Measuring error sensitivity analysis method for optical contourgraph

Abstract

The invention relates to the field of instrument design, in particular to a measurement error sensitivity analysis method for an optical contourgraph. Comprising the following steps: S1, geometric error analysis; s2, establishing a topological structure; s3, establishing a measurement error model; s4, defining an error sensitivity evaluation index; s5, analyzing error sensitivity; s6, sensitive error identification; according to the method, based on the normal vector measurement characteristics of the optical contourgraph, traditional space error evaluation indexes with six components are unified into a comprehensive evaluation index, and meanwhile, the position deviation and the attitude deviation between a sensor and a workpiece to be measured are comprehensively considered; the influence degree of each geometric error of the optical contourgraph on the final measurement error can be more accurately and intuitively obtained, a powerful basis is provided for measurement precision design and measurement error compensation of the optical contourgraph, and the measurement precision of the optical contourgraph can be improved.

Description

Technical Field

[0001] The invention relates to the field of instrument design, and in particular to a measurement error sensitivity analysis method for an optical profiler. Background Art

[0002] Due to its high measurement accuracy and wide application range, optical profilers are widely used in optics, aerospace, automobiles, semiconductors and other fields. There are many factors that affect the measurement accuracy of profilers, including geometric errors, sensor errors, control errors, etc. Among them, geometric errors cause the actual spatial position of optical sensors to shift, resulting in spatial position errors, which in turn affect the measurement accuracy of profilers. With the continuous improvement of accuracy requirements, improving the manufacturing accuracy of components to improve measurement accuracy will lead to a significant increase in costs. In this case, using error compensation to improve measurement accuracy is a more economical method. However, the premise of accurate error compensation is to accurately analyze the measurement errors. Therefore, in order to ensure the measurement accuracy and economy of the profiler, it is necessary to use accurate error analysis methods to understand the contribution of various errors to spatial errors.

[0003] For a multi-axis optical profiler, it is necessary to ensure that the sensor is perpendicular to the normal of the surface to be measured during the measurement process to reduce the influence of the sensor tilt on the measurement result; therefore, the influence of the posture errors of the sensor in three directions on the measurement result needs to be comprehensively considered in the error model; however, when the error sensitivity index has six items, it is difficult to determine the influence of a single geometric error on the measurement error, that is, the geometric error that has a greater impact on the position error may have a smaller impact on the posture error; therefore, it is necessary to propose a more comprehensive and reasonable error sensitivity evaluation method to more accurately evaluate the influence of each error component on the final measurement error. Summary of the invention

[0004] The purpose of the present invention is to provide a measurement error sensitivity analysis method for an optical profiler, so as to provide strong support for error compensation of the optical profiler.

[0005] Based on the above purpose, the present invention adopts the following technical solution:

[0006] A measurement error sensitivity analysis method for an optical profiler comprises the following steps:

[0007] S1. Geometric error analysis: According to the characteristics of the optical profiler, the position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of each motion axis are established;

[0008] S2. Establishing the topological structure: Based on the theory of multi-rigid body system, each motion axis is regarded as a rigid body, the measurement structure is simplified in a low-sequence manner, and the topological structure of the measurement device is established;

[0009] S3. Establish a measurement error model: Use the homogeneous coordinate transformation method to describe the positional relationship between each component and the reference coordinate system; establish an independent local coordinate system for each rigid body, describe the relative motion between rigid bodies by means of homogeneous coordinate transformation, establish a transfer matrix between adjacent motion axes (rigid bodies), and establish a mathematical model of measurement point errors;

[0010] S4. Define the error sensitivity evaluation index: According to the characteristics of normal measurement of optical profiler, establish the equivalent working distance deviation (WDE e ) as the measurement error sensitivity index;

[0011] S5. Error sensitivity analysis: Select a standard measurement object, use an optical profilometer to measure the standard measurement points, solve the motion of the moving axis based on the measured measurement point positions, and use partial differential method to quantitatively calculate and analyze the error sensitivity of various geometric errors;

[0012] S6. Sensitive error identification: Based on the results of the error sensitivity analysis in S5, define the critical error; the error exceeding the critical error is the key geometric error that affects the final measurement error.

[0013] Preferably, the PDGEs in step S1 include errors caused by manufacturing defects of the moving axis's own components, and the values ​​of various errors change with the spatial position of the instrument; each moving axis has PDGEs in six directions, including three linearity errors and three angular errors; PIGEs include errors caused by the deviation of the actual moving axis from its ideal axis during the assembly process of the instrument, including perpendicularity errors and position errors between various axis systems; the error value is a fixed value and does not change with the movement of the axes; the geometric errors of the optical profiler also include installation errors caused by the installation process of the workpiece to be measured and the optical sensor, as well as measurement errors that directly affect the measurement reference of the workpiece during the measurement process, thereby generating measurement errors.

[0014] Preferably, in step S3, the process of establishing the measurement error model includes:

[0015] Based on the theory of multi-rigid body system, each motion axis of the optical profiler is regarded as a rigid body. For each rigid body, a local coordinate system is established in turn. The transfer matrix between adjacent motion axes can be expressed as:

[0016]

[0017] In the formula, is the position transfer matrix, is the position-independent geometric error (position error) transfer matrix, is the motion transfer matrix, is the position-related error (motion error) transfer matrix; in the ideal case where the geometric error components are not considered, and are all unit matrices.

[0018] Preferably, based on the transfer matrix formula between adjacent motion axes, each error component is regarded as a small motion of a rigid body, and the error transfer matrix can be expressed as follows:

[0019]

[0020] Where, δx, δy, δz, εx, εy, εz represent the position error of each axis along the X, Y, and Z directions and the angular error around the X, Y, and Z directions respectively;

[0021] The position coordinates Ps and attitude coordinates Os of the sensor measurement point in the instrument coordinate system and the position coordinates Pw and attitude coordinates Ow of the point to be measured on the workpiece surface in the instrument coordinate system can be expressed as:

[0022]

[0023] Where k represents the number of rigid bodies in the sensor chain in the optical profiler topology, m represents the number of rigid bodies in the workpiece chain, and P s ' and O s ' is the position coordinate of the sensor measurement point in the sensor coordinate system, P w ' and O w ' is the position coordinates of the point to be measured on the workpiece surface in the workpiece coordinate system;

[0024] Ideally, the sensor measurement point should coincide with the point to be measured on the workpiece surface, that is, Ps = Pw and Os = Ow; then the spatial error of the sensor measurement point under the influence of various geometric errors can be expressed as:

[0025]

[0026] Where P e represents the spatial position error of the sensor measurement point, O e Represents the spatial attitude error of the sensor measurement point.

[0027] Preferably, in step S4, the process of defining the error sensitivity evaluation index includes:

[0028] For an optical profiler, the optical axis of the sensor coincides with the normal of the surface to be measured in an ideal state; therefore, the sensitivity index is a function related to the surface profile of the workpiece to be measured and the spatial position of the measured point; the surface profile of the workpiece to be measured takes the quadratic surface as an example to establish the measurement error sensitivity index; the general equation of the quadratic surface in the workpiece coordinate system can be expressed as:

[0029] F(x,y,z)=a 11 x 2 +a 22 y 2 +a 33 z 2 +a 12 xy+a 23 yz+a 31 zx+a1x+a2y+a3z+a4=0

[0030] For a point P0(x0,y0,z0) on the surface, the normal vector at that point can be expressed as:

[0031]

[0032] For position error, the contribution of each error component to the position error of the measured point can be regarded as its contribution to the position error P e According to the characteristics of normal measurement of optical sensors, the position error P e It can be divided into two directions: the tangent direction T and the normal direction N of the measured point; for optical sensors such as laser displacement sensors and dispersive confocal sensors, the measuring point formed by the measuring light beam on the surface of the workpiece to be measured is actually a light spot, and the measured data value is the average value of the height information in the light spot area, so the tangential position error has little effect on the measurement error; in addition, the measurement data of this type of optical sensor is essentially the distance from the sensor to the surface to be measured; therefore, the normal position error has a more significant effect on the measurement error; in summary, the effect of position error on the measurement error can be referred to as "projected working distance deviation" WDE p It is characterized by the projection of the position error on the normal direction of the surface to be measured, and its calculation formula is as follows:

[0033]

[0034] In the formula, is the vector of spatial position error of the sensor measurement point;

[0035] Similar to the spatial position error, the contribution of each error component to the spatial attitude error can be regarded as its contribution to the measured spatial attitude error O e Projection on; define the equivalent working distance deviation (WDE e ) is the measurement error sensitivity index, as shown in the following formula:

[0036]

[0037] In the formula, R s is the effective turning radius of the sensor measurement point, θ is the sensor inclination angle caused by the attitude error, R s The calculation formulas for and θ are as follows:

[0038]

[0039] Where L is the sensor length and d0 is the sensor theoretical working distance.

[0040] Preferably, in step S5, the process of error sensitivity analysis includes:

[0041] According to the measurement error mathematical model, the system's equivalent working distance deviation WDE can be further defined e The partial derivative of each error is the error sensitivity coefficient SC i , the formula is as follows:

[0042]

[0043] Where e i is the value of each error component; in order to quantitatively describe the influence of each error parameter on the measurement error, it needs to be normalized, and the formula is as follows:

[0044]

[0045] Where sc i is the quantitative sensitivity coefficient; it can be seen that in the above formula, the sum of each term is 1; by comparing the errors sc i The numerical value of can be used to determine the influence of the i-th error on the measurement error.

[0046] Preferably, the standard measurement object is the outer contour surface of a hemispherical shell, the angle difference between two adjacent calibration points on the same generatrix is ​​15°, and the angle difference between two adjacent calibration points on a uniform radial circular section is 45°.

[0047] Preferably, in step S5, each linearity error is 1 μm, and each angle error is 1 μrad.

[0048] Preferably, in step S6, based on the average sensitivity coefficient, the critical error of the spatial position error is set to 0.05, and the critical error of the spatial angle error is set to 0.08.

[0049] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, any step of the above-mentioned measurement error sensitivity analysis method for an optical profiler is implemented.

[0050] The beneficial effects of the present invention are as follows:

[0051] The error sensitivity analysis method proposed in this invention is based on the normal measurement characteristics of the optical profiler, and the traditional spatial error evaluation indicators of the six components are unified into a comprehensive evaluation indicator, namely, the equivalent working distance deviation WDE.e ; This evaluation index can comprehensively consider the position deviation and posture deviation between the sensor and the workpiece to be measured, and can more accurately and intuitively obtain the influence of various geometric errors of the optical profiler on the measurement error, and screen out the key errors that affect the measurement error, thereby providing strong support for the measurement accuracy design and measurement error compensation of the optical profiler, and helping to improve the measurement accuracy of the optical profiler. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a schematic diagram of the process of Example 1 of the present invention;

[0053] Figure 2 Schematic diagram of the motion mechanism of the four-axis optical profiler according to Embodiment 1 of the present invention;

[0054] Figure 3 This is a topological structure diagram of a four-axis optical profiler according to Embodiment 1 of the present invention;

[0055] Figure 4 This is a schematic diagram of the structure of the error sensitivity analysis object according to Embodiment 1 of the present invention;

[0056] Figure 5 The analysis result of the average sensitivity coefficient of the position error in Example 1 of the present invention;

[0057] Figure 6 The analysis result of the average sensitivity coefficient of the angle error in Example 1 of the present invention;

[0058] Figure 7 The following are the results of the sensitive error verification experiment in Example 2 of the present invention. DETAILED DESCRIPTION

[0059] Example 1

[0060] The following is a further explanation of the present invention in conjunction with specific embodiments. Figure 1 As shown, this embodiment is a measurement error sensitivity analysis method for an optical profiler; Figure 2 As shown, taking a four-axis optical profiler as an example, this embodiment includes the following steps:

[0061] S1. Geometric error analysis: According to the characteristics of the optical profiler, the position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of each motion axis are established; e.g. Figure 2 As shown, the X-axis and Z-axis are two linear moving guide rails, and the B-axis and C-axis are two rotating moving turntables; the C-axis is installed on the X-axis for mounting the workpiece to be measured; the B-axis is installed on the Z-axis for mounting the sensor; according to measurement requirements, the travels of the X-axis and Z-axis are 200mm and 450mm respectively, and the travels of the B-axis and C-axis are both 0°-360°.

[0062] For a four-axis optical profiler, each axis has 6 PDGEs, so there are 24 PDGEs in total for the four axes; there is one PIGE between the two linear motion axes, and the two rotary motion turntables each have 4 PIGEs, so there are 9 PIGEs between the four motion axes; for the workpiece and the sensor, there are 6 installation errors (3 linear errors and 3 angular errors) during their installation, for a total of 12 errors; in summary, there are 45 geometric errors in the four-axis optical profiler, as shown in Table 1.

[0063] Table 1 Geometric error table of four-axis optical profiler

[0064]

[0065] S2, establish the topology structure: Figure 3 As shown in the figure, based on the theory of multi-rigid body system, each motion axis is regarded as a rigid body, the measurement structure is simplified in a low-sequence manner, and the topological structure of the four-axis optical profiler is established; the bed is set as the serial number 0 rigid body, and the other rigid bodies are named in sequence, such as 1 represents the X-axis; there are two motion transfer chains in the device, namely the bed-Z axis-B axis-sensor transfer chain, and the bed-X axis-C axis-workpiece transfer chain; ideally, the intersection of the two motion transfer chains is the measurement point; for each rigid body, local coordinate systems 0-6 are established in sequence, in the following order: bed coordinate system 0, Z axis coordinate system 1, B axis coordinate system 2, sensor coordinate system 3, X axis coordinate system 4, C axis coordinate system 5, measurement (workpiece) coordinate system 6.

[0066] S3. Establish a measurement error model: Use the homogeneous coordinate transformation method to describe the positional relationship between each component and the reference coordinate system; establish an independent local coordinate system for each rigid body, describe the relative motion between the rigid bodies through homogeneous coordinate transformation, establish a transfer matrix between adjacent motion axes (rigid bodies), and establish a mathematical model of measurement point errors.

[0067] In this embodiment, in order to simplify the calculation, the Z-axis coordinate system is overlapped with the B-axis coordinate system, and the X-axis, C-axis and workpiece coordinate system are overlapped; the displacement coordinate of the i-axis relative to the origin of the j-axis coordinate system is assumed to be The transformation matrix from i coordinate to j coordinate is The displacements of the X-axis and Z-axis are x and z respectively, and the rotation angles of the B-axis and C-axis are β and γ respectively; the sensor distance reading is d; then the transfer matrix between adjacent motion axis systems in the above 7 motion axis systems is as follows:

[0068]

[0069] Therefore, the position coordinates of the sensor measurement point in the bed coordinate system are Ps And the posture coordinates O s And the position coordinates P of the point to be measured on the workpiece surface in the bed coordinate system w And the posture coordinates O w In can be expressed as:

[0070]

[0071] Among them, the position coordinates P of the sensor measurement point in the sensor coordinate system are defined respectively s ' is (0,0,-(L+d0),1) T , attitude coordinate O s ' is (0,0,-1,0) T And the position coordinates P of the point to be measured on the workpiece surface in the workpiece coordinate system w ' is (0,0,D+H,1) T , attitude coordinate O w ' is (0,0,1,0) T ; In the above formula, L is the sensor length, d0 is the sensor working distance, D is the distance from the X-axis table to the workpiece clamping fixture surface, and H is the distance from the clamping fixture surface to the workpiece to be measured point; then the spatial position error P of the sensor measurement point under the influence of various geometric errors is e And the spatial attitude error O e It can be expressed as:

[0072]

[0073] S4. Define the error sensitivity evaluation index: According to the characteristics of normal measurement of optical profiler, the equivalent working distance deviation (WDEe) is established as the measurement error sensitivity index; for optical profiler, it is necessary to make the optical axis of the sensor coincide with the normal line of the measured surface of the workpiece as much as possible. Therefore, the sensitivity index is a function related to the surface profile of the workpiece to be measured and the spatial position of the measured point; such as Figure 4 As shown, in this embodiment, the outer contour surface of the hemispherical shell is used as the measurement object for error sensitivity analysis. The outer contour surface can be expressed by the general equation of the quadratic surface, and the expression is as follows:

[0074] F(x,y,z)=a 11 x 2 +a 22 y 2 +a 33 z 2 +a 12 xy+a 23 yz+a 31 zx+a1x+a2y+a3z+a4=0

[0075] For a point on the measured object, the normal vector at that point can be expressed as:

[0076]

[0077] For position error, the contribution of each error component to the position error of the measured point can be regarded as its contribution to the position error P e According to the characteristics of normal measurement of optical sensors, the position error P e It can be divided into two directions: the tangent direction T and the normal direction N of the measured point. For optical sensors such as laser displacement sensors and dispersive confocal sensors, the measuring point formed by the measuring beam on the surface of the workpiece to be measured is essentially a light spot, and the measured data value is the average value of the height information in the light spot area. Therefore, the tangential position error has little effect on the measurement error; in addition, the measurement data of this type of optical sensor is essentially the distance from the sensor to the surface to be measured; therefore, the normal position error has a more significant effect on the measurement error; in summary, the effect of the position error on the measurement error can be referred to as the "projected working distance deviation" WDE p It is characterized by the projection of the position error on the normal direction of the surface to be measured, and is calculated as follows:

[0078]

[0079] Similar to the position error, the contribution of each error component to the attitude error can be regarded as its contribution to the measured attitude error O e Subsequently, a new measurement error sensitivity index is defined as the equivalent working distance deviation (WDE e ), as shown below:

[0080]

[0081] Among them, R s is the effective gyration radius of the sensor measurement point, and θ is the sensor inclination angle caused by the attitude error, which is equal to:

[0082]

[0083] S5. Error sensitivity analysis: Select a standard measurement object, use an optical profilometer to measure the standard measurement points, solve the movement of the moving axis based on the measured measurement point positions, and use partial differential method to quantitatively calculate and analyze the error sensitivity of various geometric errors.

[0084] According to the measurement error mathematical model, the system's equivalent working distance deviation WDE can be further defined e The partial derivative of each error is the error sensitivity coefficient SC i , which is calculated as follows:

[0085]

[0086] Furthermore, in order to quantitatively describe the influence of various error parameters on the measurement error, it is necessary to normalize them to obtain the quantitative sensitivity coefficient sc i , as shown below:

[0087]

[0088] It can be seen that in the above formula, each sc i The sum is 1. By comparing the errors sc i The numerical value can be used to determine the influence of the i-th error on the measurement error.

[0089] like Figure 4 As shown in the figure, the measurement object used in this embodiment is the outer contour surface of a hemispherical shell, and the diameter of the hemispherical shell is 100 mm. Considering the actual measurement process, the sensitivity calculation and analysis takes the spherical cap vertex as the origin of the workpiece coordinate system, the Z direction points from the sphere center to the spherical cap vertex, and the X / Y direction is the two perpendicular radial directions in the circular section. Since the optical profiler adopts concentric circle tomographic trajectory scanning measurement, the 48 point positions marked in the figure are selected for sensitivity analysis ( Figure 4 The angle difference between two adjacent points on the same generatrix is ​​15°, and the angle difference between two adjacent points on the same radial circular section is 45°.

[0090] According to the position measurement results of the optical profiler on the above 48 points, the results are brought into the above error sensitivity evaluation index model to calculate the movement of the four motion axes of the optical profiler. For the convenience of calculation and comparison, in the error sensitivity calculation and analysis process, each linear error is taken as 1μm, and each angular error is taken as 1μrad. By comparing the sensitivity coefficients sc of the equivalent working distance deviation of each geometric error at the above 48 measurement positions, i The average value of can be used to determine the key geometric errors that affect the measurement accuracy; the average sensitivity coefficient of position error and angle error is as follows Figure 5 and Figure 6 shown.

[0091] S6. Sensitive error identification: Based on the results of the error sensitivity analysis in S5, the critical error is defined; the error exceeding the critical error is the key geometric error that affects the final measurement error; since the units of the position error and the angle error are different, the above two errors are classified and analyzed, and defined as follows: In the position error, the error with the absolute value of the average sensitivity coefficient exceeding 0.005, and in the angle error, the error with the absolute value of the average sensitivity coefficient exceeding 0.08 is the critical error, that is, the error exceeding the critical error is the sensitive error that has a key impact on the final measurement result.

[0092] Table 2 Sensitive geometric error table

[0093]

[0094] In summary, after analyzing the various geometric errors of the optical profiler according to the method involved in this embodiment, the 16 errors listed in Table 2 are sensitive errors that have a key impact on the final measurement results, that is, key errors; by compensating for the above 16 errors, the measurement accuracy of the optical profiler can be more effectively improved.

[0095] Example 2

[0096] This embodiment is a sensitive error verification experiment based on the analysis results of Example 1. In order to verify the effectiveness of the error sensitivity analysis method in Example 1, a comparative simulation experiment group as shown in Table 3 below is designed. Through numerical simulation, the deviations caused by the equivalent working distance deviation of the sensor when compensating for critical geometric errors and other non-critical geometric errors are calculated and compared.

[0097] Table 3 Simulation experiment parameter settings

[0098]

[0099]

[0100] The simulation results are as follows Figure 7 As shown by Figure 7 It can be seen that compared with the initial setting parameters (experimental group 1), after compensating for the 16 critical errors identified by this method (experimental group 2), the average equivalent working distance deviation of the sensor was reduced by 30.28%; and after compensating for the other 29 non-critical errors (experimental group 3), the equivalent working distance deviation of the sensor was reduced by 19.72%; this result shows that the effect of compensating only for 16 critical errors is better than the effect of compensating only for 29 non-critical errors, which verifies the effectiveness of this error sensitivity analysis method.

[0101] The above description is only a further explanation of the present invention in combination with specific embodiments. All descriptions do not limit the scope of protection of the present invention. Any changes or replacement schemes that can be easily thought of by any technician in this field within the technical scope disclosed by the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A measurement error sensitivity analysis method for an optical profiler, characterized in that: The following steps are involved: S1. Geometric error analysis: According to the characteristics of the optical profiler, the position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of each motion axis are established; S2. Establishing the topological structure: Based on the theory of multi-rigid body system, each motion axis is regarded as a rigid body, the measurement structure is simplified in a low-sequence manner, and the topological structure of the measurement device is established; S3. Establish a measurement error model: Use the homogeneous coordinate transformation method to describe the positional relationship between each component and the reference coordinate system; establish an independent local coordinate system for each rigid body, describe the relative motion between rigid bodies by means of homogeneous coordinate transformation, establish a transfer matrix between adjacent motion axes (rigid bodies), and establish a mathematical model of measurement point errors; S4. Define the error sensitivity evaluation index: According to the characteristics of normal measurement of optical profiler, establish the equivalent working distance deviation (WDE e ) as the measurement error sensitivity index; S5. Error sensitivity analysis: Select a standard measurement object, use an optical profilometer to measure the standard measurement points, solve the motion of the moving axis based on the measured measurement point positions, and use partial differential method to quantitatively calculate and analyze the error sensitivity of various geometric errors; S6. Sensitive error identification: Based on the results of the error sensitivity analysis in S5, define the critical error; the error exceeding the critical error is the key geometric error that affects the final measurement error.

2. The measurement error sensitivity analysis method for an optical profiler according to claim 1, characterized in that: The PDGEs in step S1 include errors caused by manufacturing defects of the moving axis's own components. Each moving axis has three linearity errors and three angular errors. The PIGEs include errors caused by the deviation of the actual moving axis from its ideal axis during the assembly process of the instrument, including verticality errors and position errors between various axis systems. The geometric errors of the optical profiler also include installation errors caused by the installation of the workpiece to be measured and the optical sensor, as well as measurement errors caused during the measurement process.

3. The measurement error sensitivity analysis method for an optical profiler according to claim 2, characterized in that: In step S3, the process of establishing the measurement error model includes: Based on the theory of multi-rigid body system, each motion axis of the optical profiler is regarded as a rigid body. For each rigid body, a local coordinate system is established in turn. The transfer matrix between adjacent motion axes can be expressed as: In the formula, is the position transfer matrix, is the position-independent geometric error (position error) transfer matrix, is the motion transfer matrix, is the position-related error (motion error) transfer matrix; in the ideal case where the geometric error components are not considered, and are all unit matrices.

4. The measurement error sensitivity analysis method for an optical profiler according to claim 3, characterized in that: Based on the transfer matrix formula between adjacent motion axes, each error component is regarded as a small motion of a rigid body, and the error transfer matrix can be expressed as follows: Where, δx, δy, δz, εx, εy, εz represent the position error of each axis along the X, Y, and Z directions and the angular error around the X, Y, and Z directions respectively; The position coordinates Ps and attitude coordinates Os of the sensor measurement point in the instrument coordinate system and the position coordinates Pw and attitude coordinates Ow of the point to be measured on the workpiece surface in the instrument coordinate system can be expressed as: Where k represents the number of rigid bodies in the sensor chain in the optical profiler topology, m represents the number of rigid bodies in the workpiece chain, and P s ' and O s ' is the position coordinate of the sensor measurement point in the sensor coordinate system, P w ' and O w ' is the position coordinates of the point to be measured on the workpiece surface in the workpiece coordinate system; Ideally, the sensor measurement point should coincide with the point to be measured on the workpiece surface, that is, Ps = Pw and Os = Ow; then the spatial error of the sensor measurement point under the influence of various geometric errors can be expressed as: Where P e represents the spatial position error of the sensor measurement point, O e Represents the spatial attitude error of the sensor measurement point.

5. The measurement error sensitivity analysis method for an optical profiler according to claim 4, characterized in that: In step S4, the process of defining the error sensitivity evaluation index includes: The measurement error sensitivity index is established based on the quadratic surface. The general equation of the quadratic surface in the workpiece coordinate system can be expressed as: F(x,y,z)=a 11 x 2 +a 22 y 2 +a 33 z 2 +a 12 xy+a 23 yz+a 31 zx+a1x+a2y+a3z+a4=0 For a point P0(x0,y0,z0) on the surface, the normal vector at that point can be expressed as: The influence of position error on measurement error is called "projected working distance deviation" WDE p It is characterized by the projection of the position error on the normal direction of the surface to be measured, and its calculation formula is as follows: In the formula, is the vector of spatial position error of the sensor measurement point; Similar to the spatial position error, the contribution of each error component to the spatial attitude error can be regarded as its contribution to the measured spatial attitude error O e Projection on the working distance; define the equivalent working distance deviation (WDE e ) is the measurement error sensitivity index, as shown in the following formula: In the formula, R s is the effective turning radius of the sensor measurement point, θ is the sensor inclination angle caused by the attitude error, R s The calculation formulas for θ and θ are as follows: Where L is the sensor length and d0 is the sensor theoretical working distance.

6. The measurement error sensitivity analysis method for an optical profiler according to claim 5, characterized in that: In step S5, the process of error sensitivity analysis includes: Define the system's equivalent working distance deviation WDE e The partial derivative of each error is the error sensitivity coefficient SC i , the formula is as follows: Where e i is the value of each error component; for SC i Normalization is performed, and the formula is as follows: Where sc i is the quantitative sensitivity coefficient; by comparing the errors sc i The size of can be used to determine the influence of the ith error on the measurement error.

7. The measurement error sensitivity analysis method for an optical profiler according to claim 6, characterized in that: The standard measurement object is the outer contour surface of a hemispherical shell, the angle difference between two adjacent calibration points on the same generatrix is ​​15°, and the angle difference between two adjacent calibration points on a uniform radial circular section is 45°.

8. The measurement error sensitivity analysis method for an optical profiler according to claim 7, characterized in that: In step S5 , each linearity error is set to 1 μm, and each angle error is set to 1 μrad.

9. The measurement error sensitivity analysis method for an optical profiler according to claim 8, characterized in that: In step S6, based on the average sensitivity coefficient, the critical error of the spatial position error is set to 0.05, and the critical error of the spatial angle error is set to 0.

08.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, any step of the measurement error sensitivity analysis method for an optical profiler according to any one of claims 1 to 9 is implemented.

Images