A high-precision error modeling method for linear laser measurement considering signal-to-noise ratio and multi-dimensional parameters simultaneously

Abstract

The application provides a high-precision error modeling method for linear laser measurement considering signal-to-noise ratio and multi-dimensional parameters simultaneously, comprising the following steps: discretizing the linear laser into a plurality of measurement points, and establishing a local parameter set for each measurement point; based on the Lambert reflection model and spatial vector geometry, a direct functional relationship between the surface posture of each measurement point and the signal-to-noise ratio of the sensor is established, and a signal-to-noise ratio error term is established according to the signal-to-noise ratio of the sensor; based on the geometric optical model, a geometric error term of each measurement point is established; the signal-to-noise ratio error term and the geometric error term are superimposed to obtain a total error, and high-precision error modeling is carried out based on the total error. The application simultaneously considers two physical sources of geometric shift and signal quality decline, has high prediction accuracy and strong universality, can be used to generate an error map to realize point-by-point error compensation, or be used for scan path optimization, and significantly improves the measurement accuracy of the linear laser measurement system.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional optical measurement and machine vision technology, specifically involving a high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters. It is particularly suitable for scenarios involving high-precision three-dimensional shape measurement of objects with complex free-form surfaces, such as industrial parts quality inspection, reverse engineering, and in-machine measurement. Background Technology

[0002] Line laser triangulation technology has been widely used in modern industrial manufacturing due to its advantages of being non-contact, high-speed, and high-density. However, its measurement accuracy is affected by a variety of complex factors, including the surface geometry of the object being measured, the geometric layout of the sensor itself, and ambient light.

[0003] To predict and compensate for these errors, existing technologies typically employ mathematical models. However, these models generally have limitations: first, most are designed for point laser sensors or simplify line lasers into ideal single-point models, ignoring the geometric differences between different points on the laser line; second, the models are mostly based on ideal geometric optics and fail to fully consider the severe impact of signal-to-noise ratio degradation caused by energy attenuation of reflected light on measurement results when measuring at edges or large angles.

[0004] A search revealed one existing technology: the point laser error model based on geometric optics proposed by Li et al. (Meas. Sci. Technol. 25 015204). The core of this technology is to establish a functional relationship between error and incident angle by analyzing the influence of the laser incident angle α on the offset of the imaging point inside the sensor. The main drawback of this model is:

[0005] 1. Limitations of the model object: It is essentially a point laser model. When directly applied to line lasers, it ignores the physical fact that the emission angle and triangulation geometry of each point on the line laser sector are independent and different.

[0006] 2. Single error attribution: It mainly attributes the source of error to geometric offset, failing to explain and model the often dominant error components caused by the sharp decline in signal quality at certain angles.

[0007] 3. Insufficient predictive ability: Therefore, this type of model cannot accurately predict the complex nonlinear behavior of the total error when the line laser scans a free-form surface, especially at the edge of the field of view, and its simulation results differ significantly from the actual measurement data.

[0008] Another existing technology is a linear laser tilt angle error modeling method based on an ideal diffuse reflection model. The core approach is to treat the measured surface as a Lambertian body, derive the geometric offset of the laser spot energy centroid on the photosensitive element caused by surface tilting based on the laser triangulation measurement principle, establish the functional relationship between the incident angle, displacement, and measurement error, and then perform error compensation. The drawback of this type of technology is:

[0009] 1. Incomplete consideration of error factors: Only the influence of the incident angle and displacement on the measurement error is considered, while the role of the azimuth angle is ignored. In actual measurements, changes in the azimuth angle will lead to changes in the spatial distribution of the reflected signal and signal attenuation, which is an important factor affecting the measurement accuracy.

[0010] 2. The physical model is too idealistic: It only derives the energy centroid shift based on geometric optics, ignoring the additional error introduced by the sharp drop in signal-to-noise ratio (SNR) when the azimuth angle increases, resulting in a large deviation between the model's predicted value and the actual error.

[0011] 3. Insufficient predictive ability: It cannot reproduce the edge effect of a sharp increase in scanning edge error, and the compensation effect is limited in the measurement of large curvature or complex curved surfaces.

[0012] Therefore, the prediction accuracy of existing models is limited, especially in that they cannot accurately reproduce the phenomenon of a sharp increase in error at the scanning edge, resulting in poor error compensation and limiting the application of line laser measurement systems in ultra-high precision applications. Summary of the Invention

[0013] This invention aims to address the technical problems of low accuracy and insufficient physical realism in existing line laser scanning error models. It provides a high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters. This method can: 1) accurately describe the unique and complex spatial geometric relationships of each point on the laser line when a line laser scanner measures an arbitrary freeform surface; 2) simultaneously consider the two core physical sources of error: geometric offset error and error caused by signal quality degradation; and 3) thereby establish a mathematical model that can accurately predict the error distribution (including edge effects) of the entire laser line, providing a solid theoretical foundation for achieving high-precision measurement path planning and error compensation.

[0014] To achieve the above objectives, the present invention adopts the following technical solution:

[0015] A high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters includes the following steps:

[0016] S1. Discretize the line laser into several measurement points. and for each measurement point Establish a local parameter set;

[0017] S2. Based on the Lambertian reflection model and spatial vector geometry, establish the measurement points for each point. The direct functional relationship between surface attitude (α, φ) and sensor signal-to-noise ratio (SNR) is established, and a signal-to-noise ratio error term is constructed based on the sensor SNR. ;

[0018] S3. Based on the geometric optics model, establish each measurement point geometric error term ;

[0019] S4. The signal-to-noise ratio error term obtained in step S2 and the geometric error term obtained in step S3 By superimposing the data, each measurement point can be obtained. Total error Based on total error Perform high-precision error modeling.

[0020] Furthermore, each measurement point in step S1 The established local parameter set includes:

[0021] Angle of incidence θ is the angle between the incident ray and the surface normal, calculated using the following formula:

[0022] = arccos( - · );

[0023] in, To point the laser source to the measurement point unit vector, For measurement points Surface normal;

[0024] Azimuth , is the dihedral angle between the incident plane and the receiving plane, calculated by the following formula:

[0025] = arccos( ( · ) / (|| || * || ||) );

[0026] in, Let be the normal vector of the incident plane. = × , To receive the normal vector of the plane, = × ;

[0027] Effective angle of incidence , satisfying tan( ) = cos( ) * tan( );

[0028] Equivalent object distance It is from the measurement point The distance to the receiver is calculated using the following formula:

[0029] = || ||;

[0030] in, From The vector pointing to the camera's optical center O is calculated using the following formula:

[0031] = O - ;

[0032] Equivalent trigonometric measurement angle θ is the angle between the incident ray and the received ray, calculated using the following formula:

[0033] = arccos( - · ) ;

[0034] Depth difference , is the depth of the current measurement point. Relative to nominal reference depth The deviation.

[0035] Furthermore, each measurement point in step S2 The direct functional relationship between the surface attitude (α, φ) and the sensor signal-to-noise ratio (SNR) is as follows:

[0036] SNR(α, φ) = * max(0, cos(γ));

[0037] in, The maximum signal-to-noise ratio of the system under ideal conditions. = / N, It is the maximum signal strength that can be received under ideal conditions;

[0038] γ is the angle between the surface normal and the received ray, and satisfies:

[0039] cos(γ) = sin(α)cos(φ)sin(θ) + cos(α)cos(θ).

[0040] Furthermore, the aforementioned signal-to-noise ratio error term The expression is as follows:

[0041] = C / (SNR(α, φ) + ε);

[0042] Where C is the error proportionality constant, and ε is a positive constant used to prevent division by zero errors.

[0043] Furthermore, the geometric error term The expression is as follows:

[0044] ;

[0045] Where R is the effective radius of the camera lens. The baseline length is the lateral distance between the center of the laser emitter and the center of the receiving lens.

[0046] .

[0047] Furthermore, the total error in step S4 Calculate as follows:

[0048] = | | + ;

[0049] (α, φ) = | | .

[0050] Compared with the prior art, the present invention has the following advantages:

[0051] 1. Extremely high prediction accuracy: Because it simultaneously considers both the effects of point-by-point changes in local geometry and signal quality degradation, the prediction results of this model are in high agreement with the actual measurement error, significantly outperforming existing simplified models;

[0052] 2. Strong universality and versatility: The vector-based calculation method makes this model not limited to sensors of specific brands or structures. As long as the relative positions of the laser and camera are known, it can be applied to various line laser triangulation systems and can predict errors on arbitrarily complex freeform surfaces;

[0053] 3. Empowering advanced measurement strategies: High-precision error prediction capabilities enable "virtual measurement" before actual measurement. Users can use this model for simulation to optimize scanning paths and sensor attitudes, proactively avoid high-error areas, and achieve measurement path planning, thereby improving measurement quality from the source.

[0054] 4. Enhanced Error Compensation: This model can generate a high-resolution, high-fidelity "error map" for the measured surface. This map can be used for precise, point-by-point error compensation of the original measurement point cloud, thereby significantly improving the absolute accuracy and surface quality of the final 3D model. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention;

[0056] Figure 2 This is a graph showing the relationship between the total error and the incident angle under different azimuth angles in Embodiment 1 of the present invention;

[0057] Figure 3 This is a graph showing the total error as a function of the azimuth angle when the incident angle is 10° in Embodiment 1 of the present invention.

[0058] Figure 4 This is a schematic diagram of the three-dimensional relationship and scan lines when a sphere is used as the object being measured in Embodiment 2 of the present invention;

[0059] Figure 5 This is a schematic diagram of the azimuth angle distribution along the scan line in Embodiment 2 of the present invention;

[0060] Figure 6 This is a schematic diagram of the incident angle distribution along the scan line in Embodiment 2 of the present invention;

[0061] Figure 7 This is a schematic diagram of the total error distribution along the scan line in Embodiment 2 of the present invention;

[0062] Figure 8 This is a comparison chart of the total error components in Embodiment 2 of the present invention;

[0063] Figure 9 This is a schematic diagram showing the relationship between total error and angle in Embodiment 2 of the present invention. Detailed Implementation

[0064] The present invention will be further explained below with reference to the accompanying drawings and embodiments.

[0065] Example 1:

[0066] This embodiment provides a high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters, including the following steps:

[0067] S1. Discretize the line laser into several measurement points. and for each measurement point Establish a local parameter set;

[0068] First, establish a global coordinate system; let the coordinates of the camera optical center in the global coordinate system be O = ( , , For a line laser, the emitted rays form a plane (the laser plane), from which the laser emission center S and the measured point cloud can be determined. = ( ,, , ).

[0069] For each measurement point :

[0070] Determine the incident direction : From the laser source towards The direction. For line lasers, all points They are all located on the same projected laser line, and the incident light rays they are on... They are coplanar and both lie within the laser plane. = - S, normalize: = / || ||;

[0071] Determine the receiving direction : is from A vector pointing to the optical center O of the camera. = O - Unitize: = / || ||;

[0072] Surface normal .

[0073] Each measurement point The established local parameter set includes:

[0074] Angle of incidence θ is the angle between the incident ray and the surface normal, calculated using the following formula:

[0075] = arccos( - · );

[0076] in, To point the laser source to the measurement point unit vector, For measurement points Surface normal;

[0077] Azimuth , is the dihedral angle between the incident plane and the receiving plane, calculated by the following formula:

[0078] = arccos( ( · ) / (|| || * || ||) );

[0079] in, Let be the normal vector of the incident plane. = × , To receive the normal vector of the plane, = × ;

[0080] Effective angle of incidence , satisfying tan( ) = cos( ) * tan( );

[0081] Equivalent object distance It is from the measurement point The distance to the receiver is calculated using the following formula:

[0082] = || ||;

[0083] in, From The vector pointing to the camera's optical center O is calculated using the following formula:

[0084] = O - ;

[0085] Equivalent trigonometric measurement angle θ is the angle between the incident ray and the received ray, calculated using the following formula:

[0086] = arccos( - · ) ;

[0087] Depth difference , is the depth of the current measurement point. Relative to nominal reference depth The deviation.

[0088] S2. Based on the Lambertian reflection model and spatial vector geometry, establish the measurement points for each point. The direct functional relationship between surface attitude (α, φ) and sensor signal-to-noise ratio (SNR) is established, and a signal-to-noise ratio error term is constructed based on the sensor SNR. ;

[0089] The signal strength S is proportional to the optical power received by the sensor. According to Lambert's cosine law, the intensity of light reflected from a point P in a specific direction is proportional to the surface normal n and the reflection direction vector v. obs The angle γ between them is proportional to the cosine of the angle.

[0090] Surface normal n: n = (sin(α)sin(φ), sin(α)cos(φ), cos(α))

[0091] Observation direction v obs (i.e., the direction pointing to the center of the receiving lens): The receiving lens is located in the YZ plane, making an angle θ with the Z-axis. Therefore, its direction vector is: v obs = (0, sin(θ), cos(θ)).

[0092] cos(γ) can be expressed by n and v. obs The dot product yields: cos(γ) = n·v obs = sin(α)cos(φ)sin(θ) + cos(α)cos(θ).

[0093] The received signal strength S is proportional to cos(γ). When cos(γ) is negative, it indicates that the surface is facing away from the lens and no signal is received. Therefore: S(α, φ) = * max(0, cos(γ));

[0094] in, It is the maximum signal strength that can be received under ideal conditions (such as α=0, φ=0).

[0095] SNR is the ratio of signal strength to noise strength. In this embodiment, we make a reasonable simplification by assuming that the noise strength N of the system is constant (mainly determined by the electronic noise of the sensor itself, and is independent of the incident light).

[0096] SNR = S / N;

[0097] Further results were obtained:

[0098] SNR(α, φ) = ( / N) * max(0, cos(γ));

[0099] This embodiment defines the maximum signal-to-noise ratio of a system under ideal conditions. = / N is a key parameter that can be calibrated experimentally.

[0100] SNR(α, φ) = * max(0, sin(α)cos(φ)sin(θ) + cos(α)cos(θ)).

[0101] This formula establishes a direct functional relationship between surface attitude (α, φ) and sensor signal-to-noise ratio.

[0102] When φ increases from 0° to 90°, cos(φ) decreases from 1 to 0, cos(γ) decreases, and therefore SNR will decrease.

[0103] When φ = 90°, cos(γ) = cos(α)cos(θ). The SNR decreases but is not zero.

[0104] When φ = 180°, cos(φ) = -1, cos(γ) will become very small or even negative, and SNR will approach 0.

[0105] In signal processing, the positioning accuracy based on centroid algorithms is approximately inversely proportional to the signal-to-noise ratio (SNR). That is, the lower the SNR, the greater the uncertainty in positioning the centroid and the larger the error.

[0106] ∝ 1 / SNR;

[0107] In this embodiment, the following mathematical model is constructed to describe this relationship:

[0108] = C / (SNR(α, φ) + ε);

[0109] Where C is the error proportionality constant, representing the severity of the influence of SNR on the error, and the unit is length (e.g., mm); ε is a very small positive constant (e.g., 0.01 * ε) used to prevent division-by-zero errors when SNR is exactly 0. This ensures the robustness of the model.

[0110] When SNR is high Approaching 0. When SNR is very low, It will increase dramatically.

[0111] S3. Based on the geometric optics model, establish each measurement point geometric error term ;

[0112] ;

[0113] Where R is the effective radius of the camera lens. The baseline length is the lateral distance between the center of the laser emitter and the center of the receiving lens.

[0114] .

[0115] S4. The signal-to-noise ratio error term obtained in step S2 and the geometric error term obtained in step S3 By superimposing the data, each measurement point can be obtained. Total error Based on total error Perform high-precision error modeling.

[0116] Total error Calculate as follows:

[0117] = | | + ;

[0118] (α, φ) = | | .

[0119] Based on the above method, simulation is performed using MATLAB, such as... Figure 2 , 3 The figures shown are graphs showing the relationship between total error and incident angle at different azimuth angles, and graphs showing the change of total error with azimuth angle when the incident angle is 10°.

[0120] When the azimuth angle φ is small: cos(φ) is close to 1, and the SNR remains at a high level. The term is very small and can be ignored. Total error. Mainly composed of The larger φ is, the better. The smaller.

[0121] When the azimuth angle φ is large, cos(φ) decreases significantly, leading to a sharp drop in SNR. The denominator in the term becomes very small, making It increased dramatically, and its value far exceeded... Changes in total error. The behavior is caused by The project is the main focus.

[0122] Therefore, the model in this embodiment predicts that as φ increases, the total error may initially decrease slightly, but will quickly be... The rapid increase in φ eventually leads to a trend where the total error increases significantly with φ.

[0123] Example 2:

[0124] This embodiment is based on the method and steps provided in Embodiment 1, using a sphere as the object being measured, and is simulated using MATLAB, such as... Figures 4 to 9 As shown in the simulation results, the total error curve exhibits a "W" shape because it is composed of the superposition of two different types of errors:

[0125] Geometric error It is high in the center, low on both sides, and then rises again at the edges.

[0126] Signal-to-noise ratio error It is lowest at the center and rises sharply to both sides.

[0127] =| | + .

[0128] like Figure 4 As shown in the figure, the green circle represents the location of the laser camera, the red circle represents the laser emission location, the shaded area is the sphere being measured, the black curve is the laser scanning line, and the blue arrow is the normal direction of each scanning point.

[0129] Analysis of azimuth angle φ:

[0130] exist Figure 5 In the azimuth distribution diagram along the scan line shown, at the scan center, the dihedral angle between the incident plane and the reflecting plane is 0, so the azimuth angle is zero at this time. However, the closer to the two ends of the scan line, the larger the dihedral angle between the incident plane and the reflecting plane becomes, and the larger the azimuth angle becomes.

[0131] Analysis of incident angle α:

[0132] exist Figure 6 In the distribution diagram of incident angles along the scan line shown, the incident angle is smallest at the scan center. The closer to the two ends of the scan line, the larger the angle between the incident ray and the surface normal, and the larger the incident angle.

[0133] Analysis of signal-to-noise ratio error :

[0134] In such Figure 8 The comparison chart of the total error components is shown below. The (dotted line) is a very typical "U" shaped curve. It is almost zero at the scan center (x=0) and rises sharply towards both ends of the scan range (x=→±25mm).

[0135] Cause analysis:

[0136] The signal-to-noise ratio (SNR) is inversely proportional to the signal-to-noise ratio (SNR), which in turn is directly proportional to cos(γ) (the angle between the surface normal and the received light). The incident angle α and azimuth angle are also relevant. Both angles are minimum at the center and increase towards both sides. This increase in angles combined leads to a decrease in cos(γ), meaning less effective light energy is reflected back to the camera. Therefore, the closer to the scan edge, the lower the SNR. The higher the value, the better. This perfectly explains... The "U" shaped trend.

[0137] Analyzing geometric errors :

[0138] Similarly, in such Figure 8 The comparison chart of the total error components is shown below. There is a local high point at the center of the scan (x=0), then it drops to a low point at approximately ±15mm x, and then rises again towards the scan edge (x=→±25mm).

[0139] Cause analysis:

[0140] It is affected by the combined effects of four independently varying parameters: , , , This just happened to lead to The minimum value is not at the center, but rather reaches its lowest point somewhere in the middle.

[0141] The total error is formed by superposition. ,like Figure 7 :

[0142] At the scan center (x=0):

[0143] Located at a local high point, It is at its lowest point.

[0144] = (a higher value) + (a value close to 0) = a local high point. This is the "hump" in the middle of the "W" shape.

[0145] In the middle area:

[0146] decline, The error is increasing, but the rate of increase is less than the rate of decrease, and the error is showing a decreasing trend.

[0147] At the scan edge:

[0148] rise, The error rate is rising sharply.

[0149] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters, characterized in that, Includes the following steps: S1. Discretize the line laser into several measurement points. and for each measurement point Establish a local parameter set; S2. Based on the Lambertian reflection model and spatial vector geometry, establish the measurement points for each point. The direct functional relationship between surface attitude (α, φ) and sensor signal-to-noise ratio (SNR) is established, and a signal-to-noise ratio error term is constructed based on the sensor SNR. ; S3. Based on the geometric optics model, establish each measurement point geometric error term ; S4. The signal-to-noise ratio error term obtained in step S2 and the geometric error term obtained in step S3 By superimposing the data, each measurement point can be obtained. Total error Based on total error Perform high-precision error modeling.

2. The high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters according to claim 1, characterized in that, Each measurement point in step S1 The established local parameter set includes: Angle of incidence θ is the angle between the incident ray and the surface normal, calculated using the following formula: = arccos( - · ); in, To point the laser source to the measurement point unit vector, For measurement points Surface normal; Azimuth , is the dihedral angle between the incident plane and the receiving plane, calculated by the following formula: = arccos( ( · ) / (|| || * || ||) ); in, Let be the normal vector of the incident plane. = × , To receive the normal vector of the plane, = × ; Effective angle of incidence , satisfying tan( ) = cos( ) * tan( ); Equivalent object distance It is from the measurement point The distance to the receiver is calculated using the following formula: = || ||； in, From The vector pointing to the camera's optical center O is calculated using the following formula: = O - ； Equivalent trigonometric measurement angle θ is the angle between the incident ray and the received ray, calculated using the following formula: = arccos( - · ) ; Depth difference , is the depth of the current measurement point. Relative to nominal reference depth The deviation.

3. The high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters according to claim 2, characterized in that, Each measurement point in step S2 The direct functional relationship between the surface attitude (α, φ) and the sensor signal-to-noise ratio (SNR) is as follows: SNR(α, φ) = * max(0, cos(γ)); in, The maximum signal-to-noise ratio of the system under ideal conditions. = / N, where N is the noise level of the system. It is the maximum signal strength that can be received under ideal conditions; γ is the angle between the surface normal and the received ray, and satisfies: cos(γ) = sin(α)cos(φ)sin(θ) + cos(α)cos(θ), where θ is the angle between the direction of the receiving lens center and the Z-axis.

4. The high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters according to claim 3, is characterized in that, The aforementioned signal-to-noise ratio error term The expression is as follows: = C / (SNR(α, φ) + ε); Where C is the error proportionality constant, and ε is a positive constant used to prevent division by zero errors.

5. The high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters according to claim 4, characterized in that, The geometric error term The expression is as follows: ； Where R is the effective radius of the camera lens. The baseline length is the lateral distance between the center of the laser emitter and the center of the receiving lens. This is the distance from the center of the receiving lens to the CCD plane. h is the reference distance; h is the distance from the laser to the measurement point; x is the distance difference. ; Effective angle of incidence; 。 6. The high-precision error modeling method for line laser measurement that simultaneously considers signal-to-noise ratio and multi-dimensional parameters according to claim 5, characterized in that, The total error in step S4 Calculate as follows: = | | + ； (α, φ) = | | ,in and These are very small normal numbers and are model parameters that need to be calibrated experimentally.

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