A high-precision flatness measurement method for large-scale low-reflectivity surfaces

Abstract

The present invention discloses a high-precision flatness measurement method for large-scale, low-reflectivity surfaces, belonging to the field of optical precision measurement technology. The method comprises the following steps: calculating the number of subapertures and the oblique incidence angle to determine the subaperture splicing path; using a phase-shifting laser interferometer to project light at the measured plane at an oblique incidence angle to collect grayscale images of interference fringes in the elliptical subaperture regions; using a phase-shifting interferometry algorithm to resolve the grayscale images of the interference fringes to obtain phase data of the subapertures; moving the measured plane according to the determined subaperture splicing path to sequentially obtain phase data for each subaperture; splicing the phase data for each subaperture to generate phase data for the entire measured plane; and restoring the overall phase data of the measured plane to the plane height data of the measured plane. This method has low dependence on polished surfaces and interferometer aperture, high measurement accuracy, and strong stability.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical precision measurement, and in particular relates to a high-precision flatness measurement method for a large-size low-reflectivity plane. Background Art

[0002] With the rapid development of modern industry, the performance requirements of mechanical equipment for high-precision planar structural parts are increasing. Traditional metal guide rails have gradually become difficult to meet the needs of high precision, high load and special environment. In this context, including Al 2 O 3. Si 2 N 4. ZrO 2 and SiC Ceramic materials such as PTFE, PTFE, and PTFE, with their exceptional properties such as high hardness, excellent wear resistance, outstanding high-temperature resistance, strong corrosion resistance, and high rigidity, have shown broad application prospects in numerous fields, including machinery manufacturing, semiconductor equipment, and medical devices. The performance of large, long structural ceramic parts, such as guide rails, depends not only on the material itself but also on the precision of their machining. Flatness is a key indicator of the machining quality of ultra-precision ceramic parts, directly affecting the accuracy and stability of planar kinematic pairs and fundamental to ensuring high-precision operation of mechanical equipment. Therefore, strict flatness control is crucial in the machining of these ceramic parts.

[0003] The measurement accuracy of the phase-shifting laser interferometer can reach the nanometer level, and the sampling density can reach 0.1 mm or even higher. Depending on the aperture of the interferometer, it is suitable for plane measurement of various apertures and can measure millions of measurement point data simultaneously. It is a high-precision and high-efficiency plane measurement instrument. However, it has high requirements for the glossiness of the measured surface and can generally only measure polished surfaces. In addition, the interference fringe pattern obtained by traditional phase-shifting laser interferometer measurement has low clarity and is highly dependent on the aperture of the reference mirror. Especially for large-sized, low-reflectivity materials, the measurement accuracy is low and the stability is poor.

[0004] Chinese patent CN111854984A discloses an interferometer for measuring the transmitted wavefront of liquid crystals. This invention is a laser-based interferometer that uses linearly polarized light output to measure the transmitted wavefront of liquid crystal blind holes or liquid crystal panels. However, this method requires the surface being measured to be parallel to the flat crystal surface when measuring flat surfaces. This method has difficulty obtaining clear interference patterns when measuring low-reflectivity surfaces, and the single measurement range does not exceed the flat crystal aperture. Summary of the Invention

[0005] The purpose of the present invention is to provide a high-precision flatness measurement method for large-scale low-reflectivity planes, so as to solve the problems of traditional phase-shifting laser interferometer in measuring material flatness, such as high dependence on the aperture of the reference mirror, low measurement accuracy, and poor stability.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] The present invention relates to a high-precision flatness measurement method for a large-scale low-reflectivity plane, which comprises the following steps:

[0008] S1. Calculate the number of subapertures and the oblique incidence angle based on the size of the measured surface and the aperture of the phase-shifting laser interferometer, and determine the subaperture stitching path.

[0009] S2. The laser beam from the phase-shifting laser interferometer is incident on the surface being measured at a calculated oblique angle of incidence. A plane mirror is placed along the path of the laser beam reflected by the surface being measured. This mirror reflects the laser beam back to the same position on the surface being measured and then returns to the phase-shifting laser interferometer. A grayscale image of the interference fringes in the elliptical sub-aperture area is collected.

[0010] S3. Use the phase-shifting interferometry algorithm to solve the grayscale image of the interference fringes and obtain the phase data of the sub-aperture;

[0011] S4. Move the measured plane according to the determined sub-aperture stitching path, and obtain the phase data of each sub-aperture in sequence according to S2 to S3;

[0012] S5. Splicing the phase data of each sub-aperture to generate the phase data of the entire measured plane;

[0013] S6. Restore the plane height data of the measured plane from the phase data of the entire measurement plane.

[0014] Preferably, the calculation formula for the number of sub-apertures in S1 is:

[0015] ,

[0016] in, N is the number of subapertures, Ly is the width of the plane, l is the center distance between the sub-apertures.

[0017] Preferably, the calculation formula for the oblique incident angle in S1 is:

[0018] ,

[0019] in, θ is the oblique incidence angle, D is the interferometer aperture, Lx is the length of the plane, l is the center distance between the sub-apertures.

[0020] Preferably, the interference fringe grayscale image collected in the elliptical sub-aperture area in S2 includes several phase difference π / 2 interference fringe grayscale data diagram, the S3 uses the phase-shifting interference algorithm to solve the interference fringe grayscale image by first calculating the wrapped phase data according to the interference fringe grayscale data diagram, and then unwrapping the wrapped phase data to obtain the phase data of each sub-aperture.

[0021] Preferably, the specific steps of performing splicing processing on the phase data of each sub-aperture in S5 include:

[0022] S5.1. For the overlapping regions of subaperture phase information, compensate for slope and height displacement errors using a least-squares global optimization algorithm to obtain a slope compensation function for each subaperture.

[0023] The calculation formula of the least squares global optimization algorithm is:

[0024] ,

[0025] in, V represents the slope compensation function of each sub-aperture, i and j Indicates the number of the subaperture, N is the number of subapertures, Zi and Zj Subaperture i and subaperture j Overlapping phase data, x and y Respectively represent the sub-aperture x Axis and y The coordinates on the axis, x i and y i Subaperture i exist x Axis and y The offset on the axis, x j and y j Subaperture j exist x Axis and y The offset on the axis, a 、 b and c They represent compensation factors respectively;

[0026] S5.2. Subtract the corresponding slope compensation function from the phase data of each subaperture to obtain phase data with a uniform slope;

[0027] S5.3. Add the phase data of all subapertures with uniform slopes and average the overlapping data to generate the phase data of the entire measured plane. The calculation formula is:

[0028] ,

[0029] in, M △φ is the phase data of the entire measured plane, M i is a subaperture with uniform slope i Phase data, N is the number of subapertures.

[0030] Preferably, the calculation formula of the plane height data in S6 is:

[0031] ,

[0032] in, M h is the plane height data of the measured plane, M △φ is the phase data of the entire measured plane, θ is the oblique incidence angle, λ 0 is the laser wavelength, n 0 is the refractive index of the medium in the interferometer cavity.

[0033] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0034] 1. The high-precision flatness measurement method for large-scale, low-reflectivity surfaces involved in the present invention enhances the low-reflectivity surface signal through oblique incidence to obtain a clear interference fringe pattern, while expanding the measurement range in a single direction. It can perform large-scale, accurate and rapid detection of the flatness of large-scale, low-reflectivity material surfaces with high accuracy and strong stability.

[0035] 2. The high-precision flatness measurement method for large-scale, low-reflectivity planes involved in the present invention calculates the number of sub-apertures and the oblique incidence angle, and simultaneously determines the sub-aperture splicing path. After obtaining the phase data of each sub-aperture, the phase data of each sub-aperture is spliced ​​to generate the overall phase data of the measured plane. Finally, the plane height data of the measured plane is restored based on the overall phase data. The dependence on the aperture of the reference mirror is reduced through sub-aperture splicing, and the dependence on the interferometer aperture is low. It is suitable for planar guide rails with a width greater than the interferometer aperture. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the high-precision flatness measurement method for large-scale low-reflectivity planes proposed by the present invention;

[0037] Figure 2 This is a schematic diagram of the optical path for oblique-incidence interferometry measurement;

[0038] Figure 3 Schematic diagram of sub-aperture stitching path planning;

[0039] Figure 4 Schematic diagram of the sub-aperture stitching algorithm;

[0040] Figure 5 Example measurement data graph;

[0041] Figure 6 Example measurement diagram. DETAILED DESCRIPTION

[0042] In order to further understand the content of the present invention, the present invention is described in detail with reference to the examples. The following examples are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0043] This embodiment takes the measurement of the surface of a ceramic material as an example to illustrate the content of the present invention in detail.

[0044] The measurement object in this example is a 1050mm x 130mm SiC ceramic surface. The measurement equipment used in this example includes a 100mm aperture horizontal phase-shifting laser interferometer using a 632.8nm He-Ne laser as the light source; a reference flat crystal with a flatness better than 1 / 20 of the wavelength; a plane mirror with a flatness better than 1 / 15 of the wavelength; a precision optical adjustment stage; and a single-axis motion platform.

[0045] The overall measurement process is as follows Figure 1 As shown in the figure, the measurement process is mainly divided into 6 steps: S1: Calculate the measurement parameters according to the above parameters; S2: Oblique incidence measurement of sub-aperture measurement stripe grayscale data; S3: Calculate the sub-aperture height data through the stripes; S4: According to the sub-aperture stitching process, measure all sub-aperture height data; S5: Stitch the sub-aperture height data; S6: Convert the actual height data and spatial resolution according to the measurement parameters, and restore the plane morphology in proportion.

[0046] A high-precision flatness measurement method for a large-scale, low-reflectivity surface comprises the following steps:

[0047] S1. According to the size of the measured plane (length Lx ,width Ly ) and the aperture of the phase-shifting laser interferometer D , calculate the number of sub-apertures and the oblique incidence angle, and determine the sub-aperture stitching path at the same time, to ensure that the elliptical measurement area formed by the oblique incidence can cover the measured surface in the length direction, and at the same time the number of sub-apertures ensures that all areas of the measured plane can be measured in the width direction;

[0048] For the subaperture spacing l To ensure that the overlapping area of ​​the two sub-apertures is not less than 1 / 4 of the sub-aperture area, the single translation distance is generally set to l=D / 2;

[0049] The calculation formula for the number of sub-apertures is:

[0050] ,

[0051] in, N is the number of subapertures, Ly is the width of the plane, l is the center distance between the sub-apertures.

[0052] The calculation formula for the oblique incident angle is:

[0053] ,

[0054] in, θ is the oblique incidence angle, D is the interferometer aperture, Lx is the length of the plane, l is the center distance of the set sub-apertures;

[0055] Adjust the oblique incidence angle according to the data and determine the sub-aperture path for stitching measurements.

[0056] S2. Figure 2 As shown in the figure, when collecting oblique-incident phase-shifting laser interferometer data, the laser of the phase-shifting laser interferometer is incident on the measured plane at the calculated oblique incident angle. A plane reflector is placed on the path where the laser beam is reflected by the measured plane. The laser beam is reflected back to the same position on the measured plane through a precision optical adjustment table, and finally returns to the phase-shifting laser interferometer through the measured plane. Due to the difference in surface height, the actual optical path and the standard optical path have an optical path difference, as shown in the following formula:

[0057]

[0058] Where: d is the optical path difference, h The height data of the measuring point.

[0059] The laser generates interference fringes on the interferometer reference flat crystal, and the CCD camera collects the grayscale image of the interference fringes in the elliptical sub-aperture area, including Figure 2 Several phase differences shown π / 2 interference fringe grayscale data graph, the number of interference fringe grayscale data graphs is generally 4-13.

[0060] S3. Use the phase-shifting interferometry algorithm to solve the interference fringe grayscale image and obtain the phase data of the sub-aperture. The specific method is: first, according to the phase difference π The wrapped phase data is calculated from the grayscale data of the interference fringe of / 2, and then the branch cutting method is used to unwrap the wrapped phase data to obtain the phase data of each sub-aperture;

[0061] In this embodiment, nine interference fringe grayscale data images are taken as an example, and the calculation formula for the wrapped phase data is:

[0062] ,

[0063] in, is the wrapped phase data, 9 phase difference images taken by the phase-shifting laser interferometer π / 2 interference fringe grayscale data;

[0064] For different numbers of interference fringe grayscale data graphs, there are corresponding wrapped phase data calculation formulas for calculating the wrapped phase data, which are conventional technical means in this field and will not be listed one by one in this embodiment; using the branch cutting method to unwrap the wrapped phase data is also a conventional technical means in this field.

[0065] S4. Refer to the attached Figure 3 With attached Figure 6 As shown, the above-mentioned measured plane is placed on a single-axis moving platform. After collecting the oblique incident phase-shifted laser interference data at one position, the measured plane is moved along the width direction of the measured plane. Based on S1, it can be seen that the single movement distance l=D / 2=50mm, and the phase data of each sub-aperture is obtained in sequence according to the method of S2 to S3 until the height data of three sub-apertures are collected, that is, Figure 5 The height data point cloud of position 1, position 2 and position 3, the XY axis unit is Pixel (pixel point), and the measurement position corresponds to Figure 6 The red light areas at positions 1, 2, and 3.

[0066] S5. Splice the phase data of each sub-aperture to generate the phase data of the entire measured plane. For the specific splicing method, refer to Figure 4 As shown, the steps include:

[0067] S5.1. For the overlapping area of ​​sub-aperture phase information, the slope and height displacement errors are compensated by the global optimization algorithm of the least squares method to obtain the slope compensation function of each sub-aperture; this embodiment requires compensation for the displacement of the x, y, and z axes and the tilt of the x and y axes of sub-aperture data No. 2 and 3; the x and y axis displacements correspond to the displacement through the mobile platform, and the mechanical coordinates xi and yi can be obtained through the mobile platform displacement sensor. zThe axis displacement and the inclination of the x and y axes are compensated by the least squares method.

[0068] The calculation formula of the global optimization algorithm of the least squares method is:

[0069] ,

[0070] in, V represents the slope compensation function of each sub-aperture, i and j Indicates the number of the subaperture, N is the number of subapertures, Z i and Z j Subaperture i and subaperture j Overlapping phase data, x and y Respectively represent the sub-aperture x Axis and y The coordinates on the axis, x i and y i Subaperture i exist x Axis and y The offset on the axis, x j and y j Subaperture j exist x Axis and y The offset on the axis, a 、 b and c They represent compensation factors respectively;

[0071] a i x+ b i y+ c i and a j x+ b j y+ c j are the compensation functions corresponding to the two sub-apertures. Based on the least squares method, we can solve a i ( i =1… N ), b i ( i =1… N )andc i ( i =1… N ), the slope compensation function of each sub-aperture is obtained, and the calculation process is the process of solving the above formula:

[0072] Derivative of the above formula:

[0073] ,

[0074] Where: S i is the slope compensation function of each sub-aperture V Pair Aperture i Corresponding compensation factor a i 、 b i and c i The partial derivative of Z ij Subaperture i and subaperture j The difference of the overlapping parts; a ij Subaperture i and subaperture j Corresponding compensation factor a The difference, that is a ij = a i - a j ; b ij Subaperture i and subaperture j Corresponding compensation factor b The difference, that is b ij = b i - b j ; c ij Subaperture i and subaperture j Corresponding compensation factor c The difference, that is c ij = c i - c j .

[0075] Simplifying it into matrix form, we can get the formula:

[0076] ,

[0077] Expanding the above formula to the surface form, we get the following formula:

[0078] ,

[0079] in: X is the horizontal coordinate matrix; Y is the vertical coordinate matrix; Mask ij Subaperture i and subaperture j The mask matrix of the overlapping part is 1, and the other areas are 0. The simplified formula is:

[0080] ,

[0081] in, Q ij and P ij Expressed as about a ij 、 b ij and c ij The coefficients of the canonical system of equations are:

[0082] ,

[0083] .

[0084] To solve the operator aperture i Corresponding compensation factor a i 、 b i and c i ,make:

[0085] ,

[0086] ,

[0087] in, k represents the compensation factor vector of plane i, i∈[1, N ], K Represents the set of compensation factor vectors for all planes.

[0088] Construct the canonical system of equations:

[0089] ,

[0090] in, A and B Expressed as the coefficient group of the canonical equations:

[0091] ,

[0092] .

[0093] Because aperture 1 is used as the reference plane, , Substitute A and B into the target equation and solve the above equation to get the compensation function coefficient vector K , that is, the compensation plane function of each sub-aperture is obtained. All the compensated sub-apertures are superimposed to obtain the complete plane surface data.

[0094] S5.2. Subtract the corresponding slope compensation function from the phase data of each subaperture to obtain phase data with uniform slope M i ( i =1… N );

[0095] S5.3. Add the phase data of all sub-apertures with uniform slopes and average the overlapping data to generate the phase data of the entire measured plane, such as Figure 5 The height data point cloud after stitching, its XY axis coordinate unit is pixel (pixel point), and the calculation formula is:

[0096] ,

[0097] in, M △φ is the phase data of the entire measured plane, M i is a subaperture with uniform slope i Phase data, N is the number of subapertures.

[0098] S6. Restore the plane height data of the measured plane from the phase data of the entire measuring plane. The calculation formula is:

[0099] ,

[0100] in, M h is the plane height data of the measured plane, M △φ is the phase data of the entire measured plane, θ is the oblique incidence angle, λ 0 is the laser wavelength, n 0 is the refractive index of the medium in the interferometer cavity;

[0101] Finally, based on the oblique incidence coefficient and the spatial resolution of the interferometer itself, the height data with pixels as the horizontal and vertical coordinates are converted into height data corresponding to the actual size, and the final result image is obtained according to the following formula:

[0102] ,

[0103] in, Kx express X Directional spatial resolution , Ky express Y Directional spatial resolution ， represents the interferometer spatial resolution.

[0104] Finally, the height data corresponding to the actual surface shape is obtained, such as Figure 5 Point cloud of height data after parameter conversion, with XY axis units in mm (actual size).

[0105] In summary, the measurement process first obtains the phase data of different positions of the measurement surface through oblique incident laser interferometry. Figure 6 As shown in the figure, the phase data of the left side, middle and side of the measured plane are measured in turn; then the measured data are spliced ​​into complete phase data through the splicing algorithm; finally, the measured point cloud data is obtained according to the interferometer related parameters and the introduced oblique incidence parameters. M h And the actual measurement space resolution corresponding to the measurement point data Kx and Ky , refer to Figure 5 shown.

[0106] The present invention has been described in detail above with reference to the embodiments. However, the contents described are only preferred embodiments of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A high-precision flatness measurement method for large-scale low-reflectivity surfaces, characterized in that: It includes the following steps: S1. Calculate the number of subapertures and the oblique incidence angle based on the size of the measured surface and the aperture of the phase-shifting laser interferometer, and determine the subaperture stitching path. S2. The laser beam from the phase-shifting laser interferometer is incident on the surface being measured at a calculated oblique angle of incidence. A plane mirror is placed along the path of the laser beam reflected by the surface being measured. This mirror reflects the laser beam back to the same position on the surface being measured and then returns to the phase-shifting laser interferometer. A grayscale image of the interference fringes in the elliptical sub-aperture area is collected. S3. Use the phase-shifting interferometry algorithm to solve the grayscale image of the interference fringes and obtain the phase data of the sub-aperture; S4. Move the measured plane according to the determined sub-aperture stitching path, and obtain the phase data of each sub-aperture in sequence according to S2 to S3; S5. Splicing the phase data of each sub-aperture to generate the phase data of the entire measured plane. The specific steps include: S5.

1. For the overlapping regions of the subaperture phase data, compensate for the slope and height displacement errors using a least-squares global optimization algorithm to obtain a slope compensation function for each subaperture. The calculation formula of the least squares global optimization algorithm is: ， in, V represents the slope compensation function of each sub-aperture, i and j Indicates the number of the subaperture, N is the number of subapertures, Zi and Zj Subaperture i and subaperture j The overlapping area of ​​the phase data, x and y Respectively represent the sub-aperture x Axis and y The coordinates on the axis, x i and y i Subaperture i exist x Axis and y The offset on the axis, x j and y j Subaperture j exist x Axis and y The offset on the axis, a 、 b and c They represent compensation factors respectively; S5.

2. Subtract the corresponding slope compensation function from each sub-aperture phase data to obtain sub-aperture phase data with a uniform slope; S5.

3. Add the phase data of all subapertures with uniform slopes and average the overlapping regions of the phase data to generate the phase data of the entire measured plane. The calculation formula is: ， in, M △φ is the phase data of the entire measured plane, M i is a subaperture with uniform slope i Phase data, N is the number of subapertures; S6. Restore the plane height data of the measured plane from the overall phase data of the measured plane. The calculation formula for the measured plane height data is: ， in, M h is the plane height data of the measured plane, M △φ is the phase data of the entire measured plane, θ is the oblique incidence angle, λ 0 is the wavelength of the laser beam, n 0 is the refractive index of the medium in the interferometer cavity.

2. The high-precision flatness measurement method for a large-scale, low-reflectivity surface according to claim 1, characterized in that: The calculation formula for the number of subapertures in S1 is: ， in, N is the number of subapertures, Ly is the width of the measured plane, l is the center distance between the sub-apertures.

3. The high-precision flatness measurement method for a large-scale, low-reflectivity surface according to claim 1, characterized in that: The calculation formula for the oblique incident angle in S1 is: ， in, θ is the oblique incidence angle, D is the aperture of the phase-shifting laser interferometer, Lx is the length of the measured plane, l is the center distance between the sub-apertures.

4. The high-precision flatness measurement method for a large-scale, low-reflectivity surface according to claim 1, characterized in that: The S2 collects the interference fringe grayscale image of the elliptical sub-aperture area including several phase difference π / 2 interference fringe grayscale data diagram, the S3 uses the phase-shifting interference algorithm to solve the interference fringe grayscale image by first calculating the wrapped phase data according to the interference fringe grayscale data diagram, and then unwrapping the wrapped phase data to obtain the phase data of each sub-aperture.

Images