CN117190908A - Calibrating device and calibrating method for line spectrum confocal sensor - Google Patents

Abstract

The invention belongs to the technical field of photoelectric detection and discloses a verification device and a verification method of a line spectrum confocal sensor. The device comprises an integrated standard device, a displacement generating device, a displacement measuring device and a driving device, wherein the driving device drives the displacement generating device to generate displacement in the vertical direction, the displacement measuring device measures the displacement generated in the vertical direction, and the integrated standard device is driven to move in the vertical direction when the displacement generating device generates displacement in the vertical direction; the line spectrum confocal sensor measures the contour displacement of the integrated standard device in the vertical direction, and compares the measured result with the measured result of the displacement measuring device, so as to obtain the limit positioning errors of the line spectrum confocal sensor in the transverse direction and the vertical direction in the vertical measuring plane, and establish an error model. The invention solves the problems that the existing linear spectrum confocal sensor is difficult to detect and can not detect.

Description

A calibration device and calibration method for a line spectrum confocal sensor

Technical field

The invention belongs to the technical field related to photoelectric detection, and more specifically, relates to a calibration device and calibration method of a line spectrum confocal sensor.

Background technique

Currently, the line spectrum confocal sensor is a non-contact line profile sensor based on spectral dispersion positioning. Its measurement accuracy can reach submicron or even nanometer level, it is insensitive to the tilt, texture and surface reflection characteristics of the object surface, and has strong anti-stray light ability. It is an important 3D measurement sensor in the fields of electronic manufacturing, new energy and semiconductor manufacturing. , which can provide strong support for material surface analysis, quality control and production process optimization.

The verification and calibration of line spectrum confocal sensors are of great significance to the analysis and assurance of their accuracy. At present, for the calibration of line spectrum confocal sensors, length measuring instruments are generally used for calibration, which is inconvenient and difficult to operate. It also cannot calibrate the lateral positioning error of the sensor. Therefore, a complete set of convenient and special instruments for effective calibration and calibration of this type of sensor is needed. device.

Contents of the invention

In view of the above defects or improvement needs of the existing technology, the present invention provides a calibration device and calibration method for a line spectrum confocal sensor, which solves the problem that the existing line spectrum confocal sensor is difficult to calibrate and cannot be calibrated.

In order to achieve the above object, according to one aspect of the present invention, a calibration device for a line spectrum confocal sensor is provided. The device includes an integrated standard, a displacement generating device, a displacement measuring device and a driving device, wherein:

The driving device is connected to the displacement generating device and is used to drive the displacement generating device to generate displacement in the vertical direction. The displacement measuring device is used to measure the displacement generated by the displacement generating device in the vertical direction. The integration The standard is arranged above the displacement generating device. When the displacement generating device is displaced in the vertical direction, the integrated standard is driven to be displaced in the vertical direction. The line spectrum confocal sensor to be calibrated is used to measure the The contour displacement of the integrated standard in the vertical direction is measured, and the measured results are compared with the measured results of the displacement measuring device to obtain the limits of the line spectrum confocal sensor to be calibrated in the lateral and vertical directions. Positioning error;

The upper top surface of the integrated standard includes an inclined surface and a horizontal surface. The inclined surface is used to detect the lateral positioning limit error of the spectrum sensor to be verified. The horizontal surface is used to detect the positioning limit error of the spectrum sensor to be verified in the vertical direction. It is further preferred. Ground, the displacement measuring device) includes a fixed unit and a moving unit, the fixed unit is fixed in position, the moving unit is fixedly connected to the displacement generating device, the displacement generating device drives the moving unit to move in the vertical direction Displacement; use the fixed unit to capture the movement signal of the mobile unit, and measure the displacement of the mobile unit in the vertical direction.

Further preferably, the moving unit includes a displacement stage, a second reflector and a dichroic prism. The displacement stage is provided at the bottom end of the displacement measuring device for contacting the displacement generating device. The second reflection mirror The mirror is arranged on one side of the vertical direction of the dichroic prism, and the horizontal movement of the displacement generating device causes the displacement stage to be displaced in the vertical direction, that is, the displacement generating device is displaced.

Further preferably, the fixing unit includes a laser, a photodetector and a first reflector. The laser and the first reflector are respectively arranged on both sides of the dichroic prism in the horizontal direction. The laser emits laser light and passes through the The dichroic prism is divided into two beams of light, one is a reference light and the other is a measurement light. The reference light and the measurement light enter the first reflector and the second reflector respectively, are reflected, and then enter the dichroic prism. Transmission, the transmitted light enters the photodetector to form interference fringes, and the up and down movement of the moving unit changes the position of the interference fringes.

Further preferably, the mobile unit further includes a third reflector, which is disposed below the dichroic prism, and the light transmitted from the dichroic prism is reflected into the photodetector through the third reflector. .

Further preferably, the displacement generating device includes a screw rod, a slide block, a conversion block and a guide rail. The screw rod is connected to the driving device and is used to convert the rotation of the output shaft of the driving device into the level of the slide block on the guide rail. movement, the conversion block is arranged above the slider and is fixedly connected to it. When the slider moves horizontally, it drives the conversion block to move horizontally. The conversion block is used to convert the horizontal movement of the slider into the The vertical displacement of the mobile unit is the displacement of the displacement generating device.

Further preferably, the conversion block is an inclined block, and its upper surface is an inclined plane. When the conversion block moves horizontally, the moving unit contacts the conversion block so that the moving unit is displaced in the vertical direction.

According to another aspect of the present invention, a method for calibrating the calibration device of the above-mentioned line spectrum confocal sensor is provided, which is characterized in that the method includes the following steps:

S1, the driving device drives the displacement generating device to move, and the displacement measuring device measures the displacement of the mobile unit in the displacement measuring device in the vertical direction, and uses the displacement as a standard displacement;

S2 The line spectrum confocal sensor to be calibrated is aligned with the horizontal plane of the integrated standard, measures the displacement of points at different positions on the horizontal plane in the vertical direction, and compares the measured displacement with the standard displacement in step S1 , to obtain the vertical error distribution and limit positioning error of the line spectrum confocal sensor to be calibrated;

The S3 line spectrum confocal sensor to be calibrated measures the inclined plane of the integrated standard, and measures the actual measured vertical heights at different positions of the same vertical height on the inclined plane, thereby obtaining the vertical height of the line spectrum confocal sensor to be calibrated. Lateral positioning error distribution and limit positioning error in the direction.

S4 uses the fitting method to obtain the error model of the sensor based on the vertical positioning error distribution and lateral positioning error distribution of the line spectrum confocal sensor to be calibrated obtained by S2 and S3.

Further preferably, in step S2, the vertical direction limit positioning error is calculated according to the following relationship:

Among them, y _{and j} are the standard displacements measured by the displacement measuring device, is the actual measurement value of the line spectrum confocal sensor to be calibrated, i is the number of points at different positions in the scanning line direction on the horizontal plane, and j is the number of different height positions within the vertical height range.

Further preferably, in step S3, the lateral direction limit positioning error is calculated according to the following relationship:

Δx=max{|Δx ^j |}

Among them, Δx ^j is the maximum lateral positioning error at the vertical height j, y _measured ^j max and y _measured ^j min are respectively the maximum and minimum values measured by the line spectrum confocal sensor at the corresponding vertical height j, α is the standard The inclination angle of the inclined plane, j is the number of different height positions within the vertical height range, and i is the number of points at different positions in the direction of the scanning line on the inclined plane.

Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

1. The integrated standard in the calibration device of the line spectrum confocal sensor provided by the present invention includes two horizontal planes and an oblique plane. Different planes are used to calibrate the positioning errors of the line spectrum confocal sensor in different directions. Two can be realized at one time. The verification method of direction is simple and convenient;

2. The conversion block in the displacement generating device of the present invention converts horizontal motion into vertical displacement. Through the inclination of the conversion block, the mechanical structure is made more precise and the resolution of vertical motion is improved. Functional transformation is achieved through a simple structure, with strong operability;

3. The displacement measuring device provided by the present invention uses optical principles to measure the vertical displacement generated by the displacement generating device. The measurement method is complete, the measurement principle is simple, and it has extremely high accuracy;

4. The calibration method provided by the present invention uses a driving device to drive the plane of the integrated standard to produce a slight displacement, which can be used to detect the positioning error of each point of the sensor along the length of the scanning line in the vertical direction, and takes into account the positioning error in the direction of the sensor line length. There is a lateral positioning error in each point measurement. The lateral positioning error of each point in the sensor line length direction is reflected in the vertical direction through the slope of the integrated standard, thereby reflecting the lateral positioning error of the sensor. At the same time, the fitting method can be used to obtain the sensor The vertical and horizontal positioning error models of each point in the vertical range of the scanning line form the verification and calibration of the sensor. The standard value of this calibration device can be directly traced to the length reference, and has stable, high-precision, fast and convenient calibration capabilities.

Description of the drawings

Figure 1 is a schematic structural diagram of a calibration device for a line spectrum confocal sensor constructed in accordance with a preferred embodiment of the present invention;

Figure 2 is a schematic diagram of the specific structure of the calibration device of the line spectrum confocal sensor constructed according to the preferred embodiment of the present invention;

Figure 3 is a structural schematic diagram of a standard device built according to a preferred embodiment of the present invention to replace the standard device;

Figure 4 is a partial schematic diagram of a standard displacement generating device constructed according to a preferred embodiment of the present invention;

Figure 5 is a schematic structural diagram of a standard displacement measurement system constructed according to a preferred embodiment of the present invention;

Figure 6 is a schematic diagram of the plane error distribution obtained from the ideal contour displacement constructed according to the preferred embodiment of the present invention and the measured contour displacement.

Throughout the drawings, the same reference numbers refer to the same elements or structures, wherein:

1-Base, 2-Motor base, 3-Driving device, 4-Reducer, 5-Right bearing seat, 6-Screw rod, 7-Support seat, 8-Support plate, 9-Laser, 10-Photodetector, 11-displacement stage, 12-third reflector, 13-beam splitting prism support frame, 14-beam splitting prism, 15-second reflector, 16-second reflector holder, 17-integrated standard, 18-column, 19-first reflector, 20-first reflector support seat, 21-conversion block, 22-sliding block, 23-guide rail, 24-left bearing seat.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

The present invention is a calibration device and calibration method for a line spectrum confocal sensor. As shown in Figure 1, the calibration device for a line spectrum confocal sensor consists of a standard plane and a standard inclined plane integrated standard device 17, a standard displacement generating device 110, and a standard displacement measurement device. The device 120 consists of three parts.

The integrated standard plane and standard inclined plane standard 17 is composed of a standard plane section and a connected standard inclined plane section, which have high plane accuracy and surface quality respectively. The integrated standard is connected to the displacement stage 11 of the standard displacement generating device, and outputs the standard displacement to the sensor to be verified and calibrated.

The structure of the standard displacement generating device 110 includes a base 1, a guide rail 23, a slider 22, a conversion block 21, a displacement stage 11, a column 18, a screw 6 and an integrated standard device 17. The conversion block 22 is fixed on the slide block 22, and the slide block 22 and the guide rail 23 form an x-axis linear motion pair. The guide rail 23 is fixedly connected to the base 1. The screw 6 passes through the center of the slide block 22 and is fixed on the right bearing seat 5 and the left bearing seat 24 at the same time. In addition, the upper surface of the conversion block 21 is an inclined surface. The displacement stage 11 and the guide rail 23 fixed on the upright column 18 form a z-direction linear motion pair, and the upright column 18 is connected to the base 1 . This structure can convert x-direction displacement into z-direction displacement and achieve high-precision subdivision control. In this embodiment, the driving device 3 adopts a stepper motor, the driving device is arranged on the motor base 2 , and the output shaft of the driving device 3 is connected to the reducer 4 .

The structure of the standard displacement measurement device is: the laser 9 and the dichroic prism 14 divide the light emitted by the laser 9 into two paths, one path of light is directed to the first reflector 19 located on the column 18 as a reference optical path, and the other path of light is directed to the displacement stage 11 The second reflecting mirror 15 serves as the measuring light path, and the two-way return light passes through the third reflecting mirror 12 and is directed to the photodetector 10 . The photodetector 10 is located on the axis on which the third reflecting mirror 12 emerges. The laser 9 is set on the support plate 8, the support plate 8 is set on the support base 7, the second reflector 15 is set on the second reflector base 16, the first reflector 19 is set on the first reflector base 20, and the light splitting The prism 14 and the third reflecting mirror 12 are installed on the spectroscope support frame 13 , and the spectroscope support frame 13 is installed on the support plate 8 . The light emitted from the laser 9 passes through the dichroic prism 14, and one path of light is directed to the first reflector 19 installed on the support plate 8, and one path of light is directed to the second reflector 15 installed on the displacement stage. The two paths of return light are split. After the prism 14, they meet at the first reflector 12, and interference occurs. The photodetector 10 receives the interference signal and inputs it into the subsequent processing circuit to obtain the change in the optical path difference of the two interference light paths, that is, the displacement measurement of the displacement stage, that is, we get Real-time standard displacement information of the standard plane and standard inclined plane integrated standard device 17.

The integrated standard 17, standard displacement generating device 110, and standard displacement measuring device 120 constitute a line spectrum confocal sensor calibration device. The standard displacement generating device 110 generates a high-resolution and wide-range displacement, which is combined with the real-time high-precision measurement of the displacement by the standard displacement measuring device 120 to form a standard displacement. The standard displacement is input to the integrated standard device 17 to form a standard plane of the standard device. Translational motion and inclined plane translational motion. The standard translational motion is output as standard to the line spectral confocal sensor. The results measured by the sensor are compared with the standard motion and combined with the corresponding algorithms and modeling to form the verification and calibration of the sensor. The standard value of this calibration device can be directly traced to the length reference, and has stable, high-precision, fast and convenient calibration capabilities.

The displacement usually expressed is the displacement of a point. The contour displacement mentioned in the present invention refers to the overall displacement of a contour line in the horizontal plane or the inclined plane, which is called the contour displacement. Specifically, the light emitted by the line spectrum confocal sensor A vertical light plane is formed, and the vertical plane intersects with the integrated standard to obtain a straight line, which is called a contour line. When the integrated standard moves in the vertical direction, it emits light from the line spectrum sensor. The light plane and the integrated standard intersect in the vertical direction to form multiple contour lines. The ideal contour line is a horizontal straight line. Multiple ideal contour lines, that is, standard contour lines, are marked on the left side of Figure 6. In the present invention , the line spectrum confocal sensor measured the contour displacement generated by the translational movement of the horizontal plane and the oblique plane of the integrated standard within the vertical measurement range respectively. This contour displacement was defined as the standard contour displacement, as shown in Figure 6, the contour displacement A series of horizontal straight lines arranged at standard intervals in the vertical plane are generated; due to sensor errors, what is actually measured is a curve with errors.

The specific working process is as follows: the computer sends out a displacement signal to drive the driving device 3 to rotate, thereby driving the screw 6 to rotate. Through the action of the screw pair, the screw nut 6 moves in the corresponding direction. The conversion block 22 is driven by the screw and guided by the guide rail 23 to move in the x direction. The conversion block 22 converts the x-direction movement of the guide rail into the z-direction linear movement of the displacement stage 11, thereby driving the z-direction standard displacement movement of the standard plane and standard inclined plane integrated standard device 17.

Generally speaking, the standard displacement generating device 110 achieves high resolution through the electronic subdivision of the stepper motor and the mechanical structural subdivision of the ramp block, thereby promoting a large range of high-resolution translation of the integrated standard. The standard displacement measuring device 120 is implemented based on the measurement principle of laser interferometer, and can obtain the standard value of the large-range high-resolution translation of the standard device in real time. The standard displacement input sensor is compared with the actual measured value of the sensor and the relationship is modeled to realize the verification and calibration of the sensor. The calibration device can be used to calibrate the accuracy characteristics of the line spectrum confocal sensor, including the linearity and accuracy of vertical height measurement of each point in the line length direction, and the positioning uncertainty of the transverse measuring point of the sensor.

When specifically applied to sensor verification and calibration work, the computer sends out a drive displacement signal, drives the standard displacement generating device to push the 110 standard plane and standard inclined plane integrated standard 17 to the designated position, and the standard displacement measuring device 120 measures the standard displacement output, and compares The measurement values of the line spectrum confocal displacement sensor 100 are used to obtain the calibration results and the error calibration model is obtained through fitting. When detecting the axial accuracy of the line spectrum confocal displacement sensor, align the line with the standard flat part, and when detecting the lateral inaccuracy of the line spectrum confocal displacement sensor, align the line with the standard inclined surface part.

The specific evaluation process is as follows:

When verifying the accuracy of the vertical direction measurement of the line spectrum confocal displacement sensor, the vertical limit positioning error is calculated according to the following relationship:

The maximum value Δy of the positioning error of each point in each line length direction within the entire height measurement range is obtained, which reflects the limit error of the sensor in the full range, and the accuracy characteristics of the sensor can be analyzed and judged from this.

Based on the obtained positioning error of each line length direction point within the entire height measurement range, an error model in the entire vertical plane is constructed, which can be used as a sensor calibration model.

When detecting the inaccuracy of the lateral measurement point positioning of the line spectrum confocal sensor, the measurement line of the line spectrum confocal sensor 100 is located at the standard slope, the measurement value of the line spectrum confocal sensor 100 is read, and the line spectrum confocal sensor is compared to the line The measurement results of each point in the long direction are used to obtain the focal line straightness of each vertical height and the focal plane flatness of the full height, and the calibration results are obtained.

The maximum positioning error in the lateral direction of j height position is

Among them, y _measured ^j max and y _measured ^j min are respectively the maximum and minimum values measured by the line spectrum confocal sensor at the corresponding vertical height of j, α is the standard inclination angle, and j is the number of different height positions within the vertical height range. , i is the number of points at different positions in the direction of the scanning line on the oblique plane. Then the maximum value of the lateral positioning error within the entire height range is the lateral positioning limit error, Δx=max{|Δx ^j |}.

The positioning error of each point in the line length direction within the entire height measurement range is obtained by detecting the series of standard contour displacements generated by the integrated standard by the calibrated sensor.

Therefore, i can be the abscissa, j*h can be the ordinate, For output, surface fitting is used to build an error model within the entire vertical plane. where h is the standard contour displacement step. This error model can be used for error compensation of the sensor's profile measurements over the entire vertical measuring range.

Similarly, the lateral positioning error model of each point of the profile measurement within the entire vertical measurement range of the sensor can be obtained.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements, etc., made within the spirit and principles of the present invention, All should be included in the protection scope of the present invention.

Claims (10)

1. A calibration device for a line spectral confocal sensor, characterized in that the device comprises an integrated etalon (17), a displacement generating device (110), a displacement measuring device (120) and a driving device (3), wherein:

the driving device (3) is connected with the displacement generating device (110) and is used for driving the displacement generating device (110) to generate displacement in the vertical direction, the displacement measuring device (120) is used for measuring the displacement generated by the displacement generating device (110) in the vertical direction, the integrated etalon (17) is arranged above the displacement generating device (110), when the displacement generating device (110) generates displacement in the vertical direction, the integrated etalon (17) is driven to generate displacement in the vertical direction, the line spectrum confocal sensor to be detected is used for measuring the profile displacement of the integrated etalon (17) in the vertical direction and comparing the measured result with the measured result of the displacement measuring device (120), so that the limit positioning error of the line spectrum confocal sensor to be detected in the transverse direction and the vertical direction is obtained;

the upper top surface of the integrated standard device (17) comprises an inclined surface and a horizontal plane, wherein the inclined surface is used for detecting the transverse positioning limit error of the spectrum sensor to be detected, and the horizontal plane is used for detecting the positioning limit error of the spectrum sensor to be detected in the vertical direction.

2. The calibrating apparatus for a linear-spectral confocal sensor according to claim 1, wherein said displacement measuring device (120) comprises a fixed unit and a moving unit, said fixed unit is fixed in position, said moving unit is fixedly connected to said displacement generating device (110), and said displacement generating device (110) drives said moving unit to displace in a vertical direction; and grabbing a movement signal of the mobile unit by using the fixed unit, and measuring the displacement of the mobile unit in the vertical direction.

3. A device for calibrating a linear-spectral confocal sensor according to claim 2, wherein said moving unit comprises a displacement stage (11), a second reflecting mirror (15) and a beam-splitting prism (14), said displacement stage (11) being arranged at the bottom end of said displacement measuring device (120) for contacting said displacement generating device (110), said second reflecting mirror (15) being arranged at one side of the beam-splitting prism (14) in the vertical direction, and wherein the horizontal movement of said displacement generating device (110) causes a displacement of said displacement stage (11) in the vertical direction.

4. A calibration device for a line spectral confocal sensor according to claim 3, wherein the fixing unit comprises a laser (9), a photodetector (10) and a first reflecting mirror (19), the laser (9) and the first reflecting mirror (19) are respectively arranged at two sides of the beam splitting prism (14) in the horizontal direction, the laser (9) emits laser light, the beam is divided into two beams of light through the beam splitting prism (14), one beam is a reference beam, the other beam is a measuring beam, the reference beam and the measuring beam respectively enter the first reflecting mirror (19) and the second reflecting mirror (15) to be reflected, then enter the beam splitting prism (14) to be transmitted, the transmitted light enters the photodetector (10) to form interference fringes, and the up-down movement of the moving unit changes the positions of the interference fringes.

5. The assay device for line spectral confocal sensors according to claim 4, wherein said mobile unit further comprises a third mirror (12), said third mirror (12) being arranged below said beam-splitting prism (14), light transmitted from said beam-splitting prism (14) being reflected by said third mirror (12) into said photodetector (10).

6. The calibrating device for the linear spectrum confocal sensor according to claim 1, wherein the displacement generating device (110) comprises a screw rod (6), a sliding block (22), a conversion block (21) and a guide rail (23), the screw rod (6) is connected with the driving device (3) and is used for converting the rotation of an output shaft of the driving device (3) into the horizontal movement of the sliding block (22) on the guide rail (23), the conversion block (21) is arranged above the sliding block (22) and is fixedly connected with the sliding block, the sliding block (22) drives the conversion block (21) to horizontally move when horizontally moves, and the conversion block (21) is used for converting the horizontal movement of the sliding block (22) into the displacement in the vertical direction of the moving unit, namely the displacement generated by the displacement generating device.

7. The calibration device for a linear-spectral confocal sensor according to claim 6, wherein said conversion block (21) is a sloping block, the upper surface of which is a sloping surface, and wherein said movement unit is in contact with said conversion block (21) such that said movement unit is displaced in the vertical direction when said conversion block (21) is moved horizontally.

8. A method of performing an assay using the assay device of the line spectral confocal sensor of any one of claims 1-7, the method comprising the steps of:

the driving device drives the displacement generating device to move, and the displacement measuring device measures the displacement of the moving unit in the displacement measuring device in the vertical direction and takes the displacement as standard displacement;

s2, aligning the line spectral confocal sensor to be detected with the horizontal plane of the integrated standard device, measuring the displacement of points at different positions on the horizontal plane in the vertical direction, and comparing the displacement obtained by the measurement with the standard displacement in the step S1 to obtain the vertical direction error distribution and the limit positioning error of the line spectral confocal sensor to be detected;

s3, measuring an inclined plane of the integrated standard device by the line spectrum confocal sensor to be detected, and measuring the actual measured vertical heights of the inclined plane at different positions of the same vertical height, thereby obtaining the transverse positioning error distribution and the limit positioning error of the line spectrum confocal sensor to be detected.

And S4, fitting according to the vertical positioning error distribution and the transverse positioning error distribution of the to-be-detected line spectrum confocal sensor obtained in the steps S2 and S3 to obtain an error model of the sensor.

9. The method according to claim 8, wherein in step S2, the vertical limit positioning error is calculated according to the following relation:

wherein y is _{Label (C)} Is the standard displacement obtained by the measurement of the displacement measuring device, y _Measuring Is the actual measured value of the line spectral confocal sensor to be detected, j is the number of different height positions in the vertical height range, and i is the number of points at different positions in the scanning line direction on the horizontal plane.

10. The method of claim 8, wherein in step S3, the lateral direction limit positioning error is calculated according to the following relation:

Δx＝max{|Δx ^j |}

wherein Deltax is ^j Is the maximum lateral positioning error, y, at vertical height j _Measuring ^j max、y _Measuring ^j min is the maximum and minimum value measured by the linear spectrum confocal sensor at the vertical height corresponding to j, alpha is the inclination angle of the standard inclined plane, j is the position numbers of different heights in the vertical height range, and i is the number of points at different positions in the scanning line direction on the inclined plane.