is the initial zero incident angle.

[0015] Further preferably, in step 2, the specific process of obtaining the analytical expression is:

[0016] Step 2.1: Take the center of the reflective surface of the reflector as the origin, the two axes of the freedom of the reflector are the X-axis and the Y-axis, and the Z-axis is the normal direction of the reflective surface, and establish the coordinate system of the reflector body;

[0017] Step 2.2: Assume that the rotation angles of the reflector in the X and Y directions of the reflector body coordinate system are θ x and θ y , the incident light and the outgoing light of the reflector are represented by P i and P o It means that when the reflector is not rotated and remains at zero position, its mirror normal vector N coincides with the Z axis of the coordinate system, then the initial zero position incident light is:

[0018] P i=[-cosβ i 0sinβ i ] T

[0019] The reflector rotates by θ around the X and Y axes of the reflector body coordinate system. x and θ y After the angle is set, the two rotation axes of the corresponding new reflector body coordinate system are converted by M x and M y Indicates that there are:

[0020]

[0021] Performing a vector product operation, we get the mirror normal vector after the mirror is rotated:

[0022]

[0023] The incident light P i To the outgoing light P o The coordinate transformation matrix R is:

[0024] R=1-2N·N T

[0025] The expression for the reflected light is:

[0026] P o =R·P i

[0027] It is defined that when the reflector is in the initial zero position, the Y axis of the sight line coordinate system is consistent with the Y axis of the reflector body coordinate system, and the Z axis is consistent with the direction of the reflected light. o Converted to the sight axis line of sight coordinate system:

[0028]

[0029] Thus, the change angle ψ of the reflected light in the X and Y directions in the visual axis sight line coordinate system is obtained. x and ψ y The analytical expressions are

[0030]

[0031] Further preferably, in step 3, for each group of reflected light angle combinations, a linear approximation result is used as an initial value, and the corresponding reflector rotation angle is calculated by a numerical method based on the analytical expression obtained in step 2.

[0032] Further preferably, the linear approximation formula is:

[0033] ψ x =2θx

[0034] ψ y =2cosβ i θ y .

[0035] Further preferably, in step 4, a polynomial fitting model is adopted.

[0036] Further preferably, when the initial zero incident angle β i =45°, the relationship between the change in the angle of the reflected light axis and the rotation angle of the reflector obtained by using the fifth-order polynomial fitting model is:

[0037] θ x =-3.948e -8 +0.5ψ x -9.529e -10 ψ y +6.372e -6 ψ x 2 +1.077e -8 ψ x ψ y +0.25ψ y 2

[0038] +4.566e -6 ψ x 3 +1.711e -6 ψ x 2 ψ y -0.25ψ x ψ y 2 -1.605e -6 ψ y 3

[0039] -0.0001266ψ x 4 -7.089e -7 ψ x 3 ψ y -0.06373ψ x 2 ψ y 2 -2.796e -7 ψ x ψ y 3

[0040] +0.0419ψ y4 -4.931e -5 ψ x 5 -1.372e -5 ψ x 4 ψ y +0.1032ψ x 3 ψ y 2

[0041] -0.0001167ψ x 2 ψ y 3 +0.01832ψ x ψ y 4 +0.0001051ψ y 5

[0042] i y =6.749e -11 -1.806e -8 ψ x +0.7071ψ y -9.214e -8 ψ x 2 -0.3535ψ x ψ y

[0043] -1.563e -8 ψ y 2 +1.607e -7 ψ x 3 -2.399e -5 ψ x 2 ψ y +8.984e -6 ψ x ψ y 2

[0044] -0.05891ψ y 3 +8.499e -7 ψ x 4 -0.02972ψ x 3 ψ y +7.038e -6 ψ x 2 ψy 2

[0045] +0.2321ψ x ψ y 3 +5.078e -7 ψ y 4 +2.912e -6 ψ x 5 -0.0001462ψ x 4 ψ y

[0046] -3.144e -5 ψ x 3 ψ y 2 -0.08336ψ x 2 ψ y 3 -0.0004709ψ x ψ y 4 +0.01111ψ y 5 .

[0047] Beneficial Effects

[0048] The high-precision visual axis pointing solution method of the two-degree-of-freedom large-stroke reflector proposed in the present invention has the following beneficial effects:

[0049] (1) The decoupling between the two rotation angles of the two-degree-of-freedom fast reflector and the change angle of the visual axis pointing of the reflected light is achieved. The angle that the reflector should rotate can be quickly calculated in real time according to the required change angle of the visual axis pointing of the aiming line, which has engineering application value.

[0050] (2) Compared with the linear approximation solution method, the proposed polynomial fitting nonlinear approximation method can greatly improve the accuracy of angle solution when the mirror rotates at a large angle, and is suitable for precise control of the line of sight pointing of a large-stroke two-degree-of-freedom mirror.

[0051] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0053] Figure 1 It is a schematic diagram of the overall technical route of the present invention.

[0054] Figure 2 Schematic diagram of a two-degree-of-freedom reflector coordinate system according to an example of the present invention.

[0055] Figure 3 This is a solution error diagram of a nonlinear polynomial fitting model used in an embodiment of the present invention.

[0056] Figure 4 This is a solution error diagram of a linear approximation model used in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention aims at the coupling relationship between the rotation angle of a two-degree-of-freedom fast reflector in two degrees of freedom and the angle change of the visual axis pointing of the reflected light, while the traditional linear approximation method has the problem of large error when performing decoupling calculation for the case where the rotation angle of the reflector is large. A nonlinear approximate relationship between the rotation angle of the reflector and the angle change of the visual axis pointing of the reflected light is obtained by a polynomial fitting method, thereby achieving decoupling of the angle relationship, so that the rotation angle of the two-degree-of-freedom large-stroke reflector can be quickly and accurately calculated.

[0058] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0059] The high-precision visual axis pointing solution method of the two-degree-of-freedom large-stroke reflector in this embodiment includes the following steps:

[0060] Step 1: Determine the initial light incident angle β of the reflector according to the installation position of the two-degree-of-freedom large-travel reflector i In this embodiment, the initial light incident angle, that is, the initial zero-position incident angle is determined to be 45°.

[0061] Step 2: Establish the coordinate system of the reflector body, and calculate the coordinate system of the reflector body according to the incident direction of the reflector and the initial zero incident angle β. i The analytical expression of the relationship between the two rotation angles of the reflector and the change in the direction of the reflected light axis is derived from the rotation direction. This analytical relationship is coupled and nonlinear. The rotation of the reflector around any axis on the two degrees of freedom will cause the direction of the reflected light to change in both dimensions.

[0062] In this embodiment, the coordinate system established is as follows Figure 2 As shown, with the center of the reflecting surface of the reflector as the origin, the axes of the two degrees of freedom of the reflector are the X-axis and the Y-axis, and the Z-axis is the normal direction of the reflecting surface.

[0063] The reflector can rotate in the X and Y directions of the reflector body coordinate system, and the rotation angles are θx and θ y The incident light and outgoing light of the reflector are represented by P i and P o The incident angle and the outgoing angle are denoted by β i and β o When the reflector is not rotated and remains at zero position, its mirror normal vector N coincides with the Z axis of the coordinate system, and the initial zero position incident light is expressed as:

[0064] P i =[-cosβ i 0 sinβ i ] T (1)

[0065] The reflector rotates by θ around the X and Y axes of the reflector body coordinate system. x and θ y After the angle is set, the two rotation axes of the corresponding new reflector body coordinate system are converted by M x and M y If it is expressed, then:

[0066]

[0067] By performing a vector product operation, we can obtain the mirror normal vector after the mirror is rotated:

[0068]

[0069] And the incident light P i To the outgoing light P o The coordinate transformation matrix R is:

[0070] R=1-2N·N T (4)

[0071] According to Snell's law, the expression of reflected light is:

[0072] P o =R·P i (5)

[0073] It is defined that when the reflector is in the initial zero position, the Y axis of the sight line coordinate system is consistent with the Y axis of the reflector body coordinate system, and the Z axis is consistent with the direction of the reflected light. o Converted to the sight axis line of sight coordinate system:

[0074]

[0075] Use ψ x and ψ yThey represent the change in the X and Y directions of the reflected light in the sight line coordinate system, respectively. The analytical expression is:

[0076]

[0077] It can be seen from equation (7) that the relationship between the rotation angle of the two-degree-of-freedom fast reflector in two degrees of freedom and the two-dimensional pointing angle of the reflected light is coupled and nonlinear, and the rotation angle of the reflector cannot be directly solved according to the required reflected light pointing. Although it is possible to obtain a more accurate calculation result by directly solving equation (7) using numerical calculation methods such as iteration method, it takes a long time because it requires continuous iteration. In addition, the fast reflector itself has the advantage of high bandwidth, so it is not applicable to solve equation (7) using numerical calculation methods.

[0078] When the deflection angle of the reflector is relatively small, the linear approximation formula shown below can be used for solution:

[0079]

[0080] However, when the travel of the reflector is large, the linear approximation formula shown in equation (8) will cause a large error and cannot achieve the precise pointing of the reflected light.

[0081] Step 3: According to the actual application scenario, the change angle of the sight line (i.e., the reflected light) in the two directions of the sight line coordinate system is discretized in a fine manner within its limit range. The linear approximation result is used as the initial value, and the two-degree-of-freedom mirror rotation angle corresponding to each group of reflected light angle combination is calculated by numerical method according to the analytical relationship in step 2, so as to construct a database of the relationship between the discrete mirror rotation angle and the change angle of the reflected light sight line pointing.

[0082] In this embodiment, the change angles of the reflected light in two directions are set to x and ψ y The range of is [-10°, 10°]. x and ψ y Perform fine discretization and for each pair of [ψ x ,ψ y ] combination, first use the linear approximation method shown in formula (8) to obtain the mirror angle combination [θ x ,θ y ] approximate value, and use it as the initial value to solve the nonlinear algebraic equations shown in equation (7) by numerical calculation method. Finally, the discrete reflector rotation angle [θ x ,θ y ] and the reflected light axis direction changes the angle [ψ x ,ψy ] is a database of relationships between .

[0083] Step 4: Perform model fitting on the database obtained in step 3 to obtain a fitting model between the rotation angle of the reflector and the change in the angle of the reflected light axis, and analyze its solution error. Here we use a polynomial fitting model.

[0084] In this embodiment, the fitting order of the polynomial is set to 5, and the polynomial fitting model between the decoupled reflected light axis pointing change angle and the reflector rotation angle is obtained as follows:

[0085]

[0086] The error between the mirror rotation angle calculated by the nonlinear polynomial model shown in formula (9) and the precise rotation angle is as follows: Figure 3 The error between the deflection angle of the reflector and the precise rotation angle calculated by the linear approximation model shown in formula (8) is as follows: Figure 4 As shown. It can be seen that the linear approximation method has a large error in calculating the rotation angle of the reflector when the sight line pointing angle changes greatly, and can no longer meet the needs of actual engineering applications. The polynomial fitting method provided by the present invention has a very small calculation error for the rotation angle of the reflector in both small and large angle situations, and the calculation accuracy has been improved by several orders of magnitude compared to the linear approximation method, which can meet the needs of actual engineering applications and realize precise control of the sight axis pointing of a large-stroke two-degree-of-freedom reflector.

[0087] Step 5: Use the model established in step 4 to accurately control the visual axis pointing of the two-degree-of-freedom large-stroke fast reflector.

[0088] It can be seen from the above embodiments that the present invention has the following significant features:

[0089] (1) The relationship between the rotation angle of the two-degree-of-freedom fast reflector and the visual axis pointing angle of the reflected light can be decoupled by constructing a polynomial fitting model, so that the angle that the reflector should rotate can be quickly calculated in real time according to the required sight line visual axis pointing, thereby achieving precise control of the reflector visual axis pointing.

[0090] (2) Compared with the linear approximation solution method, the proposed polynomial fitting nonlinear approximation method can greatly improve the accuracy of the two-degree-of-freedom mirror rotation angle solution. Especially for long-stroke mirrors, the linear approximation method has a large error and is not applicable, while the method provided by the present invention has a very small error and meets the needs of practical engineering applications.

[0091] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A high-precision visual axis pointing solution method for a two-degree-of-freedom long-travel reflector, characterized in that: The following steps are involved: Step 1: Determine the initial zero-position incident angle of the reflector according to the installation position of the two-degree-of-freedom long-travel reflector; Step 2: Establish the coordinate system of the reflector body, and obtain the analytical expression of the relationship between the two rotation angles of the reflector and the change angle of the reflected light axis direction according to the incident direction, the initial zero incident angle and the rotation direction of the reflector; Step 3: According to the actual application scenario, the change angle of the reflected light axis direction is discretized in a fine manner within its limit range to obtain several groups of reflected light angle combinations; for each group of reflected light angle combinations, the corresponding reflector rotation angle is calculated according to the analytical expression obtained in step 2, and a database of the relationship between the discrete reflector rotation angle and the change angle of the reflected light axis direction is constructed; Step 4: Perform model fitting on the database obtained in step 3 to obtain a fitting model between the rotation angle of the reflector and the change angle of the reflected light axis direction; Step 5: Use the model established in step 4 to accurately control the visual axis pointing of the two-degree-of-freedom large-stroke fast reflector.

2. According to claim 1, a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector, characterized in that: In step 2, the analytical expression obtained is: where ψ x and ψ y Respectively represent the change angle of the reflected light in the X and Y directions in the visual axis sight line coordinate system, θ x and θ y is the rotation angle of the reflector in the X and Y directions of the reflector body coordinate system, β i is the initial zero incident angle.

3. According to claim 2, a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector, characterized in that: In step 2, the specific process of obtaining the analytical expression is: Step 2.1: Take the center of the reflective surface of the reflector as the origin, the two axes of the freedom of the reflector are the X-axis and the Y-axis, and the Z-axis is the normal direction of the reflective surface, and establish the coordinate system of the reflector body; Step 2.2: Assume that the rotation angles of the reflector in the X and Y directions of the reflector body coordinate system are θ x and θ y , the incident light and the outgoing light of the reflector are represented by P i and P o It means that when the reflector is not rotated and remains at zero position, its mirror normal vector N coincides with the Z axis of the coordinate system, then the initial zero position incident light is: P i =[-cosβ i 0sinβ i ] T The reflector rotates by θ around the X and Y axes of the reflector body coordinate system. x and θ y After the angle is set, the two rotation axes of the corresponding new reflector body coordinate system are converted by M x and M y Indicates that there are: Performing a vector product operation, we get the mirror normal vector after the mirror is rotated: The incident light P i To the outgoing light P o The coordinate transformation matrix R is: <h2 style=";text-align:left;direction:ltr">R=1-2N·N<h2 style=";text-align:left;direction:ltr"> T The expression for the reflected light is: P o =R·P i It is defined that when the reflector is in the initial zero position, the Y axis of the sight line coordinate system is consistent with the Y axis of the reflector body coordinate system, and the Z axis is consistent with the direction of the reflected light. o Converted to the sight axis line of sight coordinate system: Thus, the change angle ψ of the reflected light in the X and Y directions in the visual axis sight line coordinate system is obtained. x and ψ y The analytical expressions are 4. According to claim 2, a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector, characterized in that: In step 3, for each combination of reflected light angles, the linear approximation result is used as the initial value, and the corresponding reflector rotation angle is calculated by numerical method according to the analytical expression obtained in step 2.

5. According to claim 4, a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector is characterized by: The linear approximation formula is: ψ x =2θ x ψ y =2cosβ i i y 。 6. According to claim 1, a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector, characterized in that: In step 4, a polynomial fitting model is used.

7. According to claim 1, a high-precision visual axis pointing solution method for a two-degree-of-freedom large-stroke reflector, characterized in that: When the initial zero incident angle β i =45°, the relationship between the change in the angle of the reflected light axis and the rotation angle of the reflector obtained by using the fifth-order polynomial fitting model is: i x =-3.948e -8 +0.5ψ x -9.529e -10 ψ y +6.372e -6 ψ x 2 +1.077e -8 ψ x ψ y +0.25ψ y 2 +4.566e -6 ψ x 3 +1.711e -6 ψ x 2 ψ y -0.25ψ x ψ y 2 -1.605e -6 ψ y 3 -0.0001266ψ x 4 -7.089e -7 ψ x 3 ψ y -0.06373ψ x 2 ψ y 2 -2.796e -7 ψ x ψ y 3 +0.0419ψ y 4 -4.931e -5 ψ x 5 -1.372e -5 ψ x 4 ψ y +0.1032ψ x 3 ψ y 2 -0.0001167ψ x 2 ψ y 3 +0.01832ψ x ψ y 4 +0.0001051ψ y 5 i y =6.749e -11 -1.806e -8 ψ x +0.7071ψ y -9.214e -8 ψ x 2 -0.3535ψ x ψ y -1.563e -8 ψ y 2 +1.607e -7 ψ x 3 -2.399e -5 ψ x 2 ψ y +8.984e -6 ψ x ψ y 2 -0.05891ψ y 3 +8.499e -7 ψ x 4 -0.02972ψ x 3 ψ y +7.038e -6 ψ x 2 ψ y 2 +0.2321ψ x ψ y 3 +5.078e -7 ψ y 4 +2.912e -6 ψ x 5 -0.0001462ψ x 4 ψ y -3.144e -5 ψ x 3 ψ y 2 -0.08336ψ x 2 ψ y 3 -0.0004709ψ x ψ y 4 +0.01111ψ y 5 。

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