Laser Reflection-Based Shield Tunnel Segment Displacement Monitoring System and Method

Abstract

This invention provides a laser reflection-based system and method for monitoring the displacement of tunnel segments in a shield tunnel. The system includes a laser emitting unit, a reflecting unit mounted on the segment to be measured, and a data processing unit. The laser emitting unit includes an identification plate and a laser emitter positioned at the center of the identification plate. The reflecting unit includes a reflector and a central hole positioned at the center of the reflector. The laser emitter and the central hole are at the same height so that the laser emitted by the laser emitter passes through the central hole. The mirror surface of the reflector faces the laser emitting unit, and the center of the reflector protrudes uniformly in all directions away from the laser emitting unit. This invention has a simple structure, wide applicability, and implements automatic monitoring and early warning throughout the process to ensure the construction quality of the shield tunnel and thus ensure the safe and efficient implementation of the overall project. This method also offers higher sensitivity and accuracy in detection results.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering technology, and in particular to a system and method for monitoring the displacement of shield tunnel segments based on laser reflection. Background Technology

[0002] In recent years, with the increasing pressure on surface traffic, the large-scale construction of subways has become unstoppable. The shield tunneling method is increasingly widely used in subway construction in my country, with cities such as Shanghai, Guangzhou, Shenzhen, and Nanjing employing it extensively. The shield tunneling method is a fully mechanized construction method within the cut-and-cover method. It involves advancing the shield machine underground, using the shield shell and tunnel segments to support the surrounding rock and prevent it from collapsing into the tunnel. Simultaneously, cutting devices excavate the soil in front of the excavation face, transporting the excavated soil out of the tunnel using haulage machinery. Jacks then apply pressure from the rear to propel the tunnel forward, assembling precast concrete tunnel segments to form the tunnel structure. In practice, due to variations in geological and hydrological conditions, problems may arise during construction, with tunnel segment displacement being a significant issue. Excessive segment displacement can lead to construction quality defects, seriously jeopardizing project safety, causing incalculable losses, and increasing the difficulty of subsequent correction and grouting processes.

[0003] Therefore, monitoring segment displacement is essential during subway tunnel construction. Currently, the most common method for segment displacement monitoring is point-based monitoring, which involves manually measuring the segment displacement at monitoring points using instruments such as levels and total stations. This method is time-consuming and labor-intensive, and cannot obtain real-time displacement values ​​(i.e., it cannot capture the dynamic displacement evolution process). Furthermore, monitoring devices using water pressure, fiber optic gratings, and sensors are expensive, the monitoring process is cumbersome, and they are highly susceptible to external disturbances, which can affect measurement accuracy, thus limiting their practicality. To overcome the aforementioned shortcomings, patent application CN202111625728.X discloses a method and device for monitoring the displacement of tunnel segments in a shield tunnel. The device includes a mobile trolley mounted on a track at the bottom of the shield tunnel, a laser rangefinder mounted on the mobile trolley, and reflectors mounted on monitoring segments on the tunnel wall. The mobile trolley can move along the track. The trolley also includes a drive mechanism that rotates the laser rangefinder along the circumferential direction of the shield tunnel, and an angle measuring mechanism that measures the rotation angle of the laser rangefinder. During operation, the device adjusts the rotation angle of the laser rangefinder so that its emitted laser beam is aligned with the center of the reflector. The coordinates of the monitoring point relative to the mobile trolley are calculated using the measurement data from the laser rangefinder and the angle measuring mechanism. The displacement value of the monitored segment is then calculated based on the difference between two coordinate measurements taken at different times. Although this method can calculate the displacement value of the monitoring point, it still has the following defects: (1) The angle of the laser rangefinder needs to be constantly adjusted during the monitoring process, and long-term use will affect the service life of the laser rangefinder; (2) Each adjustment makes the laser emitted by the laser rangefinder aligned with the center of the reflector (but the center of the reflector is not marked), and there is an error in the manual adjustment. The calculation formula needs to be substituted with the rotation angle twice, which leads to the error in the measurement result; (3) It cannot complete the real-time dynamic monitoring of the displacement value of the pipe segment to be measured.

[0004] In view of this, it is necessary to design an improved laser reflection-based shield tunnel segment displacement monitoring system and method to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a shield tunnel segment displacement monitoring system and method based on laser reflection. This system sets a reflector at a certain angle and sets a central hole in the center of the reflector. Based on the distance of the laser reflected from the origin on the identification plate and the orientation of the reflected laser, the data processing unit can realize real-time dynamic monitoring of the offset value and offset orientation of the segment under test. This method has higher detection sensitivity and accuracy.

[0006] To achieve the above-mentioned objectives, this invention provides a shield tunnel segment displacement monitoring system based on laser reflection, comprising a laser emitting unit, a reflecting unit disposed on the segment to be measured, and a data processing unit; the laser emitting unit includes an identification plate and a laser emitter disposed at the center of the identification plate; the reflecting unit includes a reflector and a central hole disposed at the center of the reflector, the laser emitter and the central hole being located at the same height so that the laser emitted by the laser emitter passes through the central hole; the mirror surface of the reflector faces the laser emitting unit, and the center of the reflector protrudes uniformly in all directions toward the side away from the laser emitting unit.

[0007] As a further improvement of the present invention, the identification plate is provided with scales along various directions centered on the laser emitter; the laser emitted by the laser emitting unit is reflected by the reflection unit onto the identification plate, and the data processing unit calculates the offset value of the tube segment to be tested based on the scale value reflected by the laser onto the identification plate.

[0008] As a further improvement of the present invention, the diameter of the central hole is equal to the diameter of the laser emitted by the laser emitter.

[0009] As a further improvement of the present invention, the angle between the mirror surface of the reflector and the vertical plane containing the central hole is 0.3-3°.

[0010] As a further improvement of the present invention, the laser emitting unit further includes a camera, the camera lens of which is positioned facing the recognition plate, for capturing in real time the scale value of the laser reflected by the recognition plate, and transmitting the scale value to the data processing unit.

[0011] As a further improvement of the present invention, the laser reflection-based shield tunnel segment displacement monitoring system also includes an early warning system connected to the data processing unit. When the offset value of the segment under test obtained by the data processing unit exceeds the threshold of the segment under test movement, the early warning system issues an alarm.

[0012] As a further improvement of the present invention, the laser emitter is equipped with an acceleration-compensated anti-vibration crystal oscillator to avoid interference caused by the construction process and the offset of the reference object.

[0013] As a further improvement of the present invention, the laser emitting unit also includes a protective box, in which the identification plate, the laser emitter and the camera are all installed, and the protective box is open on the side facing the reflector.

[0014] To achieve the above-mentioned objectives, this invention also provides a method for monitoring the displacement of tunnel segments based on laser reflection, which uses the aforementioned laser reflection-based tunnel segment displacement monitoring system and includes the following steps:

[0015] S1. The reflector is mounted on the tube segment to be tested, and the laser emitting unit is mounted through the bracket, while ensuring that the laser emitted by the laser emitter passes through the central hole in the center of the reflector;

[0016] S2. Activate the laser emitter and the data processing unit to record the distance of the laser reflected onto the identification plate in real time; the data processing unit calculates the displacement value of the tube segment under test based on the recorded distance.

[0017] As a further improvement of the present invention, the formula for calculating the displacement value of the segment to be measured is as follows:

[0018]

[0019]

[0020] X1 + Y1 = X (3)

[0021] From formulas (1)-(3), we can obtain that

[0022] Where Y1 is the distance the test tube segment moves up and down;

[0023] X is the distance from the vertical plane containing the central hole of the reflector to the identification plate, which is a known value;

[0024] Y2 is the distance the laser light reflects onto the identification plate, which is a known value;

[0025] θ is the angle between the mirror surface of the reflector and the vertical plane containing the central hole, and is a known value.

[0026] The beneficial effects of this invention are:

[0027] (1) The laser reflection-based shield tunnel segment displacement monitoring system provided by this invention sets a reflector at a certain angle and sets a central hole at the center of the reflector. Based on the distance of the laser reflected from the origin on the identification plate and the orientation of the reflected laser, the data processing unit realizes real-time dynamic monitoring of the offset value and offset orientation of the segment under test. The system has a simple structure, wide applicability, and automatic monitoring throughout the process, greatly reducing labor and material costs. At the same time, the detection process of this device is not affected by construction or the movement of reference objects. It can also automatically monitor and provide early warning in real time to ensure the construction quality of the shield tunnel and thus ensure the safe and efficient development of the overall project. It is of great significance for the study of the displacement evolution characteristics of shield tunnel segments and the application of automatic monitoring and early warning.

[0028] (2) The laser reflection-based shield tunnel segment displacement monitoring method provided by this invention utilizes a simple device to achieve real-time dynamic monitoring of the offset value and offset orientation of the segment under test based on the distance of the laser reflected from the origin on the identification plate and the orientation of the reflected laser. In the specific calculation process, the angle of the reflector and the distance of the vertical plane containing the center hole of the reflector from the identification plate are constant values, while the distance of the laser reflected to the identification plate is a variable value. That is, there is only one variable value in the entire calculation process. It can be seen that there are fewer influencing factors in the calculation process, and the detection sensitivity and accuracy of the detection results are higher. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the structure of the shield tunnel segment displacement monitoring system based on laser reflection according to the present invention.

[0030] Figure 2 for Figure 1 Side view of the middle reflector unit 2.

[0031] Figure 3 This illustrates the effect of differences in mirror thickness on laser reflection.

[0032] Figure 4 Geometric diagram for calculating the offset value of the segment under test.

[0033] Figure 5 This is a flowchart of the shield tunnel segment displacement monitoring method based on laser reflection according to the present invention.

[0034] Figure Labels

[0035] 1-Laser emitting unit; 2-Reflection unit; 3-Data processing unit; 11-Identification board; 12-Laser emitter; 13-Camera; 14-Protective box; 21-Reflector; 22-Center hole. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] It should also be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and / or processing steps closely related to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0038] Additionally, it should be noted that the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0039] Please see Figures 1 to 2 As shown, this invention provides a shield tunnel segment displacement monitoring system based on laser reflection, including a laser emitting unit 1, a reflecting unit 2 disposed on the segment to be measured, and a data processing unit 3. The laser emitting unit 1 includes an identification plate 11 and a laser emitter 12 disposed at the center of the identification plate 11; the reflecting unit 2 includes a reflector 21 and a central hole 22 disposed at the center of the reflector 21. The mirror surface of the reflector 21 faces the laser emitting unit 1, and the center of the reflector 21 protrudes uniformly in all directions away from the laser emitting unit 1, i.e., the reflector 21 is shaped like... Figure 2 The cone-shaped structure is shown. In the initial state, the laser emitter 12 and the central hole 22 are at the same height, so that the laser emitted by the laser emitter 12 just passes through the central hole 22 of the reflector 21. With this configuration, when the tube under test does not shift, the laser emitted by the laser emitter 12 just passes through the central hole 22 of the reflector 21, so that the reflected laser cannot be detected on the recognition plate 11; when the tube under test shifts, the reflector 21 also shifts, and the laser emitted by the laser emitter 12 shines on the mirror surface of the reflector 21 at a certain angle. The reflector 21 will reflect the laser onto the recognition plate 11. By monitoring the distance between the laser reflected on the recognition plate 11 and the laser emitter 12, the data processing unit 3 processes and calculates the distance to obtain the offset value of the tube under test; at the same time, by the orientation of the laser reflected on the recognition plate 11, the offset orientation of the tube under test is obtained.

[0040] Specifically, the laser emitter 12 is equipped with an acceleration-compensated anti-vibration crystal oscillator to avoid interference caused by the construction process and the displacement of the reference object. The structure of the acceleration-compensated anti-vibration crystal oscillator and its compensation method can be referred to the patent application number CN114629438A: "An acceleration-compensated anti-vibration crystal oscillator and its compensation method".

[0041] The identification plate 11 is marked with scales along various directions with the laser emitter 12 as the origin. The laser emitted by the laser emitting unit 1 is reflected by the reflection unit 2 onto the identification plate 11. The data processing unit 3 processes and calculates the distance between the laser reflected on the identification plate 11 and the origin (i.e., the laser emitter 12) to obtain the offset value of the tube segment under test.

[0042] like Figure 1 As shown, the laser emitting unit 1 also includes a camera 13. The camera of the camera 13 is set facing the recognition plate 11 to capture the scale value of the laser reflected by the recognition plate 11 in real time and transmit the scale value to the data processing unit 3 (the camera 13 and the data processing unit 3 are connected by a wire).

[0043] In some embodiments, the laser emitting unit 1 further includes a protective case 14, in which the identification plate 11, the laser emitter 12, and the camera 13 are all installed to protect them. The protective case 14 has an opening on the side facing the reflector 21, and the size of the opening will not interfere with the reflected laser. At the same time, the size of the identification plate 11 is sufficient to reflect lasers from all directions, that is, all lasers reflected by the reflector 21 can be reflected onto the identification plate 11.

[0044] like Figure 2 As shown, the reflector 21 has a conical structure, and the angle between the mirror surface of the reflector 21 and the vertical plane containing the central hole 22 is θ, with θ ranging from 0.3° to 3°. The diameter of the central hole 22 is equal to the diameter of the laser emitted by the laser emitter 12. With this configuration, when the tube under test is not displaced, the laser emitted by the laser emitter 12 passes just through the central hole 22 of the reflector 21; when the tube under test has a slight displacement, the reflected laser can be detected on the recognition plate 11, thereby improving the detection accuracy and sensitivity of the device.

[0045] In addition, the mirror surface of reflector 21 needs to have a certain thickness. Under abnormal circumstances, such as when the identification plate 11 tilts slightly for some reason, the laser emitter 12 shifts, causing the emitted laser to tilt slightly, as... Figure 3 As shown in b, when the mirror surface of the reflector 21 is too thin, the laser emitted by the laser emitter 12 will still pass through the central hole 22, creating the illusion that the laser emitter 12 and the central hole 22 are at the same height, thus causing deviation in the detection results. Figure 3 As shown in Figure a, when the mirror surface of the reflector 21 has a certain thickness, the laser emitted by the laser emitter 12 will still be reflected onto the identification plate 11, making the staff aware that the laser emitter 12 has shifted.

[0046] The data processing unit 3 includes an image processing module and a data analysis and calculation module. The camera 13 outputs the scale value of the reflected laser on the recognition plate 11 to the data processing unit 3. The image processing module processes the data in the captured image and then transmits the data to the data analysis and calculation module. The offset value (i.e., displacement value) and offset orientation of the test tube segment are detected through the analysis and calculation of the data analysis and calculation module.

[0047] The data analysis and calculation module calculates the offset value of the segment under test based on the tangent theorem, the geometric relationship between the reference and monitoring points, and the tilt angle of reflector 21. Specifically, the calculation of the displacement value of the segment under test is as follows: Figure 4 As shown. Y1 is the offset value of the tube segment to be tested; Y2 is the distance of the laser reflection onto the recognition plate 11, which can be captured by the camera 13 and then recognized by the image processing module, and is a known value; X is the distance of the vertical plane where the center hole 22 of the reflector 21 is located from the recognition plate 11, which is a preset fixed value and is a known value; θ is the angle between the mirror surface of the reflector 21 and the vertical plane where the center hole 22 is located, which is a preset fixed value and is a known value; Although X1 and X2 are unknowns, they are only used as intermediate parameters and do not need to be calculated.

[0048]

[0049]

[0050] X1 + Y1 = X (3)

[0051] From formulas (1)-(3), we can obtain that

[0052] Another form of the calculation result of Y1 can be further converted using the following formula:

[0053]

[0054] Substituting formula (4) into the above formula for calculating Y1, we can obtain...

[0055]

[0056] The following explains θ: Based on the actual engineering situation, the distance X between the vertical plane where the center hole 22 of the reflector 21 is located and the recognition plate 11 is generally 3-30m. The maximum vertical dimension of the reflector 21 is about 0.3m, that is, Y1 is about 0.30m. The maximum dimension of the scale in the recognition plate 11 with the laser emitter 12 as the origin along each direction is about 0.30m, that is, Y2 is about 0.30m.

[0057] From another form of the formula for calculating Y1, we can obtain:

[0058] (2Y1-Y2)tan 2 θ-2Xtanθ+Y2=0 (5)

[0059] The angle θ of the reflector 21 is designed based on the actual engineering conditions (X, Y1, Y2).

[0060] When X = 5, Y1 = 0.3, and Y2 = 0.3, we can obtain tanθ = 0.030027 and 33.3033. Obviously, 33.3033 is unreasonable and needs to be discarded. At this time, θ = 1.719°.

[0061] Similarly, when X = 3, Y1 = 0.3, and Y2 = 0.3, tanθ = 0.0501256 and θ = 2.869°.

[0062] Similarly, when X = 15, Y1 = 0.3, and Y2 = 0.3, tanθ = 0.010001 and θ = 0.573°.

[0063] Similarly, when X = 30, Y1 = 0.3, and Y2 = 0.3, tanθ = 0.0050001 and θ = 0.286°.

[0064] The calculation results above show that the preferred value of θ is 0.3-3°. The value of θ X can be freely adjusted. When the value of X is large, the value of θ can be appropriately reduced.

[0065] The specific offset orientation of the test tube segment is as follows: (1) If the reflected laser detected by the identification plate 11 is located directly above the origin, it indicates that the test tube segment is offset directly downwards; (2) If the reflected laser detected by the identification plate 11 is located directly below the origin, it indicates that the test tube segment is offset directly upwards; (3) If the reflected laser detected by the identification plate 11 is located directly to the left of the origin, it indicates that the test tube segment is offset directly to the right; (4) If the reflected laser detected by the identification plate 11 is located directly to the right of the origin, it indicates that the test tube segment is offset directly to the right. (5) If the reflected laser detected on the identification plate 11 is located to the upper left of the origin, it indicates that the tube under test is shifted to the lower right; (6) If the reflected laser detected on the identification plate 11 is located to the lower left of the origin, it indicates that the tube under test is shifted to the upper right; (7) If the reflected laser detected on the identification plate 11 is located to the upper right of the origin, it indicates that the tube under test is shifted to the lower left; (8) If the reflected laser detected on the identification plate 11 is located to the lower right of the origin, it indicates that the tube under test is shifted to the upper left.

[0066] The laser reflection-based shield tunnel segment displacement monitoring system also includes an early warning system (not shown in the figure) connected to the data processing unit 3. The camera 13 transmits the scale value of the reflected laser light on the identification plate 11 to the data processing unit 3. The image processing module processes the data in the captured image and then transmits the data to the data analysis and calculation module. The data analysis and calculation module detects the offset value and orientation of the segment under test. When the offset value of the segment under test exceeds the offset threshold (which is preset), the data processing unit 3 transmits the signal to the early warning system, which then triggers an alarm to alert the staff that the offset value of the segment under test is too large.

[0067] This invention also provides a method for monitoring the displacement of shield tunnel segments based on laser reflection, using the aforementioned laser reflection-based shield tunnel segment displacement monitoring system, and includes the following steps (as shown in Figure 5):

[0068] S1. Installation

[0069] Relevant devices are installed at the monitoring and reference points of the shield tunnel segments. Specifically, the reflector 21 is installed on the segment to be tested, and the laser emitting unit 1 is installed through the bracket. Then, the laser is calibrated so that the laser emitted by the laser emitter 12 passes through the center hole 22 in the center of the reflector 21. After calibration, the device is fixed.

[0070] S2. Monitoring

[0071] The laser emitter 12 and data processing unit 3 are activated. The camera 13 records the scale value of the reflected laser on the recognition plate 11 in real time and sends the scale value to the data processing unit 3. The image processing module processes the data in the captured photo and then transmits the data to the data analysis and calculation module. The offset value and offset orientation of the test tube segment are detected through the analysis and calculation of the data analysis and calculation module.

[0072] When the offset value of the segment under test exceeds the threshold value of the segment offset (the threshold value is set in advance), the data processing unit 3 transmits the signal to the early warning system, and the early warning system starts to alarm to remind the staff that the offset value of the segment under test is too large.

[0073] In summary, the purpose of this invention is to provide a shield tunnel segment displacement monitoring system and method based on laser reflection. This system sets a reflector at a certain angle and sets a central hole at the center of the reflector. Based on the distance of the reflected laser from the origin on the identification plate and the direction of the reflected laser, the data processing unit can achieve real-time dynamic monitoring of the offset value and offset direction of the segment under test. The device has a simple structure, wide applicability, and the entire process is automatically monitored, significantly reducing labor and material costs. It can automatically monitor and provide early warning in real time to ensure the construction quality of the shield tunnel, thereby ensuring the safe and efficient progress of the overall project. This method also offers higher sensitivity and accuracy in detection results.

[0074] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A laser reflection based shield tunnel segment displacement monitoring system, characterized in that, The system comprises a laser emitting unit, a reflecting unit arranged on a pipe piece to be measured, and a data processing unit; the laser emitting unit comprises an identification plate and a laser emitter arranged at the center of the identification plate; the reflecting unit comprises a mirror and a center hole arranged at the center of the mirror, the laser emitter and the center hole are at the same height so that the laser emitted by the laser emitter passes through the center hole; the mirror surface of the mirror faces the laser emitting unit, and the center of the mirror protrudes uniformly to the side away from the laser emitting unit in each direction; The identification plate is provided with scales centered on the laser emitter and in each direction; the laser emitted by the laser emitting unit is reflected to the identification plate by the reflecting unit, and the data processing unit obtains the offset value of the pipe piece to be measured according to the scale value of the laser reflected to the identification plate; The laser emitting unit further comprises a camera, the camera head of the camera faces the identification plate and is arranged for real-time shooting of the scale value of the laser reflected by the identification plate, and the scale value is transmitted to the data processing unit.

2. The laser reflection based shield tunnel segment displacement monitoring system according to claim 1, wherein, The aperture of the center hole is equal to the diameter of the laser emitted by the laser emitter.

3. The laser reflection based shield tunnel segment displacement monitoring system according to claim 1, wherein, The angle between the mirror surface of the mirror and the vertical plane where the center hole is located is 0.3-3°.

4. The laser reflection based shield tunnel segment displacement monitoring system according to claim 1, wherein, The shield tunnel pipe piece displacement monitoring system based on laser reflection further comprises a warning system connected with the data processing unit, and the warning system alarms when the offset value of the pipe piece to be measured obtained by the data processing unit exceeds the threshold value of the movement of the pipe piece to be measured.

5. The laser reflection based shield tunnel segment displacement monitoring system according to claim 1, wherein, An acceleration compensation anti-vibration crystal oscillator is installed in the laser emitter to avoid interference caused by the offset of the reference object in the construction process.

6. The laser reflection based shield tunnel segment displacement monitoring system according to claim 5, wherein, The laser emitting unit further comprises a protective box, the identification plate, the laser emitter, and the camera are installed in the protective box, and one side of the protective box facing the mirror is provided with an opening.

7. A method for monitoring displacement of a shield tunnel segment based on laser reflection, characterized in that, The shield tunnel pipe piece displacement monitoring system based on laser reflection is used for detection, comprising the following steps: S1. Install the mirror on the pipe piece to be measured, and install the laser emitting unit through a support while keeping the laser emitted by the laser emitter passing through the center hole at the center of the mirror; S2. Start the laser emitter and the data processing unit, and record the distance of the laser reflected to the identification plate in real time; the data processing unit calculates the displacement value of the pipe piece to be measured according to the recorded distance.

8. The laser reflection based shield tunnel segment displacement monitoring method according to claim 7, wherein, The calculation formula of the displacement value of the pipe piece to be measured is: (1) (2) X1+Y1=X (3) From equations (1)-(3), Wherein, Y1 is the offset value of the pipe piece to be measured; X is the distance between the vertical plane where the center hole of the mirror is located and the identification plate, which is a known value; Y2 is the distance of the laser reflected to the identification plate, which is a known value; θ is the angle between the mirror surface of the mirror and the vertical plane where the center hole is located, which is a known value.

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