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

Abstract

The invention discloses a longitudinal large-scale three-dimensional shape measurement method based on non-uniform sparse sampling, belongs to the field of optical detection, and meets the requirement for rapid detection of a millimeter-level longitudinal large-size microstructure. Firstly, the number of interferograms is greatly reduced through micron-sized non-uniform interval sampling; on the basis, non-uniform sparse sampling interference signals are reconstructed into uniform interference signals through linear interpolation and sparse reconstruction. And finally, accurately recovering the three-dimensional shape information of the sample by using a sampling envelope algorithm. According to the method, the interference pattern acquisition efficiency is improved and the interference pattern processing data volume is reduced through high-speed acquisition, and the recovery error of the measurement method is less than 1% while the measurement speed is effectively improved. The method is suitable for realizing rapid detection of the three-dimensional shape of the longitudinal large-scale microstructure sample in the fields of semiconductor manufacturing, optical processing, machining and the like.

Description

Technical Field

[0001] The present invention belongs to the field of optical detection, and particularly relates to a longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling. Background Art

[0002] With the development in fields such as semiconductor manufacturing, optical processing, and machining, various structures can be mass-produced, thus requiring a white light interferometer to be able to rapidly and batch-detect the three-dimensional profile of a sample surface in the industrial field to improve the detection efficiency, which poses a challenge to the current white light interferometer.

[0003] As is well known, a scanning white light interferometer is widely used in the measurement of the three-dimensional profile of a sample surface. Its basic principle is to drive a piezoelectric ceramic to change the optical path difference between two arms to obtain the three-dimensional information of the sample. Although the scanning white light interferometer has the characteristic of high measurement accuracy, the sampling interval required by its algorithm is the Nyquist sampling theorem (one-eighth wavelength), and uniform sampling is required. For millimeter-scale (large-scale) samples, the traditional white light algorithm needs to take thousands of photos, with a large amount of calculation and a long sampling time. At the same time, the piezoelectric ceramic has a movement stroke of only a few hundred micrometers and cannot measure millimeter-scale samples.

[0004] In response to the problem of the slow detection speed of the existing white light interferometer, some scholars have studied sparse sampling strategies. Ogawa proposed a square envelope algorithm in "Sampling Theorem for Surface Profiling by White-Light Interferometry" to save calculation costs, but the implementation of this method also uses a piezoelectric ceramic to drive for uniform sampling of micrometer-scale samples. For millimeter-scale samples, non-uniform sampling needs to be considered and a high-speed motor with a larger stroke is required. In the context of being driven by a high-speed motor, the present invention realizes rapid three-dimensional topography measurement of longitudinal large-scale samples by further expanding the sampling interval and using a non-uniform sparse reconstruction method. Summary of the Invention

[0005] The purpose of the present invention is to provide a longitudinal large-scale rapid three-dimensional topography measurement method based on non-uniform sparse sampling to solve the problem of the detection speed of wide-field large-scale three-dimensional topography.

[0006] The technical solution for realizing the purpose of the present invention is as follows: A longitudinal large-scale rapid three-dimensional topography measurement method based on non-uniform sparse sampling, the steps are as follows:

[0007] Step 1: Detect the sample by combining the Linnik-type interference optical path and the 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 interference pattern, while the laser ranging optical path calculates the position information of the interference pattern. Both are synchronously triggered by the signal emitted by the motor. The target surface of the CCD camera has M×N pixel points.

[0008] Step 2: Determine the motor scanning speed v and the CCD camera frame rate f. According to the requirement that there are at least n sampling points within the coherence length of the light source, calculate the bandwidth of the light source at this time according to the coherence formula of the light source, and replace the appropriate filter in the light source.

[0009] Step 3: Perform sparse sampling during the scanning movement of the CCD camera to obtain the first interference signal intensity matrix A, whose size is M×N×H, where H represents the number of sampling points; the laser ranging optical path synchronously calculates the distances between the corresponding sampling points to obtain the first position information matrix Z, whose size is 1×H.

[0010] Step 4: Perform linear interpolation on the first position information matrix Z to obtain the second position information matrix X, whose size is 1×H1, where H1 represents the number of sampling points after linear interpolation; then combine the first interference signal intensity matrix A and the second position information matrix X for quadratic interpolation to obtain the third interference signal intensity matrix C and the third position information matrix Q, whose sizes are M×N×H1 and 1×H1 respectively.

[0011] Step 5: Combine the third interference signal intensity matrix C and the third position information matrix Q, and derive the sparse reconstruction formula based on the band-pass sampling theorem and the interference principle to obtain the fourth interference signal intensity matrix D and the fourth position information matrix V. Among them, the size of matrix D is M×N×H2, and the size of matrix V is 1×H2, where H2 represents the number of sampling points after the sparse signal interpolation and restoration.

[0012] Step 6: Combine the fourth interference signal intensity matrix D and the fourth position information matrix V, and obtain the sampling envelope data matrix F according to the sampling envelope theorem, whose size is M×N×H2; use the centroid method for the sampling envelope data matrix F to obtain the topography data matrix P, whose size is M×N.

[0013] Compared with the prior art, the remarkable advantages of the present invention are as follows:

[0014] (1) Developed a processing method for adapting to non-uniform sparse sampling interference signals, which can restore the interference signal with sparse sampling points and ensure that the three-dimensional topography of the sample can be restored even during variable-speed movement.

[0015] (2) The present invention meets the requirements for rapid detection of millimeter-level longitudinal large-scale (≥100um) microstructures.

[0016] (3) By controlling the bandwidth of the light source and changing the maximum nominal sampling interval value, it is applicable to the rapid detection of samples with different heights. Description of the Drawings

[0017] Figure 1 It is a schematic diagram of the optical path of the experimental device.

[0018] Figure 2 It is a flow chart of the wide-field large-scale rapid three-dimensional topography measurement method based on non-uniform sparse sampling of the present invention.

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

[0020] Figure 4 It is a schematic diagram of the third interference signal intensity matrix C at (200, 200).

[0021] Figure 5 It is a schematic diagram of the fourth interference signal intensity matrix D at (200, 200).

[0022] Figure 6 It is a schematic diagram of the sampling envelope data matrix F at (200, 200). Detailed Description of the Invention

[0023] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be given in conjunction with the drawings in the specification.

[0024] Aiming at the defect that the white light interferometer has a slow detection speed for longitudinally large-scale samples, the present invention first proposes a longitudinal large-scale rapid three-dimensional topography measurement method based on non-uniform sparse sampling, which is applicable to the non-uniform sparse sampling of millimeter-level samples, effectively reducing data redundancy and improving the measurement efficiency of the instrument.

[0025] Combined with Figure 2 , a longitudinal large-scale rapid three-dimensional topography measurement method based on non-uniform sparse sampling is as follows:

[0026] Step 1: As Figure 1 shown, the sample is detected by combining the Linnik-type interference optical path 1 and the 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 interference pattern, while the laser ranging optical path calculates the position information of the interference pattern. Both are synchronously triggered by the signal emitted by the motor. The target surface of the CCD camera has a total of M×N pixel points.

[0027] Step 2: Determine the motor scanning speed v and the CCD camera frame rate f. According to the requirement that there are at least n1 sampling points within the coherence length of the light source, calculate the bandwidth of the light source at this time according to the coherence formula of the light source, and replace the filter at the light source with a suitable one.

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

[0029]

[0030] Among them, λ c is the central wavelength of the light source, and Δλ is the bandwidth of the light source.

[0031] Step 3: According to the CCD camera, perform sparse sampling during the scanning movement to obtain the first interference signal intensity matrix A, with a size of M×N×H; synchronously calculate the distances between the corresponding sampling points in the laser ranging optical path to obtain the first position information matrix Z, with a size of 1×H.

[0032] Step 4: Perform linear interpolation on the first position information matrix Z to obtain the second position information matrix X, with a size of 1×H1. Then, combine the first interference signal intensity matrix A and the second position information matrix X to perform quadratic interpolation to obtain the third interference signal intensity matrix C and the third position information matrix Q, with sizes of M×N×H1 and 1×H1 respectively.

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

[0034] Δ1 = (Z(H) - Z(1)) / (H - 1)

[0035] Among them, Δ1 is the interval value between two adjacent elements in the second position information matrix X, Z(H) is the value of the last element in the first position information matrix Z, and Z(1) is the value of the first element in the first position information matrix Z. Then, combine the second position information matrix X and the first interference signal intensity matrix A to perform quadratic interpolation. The calculation formula is as follows:

[0036]

[0037] Among them, A(x, y, i) is the value of the i-th element at the pixel point in the x-th row and y-th column of the first interference signal intensity matrix A. Z i is the i-th element in the first position information matrix Z, and X j is the j-th element in the second position information matrix X.

[0038] Finally, obtain the third interference signal intensity matrix C, with a size of M×N×H1, and its element value is C(x, y, j); and assume that the third position information matrix Q is equal to the second position information X, with a size of 1×H1.

[0039] Step 5: Combine the third interference signal intensity matrix C and the third position information matrix Q, and derive a sparse reconstruction formula based on the bandpass sampling theorem and the interference principle to obtain the fourth interference signal intensity matrix D and the fourth position information matrix V. The size of matrix D is M×N×H2, and the size of matrix V is 1×H2.

[0040] Derive an improved sparse signal restoration formula based on the bandpass sampling theorem and the interference principle. The calculation formula is as follows:

[0041]

[0042] In the formula, the value range of the abscissa x is (1:1:M), the value range of the ordinate y is (1:1:N), and the value range of z is (1:1:H2). Let the value range of the elements in the fourth position information matrix V be There are a total of H2 element values, and z represents the element value in the fourth position information matrix V; z1 is the element value in the third position information matrix Q; λ c is the central 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; Δ1 is the interval value between two adjacent elements in the second position information matrix Q.

[0043] Step 6: Combine the fourth interference signal intensity matrix D and the fourth position information matrix V, and obtain the sampling envelope data matrix F with a size of M×N×H2 according to the sampling envelope theorem; use the centroid method for the sampling envelope data matrix F to obtain the topography data matrix P with a size of M×N.

[0044] The calculation formula of the sampling envelope theorem is as follows:

[0045]

[0046] In the formula, the value range of the abscissa x is (1:1:M), the value range of the ordinate y is (1:1:N), and the coefficient n is and represents rounding down; the value range of z is (1:1:H2).

[0047] Example 1:

[0048] Step 1: As Figure 1 shown, detect the sample by combining the Linnik-type interference optical path and the laser ranging optical path. Both optical paths are controlled by the same motor for synchronous movement. In the near-infrared interference optical path, the CCD camera samples the interference pattern, while the laser ranging optical path calculates the position information of the interference pattern. Both are synchronously triggered by the signal emitted by the motor. The target surface of the CCD camera has 400×400 pixel points. Figure 3This is a schematic diagram of the sample. The stepped part is within the dashed box, and its three-dimensional morphology needs to be restored.

[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. The central wavelength λ of the light source c is 0.83 μm. Calculate the bandwidth Δλ to be approximately 14 nm according to the above formula, and select a matching filter.

[0050] Step 3: Perform sparse sampling during the scanning movement of the CCD camera to obtain the first interference signal intensity matrix A, with a size of 400×400×100; synchronously calculate the distances between the corresponding sampling points in the laser ranging optical path to obtain the first position information matrix Z, with a size of 1×100.

[0051] Step 4: Perform linear interpolation on the first position information matrix Z with a sampling interval of 5 μm to obtain the second position information matrix X with a size of 1×100. Then, combine the first interference signal intensity matrix A and the second position information matrix X for quadratic interpolation to obtain the third interference signal intensity matrix C and the third position information matrix Q, with sizes of 400×400×100 and 1×100 respectively. When the third interference signal intensity matrix C is at (200, 200), as Figure 4 shown.

[0052] Step 5: Combine the third interference signal intensity matrix C and the third position information matrix Q, and derive the sparse reconstruction formula based on the band-pass sampling theorem and the interference principle to obtain the fourth interference signal intensity matrix D and the fourth position information matrix V, with a sampling interval of 1.67 μm. The size of matrix D is 400×400×300, and the size of matrix V is 1×300. When the fourth interference signal intensity matrix D is at (200, 200), as Figure 5 shown.

[0053] Step 6: Combine the fourth interference signal intensity matrix D and the fourth position information matrix V, and obtain the sampling envelope data matrix F with a size of 400×400×300 according to the sampling envelope theorem; then use the centroid method on the sampling envelope data matrix F to obtain the morphology data matrix P with a size of 400×400. When the sampling envelope data matrix F is at (200, 200), as Figure 6 shown.

Claims

1. A longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling, characterized in that, The steps are as follows: Step 1: Use a Linnik-type interference optical path and a laser ranging optical path to jointly detect the sample. The above two optical paths are controlled by the same motor and perform synchronous movement. The motor emits a signal to synchronously trigger the two optical paths; the near-infrared interference optical path uses a CCD camera to collect the interference pattern of the sample, and the laser ranging optical path calculates the position information of the interference pattern; assume that the target surface of the CCD camera has a total of M×N pixel points; Step 2: Determine the motor scanning speed as v and the camera frame rate as f. According to the requirement of at least H sampling points within the coherence length of the light source, calculate the bandwidth of the light source at this time by combining the light source coherence length formula, and place a matching filter at the light output port of the light source; Step 3: The CCD camera performs sparse sampling during the scanning movement to obtain the first interference signal intensity matrix A, with a size of M×N×H. The laser ranging optical path synchronously calculates the distances between the corresponding sampling points to obtain the first position information matrix Z, with a size of 1×H; Step 4: Perform linear interpolation on the first position information matrix Z to obtain the second position information matrix X, with a size of 1×H1, where H1 represents the number of sampling points after linear interpolation. After performing quadratic interpolation by combining the first interference signal intensity matrix A and the second position information matrix X, obtain the third interference signal intensity matrix C and the third position information matrix Q, with sizes of M×N×H1 and 1×H1 respectively; Step 5: Combine the third interference signal intensity matrix C and the third position information matrix Q, and derive the sparse reconstruction formula based on the bandpass sampling theorem and the interference principle to obtain the fourth interference signal intensity matrix D and the fourth position information matrix V; where the size of the fourth interference signal intensity matrix D is M×N×H2, and the size of the fourth position information matrix V is 1×H2, and H2 represents the number of sampling points after the sparse signal is restored; Step 6: Combine the fourth interference signal intensity matrix D and the fourth position information matrix V, and obtain the sampling envelope data matrix F, with a size of M×N×H2, according to the sampling envelope theorem; Use the centroid method for the sampling envelope data matrix F to obtain the topography data matrix P, with a size of M×N.

2. The longitudinal large-scale three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, wherein, In Step 2, the formula for the light source coherence length L is as follows: where λ c is the central wavelength of the light source, and Δλ is the bandwidth of the light source.

3. The longitudinal large-scale fast three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, characterized in that In Step 5, perform linear interpolation on the first position information matrix Z to obtain the second position information matrix X, with a size of 1×H1, where H1 represents the number of sampling points after linear interpolation. After performing quadratic interpolation by combining the first interference signal intensity matrix A and the second position information matrix X, obtain the third interference signal intensity matrix C and the third position information matrix Q, specifically as follows: Perform linear interpolation on the first position information matrix Z to obtain the second position information matrix X, with a size of 1×H1, and the calculation formula is as follows: Δ1 = (Z(H) - Z(1)) / (H - 1) where Δ1 is the interval value between two adjacent elements in the second position information matrix X, Z(H) is the value of the last element of the first position information matrix Z, and Z(1) is the value of the first element of the first position information matrix Z; Perform quadratic interpolation processing by combining the second position information matrix X and the first interference signal intensity matrix A, and the calculation formula is as follows: Among them, A(x, y, i) is the value of the i-th element at the pixel point in the x-th row and y-th column of the first interference signal intensity matrix A, and Z i is the value of the i-th element in the first position information matrix Z, and X j is the value of the j-th element in the second position information matrix X; Finally, the third interference signal intensity matrix C with a size of M×N×H1 is obtained, and its elements are C(x,y,j); and let the third position information matrix Q be equal to the second position information X with a size of 1×H1.

4. The longitudinal large-scale fast three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, characterized in that In step 6, the third interference signal intensity matrix C and the third position information matrix Q are combined, and a sparse reconstruction formula is derived based on the band-pass sampling theorem and the interference principle to obtain the fourth interference signal intensity matrix D and the fourth position information matrix V; where the size of the fourth interference signal intensity matrix D is M×N×H2, and the size of the fourth position information matrix V is 1×H2, which is specifically as follows: The improved sparse signal reduction calculation formula is as follows: In the formula, the value range of the abscissa x is (1:1:M), the value range of the ordinate y is (1:1:N), and it is assumed that the value range of the elements in the fourth position information matrix V is There are a total of H2 element values, z represents the element value in the fourth position information matrix V; z1 is the element value in the third position information matrix Q; λ c is the central 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; Δ1 is the interval value between two adjacent elements in the second position information matrix X.

5. The longitudinal large-scale fast three-dimensional topography measurement method based on non-uniform sparse sampling according to claim 1, characterized in that In step 7, the fourth interference signal intensity matrix D and the fourth position information matrix V are combined, and according to the sampling envelope theorem, the envelope data matrix F with a size of M×N×H2 is obtained; the centroid method is used for the sampling envelope data matrix F to obtain the topography data matrix P, which is specifically as follows: The calculation formula of the sampling envelope theorem is as follows: wherein, the value range of the abscissa x is (1:1:M), the value range of the ordinate y is (1:1:N), and the coefficient n is and represents rounding down, and z represents the element in the fourth position information matrix V; The centroid method is used for the sampling envelope data matrix F to obtain the topography data matrix P.

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