A cubic mirror coordinate system establishment method based on measured angle values

Abstract

The application belongs to the technical field of photoelectric equipment calibration, and particularly relates to a cubic lens coordinate system establishment method based on measured angle values, which comprises the following steps: establishing a coordinate system fixedly connected with a cubic lens; measuring the measured angle values of the angles between adjacent surfaces of the cubic lens, and calculating the vector expressions of the normal vectors of the surfaces of the cubic lens in the coordinate system; and transferring a reference vector A to the coordinate system of the cubic lens or transferring the reference vector A in the coordinate system of the cubic lens to a new coordinate system by using the cubic lens. The cubic lens coordinate system establishment method based on measured angle values can realize high-precision reference transfer, and can also reduce the processing difficulty and manufacturing cost of the cubic lens.

Description

Technical Field

[0001] This application belongs to the field of optoelectronic equipment calibration technology, specifically relating to a method for establishing a cubic mirror coordinate system based on measured angle values. Background Technology

[0002] Cubic mirrors are widely used in aviation and aerospace fields as a high-precision reference transfer medium, and their accuracy directly affects the attitude measurement accuracy of the equipment. An ideal cubic mirror has all adjacent faces perpendicular to each other. By observing any two adjacent faces, a coordinate system can be established, realizing the transfer of measurement reference and coordinate transformation.

[0003] Ideally, the included angle between adjacent faces of a cubic mirror is 90°. However, in actual manufacturing, there will inevitably be machining errors at each 90° angle. To achieve high-precision measurement, the machining accuracy requirements for the included angle between adjacent faces of a cubic mirror are usually very high, requiring an error of no more than 5″, or even better than 2″ or 1″. This will greatly increase the difficulty and cost of manufacturing a cubic mirror. Summary of the Invention

[0004] Therefore, it is necessary to provide a method for establishing a cubic mirror coordinate system based on measured angle values ​​to address the shortcomings of existing technologies, thereby achieving high-precision reference transfer while reducing the processing difficulty and manufacturing cost of the cubic mirror.

[0005] To solve the above problems, this application adopts the following technical solution:

[0006] A method for establishing a cube mirror coordinate system based on measured angle values ​​includes the following steps:

[0007] Establish a coordinate system fixed to the cubic mirror;

[0008] Measure the actual angle values ​​of the angles between adjacent faces of the cube mirror, and calculate the vector expressions of the normal vectors of each face of the cube mirror in this coordinate system;

[0009] A cubic mirror is used for reference transfer, transferring the reference vector A to the cubic mirror coordinate system, or transferring the reference vector A that is already in the cubic mirror coordinate system to the new coordinate system.

[0010] In some embodiments, the specific steps for establishing a coordinate system fixed to the cubic mirror are:

[0011] Take any vertex of the cube mirror as the origin O of the coordinate system, and any one of the three faces of the cube mirror at that vertex as the object of observation, denoted as face 1#. Place the origin of the coordinate system at the lower left corner of face 1#. Take the vertical edge of face 1# that passes through the origin as the z-axis of the coordinate system, with the positive direction pointing upwards. Take the axis parallel to the normal vector of face 1# that passes through the origin as the y-axis, with the positive direction opposite to the normal vector of face 1#. The x-axis is perpendicular to the yOz plane. Establish a right-hand rectangular coordinate system O-xyz. According to the right-hand rule, the other three upright planes of the cube mirror are denoted as 2#, 3#, and 4#, respectively. The top face of the cube mirror is denoted as 5#, and the bottom face is denoted as 6#.

[0012] In some embodiments, the specific steps for measuring the measured angle values ​​of the angles between adjacent faces of the cubic mirror and calculating the vector expressions of the normal vectors of each face of the cubic mirror in this coordinate system are as follows:

[0013] Let the normal vectors of surfaces 1-6 of the cube mirror be n1(x1, y1, z1), n2(x2, y2, z2), n3(x3, y3, z3), n4(x4, y4, z4), n5(x5, y5, z5), and n6(x6, y6, z6), respectively, all pointing outwards from the cube mirror. Since the normal vector n1 of surface 1 is opposite to the Oy axis, n1 = (0, -1, 0). The normal vector n4 of surface 4 is perpendicular to the z-axis, and z4 = 0. i (i = 2, 3, ..., 6) is a unit vector, therefore

[0014]

[0015] Given the included angles between adjacent faces of a cubic mirror: According to the formula for the dot product of vectors, we have

[0016]

[0017] The vector n can be obtained by solving formulas (1) and (2). i The coordinates of (i = 2, 3, ..., 6) in the coordinate system P-xyz.

[0018] In some embodiments, the specific steps of using a cubic mirror to transfer the reference vector A to the cubic mirror coordinate system, or to transfer the reference vector A already in the cubic mirror coordinate system to a new coordinate system, are as follows:

[0019] When it is necessary to transfer the reference vector A to the cube mirror coordinate system, the normal vectors k1 and k2 of any two adjacent planes of the cube mirror and the coordinates of the reference vector A in the same measurement coordinate system are observed by autocollimation. The relationship between the reference vector A and k1 and k2 is established, and the reference vector A can be transferred to the cube mirror coordinate system.

[0020] When it is necessary to transfer the reference vector A, which is already in the cubic mirror coordinate system, to the new coordinate system, the reference vector A can be linearly represented by the normal vectors k1, k2 and k1×k2 of the two adjacent surfaces of the cubic mirror.

[0021] In some embodiments, the reference transfer is performed using a cube mirror, transferring the reference vector A to the cube mirror coordinate system, or transferring the reference vector A already in the cube mirror coordinate system to a new coordinate system. Angle measurement and mutual aiming are achieved using a first theodolite and a second theodolite, thereby realizing reference transfer and transformation.

[0022] In some embodiments, the specific steps for using the first theodolite and the second theodolite to perform angle measurement and mutual aiming, and to realize reference transfer and conversion are as follows:

[0023] Let the measuring coordinate system of the first theodolite be O. T1 -x T1 y T1 z T1 The second theodolite's measuring coordinate system is O. T2 -x T2 y T2 z T2 ,

[0024] Using the autocollimation of the first theodolite to measure the reference vector A, its coordinate system O is obtained. T1 -x T1 y T1 z T1 The coordinates in the space are denoted as AO. T1 (x AT y AT , z AT );

[0025] Using the autocollimation of the first theodolite, a plane of the cube mirror is measured. The normal vector of this plane is k1. The coordinate system O is measured to be k1. T1 -x T1 y T1 z T1 The coordinates in the middle are denoted as

[0026] Using the autocollimation of the second theodolite, the plane adjacent to the plane with normal vector k1 of the cube mirror is measured, and its normal vector is k2. Using the mutual alignment of the first and second theodolites, vector k2 is transferred to the measurement coordinate system of the first theodolite, and the coordinate system O of vector k2 is calculated. T1 -x T1 y T1 z T1 The coordinates in the middle are denoted as Vectors A, k1, and k2 are in the same coordinate system O. T1 -xT1 y T1 z T1 Given coordinates, vector A can be linearly represented by vectors k1, k2, and k1×k2, i.e.

[0027] A = λ1k1 + λ2k2 + λ3(k1 × k2)

[0028] Using vectors A, k1, and k2 in the same coordinate system O T1 -x T1 y T1 z T1 Using the coordinates below, solve the three-variable linear equation to calculate λ1, λ2, and λ3;

[0029] The coordinates of vectors k1 and k2 in the cubic mirror coordinate system O-xyz have been calculated. Substituting them into A=λ1k1+λ2k2+λ3(k1×k2), the coordinates of the reference vector A in the cubic mirror coordinate system O-xyz can be calculated, thus realizing high-precision reference transfer.

[0030] If the reference vector A has already been transferred to the cube mirror coordinate system, it is only necessary to obtain the coordinates of the normal vectors k1 and k2 of any two planes of the cube mirror containing the reference vector A in the new coordinate system to transfer the reference vector A to the new coordinate system.

[0031] The technical solution adopted in this application has the following effects:

[0032] This application establishes a coordinate system fixed to a cube mirror. By measuring the angles between adjacent faces of the cube mirror, the coordinates of the normal vectors of each face in this coordinate system are calculated. Thus, the coordinates of the normal vectors of the six planes of the cube mirror in the cube mirror coordinate system are known. When using this cube mirror for reference transformation, simply observing any two adjacent planes of the cube mirror and the vector to be transferred via autocollimation yields the coordinate expression of that vector in the cube mirror coordinate system. Since the measurement accuracy of the angles between adjacent faces of the cube mirror is very high, typically better than 0.5″, the normal vectors of each face of the cube mirror can be accurately reconstructed in the cube mirror coordinate system, achieving high-precision reference transfer and transformation.

[0033] This application uses the measured values ​​of the included angles between adjacent faces of a cubic mirror as the basis for calculation, and does not require that the included angles deviate from 90° (the theoretical value), that is, it allows for a large deviation between the included angles between adjacent faces of the cubic mirror and 90°. In contrast, traditional cubic mirrors require that the deviation of the included angles between adjacent faces from 90° not exceed 5″, or even 2″ or 1″, which is difficult to manufacture and costly. Therefore, the method of this application greatly reduces the manufacturing difficulty and cost of cubic mirrors, and has good prospects for engineering applications. Attached Figure Description

[0034] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 A schematic diagram illustrating the numbering of each facet of the cube mirror and the definition of the cube mirror coordinate system provided in the embodiments of this application;

[0036] Figure 2 This is a schematic diagram illustrating the establishment of a cubic mirror measurement coordinate system and the transfer of references, as provided in an embodiment of this application. Detailed Implementation

[0037] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0038] In the description of this application, it should be understood that the terms "upper", "lower", "horizontal", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application 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, and therefore should not be construed as a limitation of this application.

[0039] 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 one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0041] Example 1

[0042] This application provides a method for establishing a cubic mirror coordinate system based on measured angle values, characterized by the following steps:

[0043] Establish a coordinate system fixed to the cubic mirror;

[0044] Measure the actual angle values ​​of the angles between adjacent faces of the cube mirror, and calculate the vector expressions of the normal vectors of each face of the cube mirror in this coordinate system;

[0045] A cubic mirror is used for reference transfer, transferring the reference vector A to the cubic mirror coordinate system, or transferring the reference vector A that is already in the cubic mirror coordinate system to the new coordinate system.

[0046] Specifically, such as Figure 1 As shown, the four sides of the cube mirror are labeled as 1#, 2#, 3#, and 4#, the upper side is labeled as 5#, and the lower side is labeled as 6#. The intersection of sides 1#, 4#, and 6# is taken as the origin O. The intersection of sides 1# and 4# is taken as the z-axis, pointing upwards. The axis passing through the origin O and parallel to the normal vector of side 1# is taken as the y-axis, with its positive direction opposite to the normal vector of side 1#. The x-axis is perpendicular to the yOz plane, establishing a right-handed rectangular coordinate system O-xyz.

[0047] The normal vectors of faces 1-6 of the cube mirror are denoted as n1(x1, y1, z1), n2(x2, y2, z2), n3(x3, y3, z3), n4(x4, y4, z4), n5(x5, y5, z5), and n6(x6, y6, z6), respectively, all pointing outwards from the cube mirror. The included angles between adjacent faces of the cube mirror are denoted as: There are a total of 12 angles, all of which are known quantities. For example, its subscript "23" indicates that the angle is the angle between plane 2 and plane 3, and the superscript "z" indicates that the intersection line of plane 2 and plane 3 is approximately parallel to the z-axis of the coordinate system.

[0048] When establishing the cubic mirror coordinate system O-xyz, let the y-axis be parallel to the normal vector of plane 1 and opposite in direction. Therefore, the normal vector of plane 1 is n1 = (0, -1, 0).

[0049] Now calculate the coordinates of the normal vectors n2, n3, n4, n5, and n6 of surfaces 2#, 3#, 4#, 5#, and 6# in the coordinate system O-xyz.

[0050] Since the z-axis is the intersection of plane 1 and plane 4, the normal vector n4 of plane 4 is perpendicular to the z-axis. Let k = (0, 0, 1), and we can obtain the vector dot product formula.

[0051]

[0052] again And x4 < 0, therefore so

[0053] For the normal vector n5 of surface #5, we can obtain the following from the vector dot product formula:

[0054]

[0055] again And z5 > 0, therefore the coordinates of the normal vector n5 of surface 5 are:

[0056]

[0057] For the normal vector n6 of surface #6, we can obtain the following from the vector dot product formula:

[0058]

[0059] again Since z6 < 0, the coordinates of the normal vector n6 of surface 6# are:

[0060]

[0061] For the normal vector n2 of surface #2, we can obtain the formula for the inner product of vectors.

[0062]

[0063] so, again Therefore Substituting z2 into this equation yields a quadratic equation in x2.

[0064]

[0065] Since x2 > 0, therefore

[0066]

[0067] Therefore, the coordinates of the normal vector n2 of surface #2 are:

[0068]

[0069] For the normal vector n3 of surface #3, since y3 > 0, let From the vector dot product formula, we can obtain

[0070]

[0071] By eliminating the radicals in equations one and three of the above system of equations, we get...

[0072]

[0073] Substitute into the equation Sorted out

[0074]

[0075] In the formula

[0076]

[0077] Clearly, the above equation is a quadratic equation in z³. Using the quadratic formula, z³ can be calculated, yielding two roots. These roots can then be used to calculate x³ and y³, which are then substituted back into the equation. In the equation, only one set of (x3, y3, z3) can satisfy the equation. This set of (x3, y3, z3) is the coordinate of the normal vector n3.

[0078] After the above calculations, the coordinates of the normal vectors n1 to n6 of the six faces of the cubic mirror in the cubic mirror coordinate system O-xyz are all obtained.

[0079] It should be noted that, in some embodiments, a portion of the cubic mirror may be selected for measurement.

[0080] For example:

[0081] If the 6# face (bottom face) of the cubic mirror is used as the mounting surface and is not included in the measurement, then the angle is not required. and Since the measured value is not needed, and the normal vector n6 of surface #6 does not need to be solved, the number of unknowns becomes 11, and the number of equations becomes 12. Similarly, the vector n can be calculated. i The coordinates of (i = 2, 3, ..., 5) in the coordinate system O-xyz.

[0082] If surfaces #6 and #3 of the cubic mirror are not involved in the measurement, then angles are not required. and Since the measured values ​​are not required, and it is not necessary to solve for the normal vectors n6 and n3 of surfaces 6# and 3#, the number of unknowns becomes 8, and the number of equations becomes 8. Similarly, the vector n can be calculated. i The coordinates of (i = 2, 4, 5) in the coordinate system O-xyz.

[0083] If surfaces #6, #3, and #2 of the cubic mirror are not involved in the measurement, then angles are not required. and Since the measured values ​​are obtained, it is not necessary to solve for the normal vectors n6, n3, and n2 of surfaces 6#, 3#, and 2#. Therefore, the number of unknowns and equations becomes 5, and the vector n can be calculated similarly. i The coordinates of (i = 4, 5) in the coordinate system O-xyz.

[0084] If only surfaces #1 and #4 of the cubic mirror are involved in the measurement, then only the angle is needed. If the measured value is obtained, then the number of unknowns becomes 2, and the number of equations becomes 2. Similarly, the coordinates of vector n4 in the coordinate system O-xyz can be calculated.

[0085] After the above calculations, the next step is to use Figure 2 This paper explains how to use the acquired cube mirror normal vector coordinates to achieve high-precision reference transfer.

[0086] Specifically, after obtaining the cube mirror normal vector that needs to be calculated, such as Figure 2 As shown, when using a cube mirror for reference transfer, a high-precision electronic theodolite is typically used as the measuring instrument. It is necessary to transfer the reference vector A to the cube mirror coordinate system, or to transfer the reference vector A, already in the cube mirror coordinate system, to a new coordinate system. Angle measurement and mutual aiming are achieved using the first and second theodolites, thus realizing reference transfer and transformation. Let the measuring coordinate system of the first theodolite be O. T1 -x T1 y T1 z T1 The second theodolite's measuring coordinate system is O. T2 -x T2 y T2 z T2 The specific steps are as follows:

[0087] First, the reference vector A is measured using the autocollimation of the first theodolite to obtain its coordinate system O. T1 -x T1 y T1 z T1 The coordinates in the middle are denoted as Using the autocollimation of the first theodolite, a plane of the cube mirror is measured. The normal vector of this plane is k1. The coordinate system O is measured to be k1. T1 -x T1 y T1 z T1 The coordinates in the middle are denoted as Using the autocollimation of the second theodolite, the plane adjacent to the plane with normal vector k1 of the cube mirror is measured, and its normal vector is k2. Using the mutual alignment of the first and second theodolites, vector k2 is transferred to the measurement coordinate system of the first theodolite, and the coordinate system O of vector k2 is calculated. T1 -x T1 y T1 z T1 The coordinates in the middle are denoted as Therefore, vectors A, k1, and k2 are in the same coordinate system O. T1 -x T1 y T1 z T1 The coordinate representation is given below. Then vector A can be linearly represented by vectors k1, k2, and k1×k2, i.e.

[0088] A = λ1k1 + λ2k2 + λ3(k1 × k2)

[0089] Using vectors A, k1, and k2 in the same coordinate system O T1-x T1 y T1 z T1 Using the coordinates below, we can solve the three-variable linear equation to calculate λ1, λ2, and λ3.

[0090] According to this application, the coordinates of vectors k1 and k2 in the cubic mirror coordinate system O-xyz have been calculated. Substituting them into A=λ1k1+λ2k2+λ3(k1×k2), the coordinates of the reference vector A in the cubic mirror coordinate system O-xyz can be calculated, thus realizing high-precision reference transfer.

[0091] Similarly, if the reference vector A has been transferred to the cube mirror coordinate system, then the reference vector A can be linearly expressed using the normal vectors of any two planes of the cube mirror (generally, the normal vectors of adjacent planes are used as long as the two normal vectors are not parallel), and λ1, λ2, and λ3 can be calculated. In this case, if you want to transfer the reference vector A to the theodolite or other cube mirror coordinate systems, you only need to obtain the coordinates of the normal vectors k1 and k2 of any two adjacent planes of the cube mirror containing the reference vector A in the new coordinate system, substitute them into the expression, and the reference vector A can be transferred to that new coordinate system.

[0092] This application establishes a coordinate system fixed to a cube mirror. By measuring the angles between adjacent faces of the cube mirror, the coordinates of the normal vectors of each face in this coordinate system are calculated. Thus, the coordinates of the normal vectors of the six planes of the cube mirror in the cube mirror coordinate system are known. When using this cube mirror for reference transformation, simply observing any two adjacent planes of the cube mirror and the vector to be transferred via autocollimation yields the coordinate expression of that vector in the cube mirror coordinate system. Since the measurement accuracy of the angles between adjacent faces of the cube mirror is very high, typically better than 0.5″, the normal vectors of each face of the cube mirror can be accurately reconstructed in the cube mirror coordinate system, achieving high-precision reference transfer and transformation.

[0093] This application uses the measured values ​​of the included angles between adjacent faces of a cubic mirror as the basis for calculation, and does not require that the included angles deviate from 90° (the theoretical value), that is, it allows for a large deviation between the included angles between adjacent faces of the cubic mirror and 90°. In contrast, traditional cubic mirrors require that the deviation of the included angles between adjacent faces from 90° not exceed 5″, or even 2″ or 1″, which is difficult to manufacture and costly. Therefore, the method of this application greatly reduces the manufacturing difficulty and cost of cubic mirrors, and has good prospects for engineering applications.

[0094] This application presents a method for establishing a cube mirror coordinate system based on measured angle values. By utilizing high-precision measured values ​​of the angles between adjacent faces of the cube mirror, it reconstructs the coordinate expression of the normal vectors of each face of the cube mirror in the cube mirror coordinate system, thereby achieving high-precision reference transfer. In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The embodiments described above are merely illustrative, such as the methods for establishing the cube mirror coordinate system and solving for the coordinates of the normal vectors of each face of the cube mirror. In actual implementation, there may be other methods for establishing or calculating the coordinate system. Any method that uses the measured values ​​of the angles between adjacent faces of the cube mirror to establish the cube mirror coordinate system or express the normal vectors of each plane of the cube mirror should be considered within the scope of protection of this application.

[0095] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for establishing a cubic mirror coordinate system based on measured angle values, characterized in that, Includes the following steps: Establish a coordinate system fixed to the cubic mirror; Measure the actual angle values ​​of the angles between adjacent faces of the cube mirror, and calculate the vector expressions of the normal vectors of each face of the cube mirror in the cube mirror coordinate system; A cubic mirror is used for reference transfer, transferring the reference vector A to the cubic mirror coordinate system, or transferring the reference vector A that is already in the cubic mirror coordinate system to the new coordinate system.

2. The method for establishing a cubic mirror coordinate system based on measured angle values ​​according to claim 1, characterized in that, The specific steps for establishing a coordinate system fixed to the cubic mirror are as follows: Take any vertex of the cube mirror as the origin O of the coordinate system, and any one of the three faces of the cube mirror at that vertex as the object of observation, denoted as face 1#. Place the origin of the coordinate system at the lower left corner of face 1#. Take the vertical edge of face 1# that passes through the origin as the z-axis of the coordinate system, with the positive direction pointing upwards. Take the axis parallel to the normal vector of face 1# that passes through the origin as the y-axis, with the positive direction opposite to the normal vector of face 1#. The x-axis is perpendicular to the yOz plane. Establish a right-hand rectangular coordinate system O-xyz. According to the right-hand rule, the other three upright planes of the cube mirror are denoted as 2#, 3#, and 4#, respectively. The top face of the cube mirror is denoted as 5#, and the bottom face is denoted as 6#.

3. The method for establishing a cubic mirror coordinate system based on measured angle values ​​according to claim 1, characterized in that, The specific steps for measuring the measured angle values ​​of the angles between adjacent faces of the cubic mirror and calculating the vector expressions of the normal vectors of each face of the cubic mirror in this coordinate system are as follows: Let the normal vectors of surfaces 1#-6# of the cubic mirror be respectively: , , , , , The directions are all towards the outside of the cube mirror, because the normal vector of the cube mirror's #1 surface... Opposite to the Oy axis direction, therefore 4# surface normal vector Perpendicular to the z-axis, Since vector n i Let i be a unit vector, where i = 2, 3, ..., 6; therefore （1） Given the included angles between adjacent faces of a cubic mirror: , , , , , , , , , , , According to the formula for the inner product of vectors, we have （2） The vector n can be obtained by solving formulas (1) and (2). i Coordinates in the xyz coordinate system.

4. The method for establishing a cubic mirror coordinate system based on measured angle values ​​according to claim 1, characterized in that, The specific steps for using a cubic mirror to transfer the reference vector A to the cubic mirror coordinate system, or to transfer the reference vector A already in the cubic mirror coordinate system to a new coordinate system, are as follows: When it is necessary to transfer the reference vector A to the cube mirror coordinate system, the normal vectors k1 and k2 of any two adjacent planes of the cube mirror and the coordinates of the reference vector A in the same measurement coordinate system are observed by autocollimation. The relationship between the reference vector A and k1 and k2 is established, and the reference vector A can be transferred to the cube mirror coordinate system. When it is necessary to transfer the reference vector A, which is already in the cubic mirror coordinate system, to the new coordinate system, the reference vector A can be linearly represented by the normal vectors k1, k2 and k1×k2 of the two adjacent surfaces of the cubic mirror.

5. The method for establishing a cubic mirror coordinate system based on measured angle values ​​according to claim 1, characterized in that, The reference transfer is achieved by using a cube mirror to transfer the reference vector A to the cube mirror coordinate system, or to transfer the reference vector A that is already in the cube mirror coordinate system to the new coordinate system. Angle measurement and mutual aiming are achieved using the first theodolite and the second theodolite, thus realizing the reference transfer and transformation.

6. The method for establishing a cubic mirror coordinate system based on measured angle values ​​according to claim 5, characterized in that, The specific steps for using the first and second theodolites to measure angles and cross-align them, and to transfer and convert references, are as follows: Let the measuring coordinate system of the first theodolite be... The second theodolite's measuring coordinate system is , Using the self-collimation measurement of the reference vector A with the first theodolite, its coordinate system is obtained. The coordinates in the middle are denoted as ; Using the autocollimation of the first theodolite, a plane of the cube mirror is measured. The normal vector of this plane is k1. The coordinate system of k1 is measured. The coordinates in the middle are denoted as ; Using the autocollimation of the second theodolite, the plane adjacent to the plane with normal vector k1 of the cube mirror is measured, and its normal vector is k2. Using the mutual alignment of the first and second theodolites, vector k2 is transferred to the measurement coordinate system of the first theodolite, and the coordinate system in which vector k2 is located is calculated. The coordinates in the middle are denoted as This results in vectors A, k1, and k2 being in the same coordinate system. Given coordinates, vector A can be linearly represented by vectors k1, k2, and k1×k2, i.e. Using vectors A, k1, and k2 in the same coordinate system Using the coordinates below, solve the three-variable linear equation to calculate... , and ; The coordinates of vectors k1 and k2 in the cubic mirror coordinate system O-xyz have been calculated. Substitute them into... In this way, the coordinates of the reference vector A in the cubic mirror coordinate system O-xyz can be calculated, realizing high-precision reference transfer; If the reference vector A has been transferred to the cube mirror coordinate system, it is only necessary to obtain the coordinates of the normal vectors k1 and k2 of any two adjacent planes of the cube mirror containing the reference vector A in the new coordinate system. Following the above method, the reference vector A can be transferred to the new coordinate system.

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