A method for reconstructing three-dimensional topography of a pattern wafer surface
By establishing image sequences and color vector spaces, calculating color gradients and dispersion features, and combining Bayesian statistical optimization focusing evaluation, the problems of color channel information loss and insufficient anti-interference ability in wafer surface 3D reconstruction are solved, achieving high-precision 3D reconstruction.
Patent Information
- Application Number
- CN202510575958.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-06
- Publication Date
- 2025-11-04
- Estimated Expiration
- 2045-05-06
AI Technical Summary
Existing technologies for 3D reconstruction of wafer surfaces suffer from problems such as loss of color channel information, inaccurate focus evaluation, difficulty in depth map optimization, and insufficient anti-interference ability, resulting in low detection sensitivity and insufficient accuracy.
A three-dimensional topography reconstruction method for patterned wafer surfaces is adopted. By establishing an image sequence space and a color vector space, color gradient and dispersion features are calculated. Focus evaluation is optimized by combining Bayesian statistical principles, and depth map optimization is performed using median filtering and guided filtering.
This improved the accuracy and stability of focused evaluation, ensured high-fidelity optimization of depth maps, and enabled high-precision 3D reconstruction of wafer surfaces.
Smart Images

Figure CN120355852B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of image processing, and in particular to a high-precision three-dimensional reconstruction method for the absolute depth of a wafer surface under a microscope. BACKGROUND
[0002] With the continuous improvement of semiconductor manufacturing process, high-precision detection of wafer surface three-dimensional topography has become a key link to ensure chip yield and performance. Traditional three-dimensional reconstruction methods are mostly based on focus stack technology, which collects a sequence of zoom images along the optical axis direction through a microscopic system, and determines the best focus position of each pixel using a focus evaluation function, thereby reconstructing the surface height information. However, the existing technology has the following significant shortcomings: the traditional method usually converts color images into grayscale images for focus evaluation, resulting in the loss of difference information between color channels, thereby reducing the detection sensitivity and even causing misjudgment of key features; in addition, existing focus evaluation functions (such as gradient amplitude, Laplace energy, etc.) are mostly based on single-channel grayscale information, which is easily disturbed by noise, and the evaluation curve often presents a multi-peak or wide-peak phenomenon, resulting in ambiguous peak positioning; depth map optimization limitations, the initial depth map often introduces errors due to noise or outliers, and traditional filtering methods (such as mean filtering) easily blur the edges while smoothing the noise, making it difficult to balance the smoothness of the surface flat area and the fidelity of the microstructure. For example, the step height of the wafer surface metal wiring or the microscopic scratch may be distorted due to excessive filtering.
[0003] In recent years, although some research has tried to combine multi-color channel information or introduce statistical models to optimize focus evaluation, the methods are mostly limited to simple weighted fusion or linear assumptions, and have not effectively solved the non-linear correlation problem of color feature information. In addition, due to the characteristics of high reflectivity and low contrast of the wafer surface, the existing technology still lacks robust anti-interference ability and adaptive optimization mechanism. SUMMARY
[0004] The present application is to solve the above-mentioned deficiencies of the prior art, and proposes a three-dimensional topography reconstruction method for pattern wafer surface, in order to make full use of color information, improve the focus evaluation accuracy and speed, avoid the information loss caused by traditional grayscale conversion, improve the speed and accuracy of peak positioning, and realize high-fidelity optimization of depth map three-dimensional reconstruction, and effectively preserve the microstructure details of the wafer surface, in order to meet the stringent detection requirements of high reflectivity and low contrast surface of the wafer surface in semiconductor manufacturing.
[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:
[0006] The three-dimensional topography reconstruction method for pattern wafer surface of the present application is characterized in that it is applied to a scene composed of a wafer to be measured, a stage, a stepping motor, a CCD camera, a microscope and a coaxial light source, and includes the following steps:
[0007] Step 1: Collect a set of zoom image sequences of the surface of the wafer to be measured , , , , wherein represents the surface image of the wafer to be measured, represents the total number of images, represents the width of a single image, is the height of a single image;
[0008] Step 2: Arrange , , , in the order of collection along the optical axis direction; take the first pixel point in the upper left corner of the first image as the origin of the image sequence space coordinate system, and take the two pixel coordinate axes of and the vertical axis parallel to the optical axis and passing through the origin as the three coordinate axes of the image sequence space coordinate system, thereby establishing the image sequence space; let any pixel point in the image sequence space be denoted as , wherein , , ;
[0009] Step 3: Based on the image sequence space and the color vector space, calculate the color gradient evaluation value and the color dispersion evaluation value of all pixels, thereby obtaining the image gradient matrix and the image dispersion matrix , wherein is the color gradient evaluation value of the pixel point in the image sequence space, is the color dispersion evaluation value of the pixel point in the color vector space;
[0010] Step 4: According to the image gradient matrix and the image dispersion matrix, obtain the normalized gradient set and the normalized dispersion set of each pixel point, and calculate the Gaussian posterior distribution function of each pixel point, take the function center position as the best focusing position of each pixel point, thereby obtaining the initial depth map of the surface of the wafer to be measured , wherein is the depth value of the pixel point ;
[0011] Step 5: Perform median filtering and guided filtering on the initial depth map in turn, to obtain the optimized depth map , which is used to realize high-precision three-dimensional reconstruction of the surface of the wafer to be measured, wherein, pixel point optimized depth value
[0012] The pattern wafer surface three-dimensional topography reconstruction method has the characteristics that the step 3 comprises:
[0013] Step 3.1: taking the black pixel point as the origin of the color vector space coordinate system and taking the red channel, the green channel and the blue channel as three base coordinate axes of the color vector space coordinate system, thereby constructing the color vector space;
[0014] Step 3.2: obtaining the mapping relationship from the image sequence space to the color vector space by using formula (1):
[0015] (1)
[0016] In formula (1), denotes mapping, denotes the corresponding vector point of the pixel point in the color vector space, , and respectively denote the components of the pixel point in the red channel, the green channel and the blue channel;
[0017] Step 3.3: obtaining the color vector of the pixel point by using formula (2):
[0018] (2)
[0019] In formula (2), , , respectively denote the unit vectors of the three base coordinate axes;
[0020] Step 3.4: in the color vector space, calculating the horizontal direction gradient and the vertical direction gradient of the pixel point by using formula (3) and formula (4), thereby obtaining the color partial derivative matrix of the pixel point :
[0021] (3)
[0022] (4)
[0023] obtaining the color vector Color vector space correlation matrix :
[0024] (5)
[0025] Step 3.5: Calculate the correlation matrix in the color vector space. Maximum eigenvalue and as pixels Color gradient evaluation value in image sequence space This allows us to traverse all pixels in the image sequence space and obtain the image gradient matrix. ;
[0026] Step 3.6: In pixels Centered on, in Swipe up to get a size of A local window, the number of pixels within the local window The The number of neighboring pixels is denoted as a pixel point. And pixels The color vector is denoted as ;in, , The length of the local window;
[0027] Step 3.7: Calculate the pixel points using equation (6) and pixels Dispersion value Thus, the pixel points are obtained. The dispersion values of all neighboring pixels within the local window are used to form the pixel. Color difference set ;
[0028] (6)
[0029] In equation (6), Color vector and color vector Euclidean distance; For pixels The color fluctuation amount, and has:
[0030] (7)
[0031] In equation (7), , , Representing pixels surrounding pixels The weight of the red, green, and blue channels;
[0032] Step 3.8: Obtain the pixel point using formula (8) Color dispersion evaluation value in color vector space , so as to traverse all pixel points in the image sequence space and obtain the image dispersion matrix ;
[0033] (8)
[0034] In formula (8), represents the variance.
[0035] Further, the step 4 comprises:
[0036] Step 4.1: Take the pixel point The data points in the third dimension of the image gradient matrix constitute the gradient set of the pixel point , and the data points in are normalized to obtain the normalized gradient set of the pixel point , so as to fit the gradient Gaussian function of the pixel point using formula (9) , wherein represents the normalized color gradient evaluation value of the pixel point .
[0037] (9)
[0038] In formula (9), represents the mean of the gradient Gaussian function , that is, the center position of the gradient Gaussian curve, represents the standard deviation of the gradient Gaussian function .
[0039] Step 4.2: Take the pixel point The data points in the third dimension of the image dispersion matrix constitute the dispersion set of the pixel point , and the data points in are normalized to obtain the normalized dispersion set of the pixel point , so as to fit the dispersion Gaussian function of the pixel point using formula (10) , wherein represents the normalized dispersion evaluation value of the pixel point .
[0040] (10)
[0041] In formula (10), represents the mean value of the dispersive Gaussian function , represents the standard deviation of the dispersive Gaussian function ;
[0042] Step 4.3: taking as the prior function and as the likelihood function, the Gaussian posterior distribution function of the pixel point is calculated according to the Bayesian statistical principle by using formula (11):
[0043] (11)
[0044] In formula (11), represents the marginal likelihood function of the pixel point ;
[0045] Step 4.4: the mean value and the variance of the Gaussian posterior distribution function are calculated by using formula (12) and formula (13) respectively, and is taken as the best focus position of the pixel point :
[0046] (12)
[0047] (13)
[0048] Step 4.5: the depth value of the pixel point is calculated by using formula (14):
[0049] (14)
[0050] In formula (21), represents the lower limit of the scan of , represents the step length of the scan;
[0051] Step 4.6: according to the processes of steps 4.1 to 4.5, the depth values of all the pixel points in the image are obtained, so as to obtain the initial depth map of the surface of the wafer to be measured .
[0052] The electronic device comprises a memory and a processor, and is characterized in that the memory is used for storing a program supporting the processor to execute any of the pattern wafer surface three-dimensional topography reconstruction methods, and the processor is configured to execute the program stored in the memory.
[0053] The computer readable storage medium stores a computer program, and the computer program is characterized in that when executed by a processor, the computer program performs the steps of any of the pattern wafer surface three-dimensional topography reconstruction methods.
[0054] Compared with the prior art, the beneficial effects of the present application are embodied in that:
[0055] 1. The present application establishes an image sequence space and a color vector space, calculates pixel color gradient and color dispersion characteristics as the basis for sharpness evaluation, fully utilizes the correlation of color channels, improves the accuracy and stability of the aggregation evaluation link, effectively solves the problem of inaccurate evaluation of low-texture and low-contrast regions in traditional focus evaluation algorithms, and thus provides a guarantee for the precision of the focus-stacked three-dimensional reconstruction;
[0056] 2. The present application proposes to use the pixel color gradient Gaussian curve as the prior distribution function and the color dispersion characteristic Gaussian curve as the likelihood function, and through the Bayesian statistical principle, a focus evaluation curve with a more accurate center position and higher steepness is obtained, the inherent error caused by interpolation fitting in the traditional peak search link is avoided, and the accuracy of depth estimation is improved, thereby realizing high-precision three-dimensional reconstruction of the wafer surface. BRIEF DESCRIPTION OF DRAWINGS
[0057] Figure 1 is the principle diagram for obtaining the depth of the measured wafer surface of the present application;
[0058] Figure 2 is the flowchart of collecting the color image sequence of the present application;
[0059] Figure 3 is the zoomed image sequence processed by the present application;
[0060] Figure 4 is the focus evaluation curve diagram of the processed image of the present application;
[0061] Figure 5 is the reconstructed wafer surface of the present application. DETAILED DESCRIPTION
[0062] In this embodiment, a pattern wafer surface three-dimensional topography reconstruction method, the principle flow is as shown in Figure 1 The present application is applied to a scene composed of a wafer to be measured, a stage, a stepping motor, a CCD camera, a microscope and a coaxial light source, and comprises the following steps:
[0063] Step 1: Collect a set of zoom image sequences of the surface of the wafer to be tested , ,…, ,…, , wherein represents the surface image of the wafer to be tested, represents the total number of images, represents the width of a single image, represents the height of a single image;
[0064] Step 1.1: The wafer image sequence collection process is shown in Figure 2 . The CCD camera works with a high-precision stepper motor to generate a uniform illumination beam through a coaxial light source. The beam forms a parallel light path through a collimating mirror, is reflected at a beam splitter, and is projected onto the surface of the object being measured by a microscope objective;
[0065] Step 1.2: Control the stepper motor to continuously approach the microscope objective to the object being measured, and monitor the global average gradient value of the CCD image in real time. When the gradient value decreases by ≤0.1% for 5 consecutive frames, it is determined that all pixels enter the out-of-focus blur state, and the Z-axis coordinate at this time is recorded as . Then control the stepper motor in reverse to gradually move the microscope objective away from the object being measured. When the gradient value of more than 95% of the pixels in the image decreases to 10% of the peak value, the Z-axis coordinate at this time is recorded as .
[0066] Step 1.3: According to the total scanning distance , calculate the displacement step size according to the formula , and set the constraint condition; multi-scale scanning control: starting from , the stepper motor moves along the Z-axis by a step size of . Each time a new position is reached, the CCD camera is triggered to take a picture, generating an image sequence , ,…, ,…, , as shown in Figure 3 .
[0067] Step 2: Establish the image sequence space and color vector space, and calculate the color gradient evaluation value and color dispersion evaluation value of all pixels, thereby obtaining the image gradient matrix and image color dispersion matrix:
[0068] Step 2.1: Arrange , ,…, ,…, in the order of acquisition along the optical axis. Each image is parallel to the two images before and after it and has the same interval; the first image the first pixel point in the upper left corner as the origin of the image sequence space coordinate system, and the two pixel coordinate axes and the vertical axis parallel to the optical axis and passing through the origin as the three coordinate axes of the image sequence space coordinate system, thereby establishing the image sequence space; let any pixel point in the image sequence space be denoted as , wherein , , , .
[0069] Step 2.2: taking the black pixel point as the origin of the color vector space coordinate system, and taking the red channel, the green channel and the blue channel as the three base coordinate axes of the color vector space coordinate system, thereby constructing the color vector space;
[0070] The mapping relationship from the image sequence space to the color vector space is obtained by using formula (15):
[0071] (15)
[0072] In formula (15), represents the mapping, represents the vector point corresponding to the pixel point in the color vector space, , and respectively represent the components of the pixel point on the red channel, the green channel and the blue channel.
[0073] The color vector of the pixel point is obtained by using formula (16):
[0074] (16)
[0075] In formula (16), , , respectively represent the unit vectors of the three base coordinate axes.
[0076] Step 2.3: in the color vector space, the horizontal direction gradient and the vertical direction gradient of the pixel point on are calculated by using formula (17) and formula (18), thereby obtaining the color partial derivative matrix of the pixel point :
[0077] (17)
[0078] (18)
[0079] Pixels are obtained using equation (19) Color vector space correlation matrix :
[0080] (19)
[0081] The spatial correlation matrix characterizes the correlation of the three channels in the RGB space, and the eigenvectors of the matrix reflect the changes of the image function in the RGB space. The magnitude of the eigenvector represents the rate of change, and the direction of the eigenvector represents the direction of change. The direction and magnitude of the maximum change in the color image function are represented by the eigenvector corresponding to the largest eigenvalue of the matrix. The spatial correlation matrix of the color vector is calculated. Maximum eigenvalue and as pixels Color gradient evaluation value This allows us to traverse all pixels in the image sequence space and obtain the image gradient matrix. .
[0082] Step 2.4: In pixels Centered on, in Swipe up to get a size of A local window, the number of pixels within the local window The The number of neighboring pixels is denoted as a pixel point. And pixels The color vector is denoted as ;in, , The length of the local window;
[0083] Calculate the pixel using equation (20) and pixels Dispersion value Thus, the pixel points are obtained. The dispersion values of all neighboring pixels within the local window are used to construct the pixel. Color difference set ;
[0084] (20)
[0085] In equation (20), Color vector and color vector The Euclidean distance is a direct representation of the similarity between two vectors. A larger Euclidean distance value indicates a greater difference between the two vectors, suggesting a higher similarity between pixels. and pixels the more obvious the color difference is; the color fluctuation of the pixel point , and has
[0086] (21)
[0087] In formula (21), the three-dimensional coordinates of the surrounding pixels of the pixel point .
[0088] The color dispersion evaluation value of the pixel point in the color vector space is obtained by using formula (22) , so as to traverse all the pixel points in the image sequence space and obtain the image dispersion matrix .
[0089] (22)
[0090] In formula (22), the variance is represented; the variance and the sum of the color difference set are calculated, and the two are multiplied to obtain the color dispersion evaluation value of the pixel point in the color vector space, which can accurately evaluate the focusing degree of the pixel.
[0091] Step 3: According to the image gradient matrix and the image dispersion matrix, the normalized gradient set and the normalized dispersion set of each pixel point are obtained, and the Gaussian posterior distribution function of each pixel point is calculated, the function center position is extracted as the best focusing position of each pixel point, so as to obtain the initial depth map of the wafer surface to be measured:
[0092] Step 3.1: Take the data points of the pixel point in the third dimension of the image gradient matrix to form a gradient set , and normalize the data points in to obtain the normalized gradient set , so as to fit the gradient Gaussian function of by using formula (23) , wherein represents the normalized color gradient evaluation value of the pixel point
[0093] (23)
[0094] In formula (23), the mean of the gradient Gaussian function, that is, the center position of the gradient Gaussian curve, the standard deviation of the gradient Gaussian function, reflecting the width of the Gaussian curve.
[0095] Step 3.2: Taking the pixel point The data points in the third dimension of the image dispersion matrix constitute a dispersion set , and the data points in are normalized to obtain a normalized dispersion set , so that is fitted into a dispersion Gaussian function using formula (24), where represents the normalized dispersion evaluation value of the pixel point .
[0096] (24)
[0097] In formula (24), represents the mean of the dispersion Gaussian function, and represents the standard deviation of the dispersion Gaussian function.
[0098] Step 3.3: Taking as the prior function and as the likelihood function, according to the Bayesian statistical principle, the Gaussian posterior distribution function Figure 4 is calculated using formula (11); the prior and likelihood functions are both Gaussian distributions, and the posterior distribution obtained according to the Bayesian formula is also a Gaussian distribution, and the posterior distribution curve is steeper, which improves the response speed and resolution of the focus evaluation;
[0099] (25)
[0100] In formula (25), represents the marginal likelihood function.
[0101] The mean and variance of the Gaussian posterior distribution function are calculated using formula (12) and formula (13) respectively, and is taken as the best focus position of the pixel point :
[0102] (28)
[0103] (29)
[0104] Step 3.4: The best focus position of the pixel point and the scanning interval are combined, and the depth value of the pixel point is calculated using formula (28) :
[0105] (28)
[0106] In formula (28), represents the lower limit of scanning, represents the step length of scanning.
[0107] Step 3.5: According to the processes of steps 3.1 to 3.4, the depth values of each pixel point in the image are obtained, and thus the depth map of the surface of the wafer to be measured is obtained ;
[0108] Step 4: The initial depth map is sequentially subjected to median filtering and guided filtering to obtain an optimized depth map , which is used to realize high-precision three-dimensional reconstruction of the surface of the wafer to be measured:
[0109] Step 4.1: In order to suppress noise interference, the initial depth map is subjected to median filtering processing, a sliding window size of 3x3 is set, outliers are removed and local fluctuations are smoothed, and a depth map is obtained:
[0110] Step 4.2: The is subjected to guided filtering to obtain a final optimized depth map ;
[0111] Step 4.3: As shown in Figure 5 , the optimized depth map is converted into three-dimensional point cloud data, combined with the calibration parameters of the microscopic system, mapped to the physical coordinate system, and through a surface fitting algorithm, a three-dimensional topographic model of the surface of the measured object is generated, and the final three-dimensional reconstruction result is output.
[0112] In this embodiment, an electronic device includes a memory for storing a program supporting a processor to execute the above method, and the processor is configured to execute the program stored in the memory.
[0113] In this embodiment, a computer readable storage medium has a computer program stored thereon, and the computer program is run by a processor to execute the steps of the above method.
Claims
1. A method for reconstructing the three-dimensional morphology of a patterned wafer surface, characterized in that, It is applied to a scenario consisting of a wafer under test, a stage, a stepper motor, a CCD camera, a microscope, and a coaxial light source, and includes the following steps: Step 1: Acquire a series of zoomed images of the surface of the wafer under test. , ,…, ,…, ,in, Indicates the first Zhang's image of the surface of the wafer to be tested. This indicates the total number of images. Indicates the width of a single image. The height of a single image; Step 2: , ,…, ,…, Arrange the images along the optical axis in the order they were acquired; place the first image... The first pixel in the upper left corner is taken as the origin of the image sequence spatial coordinate system, and... The two pixel coordinate axes and the vertical axis parallel to the optical axis and passing through the origin are used as the three coordinate axes of the image sequence space coordinate system to establish the image sequence space; let any pixel point in the image sequence space be denoted as... ,in, , , ; Step 3: Based on the image sequence space and color vector space, calculate the color gradient evaluation value and dispersion evaluation value of all pixels to obtain the image gradient matrix. and image dispersion matrix ,in, For pixels Color gradient evaluation value in image sequence space For pixels Dispersion evaluation value in color vector space; Step 4: Based on the image gradient matrix and image dispersion matrix, obtain the normalized gradient set and normalized dispersion set for each pixel, and calculate the Gaussian posterior distribution function for each pixel. Extract the center position of the function as the optimal focusing position for each pixel, thereby obtaining the initial depth map of the wafer surface under test. ,in, For pixels The depth value; Step 5: Create the initial depth map Median filtering and guided filtering are performed sequentially to obtain the optimized depth map. It is used to achieve high-precision three-dimensional reconstruction of the surface of the wafer under test, wherein, For pixels Optimized depth value.
2. The method for reconstructing the three-dimensional morphology of a patterned wafer surface according to claim 1, characterized in that, Step 3 includes: Step 3.1: Construct a color vector space by using the black pixel as the origin of the color vector space coordinate system and the red, green, and blue channels as the three base coordinate axes of the color vector space coordinate system. Step 3.2: Use equation (1) to obtain the mapping relationship from the image sequence space to the color vector space: (1) In equation (1), Represents a mapping. Represents the relationship between pixels in the color vector space. The corresponding vector point, , and They represent pixels on The weight of the red, green, and blue channels; Step 3.3: Obtain the pixel points using equation (2) Color vector : (2) In equation (2), , , These represent the unit vectors of the three base coordinate axes; Step 3.4: In the color vector space, calculate using equations (3) and (4). pixels on Horizontal gradient and vertical gradient Thus, the pixel points are obtained. Color partial derivative matrix : (3) (4) Pixels are obtained using equation (5) Color vector space correlation matrix : (5) Step 3.5: Calculate the correlation matrix in the color vector space. Maximum eigenvalue and as pixels Color gradient evaluation value in image sequence space This allows us to traverse all pixels in the image sequence space and obtain the image gradient matrix. ; Step 3.6: In pixels Centered on, in Swipe up to get a size of A local window, the number of pixels within the local window The The number of neighboring pixels is denoted as a pixel point. And pixels The color vector is denoted as ;in, , The length of the local window; Step 3.7: Calculate the pixel points using equation (6) and pixels Dispersion value Thus, the pixel points are obtained. The dispersion values of all neighboring pixels within the local window are used to form the pixel. Color difference set ; (6) In equation (6), Color vector and color vector Euclidean distance; For pixels The color fluctuation amount, and has: (7) In equation (7), , , Representing pixels surrounding pixels The weight of the red, green, and blue channels; Step 3.8: Obtain the pixel points using equation (8) Dispersion evaluation value in color vector space This allows us to traverse all pixels in the image sequence space and obtain the image dispersion matrix. ; (8) In equation (8), Indicates variance.
3. The method for reconstructing the three-dimensional morphology of a patterned wafer surface according to claim 2, characterized in that, Step 4 includes: Step 4.1: Extract pixels In the image gradient matrix The data points in the third dimension constitute the pixels. gradient set and will The data points in the data are normalized to obtain the pixel points. Normalized gradient set Thus, by using equation (9) Fit to pixels gradient Gaussian function ,in, Represents pixels Normalized color gradient evaluation value; (9) In equation (9), Represents the gradient Gaussian function The mean value, i.e., the center position of the gradient Gaussian curve, Represents the gradient Gaussian function Standard deviation; Step 4.2: Extract pixels In the image dispersion matrix The data points in the third dimension constitute the pixels. Dispersion set and will The data points in the data are normalized to obtain the pixel points. Normalized dispersive set Thus, by using equation (10) Fit to pixels Dispersive Gaussian function ,in, Represents pixels Normalized dispersion evaluation value; (10) In equation (10), Represents the dispersive Gaussian function The mean, Represents the dispersive Gaussian function Standard deviation; Step 4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require As a priori function, As the likelihood function, according to the Bayesian statistical principle, the pixel point is calculated using equation (11). Gaussian posterior distribution function : (11) In equation (11), Represents pixels The marginal likelihood function; Step 4.4: Calculate the Gaussian posterior distribution function using equations (12) and (13) respectively. mean and variance and will As pixels Optimal Focusing Position : (12) (13) Step 4.5: Calculate the pixel points using equation (14) depth value : (14) In equation (21), express The lower limit of scanning, Indicates the scan step size; Step 4.6: Following the steps 4.1 to 4.5, traverse all pixels in the image and obtain the depth value of each pixel to obtain the initial depth map of the surface of the wafer under test. .
4. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the three-dimensional topography reconstruction method for patterned wafer surfaces according to any one of claims 1-3, and the processor is configured to execute the program stored in the memory.
5. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when run by a processor, performs the steps of the three-dimensional topography reconstruction method for the patterned wafer surface as described in any one of claims 1-3.