A method for fast reconstruction of white light interferometric three-dimensional topography
By continuously acquiring and preprocessing data using a white light interferometer system, combined with a focusing metric algorithm and an improved centroid method, the limitations of white light interferometry and focusing morphology restoration methods were overcome, achieving efficient and accurate 3D morphology reconstruction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- JIANGXI GAORUI OPTOELECTRONICS CO LTD
- Filing Date
- 2024-09-20
- Publication Date
- 2026-05-12
Smart Images
Figure CN119206072B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of optical measurement technology, specifically relating to a method for rapid reconstruction of three-dimensional topography using white light interference. Background Technology
[0002] The precision manufacturing industry has advanced to the micro-nano scale in terms of processing accuracy. Since the microscopic morphology of micro- and nano-components significantly affects process performance and lifespan, high-precision inspection of them has become an essential requirement. Early non-optical inspection methods were contact measurements, which had limited applicability and increased the risk of sample damage. It was not until the introduction of optical technology that non-contact measurement was achieved.
[0003] The focus topography restoration utilizes variations in surface roughness and reflectivity to generate images with abundant texture. The depth of each pixel is obtained by calculating the focus metric value at each scan location in the image stack, finding a single maximum value on the acquired focus curve to detect the focus location. However, due to the presence of noise and textureless regions, the focus metric often exhibits local maxima, which hinders the accurate location of the focus metric peak.
[0004] White light interferometry exhibits excellent morphology recovery capabilities for smooth surfaces, with a longitudinal resolution reaching fractions of a nanometer. However, its calculation results may still suffer from significant deviations when dealing with interference signals in rough surface regions with steep slopes. White light interferometry obtains the depth of each pixel by processing the intensity signal at each scan position in the image stack. The maximum value, i.e., the zero optical path difference point, is found on the acquired intensity modulation curve. Periodic fluctuations exist in the focus variation signal, with frequencies similar to those of the white light interference fringes. Based on this, it can be seen that white light interferometry and focused morphology recovery reconstruction share the same principle: obtaining a Gaussian envelope curve from the image stack of each pixel and finding the extreme points.
[0005] Therefore, both focused topography and white light interferometry are difficult to measure both smooth surfaces and rough surfaces with large slopes. They have a narrow range of applications, are very limited, and have low reconstruction accuracy. In addition, since both methods require traversing every pixel when used alone, they also cause problems such as large computational load, long time consumption, and poor timeliness. Summary of the Invention
[0006] The purpose of this invention is to address the above-mentioned problems by proposing a fast three-dimensional topography reconstruction method using white light interferometry, which can reduce computational load and improve reconstruction efficiency and accuracy.
[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0008] The present invention proposes a method for rapid reconstruction of three-dimensional topography using white light interferometry, comprising the following steps:
[0009] S1. Use a white light interferometer system to continuously acquire N frames of interference images of the sample under test;
[0010] S2. Preprocess the acquired interferometric image. The preprocessing includes:
[0011] S21. Locate the interference regions in all interferometric images to obtain the interferometric image to be reconstructed, as follows:
[0012] S211. Obtain the maximum scaling factor k max The formula is as follows:
[0013]
[0014] k max =max{k2,k3,...,k n ,...,k N};
[0015] In the formula, I(n) represents the interference light intensity distribution when the number of scanning steps is n, and k n The scaling factor is n when the number of scanning steps is n, where n = 2 to N, and N is the number of scanning steps of the white light interference system, i.e., the number of frames of the interference image;
[0016] S212, Set the maximum scaling factor k max Interference images preceding the corresponding scan step number when they appear are considered redundant data and deleted. The retained interference images are then used as the interference images to be reconstructed to complete the localization of the interference interval.
[0017] S22. Divide each interferometric image to be reconstructed into several regions, and reduce the number of pixels in each region to complete the region pixel reconstruction and obtain the corresponding reconstructed image.
[0018] S3. Calculate the focus metric value of each pixel in each reconstructed image using the focus metric algorithm;
[0019] S4. Based on the improved centroid method, the zero optical path difference point of each pixel in the entire reconstructed image is found to recover the three-dimensional morphology of the sample under test. The formula of the improved centroid method is as follows:
[0020] m(n) = [FM(n) - FM(n-1)] 2 ;
[0021]
[0022] In the formula, FM(n) is the focus metric of pixel (x,y) when the number of scan steps is n, m(n) is the square of the difference between the focus metric of pixel (x,y) in the reconstructed images of two adjacent frames, and h is the height of the sample under test at pixel (x,y).
[0023] Preferably, the focus metric algorithm is as follows:
[0024]
[0025] In the formula, FM(x,y) is the focus metric of the pixel coordinates (x,y) within the evaluation window, and G(x,y) is the gradient value of the pixel coordinates (x,y) within the evaluation window. G x G represents the lateral gradient value. y This represents the longitudinal gradient value. Ω represents the average gradient within the evaluation window, x represents the x-coordinate of a pixel within the evaluation window, and y represents the y-coordinate of a pixel within the evaluation window.
[0026] Preferably, each interferometric image to be reconstructed is divided into several regions, and the number of pixels in each region is reduced to complete the region pixel reconstruction, as follows:
[0027] S221. Let the upper left corner of the interferometric image to be reconstructed be the image origin. Divide the interferometric image to be reconstructed into several regions with four adjacent pixels as the unit.
[0028] S222. Perform region pixel reconstruction for each region. The reconstruction formula is as follows:
[0029] I′(i / 2,j / 2)=(I(i-1,j-1)+I(i,j-1)+I(i-1,j)+I(i,j)) / 4;
[0030] In the formula, I′(i / 2,j / 2) is the gray value of the reconstructed region pixel, I(i,j) is the gray value of the pixel in the i-th row and j-th column of the interferometric image to be reconstructed, i,j∈M, and M is the total number of horizontal pixels or vertical pixels of the interferometric image to be reconstructed.
[0031] Preferably, the white light interferometer system includes a white light source, a first lens, a camera, a second lens, a beam splitter, a piezoelectric ceramic platform, and an objective lens, wherein:
[0032] The first and second lenses are located on opposite sides of the beam splitter with their optical axes perpendicular to each other. The objective lens is mounted on a piezoelectric ceramic platform and is driven by the piezoelectric ceramic platform to scan the sample under test. The light emitted from the white light source is collimated by the first lens and reflected by the beam splitter. The reflected light passes through the piezoelectric ceramic platform and the objective lens in sequence and illuminates the sample under test. The light reflected from the sample under test then passes through the objective lens and the piezoelectric ceramic platform in sequence and is transmitted through the beam splitter. The transmitted light is focused by the second lens onto the camera, and the camera acquires the interference image of the sample under test.
[0033] Preferably, the objective lens is a Mirau interference objective lens.
[0034] Preferably, the piezoelectric ceramic platform with an animal microscope performs equally spaced nanoscale scanning of the sample under test.
[0035] Preferably, the beam splitter is a 45° beam splitter prism.
[0036] Preferably, the camera acquires the interference image of the sample under test when there is only one interference fringe in the field of view, and the scanning step of the objective lens is 100 nm.
[0037] Preferably, the surface of the sample being tested is a smooth surface.
[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0039] This application continuously acquires several frames of interference images of the sample under test using a white light interferometer system and performs preprocessing, including interference interval localization and regional pixel reconstruction to obtain reconstructed images. Then, a focus metric algorithm is used to calculate the focus metric value of each pixel in each reconstructed image. Based on the improved centroid method, the zero optical path difference point of each pixel in all reconstructed images is found to restore the three-dimensional morphology of the sample under test. This greatly reduces the amount of computation and burr noise, improves the timeliness by nearly five times, and enhances the reconstruction efficiency and accuracy, with a wide range of applications. Attached Figure Description
[0040] Figure 1 This is a flowchart of the fast three-dimensional topography reconstruction method using white light interferometry according to the present invention;
[0041] Figure 2 This is a schematic diagram of the white light interference system of the present invention;
[0042] Figure 3 The images shown are the original interference image (a) and the reconstructed image (b) of this invention.
[0043] Figure 4 The images shown are the reconstructed image (a) and the original interferometric image (b) of the sample under test in this invention at frame 70.
[0044] Figure 5 The results of sample reconstruction using existing techniques employing focused morphology restoration methods;
[0045] Figure 6 This is the reconstruction result of the test sample using the method of the present invention.
[0046] Explanation of reference numerals in the attached figures: 1. White light source; 2. First lens; 3. Camera; 4. Second lens; 5. Beam splitter; 6. Piezoelectric ceramic platform; 7. Objective lens; 8. Sample under test. Detailed Implementation
[0047] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0048] It should be noted that, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of the application.
[0049] like Figure 1-6 As shown, a method for rapid reconstruction of three-dimensional topography using white light interference includes the following steps:
[0050] S1. Use a white light interferometer system to continuously acquire N frames of interference images of the sample under test.
[0051] In one embodiment, the white light interferometer system includes a white light source 1, a first lens 2, a camera 3, a second lens 4, a beam splitter 5, a piezoelectric ceramic platform 6, and an objective lens 7, wherein:
[0052] The first lens 2 and the second lens 4 are located on opposite sides of the beam splitter 5, with their optical axes perpendicular to each other. The objective lens 7 is mounted on the piezoelectric ceramic platform 6 and is driven by the piezoelectric ceramic platform 6 to scan the sample under test. The light emitted by the white light source 1 is collimated by the first lens 2 and reflected by the beam splitter 5. The reflected light passes through the piezoelectric ceramic platform 6 and the objective lens 7 in sequence and illuminates the sample under test. The light reflected by the sample under test passes through the objective lens 7 and the piezoelectric ceramic platform 6 in sequence and is transmitted through the beam splitter 5. The transmitted light is focused by the second lens 4 onto the camera 3, and the camera 3 acquires the interference image of the sample under test.
[0053] like Figure 2 As shown, the white light interferometry system includes a white light source 1, a first lens 2, a camera 3, a second lens 4, a beam splitter 5, a piezoelectric ceramic platform 6, and an objective lens 7. Its measurement principle is as follows:
[0054] White light source 1 has broad spectral characteristics and emits low-coherence light. After being collimated by the first lens 2, it is split by the beam splitter 5. The reflected light passes sequentially through the piezoelectric ceramic platform 5 and the objective lens 7 to illuminate the sample 8 under test. The sample 8 under test is placed horizontally, and the objective lens 7 is perpendicular to the sample 8 under test, i.e., the depth direction. The piezoelectric ceramic platform 6 can support the objective lens 7 to perform nanometer-level scanning of the sample 8 under test along the depth direction at equal intervals. Interference can occur within the objective lens 7. The light beam reflected by the sample 8 under test returns from the original optical path, is transmitted through the beam splitter 5, and is focused by the second lens 4 onto the camera 3, recording the positions where interference fringes appear and disappear. The camera 3 is used for continuous acquisition at equal intervals. In this embodiment, the sample 8 under test is a smooth silicon wafer. When there is only one interference fringe in the field of view, the positions where the interference fringe appears and disappears are recorded. The scanning step size is 100 nm, and 117 frames of images are continuously acquired. The 70th frame of the interference image is shown below. Figure 4 As shown in (b).
[0055] In one embodiment, objective 7 is a Mirau interference objective. Alternatively, other commonly used interference objectives known to those skilled in the art may also be used.
[0056] In one embodiment, the piezoelectric ceramic platform 6, equipped with an animal mirror 7, performs equally spaced nanoscale scanning of the sample under test.
[0057] In one embodiment, the beam splitter 5 is a 45° beam splitter prism.
[0058] In one embodiment, the camera 3 acquires the interference image of the sample under test when there is only one interference fringe in the field of view, and the scanning step of the objective lens 7 is 100 nm.
[0059] In one embodiment, the surface of the sample being tested is a smooth surface.
[0060] S2. Preprocess the acquired interferometric image. The preprocessing includes:
[0061] S21. Locate the interference regions in all interferometric images to obtain the interferometric image to be reconstructed, as follows:
[0062] S211. Obtain the maximum scaling factor k max The formula is as follows:
[0063]
[0064] k max =max{k2,k3,...,k n ,…,k N};
[0065] In the formula, I(n) represents the interference light intensity distribution when the number of scanning steps is n, and k nThe scaling factor is n when the number of scanning steps is n, where n = 2 to N, and N is the number of scanning steps of the white light interference system, i.e., the number of frames of the interference image;
[0066] S212, Set the maximum scaling factor k max Interference images preceding the corresponding scan step number when they appear are considered redundant data and deleted. The retained interference images are then used as the interference images to be reconstructed to complete the localization of the interference interval.
[0067] S22. Divide each interferometric image to be reconstructed into several regions, and reduce the number of pixels in each region to complete the region pixel reconstruction and obtain the corresponding reconstructed image.
[0068] In one embodiment, each interferometric image to be reconstructed is divided into several regions, and the number of pixels in each region is reduced to complete the region pixel reconstruction, as follows:
[0069] S221. Let the upper left corner of the interferometric image to be reconstructed be the image origin. Divide the interferometric image to be reconstructed into several regions with four adjacent pixels as the unit.
[0070] S222. Perform region pixel reconstruction for each region. The reconstruction formula is as follows:
[0071] I′(i / 2,j / 2)=(I(i-1,j-1)+I(i,j-1)+I(i-1,j)+I(i,j)) / 4;
[0072] In the formula, I′(i / 2,j / 2) is the gray value of the reconstructed region pixel, I(i,j) is the gray value of the pixel in the i-th row and j-th column of the interferometric image to be reconstructed, i,j∈M, and M is the total number of horizontal pixels or vertical pixels of the interferometric image to be reconstructed.
[0073] Image preprocessing, including interferometric interval localization and region pixel reconstruction, can effectively improve timeliness and reduce computational load. It performs interferometric interval localization on continuously acquired interferometric images, within k... n The maximum scaling factor k appears max When the positioning ends; in this embodiment, Therefore, the interferometric images before frame 32 can be considered redundant data and deleted, reducing the number of images from 117 frames to 86 frames. The interferometric images to be reconstructed in subsequent steps are these 86 frames, and the interferometric interval localization takes approximately 0.137 seconds. Then, region pixel reconstruction is performed on the interferometric images to be reconstructed. Since the calculation of pixel focus metric values usually requires selecting a certain neighborhood range of the pixel as the evaluation window, and using the average of the focus metric values of all pixels within this evaluation window as the evaluation function for that pixel, let's assume the top-left corner of the original interferometric image I is the image origin, and there are a total of M pixels along the horizontal or vertical direction. Starting from the top-left corner, taking four adjacent pixels as units, the average of their gray values is taken as a new reconstructed pixel gray value, and the reconstructed image is I′.
[0074] like Figure 3 As shown, the number of pixels in the image after region pixel reconstruction is halved, such as... Figure 3 (b) shows that the original interferometric image recorded had a pixel count of 500×500, which was reduced to 250×250 after reconstruction. The reconstruction took approximately 0.84 seconds. Figure 3 As shown in (a).
[0075] S3. Calculate the focus metric value of each pixel in each reconstructed image using the focus metric algorithm.
[0076] In one embodiment, the focusing metric algorithm is as follows:
[0077]
[0078] In the formula, FM(x,y) is the focus metric of the pixel coordinates (x,y) within the evaluation window, and G(x,y) is the gradient value of the pixel coordinates (x,y) within the evaluation window. G x G represents the lateral gradient value. y This represents the longitudinal gradient value. Ω represents the average gradient within the evaluation window, x represents the x-coordinate of a pixel within the evaluation window, and y represents the y-coordinate of a pixel within the evaluation window.
[0079] In this embodiment, a focus metric algorithm is used to calculate the focus metric value of each pixel in each frame of the reconstructed image. A 3×3 evaluation window is used. The focus topography measurement and reconstruction results in existing technologies are as follows: Figure 5 As shown, in addition to the effects of dust, both the upper and lower surfaces have a large amount of burr noise and pit defects. The calculation of the focus metric value of the original interferometric image took about 246.27 seconds, while the calculation of the focus metric value of the interferometric image after image preprocessing took about 50.77 seconds.
[0080] S4. Based on the improved centroid method, the zero optical path difference point of each pixel in the entire reconstructed image is found to recover the three-dimensional morphology of the sample under test. The formula of the improved centroid method is as follows:
[0081] m(n) = [FM(n) - FM(n-1)] 2 ;
[0082]
[0083] In the formula, FM(n) is the focus metric of pixel (x,y) when the number of scan steps is n, m(n) is the square of the difference between the focus metric of pixel (x,y) in the reconstructed images of two adjacent frames, and h is the height of the sample under test at pixel (x,y).
[0084] In this embodiment, the centroid of the curve, i.e., the zero optical path difference point, is found using the improved centroid method, thereby restoring the three-dimensional shape of the object. The image after preprocessing in this example consists of 86 frames. The reconstruction result according to the method provided by this invention is as follows: Figure 6 As shown, compared with the existing technology that only uses the focused topography restoration algorithm, the burr noise in other parts is greatly reduced except for the protrusions caused by dust on the upper surface. The original interferometric image improved centroid method takes about 4.5 seconds, and the image improved centroid method after image preprocessing takes about 0.98 seconds.
[0085] The total time for composite 3D topography reconstruction after image preprocessing is approximately 51.75 seconds. Including the reconstruction time, the total time for the method of this invention is approximately 52.727 seconds. The technical solution adopted in this invention greatly reduces the amount of computation and the noise of burrs, and improves the timeliness by nearly 5 times compared with the existing technical solution.
[0086] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0087] The embodiments described above are merely specific and detailed examples of the embodiments described in this application, and should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the appended claims.
Claims
1. A method for rapid reconstruction of three-dimensional topography using white light interference, applied to white light interference systems, characterized in that: The method for rapid reconstruction of three-dimensional topography by white light interference includes the following steps: S1. Use a white light interferometer system to continuously acquire N frames of interference images of the sample under test; S2. Preprocess the acquired interferometric image, the preprocessing including: S21. Locate the interference regions in all interferometric images to obtain the interferometric image to be reconstructed, as follows: S211. Obtain the maximum scaling factor k max The formula is as follows: k max =max{k2,k3,...,k n ,...,k N }; In the formula, I(n) represents the interference light intensity distribution when the number of scanning steps is n, and k n The scaling factor is n when the number of scanning steps is n, where n = 2 to N, and N is the number of scanning steps of the white light interference system, i.e., the number of frames of the interference image; S212, Set the maximum scaling factor k max Interference images preceding the corresponding scan step number when they appear are considered redundant data and deleted. The retained interference images are then used as the interference images to be reconstructed to complete the localization of the interference interval. S22. Divide each interferometric image to be reconstructed into several regions, and reduce the number of pixels in each region to complete the region pixel reconstruction and obtain the corresponding reconstructed image. S3. Calculate the focus metric value of each pixel in each reconstructed image using the focus metric algorithm; S4. Based on the improved centroid method, the zero optical path difference point of each pixel in the entire reconstructed image is found to recover the three-dimensional morphology of the sample under test. The formula of the improved centroid method is as follows: m(n)=[FM(n)-FM(n-1)] 2 ; In the formula, FM(n) is the focus metric of pixel (x,y) when the number of scan steps is n, m(n) is the square of the difference between the focus metric of pixel (x,y) in the reconstructed images of two adjacent frames, and h is the height of the sample under test at pixel (x,y).
2. The method for rapid reconstruction of three-dimensional topography by white light interference as described in claim 1, characterized in that: The focus metric algorithm is defined by the following formula: In the formula, FM(x,y) is the focus metric of the pixel coordinates (x,y) within the evaluation window, and G(x,y) is the gradient value of the pixel coordinates (x,y) within the evaluation window. G x G represents the lateral gradient value. y This represents the longitudinal gradient value. Ω represents the average gradient within the evaluation window, x represents the x-coordinate of a pixel within the evaluation window, and y represents the y-coordinate of a pixel within the evaluation window.
3. The method for rapid reconstruction of three-dimensional topography by white light interference as described in claim 1, characterized in that: The process involves dividing each interferometric image to be reconstructed into several regions, and reducing the number of pixels in each region to complete the region pixel reconstruction, as follows: S221. Let the upper left corner of the interferometric image to be reconstructed be the image origin. Divide the interferometric image to be reconstructed into several regions with four adjacent pixels as the unit. S222. Perform region pixel reconstruction for each region, and the reconstruction formula is as follows: I'(i / 2,j / 2)=(I(i-1,j-1)+I(i,j-1)+I(i-1,j)+I(i,j)) / 4; In the formula, I'(i / 2,j / 2) is the gray value of the reconstructed region pixel, I(i,j) is the gray value of the pixel in the i-th row and j-th column of the interferometric image to be reconstructed, i,j∈M, and M is the total number of horizontal pixels or vertical pixels of the interferometric image to be reconstructed.
4. The method for rapid reconstruction of three-dimensional topography by white light interferometry as described in claim 1, characterized in that: The white light interference system includes a white light source (1), a first lens (2), a camera (3), a second lens (4), a beam splitter (5), a piezoelectric ceramic platform (6), and an objective lens (7), wherein: The first lens (2) and the second lens (4) are located on opposite sides of the beam splitter (5) and their optical axes are perpendicular to each other. The objective lens (7) is mounted on the piezoelectric ceramic platform (6) and is driven by the piezoelectric ceramic platform (6) to scan the sample under test. The light emitted by the white light source (1) is collimated by the first lens (2) and reflected by the beam splitter (5). The reflected light passes through the piezoelectric ceramic platform (6) and the objective lens (7) in sequence and illuminates the sample under test. The light reflected by the sample under test passes through the objective lens (7) and the piezoelectric ceramic platform (6) in sequence and is transmitted through the beam splitter (5). The transmitted light is focused by the second lens (4) onto the camera (3) and the camera (3) acquires the interference image of the sample under test.
5. The method for rapid reconstruction of three-dimensional topography by white light interference as described in claim 4, characterized in that: The objective lens (7) is a Mirau interference objective lens.
6. The method for rapid reconstruction of three-dimensional topography by white light interference as described in claim 4, characterized in that: The piezoelectric ceramic platform (6) drives the objective lens (7) to perform equal-interval nanoscale scanning of the sample under test.
7. The method for rapid reconstruction of three-dimensional topography by white light interference as described in claim 4, characterized in that: The beam splitter (5) is a 45° beam splitter prism.
8. The method for rapid reconstruction of three-dimensional topography by white light interference as described in claim 4, characterized in that: The camera (3) acquires the interference image of the sample under test when there is only one interference fringe in the field of view, and the scanning step of the objective lens (7) is 100 nm.
9. The method for rapid reconstruction of three-dimensional topography by white light interference as described in any one of claims 1 to 8, characterized in that: The surface of the sample being tested is smooth.