Catheter waviness measuring method and device based on auto-collimation laser tracker

Abstract

The invention relates to the technical field of precision measurement and detection in optics, in particular to a conduit surface shape precision detection technology in neutron mirror optics, and provides a conduit waviness measurement method and device based on an auto-collimation laser tracker. According to the method, a high-precision laser tracker is installed on a granite guide rail, a conduit to be measured is placed on a marble table top, the laser tracker slides along the guide rail, space vector coordinates of a reflecting surface are obtained in a full-automatic auto-collimation mode, and data are exported to a computer to calculate waviness parameters after multiple times of measurement; according to the invention, the laser tracker with strong versatility is adopted, so that one machine with multiple purposes is realized, and the cost is reduced; by utilizing the full-automatic auto-collimation function, the manual operation proportion is reduced, and the efficiency is improved; a parameter optimization fitting algorithm is provided for the bent catheter measurement problem, and it is guaranteed that the result is accurate and reliable; high-precision hardware and an innovative algorithm are combined, and universal high-precision measurement is achieved.

Description

Technical Field

[0001] This invention relates to the field of precision measurement and detection technology in optics, and particularly to the detection technology of duct surface shape accuracy in the field of neutron mirror optics, specifically a method and device for measuring duct waviness based on a self-collimating laser tracker. Background Technology

[0002] In the field of neutron mirror optics, key optical components such as neutron conduits typically have an incident angle for reflecting neutrons that is extremely small, generally between 0.1° and 1°. Such a small incident angle means that the surface finish of the mirror or substrate must be extremely precise. Even a tiny deviation between the actual surface profile and the ideal plane will alter the neutron reflection conditions, leading to neutron loss, ultimately reducing the neutron flux and affecting the performance of the entire optical system.

[0003] Currently, although some methods exist for measuring waviness, these existing technologies have many problems. Firstly, equipment compatibility is severely lacking. For example, with autocollimating theodolites, due to their narrow application, domestic Leica manufacturers have ceased production, forcing imports at high prices. Related spare parts are either out of stock or discontinued, making it very costly to modify them to measure guide tube accuracy. Secondly, manual operation constitutes a large proportion of existing measurement techniques. This not only demands extremely high professional skills from operators but also requires them to meticulously aim the theodolite's collimating lens and finely adjust the theodolite's base posture for extended periods to achieve collimation. Even slight errors can lead to significant measurement inaccuracies. Therefore, measurement efficiency is low and labor intensity is high. Furthermore, prolonged repetitive operations can easily cause operator fatigue, further affecting the accuracy and efficiency of the measurement.

[0004] Furthermore, existing data processing methods are not rigorous enough when dealing with conduits with complex curved surfaces. Measuring curved conduits (such as elliptical, circular, and parabolic shapes) presents inherent challenges, including uncertain measurement starting points, non-parallel orientation of the guide rail and the curved surface, and inaccurate determination of the distance from the measuring machine to the surface of the conduit under test. Existing technologies lack rigorous mathematical models to address these issues, resulting in low reliability of measurement results and difficulty in accurately assessing the waviness performance of complex conduit types and the impact of waviness on neutron reflection. Therefore, developing a conduit waviness measurement technique that can solve the above problems is of significant practical importance. Summary of the Invention

[0005] To address the aforementioned issues, this invention aims to provide a method and device for measuring the waviness of a conduit based on a self-collimating laser tracker. This method is particularly suitable for measuring the waviness of optical components such as neutron conduits that require extremely high surface shape processing accuracy, thereby meeting the stringent control requirements for surface shape accuracy in precision optical applications such as neutron reflection.

[0006] The technical solution adopted in this invention is: a method for measuring duct waviness based on a self-collimating laser tracker, comprising the following steps: S1. A high-precision laser tracker is used as the core measuring device and is installed on a granite guide rail. The tube to be tested is placed on a stable marble table. S2. The laser tracker slides along the guide rail at equal intervals. In the fully automatic self-collimation mode, the emitted self-collimated beam illuminates the optical reflective surface of the duct sidewall. The tracker will automatically adjust its attitude to make the back-and-forth beams coincide, and at the same time obtain the spatial vector coordinates of the reflective surface. S3. Perform 3 to 5 repeated measurements at each measurement position, push the tracker to the next measurement position, usually displace 50mm on the guide rail, and repeat the spatial coordinate measurement of self-collimation tracking. S4. Export the measured data table, transfer it to the computer for storage and analysis, and calculate the waviness parameter σ as an indicator to measure the surface shape processing accuracy of the reflective surface.

[0007] A method for measuring catheter waviness based on a self-collimating laser tracker, wherein the waviness parameter σ is calculated using the following formula: in, α i,real ( x )and α i,nominal ( x These represent the actual normal direction and the normal direction of the standard plane, respectively. n This represents the number of data points.

[0008] The performance requirements of the laser tracker are as follows: within the incident angle of ±30°, the accuracy of distance measurement is better than 10μm, the accuracy of angle measurement is better than 0.5″, and the accuracy requirement of 3″ for waviness measurement is met.

[0009] Furthermore, for conduits with different geometries, the methods for calculating waviness include: The azimuth and elevation angles of each vector are calculated based on the coordinate measurement results of the tracker. First, the azimuth (horizontal angle) and elevation (vertical angle) of each vector in the spherical coordinate system are calculated respectively. For straight, tapered neutron conduits, the normal of the first measurement point is taken as the nominal surface normal; For curved neutron conduits, the relative surface normal deviation is accurately extracted from the absolute coordinate measurements by optimizing the relative attitude parameters (slope k, starting point offset xs, distance d) between the guide rail and the conduit.

[0010] The curved neutron conduit includes elliptical conduits, circular conduits, and parabolic conduits. Its waviness is calculated by establishing a geometric model of the measurement system, transforming the mechanical installation parameters (k, xs, d) into mathematically optimizable variables, and using iterative calculations to achieve the best match between the theoretical model and the angular change trend of the measurement data.

[0011] A device for measuring the duct waviness based on a self-collimating laser tracker, comprising: A high-precision laser tracker, mounted on a granite guide rail, is used to measure the spatial vector coordinates of the reflective surface of the duct sidewall; Granite guide rails are used to support and guide the linear movement of the laser tracker; The marble countertop is used to place the test tube and has vibration isolation function; A computer is used to store and analyze data measured by the laser tracker and to calculate waviness parameters.

[0012] The laser tracker has a fully automatic self-collimation function, which can automatically adjust the posture to make the back and forth light rays overlap. During measurement, the personnel only need to move the device along the guide rail and trigger the measurement.

[0013] The computer is equipped with specialized data processing software to perform the conversion of coordinate data to angle data, the translation of data with relative changes, the optimization of ray parameters, and finally to obtain the waviness result based on the waviness calculation formula.

[0014] The beneficial effects achieved by this invention are as follows: This invention employs a high-precision laser tracker as the core measuring device, which is itself a versatile and widely applicable large-size spatial coordinate measuring instrument. Unlike existing technologies where equipment is dedicated to specific tasks and lacks compatibility, the measuring system constructed in this invention, using a laser tracker in its measuring head, can not only perform duct waviness measurements but also be widely applied to collimation and installation during the construction phase of the device and other spatial coordinate measurement tasks during operation. For example, during the construction of an optical device, this laser tracker can be used for the collimation and installation of various optical components, ensuring the precise alignment of the optical system; during device operation, it can also be used in other scenarios requiring high-precision spatial coordinate measurements. This "one machine, multiple uses" characteristic significantly improves the utilization rate of the equipment, avoids the high costs associated with purchasing dedicated equipment for a single measurement task, and effectively solves the problems of insufficient equipment compatibility and high specialization costs.

[0015] This invention fully utilizes the fully automatic self-collimation function of a laser tracker. During the measurement process, the device automatically adjusts its attitude to lock the reflected light, and the operator only needs to push or drive the device via a motor to move it on the guide rail and trigger the measurement. Compared with existing technologies that involve multiple manual operations, require highly skilled personnel, have low measurement efficiency, and are labor-intensive, this invention significantly reduces the proportion of manual operation. Operators do not need to perform complex professional operations; they only need to complete simple equipment movement and measurement triggering actions, freeing them from tedious professional tasks. When combined with a motor-driven guide rail, fully automated measurement can be achieved, further improving measurement efficiency. Even non-professionals can quickly complete high-precision measurements, greatly reducing reliance on manpower and workload.

[0016] This invention addresses the inherent challenges in measuring curved guide tubes (such as ellipses, circles, and parabolas), including uncertain starting points, non-parallelism between the guide rail and the curved surface, and unknown distances. It proposes a unique parameter optimization and fitting algorithm. By establishing a geometric model of the measurement system, the aforementioned uncertainties are transformed into optimizable mathematical parameters (such as guide rail slope k, measurement starting point offset xs, and distance d), and these parameters are accurately inverted using computer iterative calculations. Existing technologies lack rigorous mathematical processing models to address these problems in the measurement of complex curved surfaces, resulting in low reliability of the results. This invention, however, can rigorously separate and calculate the true surface normal deviation from the original measurement data, ensuring high accuracy and reliability of the waviness assessment results even for complex curved surfaces, thus solving the problem of inaccurate data processing in the measurement of complex curved surfaces.

[0017] This invention requires extremely high precision in measuring the surface waviness of the neutron conduit, for example, an accuracy of 3 arcseconds. The commercially available high-precision laser tracker used in this invention has an angle measurement accuracy better than 0.5 arcseconds and a distance measurement accuracy better than 10 μm, far exceeding the precision requirements for neutron conduit waviness measurement. By combining this high-precision hardware with innovative data processing algorithms, this solution successfully applies a general-purpose measurement device to an extremely high-precision, specialized measurement task. While ensuring measurement accuracy, it also considers the versatility and feasibility of the solution, achieving a generalized high-precision measurement that meets extremely high precision requirements. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the reflection from the actual corrugated surface in this invention; Figure 2 This is a schematic diagram of the laser tracker waviness measurement in this invention; Figure 3 This is a schematic diagram of the laser tracker measuring the bent conduit in this invention; Figure 4 In this invention, the elliptical conduit and the air-bearing guide rail are simplified to ellipses and arbitrary rays; Figure 5 Before the optimization of the ray (linear guide) parameters in this invention, the curve trend was different and the error was large. Figure 6 In this invention, after the parameters of the ray (linear guide) are optimized, the trend is the same and the error is reduced. Detailed Implementation

[0019] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings: like Figure 1-6 As shown, the present invention provides a method, device and overall scheme for measuring the waviness of a neutron conduit based on a self-collimating laser tracker, which is particularly suitable for high-precision measurement of the waviness of a neutron conduit in the field of neutron mirror optics. Figure 1 A schematic diagram of reflection from an actual corrugated surface is shown, illustrating the effect of waviness on neutron reflection. Figure 2 This is a schematic diagram of a laser tracker measuring waviness, illustrating how the laser tracker measures the reflective surface of the duct sidewall using a self-collimated beam. Figure 3 A schematic diagram of a laser tracker measuring a curved conduit is shown, illustrating the geometric relationships during the measurement process. Figure 4 The elliptical duct and air-bearing guide rail are simplified into ellipses and arbitrary rays to explain the geometric model for parameter optimization. Figure 5 and Figure 6 The curve trends before and after parameter optimization for the ray (linear guide) are shown, illustrating the effect of parameter optimization on reducing errors. The following, in conjunction with the appendix... Figure 1-6 The specific embodiments of the measurement method of the present invention will be described in detail below: S1: Equipment Installation and Preparation A high-precision laser tracker is used as the core measuring device, which is securely mounted on a granite linear guide. The granite guide has high rigidity and a low coefficient of thermal expansion, ensuring stability during the measurement process. Simultaneously, the conduit under test is placed on a stable marble table, which has vibration isolation capabilities, reducing the impact of external vibrations on the measurement results.

[0020] S2: Spatial measurement of autocollimation tracking Start the laser tracker and put it into fully automatic self-collimation mode. The self-collimated beam emitted by the laser tracker illuminates the optical reflective surface of the duct sidewall. When the reflected beam is within the instrument's detection range, the laser tracker displays a green light to indicate that it has entered the self-collimation state. The laser tracker will automatically adjust its attitude to make the returning beams coincide. At this time, the spatial vector coordinates of the reflecting surface can be obtained by measurement.

[0021] S3: Equal-interval movement and repeated measurements The operator (or the operator via motor drive) moves the laser tracker along the guide rail at equal intervals, typically 50mm at a time. At each measurement position, the laser tracker repeats the self-collimated spatial coordinate measurement 3-5 times to improve the accuracy and reliability of the data.

[0022] S4: Data Processing and Analysis The measured data is exported to a table and transferred to a computer for storage and analysis. The computer is equipped with specialized data processing software to perform the following tasks: Coordinate angle conversion: Convert spatial vector coordinates into azimuth and elevation angles.

[0023] Relative change data translation: For curved ducts, the relative surface normal deviation is accurately extracted from the absolute coordinate measurements by optimizing the relative attitude parameters (slope k, starting offset xs, distance d) between the guide rail and the duct.

[0024] Ray parameter optimization: Using computer code loops and the bisection method to solve for and optimize ray parameters, so that the angle variation trend of the theoretical model and the measurement data achieves the best match.

[0025] Wrinkle calculation: Based on the formula for calculating the wrinkle parameter σ: in, α i,real ( x )and α i,nominal ( x These represent the actual normal direction and the normal direction of the standard plane, respectively. n This represents the number of data points.

[0026] II. Implementation Methods of Measuring Equipment High-precision laser tracker: As the core measuring device, it is mounted on a granite guide rail and used to measure the spatial vector coordinates of the reflective surface of the duct sidewall. The laser tracker has a fully automatic self-collimation function, which can automatically adjust the attitude to make the forward and backward light rays coincide. During measurement, the operator only needs to move the device along the guide rail and trigger the measurement.

[0027] Granite guide rails support and guide the linear movement of the laser tracker, ensuring stability and accuracy during measurement. A marble tabletop is used to place the guide tube under test and provides vibration isolation, reducing the impact of external vibrations on the measurement results. A computer equipped with specialized data processing software stores and analyzes the data measured by the laser tracker and calculates waviness parameters.

[0028] Example: A comprehensive scheme for measuring duct waviness based on a self-collimating laser tracker (I) Definition and Calculation of Waviness Waviness parameter σ: As an indicator of the machining accuracy of a reflective surface, it represents the standard deviation of the deviation distribution between the actual surface normal direction and the nominal direction. Mathematically, it is calculated using the following formula: like Figure 1 As shown, where, α i,real ( x )and α i,nominal ( x These represent the actual normal direction and the normal direction of the standard plane, respectively. n This represents the number of data points.

[0029] Unlike measuring devices based on direct angle measurement, such as autocollimating total stations and autocollimating theodolites, the core capability of the laser tracker is high-precision distance measurement. The selected autocollimating laser tracker achieves a distance measurement accuracy better than 10μm and an angle measurement accuracy better than 0.5″ within an incident angle range of ±30°, meeting the 3″ accuracy requirement for waviness measurement. Furthermore, like total stations and theodolites, the laser tracker benefits from the full-angle spatial measurement range of the laser tracker testing platform, enabling it to meet the measurement needs of all types of conduits. Based on the waviness measurement principle and device placement, the following results were obtained: Figure 2 As shown.

[0030] Because the laser tracker measures the spatial coordinates of a point on the self-collimated reflecting surface with the machine center as the origin, the non-ideal surface of the guide tube under test causes the laser tracker to adaptively yaw the reflecting surface to regain its self-collimation state (the machine displays a green light) and measure the spatial coordinates. The laser tracker moves at equal intervals on the granite linear guide rail and repeats the self-collimation coordinate measurement. After data processing, the angle data and waviness results can be obtained.

[0031] Calculation of waviness for different geometries: In this embodiment, the laser tracker measures the spatial coordinates of a point on the collimated reflection surface with the machine center as the origin. Therefore, when the laser tracker moves at equal intervals on the linear guide rail and measures the spatial coordinates, these coordinates are precisely directional vector coordinates, v1( x 1, y 1, z 1) v2( x 2, y 2, z 2) v3 x 3, y 3, z 3)……v n ( x n , y n , zn ).

[0032] Subsequently, the azimuth and elevation angles of each vector are calculated based on the coordinate measurement results of the tracker: In this embodiment, the azimuth (horizontal angle) and elevation (vertical angle) of each vector in the spherical coordinate system are calculated respectively. v azimuth of 1 α 1 and elevation angle β 1: (2) (3) vector v n azimuth α n With elevation angle β n : (4) (5) The angular deviations in the horizontal and vertical directions can be obtained simply by subtraction. Since the duct waviness measurement focuses more on the neutron propagation direction, i.e., the horizontal azimuth deviation, subsequent calculations only consider the azimuth variation.

[0033] For straight and tapered neutron conduits: the nominal surface normal is a constant, while waviness measurement examines relative changes. Therefore, the normal of the first measurement point is usually taken as the nominal surface normal.

[0034] (6) Then substitute formula (6) back into formula (1).

[0035] Bending neutron conduit: The direction of the nominal surface normal changes with the measurement position, and in order to ensure the grazing incident angle, the conduit is designed to have a large radius of curvature.

[0036] The following considers several common surface shapes: ① elliptical conduit; ② circular conduit; ③ parabolic conduit. The overall device is as follows: Figure 3 As shown: Because the normal angle of a curved duct changes continuously and varies throughout the direction of the guide rail's movement, the current measurement system can guarantee the straightness of the guide rail measurement and ensure a visual reading error of less than 1mm and a measurement interval of 50mm. However, the current system has the following three uncertainties when measuring curved ducts: Firstly, the measurement starting point X... sThe problem is unclear because: firstly, the graduations on the measuring guide rail cannot match the specific position of the guide tube being aimed at by the laser; secondly, the slope k of the measuring guide rail cannot be perfectly parallel to the curved guide tube, making it impossible to accurately match the measuring interval on the guide rail with the actual measuring surface of the guide tube; and thirdly, the distance d from the measuring machine to the surface of the guide tube cannot be accurately determined. Therefore, this problem can be simplified to... Figure 4 As shown, the ellipse with (0,0) as the origin and any ray located in the fourth quadrant are represented.

[0037] In this embodiment, in addition to mathematically simplifying the system principle, it also includes... Figure 3 As shown, the theoretical normal angle of the ellipse and the angle measured by the laser tracker are not directly related and need to be "translated" to examine the relative change of the angle. First, at any point on the ellipse... x The theoretical normal angle at that location is: Considering the uncertainty of the measurement starting point, the actual measurement starting point is... x 1+ x s (in x 1 is the starting point of the segment. x s (If the offset is to be optimized), then the relative angle change is: (7) The laser tracker measures the absolute angle values ​​in the machine coordinate system. θ M It needs to be translated, subtracting the angle value of the first measuring point: (8) Combining the two formulas (7) and (8) above, the relative relationship between the theoretical normal angle of the ellipse and the angle measured by the laser tracker can be expressed as: in This represents the measurement error. The x in the formula is not uniformly distributed, but is affected by the ray parameter. k / d / x s The implicit effects of these three parameters, in turn, influence the actual change in the normal angle: First, the coordinates of the discrete points are determined by the ray parameters: Furthermore, the ellipse normal intersects the ray, and the point (xi, yi) on the ray and the point (x0, y0) on the ellipse must satisfy the following: in: , and a and b are the major and minor axes of the ellipse; Finally, we can summarize the following: x Implicit equations for 0, x 0 xi , k , xs and d change.

[0038] The results can be easily obtained by using computer code loops and the binary search method. Therefore, optimizing the ray parameters (k, xs, d) is to find the true relative orientation of the linear guide rail and the elliptical guide rail under test in actual guide rail measurement. Below is an example of optimizing the ray (linear guide rail) parameters: Following this logic, under this methodology, the formula for a circular duct is... parabolic conduit formula Similar formulas can be used to derive these formulas and then implemented into the program code for actual measurement.

[0039] (II) Measurement Methods Coordinate measurements are performed directly using a high-precision laser tracker. The laser tracker is mounted on a granite guide rail, and the guide tube under test is placed on a stable marble tabletop (with vibration isolation function).

[0040] The laser tracker is mounted on a high-precision granite guide rail and slids along the beam at equal intervals during measurement. The guide tube to be measured is placed on a marble measuring platform, stably raised to approximately the same height as the tracker. The laser tracker is powered on and enters fully automatic autocollimation mode. The autocollimated beam emitted by the tracker illuminates the optical reflective surface of the guide tube's sidewall. When the reflected light is approximately within the tracker's detection range, the tracker automatically adjusts its attitude to ensure that the returning light rays coincide, achieving an autocollimation accuracy better than 0.5″. A measurement is then completed, yielding the spatial vector coordinates from the theodolite's built-in coordinate origin to the reflecting surface.

[0041] To enhance measurement accuracy and eliminate random error interference, each measurement position typically requires 3-5 repeated measurements. Moving the tracker to the next measurement position, usually by a 50mm displacement on the guide rail, utilizes the tracker's automatic alignment function. No additional operation is required; simply wait for the green light on the equipment to illuminate, indicating successful self-alignment, and then click to take measurements multiple times. Export the data obtained from the tracker to a table and transfer it to a computer for storage and analysis.

[0042] In this embodiment, the data point density is typically selected between 50 mm and 100 mm, and it needs to cover the entire catheter measurement surface as comprehensively as possible to ensure the reliability of the program optimization parameters.

[0043] In this embodiment, the measurement positions are vector coordinate measurements at the centerline position of each side and along its entire length. After data processing, each side is assigned a waviness value.

[0044] (III) Data Analysis In this embodiment, data processing uses specialized data processing software to analyze vector coordinate data, complete steps such as coordinate angle conversion, relative data translation, and ray parameter optimization, and finally obtains the waviness result based on formula (1).

[0045] In this embodiment, the results are evaluated by analyzing the measured waviness value, assessing its assembly accuracy and substrate processing accuracy, and finally evaluating its impact on neutron reflection to determine whether it meets the design requirements and application standards.

[0046] The overall solution of this embodiment includes the aforementioned measuring equipment and method, achieving compatible measurements of neutron conduits in straight, conical, and various curved shapes. This solution significantly reduces the cost of dedicated equipment purchases, improves equipment utilization, greatly reduces manual operation intensity, enhances measurement efficiency, and enables non-professionals to perform high-precision measurements.

Claims

1. A method for measuring the waviness of a duct based on a self-collimating laser tracker, characterized in that, Includes the following steps: S1. A high-precision laser tracker is used as the core measuring device and is installed on a granite guide rail. The tube to be tested is placed on a stable marble table. S2. The laser tracker slides along the guide rail at equal intervals. In the fully automatic self-collimation mode, the emitted self-collimated beam illuminates the optical reflective surface of the duct sidewall. The tracker will automatically adjust its attitude to make the back-and-forth beams coincide, and at the same time obtain the spatial vector coordinates of the reflective surface. S3. Perform 3 to 5 repeated measurements at each measurement position, push the tracker to the next measurement position, usually displace 50mm on the guide rail, and repeat the spatial coordinate measurement of self-collimation tracking. S4. Export the measured data table, transfer it to the computer for storage and analysis, and calculate the waviness parameter σ as an indicator to measure the surface shape processing accuracy of the reflective surface.

2. The method for measuring duct waviness based on a self-collimating laser tracker according to claim 1, characterized in that, The formula for calculating the waviness parameter σ is: in, α i,real ( x )and α i,nominal ( x These represent the actual normal direction and the normal direction of the standard plane, respectively. n This represents the number of data points.

3. The method for measuring duct waviness based on a self-collimating laser tracker according to claim 1, characterized in that, The performance requirements of the laser tracker are as follows: within the incident angle of ±30°, the accuracy of distance measurement is better than 10μm, the accuracy of angle measurement is better than 0.5″, and the accuracy requirement of 3″ for waviness measurement is met.

4. The method for measuring duct waviness based on a self-collimating laser tracker according to claim 1, characterized in that, For conduits with different geometries, the methods for calculating waviness include: The azimuth and elevation angles of each vector are calculated based on the coordinate measurement results of the tracker. First, the azimuth (horizontal angle) and elevation (vertical angle) of each vector in the spherical coordinate system are calculated respectively. For straight, tapered neutron conduits, the normal of the first measurement point is taken as the nominal surface normal; For curved neutron conduits, the relative surface normal deviation is accurately extracted from the absolute coordinate measurements by optimizing the relative attitude parameters (slope k, starting point offset xs, distance d) between the guide rail and the conduit.

5. The method for measuring duct waviness based on a self-collimating laser tracker according to claim 4, characterized in that, The curved neutron conduit includes elliptical conduits, circular conduits, and parabolic conduits. Its waviness is calculated by establishing a geometric model of the measurement system, transforming the mechanical installation parameters (k, xs, d) into mathematically optimizable variables, and using iterative calculations to achieve the best match between the theoretical model and the angular change trend of the measurement data.

6. A device for measuring the waviness of a duct based on a self-collimating laser tracker, characterized in that, include: A high-precision laser tracker, mounted on a granite guide rail, is used to measure the spatial vector coordinates of the reflective surface of the duct sidewall; Granite guide rails are used to support and guide the linear movement of the laser tracker; The marble countertop is used to place the test tube and has vibration isolation function; A computer is used to store and analyze data measured by the laser tracker and to calculate waviness parameters.

7. The duct waviness measurement device based on a self-collimating laser tracker according to claim 6, characterized in that, The laser tracker has a fully automatic self-collimation function, which can automatically adjust the posture to make the back and forth light rays overlap. During measurement, the personnel only need to move the device along the guide rail and trigger the measurement.

8. A duct waviness measurement device based on a self-collimating laser tracker according to claim 6, characterized in that, The computer is equipped with specialized data processing software to perform the conversion of coordinate data to angle data, the translation of data with relative changes, the optimization of ray parameters, and finally to obtain the waviness result based on the waviness calculation formula.

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