A method for calibrating a hand-held light pen measurement system

Abstract

The application provides a kind of handheld light pen measurement system calibration method, including target coordinate calculation step, obtain the image of different angles of light pen with probe as fixed point rotation as mark point image, the center coordinates of probe in camera coordinate system are obtained by conversion strategy with mark point image and light pen model;Target model construction step, according to the center coordinates of probe in multiple camera coordinate system, construct target model based on standard deviation;Distance parameter calculation step, the optimal distance parameter of mark point and probe center is obtained by iterative algorithm to solve target model;Mark point coordinate optimization step, the mark point light pen coordinate is optimized by beam method adjustment algorithm with distance parameter;Probe center calibration step, the light pen coordinate of probe center is deduced back with distance parameter and optimized mark point light pen coordinate, the advantage of the application is that high-precision measuring tool is not needed, and light pen measurement system can be calibrated only through image information.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machine vision measurement, and more particularly to a calibration method of a handheld light pen measurement system. BACKGROUND

[0002] The handheld light pen measurement system is a three-dimensional coordinate measurement technology integrating portability, high precision and flexibility, and is widely used in the fields of aerospace, automobile manufacturing and part detection. The system is usually composed of a light pen with optical marker points, an industrial camera and a computer. Compared with traditional fixed measurement equipment, the system has the advantages of free operation, suitability for complex curved surface and difficult-to-contact area measurement, and is particularly suitable for local precision detection of large workpieces. However, in actual application, the measurement accuracy of the light pen system is affected by various factors, such as insufficient machining and assembly precision of the light pen model, frequent replacement of ruby probes when measuring industrial parts of different depths, and mechanical wear of the light pen during long-term use, which may cause the coordinates of the marker points and the probe center to deviate, thereby significantly affecting the accuracy of the solution of the probe center coordinates and reducing the measurement accuracy of the system.

[0003] Currently, the calibration methods for the light pen measurement system mainly fall into two categories: one relies on high-precision measurement tools such as three-coordinate measuring machines to realize calibration by directly measuring the three-dimensional coordinate information of the light pen marker points. Although this method can provide high measurement accuracy, it has strong dependence on external measurement equipment, complex operation process and high environmental requirements, which limits the flexibility of the measurement system in actual industrial applications. The other calibration method attempts to be independent of external measurement equipment, but these methods often have strict implementation conditions and the final measurement accuracy is difficult to meet the actual demand. In addition, since the light pen marker points are usually transparent or semi-transparent micro-LEDs with small internal light-emitting chip size and certain light reflection characteristics on the surface, it is difficult for the three-coordinate measuring machine to accurately locate the light-emitting center, thereby introducing uncertainty in measurement error. At the same time, to meet the measurement needs of workpieces of different depths and structural characteristics, the light pen needs to frequently replace the probe, and the small offset introduced during the replacement process further aggravates the change of the probe center coordinates, affecting the system measurement accuracy. Therefore, it is of great practical significance and application value to develop a method for calibrating the light pen measurement system without relying on high-precision measurement tools and only through image information. SUMMARY

[0004] In view of the deficiencies of the prior art, the purpose of the present application is to provide a calibration method for a handheld light pen measurement system, which establishes the mapping relationship between the light pen coordinate system and the camera coordinate system, combines multiple sets of image information for sensitivity analysis and optimization calculation, and obtains the optimal coordinate parameters of the marker point and the probe center, so as to realize efficient and accurate calibration of the light pen measurement system, thereby avoiding the dependence on external high-precision measurement equipment and significantly improving the flexibility and measurement accuracy of the calibration process.

[0005] To achieve the above purpose, the present application provides the following technical solutions:

[0006] A calibration method for a handheld light pen measurement system, comprising the following steps:

[0007] A target coordinate calculation step, which obtains images of the light pen rotating at different angles with the probe as a fixed point as marker point images, the marker point images including a marker point and a probe center, and obtains the probe center coordinates in the camera coordinate system by converting the marker point images and the light pen model through a conversion strategy;

[0008] A target model construction step, which constructs a target model based on the probe center coordinates in the camera coordinate system according to the standard deviation;

[0009] A distance parameter calculation step, which obtains the optimal distance parameters of the marker point and the probe center by solving the target model through an iterative algorithm;

[0010] A marker point coordinate optimization step, which optimizes the marker point light pen coordinates by the light beam adjustment algorithm through the distance parameters;

[0011] A probe center calibration step, which inversely calculates the probe center light pen coordinates from the distance parameters and the optimized marker point light pen coordinates.

[0012] Further, the target model construction step includes a sensitivity analysis strategy, which includes applying a fixed disturbance to each coordinate component of the ideal light pen in the light pen model, calculating the coordinate standard deviation of the probe center in the camera coordinate system before and after the disturbance, and then calculating the sensitivity coefficient according to the coordinate standard deviation and screening out the coordinate components that have a great impact on the standard deviation.

[0013] Further, the sensitivity analysis strategy includes a sensitivity coefficient construction formula, which is configured as:

[0014] ,

[0015] ,

[0016] ,

[0017] ,

[0018] wherein, is a sensitivity value coefficient, is a standard deviation of the X, Y, Z three directions respectively, is the total number of images taken, is a fixed perturbation size, is a coordinate component calculated according to the perturbed coordinates, is a standard deviation of the X, Y, Z three directions of the probe center coordinates in the camera coordinate system of the first group, , is a coordinate component of the X, Y, Z three directions of the probe center after the perturbation of the first group, , is a coordinate component of the X, Y, Z three directions of the probe center after the perturbation of the first group, , is a mean value of the X, Y, Z three directions of the probe center coordinates in the camera coordinate system of the first group.

[0019] Further, the target model construction step further includes a weighted constraint strategy, the weighted constraint strategy includes randomly perturbing the coordinate components that have a large impact on the standard deviation, then dynamically adjusting the coordinate weight through adaptive weighting of the sensitivity value coefficient, and introducing a regularization constraint to construct a target function of the target model.

[0020] Further, the target function is configured as:

[0021] ,

[0022] ,

[0023] ,

[0024] wherein, is a coordinate weight, is a regularization coefficient, is a 24 ideal light pen coordinate component, is a coordinate component after the second time perturbation of the ideal coordinate component, is a random perturbation size.

[0025] Further, the iterative algorithm includes a trust region gradient descent algorithm, and the trust region gradient descent algorithm is configured as:

[0026] ,

[0027] ,

[0028] wherein, is a step number of the current iteration, is a next iteration, is the learning rate, The step size set for the trust region algorithm.

[0029] Furthermore, the distance parameter calculation step includes an iterative termination constraint strategy, which includes stopping the iteration when the standard deviation of the camera coordinates of each group of probe centers is less than a threshold M, outputting the disturbance variable, and calculating the distance parameters between the marker points and the marker points and the probe center based on the coordinates after the disturbance.

[0030] Furthermore, in the marker point coordinate optimization step, the distance parameter between the marker points is introduced into the bundle adjustment algorithm, and the error function is iteratively optimized by using the nonlinear least squares method to obtain the optimized marker point light pen coordinates. The error function after iterative optimization is configured as follows:

[0031] ,

[0032] in, is the actual observed image coordinate of the marker point, is the reprojected coordinate of the marker point, is the weight factor, is the distance parameter between the landmark points, is the coordinate of each optimization, , .

[0033] Furthermore, a distance constraint formula is configured in the probe center calibration step, and the distance constraint formula is configured as follows:

[0034] ,

[0035] in, is the probe center coordinate, is the optimized marker point light pen coordinate, is the distance parameter between the marker point and the probe center.

[0036] Furthermore, the conversion strategy includes constructing a light pen coordinate system on the light pen model, extracting the ideal light pen coordinates of the landmark point and the probe center respectively, calculating the pose matrix of the light pen coordinate system and the camera coordinate system through the PNP algorithm, and converting the ideal light pen coordinates of the probe center into the probe center coordinates in the camera coordinate system.

[0037] The beneficial effects of the present application: by establishing the mapping relationship between the light pen coordinate system and the camera coordinate system, combining sensitivity analysis to screen key coordinates and dynamically adjusting the weight, while introducing regularization constraints and geometric constraints, the calibration accuracy and robustness are improved, this method does not need to rely on high-precision external measuring equipment, only through image information can realize high-precision calibration of the light pen measurement system, reduce the operation complexity and cost, in addition, this method is suitable for different depth and structure feature workpiece measurement demand, especially suitable for complex curved surface or large workpiece local precision detection, has wide application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is the overall flowchart of the present application;

[0039] Figure 2 is the light pen model schematic diagram in the present application;

[0040] Figure 3 is the multi-pose acquisition diagram of the light pen in the present application;

[0041] Figure 4 is the image coordinate acquisition diagram of the mark point in the present application;

[0042] Figure 5 is the coordinate component diagram for A-H mark points in the present application;

[0043] Figure 6 is the principle diagram of bundle adjustment in the present application;

[0044] Figure 7 is the coordinate comparison diagram before and after calibration in the present application. DETAILED DESCRIPTION

[0045] The present application will be further described in detail below in combination with the drawings and examples. Wherein the same parts are represented by the same reference signs. It should be noted that the words "front", "back", "left", "right", "up" and "down" used in the following description refer to the directions in the drawings, and the words "bottom surface" and "top surface", "inner" and "outer" refer to the directions towards or away from the geometric center of a particular part.

[0046] Since the light pen marking points are mostly made of transparent or translucent packaged micro LEDs, the internal light-emitting chip is tiny in size and has a certain reflective property on the surface, making it difficult for the three-dimensional coordinate measuring machine to accurately locate its light-emitting center, thus causing uncertainty in the measurement error. In addition, in order to meet the measurement needs of workpieces with different depths and structural features, the light pen needs to frequently replace the ruby ​​probe, and the replacement process may also introduce a slight offset, further affecting the coordinates of the probe center, thereby affecting the measurement accuracy of the system. The present invention provides a calibration method for a handheld light pen measurement system, which achieves high-precision calibration by combining image information without relying on external high-precision measurement equipment. The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Figure 1 As shown, the calibration process of the present invention includes:

[0047] The target coordinate calculation step requires the preparation of a conical calibration piece. Its design ensures that the spatial position of the probe center remains unchanged under different postures of the light pen. This feature provides a basic guarantee for subsequent calculations. Then, Figure 3 As shown in FIG, the light pen is placed in the conical calibration piece, and the probe is kept fixed. The light pen body is rotated to capture multiple sets of images as marker point images through an industrial camera, as shown in FIG. Figure 2 As mentioned above, the seven marker points in each marker point image are named A, B, C, D, E, F, and H respectively. After obtaining the marker point image, it needs to be preprocessed to extract the image coordinates of the marker points, as shown in the following example: Figure 4 As shown in the figure, the marker point image is first binarized, and then the image coordinates of the marker point are obtained by the ellipse fitting method of sub-pixel interpolation. This method significantly improves the accuracy of marker point center positioning by linear interpolation calculation of the grayscale values ​​of the edge pixels of the marker point. For example, in practical applications, if the grayscale distribution of the edge pixels of marker point A presents a non-uniform characteristic, its center position can be accurately determined by sub-pixel interpolation, thereby providing reliable data for subsequent calculations.

[0048] The light pen coordinate system is established with the mark point in the upper left corner of the light pen model as the origin. That is, the direction along the length of the light pen is defined as the positive direction of the X axis, the direction perpendicular to the plane of the light pen is the positive direction of the Z axis, and the Y axis direction is determined by the right-hand rule. On this basis, the ideal coordinates of the mark point AF and the probe center H in the light pen coordinate system are obtained, as shown in the following table.

[0049]

[0050] According to the image coordinates of the marker points, the ideal light pen coordinates, and the camera intrinsic parameters, the PNP algorithm is used to obtain the pose information between the light pen coordinate system and the camera coordinate system. Then, combined with the ideal light pen coordinates of the probe center, the coordinates of the probe center in the camera coordinate system are obtained. That is, the rotation matrix and translation vector between the light pen coordinate system and the camera coordinate system are calculated. The calculation formula is configured as follows:

[0051] ,

[0052] ,

[0053] ,

[0054] wherein, is a distortion factor for compensating lens distortion, is an image coordinate, is a light pen coordinate, is a camera coordinate, is an intrinsic matrix of the camera, is a camera coordinate of the probe center, is a light pen coordinate of the probe center, is a rotation matrix of the camera, is a translation vector of the camera, through the above formula, the probe center coordinate in the camera coordinate system can be accurately solved.

[0055] The target model construction step constructs a target model according to the probe center coordinates in the camera coordinate system, and the standard deviation is used as the basis, specifically, the target model construction step includes a sensitivity analysis strategy, the sensitivity analysis strategy includes applying a fixed disturbance to the ideal light pen coordinate components in the light pen model one by one, that is, a fixed disturbance with an amplitude of 0.1 mm is added to the 24 coordinate components one by one, and only one coordinate component is disturbed each time, and the remaining coordinates remain unchanged, and the coordinate formula after disturbance is configured as: wherein, is a disturbed coordinate, is a coordinate component of the 7 marker points and the probe center, , is a fixed disturbance variable, the coordinate after disturbance, that is, a new light pen coordinate of a group of marker points and the probe center, is obtained, the PNP algorithm is used again to calculate the pose transformation matrix of the light pen to the camera, the light pen coordinate of the probe center after disturbance is further obtained, and the coordinate of the probe center in the camera coordinate system is obtained, through the above process repeated on the N groups of collected images, N probe center coordinates are obtained, the standard deviation is calculated in the X, Y and Z directions respectively, and the formula is configured as:

[0056] ,

[0057] ,

[0058] ,

[0059] wherein, are the standard deviations of the X, Y and Z directions respectively, the total number of images to be taken, the first X, Y, and Z coordinate components of the probe center after the disturbance, the total number of images to be taken, the average values of the X, Y, and Z coordinate components of the probe center in the camera coordinate system, .

[0060] The sensitivity coefficient represents the average change in the standard deviation of each coordinate value before and after the disturbance, and the final result is shown in Figure 5 The sensitivity coefficient is configured as:

[0061] ,

[0062] wherein, is the sensitivity coefficient, the first the standard deviations of the X, Y, and Z coordinate components of the probe center in the camera coordinate system calculated based on the disturbed coordinates, , is the fixed disturbance size. In actual operation, if the standard deviation of an ideal light pen coordinate on the probe center has a greater impact, its sensitivity coefficient is higher, indicating that the coordinate has a greater contribution to the optimization model.

[0063] A higher weight is assigned to the light pen coordinate with a higher sensitivity value, and the normalized weight formula is configured as:

[0064] ,

[0065] wherein, is the coordinate weight, The second disturbance variable of the ideal coordinate is controlled by the weight, and the higher the sensitivity value, the higher the disturbance weight. The second disturbed coordinate formula is configured as:

[0066] ,

[0067] wherein, is the coordinate component after the second disturbance of the ideal coordinate component, is the random disturbance size, ranging from 0.01 to 0.2.

[0068] According to the obtained coordinates after the second disturbance of the ideal coordinates, i.e., the new marker point and the probe center coordinates, N sets of camera coordinates of the probe center are calculated based on N sets of images, and the standard deviations in three directions are calculated. At the same time, considering that excessive disturbance may introduce model instability or overfitting risk, a regularization term is introduced in the optimization objective function to constrain the disturbance amplitude, and the final objective function formula is configured as:

[0069] ,

[0070] wherein, is a regularization coefficient, used to avoid the model instability or overfitting caused by the too large weight of a single parameter, is the 24 ideal light pen coordinate components, through the dynamic adjustment of the weight and the introduction of the regularization constraint, the target model can maintain high robustness under complex conditions.

[0071] The distance parameter calculation step obtains the optimal distance parameters between the landmark points and the probe center through an iterative algorithm. Specifically, the iterative algorithm includes a trust region gradient descent algorithm, and the trust region gradient descent algorithm is configured as:

[0072] ,

[0073] ,

[0074] wherein, is the step number of the current iteration, is the next iteration, is the learning rate, is the step length set by the trust region algorithm, and the optimal solution is finally obtained through step-by-step approximation. In actual application, the accuracy of the distance parameter directly affects the subsequent calibration result, and therefore the convergence and stability of the iteration process need to be ensured.

[0075] The distance parameter calculation step includes an iteration termination constraint strategy. The iteration termination constraint strategy includes stopping iteration when the standard deviation of the camera coordinates of each group of probe centers is less than a threshold M (0.05), outputting the disturbance variable , and calculating the distance parameters between the landmark points and the probe center according to the disturbed coordinates.

[0076] The landmark point coordinate optimization step introduces the distance parameters between the landmark points into the light beam adjustment algorithm, and obtains the optimized landmark point light pen coordinates by using a nonlinear least squares method to iteratively optimize the error function, as shown in Figure 6 The error function after iterative optimization is configured as:

[0077] ,

[0078] wherein, is the actually observed marker image coordinate, is the re-projection coordinate of the marker, is a weight factor, used to balance the influence of image error and geometric constraint, is the distance parameter between the landmark points, is the coordinate of each optimization, , By this algorithm, not only the light pen coordinates of the marker points are optimized, but also the geometric relationship consistency between the marker points is ensured, thereby improving the calibration accuracy.

[0079] The probe center calibration step reverses the probe center light pen coordinates from the distance parameters and the optimized marker point light pen coordinates. For the improved error function, the marker point light pen coordinates are optimized by using the nonlinear least squares, and after obtaining the optimized marker point light pen coordinates, the distance parameters obtained in the first stage calibration are combined to calculate the probe center coordinates in the light pen coordinate system through iterative calculation. After calibration, the coordinates of the calibrated marker points and the probe center in the light pen coordinate system are output. The coordinate comparison before and after calibration is shown in Figure 6 . The distance constraint target function algorithm is configured as:

[0080] ,

[0081] wherein, is the probe center coordinate, , is the optimized marker point light pen coordinate, is the distance parameter between the marker point and the probe center, as shown in Figure 7 The coordinate comparison before and after calibration clearly shows the calibration effect, and the calibrated coordinates have higher accuracy and consistency.

[0082] Calibration principle: ①, calibration target: the coordinates of 7 marker points and a probe center in the light pen coordinate system;

[0083] ②, in the first stage of calibration, the target is to determine the distance parameters between the probe center and the marker points on the light pen. Initially, the sensitivity analysis method is used to select ideal coordinates (the purpose of this step: select the coordinates with high sensitivity to assign higher perturbation weight to accelerate algorithm convergence; method: add a fixed perturbation of 0.1 mm to the ideal coordinates to obtain a new set of marker points and probe center coordinates, then calculate the probe center coordinates obtained from N images, and calculate the standard deviation before and after perturbation, and then calculate the sensitivity coefficient according to the formula, so as to select the coordinates with high sensitivity), and then apply weighted perturbation to the selected coordinates;

[0084] Subsequently, the 3D coordinates of the probe center of each group of images after the second disturbance in the camera coordinate system are solved, and the standard deviations in the X, Y and Z directions are calculated. When the standard deviations in all three directions are minimized, the disturbance variable at this time is output. The disturbance variable is added to the ideal coordinates to obtain the disturbance coordinates. The distance parameters between the marker points and between the marker points and the probe center are calculated using the distance formula between two points. (In fact, a fixed disturbance is first given to the ideal coordinates to observe which points have a large impact on the final standard deviation. Then, the points with a large impact are selected and a large weight is given to these points during the second disturbance. Finally, the size of the disturbance is adjusted to minimize the standard deviation of the N groups of probe center coordinates in the XYZ directions).

[0085] ③、The reason for the second stage calibration: The main purpose of the first stage calibration is to obtain the distance parameters between the marker points and the probe center. However, in actual applications, due to manufacturing and assembly errors, especially inaccurate welding of infrared LEDs, deviations may occur, resulting in differences between the ideal coordinates obtained by the light pen model and the actual coordinates in the real world. In addition, due to various factors such as internal and external camera parameter errors, inaccurate image observation, and position deviation of the marker points, the actual projection points on the image plane deviate from their observed positions. Therefore, in the second stage of calibration, a beam adjustment algorithm is applied to optimize the coordinates of the marker points in the light pen coordinate system.

[0086] ④、Second stage calibration: Introduce the distance parameters between the marker points obtained in the first stage of calibration to constrain the optimization of the marker points. This step optimizes the marker point coordinates by minimizing the projection error between the image coordinates of the marker points obtained by the camera and the corresponding projection points. The optimized marker point coordinates are combined with the distance parameters between the marker points and the probe center obtained in the first stage to iteratively solve the optimized coordinates of the probe center, and the calibration is completed.

[0087] The above is only a preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution that falls within the scope of the present application is within the protection scope of the present application. It should be noted that for ordinary technical personnel in the technical field, some improvements and refinements without departing from the principles of the present application are also considered within the protection scope of the present application.

Claims

1. A calibration method for a handheld light pen measurement system, characterized in that: The steps include: The target coordinate calculation step obtains images of the light pen rotating at different angles with the probe as a fixed point as marker point images, wherein the marker point images include the marker point and the probe center, and the marker point images and the light pen model are converted using a conversion strategy to obtain the probe center coordinates in the camera coordinate system; The target model construction step is to construct the target model based on the center coordinates of the probes in the multiple camera coordinate systems and the standard deviation; a distance parameter calculation step, solving the target model through an iterative algorithm to obtain the optimal distance parameter between the marker point and the probe center; Mark point coordinate optimization step, optimizing the marker point light pen coordinates by using the distance parameter through a bundle adjustment algorithm; The probe center calibration step is to reversely calculate the probe center light pen coordinates using the distance parameters and the optimized marker point light pen coordinates; The target model construction step includes a sensitivity analysis strategy, which includes applying fixed perturbations to the ideal light pen coordinate components in the light pen model one by one, calculating the coordinate standard deviation of the probe center in the camera coordinate system before and after the perturbation, then calculating the sensitivity value coefficient based on the coordinate standard deviation, and screening out the coordinate components that have a large impact on the standard deviation; The target model construction step also includes a weighted constraint strategy, which includes randomly perturbing the coordinate components that have a large impact on the standard deviation, dynamically adjusting the coordinate weights of the sensitive value coefficients through adaptive weighting, and introducing regularization constraints to construct the objective function of the target model.

2. The calibration method for a handheld optical pen measurement system according to claim 1, characterized in that: The sensitivity analysis strategy includes a sensitive value coefficient construction formula, and the sensitive value coefficient construction formula is configured as follows: ， ， ， ， in, is the sensitivity coefficient, are the standard deviations in the X, Y, and Z directions respectively. is the total number of captured images, To fix the perturbation size, are calculated based on the perturbed coordinates. The standard deviation of the probe center coordinates in the X, Y, and Z directions in the group camera coordinate system, , Respectively The coordinate components of the probe center in the X, Y, and Z directions after the group disturbance, , for The mean of the probe center coordinates in the X, Y, and Z directions in the group camera coordinate system.

3. The calibration method of a handheld optical pen measurement system according to claim 1, characterized in that: The objective function is configured as: ， ， ， in, is the coordinate weight, is the regularization coefficient, are 24 ideal light pen coordinate components, is the coordinate component after the second perturbation of the ideal coordinate component, is the random perturbation size, is the sensitivity coefficient, are the standard deviations in the X, Y, and Z directions respectively.

4. The calibration method for a handheld optical pen measurement system according to claim 3, characterized in that: The iterative algorithm includes a trust region gradient descent algorithm, and the trust region gradient descent algorithm is configured as follows: ， ， in, is the number of steps in the current iteration, For the next iteration, is the learning rate, The step size set for the trust region algorithm.

5. The calibration method of a handheld optical pen measurement system according to claim 4, characterized in that: The distance parameter calculation step includes an iterative termination constraint strategy, which includes stopping the iteration when the standard deviation of the camera coordinates of each group of probe centers is less than a threshold M, outputting the disturbance variable, and calculating the distance parameters between the marker points and the marker points and the probe center based on the coordinates after the disturbance.

6. The calibration method of a handheld optical pen measurement system according to claim 5, characterized in that: The marker point coordinate optimization step introduces the distance parameter between the marker points into the bundle adjustment algorithm, and iteratively optimizes the error function by using the nonlinear least squares method to obtain the optimized marker point light pen coordinates. The error function after iterative optimization is configured as follows: ， in, is the actual observed image coordinate of the marker point, is the reprojected coordinate of the marker point, is the weight factor, is the distance parameter between the landmark points, is the coordinate of each optimization, , .

7. The calibration method of a handheld optical pen measurement system according to claim 6, characterized in that: The probe center calibration step is configured with a distance constraint formula, which is configured as follows: ， in, is the probe center coordinate, is the optimized marker point light pen coordinate, is the distance parameter between the marker point and the probe center.

8. The calibration method for a handheld optical pen measurement system according to claim 1, characterized in that: The conversion strategy includes constructing a light pen coordinate system on the light pen model, extracting the ideal light pen coordinates of the landmark point and the probe center respectively, calculating the pose matrix of the light pen coordinate system and the camera coordinate system through the PNP algorithm, and converting the ideal light pen coordinates of the probe center into the probe center coordinates in the camera coordinate system.

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