Quick tilt compensation method based on Zernike polynomial and electronic equipment

Abstract

The invention relates to a rapid tilt compensation method based on a Zernike polynomial. The method comprises the following steps: acquiring a two-dimensional image matrix output by a digital holographic microscope; the two-dimensional image matrix is preprocessed; the preprocessed image intensity matrix is projected to a Zernike polynomial base # imgabs0 #, Zernike fitting is achieved, and a Zernike model of a related sample to be detected is obtained; calculating tilt term coefficients alpha x and alpha y of a first-order polynomial in the Zernike model; and calculating out-of-focus aberration # imgabs1 #, performing tilt compensation on the preprocessed image intensity matrix by adopting tilt term coefficients alpha x and alpha y, and outputting the compensated image intensity matrix. The invention further discloses the corresponding electronic equipment. According to the method, the shot image can be quickly and effectively compensated and corrected, and the robustness and the calculation speed are considerable.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor optical imaging technology, and particularly relates to a tilt compensation method based on a physical model. Background Art

[0002] The tilt effect refers to the phenomenon that due to the tilt of an object, device or system relative to a reference plane or axis, its performance, measurement results or behavior change, and usually tilt compensation is required to correct it. Tilt compensation algorithms are mainly used to correct the tilt effect in images, sensor data or other signals to ensure the accuracy and consistency of the data, and are widely used in the imaging field.

[0003] Currently, the commonly used tilt compensation algorithms can be divided into five categories according to their basic logic: First, the methods based on geometric transformation, such as affine transformation and perspective transformation. However, affine transformation cannot handle some non-linear deformations, and perspective transformation requires accurate four corresponding points, which are difficult to obtain in practical applications; Second, the tilt compensation algorithms based on feature matching, such as SIFT (Scale-Invariant Feature Transform) and SURF (Speeded-Up Robust Features). The robustness and feature matching accuracy of these two types of algorithms are quite suitable, but there are patent problems, which limit commercial applications; Third, the methods based on model fitting, mainly RANSAC (Random Sample Consensus) and Hough Transform. However, the methods based on model fitting all require certain empirical values for modeling, and the computational complexity is very high, and the corresponding robustness and computational speed are slightly inferior; Moreover, there are the tilt compensation methods based on deep learning, such as convolutional neural network (CNN) and generative adversarial network (GAN). However, deep learning networks all require a large amount of data for prior training, and at the same time have high requirements for hardware, and the training takes a long time; The last category is the tilt compensation algorithms based on physical models. The commonly used one is the gravity compensation method, which is mainly used for gravity correction on unmanned aerial vehicles, but this method requires additional sensors to obtain necessary information.

[0004] In summary, among the existing several tilt compensation algorithms, on the one hand, it is difficult to achieve the simultaneous matching of robustness and quality accuracy, and on the other hand, it will be affected by the dynamic blur brought by dynamic measurement, or restricted by the rigidity of the application platform, greatly reducing its applicable range. Therefore, for the field of microscopic imaging, a tilt compensation algorithm with the characteristics of large angle, high precision, fast speed and high robustness is still vacant. Summary of the Invention

[0005] To solve the above problems, the present invention proposes a fast tilt compensation method based on Zernike polynomials, which belongs to the tilt compensation algorithm based on physical models. Based on the basic design logic of Zernike orthogonal polynomials, this method can quickly and effectively perform real-time dynamic compensation and correction on the captured images with tilt angles within a certain range. At the same time, it can also effectively identify the wavefront aberration such as defocus, and perform corresponding operations according to the degree of defocus, thereby realizing the aberration correction of the optical system.

[0006] To achieve the above invention purpose, the technical solution of the present invention is as follows:

[0007] The first aspect of the present invention discloses a fast tilt compensation method based on Zernike polynomials, which includes the following steps:

[0008] Data acquisition: Obtain the two-dimensional image matrix output by the digital holographic microscope. The two-dimensional image matrix is converted from the holographic image of the sample to be measured, contains intensity, position and phase delay information, and can characterize the surface topography characteristics of the sample to be measured;

[0009] Image preprocessing: Preprocess the two-dimensional image matrix to obtain the preprocessed image intensity matrix;

[0010] Zernike fitting: Project the preprocessed image intensity matrix onto the Zernike polynomial basis to achieve Zernike fitting and obtain the Zernike model of the sample to be measured;

[0011] Tilt term coefficient calculation: Calculate the tilt term coefficients α x , α y ;

[0012] Defocus aberration calculation and judgment: Calculate the defocus aberration based on the second-order polynomial in the Zernike model If the defocus aberration perform tilt compensation;

[0013] Tilt compensation: Use the tilt term coefficients α x , α y to perform tilt compensation on the preprocessed image intensity matrix and output the compensated image intensity matrix.

[0014] As an optional solution, the defocus aberration calculation and judgment step further includes: If first correct the preprocessed image intensity matrix, and then perform tilt compensation after correction; if adjust the focusing position of the sample to be measured and re-take the holographic image.

[0015] As an alternative, an adaptive focusing algorithm is used to correct the preprocessed image intensity matrix; the adaptive focusing algorithm is a fast autofocus method based on topological structure and Monte Carlo algorithm.

[0016] As an alternative, in the data acquisition step, the output two-dimensional image matrix is expressed as:

[0017]

[0018] In the Zernike fitting step, the projection calculation method of (x, y) → (ρ, θ) is defined as follows:

[0019]

[0020] In the formula, x and y are the coordinates of the pixel points; ρ is the radius variable in polar coordinates, and its value range is [0, 1]; θ is the angle variable in polar coordinates, and its value range is [0, 2π].

[0021] As an alternative, in the image preprocessing step, the preprocessing includes normalization processing, and the normalized image intensity data I norm (x, y) is expressed as:

[0022] I norm (x, y) = Normalize[I(x, y) - G(x, y) * I(x, y)]

[0023] In the formula, I(x, y) represents the two-dimensional image matrix output by the data acquisition step, Normalize represents the normalization operation, and G(x, y) is the Gaussian kernel.

[0024] As an alternative, in the image preprocessing step, the obvious high-frequency information is first subjected to high-frequency filtering, and then normalized after filtering; the obvious high-frequency information refers to the data information outside the measurement range.

[0025] As an alternative, in the tilt term coefficient calculation step, the tilt term coefficient α x , α y The expression is as follows:

[0026]

[0027] As an alternative, in the tilt compensation step, the compensation calculation formula is as follows:

[0028]

[0029] In the formula, x and y are the coordinates of the pixel points in the two-dimensional image matrix output by the data acquisition step;

[0030] The compensated image intensity matrix I(x′, y′) is obtained.

[0031] As an optional solution, in the defocus aberration calculation and determination step, the calculation formula for the defocus aberration is as follows:

[0032]

[0033] A second aspect of the present invention discloses an electronic device, which includes a processor and a memory; the processor is used to call a computer program stored in the memory to execute the fast tilt compensation method based on Zernike polynomials described in the first aspect of the present invention or any one of its optional solutions.

[0034] The present invention has the following beneficial effects:

[0035] (1) Through rigorous mathematical reasoning and physical modeling, the fast tilt compensation method designed based on Zernike polynomials in the present invention has the characteristics of high calculation efficiency. The time error of the delayed display of the result is within 1 s. Moreover, based on the real-time and dynamic characteristics of the holographic camera during image acquisition and result output, real-time dynamic tilt compensation can be performed using the tilt coefficient, achieving high robustness applicable to both static systems and dynamic scenarios.

[0036] (2) Based on the Zernike model, the present invention can not only perform real-time dynamic compensation and correction on captured images with tilt angles within a certain range, but also effectively identify defocus and perform adaptive focusing or manual focal length adjustment operations according to the defocus degree, effectively solving this wavefront aberration of defocus.

[0037] (3) For the blurring problem caused by factors such as jitter in dynamic measurement, the present invention can achieve dynamic wavefront reconstruction through real-time Zernike model update (i.e., dynamic update of Zernike coefficients). Combined with the adaptive focusing algorithm, it can also efficiently compensate for rapidly changing aberrations, display the image of the measured sample clearly at a high speed, and the fast calculation ensures that it will not affect image acquisition and reconstruction in the dynamic state. Especially in the field of high-precision measurement, its advantages and progressiveness are particularly prominent.

[0038] (4) On the premise of ensuring imaging quality, the present invention can also combine with the existing adaptive focusing algorithm, get rid of the dependence on the sample test platform, and be applicable to both rigid platforms and flexible platforms.

[0039] (5) The present invention can also break through the limitation that Zernike correction is not applicable to large-angle tilts, and expand the application angle range of Zernike correction itself from an angle range of -1 to 1 degree to an angle range of -5 to 5 degrees.

[0040] (6) The present invention can be widely applied to the fields of optics, image processing, and semiconductors, and is particularly suitable for solving the problems of non-linear deformation and rigid platform constraint existing in the semiconductor industrial production process. Description of the Drawings

[0041] Figure 1 It is a schematic diagram of the process of the present invention;

[0042] Figure 2 It is a 3D reconstruction diagram of a wafer without tilt compensation;

[0043] Figure 3 It is a 3D reconstruction diagram of a wafer with tilt compensation;

[0044] Figure 4 It is a 3D diagram of a ceramic step + ramp surface without tilt compensation;

[0045] Figure 5 It is a 3D diagram of a ceramic step + ramp surface with tilt compensation;

[0046] Figure 6 It is a 3D diagram of a ceramic standard block without tilt compensation;

[0047] Figure 7 It is a 3D diagram of a ceramic standard block with tilt compensation. Detailed Embodiment

[0048] The technical solution of the present invention will be further explained and described below in conjunction with specific embodiments and the drawings.

[0049] A high-resolution three-dimensional microscopic imaging system based on holographic imaging technology can record and reconstruct the amplitude (light intensity) and phase information of a sample to be measured.

[0050] The present invention mainly measures the sample based on a digital holographic microscopic optical system, and mainly depends on Zernike polynomials in the algorithm.

[0051] The digital holographic microscopy optical system mainly includes a digital holographic microscope and a computer communicatively connected thereto. Among them, the digital holographic microscope (Digital Holographic Microscopy, abbreviated as DHM) mainly uses the interference principle to collect the holographic image of the sample to be measured through a high-resolution camera (the core component of the digital holographic microscope) and transmit it to the computer; the computer numerically reconstructs the holographic image through the stored algorithm to achieve high-resolution three-dimensional microscopic observation of the sample, and obtains the three-dimensional amplitude information (i.e., light intensity information) and phase information of the sample to be measured, and then completes the digital three-dimensional reconstruction. During the use of the digital holographic microscope, affected by the depth of field of the camera, the data of the super-depth-of-field part caused by the large tilt angle of the test platform where the sample is collected often introduces defocus aberration, which affects the quality of digital image reconstruction.

[0052] Zernike polynomials are a set of orthogonal polynomials defined on the unit circle, which can effectively describe the aberrations in an optical system and provide a mathematical tool for aberration correction. Zernike polynomials consist of a radial polynomial and an angular function, and are usually expressed in polar coordinate form The expression is:

[0053]

[0054] In the formula, n is the radial order (non-negative integer), which determines the complexity of the polynomial; m is the azimuthal frequency (integer, ranging from -n to n, with a step of 2), which reflects the change along the angular direction; ρ is the radius variable in polar coordinates, with a value range of [0,1]; θ is the angle variable in polar coordinates, with a value range of [0,2π]; is the radial polynomial, and the specific definition is as follows:

[0055]

[0056] In the formula, k is the summation variable, and the value range is

[0057] The present invention provides a fast tilt compensation method based on Zernike polynomials, which mainly includes the following steps:

[0058] Step 1, data acquisition.

[0059] Based on a digital holographic microscopy optical system, the present invention uses a camera of digital holographic microscopy to capture an image to obtain a holographic image of a sample to be measured, and this process is also data acquisition. During operation, first, relevant hardware in the digital holographic microscope (such as a beam splitter prism, a plane mirror, a CCD sensor, etc.) is adjusted so that the sample to be measured (abbreviated as "sample") is within the depth of field of the camera, that is, the sample is placed near the focusing position; then, the holographic image of the sample is collected by the camera and converted into a two-dimensional image matrix I(x, y) and transmitted to a computer. This matrix contains the light intensity, position, and corresponding phase delay information of the photographed object. The expression of the two-dimensional image matrix I(x, y) is as follows:

[0060]

[0061] In the formula: x and y are the coordinates of the pixel points, representing the relative position information in the two-dimensional image rectangle information, A(x, y) is the light intensity of the pixel point, φ(x, y) is the phase of the pixel point, and the exponential part in the formula represents the phase delay.

[0062] It should be noted that the samples that can be detected by the present invention can be items such as wafers, mirrors, glass, ceramics, etc. The collected holographic image of the sample reflects the morphological characteristics of the sample surface, and the morphological characteristics include, but are not limited to, the microscopic structural characteristics of the sample surface and defect information such as scratches.

[0063] Step 2: Image preprocessing.

[0064] In order to reduce the influence of noise information on the tilt compensation algorithm, it is usually necessary to preprocess the two-dimensional image matrix I(x, y). The preprocessing mainly includes normalization processing, and after preprocessing, a normalized image intensity matrix I norm .

[0065] The normalized image intensity data I norm is expressed as follows:

[0066] I norm (x, y) = Normalize[I(x, y) - G(x, y) * I(x, y)] (4)

[0067] In the formula, Normalize represents the normalization operation, G(x, y) is a Gaussian kernel, and is usually defined as follows:

[0068]

[0069] In the formula, σ is the standard deviation of the Gaussian kernel.

[0070] It is understandable that when there is obvious high-frequency information in the image, the preprocessing also includes high-frequency filtering. For such images, it is usually necessary to first filter using the Gaussian function and then perform normalization processing. If obvious high-frequency information appears in the image, the image will present highlighted information that is visible to the naked eye and outside the measurement range. Most of this information is introduced by noise, but not all images will have such information. Therefore, the criterion for defining high-frequency information in the present invention is whether the intensity data of the normalized image is within the measurement range. For example, if the height range of the sample to be measured is 0-200um, and information with a height greater than 200um appears, it is obvious high-frequency information.

[0071] Step 3, Zernike fitting.

[0072] Project the processed normalized intensity data I norm (x, y) onto a series of Zernike polynomials of the Zernike polynomial basis to achieve Zernike fitting.

[0073] It is understandable that the Zernike polynomial basis refers to a function space composed of a series of Zernike polynomials. These polynomials, as basis functions, can be used to expand and represent any function defined on the unit circle. Specifically, the basis of the Zernike polynomial consists of Zernike polynomials with different radial orders n (abbreviated as "n") and angular frequencies m (abbreviated as "m"). According to the definition of the correlation coefficients of the Zernike polynomial basis, the polynomial represents the constant term, indicating the average light intensity or the overall smoothness of the wavefront; the first-order polynomials and represent tilt, indicating the linear tilt of the wavefront; the second-order polynomial represents defocus, indicating the quadratic curvature of the wavefront; the second-order polynomial represents astigmatism, indicating the asymmetry of the wavefront.

[0074] Specifically, projecting the normalized intensity data I norm (x, y) onto a series of Zernike polynomials of the Zernike polynomial basis is actually a projection from (x, y) → (ρ, θ), and the projection method is defined as follows:

[0075]

[0076] After the projection is completed, Zernike fitting can be achieved, and a specific Zernike model for the sample to be measured can be obtained.

[0077] Step 4, calculate the tilt term coefficient.

[0078] Since the present invention only corrects the tilt in the plane direction of the sample, only the tilts in the x-axis and y-axis directions need to be corrected. Based on the exclusive Zernike model of the sample to be measured, for the normalized intensity data after Zernike fitting, according to the definition of the correlation coefficient of the Zernike polynomial basis, only the first-order polynomial needs to be calculated, that is, n = 1.

[0079]

[0080] Among them, the radial polynomial

[0081] Therefore, the above two polynomials (7) and (8) can be simplified as:

[0082]

[0083] Thus, the first-order polynomial can be simplified to two parameters, α x , α y and these two parameters are used as the tilt term coefficients.

[0084] Step 5: Calculate the defocus aberration Judge the defocus degree.

[0085] According to the definition of the correlation coefficient of the Zernike polynomial basis, when calculating the defocus aberration, n and m are taken as 2 and 0 respectively. When using a digital holographic microscopy optical system, the defocus aberration brought by the super-depth-of-field data often affects the tilt compensation error. Therefore, based on the exclusive Zernike model of the sample to be measured, the defocus aberration can also be calculated first through the Zernike polynomial Then, according to the defocus aberration Judge the overall offset of the data collected in Step 1 relative to the data collected at the ideal position, and analyze whether it is necessary to further process the data.

[0086] Among them, the calculation formula of the defocus aberration is as follows:

[0087]

[0088] It can be understood that if indicates that the actual imaging plane is in front of the theoretical focal plane (under-focus), means that the actual imaging plane is behind the theoretical focal plane (over-focus). Whether under-focus or over-focus, it is necessary to return to Step 1 to readjust the focusing position of the digital holographic microscope, or use an adaptive focusing algorithm to correct the input data in Step 1.

[0089] Among them, the adaptive focusing algorithm can refer to the technical solution described in the patent application with the publication number CN118778220A and the invention title "A Fast Automatic Focusing Method Based on Topological Structure and Monte Carlo Algorithm" submitted by the applicant before. The specific algorithm process is explained in detail in this patent, and will not be elaborated in this invention.

[0090] Generally, the larger the absolute value of , the more serious the defocus; conversely, if is close to zero, it indicates that there is almost no defocus, and the next step of tilt compensation can be carried out. For example, it can be set that when directly enter step 6 for tilt compensation; when the absolute value of is within the range of 0 to 1, that is it indicates that the defocus is within an acceptable range, and the adaptive focusing algorithm is selected to correct the normalized image intensity data, and then tilt compensation is carried out after correction;

[0091] Step 6, perform tilt compensation and output the holographic imaging result.

[0092] Through the tilt term coefficient α x , α y calculated in step 4, perform corresponding position fitting on the normalized image intensity matrix I norm obtained in step 2, perform tilt compensation using the relationship in formula (12), and calculate the compensated image intensity matrix I(x′, y′) to realize the adjustment of the pixel position in the holographic image.

[0093]

[0094] It can be understood that I(x′, y′) after fitting represents the intensity information after the adjustment of the pixel position in the holographic image.

[0095] For different image features (that is, the surface topography of the sample to be measured, for example, the ceramic surface is relatively smooth and the feature information is relatively less; the surface of the wafer is in the shape of tin balls, and there will be more relative feature information), different compensation schemes can be used. It should be noted that formula (12) is more suitable for tilt compensation correction of small angles (-1 to 1 degree), which is also the conventional compensation range of Zernike; for tilt compensation of large angles (-5 to 5 degrees), the parameter of the reconstruction angle can be introduced to correct the image data collected by the holographic camera first to achieve large-angle compensation.

[0096] It is understandable that tilt compensation is the last step in holographic microscopy. Therefore, after compensation, the holographic imaging result can be output, that is, the final imaging effect data is output after position fitting or holographic camera acquisition and reconstruction. Further, after tilt compensation is completed, the effect of tilt compensation can be evaluated by comparing the image quality before and after compensation.

[0097] In summary, through rigorous mathematical reasoning and physical modeling, based on the Zernike polynomial coefficients, the present invention designs a fast tilt compensation method with considerable robustness and calculation speed. It can not only perform real-time dynamic compensation and correction on the captured images with tilt angles within a certain range, but also effectively identify wavefront aberrations such as defocus, and perform corresponding operations according to the degree of defocus, thereby realizing aberration correction of the optical system.

[0098] Based on the tilt compensation method described in the present invention, two specific application cases are given below to verify the tilt compensation effect of the present invention.

[0099] Application case 1: Detection of the surface topography of a wafer. A wafer usually consists of multiple die units. The height of a single solder ball in the micro-structure on the wafer surface is about 80um, and the height of the groove between adjacent solder balls is 15um.

[0100] When detecting the surface topography of a wafer, without using the tilt compensation method disclosed in the present invention, the detection result is restricted by the rigid platform. Given that the measurement accuracy is in the nm-um level, a small-angle tilt of the measurement platform will greatly affect the imaging effect. The specific 3D effect diagram is as Figure 2 shown. Obviously, without tilt compensation, since it is difficult to adjust the platform to be absolutely flat, it will cause a height difference in the adjacent die units that should be in the same plane during the measurement due to the tilt effect.

[0101] After tilt compensation is performed using the tilt compensation method disclosed in the present invention, the imaging result is as Figure 3 shown. It can be seen that the colors of the three measured die units are basically the same, that is to say, the height difference caused by tilt between the three die units is corrected.

[0102] Application case 2: Detection of surface defects of ceramics. When detecting surface defects of ceramics, a ceramic standard block with a thickness of 1mm and a ceramic ramp with a height deviation of 0.5mm are usually used for combined measurement. Among them, the ceramic standard block is used as a reference standard, which is a ceramic block with known dimensions and surface quality for calibrating and verifying the detection equipment; the ceramic ramp is a ceramic inclined plane with a specific angle for simulating different surface states to help the detection equipment identify surface defects at different angles and curvatures.

[0103] When the tilt compensation method disclosed in the present invention is not used, the small-angle tilt of the measurement platform causes the surface of the ceramic standard block to present a tilted imaging effect, and at the same time, it will also affect the reconstruction result of the topography of the ceramic ramp surface. The specific 3D effect diagram is as Figure 4 shown.

[0104] After tilt compensation by the tilt compensation method disclosed in the present invention, the result is as Figure 5 shown. The tilt of the surface of the upper half of the ceramic standard block caused by the measurement platform has been effectively corrected.

[0105] Among them, Figure 6 and Figure 7 respectively show the schematic diagrams of the effect comparison of a single ceramic standard block before and after tilt compensation without using the tilt compensation algorithm disclosed in the present invention and after using the tilt compensation method disclosed in the present invention. It can be seen that the tilt compensation accuracy of the present invention reaches the nm level.

[0106] Furthermore, an electronic device is also disclosed in the embodiments of the present invention, which mainly includes a processor and a memory. The processor is mainly used to call the computer program stored in the memory and execute the above-mentioned fast tilt compensation method based on Zernike polynomials. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the program code in the above-mentioned electronic device and computer-readable storage medium can refer to the corresponding process in the foregoing method embodiments, and will not be elaborated here.

[0107] Finally, it should be noted that although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, rather than restrictive. Under the inspiration of this specification, those of ordinary skill in the art can also make many forms without departing from the scope protected by the claims of the present invention, and these all belong to the scope of protection of the present invention.

Claims

1. A fast tilt compensation method based on Zernike polynomials, characterized in that, It includes the following steps: Data acquisition: Obtain a two-dimensional image matrix output by a digital holographic microscope, which is converted from the holographic image of the sample to be measured, contains intensity, position, and phase delay information, and can characterize the surface topography features of the sample to be measured; Image preprocessing: Preprocess the two-dimensional image matrix to obtain a preprocessed image intensity matrix; Zernike fitting: Project the preprocessed image intensity matrix onto the Zernike polynomial basis to achieve Zernike fitting and obtain the Zernike model of the sample to be measured; Calculation of tilt term coefficient: Calculate the tilt term coefficient α of the first-order polynomial in the Zernike model x , α y ; Defocus aberration calculation and judgment: Calculate the defocus aberration based on the second-order polynomial of the Zernike model If the defocus aberration Proceed to the next step of tilt compensation; Skew compensation: Using the skew term coefficient α x , α y Perform skew compensation on the preprocessed image intensity matrix and output the compensated image intensity matrix.

2. The rapid tilt compensation method according to claim 1, wherein The defocus aberration calculation and judgment steps further include: If first correct the preprocessed image intensity matrix, and then perform tilt compensation after correction; If it is necessary to adjust the focusing position of the sample to be measured and re-take the holographic image.

3. The rapid tilt compensation method according to claim 2, wherein Use an adaptive focusing algorithm to correct the preprocessed image intensity matrix; the adaptive focusing algorithm is a fast automatic focusing method based on topological structure and Monte Carlo algorithm.

4. The rapid tilt compensation method according to any one of claims 1 to 3, characterized in that In the data acquisition step, the output two-dimensional image matrix is expressed as: In the Zernike fitting step, the projection calculation method of (x, y) → (ρ, θ) is defined as follows: In the formula, x and y are the coordinates of pixel points; ρ is the radius variable in polar coordinates, and its value range is [0, 1]; θ is the angle variable in polar coordinates, and its value range is [0, 2π].

5. The rapid tilt compensation method according to claim 4, wherein In the image preprocessing step, the preprocessing includes normalization processing, and the normalized image intensity data I norm (x, y) is expressed as: I norm (x,y) = Normalize[I(x,y) - G(x,y) * I(x,y)] In the formula, I(x, y) represents the two-dimensional image matrix output by the data acquisition step, Normalize represents the normalization operation, and G(x, y) is the Gaussian kernel.

6. The rapid tilt compensation method according to claim 4, characterized in that, In the image preprocessing step, high-frequency filtering is first performed on the obvious high-frequency information, and then normalization processing is performed after filtering; the obvious high-frequency information refers to the data information outside the measurement range.

7. The rapid tilt compensation method according to claim 4, wherein In the step of calculating the tilt term coefficient, the tilt term coefficient α x , α y has the following expression:

8. The rapid tilt compensation method according to claim 4, wherein In the tilt compensation step, the compensation calculation formula is as follows: In the formula, x and y are the coordinates of pixel points in the two-dimensional image matrix output by the data acquisition step; After compensation, the image intensity matrix I(x′, y′) is obtained.

9. The rapid tilt compensation method according to claim 4, wherein, In the defocus aberration calculation and judgment step, the calculation formula of defocus aberration is as follows:

10. An electronic device, characterized in that, It includes a processor and a memory; the processor is used to call the computer program stored in the memory and execute the fast tilt compensation method based on Zernike polynomial described in any one of claims 1 to 9.

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