An angular decoupling method for folded optical paths in multi-degree-of-freedom measurement systems

Abstract

An angle decoupling method for a folded optical path in a multi-degree-of-freedom measurement system, belonging to the technical field of multi-degree-of-freedom measurement. To solve the problem of accurate angle decoupling of the folded optical path in the multi-degree-of-freedom measurement system, the present invention obtains the normal vector of the spot position sensor according to the spatial positions and angles of each reflection device in the multi-degree-of-freedom measurement system; makes the incident light deflect a certain angle around the X-axis or Y-axis to obtain the intersection coordinates of the incident light with a deflection angle and the spot position sensor; uses a transformation matrix to transform the intersection coordinates of the incident light with a deflection angle and the spot position sensor onto the XOY plane to obtain the transformed intersection coordinates; uses a rotation matrix with an angle of the misalignment angle θ zd‑z about the Z-axis to transform the transformed intersection coordinates so that the X component or Y component of the intersection coordinates after the re-transformation is 0; constructs an angle decoupling formula using the angle θ zd‑z and the rotation matrix to correct the angle coupling error caused by the folded optical path.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-degree-of-freedom measurement, and in particular relates to an angle decoupling method of a folded optical path in a multi-degree-of-freedom measurement system. Background Art

[0002] Multi-degree-of-freedom measurement systems play a vital role in the field of precision machining and manufacturing, and are often used in complex measurement environments such as CNC machine tools. In order to achieve convenient measurement in complex environments, miniaturization is an inevitable development trend of multi-degree-of-freedom measurement systems. The autocollimation principle is a simple angle measurement method that is easy to integrate with other modules and is widely used in multi-degree-of-freedom measurement systems. However, in the autocollimation method, if you want to improve the angle measurement resolution, you need to increase the focal length of the lens, which increases the volume of the entire measurement system, making the measurement system more cumbersome and inconvenient to use. Folding the optical path is an effective means to reduce the volume of optical equipment, and it is also the most direct way to increase the optical path under the premise that the space occupied by the equipment remains unchanged. Therefore, the method of folding the optical path can be used to reduce the volume of the measurement system while taking into account the large focal length of the converging lens. However, the spatial position and angle of the reflector in the folded optical path will affect the angle of the light beam received by the detector, which is manifested as coupling between angles in the autocollimation angle measurement structure, which will greatly affect the angle measurement accuracy of the system.

[0003] In multi-degree-of-freedom measurement systems, angle coupling is often the first problem to be solved. For different angle measurement structures, the angle coupling situation is also different. At present, there are many studies on the angle coupling problem. For example, Diao Kuan from Huazhong University of Science and Technology proposed a measurement method based on crosstalk decoupling to measure the six-degree-of-freedom motion error of linear stages (DIAO K, CHEN C, LEACH R, et al. Crosstalk decoupling measurement method to determine the six degrees of freedom of motion error of linear stages [J]. Applied Optics, 2022, 61 (6)). In this method, the spot position output by the three four-quadrant detectors in the motion unit contains information on the two straightness and three angular errors of the motion unit. The geometric relationship between the spot position, the detector and the center point of the motion unit is used for settlement, and finally the straightness and angular errors are decoupled. Yu Liang from Harbin Institute of Technology proposed a single-beam three-degree-of-freedom homodyne interferometer (YU L, MOLNAR G, WERNER C, et al. A single-beam 3DoF homodyne interferometer [J]. Measurement Science and Technology, 2020, 31 (8)), which can measure displacement, roll angle and pitch angle. The information of the roll angle and pitch angle is coupled in the interference fringes, and the two angles need to be decoupled. This method achieves angle decoupling by calculating the frequency components of the interference fringes in the x and y directions of the detector. Zheng Fajia from Beijing Jiaotong University proposed a multi-degree-of-freedom measurement model (ZHENG F, FENG Q, ZHANG B, et al. Effect of detector installation error on the measurement accuracy of multi-degree-of-freedom geometric errors of a linear axis[J]. Measurement Science and Technology, 2020, 31(9).), and studied the crosstalk between horizontal straightness, vertical straightness, yaw angle, and pitch angle caused by the installation error of the detector in the multi-degree-of-freedom measurement system based on the autocollimation principle, and gave the final measurement model to eliminate the coupling between the various degrees of freedom. However, in the current research, no research has analyzed the angular coupling problem caused by the folded optical path in the autocollimation structure of the multi-degree-of-freedom measurement system. Summary of the invention

[0004] The problem to be solved by the present invention is to accurately decouple the angle of a folded optical path in a multi-degree-of-freedom measurement system, and a method for decoupling the angle of a folded optical path in a multi-degree-of-freedom measurement system is proposed.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A method for decoupling the angle of a folded optical path in a multi-degree-of-freedom measurement system, using beam tracing and coordinate transformation, quantifies and corrects the angle coupling error introduced by the folded optical path in the multi-degree-of-freedom measurement system, comprising the following steps:

[0007] S1. Obtain the normal vector of the light beam received by the spot position sensor according to the spatial position and angle of each reflective device in the multi-degree-of-freedom measurement system;

[0008] S2. Deflect the incident light around the X-axis or Y-axis by a certain angle, and perform beam tracing to obtain the coordinates of the intersection of the incident light with the deflection angle and the light spot position sensor;

[0009] S3. According to the normal vector of the spot position sensor obtained in step S1, a transformation matrix is ​​obtained, and the coordinates of the intersection of the incident light with an angle and the spot position sensor are transformed to the XOY plane using the transformation matrix to obtain the transformed intersection coordinates;

[0010] S4. Using a mismatch angle θ around the Z axis zd-z The rotation matrix is ​​used to transform the intersection coordinates transformed in step S3 so that the X component or Y component of the intersection coordinates transformed again is 0;

[0011] S5. Use the angle θ obtained in step S4. zd-z The angle decoupling formula is constructed with the rotation matrix to correct the angle coupling error caused by the folded optical path.

[0012] Furthermore, the angle measurement module in the multi-degree-of-freedom measurement system is simplified, and the light source, lens, reflector and light spot position sensor are retained; the light emitted by the light source is transmitted through the lens, and sequentially passes through the first reflector, the second reflector, the third reflector, and then is reflected by the second reflector and the fourth reflector, and then is received by the light spot position sensor, and the light spot position sensor outputs the position coordinates of the light spot;

[0013] Furthermore, a reference coordinate system, a beam coordinate system and a sensor coordinate system are established for the simplified angle measurement module. The reference coordinate system O-XYZ is assumed to be a right-handed system, the center of the lens is the coordinate zero point, and the ideal outgoing beam direction of the light source is the positive direction of the Z axis.

[0014] Set the first beam coordinate system O l -Xl Y l Z l , the second beam coordinate system O l-14 -X l-14 Y l-14 Z l-14 , the third beam coordinate system O l-151 -X l-151 Y l-151 Z l-151 , the fourth beam coordinate system O l-16 -X l-16 Y l-16 Z l-16 , the fifth beam coordinate system

[0015] O l-152 -X l-152 Y l-152 Z l-152 , the sixth beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 The Z-axis direction is the same as the beam propagation direction, wherein the first beam coordinate system O l -X l Y l Z l is the light beam coordinate system of the light source, and the second light beam coordinate system O l-14 -X l-14 Y l-14 Z l-14 is the coordinate system of the light beam after being reflected by the first reflector, and the third light beam coordinate system O l-151 -X l-151 Y l-151 Z l-151 is the coordinate system of the light beam after being reflected by the second reflector for the first time, and the fourth light beam coordinate system O l-16 -X l-16 Y l-16 Z l-16 is the coordinate system of the light beam after being reflected by the third reflector, and the fifth light beam coordinate system O l-152 -X l-152 Y l-152 Z l-152 is the coordinate system of the light beam after being reflected by the second reflector. The sixth light beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 is the coordinate system of the light beam after being reflected by the fourth reflector; O 18 -X 18 Y 18 Z 18is the light spot position sensor coordinate system, and the intersection of the light beam reflected by the fourth reflector and the light spot position sensor is the zero point of the coordinate system.

[0016] Furthermore, the specific implementation method of step S1 includes the following steps:

[0017] S1.1. Set the ideal output light of the light source l i The direction vector is expressed as:

[0018]

[0019] Set the unit normal vector of the first reflector Unit normal vector of the second reflector Unit normal vector of reflector No. 3 and the unit normal vector of the fourth reflector Respectively expressed as:

[0020]

[0021] Among them, a k 、b k 、c k are the direction cosines of the normal vector of the kth reflector relative to the X, Y, and Z axes in the reference coordinate system O-XYZ, k=1, 2, 3, 4;

[0022] S1.2. According to the law of reflection, the reflection transformation matrix R of the kth reflector Mk It is expressed as:

[0023]

[0024] R M1 is the reflection transformation matrix of the No. 1 reflector, R M2 is the reflection transformation matrix of the second reflector, R M3 is the reflection transformation matrix of the third reflector, R M4 is the reflection transformation matrix of the fourth reflector;

[0025] S1.3. Ideal incident light i Direction vector after the first reflection from reflector No. 1 and the direction vector after the first reflection from the second reflector Respectively expressed as:

[0026]

[0027] The three coordinate components in the beam direction vector are abbreviated as l ojx (a k ,b k ,c k ), lojy (a k ,b k ,c k ), l ojz (a k ,b k ,c k ) means about a k 、b k and c k The expression of, where j represents the number of times the light beam is reflected by each mirror, here j = 1, 2;

[0028] The direction vector of the light beam after it is reflected by the third reflector, and then by the second and fourth reflectors and It is expressed as:

[0029]

[0030] For the convenience of expression, in the subsequent derivation, l ojx (a k ,b k ,c k ), l ojy (a k ,b k ,c k ) and l ojz (a k ,b k ,c k )Use l ojx , l ojy and l ojz Indicates that, here j = 3, 4, 5;

[0031] S1.4. Ideal incident light i After being reflected by four reflectors in sequence, it is received by the spot position sensor. In order to avoid the spot position data output by the spot position sensor containing cosine error, the plane where the spot position sensor is located should be perpendicular to the received beam, that is, the direction vector is the normal vector of the plane where the light spot position sensor is located.

[0032] Furthermore, the specific implementation method of step S2 includes the following steps:

[0033] S2.1. When the incident light has a deflection angle β along the Y-axis, the direction vector of the incident light is expressed as:

[0034]

[0035] Among them, l i' indicates that there is a general incident light with a deflection angle around the Y axis, and the β in the coordinate is a small angle approximation of tanβ;

[0036] S2.2. Assume that the light beam passes through the zero point of the reference coordinate system O-XYZ, obtain the straight line equation of the light beam according to the light beam direction vector, and then use beam tracing to obtain the coordinates of the intersection of the incident light and each plane according to the position and angle of the plane where each reflector and the spot position sensor are located;

[0037] The calculated incident light l i 'The general first intersection coordinate P with the No. 1 reflector M1 'for:

[0038]

[0039] The general second intersection coordinates P of the reflected light from the first reflector and the second reflector M2 'for:

[0040] P M2 '=[P x-M2 ,P y-M2 ,P z-M2 ] T (9)

[0041] Among them, P x-M2 , P y-M2 and P z-M2 is the general second intersection point P M2 'The three coordinate components in the coordinates are expanded as follows:

[0042]

[0043] Generally the second intersection point P M2 'The position coordinates on the plane of the second reflector are related to the position and angle of the plane where the first reflector and the second reflector are located, and at the general second intersection point P M2 The three coordinate components of ' all contain the component of deflection angle β;

[0044] It is thus obtained that after the light beam is reflected by the No. 1 reflector and the No. 2 reflector, there is an angle coupling phenomenon. When the light beam is reflected by the No. 3 reflector, the No. 2 reflector, and the No. 4 reflector and is finally received by the spot position sensor, the light beam intersects with the plane of the spot position sensor at the general third intersection point P. PSD1 ', repeat the above beam tracing process to obtain the general third intersection point P PSD1 'Coordinates:

[0045] P PSD1 '=[P x-PSD1 ,P y-PSD1 ,P z-PSD1 ]T (11)

[0046] Among them, P x-PSD1 , P y-PSD1 and P z-PSD1 is the general third intersection point P PSD1 'Three coordinate components in the coordinates; generally the third intersection point P PSD1 The three coordinate components of ' all contain the position and angle information of each reflector plane and the light spot position sensor plane, as well as the deflection angle β.

[0047] Furthermore, the specific implementation method of step S3 includes the following steps:

[0048] S3.1. First, use the direction vector Calculate the transformation matrix T zd , the sensor coordinate system O 18 -X 18 Y 18 Z 18 Z 18 The direction of the axis is rotated to the Z-axis direction of the reference coordinate system O-XYZ, according to the definition of the rotation matrix and the direction vector The direction cosines give the transformation matrix T zd The expression is:

[0049]

[0050] S3.2. Transform the matrix T zd With direction vector After multiplication, we get:

[0051]

[0052] in, Represents the direction vector of the Z axis of the reference coordinate system;

[0053] After the transformation matrix T zd After the transformation, the angular coupling on the spot position sensor plane will be converted to the XOY plane of the reference coordinate system, that is, after the transformation, point P PSD1 'On the XOY plane; let the point on the XOY plane at this time be the transformed intersection coordinate P PSD1 ",but:

[0054] P PSD1 ” = T zd ·P PSD1 '=[P zd-x ,P zd-y ,0] T (14)

[0055] Among them, Pzd-x and P zd-y For about a k 、b k 、c k 、x k ,y k 、z k and β, k = 1, 2, 3, 4; a k 、b k 、c k and x k ,y k 、z k The six parameters correspond to the position and angle of the reflector in the folded optical path. When the folded optical path design is completed, the specific values ​​of the six parameters are also determined.

[0056] Furthermore, the specific implementation method of step S4 includes the following steps:

[0057] S4.1. According to the definition of the rotation matrix, the angle around the Z axis is the mismatch angle θ zd-z The rotation matrix R zd-z It is expressed as:

[0058]

[0059] S4.2. Set point P PSD1 "The coordinates are rotated by the matrix R zd-z The coordinates obtained after transformation are P PSD1 ”' means:

[0060]

[0061] From formula (15), we can see that when point P PSD1 When the coordinates of ' contain only the X-axis component, that is, when the Y-axis component is zero, then:

[0062] cosθ zd-z ·P zd-y -sinθ zd-z ·P zd-x = 0. (17)

[0063] Furthermore, the specific implementation method of step S5 includes the following steps:

[0064] S5.1. Based on P zd-x and P zd-y The value of is known after the position parameters of each device in the folded optical path are determined, so the mismatch angle θ is obtained based on formula (17): zd-z ;

[0065] S5.2. Based on the mismatch angle obtained in step S5.1, the angle coupling model of the self-collimation angle measurement structure including the folded optical path is constructed using a two-dimensional rotation matrix:

[0066]

[0067] in, is the pitch angle after model correction, is the yaw angle after model correction.

[0068] Beneficial effects of the present invention:

[0069] The angle decoupling method of the folded optical path in the multi-degree-of-freedom measurement system described in the present invention combines the beam tracing method with the coordinate transformation when analyzing the folded optical path, which greatly simplifies the calculation process. A complete beam tracing requires obtaining the direction of the beam and the intersection of the beam and the interface. If only the beam tracing method is used to obtain the mismatch angle θ zd-z , at least two complete beam tracing processes are required. For a folded optical path containing multiple reflectors, the calculation process will be extremely complicated. However, combining the beam tracing method with coordinate transformation only requires one complete beam tracing process, that is, calculating the intersection point and direction once. Therefore, the analysis process of the folded optical path in the method proposed by the present invention reduces the amount of calculation and realizes the rapid analysis of the angle coupling error of the folded optical path. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a schematic diagram of the structure of the multi-degree-of-freedom measurement system of the present invention;

[0071] Figure 2 This is a simplified structural diagram of an angle measurement module of a multi-degree-of-freedom measurement system according to the present invention;

[0072] Figure 1 Middle: 1 is a fixed unit, 2 is a mobile unit, 3 is a non-polarizing beam splitter, 4 is a light spot position sensor No. 1, 5 is a cone, 6 is a lens, 7 is a reflector No. 1, 8 is a reflector No. 2, 9 is a reflector No. 3, 10 is a reflector No. 4, and 11 is a light spot position sensor No. 2;

[0073] Figure 2 In the middle: 12 is a light source, 13 is a lens, 14 is a first reflector, 15 is a second reflector, 16 is a third reflector, 17 is a fourth reflector, and 18 is a light spot position sensor;

[0074] Figure 3 The present invention provides a flow chart of an angle decoupling method for a folded optical path in a multi-degree-of-freedom measurement system. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0076] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0077] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 -Attached Figure 3 The detailed instructions are as follows: Specific implementation method one:

[0079] A method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system is proposed. The angle coupling error introduced by the folded optical paths in the multi-degree-of-freedom measurement system is quantified and corrected by using beam tracing and coordinate transformation.

[0080] Comparative Example Figure 1It is a multi-degree-of-freedom measurement system including a folded optical path. The measurement system consists of two parts, one is a fixed unit 1, and the other is a mobile unit 2. The fixed unit 1 includes a laser and an interference optical path, which are used to provide a light source for the measurement system and to measure displacement in conjunction with the mobile unit. The mobile unit includes a horizontal straightness and vertical straightness measurement module and a yaw angle and pitch angle measurement module. After the light emitted from the light source enters the moving unit, it is split for the first time by the non-polarizing beam splitter 3. After the split light is transmitted through the non-polarizing beam splitter 3, it is directly received by the No. 1 light spot position sensor 4. The No. 1 light spot position sensor 4 can output the position change of the light spot it receives, which is used to measure the horizontal straightness and vertical straightness; after the split light is reflected by the angle cone 5, it enters the angle cone 5 and is reflected back to the non-polarizing beam splitter 3. At this time, the light beam is split for the second time by the non-polarizing beam splitter 3. The split light is reflected back to the fixed unit 1 and enters the interference light path in the fixed unit 1 to measure the displacement; the split light reaches the lens 6, and after transmitting through the lens 6, it is reflected by the No. 1 reflector 7, the No. 2 reflector 8, the No. 3 reflector 9, the No. 2 reflector 8 and the No. 4 reflector 10 in sequence, and is received by the No. 2 light spot position sensor 11, which is used to measure the yaw angle and the pitch angle. The second reflector 8 and the fourth reflector 10 are at a certain angle to the XOZ plane, so that the light beam reflected by the fourth reflector 10 is parallel to the X axis; the second light spot position sensor 11 is located at the focus of the lens 6, that is, the light beam converges on the plane of the second light spot position sensor 11. The yaw angle and pitch angle measurement module in the multi-degree-of-freedom measurement system adopts the principle of autocollimation angle measurement, that is, according to the position change Δ of the light spot in two directions output by the second light spot position sensor 11, the yaw angle and pitch angle measurement module in the multi-degree-of-freedom measurement system are x and Δ y The deflection angle is measured by comparing the focal length f of lens 6 with With pitch angle

[0081]

[0082] The angle measurement module in the multi-degree-of-freedom measurement system is simplified, and the resulting structure is as follows: Figure 2 As shown, the light emitted by the light source 12 is transmitted through the lens 13, passes through the No. 1 reflector 14, the No. 2 reflector 15, the No. 3 reflector 16 in sequence, and is reflected again by the No. 2 reflector 15 and the No. 4 reflector 17, and is received by the light spot position sensor 18, which outputs the position coordinates of the light spot.

[0083] For the simplified angle measurement module, a reference coordinate system, a beam coordinate system and a sensor coordinate system are established. The reference coordinate system O-XYZ is set as a right-handed system, the center of the lens is the coordinate zero point, and the ideal outgoing beam direction of the light source is the positive direction of the Z axis. Set the first beam coordinate system O l -X l Y l Zl , the second beam coordinate system O l-14 -X l-14 Y l-14 Z l-14 , the third beam coordinate system O l-151 -X l-151 Y l-151 Z l-151 , the fourth beam coordinate system O l-16 -X l-16 Y l-16 Z l-16 , the fifth beam coordinate system O l-152 -X l-152 Y l- 152 Z l-152 , the sixth beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 The Z-axis direction is the same as the beam propagation direction, wherein the first beam coordinate system O l -X l Y l Z l is the light beam coordinate system of the light source, and the second light beam coordinate system O l-14 -X l-14 Y l-14 Z l-14 is the coordinate system of the light beam after being reflected by the first reflector, and the third light beam coordinate system O l-151 -X l-151 Y l-151 Z l-151 is the coordinate system of the light beam after being reflected by the second reflector for the first time, and the fourth light beam coordinate system O l-16 -X l-16 Y l-16 Z l-16 is the coordinate system of the light beam after being reflected by the third reflector, and the fifth light beam coordinate system O l-152 -X l-152 Y l-152 Z l-152 is the coordinate system of the light beam after being reflected by the second reflector. The sixth light beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 is the coordinate system of the light beam after being reflected by the fourth reflector; O 18 -X 18 Y 18 Z 18 is the light spot position sensor coordinate system, and the intersection of the light beam reflected by the fourth reflector and the light spot position sensor is the zero point of the coordinate system;

[0084] The steps include:

[0085] S1. Obtain the normal vector of the light beam received by the spot position sensor according to the spatial position and angle of each reflector in the multi-degree-of-freedom measurement system;

[0086] The specific implementation method of step S1 includes the following steps:

[0087] S1.1. Set the ideal output light of the light source l i The direction vector is expressed as:

[0088]

[0089] Set the unit normal vector of the first reflector Unit normal vector of the second reflector Unit normal vector of reflector No. 3 and the unit normal vector of the fourth reflector Respectively expressed as:

[0090]

[0091] Among them, a k 、b k 、c k are the direction cosines of the normal vector of the kth reflector relative to the X, Y, and Z axes in the reference coordinate system O-XYZ, k=1, 2, 3, 4;

[0092] S1.2. According to the law of reflection, the reflection transformation matrix R of the kth reflector Mk It is expressed as:

[0093]

[0094] R M1 is the reflection transformation matrix of the No. 1 reflector, R M2 is the reflection transformation matrix of the second reflector, R M3 is the reflection transformation matrix of the third reflector, R M4 is the reflection transformation matrix of the fourth reflector;

[0095] S1.3. Ideal incident light i Direction vector after the first reflection from reflector No. 1 and the direction vector after the first reflection from the second reflector Respectively expressed as:

[0096]

[0097] The three coordinate components in the beam direction vector are abbreviated as l ojx (a k ,bk ,c k ), l ojy (a k ,b k ,c k ), l ojz (a k ,b k ,c k ) means about a k , b k and c k The expression of, where j represents the number of times the light beam is reflected by each mirror, here j = 1, 2;

[0098] The direction vector of the light beam after it is reflected by the third reflector, and then by the second and fourth reflectors and It is expressed as:

[0099]

[0100] For the convenience of expression, in the subsequent derivation, l ojx (a k ,b k ,c k ), l ojy (a k ,b k ,c k ) and l ojz (a k ,b k ,c k )Use l ojx , l ojy and l ojz Indicates that, here j = 3, 4, 5;

[0101] Assume that the incident ideal beam l i The intersection points with each reflector and the spot position sensor in the folded light path are the ideal first intersection points P 14 (x1, y1, z1), ideal second intersection point P 151 (x2, y2, z2), ideal third intersection point P 16 (x3,y3,z3), ideal fourth intersection point P 152 (x 22 ,y 22 ,z 22 ), ideal fifth intersection point P 17 (x4,y4,z4) and the ideal sixth intersection point P 18 (x PSD1 ,y PSD1 ,z PSD1 ), where the ideal second intersection point P 151is the coordinate of the intersection point where the light beam first intersects the plane of the second reflector, the ideal fourth intersection point P 152 is the coordinate of the intersection point where the light beam intersects the plane of the second reflector. Therefore, based on the above direction vector and the intersection point coordinates, the expression of the plane where each reflector and the light spot position sensor are located can be obtained.

[0102] S1.4. Ideal incident light i After being reflected by four reflectors in sequence, it is received by the spot position sensor. In order to avoid the spot position data output by the spot position sensor containing cosine error, the plane where the spot position sensor is located should be perpendicular to the received beam, that is, the direction vector is the normal vector of the plane where the light spot position sensor is located.

[0103] S2. Deflect the incident light around the X-axis or Y-axis by a certain angle, and perform beam tracing to obtain the coordinates of the intersection of the incident light with the deflection angle and the light spot position sensor;

[0104] Furthermore, the specific implementation method of step S2 includes the following steps:

[0105] S2.1. When the incident light has a deflection angle β along the Y-axis, the direction vector of the incident light is expressed as:

[0106]

[0107] Among them, l i ' indicates that there is a general incident light with a deflection angle around the Y axis, and the β in the coordinate is a small angle approximation of tanβ;

[0108] S2.2. Assume that the light beam passes through the zero point of the reference coordinate system O-XYZ, obtain the straight line equation of the light beam according to the light beam direction vector, and then use beam tracing to obtain the coordinates of the intersection of the incident light and each plane according to the position and angle of the plane where each reflector and the spot position sensor are located;

[0109] The calculated incident light l i 'The general first intersection coordinate P with the No. 1 reflector M1 'for:

[0110]

[0111] The general second intersection coordinates P of the reflected light from the first reflector and the second reflector M2 'for:

[0112] P M2 '=[P x-M2 ,P y-M2 ,P z-M2 ] T (9)

[0113] Among them, P x-M2 , P y-M2 and P z-M2 is the general second intersection point P M2 'The three coordinate components in the coordinates are expanded as follows:

[0114]

[0115] Generally the second intersection point P M2 'The position coordinates on the plane of the second reflector are related to the position and angle of the plane where the first reflector and the second reflector are located, and at the general second intersection point P M2 The three coordinate components of ' all contain the component of deflection angle β;

[0116] It is thus obtained that after the light beam is reflected by the No. 1 reflector and the No. 2 reflector, there is an angle coupling phenomenon. When the light beam is reflected by the No. 3 reflector, the No. 2 reflector, and the No. 4 reflector and is finally received by the spot position sensor, the light beam intersects with the plane of the spot position sensor at the general third intersection point P. PSD1 ', repeat the above beam tracing process to obtain the general third intersection point P PSD1 'Coordinates:

[0117] P PSD1 '=[P x-PSD1 ,P y-PSD1 ,P z-PSD1 ] T (11)

[0118] Among them, P x-PSD1 , P y-PSD1 and P z-PSD1 is the general third intersection point P PSD1 'Three coordinate components in the coordinates; generally the third intersection point P PSD1 The three coordinate components of ' all contain the position and angle information of each reflector plane and the light spot position sensor plane, as well as the deflection angle β.

[0119] The angular coupling error caused by the folded optical path is caused by the mismatch between the beam coordinate system and the detector coordinate system.

[0120] In order to express the angle coupling problem more intuitively, the mismatch angle θ is introduced here. zd-z ,θ zd-z Angle is the sixth beam coordinate system O after being reflected by the fourth reflector l-17 -X l-17 Y l-17 Z l-17 X in l-17 Axis and Y l-17 Axis and sensor coordinate system O 18 -X 18Y 18 Z 18 X in 18 Axis and Y 18 The angle between the axes, such as Figure 2 First, in order to avoid the cosine error in the spot position information received by the spot position sensor in actual measurement, the spot position sensor is often placed perpendicular to its incident light beam, that is, Z 18 With the beam coordinate system Z l-17 The direction is consistent; secondly, let the sensor coordinate system O 18 -X 18 Y 18 Z 18 X in 18 The axis is parallel to the XOZ plane of the reference coordinate system O-XYZ. When the incident light has a deflection angle β around the Y axis, it is the general incident light l i ', if there is no angle coupling in the folded light path, the spot position on the spot position sensor will only be along the X 18 However, in reality, due to the sensor coordinate system O 18 -X 18 Y 18 Z 18 With the sixth beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 Mismatch, the change in the spot position on the spot position sensor is X 18 and Y 18 There are components in both directions. Therefore, this angular coupling phenomenon can be expressed as the sensing coordinate system O 18 -X 18 Y 18 Z 18 With the sixth beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 Medium X l-17 Axis and X 18 Axis or Y l-17 Axis and Y 18 Angle between the axes θ zd-z ,like Figure 2 At this time, formula (1) cannot correct the angle coupling error and is no longer applicable to angle calculation.

[0121] S3. According to the normal vector of the spot position sensor obtained in step S1, a transformation matrix is ​​obtained, and the coordinates of the intersection of the incident light with an angle and the spot position sensor are transformed to the XOY plane using the transformation matrix to obtain the transformed intersection coordinates;

[0122] Mismatch angle θ zd-zThe plane where it is located is transformed to the XOY plane of the reference coordinate system O-XYZ, so as to facilitate the mismatch angle θ zd-z Quantify;

[0123] In calculating the mismatch angle θ zd-z When the light beam is reflected by the fourth reflector, the coordinate system of the light beam and the X coordinate system of the sensor need to be obtained. l-17 Axis and X 18 Axis or Y l-17 Axis and Y 18 However, from the above derivation process, we can know that by the ideal incident light l i Performing vector calculations, we can only get Z l-17 Axis and Z 18 In order to obtain the direction of other coordinate axes, it is necessary to use the ideal incident light l i and general incident light l i 'Perform two complete beam tracings, that is, you need to find l i and l i 'The intersection with the plane of the spot position sensor. If the number of reflectors in the folded light path is small, this is acceptable; if the number of reflectors is large, the amount of calculation will be greatly increased, making the solution process too complicated. Therefore, in order to simplify the calculation process, the sensor coordinate system can be first converted to the reference coordinate system, and then the mismatch angle θ can be calculated using the rotation matrix and the converted intersection coordinates. zd-z .

[0124] Furthermore, the specific implementation method of step S3 includes the following steps:

[0125] S3.1. First, use the direction vector Calculate the transformation matrix T zd , the sensor coordinate system O 18 -X 18 Y 18 Z 18 Z 18 The direction of the axis is rotated to the Z-axis direction of the reference coordinate system O-XYZ, according to the definition of the rotation matrix and the direction vector The direction cosines give the transformation matrix T zd The expression is:

[0126]

[0127] S3.2. Transform the matrix T zd With direction vector After multiplication, we get:

[0128]

[0129] in, Represents the direction vector of the Z axis of the reference coordinate system;

[0130] After the transformation matrix T zd After the transformation, the angular coupling on the spot position sensor plane will be converted to the XOY plane of the reference coordinate system, that is, after the transformation, point P PSD1 'On the XOY plane; let the point on the XOY plane at this time be the transformed intersection coordinate P PSD1 ",but:

[0131] P PSD1 ” = T zd ·P PSD1 '=[P zd-x ,P zd-y ,0] T (14)

[0132] Among them, P zd-x and P zd-y For about a k , b k 、c k 、x k ,y k 、z k and β, k = 1, 2, 3, 4; a k , b k 、c k and x k ,y k 、z k These six parameters correspond to the position and angle of the reflector in the folded optical path. When the folded optical path design is completed, the specific values ​​of these six parameters are also determined.

[0133] S4. Using a mismatch angle θ around the Z axis zd-z The rotation matrix is ​​used to transform the intersection coordinates transformed in step S3 so that the X component or Y component of the intersection coordinates transformed again is 0;

[0134] According to formula (14) finally obtained in step S3, if the angle coupling is to be eliminated, a rotation transformation of a certain angle around the Z-axis direction in the reference coordinate system O-XYZ is required so that the coordinates of the point only contain the coordinate components in the X-axis direction. Since the point is on the XOY plane, there must be a certain angle value that satisfies this condition. This angle is the mismatch angle θ. zd-z .

[0135] Furthermore, the specific implementation method of step S4 includes the following steps:

[0136] S4.1. According to the definition of the rotation matrix, the angle around the Z axis is the mismatch angle θ zd-z The rotation matrix Rzd-z It is expressed as:

[0137]

[0138] S4.2. Set point P PSD1 "The coordinates are rotated by the matrix R zd-z The coordinates obtained after transformation are P PSD1 ”' means:

[0139]

[0140] From formula (16), we can see that when point P PSD1 When the coordinates of ' contain only the X-axis component, that is, when the Y-axis component is zero, then:

[0141] cosθ zd-z ·P zd-y -sinθ zd-z ·P zd-x = 0. (17)

[0142] S5. Use the angle θ obtained in step S4. zd-z The angle decoupling formula is constructed with the rotation matrix to correct the angle coupling error caused by the folded optical path.

[0143] Furthermore, the specific implementation method of step S5 includes the following steps:

[0144] S5.1. Based on P zd-x and P zd-y The value of is known after the position parameters of each device in the folded optical path are determined, so the mismatch angle θ is obtained based on formula (17): zd-z ;

[0145] S5.2. Based on the mismatch angle obtained in step S5.1, the angle coupling model of the self-collimation angle measurement structure including the folded optical path is constructed using a two-dimensional rotation matrix:

[0146]

[0147] in, is the pitch angle after model correction, is the yaw angle after model correction.

[0148] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0149] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system, characterized in that: The angular coupling error introduced by the folded optical path in the multi-degree-of-freedom measurement system is quantified and corrected by using beam tracing and coordinate transformation, including the following steps: S1. Obtain the normal vector of the light beam received by the spot position sensor according to the spatial position and angle of each reflector in the multi-degree-of-freedom measurement system; The angle measurement module in the multi-degree-of-freedom measurement system is simplified, and the light source, lens, reflector and light spot position sensor are retained; the light emitted by the light source is transmitted through the lens, and passes through the first reflector, the second reflector, the third reflector, and then is reflected by the second reflector and the fourth reflector, and then is received by the light spot position sensor, which outputs the position coordinates of the light spot; S2. Deflect the incident light around the X-axis or Y-axis by a certain angle, and perform beam tracing to obtain the coordinates of the intersection of the incident light with the deflection angle and the light spot position sensor; S3. According to the normal vector of the spot position sensor obtained in step S1, a transformation matrix is ​​obtained, and the coordinates of the intersection of the incident light with an angle and the spot position sensor are transformed to the XOY plane using the transformation matrix to obtain the transformed intersection coordinates; S4. Using a mismatch angle θ around the Z axis zd-z The rotation matrix is ​​used to transform the intersection coordinates transformed in step S3 so that the X component or Y component of the intersection coordinates transformed again is 0; S5. Using the angle θ obtained in step S4 zd-z The angle decoupling formula is constructed with the rotation matrix to correct the angle coupling error caused by the folded optical path.

2. The method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system according to claim 1, characterized in that: For the simplified angle measurement module, a reference coordinate system, a beam coordinate system and a sensor coordinate system are established. The reference coordinate system O-XYZ is assumed to be a right-handed system, the center of the lens is the coordinate zero point, and the ideal outgoing beam direction of the light source is the positive direction of the Z axis. Set the first beam coordinate system O l -X l Y l Z l , the second beam coordinate system O l-14 -X l-14 Y l-14 Z l-14 , the third beam coordinate system O l-151 -X l-151 Y l-151 Z l-151 , the fourth beam coordinate system O l-16 -X l-16 Y l-16 Z l-16 , the fifth beam coordinate system O l-152 -X l- 152 Y l-152 Z l-152 , the sixth beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 The Z-axis direction is the same as the beam propagation direction, wherein the first beam coordinate system O l -X l Y l Z l is the light beam coordinate system of the light source, and the second light beam coordinate system O l-14 -X l-14 Y l- 14 Z l-14 is the coordinate system of the light beam after being reflected by the first reflector, and the third light beam coordinate system O l-151 -X l-151 Y l-151 Z l-151 is the coordinate system of the light beam after being reflected by the second reflector for the first time, and the fourth light beam coordinate system O l-16 -X l-16 Y l-16 Z l-16 is the coordinate system of the light beam after being reflected by the third reflector, and the fifth light beam coordinate system O l-152 -X l-152 Y l-152 Z l-152 is the coordinate system of the light beam after being reflected by the second reflector. The sixth light beam coordinate system O l-17 -X l-17 Y l-17 Z l-17 is the coordinate system of the light beam after being reflected by the fourth reflector; O 18 -X 18 Y 18 Z 18 is the light spot position sensor coordinate system, and the intersection of the light beam reflected by the fourth reflector and the light spot position sensor is the zero point of the coordinate system.

3. The method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system according to claim 2, characterized in that: The specific implementation method of step S1 includes the following steps: S1.

1. Set the ideal output light of the light source l i The direction vector is expressed as: Set the unit normal vector of the first reflector Unit normal vector of the second reflector Unit normal vector of reflector No. 3 and the unit normal vector of the fourth reflector Respectively expressed as: Among them, a k 、b k 、c k are the direction cosines of the normal vector of the kth reflector relative to the X, Y, and Z axes in the reference coordinate system O-XYZ, k=1, 2, 3, 4; S1.

2. According to the law of reflection, the reflection transformation matrix R of the kth reflector Mk It is expressed as: R M1 is the reflection transformation matrix of the No. 1 reflector, R M2 is the reflection transformation matrix of the second reflector, R M3 is the reflection transformation matrix of the third reflector, R M4 is the reflection transformation matrix of the fourth reflector; S1.

3. Ideal incident light i Direction vector after the first reflection from reflector No. 1 and the direction vector after the first reflection from the second reflector Respectively expressed as: The three coordinate components in the beam direction vector are abbreviated as l ojx (a k ,b k ,c k ), l ojy (a k ,b k ,c k ), l ojz (a k ,b k ,c k ) means about a k 、b k and c k The expression of, where j represents the number of times the light beam is reflected by each mirror, here j = 1, 2; The direction vector of the light beam after it is reflected by the third reflector, and then by the second and fourth reflectors and It is expressed as: For the convenience of expression, in the subsequent derivation, l ojx (a k ,b k ,c k ), l ojy (a k ,b k ,c k ) and l ojz (a k ,b k ,c k )Use l ojx , l ojy and l ojz Indicates that, here j = 3, 4, 5; S1.

4. Ideal incident light i After being reflected by four reflectors in sequence, it is received by the spot position sensor. In order to avoid the spot position data output by the spot position sensor containing cosine error, the plane where the spot position sensor is located should be perpendicular to the received beam, that is, the direction vector is the normal vector of the plane where the light spot position sensor is located.

4. The method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system according to claim 3, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. When the incident light has a deflection angle β along the Y-axis, the direction vector of the incident light is expressed as: Among them, l i ' indicates that there is a general incident light with a deflection angle around the Y axis, and the β in the coordinate is a small angle approximation of tanβ; S2.

2. Assume that the light beam passes through the zero point of the reference coordinate system O-XYZ, obtain the straight line equation of the light beam according to the light beam direction vector, and then use beam tracing to obtain the coordinates of the intersection of the incident light and each plane according to the position and angle of the plane where each reflector and the spot position sensor are located; The calculated incident light l i 'The general first intersection coordinate P with the No. 1 reflector M1 'for: The general second intersection coordinates P of the reflected light from the first reflector and the second reflector M2 'for: P M2 ' =[P x-M2 ,P y-M2 ,P z-M2 ] T (9) Among them, P x-M2 , P y-M2 and P z-M2 is the general second intersection point P M2 'The three coordinate components in the coordinates are expanded as follows: Generally the second intersection point P M2 'The position coordinates on the plane of the second reflector are related to the position and angle of the plane where the first reflector and the second reflector are located, and at the general second intersection point P M2 The three coordinate components of ' all contain the component of deflection angle β; It is thus obtained that after the light beam is reflected by the first and second reflectors, there is an angle coupling phenomenon; when the light beam is reflected by the third, second and fourth reflectors and is finally received by the spot position sensor, the light beam intersects with the plane of the spot position sensor at the third general intersection point P. PSD1 ', repeat the above beam tracing process to obtain the general third intersection point P PSD1 'Coordinates: P PSD1 ' =[P x-PSD1 ,P y-PSD1 ,P z-PSD1 ] T (11) Among them, P x-PSD1 , P y-PSD1 and P z-PSD1 is the general third intersection point P PSD1 'Three coordinate components in the coordinates; generally the third intersection point P PSD1 The three coordinate components of ' all contain the position and angle information of each reflector plane and the light spot position sensor plane, as well as the deflection angle β.

5. The method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system according to claim 4, characterized in that: The specific implementation method of step S3 includes the following steps: S3.

1. First, use the direction vector Calculate the transformation matrix T zd , the sensor coordinate system O 18 -X 18 Y 18 Z 18 Z 18 The direction of the axis is rotated to the Z-axis direction of the reference coordinate system O-XYZ, according to the definition of the rotation matrix and the direction vector The direction cosines give the transformation matrix T zd The expression is: S3.

2. Transform the matrix T zd With direction vector After multiplication, we get: in, Represents the direction vector of the Z axis of the reference coordinate system; After the transformation matrix T zd After the transformation, the angular coupling on the spot position sensor plane will be converted to the XOY plane of the reference coordinate system, that is, after the transformation, point P PSD1 'On the XOY plane; let the point on the XOY plane at this time be the transformed intersection coordinate P PSD1 ",but: P PSD1 ”=T zd ·P PSD1 '=[P zd-x ,P zd-y ,0] T (14) Among them, P zd-x and P zd-y For about a k 、b k 、c k 、x k ,y k 、z k and β, k = 1, 2, 3, 4; a k 、b k 、c k and x k ,y k 、z k The six parameters correspond to the position and angle of the reflector in the folded optical path. When the folded optical path design is completed, the specific values ​​of the six parameters are also determined.

6. The method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system according to claim 5, characterized in that: The specific implementation method of step S4 includes the following steps: S4.

1. According to the definition of the rotation matrix, the angle around the Z axis is the mismatch angle θ zd-z The rotation matrix R zd-z It is expressed as: S4.

2. Set point P PSD1 "The coordinates are rotated by the matrix R zd-z The coordinates obtained after transformation are P PSD1 ”' means: From formula (15), we can see that when point P PSD1 When the coordinates of ' contain only the X-axis component, that is, when the Y-axis component is zero, then: cosθ zd-z ·P zd-y -sinθ zd-z ·P zd-x =0 (17)。 7. The method for angle decoupling of folded optical paths in a multi-degree-of-freedom measurement system according to claim 6, characterized in that: The specific implementation method of step S5 includes the following steps: S5.

1. Based on P zd-x and P zd-y The value of is known after the position parameters of each device in the folded optical path are determined, so the mismatch angle θ is obtained based on formula (17): zd-z ; S5.

2. Based on the mismatch angle obtained in step S5.1, the angle coupling model of the self-collimation angle measurement structure including the folded optical path is constructed using a two-dimensional rotation matrix: in, is the pitch angle after model correction, is the yaw angle after model correction.

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