A fast white light interferometry in-situ measurement method based on grayscale-height mapping

Abstract

The present invention discloses a fast white light interferometry in-situ measurement method based on grayscale-height mapping. Based on the principle of white light interferometry, the present invention scans a plane with the same material as the measured surface in a vertical direction before measurement, records interference images of different sampling heights, obtains a set of interference signals, aligns the interference coherence peaks and performs filtering and noise reduction processing to establish a grayscale-height mapping; during measurement, two interference images are collected at a specific interval, and the possible height point sets corresponding to the two sets of grayscales are found respectively. By finding the point with the smallest difference between the two sets of points, the reconstructed height of the corresponding pixel point is obtained; then, the pixel points with whole-cycle errors are filtered out by the height difference between adjacent pixel points, and reliable points are marked. The surface morphology of the microstructure is quickly reconstructed by interpolation of reliable points. The present invention can reduce the number of images required while maintaining the same accuracy as the scanning white light interferometry method, thereby greatly improving the measurement efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical precision measurement, and relates to an in-situ measurement method for a microstructured optical surface, and in particular to a fast white light interferometry in-situ measurement method based on grayscale-height mapping. Background Art

[0002] Microstructured optical components, with their advantages of small size, light weight, and ease of integration, are widely used in fields such as fiber-optic communications, biomedicine, laser technology, and aerospace. The surface accuracy requirements for microstructured optical components are generally submicron, with roughness at the nanometer level, placing very high demands on processing technology. In-situ measurement can monitor workpiece surface form and position errors and surface microtopography during processing. This measurement process does not require the workpiece to be removed from the machine tool, thus shortening measurement time, avoiding repeated clamping errors, and greatly improving measurement accuracy and processing efficiency. Therefore, in-situ measurement has gradually become the primary technical means to ensure the processing quality of microstructured optical components.

[0003] In-situ measurement methods can be categorized into probe scanning and full-field-of-view measurement. Probe scanning utilizes machine tool axis motion to scan the surface topography of the workpiece point by point. This method can be further divided into contact and non-contact probe measurement. Contact probes inevitably damage the surface when measuring soft materials. Non-contact probes, primarily based on tunneling current and optical principles, effectively address the issue of contact damage between the probe and the surface being measured. However, the generation of tunneling current requires the workpiece to be conductive, making it difficult to use for measuring most optical materials. Furthermore, the tunneling current method relies on the motion of piezoelectric ceramics to track the surface topography, and its measurement accuracy depends on the accuracy with which the piezoelectric ceramics track the tunneling current. Accurately tracking complex, highly dynamic trajectories poses significant challenges to the control of the piezoelectric ceramics, making it difficult to achieve high measurement efficiency with the tunneling current method. Optical probes offer higher-efficiency measurement without damaging the surface. For example, many researchers have integrated optical probes, such as dispersive confocal sensors and interferometric probes, into ultra-precision lathes, enabling in-situ measurement of complex surfaces. The spiral scanning process of this type of measurement is formed by the rotation of the workpiece and the lateral feed of the probe. It requires the use of special master parts to accurately align the spindle and the probe. At the same time, the probe needs to be kept tightly fixed during the iterative processing, which reduces the flexibility of the system.

[0004] In-situ measurement technology based on probe scanning has the problems of low measurement efficiency and measurement accuracy being affected by machine tool motion errors. In contrast, full-field-of-view measurement technology does not rely on machine tool motion, the measurement process has high flexibility, and there is no need for point-by-point scanning, so the measurement efficiency is high. However, the full-field-of-view method still faces many challenges in microstructure measurement. For example, stereo photogrammetry and structured light measurement can achieve in-situ measurement of surface three-dimensional morphology, but their resolution is low, and the measurement accuracy is generally tens or several microns. It is generally used to measure the macroscopic morphology of the surface. Laser phase shift interferometry technology can be flexibly adjusted according to the in-situ measurement environment, but each set of images needs to have an accurate phase shift, and the required interference images are generally more than 3. It is very sensitive to environmental vibrations and will cause phase ambiguity.

[0005] White-light interferometry is a full-field-of-view measurement technology that uses a broad-spectrum light source to create different contrast levels for each level of interference fringes. This overcomes the phase ambiguity problem present in traditional microscopic interferometry techniques, allowing for sub-nanometer measurement resolution and high-precision measurement of microstructures. Traditional white-light interferometry generally uses scanning white-light interferometry, which requires scanning perpendicular to the surface being measured at a certain step length to obtain multiple interference images. The surface topography is then reconstructed by analyzing the interference signal at each pixel and finding its coherence peak position. During in-situ measurement based on scanning white-light interferometry, vertical scanning may be affected by environmental factors such as machine tool vibration, resulting in inaccurate measurement results. Summary of the Invention

[0006] The purpose of the present invention is to provide a fast white light interferometry in-situ measurement method based on grayscale-height mapping, which improves the measurement efficiency while maintaining the same accuracy as the scanning white light interferometry method.

[0007] The technical solution adopted by the present invention is: a fast white light interferometry in-situ measurement method based on grayscale-height mapping, comprising the following steps:

[0008] Step 1: Before measurement, a white light interferometer is used to scan a plane with the same material as the measured surface in a vertical direction. Interference images at different sampling heights are recorded to obtain a set of interference signals. The coherence peaks of the interference signals are aligned and filtered for noise reduction to establish a grayscale-height mapping.

[0009] Step 2: Sampling the white light interference fringes on the surface to be measured: First, adjust the distance between the white light interferometer and the surface to be measured according to the interference image so that the interference image meets the sampling conditions, capture the first interference image, and obtain grayscale matrix 1; then, move the white light interferometer a distance d in a direction perpendicular to the surface to be measured, and capture the second interference image to obtain grayscale matrix 2;

[0010] Step 3: According to the grayscale-height mapping, find the multiple height values ​​corresponding to the grayscale value of each pixel in the two sets of grayscale matrices;

[0011] Step 4: Set the multiple height values ​​corresponding to the grayscale value of each pixel in the first grayscale matrix as the first set of position points, and subtract the moving distance d from the multiple height values ​​corresponding to the grayscale value of each pixel in the second grayscale matrix to obtain the second set of position points;

[0012] Step 5: Find the two positions with the smallest absolute difference between the two groups of position points in each pixel. The average height value of the two positions is the reconstructed height Z of the pixel. (i，j) , where i and j represent the pixel positions, i.e. the pixel at row i and column j in the grayscale matrix;

[0013] Step 6: Use the reliable point marking algorithm to process the height reconstructed for each pixel: by using a traversal program to compare the height values ​​of all adjacent pixels, the difference dh1 between the adjacent pixel heights is compared with the set threshold h1, and reliable points are marked. The threshold h1 is set to be less than the average period length of the white light interference signal;

[0014] Step 7: Interpolate all reliable points to obtain the measured surface morphology.

[0015] Furthermore, in step 2, satisfying the sampling condition means that a zero-order fringe appears on the interference image, and the remaining fringes are in the first five interference fringes.

[0016] Furthermore, in step 6, the reliable point marking algorithm is as follows: Let dh1 = abs(Z (i，j+1) -Z (i，j) ), when dh1≤h1, mark the pixel at position (i, j+1) as a reliable point;

[0017] When dh1>h1, the position (i, j+1) is marked as an unreliable point and processed by the following formula:

[0018] Z' (i，j+1) =Z (i，j+1) -dw1

[0019] in:

[0020] dw1=round((Z (i，j+1) -Z (i，j) ) / w a )×w a

[0021] The round(·) operator rounds the argument to the nearest integer. ais the average period length of the white light interference signal. During the traversal process, for unreliable points, Z (i，j+1) Replace with Z' (i，j+1) , so that the subsequent traversal process can continue.

[0022] Furthermore, d ranges from 30 to 70 nm.

[0023] The beneficial effects of the present invention are as follows: by establishing grayscale-height mapping, the present invention collects two interference images at specific intervals, and thereby realizes rapid reconstruction of the surface morphology of the microstructure. The number of interference images required can be greatly reduced while maintaining the comparable accuracy of the scanning white light interference method. The measuring device is simple and low-cost. Only an industrial camera with a white light interference objective lens is required, and no complex centering method is required to realize in-situ measurement in ultra-precision machining. The proposed method avoids the process of mechanical scanning in the vertical direction in scanning white light interference, and only two interference images are used to complete measurement and reconstruction, making the interference measurement system more stable and the measurement process faster. It has broad application prospects in in-situ measurement of microstructures.

[0024] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a structural schematic diagram of a fast white light interferometry in-situ measurement system based on grayscale-height mapping according to the present invention;

[0026] Figure 2 This is a flow chart of a fast white light interferometry in-situ measurement method based on grayscale-height mapping of the present invention;

[0027] Figure 3 This is a flow chart of a reliable point marking algorithm for a fast white light interferometry in-situ measurement method based on grayscale-height mapping of the present invention.

[0028] Figure 4 This is a schematic diagram of the sampling process of a fast white light interferometry in-situ measurement method based on grayscale-height mapping of the present invention.

[0029] Figure 5 This is a schematic diagram of the in-situ measurement results of a typical optical surface using a fast white light interferometry in-situ measurement method based on grayscale-height mapping of the present invention.

[0030] Reference numerals in the figure: 1. ultra-precision air-bearing spindle, 2. workpiece, 3. white light interference objective lens, 4. tube lens, 5. white light source, 6. CCD, 7. computer. DETAILED DESCRIPTION

[0031] The preferred embodiment of the present invention is shown in Figure 1 The workpiece cutting process and in-situ surface measurement experiments were conducted on a four-axis ultra-precision machine tool. The white-light interferometer device consists of a white-light interferometer objective lens 3, a white-light light source 5, a tube lens 4, and a CCD camera 6. The workpiece 2 is mounted on the machine tool's ultra-precision air-bearing spindle 1 for cutting. The natural diamond tool and the white-light interferometer device are mounted on the machine tool's B-axis worktable. The precise motion of the machine tool allows for high-precision adjustment of the relative position of the camera 6 and the measured surface, enabling in-situ measurement during ultra-precision machine tool processing.

[0032] White light is a short-coherent light source composed of components with relatively wide bandwidths, typically producing interference within a range of only a few micrometers. For LED light sources, due to their yellow-blue bimodal spectrum, they can be viewed as the superposition of two Gaussian light sources with central wavelengths λ1 and λ2, and spectral widths dλ1 and dλ2, respectively. The resulting interference signal can be expressed as:

[0033]

[0034] Among them, u is the peak number, v u is the proportionality coefficient, I u，1 with I u，2 Represent the reference light and the measurement light respectively, z represents the scanning height, h0 represents the height of the measured surface, and φ represents the additional phase caused by reflection. The difference between λ1 and λ2 results in the superposition of I a The period length of each order interference fringe is different. Its average period length is recorded as w a , which can be calculated by dividing the coherence length by the number of interference fringes.

[0035] The above theory shows that when the light source intensity and wavelength are constant, the white-light interference signal is primarily influenced by the surface height and the additional phase caused by reflection. Surface height only affects the overall position of the white-light interference signal and has no significant effect on its shape. Different materials exhibit different additional phases upon reflection. For most microstructured surfaces, which consist of only a single material, variations in the additional phase are negligible, and their impact on the white-light interference signal is negligible. Therefore, it can be assumed that the grayscale value of the white-light interference signal is modulated only by surface height.

[0036] During the measurement process, the non-uniformity of the light source will lead to uneven light intensity distribution and inconsistent light wavelength at each pixel of the imaging camera. The non-uniformity of light intensity will affect the DC component and visibility of the interference signal, and the inconsistency of light wavelength will cause the shape of the interference signal (such as period and amplitude) to change. Figure 2 In order to reduce the influence of these factors on the measurement, it is necessary to scan the plane with the same material as the measured surface vertically before measurement, record the interference images at different sampling heights, and obtain a set of interference signals Ia(i，j) (z orig ), where i and j represent pixel positions, z orig Represents the sampling height relative to the sampling starting position. On this basis, the scanning white light interferometry method is used to process the above interference signal to reconstruct the relative height H of each point on the plane. (i，j) By calculating I a(i，j) (z orig -H (i，j) ) Align the peak values ​​of all pixel interference signals. After alignment, perform noise reduction through mean filtering to obtain a set of standard interference signals I a(i，j) (z). In subsequent measurements, the exposure conditions must be kept constant to ensure that the standard interference signal remains unchanged.

[0037] First, the mirror copper before processing is scanned to obtain a set of standard interference signals.

[0038] Then, a sinusoidal surface with a period of 0.45 mm and an amplitude of 0.7 μm was machined on the copper surface.

[0039] The white light interference fringes are sampled, and the sampling process is as follows: Figure 4 As shown. According to the interference image, adjust the distance between the white light interferometer and the measured surface so that the interference image meets the sampling conditions, that is, the zero-order fringe appears on the image, and the remaining fringes are within the first 5-order interference fringes. Record the sampling position, take the first interference image, and obtain the grayscale matrix I p1(i，j) Then, the white light interferometer is moved a distance d in a direction perpendicular to the surface to be measured, and a second interference image is taken at this location to obtain the grayscale matrix I p2(i，j) ;

[0040] The height value is obtained by grayscale-height mapping: the following formula is used to calculate each pixel and obtain two sets of height values ​​z p1(i，j，m) With z p2(i，j，n) , m and n represent the number of two sets of height values ​​respectively.

[0041] I p1(i,j) -I a(i,j) (z)=0

[0042] I p2(i,j) -I a(i,j) (z)=0

[0043] The height values ​​corresponding to the grayscale value of each pixel in the first grayscale matrix are set as the first set of position points, and the second set of position points is obtained by subtracting the moving distance d from the height values ​​corresponding to the grayscale value of each pixel in the second grayscale matrix:

[0044] z' p2(i,j，n) =z p2(i,j,n) -d

[0045] Find the two positions with the smallest absolute difference between the two groups of position points in each pixel (z p1(i，j，m’) ,I p1(i，j) ) and (z p2(i,j,n′) ,I p2(i,j) ):

[0046]

[0047] Among them, m a and n a Respectively represent the number of these two set points.

[0048] Reconstruction height Z (i，j) It can be expressed as:

[0049] Z (i，j) =(z p1(i，j，m’) +z p2(i，j，n’) ) / 2

[0050] It is important to note that during the measurement and reconstruction process, the height of the surface to be measured must be within the coherence length range. Furthermore, since the visibility of secondary interference fringes is low, which can lead to large reconstruction errors, the height of the surface to be measured must be limited to within the height of the center 5-order fringes.

[0051] In the process of surface reconstruction, when there is an error in the gray value of a pixel, the gray value I p1(i，j) becomes The height value obtained by the grayscale-height mapping is z p1(i，j，m) becomes When calculating the point with the minimum absolute difference, the incorrect period may be selected. When the intersection point is taken according to the correct grayscale value, the position differences on different periods are dz1 and dz2 respectively. In this case, dz1 < dz2, and the position corresponding to dz1 is the correct point with the minimum position difference. When the grayscale value changes, the position differences become dz'1 and dz'2 respectively. In this case, dz'1 > dz'2, and the point corresponding to dz'2 will be incorrectly selected as the point with the minimum position difference, resulting in an incorrect reconstructed height.

[0052] The points of the full cycle jump are discrete, combined with Figure 3 , we can use the traversal program to compare the values ​​of adjacent points, compare the difference between adjacent points with the set threshold h1, and mark the reliable points. The threshold h1 is set to be smaller than the average period length of the white light interference signal fringes to preserve the original height jump of the surface. The reliable point marking algorithm is as follows: Let dh1 = abs(Z (i，j+1) -Z (i，j)), when dh1≤h1, mark the pixel at position (i, j+1) as a reliable point; when dh1>h1, mark it as an unreliable point. Reconstruct it to the correct period using the following formula:

[0053] Z' (i，j+1) =Z (i，j+1) -dw1

[0054] in:

[0055] dw1=round((Z (i，j+1) -Z (i，j) ) / w a )×w a

[0056] The round(·) operator rounds the argument to the nearest integer. a is the average period length of the white light interference signal fringes. In the traversal process, for unreliable points, Z (i，j+1) Replace with Z' (i，j+1) , so that subsequent traversal can proceed correctly.

[0057] The reconstructed reliable point cloud is as follows Figure 5 As shown in Figure (a), its reliable points account for 52.7% of the total number of reconstructed points. Figure 5 Figure (b) shows the surface reconstructed by reliable point interpolation. Figure 5 Figure (c) shows the cross-sectional comparison between the reconstruction result and the scanning white light interference reconstruction surface. Figure 5 Figure (d) shows the corresponding cross-sectional error. The root mean square error between the surface reconstructed by reliable point interpolation and the surface reconstructed by scanning white light interferometry is 9.1367 nm, indicating high reconstruction accuracy.

[0058] Through the above method, the present invention pre-establishes the grayscale-height mapping, and can complete the measurement and reconstruction of the small-angle optical surface morphology with only two grayscale images. While maintaining the same accuracy as scanning white light interferometry, it can reduce the number of images required, making the interferometric measurement system more stable and the measurement process faster.

[0059] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A fast white light interferometry in-situ measurement method based on grayscale-height mapping, characterized in that: The following steps are involved: Step 1: Before measurement, a white light interferometer is used to scan a plane with the same material as the measured surface in a vertical direction. Interference images at different sampling heights are recorded to obtain a set of interference signals. The coherence peaks of the interference signals are aligned and filtered for noise reduction to establish a grayscale-height mapping. Step 2: Sampling the white light interference fringes on the surface to be measured: First, adjust the distance between the white light interferometer and the surface to be measured according to the interference image so that the interference image meets the sampling conditions, capture the first interference image, and obtain grayscale matrix 1; then, move the white light interferometer a distance d in a direction perpendicular to the surface to be measured, and capture the second interference image to obtain grayscale matrix 2; Step 3: According to the grayscale-height mapping, find the multiple height values ​​corresponding to the grayscale value of each pixel in the two sets of grayscale matrices; Step 4: Set the multiple height values ​​corresponding to the grayscale value of each pixel in the first grayscale matrix as the first set of position points, and subtract the moving distance d from the multiple height values ​​corresponding to the grayscale value of each pixel in the second grayscale matrix to obtain the second set of position points; Step 5: Find the two positions with the smallest absolute difference between the two groups of position points in each pixel. The average height value of the two positions is the reconstructed height Z of the pixel. (i，j) , where i and j represent the pixel positions, i.e. the pixel at row i and column j in the grayscale matrix; Step 6: Use the reliable point marking algorithm to process the height reconstructed for each pixel: by using a traversal program to compare the height values ​​of all adjacent pixels, the difference dh1 between the adjacent pixel heights is compared with the set threshold h1, and reliable points are marked. The threshold h1 is set to be less than the average period length of the white light interference signal; Step 7: Interpolate all reliable points to obtain the measured surface morphology.

2. The rapid white light interferometry in-situ measurement method based on grayscale-height mapping according to claim 1, characterized in that: In step 2, satisfying the sampling condition means that a zero-order fringe appears on the interference image, and the remaining fringes are in the first five interference fringes.

3. The rapid white light interferometry in-situ measurement method based on grayscale-height mapping according to claim 1 or 2, characterized in that: In step 6, the reliable point marking algorithm is as follows: Let dh1 = abs(Z (i，j+1) -Z (i，j) ), when dh1≤h1, the pixel at position (i, j+1) is marked as a reliable point; when dh1>h1, the pixel at position (i, j+1) is marked as an unreliable point and processed by the following formula: WITH' (i，j+1) =Z (i，j+1) -dw1 in: dw1=round((Z (i，j+1) -WITH (i,j) ) / In a )×in a The round(·) operator rounds the argument to the nearest integer. a is the average period length of the white light interference signal. During the traversal process, for unreliable points, Z (i，j+1) Replace with Z' (i，j+1) , so that the subsequent traversal process can continue.

4. The rapid white light interferometry in-situ measurement method based on grayscale-height mapping according to claim 1, characterized in that: The range of d is 30-70 nm.

Images