Longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling

Abstract

The application discloses a longitudinal large-scale three-dimensional profile measurement method based on non-uniform sparse sampling, and belongs to the field of optical detection, and meets the demand of rapid detection of millimeter-level longitudinal large-size microstructure. Firstly, the number of interference patterns is greatly reduced through micron-level non-uniform interval sampling. On this basis, the non-uniform sparse sampling interference signal is reconstructed into a uniform interference signal through linear interpolation and sparse reconstruction. Finally, the three-dimensional profile information of the sample is accurately restored by using a sampling envelope algorithm. The application improves the interference pattern acquisition efficiency and reduces the interference pattern processing data amount through high-speed acquisition, and the measurement method has a measurement speed effectively improved and a recovery error less than one percent. The application is suitable for realizing the three-dimensional profile rapid detection of longitudinal large-scale microstructure samples in the fields of semiconductor manufacturing, optical processing, mechanical processing and the like.

Description

Technical Field

[0001] This invention belongs to the field of optical detection, specifically relating to a longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling. Background Technology

[0002] With the development of semiconductor manufacturing, optical processing, and mechanical processing, various structures can be mass-produced, which requires white light interferometers to achieve rapid batch detection of the three-dimensional contours of sample surfaces in the industrial field and improve detection efficiency. This poses a challenge to current white light interferometers.

[0003] As is well known, scanning white light interferometry is widely used for measuring the three-dimensional contours of sample surfaces. Its basic principle is to obtain the three-dimensional information of the sample by changing the optical path difference between the two arms through piezoelectric ceramics. Although scanning white light interferometry is characterized by high measurement accuracy, its algorithm requires a sampling interval that conforms to the Nyquist sampling theorem (one-eighth of the wavelength) and requires uniform sampling. For millimeter-scale (large-scale) samples, traditional white light algorithms require taking thousands of images, resulting in high computational load and long sampling time. Furthermore, the piezoelectric ceramics have a travel distance of only a few hundred micrometers, making it impossible to measure millimeter-scale samples.

[0004] To address the slow detection speed of existing white-light interferometry, some researchers have explored sparse sampling strategies. Ogawa, in his paper "Sampling Theorem for Surface Profiling by White-Light Interferometry," proposed a squared envelope algorithm to save computational costs. However, this method still relies on piezoelectric ceramics to drive uniform sampling of micrometer-scale samples. For millimeter-scale samples, non-uniform sampling and the use of high-speed motors with greater stroke are necessary. This invention, using a high-speed motor drive, further expands the sampling interval and employs a non-uniform sparse reconstruction method to achieve rapid three-dimensional topography measurement of large-scale longitudinal samples. Summary of the Invention

[0005] The purpose of this invention is to provide a fast three-dimensional topography measurement method based on non-uniform sparse sampling at a large longitudinal scale, so as to solve the problem of detection speed for wide-field, large-scale three-dimensional topography.

[0006] The technical solution to achieve the purpose of this invention is as follows: a method for rapid three-dimensional topography measurement at a large longitudinal scale based on non-uniform sparse sampling, comprising the following steps:

[0007] Step 1: Sample detection is performed by combining a Linnik-type interference optical path with a laser ranging optical path. Both optical paths are controlled by the same motor and move synchronously. In the near-infrared interference optical path, the CCD camera samples the interferogram, while the laser ranging optical path calculates the position information of the interferogram. Both are synchronously triggered by signals emitted by the motor. The CCD camera's target surface has a total of Each pixel.

[0008] Step 2: Determine the motor scanning speed and CCD camera frame rate Based on at least one within the coherence length of the light source The requirements of each sampling point are determined, and the bandwidth of the light source is calculated according to the coherence formula of the light source. In addition, the appropriate filter is replaced when the light source is in use.

[0009] Step 3: Obtain the first interference signal intensity matrix by performing sparse sampling during the scanning movement of the CCD camera. Its size is H represents the number of sampling points; the laser ranging optical path synchronously calculates the distance between the corresponding sampling points to obtain the first position information matrix. Its size is .

[0010] Step 4: Analyze the first position information matrix. Perform linear interpolation to obtain the second position information matrix. Size is H1 represents the number of sampling points after linear interpolation; then, the first interferometric signal intensity matrix A and the second position information matrix are combined. Perform a second interpolation to obtain the third interference signal intensity matrix. and the third position information matrix Their sizes are respectively and .

[0011] Step 5: Combine with the third interference signal intensity matrix and the third position information matrix Based on the bandpass sampling theorem and the principle of interference, the sparse reconstruction formula is derived, and the fourth interference signal intensity matrix is ​​obtained. and the fourth position information matrix The matrix The size is The size of matrix V is H2 represents the number of sampling points after sparse signal interpolation and restoration.

[0012] Step 6: Combine with the fourth interference signal intensity matrix and the fourth position information matrix According to the sampling envelope theorem, the sampling envelope data matrix is ​​obtained. Size is ; for the sampled envelope data matrix The centroid method was used to obtain the topographic data matrix. Size is .

[0013] Compared with the prior art, the significant advantages of this invention are:

[0014] (1) A processing method adapted to non-uniform sparse sampling interference signals was developed, which can restore the interference signal with sparse sampling points and ensure that the three-dimensional morphology of the sample can be restored even in variable speed motion.

[0015] (2) This invention meets the need for rapid detection of millimeter-scale longitudinal large-scale (≥100 μm) microstructures.

[0016] (3) By controlling the bandwidth of the light source, the maximum nominal sampling interval value can be changed to adapt to the rapid detection of samples of different heights. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the optical path of the experimental setup.

[0018] Figure 2 This is a flowchart of the fast three-dimensional topography measurement method for wide-field large-scale based on non-uniform sparse sampling according to the present invention.

[0019] Figure 3 This is a schematic diagram of the sample.

[0020] Figure 4 The third interference signal intensity matrix exist A diagram showing the time.

[0021] Figure 5 The fourth interference signal intensity matrix exist A diagram showing the time.

[0022] Figure 6 For the sampled envelope data matrix exist A diagram showing the time. Detailed Implementation

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0024] This invention addresses the drawback of white light interferometers being slow in detecting large-scale longitudinal samples. It proposes for the first time a rapid three-dimensional topography measurement method based on non-uniform sparse sampling for large-scale longitudinal samples. This method is applicable to non-uniform sparse sampling of millimeter-scale samples, effectively reducing data redundancy and improving the efficiency of instrument measurement.

[0025] Combination Figure 2 A fast three-dimensional topography measurement method based on non-uniform sparse sampling at a large longitudinal scale is proposed, with the following steps:

[0026] Step 1, as follows Figure 1 As shown, the sample is detected by combining Linnik-type interference optical path 1 with laser ranging optical path 2. Both optical paths are controlled by the same motor and move synchronously. In the near-infrared interference optical path, the CCD camera samples the interferogram, while the laser ranging optical path calculates the position information of the interferogram. Both are synchronously triggered by signals emitted by the motor. The CCD camera's target surface has a total of Each pixel.

[0027] Step 2: Determine the motor scanning speed and CCD camera frame rate Based on at least one within the coherence length of the light source Based on the requirements of each sampling point, the bandwidth of the light source is calculated according to the coherence formula of the light source, and a suitable filter is replaced at the light source.

[0028] The formula for calculating the coherence length of a light source is as follows:

[0029]

[0030] in, The center wavelength of the light source This represents the bandwidth of the light source.

[0031] Step 3: Obtain the first interference signal intensity matrix by performing sparse sampling during the scanning movement of the CCD camera. Its size is The laser ranging optical path synchronously calculates the distance between corresponding sampling points to obtain the first position information matrix. Its size is .

[0032] Step 4: Analyze the first position information matrix. Perform linear interpolation to obtain the second position information matrix. Size is Then, the first interference signal intensity matrix A and the second position information matrix are combined. Perform a second interpolation to obtain the third interference signal intensity matrix. and the third position information matrix Their sizes are respectively and .

[0033] The formula for linear interpolation is as follows:

[0034]

[0035] in, It is the second position information matrix The interval between two adjacent elements in the middle. This is the value of the last element of the first position information matrix Z. This is the first element value of the first position information matrix Z. Then, it is combined with the second position information matrix. The quadratic interpolation is performed between the first interference signal intensity matrix A and the matrix A, and the calculation formula is as follows:

[0036]

[0037] in, Let be the value of the i-th element at the x-th row and y-th column of the first interference signal intensity matrix A. This represents the value of the i-th element in the first position information matrix Z. Let be the value of the j-th element in the second position information matrix X.

[0038] Finally, the intensity matrix of the third interference signal is obtained. Size is Its element value is And let the third position information matrix be... Equal to the second position information X, with a size of .

[0039] Step 5: Combine with the third interference signal intensity matrix and the third position information matrix Based on the bandpass sampling theorem and the principle of interference, the sparse reconstruction formula is derived, and the fourth interference signal intensity matrix is ​​obtained. and the fourth position information matrix The matrix The size is ,matrix The size is .

[0040] Based on the bandpass sampling theorem and the principle of interference, an improved formula for sparse signal restoration is derived, and the calculation formula is as follows:

[0041]

[0042] In the formula, the horizontal axis The range of values ​​is y-axis The range of values ​​is , The range of values ​​is Let the range of values ​​for the elements in the fourth position information matrix V be... There are a total of H2 element values. This represents the element value in the fourth position information matrix V; These are the element values ​​in the third position information matrix Q; λ is the center wavelength of the light source; min(Q) is the minimum value in the third position information matrix Q; max(Q) is the maximum value in the third position information matrix Q; It is the interval value between two adjacent elements in the second position information matrix Q.

[0043] Step 6: Combine with the fourth interference signal intensity matrix and the fourth position information matrix According to the sampling envelope theorem, the sampling envelope data matrix is ​​obtained. Size is ; for the sampled envelope data matrix The centroid method was used to obtain the topographic data matrix. Size is .

[0044] The formula for calculating the sampling envelope theorem is as follows:

[0045]

[0046] In the formula, the horizontal axis The range of values ​​is y-axis The range of values ​​is The coefficient n is ,and" " indicates rounding down; The range of values ​​is .

[0047] Example 1:

[0048] Step 1, as follows Figure 1 As shown, a Linnik-type interference optical path and a laser ranging optical path are combined to detect the sample. Both optical paths are controlled by the same motor and move synchronously. In the near-infrared interference optical path, the CCD camera samples the interferogram, while the laser ranging optical path calculates the position information of the interferogram. Both are synchronously triggered by signals emitted by the motor. The target surface of the CCD camera has a total of 400×400 pixels. Figure 3 This is a schematic diagram of the sample, where the area within the dashed box represents the step section, and its three-dimensional shape needs to be reconstructed.

[0049] Step 2: The motor scanning speed is 5 mm / s and the CCD camera frame rate is 1000 fps. There are at least 10 sampling points within the coherence length of the light source, and the center wavelength of the light source is... It is 0.83 μm. The bandwidth is calculated using the formula above. Approximately 14 nm, select a matching filter.

[0050] Step 3: Obtain the first interference signal intensity matrix by performing sparse sampling during the scanning movement of the CCD camera. Its size is The laser ranging optical path synchronously calculates the distance between corresponding sampling points to obtain the first position information matrix. Its size is .

[0051] Step 4: Analyze the first position information matrix. Linear interpolation was performed with a sampling interval of 5 μm to obtain the second position information matrix. Size is Then, the first interference signal intensity matrix A and the second position information matrix are combined. Perform a second interpolation to obtain the third interference signal intensity matrix. and the third position information matrix Their sizes are respectively and The third interference signal intensity matrix exist Shi Ru Figure 4 As shown.

[0052] Step 5: Combine with the third interference signal intensity matrix and the third position information matrix Based on the bandpass sampling theorem and the principle of interference, the sparse reconstruction formula is derived, and the fourth interference signal intensity matrix is ​​obtained. and the fourth position information matrix The sampling interval is 1.67 μm. The matrix... The size is ,matrix The size is Fourth interference signal intensity matrix exist Shi Ru Figure 5 As shown.

[0053] Step 6: Combine with the fourth interference signal intensity matrix and the fourth position information matrix According to the sampling envelope theorem, the sampling envelope data matrix is ​​obtained. Size is Then, the sampled envelope data matrix... The centroid method is used to obtain the topographic data matrix. Size is Sampling envelope data matrix exist At times, such as Figure 6 As shown.

Claims

1. A method for measuring large-scale three-dimensional topography in the longitudinal direction based on non-uniform sparse sampling, characterized in that, The steps are as follows: Step 1: The sample is detected using both a Linnik-type interference optical path and a laser ranging optical path. Both optical paths are controlled by the same motor and move synchronously. The motor emits signals to trigger both optical paths synchronously. The near-infrared interference optical path uses a CCD camera to acquire the interference pattern of the sample, while the laser ranging optical path calculates the position information of the interference pattern. Assume the CCD camera target surface has a total of... 1 pixel; Step 2: Determine the motor scanning speed as follows Camera frame rate Based on at least one within the coherence length of the light source Based on the requirements of each sampling point, the bandwidth of the light source is calculated using the coherence length formula, and a matching filter is placed at the light outlet of the light source. Step 3: The CCD camera performs sparse sampling during scanning movement to obtain the first interference signal intensity matrix. Its size is The laser ranging optical path synchronously calculates the distance between the corresponding sampling points to obtain the first position information matrix. Its size is ; Step 4: Analyze the first position information matrix. Perform linear interpolation to obtain the second position information matrix. Size is H1 represents the number of sampling points after linear interpolation, combined with the first interferometric signal intensity matrix. Second position information matrix After performing a second interpolation, the third interference signal intensity matrix is ​​obtained. and the third position information matrix Their sizes are respectively and ; Step 5: Combine with the third interference signal intensity matrix and the third position information matrix Based on the bandpass sampling theorem and the principle of interference, the sparse reconstruction formula is derived, and the fourth interference signal intensity matrix is ​​obtained. and the fourth position information matrix The fourth interference signal intensity matrix The size is Fourth position information matrix The size is H2 represents the number of sampling points after the sparse signal is restored; Step 6: Combine with the fourth interference signal intensity matrix and the fourth position information matrix According to the sampling envelope theorem, the sampling envelope data matrix is ​​obtained. Size is ; For the sampled envelope data matrix The centroid method was used to obtain the topographic data matrix. Size is .

2. The longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, characterized in that, In step 2, the formula for the coherence length L of the light source is as follows: ， in, The center wavelength of the light source This represents the bandwidth of the light source.

3. The longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, characterized in that, Step 4, process the first position information matrix. Perform linear interpolation to obtain the second position information matrix. Size is H1 represents the number of sampling points after linear interpolation, combined with the first interferometric signal intensity matrix. Second position information matrix Perform a second interpolation to obtain the third interference signal intensity matrix. and the third position information matrix The details are as follows: For the first position information matrix The second position information matrix is ​​obtained by performing linear interpolation. Size is The calculation formula is as follows: ， in, It is the second position information matrix The interval between two adjacent elements in the middle. This is the value of the last element of the first position information matrix Z. This is the value of the first element of the first position information matrix Z; Combined with the second position information matrix With the first interference signal intensity matrix The formula for quadratic interpolation is as follows: ， in, Let be the value of the i-th element at the x-th row and y-th column of the first interference signal intensity matrix A. This represents the value of the i-th element in the first position information matrix Z. This represents the value of the j-th element in the second position information matrix X; Finally, the intensity matrix of the third interference signal is obtained. Size is Its elements are And let the third position information matrix be... Equal to the second position information X, with a size of .

4. The longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, characterized in that, In step 5, the third interference signal intensity matrix is ​​combined. and the third position information matrix Based on the bandpass sampling theorem and the principle of interference, the sparse reconstruction formula is derived, and the fourth interference signal intensity matrix is ​​obtained. and the fourth position information matrix The fourth interference signal intensity matrix The size is Fourth position information matrix The size is The details are as follows: The improved formula for sparse signal reconstruction is as follows: ， In the formula, the horizontal axis The range of values ​​is y-axis The range of values ​​is Let the fourth position information matrix be... The range of values ​​for the elements in the middle is: There are a total of Each element value This represents the element value in the fourth position information matrix V; These are the element values ​​in the third position information matrix Q; The wavelength is the center wavelength of the light source; min(Q) is the minimum value in the third position information matrix Q; max(Q) is the maximum value in the third position information matrix Q; It is the second position information matrix The interval between two adjacent elements.

5. The longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 4, characterized in that, In step 6, the fourth interference signal intensity matrix is ​​combined. and the fourth position information matrix According to the sampling envelope theorem, the envelope data matrix is ​​obtained. Size is ; For the sampled envelope data matrix The centroid method was used to obtain the topographic data matrix. The details are as follows: The formula for calculating the sampling envelope theorem is as follows: ， In the formula, the horizontal axis The range of values ​​is y-axis The range of values ​​is The coefficient n is ,and" " indicates rounding down, That is, the elements in the fourth position information matrix V; For the sampled envelope data matrix The centroid method is used to obtain the topographic data matrix. .

Images