Method for eliminating artifacts in scanning white light interferometry

Abstract

The invention relates to the technical field of scanning white light interference, in particular to a method for eliminating artifacts in scanning white light interference measurement, which comprises the following steps of: obtaining a white light interference signal of a certain pixel point at a certain position in an optical axis direction from a collected white light interference pattern; calculating initial height distribution of the surface of the measured object by adopting a common reference point-based generalized cross-correlation algorithm; if an artifact exists, selecting an adjacent reference point in the artifact area, calculating a relative height difference between each pixel point in the artifact area and the adjacent reference point through a generalized cross-correlation algorithm based on the adjacent reference point, and calculating a relative height difference between each pixel point in the artifact area and the adjacent reference point; and performing artifact correction on the initial height distribution according to the initial height distribution to obtain new height distribution meeting a preset correction precision requirement. And if the artifacts do not exist, directly outputting the initial height distribution. According to the method, the problem that artifacts appear in a reconstruction result due to white light interference signal distortion in the scanning white light interferometry can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of scanning white light interferometry, and particularly to a method for eliminating artifacts in scanning white light interferometry. Background Art

[0002] Scanning white light interferometry is a three-dimensional surface profile measurement technology with the advantages of non-contact, wide measurement range, and high precision, and has been widely used in the fields of microstructure detection, ultra-precision machining, thin film measurement, and surface roughness evaluation. This technology uses a broadband light source with a short coherence length, and the interference intensity reaches the maximum only when the optical path difference between the reference light and the object light is zero, so as to realize the surface profile measurement without 2π ambiguity. However, when the surface gradient of the object to be measured is large, the white light interference signal is easily distorted, resulting in artifacts in the reconstruction result, that is, there are incorrect height jumps that are integer multiples of the central wavelength of the illumination light source, rather than the features actually existing on the surface of the object to be measured. This artifact phenomenon seriously affects the measurement accuracy and reliability of scanning white light interferometry. Summary of the Invention

[0003] The purpose of the present invention is to propose a method for eliminating artifacts in scanning white light interferometry, which can solve the technical problem that artifacts appear in the reconstruction result due to the distortion of the white light interference signal in scanning white light interferometry.

[0004] To achieve this purpose, the present invention adopts the following technical solutions:

[0005] A method for eliminating artifacts in scanning white light interferometry includes the following steps:

[0006] S1. Collect white light interference patterns at different positions of the object to be measured in the optical axis direction, and obtain the white light interference signal of a certain pixel point at a certain position in the optical axis direction through preprocessing, including the white light interference signal of the measurement point and the white light interference signal of the common reference point;

[0007] S2. According to the white light interference signal of the measurement point and the white light interference signal of the common reference point, calculate the preliminary height distribution of the surface of the object to be measured by using the generalized cross-correlation algorithm based on the common reference point;

[0008] S3. Use the adjacent point cross-correlation accumulation algorithm to accurately locate the artifact area in the preliminary height distribution of the object to be measured. If there is an artifact area, go to step S4; if there is no artifact area, directly output the preliminary height distribution;

[0009] S4. Select adjacent reference points in the artifact area, calculate the relative height difference between each pixel point in the artifact area and the adjacent reference points by using the generalized cross-correlation algorithm based on the adjacent reference points, and perform artifact correction on the preliminary height distribution accordingly to obtain a new height distribution;

[0010] S5. Iteratively apply the previous step S4 until the new height distribution meets the preset correction accuracy requirement, and output the final new height distribution.

[0011] Preferably, in S1, the following steps are specifically included:

[0012] S11. Define the white light interference signal of a pixel at a certain position along the optical axis in the white light interference pattern as:

[0013]

[0014] Wherein, z represents the vertical scanning distance along the optical axis; m and n represent pixel coordinates, m=1,2,…,M-1,M, n=1,2,…,N-1,N, M and N represent the maximum number of pixels in the y direction and x direction respectively; a(m,n) represents the background intensity; h(m,n) represents the actual surface height of the object being measured; g[zh(m,n)] represents the coherence envelope; represents the phase shift; λ 0 represents the central wavelength of the light source; η represents random noise;

[0015] S12, remove the background intensity and some random noise in the white light interference pattern by numerical filtering, and obtain the white light interference signal of a certain pixel point at a certain position along the optical axis direction:

[0016]

[0017] Preferably, in S2, the following steps are specifically included:

[0018] S21, using the generalized cross-correlation algorithm based on the common reference point, obtain the measured point P (m 1 ,n 1 ) of the white light interference signal I(m 1 ,n 1 ,z) and the common reference point CRP(m CRP ,n CRP ) of the white light interference signal I(m CRP ,n CRP ,z)’s cross-correlation results:

[0019]

[0020] Among them, f z represents the frequency variable relative to z, and the symbol "*" represents the complex conjugate operation. and Respectively represent I(m CRP ,n CRP ,z) and I(m 1 ,n 1 ,z), Denotes the inverse Fourier transform, C CRP&P The maximum value in CRP&P (z) represents the relative height difference between the point to be measured and the common reference point, that is, the preliminary height distribution of the surface of the object to be measured.

[0021] Preferably, in S3, it specifically includes the following steps:

[0022] S31. Use the adjacent point cross-correlation accumulation algorithm to calculate the height distribution h 1 of the first column of pixel points in the artifact area of 1 (m,n), and set h 2 (m,1), and set h 2 (1,1) = 0nm;

[0023] S32. Calculate the height difference d between each pixel point (m′,1) in the first column and the previous pixel point (m′-1,1):

[0024]

[0025] d = find{C(z) = max[C(z)]}

[0026] where m′ = 2,…,M - 1,M;

[0027] S33. Calculate row by row to obtain the new height distribution h 2 (m,n);

[0028] S34. Calculate the difference map of the preliminary height distribution h 1 (m,n) and the new height distribution h 2 (m,n) along the x direction;

[0029] D i (p,q) = h i (m,n′) - h i (m,n′ - 1), i = 1,2

[0030] where n′ = 2,…,N - 1,N, p = 1,2,…,M - 1,M, q = 1,2,…,N - 1;

[0031] S34. To distinguish the influence of artifacts and noise, set a threshold: ε = λ 0 / 4; if D 1 (p,q) - D 2 (p,q) ≥ ε, then the pixel point (p,q) is defined as a boundary pixel point; otherwise, it is not defined;

[0032] S35. When determining all the boundary pixels {q 1 ,q 2 ,…,q k}, after 0 ≤ k ≤ K, the artifact region (GSR) is expressed as:

[0033]

[0034] Preferably, in S4, it specifically includes the following steps:

[0035] S41. For the i-th artifact region in the p-th row, h GSR (m, i) = {h 1 (m, n) | q 2i-1 -1 < n < q 2i} and select the nearest pixel (p, q 2i-1 -1) as the adjacent reference point;

[0036] S42. Use the generalized cross-correlation method based on the adjacent reference point to calculate the relative height difference between all pixel points in the artifact region and their corresponding adjacent reference points, and replace the height of the corresponding pixel points in the preliminary height distribution h 1 (m, n).

[0037] One of the above technical solutions has the following beneficial effects:

[0038] 1. Improve measurement accuracy: By using the signal characteristics of adjacent points for cross-correlation operation to correct errors, the morphology of high surface gradient samples can be accurately restored, artifacts can be effectively eliminated, and thus the measurement accuracy can be significantly improved.

[0039] 2. Enhance adaptability: There are no specific requirements for the signal source, and there is no need to shape or correct the signal. Therefore, it has strong adaptability and flexibility. It can be applied to different types of samples and measurement environments to meet the needs of different fields.

[0040] 3. Expand the application range: By eliminating artifacts, the application ability of scanning white light interferometry in the field of precision measurement is improved. It can be used not only to measure the flat sample surface, but also to measure samples with complex morphology and high surface gradient, providing strong technical support for scientific research, industrial production and other fields. Brief Description of the Drawings

[0041] Figure 1 is the flow schematic diagram of the present invention;

[0042] Figure 2 is the experimental optical path diagram of the Linnik type scanning white light interference system in the first to third embodiments of the present invention;

[0043] Figure 3 is the measurement result of the generalized cross-correlation algorithm based on the common reference point for the 120-nanometer-high step located on the optically smooth surface in the second embodiment of the present invention;

[0044] Figure 4 Measurement results of the generalized cross - correlation algorithm based on adjacent reference points for a 120 - nanometer - high step located on an optically smooth surface in the second embodiment of the present invention;

[0045] Figure 5 Cross - sectional comparison between the measurement results of the generalized cross - correlation algorithm based on a common reference point and the measurement results of the generalized cross - correlation method based on adjacent reference points for a 120 - nanometer - high step located on an optically smooth surface in the second embodiment of the present invention;

[0046] Figure 6 Measurement results of the generalized cross - correlation algorithm based on a common reference point using complex multi - elevation steps in the third embodiment of the present invention;

[0047] Figure 7 Measurement results of the generalized cross - correlation algorithm based on adjacent reference points using complex multi - elevation steps in the third embodiment of the present invention;

[0048] Figure 8 Cross - sectional comparison between the measurement results of the generalized cross - correlation algorithm based on a common reference point and the measurement results of the generalized cross - correlation method based on adjacent reference points using complex multi - elevation steps in the third embodiment of the present invention. Detailed implementation manners

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings and through specific implementation manners.

[0050] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention.

[0051] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0052] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, or an indirect connection through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0053] As Figure 1 shown, a method for eliminating artifacts in scanning white-light interference measurement includes the following steps:

[0054] S1. Collect white-light interference patterns of the object to be measured at different positions in the optical axis direction, and obtain the white-light interference signal of a certain pixel at a certain position in the optical axis direction through preprocessing, including the white-light interference signal of the point to be measured and the white-light interference signal of the common reference point;

[0055] S2. According to the white-light interference signal of the point to be measured and the white-light interference signal of the common reference point, calculate the preliminary height distribution of the surface of the object to be measured by using the generalized cross-correlation algorithm based on the common reference point;

[0056] S3. Use the adjacent-point cross-correlation accumulation algorithm to accurately locate the artifact area in the preliminary height distribution of the object to be measured. If there is an artifact area, go to step S4; if there is no artifact area, directly output the preliminary height distribution;

[0057] S4. Select adjacent reference points in the artifact area, calculate the relative height difference between each pixel point in the artifact area and the adjacent reference points by using the generalized cross-correlation algorithm based on the adjacent reference points, and accordingly correct the artifacts in the preliminary height distribution to obtain a new height distribution;

[0058] S5. Iteratively apply the previous step S4 until the new height distribution meets the preset correction accuracy requirements, and output the final new height distribution.

[0059] The working principle of a method for eliminating artifacts in scanning white-light interference measurement according to the present invention is as follows:

[0060] Step S1 is mainly for data collection and preprocessing: First, collect white-light interference patterns of the object to be measured at different positions in the optical axis direction through a scanning white-light interference measurement system. Then, preprocess these interference patterns to extract the white-light interference signal of a certain pixel at a certain position along the optical axis direction. These signals include the white-light interference signal of the point to be measured and the white-light interference signal of the common reference point. The common reference point refers to a reference point whose position is fixed and the signal is stable during the whole measurement process.

[0061] Step S2 mainly involves height distribution calculation and artifact judgment: Using the generalized cross-correlation algorithm based on a common reference point, the preliminary height distribution of the surface of the object to be measured is calculated according to the white-light interference signal of the point to be measured and the white-light interference signal of the common reference point.

[0062] Step S3 mainly involves artifact region localization: The adjacent-point cross-correlation accumulation algorithm is adopted to accurately locate the artifact region in the preliminary height distribution of the object to be measured. This method utilizes the correlation between adjacent pixel points and enhances the signal characteristics of the artifact region by accumulating the cross-correlation values, thereby achieving accurate identification of the artifact region. At the same time, the recognition result is judged to determine whether there are artifacts in the preliminary height distribution. If there are artifacts, the next step of artifact correction is carried out; if not, the preliminary height distribution is directly output.

[0063] Step S4 mainly involves artifact correction: Adjacent reference points are selected within the artifact region. Adjacent reference points refer to points adjacent to the point to be measured with stable signals, and they have similar physical properties to the point to be measured. Using the generalized cross-correlation algorithm based on adjacent reference points, the relative height differences between each pixel point in the artifact region and the adjacent reference points are calculated. And based on the calculated relative height differences, the artifacts are corrected. This correction method can accurately compensate and correct the artifacts based on the signal characteristics of adjacent points.

[0064] Step S5 mainly involves iterative correction and output: Repeat Step S4, iteratively applying the generalized cross-correlation algorithm based on adjacent reference points for artifact correction until the preset correction accuracy requirement is met. Finally, the new height distribution of the reconstructed object to be measured is output, which has eliminated the influence of artifacts and has higher measurement accuracy and reliability.

[0065] In summary, the beneficial effects of the present invention are as follows:

[0066] 1. Improve measurement accuracy: By using the signal characteristics of adjacent points for cross-correlation operation to correct errors, the morphology of samples with high surface gradients can be accurately restored, effectively eliminating artifacts, thereby significantly improving measurement accuracy.

[0067] 2. Enhance adaptability: There are no specific requirements for the signal source, and there is no need to shape or correct the signal. Therefore, it has strong adaptability and flexibility. It can be applied to different types of samples and measurement environments to meet the needs of different fields.

[0068] 3. Expand the application range: By eliminating artifacts, the application ability of scanning white-light interferometry in the field of precision measurement is improved. It can not only be used to measure the flat surface of samples, but also be used to measure samples with complex morphology and high surface gradients, providing strong technical support for fields such as scientific research and industrial production.

[0069] To further illustrate, in S1, the following steps are specifically included:

[0070] S11. Define the white light interference signal of a pixel at a certain position along the optical axis in the white light interference pattern as:

[0071]

[0072] Wherein, z represents the vertical scanning distance along the optical axis; m and n represent pixel coordinates, m=1,2,…,M-1,M, n=1,2,…,N-1,N, M and N represent the maximum number of pixels in the y direction and x direction respectively; a(m,n) represents the background intensity; h(m,n) represents the actual surface height of the object being measured; g[zh(m,n)] represents the coherence envelope; represents the phase shift; λ 0 represents the central wavelength of the light source; η represents random noise;

[0073] Since in an ideal white light interferometer system, And when z=h(m,n), the white light interference signal I t (m,n,z) reaches its peak value.

[0074] S12, remove the background intensity and some random noise in the white light interference pattern by numerical filtering, and obtain the white light interference signal of a certain pixel point at a certain position along the optical axis direction:

[0075]

[0076] To further illustrate, in S2, the following steps are specifically included:

[0077] S21, using the generalized cross-correlation algorithm based on the common reference point, obtain the measured point P (m 1 ,n 1 ) of the white light interference signal I(m 1 ,n 1 ,z) and the common reference point CRP(m CRP ,n CRP ) of the white light interference signal I(m CRP ,n CRP ,z)’s cross-correlation results:

[0078]

[0079] Among them, f z represents the frequency variable relative to z, and the symbol "*" represents the complex conjugate operation. and Respectively represent I(m CRP ,n CRP ,z) and I(m 1 ,n1 , the Fourier transform result of z) represents the inverse Fourier transform, C CRP&P (z), the maximum value in represents the relative height difference between the point to be measured and the common reference point, that is, the preliminary height distribution of the surface of the object to be measured.

[0080] In this embodiment, the common reference point is selected on an optically smooth plane. Therefore, when the pixel point to be measured is located at the step edge or on a rough surface, due to the influence of various optical error factors such as diffraction, dispersion, chromatic aberration, and multiple reflections, the correlation between the two white-light interference signals decreases, resulting in incorrect cross-correlation peak positioning and thus generating artifacts.

[0081] At this time, the generalized cross-correlation algorithm based on the common reference point not only utilizes the coherence and phase information of the two white-light interference signals simultaneously, but also can calculate the relative height difference between the pixel point to be measured and the common reference point. Compared with the envelope peak positioning or phase analysis method, the generalized cross-correlation algorithm based on the common reference point not only has higher measurement accuracy, but also has a simpler calculation process, can overcome the influence of dispersion, and can achieve high-precision contour measurement even when the white-light interference signal is asymmetric.

[0082] For further explanation, in S3, it specifically includes the following steps:

[0083] S31. Use the adjacent-point cross-correlation accumulation algorithm to calculate the height distribution h of the first column of pixel points in the artifact region of the preliminary height distribution h 1 (m, n), and set h 2 (m, 1), and set h 2 (1, 1) = 0 nm;

[0084] S32. Calculate the height difference d between each pixel point (m′, 1) and the previous pixel point (m′ - 1, 1) in the first column:

[0085]

[0086] d = find{C(z) = max[C(z)]}

[0087] where m′ = 2, …, M - 1, M;

[0088] S33. Calculate row by row to obtain the new height distribution h of all pixel points in the first column 2 (m, n);

[0089] In the adjacent-point cross-correlation accumulation algorithm, the height of each pixel point is determined by cross-correlation with the previous pixel point. The relative height differences between these adjacent pixel points are very accurate. However, during the accumulation process, any error in a single cross-correlation calculation will propagate to subsequent calculations.

[0090] S34. Calculate the preliminary height distribution h along the x direction respectively 1 (m, n) and the new height distribution h 2 (m, n) difference map;

[0091] D i (p, q) = h i (m, n′) - h i (m, n′ - 1), i = 1, 2

[0092] where n′ = 2, …, N - 1, N, p = 1, 2, …, M - 1, M, q = 1, 2, …, N - 1;

[0093] In the ideal case, D 1 (p, q) = D 2 (p, q). However, in reality, due to the influence of noise and artifacts, the two are not equal. Therefore, obtaining the difference map helps to identify the artifact regions.

[0094] S34. To distinguish the influence of artifacts and noise, set a threshold: ε = λ 0 / 4; if D 1 (p, q) - D 2 (p, q) ≥ ε, then the pixel point (p, q) is defined as a boundary pixel point; otherwise, it is not defined;

[0095] S35. When determining all the boundary pixels {q 1 , q 2 , …, q k} in the p-th row, 0 ≤ k ≤ K, then the artifact region (GSR) is expressed as:

[0096]

[0097] Since in the regions with large surface gradients, the white light interference signal is prone to distortion, resulting in a decrease in the correlation with the co-reference point signal, and thus an uncertain error in the cross-correlation peak positioning occurs. In these regions with large surface gradients, the reconstruction results of the generalized cross-correlation algorithm based on the co-reference point will have an incorrect height jump that is an integer multiple of (i.e., the central wavelength of the illumination light source), which is called an artifact.

[0098] To address this issue, the generalized cross-correlation method based on neighboring reference points takes advantage of the similarity of the physical characteristics in the neighborhood. It selects the pixels closest to the artifact region as the new reference points (i.e., neighboring reference points), and calculates the relative height differences between each point in the artifact region and the neighboring reference points through cross-correlation, thereby correcting the artifacts. This method can more accurately reflect the local true height distribution and reduce the measurement errors caused by the common reference points far from the artifact region. In addition, this method does not require prior information of the light source or signal shaping operations, and is applicable to the surface topography measurement of complex multi-elevation samples.

[0099] For further illustration, in S4, it specifically includes the following steps:

[0100] S41. For the i-th artifact region in the p-th row, h GSR (m, i) = {h 1 (m, n) | q 2i-1 -1 < n < q 2i} and select the nearest pixel (p, q 2i-1 -1) as the neighboring reference point;

[0101] S42. Use the generalized cross-correlation method based on neighboring reference points to calculate the relative height differences between all pixel points in the artifact region and their corresponding neighboring reference points, and replace the heights of the corresponding pixel points in the preliminary height distribution h 1 (m, n).

[0102] To further understand the working principle of the present invention, three embodiments are provided by the present invention.

[0103] The First Embodiment

[0104] This embodiment will further illustrate a method for eliminating artifacts in scanning white-light interference measurement and a Linnik-type scanning white-light interference system according to the present invention in combination with the drawings and embodiments.

[0105] Please refer to Figure 1 , a method for eliminating artifacts in scanning white-light interference measurement in this embodiment includes the following steps:

[0106] Step 1. Use a Linnik-type scanning white-light interference system to scan the object along the optical axis direction and record a series of white-light interference patterns I(m CRP , n CRP , z), where CRP represents the common reference point.

[0107] Step 2. Use the common reference point generalized cross-correlation algorithm to calculate the preliminary height distribution h 1 (m, n).

[0108] Step 3. Locate the artifact region in h 1 and select the neighboring reference point (ARP).

[0109] Step 4: Correct the artifacts using the generalized cross-correlation algorithm based on adjacent reference points.

[0110] Step 5: Output the final new height distribution.

[0111] Please refer to Figure 2 , the Linnik type scanning white light interference system includes: a halogen lamp 201, a first lens 202, a pinhole filtering device 203, a second lens 204, a first tube lens 205, a beam splitter 206, a first objective lens 207, a piezoelectric ceramic micro-displacement stage 208, a second objective lens 209, a plane mirror 210, a second tube lens 211, and an image sensor 212. The halogen lamp has a white color, the light source center wavelength of the halogen lamp is 660 nm, and the bandwidth is 200 nm.

[0112] The working principle of the Linnik type scanning white light interference system is as follows: When the white light emitted by the halogen lamp passes through the first lens 202, the pinhole filtering device 203, and the second lens 204 in sequence, it forms collimated white light, which is converged by the first tube lens 205. After passing through the beam splitter 206, it is divided into two beams of light. One beam of light is transformed into a plane wave after passing through the first objective lens 207 and irradiates the sample on the piezoelectric ceramic micro-displacement stage 208 to form an object light O WL ; the other beam of light is transformed into a plane wave after passing through the second objective lens 209 and irradiates the plane mirror 210 to form a reference light R WL . The object light O WL returns and passes through the first objective lens 207 and the beam splitter 206, and is converged by the second tube lens 211 onto the image sensor 212 for imaging. The reference light R WL is reflected by the plane mirror 210 and then returns through the second objective lens 209, the beam splitter 206, and the second tube lens 211, and is incident parallel to the target surface of the image sensor 212 to interfere with the object light O WL . When the optical path difference between the object light O WL and the reference light R WL is zero, the interference intensity reaches the maximum. During the process of driving the piezoelectric ceramic micro-displacement stage 208 to perform an optical axis scan on the sample, the image sensor 212 records a series of white light interference patterns at different optical axis positions.

[0113] Second Embodiment

[0114] This embodiment will further illustrate a method for eliminating artifacts in scanning white light interference measurement of the present invention in combination with the accompanying drawings and embodiments. In this embodiment, the height of the optically smooth surface measured is a 120-nanometer step.

[0115] Step 1: Collect a series of white light interference patterns at different optical axis positions:

[0116] Build asFigure 2 The optical path of the Linnik type scanning white light interference system shown. A computer is used to drive the piezoelectric ceramic micro-displacement stage 208 and the image sensor 212 to collect a group of interference patterns at different optical axis positions. The interference signal intensity of the pixel point (m, n) in the interference pattern at a certain position z along the optical axis direction can be expressed as:

[0117]

[0118] Step 2: Convert the collected interference pattern into an interference pattern with the background intensity and part of the random noise removed:

[0119] The interference pattern with the background intensity and part of the random noise removed by numerical filtering can be expressed as:

[0120]

[0121] Step 3: Obtain the preliminary height distribution h of the sample including the artifact region 1 :

[0122] Applying the generalized cross-correlation algorithm based on the common reference point, the cross-correlation result of the white light interference signal I(m 1 , n 1 ) of the pixel point P(m 1 , n 1 , z) to be measured and the white light interference signal I(m CRP , n CRP ) of the common reference point pixel point CRP(m CRP , n CRP , z) can be obtained:

[0123]

[0124] Please refer to Figure 3 , the preliminary height distribution has incorrect height jumps in the region with a large surface gradient, that is, at the step jump edge region.

[0125] Step 4: Precise positioning of the artifact region in the preliminary height distribution h 1 of the item to be measured:

[0126] Using the adjacent point cross-correlation accumulation algorithm, first calculate the height distribution h 1 of the first column of pixel points in the artifact region in the preliminary height distribution h 2 (m, 1), and set h 2 (1, 1) = 0 nm. Then calculate the height difference d between each pixel point (m′, 1) and the previous pixel point (m′ - 1, 1):

[0127]

[0128] d = find{C(z) = max[C(z)]}

[0129] Then calculate row by row to obtain the height distribution h of all pixel points in the first column 2 (m, n). Then, calculate the difference map of h 1 (m, n) and h 2 (m, n).

[0130] D i (p, q) = h i (m, n′) - h i (m, n′ - 1), i = 1, 2

[0131] This difference map helps to identify the artifact region. In an ideal situation, D 1 (p, q) = D 2 (p, q). However, in reality, due to the influence of noise and artifacts, the two are not equal. To distinguish the influence of artifacts and noise, we set a threshold: ε = λ 0 / 4. If D 1 (p, q) - D 2 (p, q) ≥ ε, then the pixel (p, q) is defined as a boundary pixel. After determining all boundary pixels {q 1 , q 2 , …, q k} in the p-th row, 0 ≤ k ≤ K, the artifact region (GSR) can be expressed as:

[0132]

[0133] Step 5. Obtain a new height distribution after correcting the artifact region for the preliminary height distribution h 1 :

[0134] For the i-th artifact region in the p-th row, h GSR (m, i) = {h 1 (m, n) | q 2i-1 - 1 < n < q 2i}, select the nearest pixel (p, q 2i-1 - 1) as the adjacent reference point ARP.

[0135] Then calculate the relative height difference between all pixel points in the artifact region and their corresponding adjacent reference points using the generalized cross-correlation method based on the adjacent reference point, and replace the heights of the corresponding pixel points in the preliminary height distribution h 1 (m, n).

[0136] Taking the artifact pixel point P gs (m, q 2i-1 ) as an example, the height difference calculated using the generalized cross-correlation method based on the adjacent reference point is After correction, it is:

[0137] h 1 (m, q 2i-1 ) = h 1 (m, n ARP ) + d' Pgs-ARP

[0138] Finally, check whether the differential graph of the corrected h 1 (m, n) satisfies: D 1 (p, q) - D 2 (p, q) < ε. If not satisfied, the generalized cross - correlation method based on adjacent reference points needs to be continued to correct the residual artifacts.

[0139] Please refer to Figure 4 , after determining the artifact area from the preliminary height distribution and using the generalized cross - correlation method based on adjacent reference points for correction, a more accurate measurement result is finally achieved.

[0140] Please refer to Figure 5 , on a 120 - nanometer step on an optically smooth surface, the cross - sectional comparison between the measurement results of the generalized cross - correlation algorithm based on a common reference point and the measurement results of the generalized cross - correlation method based on adjacent reference points highlights the gain effect of a method for eliminating artifacts in scanning white - light interferometry described in the present invention, effectively eliminating artifacts in scanning white - light interferometry.

[0141] So far, through the method proposed in the present invention, the height distribution containing artifacts can be restored from a series of white - light interferograms, and further an accurate height distribution for eliminating artifacts in scanning white - light interferometry can be obtained.

[0142] The Third Embodiment

[0143] This embodiment will further illustrate the beneficial effects of a method for eliminating artifacts in scanning white - light interferometry described in the present invention in combination with the drawings and examples, and in this embodiment, steps with complex multi - elevation are measured.

[0144] Step 1: Collect multiple groups of white - light interferograms to ensure covering different optical axis positions:

[0145] According to Figure 2 shown, build the optical path of a Linnik - type scanning white - light interferometer system. Control the piezoelectric ceramic micro - displacement stage 208 and the image sensor 212 through a computer to collect a group of interferograms at different optical axis positions.

[0146] Step 2: Process the collected interferograms into interferograms with background intensity and part of the random noise removed.

[0147] Step 3: Obtain the preliminary height distribution of the sample containing the artifact area:

[0148] Please refer to Figure 6 , artifacts occur in the measurement results of the common reference point generalized cross-correlation algorithm for complex multi-elevation steps. In non-optically smooth surfaces at different heights, incorrect height jumps occur; and at the edges of different elevation steps, the artifact phenomenon is more significant.

[0149] Step 4: Precise positioning of the artifact area in the preliminary height distribution of the sample:

[0150] Using the adjacent point cross-correlation accumulation algorithm, the first column of pixels in the preliminary height distribution was calculated first. Then, the height difference between each pixel point and the previous pixel point was calculated, row by row, to obtain a new height distribution. Then, the difference map between the preliminary height distribution along the x direction and the new height distribution was calculated. This difference map helps to identify the artifact area, and on this basis, an artifact threshold was set: ε = λ 0 / 4. If the difference between the difference map of the preliminary height distribution and the new height distribution is greater than or equal to the threshold, then this pixel is defined as a boundary pixel, and the precise artifact area is obtained in this way.

[0151] Step 5: Obtain a new height distribution after correcting the artifact area in the preliminary height distribution of the sample:

[0152] First, for the i-th artifact area in the p-th row, select the nearest pixel (p, q 2i-1 -1) as the adjacent reference point ARP.

[0153] Then, use the generalized cross-correlation method based on the adjacent reference point to calculate the relative height difference between all pixel points in the artifact area and their corresponding adjacent reference point ARP, and replace the height of the corresponding pixel points in the preliminary height distribution.

[0154] Finally, check whether the difference map of the corrected preliminary height distribution satisfies that the difference between the difference map of the preliminary height distribution and the new height distribution is greater than or equal to the threshold. If not, it is necessary to continue to correct the residual artifacts using the generalized cross-correlation method based on the adjacent reference point.

[0155] Please refer to Figure 7 , the incorrect artifact phenomenon in the preliminary height distribution of the complex multi-elevation steps was corrected using the generalized cross-correlation method based on the adjacent reference point, and finally more accurate measurement results were achieved.

[0156] Please refer to Figure 8The cross-sectional comparison between the measurement results of the generalized cross-correlation algorithm based on common reference points and the measurement results of the generalized cross-correlation method based on adjacent reference points of complex multi-elevation steps highlights the gain effect of the method for eliminating artifacts in scanning white light interferometry described in the present invention, and effectively eliminates artifacts caused by the distortion of white light interference signals in areas with large surface gradients in scanning white light interferometry.

[0157] Thus, through the method proposed in the present invention, the height distribution including artifacts can be recovered from a series of white light interference patterns, and the accurate height distribution eliminating artifacts in scanning white light interferometry can be further obtained.

[0158] In summary, the present invention proposes a method for eliminating artifacts in scanning white light interferometry, which effectively eliminates the artifact phenomenon and realizes high-precision surface three-dimensional morphology measurement. The method proposed by the present invention has a gradual operation, strong adaptability, and is applicable to a variety of sample types, providing a solid technical foundation for the application of scanning white light interferometry in a wider range of fields.

[0159] The technical principle of the present invention is described above in conjunction with specific embodiments. These descriptions are only for explaining the principle of the present invention and cannot be interpreted as limiting the scope of protection of the present invention in any way. Based on the explanations herein, those skilled in the art can associate other specific embodiments of the present invention without creative work, and these equivalent variations or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for eliminating artifacts in scanning white light interferometry, characterized in that: The following steps are involved: S1. Collect white light interference patterns of the object to be measured at different positions in the optical axis direction, and obtain the white light interference signal of a certain pixel point at a certain position in the optical axis direction through preprocessing, including the white light interference signal of the point to be measured and the white light interference signal of the common reference point; S2, according to the white light interference signal of the point to be measured and the white light interference signal of the common reference point, a generalized cross-correlation algorithm based on the common reference point is used to calculate the preliminary height distribution of the surface of the object to be measured; S3, using the adjacent point cross-correlation accumulation algorithm to accurately locate the artifact area in the preliminary height distribution of the measured object, if there is an artifact area, proceed to step S4; if there is no artifact area, directly output the preliminary height distribution; S4, selecting adjacent reference points in the artifact area, calculating the relative height difference between each pixel point in the artifact area and the adjacent reference point by a generalized cross-correlation algorithm based on the adjacent reference points, and performing artifact correction on the preliminary height distribution based on the calculated relative height difference to obtain a new height distribution; S5. Iteratively apply the previous step S4 until the new height distribution meets the preset correction accuracy requirement, and output the final new height distribution.

2. A method for eliminating artifacts in scanning white light interferometry according to claim 1, characterized in that: In S1, the following steps are specifically included: S11. Define the white light interference signal of a pixel at a certain position along the optical axis in the white light interference pattern as: Wherein, z represents the vertical scanning distance along the optical axis; m and n represent pixel coordinates, m=1,2,…,M-1,M, n=1,2,…,N-1,N, M and N represent the maximum number of pixels in the y direction and x direction respectively; a(m,n) represents the background intensity; h(m,n) represents the actual surface height of the object being measured; g[zh(m,n)] represents the coherence envelope; represents phase shift; λ0 represents the central wavelength of the light source; η represents random noise; S12, remove the background intensity and some random noise in the white light interference pattern by numerical filtering, and obtain the white light interference signal of a certain pixel point at a certain position along the optical axis direction:

3. A method for eliminating artifacts in scanning white light interferometry according to claim 1, characterized in that: In S2, the following steps are specifically included: S21, using the generalized cross-correlation algorithm based on the common reference point, the white light interference signal I(m1,n1,z) of the test point P(m1,n1) and the common reference point CRP(m CRP ,n CRP ) of the white light interference signal I(m CRP ,n CRP ,z)’s cross-correlation results: Among them, f z represents the frequency variable relative to z, and the symbol "*" represents the complex conjugate operation. and Respectively represent I(m CRP ,n CRP ,z) and I(m1,n1,z), represents the inverse Fourier transform, C CRP&P The maximum value in (z) represents the relative height difference between the point to be measured and the common reference point, that is, the preliminary height distribution of the surface of the object to be measured.

4. A method for eliminating artifacts in scanning white light interferometry according to claim 1, characterized in that: In S3, the following steps are specifically included: S31, using the adjacent point cross-correlation accumulation algorithm, in the artifact area of ​​the preliminary height distribution h1(m,n), calculate the height distribution h2(m,1) of the first column of pixels, and set h2(1,1)=0nm; S32. Calculate the height difference d between each pixel point (m′, 1) and the previous pixel point (m′-1, 1) in the first column: d = find{C(z) = max[C(z)]} Where, m′=2,…,M-1,M; S33, calculating row by row to obtain a new height distribution h2(m,n) of all pixels in the first column; S34, respectively calculating and obtaining the difference graphs of the preliminary height distribution h1(m,n) and the new height distribution h2(m,n) along the x direction; D i (p,q)=h i (m,n′)-h i (m,n′-1),i=1,2 Where n′=2,…,N-1,N,p=1,2,…,M-1,M,q=1,2,…,N-1; S34, in order to distinguish the influence of artifacts and noise, set the threshold: ε = λ0 / 4; if D1(p,q)-D2(p,q)≥ε, the pixel point (p,q) is defined as a boundary pixel point; otherwise, it is not defined; S35, when all boundary pixels {q1, q2, ..., q k }, 0≤k≤K, then the artifact region (GSR) is expressed as:

5. The method for eliminating artifacts in scanning white light interferometry according to claim 1, characterized in that: In S4, the following steps are specifically included: S41. For the i-th artifact region in the p-th row, h GSR (m,i)={h1(m,n)|q 2i-1 -1<n<q 2i }, select the nearest pixel (p,q 2i-1 -1) as a neighboring reference point; S42, using a generalized cross-correlation method based on neighboring reference points to calculate the relative height differences between all pixel points in the artifact area and their corresponding neighboring reference points, and replacing the heights of the corresponding pixel points in the preliminary height distribution h1(m,n).

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