Fast tilt compensation method based on zernike polynomials and electronic device

Abstract

The application discloses a fast tilt compensation method based on Zernike polynomials, which comprises the following steps: obtaining a two-dimensional image matrix output by a digital holographic microscope; pre-processing the two-dimensional image matrix; projecting the pre-processed image intensity matrix onto a Zernike polynomial base, realizing Zernike fitting, and obtaining a Zernike model about a sample to be measured; calculating tilt term coefficients alpha x , alpha y of a first-order polynomial in the Zernike model; calculating defocus aberration by using the tilt term coefficients alpha x , alpha y ; performing tilt compensation on the pre-processed image intensity matrix, and outputting a compensated image intensity matrix. Further, corresponding electronic equipment is disclosed. The application can quickly and effectively compensate and correct a photographed image, and is quite considerable in robustness and calculation speed.

Description

Technical Field

[0001] This invention relates to the field of semiconductor optical imaging technology, and more specifically to a tilt compensation method based on a physical model. Background Technology

[0002] Tilt effects refer to the phenomenon where the performance, measurement results, or behavior of an object, device, or system changes due to its tilt relative to a reference plane or axis, and are usually corrected through tilt compensation. Tilt compensation algorithms are mainly used to correct tilt effects in images, sensor data, or other signals, ensuring data accuracy and consistency, and are widely used in the imaging field.

[0003] Currently, commonly used tilt compensation algorithms can be divided into five main categories based on their basic logic: First, methods based on geometric transformations, such as affine transformations and perspective transformations. However, affine transformations cannot handle some nonlinear deformations, and perspective transformations require four precise corresponding points, which are difficult to obtain in practical applications. Second, tilt compensation algorithms based on feature matching, such as SIFT (Scale-Invariant Feature Transform) and SURF (Speeded-Up Robust Features). These two types of algorithms have suitable robustness and feature matching accuracy, but patent issues limit their commercial application. Third, methods based on model fitting, mainly RANSAC (Random Sample Consensus) and Hough. Transform is one approach, but model-fitting methods require empirical modeling, resulting in high computational complexity and slightly inferior robustness and speed. Another approach is tilt compensation based on deep learning, such as convolutional neural networks (CNNs) and generative adversarial networks (GANs). However, deep learning networks require a large amount of prior data for training, have high hardware requirements, and take a long time to train. The last category is tilt compensation algorithms based on physical models, commonly using gravity compensation methods, mainly for gravity correction on drones. However, this method requires additional sensors to obtain the necessary information.

[0004] In summary, existing tilt compensation algorithms struggle to simultaneously balance robustness and accuracy. Furthermore, they are susceptible to dynamic blurring caused by dynamic measurements or are constrained by the rigidity of the application platform, significantly limiting their applicability. Therefore, a tilt compensation algorithm that combines large-angle, high-precision, fast, and highly robust characteristics for the field of microscopic imaging remains unmet. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a fast tilt compensation method based on Zernike polynomials. This method belongs to the category of tilt compensation algorithms based on physical models. Based on the fundamental design logic of Zernike orthogonal polynomials, it can quickly and effectively perform real-time dynamic compensation and correction on images captured with tilt angles within a certain range. It can also effectively identify wavefront distortion such as defocus and perform corresponding operations based on the degree of defocus, thereby achieving optical system aberration correction.

[0006] To achieve the above-mentioned objectives, the technical solution of this invention is as follows:

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

[0008] Data acquisition: Acquire a two-dimensional image matrix output by a digital holographic microscope. The two-dimensional image matrix is ​​obtained by converting the holographic image of the sample under test, and contains information on light intensity, position and phase delay, and can characterize the surface morphology of the sample under test.

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

[0010] Zernike Fitting: Projecting the preprocessed image intensity matrix onto a Zernike polynomial basis. The Zernike fit is then implemented, and a Zernike model for the sample to be tested is obtained.

[0011] Calculation of sloping term coefficients: Calculate the sloping term coefficients α of the first-order polynomial in the Zernike model. x ,α y ;

[0012] Defocus aberration calculation and judgment: Defocus aberration is calculated based on the second-order polynomial in the Zernike model. If the image is out of focus Perform tilt compensation;

[0013] Inclination compensation: using the aforementioned inclination term coefficient α x ,α y The preprocessed image intensity matrix is ​​tilt compensated, and the compensated image intensity matrix is ​​output.

[0014] As an optional solution, the defocus aberration calculation and judgment steps further include: if First, the intensity matrix of the preprocessed image is corrected, and then tilt compensation is performed; if Adjust the focus position of the sample to be tested and re-capture 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 topology and Monte Carlo algorithm.

[0016] As an optional solution, the output two-dimensional image matrix in the data acquisition step is represented as follows:

[0017]

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

[0019]

[0020] In the formula, x and y are the coordinates of the pixel; 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].

[0021] As an optional approach, the image preprocessing step includes normalization processing, and the preprocessed normalized image intensity data I norm (x,y) can be represented 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 optional approach, in the image preprocessing step, high-frequency information is first subjected to high-frequency filtering, and then normalized; the high-frequency information refers to data information that is not within the measurement range.

[0025] As an optional solution, in the step of calculating the tilt term coefficient, the tilt term coefficient α x ,α y The expression is as follows:

[0026]

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

[0028]

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

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

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

[0032]

[0033] A second aspect of the present invention discloses an electronic device comprising a processor and a memory; the processor is configured to invoke a computer program stored in the memory to execute the fast tilt compensation method based on Zernike polynomials as described in the first aspect of the present invention or any alternative embodiment thereof.

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

[0035] (1) This invention uses rigorous mathematical reasoning and physical modeling to develop a fast tilt compensation method based on Zernike polynomial design. It has the characteristics of high computational efficiency and the error of the delayed display time of the result is within 1 second. Furthermore, based on the real-time and dynamic characteristics of the holographic camera in image acquisition and result output, the tilt coefficient can be used for real-time dynamic tilt compensation, achieving high robustness applicable to both static systems and dynamic scenes.

[0036] (2) Based on the Zernike model, this invention can not only perform real-time dynamic compensation and correction for images with tilt angles within a certain range, but also effectively identify out-of-focus and perform adaptive focusing or manual adjustment of focus according to the degree of out-of-focus, effectively solving the wavefront distortion caused by out-of-focus.

[0037] (3) For the blurring problem caused by jitter and other factors in dynamic measurement, the present invention can realize dynamic wavefront reconstruction by updating the Zernike model in real time (that is, dynamically updating the Zernike coefficients). Combined with the adaptive focusing algorithm, it can also efficiently compensate for rapidly changing aberrations and realize the dynamic clear image display of the measured sample by updating at a high rate. At the same time, the fast calculation ensures that it will not affect the acquisition and reconstruction of the image in the dynamic state. Its advantages and progress are particularly prominent in the field of high-precision measurement.

[0038] (4) While ensuring imaging quality, this invention can also combine existing adaptive focusing algorithms to get rid of dependence on sample testing platforms and can be applied to both rigid and flexible platforms.

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

[0040] (6) This invention can be widely applied in the fields of optics, image processing and semiconductors, and is particularly suitable for solving the problems of nonlinear deformation and rigid platform constraints in the semiconductor industrial production process. Attached Figure Description

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

[0042] Figure 2 This is a 3D reconstruction of a wafer without tilt compensation.

[0043] Figure 3 A 3D reconstruction of the wafer after tilt compensation;

[0044] Figure 4 3D model of ceramic steps and slope surface without tilt compensation;

[0045] Figure 5 3D model of a ceramic step with slope compensation;

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

[0047] Figure 7 This is a 3D image of a ceramic standard block after tilt compensation. Detailed Implementation

[0048] The technical solution of the present invention will be further explained and described below with reference to specific embodiments and accompanying 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 the sample under test.

[0050] This invention primarily relies on a digital holographic microscopy optical system for sample measurement, and its algorithm mainly depends on Zernike polynomials.

[0051] A digital holographic microscopy optical system mainly consists of a digital holographic microscope and a computer connected to it. The digital holographic microscope (DHM) primarily utilizes the principle of interference to acquire holographic images of the sample under test through a high-resolution camera (the core component of the digital holographic microscope) and transmits them to the computer. The computer then uses stored algorithms to numerically reconstruct the holographic images, enabling high-resolution three-dimensional microscopic observation of the sample and obtaining its three-dimensional amplitude information (i.e., light intensity information) and phase information, thereby completing the digital three-dimensional reconstruction. During the use of a digital holographic microscope, the depth of field of the camera, particularly the large tilt angle of the test platform where the sample is acquired, often introduces defocus aberrations due to the excessive depth of field, affecting the quality of the digital image reconstruction.

[0052] Zernike polynomials are a set of orthogonal polynomials defined on the unit circle that can effectively describe aberrations in optical systems and provide mathematical tools for aberration correction. Zernike polynomials consist of radial polynomials and angular functions, and are typically expressed in polar coordinates. The expression is:

[0053]

[0054] In the formula, n is the radial order (a non-negative integer), which determines the complexity of the polynomial; m is the azimuth frequency (an integer, ranging from -n to n, with a step size 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]. It is a radial polynomial, specifically defined as follows:

[0055]

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

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

[0058] Step 1: Data collection.

[0059] This invention is based on a digital holographic microscopy optical system. It uses a camera in a digital holographic microscope to capture holographic images of the sample under test; this process is also known as data acquisition. During operation, the relevant hardware in the digital holographic microscope (e.g., beam splitter, plane mirror, CCD sensor, etc.) is first adjusted so that the sample under test (hereinafter referred to as "sample") is within the depth of field of the camera, that is, placed near the focus position. Then, the holographic image of the sample is acquired by the camera and converted into a two-dimensional image matrix I(x,y) which is transmitted to the computer. This matrix contains the light intensity, position, and corresponding phase delay information of the photographed object. The expression for the two-dimensional image matrix I(x,y) is as follows:

[0060]

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

[0062] It is worth noting that the samples that can be detected by this invention can be items such as wafers, mirrors, glass, and ceramics. The acquired holographic images of the samples reflect the morphological features of the sample surface, including but not limited to the microstructural features of the sample surface and defect information such as scratches.

[0063] Step 2: Image preprocessing.

[0064] To reduce the impact of noise on tilt compensation algorithms, preprocessing of the two-dimensional image matrix I(x,y) is typically required. Preprocessing mainly includes normalization, resulting in a normalized image intensity matrix I. norm .

[0065] Normalized image intensity data I norm It 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, and G(x,y) is the Gaussian kernel, which is usually defined as follows:

[0068]

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

[0070] Understandably, when there is significant high-frequency information in an image, preprocessing also includes high-frequency filtering. For such images, Gaussian filtering is typically used first, followed by normalization. If significant high-frequency information appears in an image, it will exhibit visible highlights outside the measurement range. This type of information is mostly introduced by noise, but not all images will show it. Therefore, the standard for defining high-frequency information in this invention is whether the normalized image intensity data is within the measurement range. For example, if the height range of the sample to be measured is 0-200 μm, and information with a height greater than 200 μm appears, it is considered significant high-frequency information.

[0071] Step 3: Zernike fitting.

[0072] The processed normalized intensity data I norm (x,y) is a series of Zernike polynomials projected onto a Zernike polynomial basis. On the above, Zernike fitting is achieved.

[0073] Understandably, a 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, a Zernike polynomial basis consists of Zernike polynomials with different radial orders n (referred to as "n") and angular frequencies m (referred to as "m"). According to the definition of the correlation coefficient of the Zernike polynomial basis, the polynomial... The constant term represents the overall stationarity of the average light intensity or wavefront; a first-order polynomial. and The term represents a tilt, indicating a linear tilt of the wavefront; a second-order polynomial. Represents defocus, indicating the quadratic curvature of the wavefront; second-order polynomial. It represents astigmatism and indicates the asymmetry of the wavefront.

[0074] Specifically, the normalized intensity data I norm (x,y) is a series of Zernike polynomials projected onto a Zernike polynomial basis. In essence, it's a projection from (x,y) to (ρ,θ), and the projection method is defined as follows:

[0075]

[0076] Once projection is complete, Zernike fitting can be achieved, and a specific Zernike model for the sample to be tested can be obtained.

[0077] Step 4: Calculate the skew term coefficient.

[0078] Since this invention only corrects tilt in the planar direction of the sample, only the tilt in the x-axis and y-axis directions needs to be corrected. Based on a dedicated Zernike model for the sample, this invention uses the normalized intensity data after Zernike fitting. According to the definition of the basis correlation coefficient of the Zernike polynomial, only the first-order polynomial needs to be calculated, i.e., n=1.

[0079]

[0080] Among them, radial polynomial

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

[0082]

[0083] Therefore, the first-order polynomial can be simplified to α x ,α y Two parameters are used as the coefficients of the skew term.

[0084] Step 5: Calculate the defocus aberration. Determine the degree of out-of-focus.

[0085] According to the definition of the Zernike polynomial basis correlation coefficient, n and m are taken as 2 and 0, respectively, when calculating defocus aberration. In digital holographic microscopy optical systems, defocus aberration caused by super-depth-of-field data often affects tilt compensation error. Therefore, this invention, based on a dedicated Zernike model of the sample under test, can first calculate the defocus aberration using Zernike polynomials. Then based on the defocus aberration Determine the overall offset of the data collected in step 1 relative to the data collected at the ideal location, and analyze whether further data processing is required.

[0086] The formula for calculating defocus aberration is as follows:

[0087]

[0088] Understandable, if This indicates that the actual imaging plane is located in front of the theoretical focal plane (underfocus). This means that the actual imaging plane is behind the theoretical focal plane (overfocus). Whether it is underfocus or overfocus, it is necessary to return to step 1 to readjust the focus position of the digital holographic microscope, or use an adaptive focusing algorithm to correct the input data in step 1.

[0089] The adaptive focusing algorithm can be found in the invention patent previously submitted by the applicant, with publication number CN118778220A and invention title "A fast automatic focusing method based on topology and Monte Carlo algorithm". The patent provides a detailed explanation of the specific algorithm process, which will not be repeated here.

[0090] generally, The larger the absolute value, the more severe the out-of-focus condition; conversely, if... A value close to zero indicates almost no out-of-focus issue, allowing for the next step of tilt compensation. For example, you can set... Proceed directly to step 6 for tilt compensation; When the absolute value is in the range of 0 to 1, that is... This indicates that the out-of-focus is within an acceptable range, and an adaptive focus algorithm is selected to correct the normalized image intensity data, followed by tilt compensation. When the absolute value is greater than 1, that is... This indicates severe out-of-focus issues, requiring you to return to step 1 to readjust the focus position and reacquire data.

[0091] Step 6: Tilt compensation and output holographic imaging results.

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

[0093]

[0094] Understandably, the fitted I(x′,y′) represents the intensity information after adjusting the pixel positions of the holographic image.

[0095] Different compensation schemes can be used for different image features (i.e., the surface morphology of the sample under test; for example, the ceramic surface is relatively smooth and has relatively less feature information; the wafer surface has a tin ball morphology and has relatively more feature information). 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 reconstruction angle parameter can be introduced to first correct the image data acquired by the holographic camera in order to achieve large angle compensation.

[0096] As is understandable, tilt compensation is the final step in holographic microscopy. Therefore, after compensation, the holographic imaging result can be output, which is the final imaging data output after position fitting or reconstruction by a holographic camera. Furthermore, 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, this invention, through rigorous mathematical reasoning and physical modeling, and based on Zernike polynomial coefficients, designs a fast tilt compensation method with considerable robustness and computational speed. It can not only perform real-time dynamic compensation and correction for images captured with tilt angles within a certain range, but also effectively identify wavefront distortion 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 this invention, two specific application examples are given below to verify the tilt compensation effect of this invention.

[0099] Application Case 1: Wafer Surface Morphology Inspection. A wafer is typically composed of multiple grain units. In the microstructure of the wafer surface, the height of a single solder ball is about 80 μm, and the trench height between adjacent solder balls is about 15 μm.

[0100] When performing wafer surface morphology inspection without using the tilt compensation method disclosed in this invention, the inspection results are constrained by a rigid platform. Given that the measurement accuracy is at the nm-µm level, even a small angle of tilt of the measurement platform will greatly affect the imaging effect. A specific 3D effect image is shown below. Figure 2 As shown. Obviously, without tilt compensation, it is difficult to adjust the platform to be absolutely flat, which will cause adjacent grain units that should be on the same plane to have height differences due to the tilt effect during the measurement process.

[0101] After tilt compensation using the tilt compensation method disclosed in this invention, the imaging result is as follows: Figure 3 As shown, the colors of the three measured grain units are basically the same, which means that the height difference between the three grain units caused by tilting has been corrected.

[0102] Application Case 2: Ceramic Surface Defect Detection. When detecting ceramic surface defects, a 1mm thick ceramic standard block is typically used in conjunction with a ceramic ramp with a height deviation of 0.5mm. The ceramic standard block serves as a reference standard, containing ceramic blocks of known dimensions and surface quality, used to calibrate and verify the testing equipment. The ceramic ramp, on the other hand, is a ceramic inclined surface with a specific angle, used to simulate different surface conditions, helping the testing equipment identify surface defects at different angles and curvatures.

[0103] Without using the tilt compensation method disclosed in this invention, even small-angle tilts of the measurement platform result in a tilted imaging effect on the surface of the ceramic standard block, which also affects the reconstruction results of the ceramic slope surface morphology. Specific 3D renderings are shown below. Figure 4 As shown.

[0104] After tilt compensation using the tilt compensation method disclosed in this invention, the result is as follows: Figure 5 As shown, the tilt of the upper ceramic standard block surface due to the measurement platform was effectively corrected.

[0105] in, Figure 6 and Figure 7 The diagrams show a comparison of the effects of tilt compensation on a single ceramic standard block before and after using the tilt compensation method disclosed in this invention. It can be seen that the tilt compensation accuracy using this invention reaches the nm level.

[0106] Furthermore, this embodiment of the invention also discloses an electronic device, 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-described fast tilt compensation method based on Zernike polynomials. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the program code in the above-described electronic device and computer-readable storage medium can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated 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 specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art, guided by this specification, can make many other forms without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A fast tilt compensation method based on Zernike polynomials, characterized in that, Includes the following steps: Data acquisition: Acquire a two-dimensional image matrix output by a digital holographic microscope. The two-dimensional image matrix is ​​obtained by converting the holographic image of the sample under test, and contains information on light intensity, position and phase delay, and can characterize the surface morphology of the sample under test. Image preprocessing: The two-dimensional image matrix is ​​preprocessed to obtain the preprocessed image intensity matrix; Zernike fitting: Projecting the preprocessed image intensity matrix onto a series of Zernike polynomials on a Zernike polynomial basis. The Zernike coefficients are dynamically updated to achieve Zernike fitting, thus obtaining a Zernike model for the sample to be tested. Calculation of sloping term coefficients: Calculate the sloping term coefficients of the first-order polynomial in the Zernike model. ; Defocus aberration calculation and judgment: Defocus aberration is calculated based on the second-order polynomial of the Zernike model. If out-of-focus aberration =0, proceed to the next tilt compensation step; the defocus aberration is used to characterize the overall offset of the data acquired in the data acquisition step relative to the data acquired at the ideal position; Inclination compensation: using the aforementioned inclination term coefficient The preprocessed image intensity matrix is ​​dynamically tilted in real time, and the compensated image intensity matrix is ​​output. The defocus aberration calculation and judgment steps also include: if First, the intensity matrix of the preprocessed image is corrected, and then tilt compensation is performed; if If so, it is necessary to adjust the focus position of the sample to be tested and re-capture the holographic image.

2. The rapid tilt compensation method as described in claim 1, characterized in that, An adaptive focusing algorithm is used to correct the intensity matrix of the preprocessed image; the adaptive focusing algorithm is a fast autofocus method based on topology and Monte Carlo algorithm.

3. The rapid tilt compensation method as described in any one of claims 1 to 2, characterized in that, In the data acquisition step, the output two-dimensional image matrix is ​​represented as follows: In the Zernike fitting step The projection calculation method is defined as follows: In the formula, These are the coordinates of the pixels; It is the radius variable in polar coordinates, with a value range of [0, 1]. It is an angle variable in polar coordinates, with a value range of [0, 2]. π ].

4. The rapid tilt compensation method as described in claim 3, characterized in that, The image preprocessing step includes normalization, resulting in normalized image intensity data. Represented as: In the formula, This represents the two-dimensional image matrix output from the data acquisition step. Represents normalization operation. It is a Gaussian kernel.

5. The rapid tilt compensation method as described in claim 3, characterized in that, In the image preprocessing step, high-frequency information is first subjected to high-frequency filtering, and then normalization is performed; the high-frequency information refers to data information that is not within the measurement range.

6. The rapid tilt compensation method as described in claim 3, characterized in that, In the step of calculating the tilt term coefficient, the tilt term coefficient The expression is as follows: 。 7. The rapid tilt compensation method as described in claim 3, characterized in that, In the tilt compensation step, the compensation calculation formula is as follows: In the formula, These are the coordinates of pixels in the two-dimensional image matrix output from the data acquisition step; The image intensity matrix is ​​obtained after compensation. .

8. The rapid tilt compensation method as described in claim 3, characterized in that, In the defocus aberration calculation and judgment steps, the formula for calculating defocus aberration is as follows: 。 9. An electronic device, characterized in that, It 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 as described in any one of claims 1 to 8.

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