Curved surface optical element surface image correction method

Abstract

The invention is suitable for the technical field of image correction, and provides a curved-surface optical element surface image correction method, which comprises the following steps of: segmenting an annular sub-image; calculating an annular sub-image correction factor; calculating a center amplification coefficient and an edge stretching coefficient; slicing an annular sub-image; center amplification; image edge stretching; and re-splicing the image, specifically, re-splicing all the corrected and processed annular sub-images to form a final corrected image. According to the invention, the original image with the distortion effect can be effectively corrected. Along with the increase of the number of the image slices, the image correction effect is better. And when the number of the slices approaches to infinite, the image is basically restored, so that the shape and the size of the surface defect of the curved-surface optical element can be accurately corrected, and the interference of the distortion effect on defect detection can be remarkably reduced or even eliminated, thereby providing a more accurate and reliable detection result.

Description

Technical Field

[0001] The present invention belongs to the technical field of image correction, and in particular relates to a method for correcting the surface image of a curved optical element. Background Art

[0002] Surface defect detection of optical components is essential to ensure the performance of optical systems. Lenses, mirrors, prisms and other components are core components of many high-tech devices, including microscopes, telescopes, camera lenses, laser systems, and various medical and industrial imaging equipment. Any tiny surface flaw may affect the way light passes through or reflects, thereby affecting image quality. With the development of technology, the application range of optical components is constantly expanding, and the requirements for accuracy are also increasing. Advanced detection technology can not only find problems that cannot be identified by traditional methods, but also promote the development of new manufacturing technologies and materials.

[0003] The detection methods of planar optical components are mainly divided into imaging method and energy method. The imaging method uses visual, filtering (high-pass, low-pass, adaptive) and grazing methods, combined with image analysis to identify surface defects of components. The energy law focuses on the quantitative analysis of scattered light energy, such as scattered energy analysis and spectrum analysis, to evaluate defect characteristics. With the leap of machine vision and AI technology, automated detection technology based on computer vision has become the new normal for planar optical component detection, significantly improving the accuracy and efficiency of detection. In addition, microscopic scattering imaging technology has also been widely used in the design of surface defect detection equipment in scientific research and industrial production. Although high-resolution microscopes (such as AFM, STM, interference microscopes, etc.) can provide detailed surface defect information, their high cost and slow detection speed limit their wide application.

[0004] The complex shape and curved surface characteristics of curved optical components make defect detection more difficult. Traditional detection methods are often not directly applicable, and higher precision and more complex algorithms are required to accurately identify and quantify defects. Optical coherence tomography (OCT) is mainly used for internal defect detection of non-transparent materials, but in some cases it can also be used for surface detection of curved optical components. The Sm-Net OCT proposed in the current study can significantly improve the adaptability and practicality of OCT imaging and expand its application field. However, this method has high hardware cost and complex detection process, and is more suitable for the detection of internal defects of materials. Infrared thermal imaging technology uses infrared radiation to detect the temperature difference of objects to find possible defects, but the detection effect of small defects is limited. The Spherical Surface Defect Evaluation System (SSDES) is based on the detection principle of microscopic scattered dark field illumination, including variable aperture angle illumination light source, automatic centering system, imaging system and multi-axis spatial posture adjustment system. It can detect surface defects of curved optical components, but its hardware is complex, the detection steps are cumbersome, and there may be errors in the hardware posture adjustment.

[0005] In order to complete the surface defect detection of curved optical components more quickly and efficiently, combining advanced machine vision technology and deep learning algorithms is a feasible solution. However, the non-planar characteristics of curved optical components cause distortion effects in the images obtained by the camera, which poses a challenge to the detection of surface defects. At present, there is no effective method to correct the image of the curved optical component obtained by a single camera from a top-down perspective to eliminate the distortion effect and restore its true shape and size. To this end, the present invention proposes a surface image correction method for curved optical components. Summary of the invention

[0006] The purpose of the present invention is to provide a method for correcting the surface image of a curved optical element, aiming to solve the problems raised in the above-mentioned background technology.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A method for correcting a surface image of a curved optical element comprises the following steps:

[0009] Step 1: segmenting the annular sub-image, specifically: dividing the half-section image of the curved optical element into equal parts with the center of the circle as the reference point to form multiple annular sub-image slices; by calculating the length of each arc segment and its projection length in the x-axis direction, finally obtaining the radius difference between the kth annular ring and the k-1th annular ring;

[0010] Step 2: Calculate the correction factor of the annular sub-image, specifically: for each annular sub-image slice, calculate its correction factor in the x-axis direction to correct the distortion of the three-dimensional image in the x-axis direction;

[0011] Step 3: Calculate the center magnification factor and edge stretching factor, specifically: calculate the center magnification factor and edge stretching factor of each circular ring according to the correction factor of the circular sub-image;

[0012] Step 4: Slicing the annular sub-image, specifically: performing an actual slicing operation on the original image to obtain a sliced ​​annular sub-image;

[0013] Step 5: center enlargement, specifically: using the Lanczos interpolation method to enlarge the center area of ​​each annular sub-image;

[0014] Step 6: Image edge stretching, specifically: stretching the edge area of ​​each annular sub-image to keep the inner diameter area of ​​the annular image unchanged, and stretching the area from the inner diameter to the outer diameter to a specified length;

[0015] Step 7: Re-stitching the images, specifically: re-stitching all the corrected and processed annular sub-images to form a final corrected image.

[0016] Furthermore, the specific process of step 1 is as follows:

[0017] Decompose the half-section of the curved optical element into n equal parts with the center O' as the reference point to obtain the arc The original center angle of the half-section is θ, and the center angle corresponding to each arc length is Define the area is the smallest unit sector area divided, and the point x is obtained by dividing it k (k=1,2,……n);

[0018] The length and The length of each arc is:

[0019] Formula 1:

[0020] Formula 2:

[0021] Among them: r represents The radius length; δ(·) means rounding the function value;

[0022] Known point x k The coordinates of (k=1,2,……n) are The projection length of each arc length in the x-axis direction is obtained through iterative calculation, and the radius difference between the kth circle and the k-1th circle is obtained as follows:

[0023] Formula 3:

[0024] Furthermore, the specific process of step 2 is as follows:

[0025] For each arc length, the length of the image in the x-axis direction is corrected to That satisfies the following equation:

[0026] Equation 4: Δx k ·T k = l k

[0027] Where: T k is the correction factor required for each arc length, Δx k is the radius difference between the kth circle and the k-1th circle, l k is the length corrected in the x-axis direction; after converting Equation 4 into an equivalent matrix, T is calculated k The value of

[0028] Furthermore, the specific process of step 3 is as follows:

[0029] Δx k Correction factor The center magnification factor is calculated as follows:

[0030] Formula 5:

[0031] The edge stretch factor calculation is as follows:

[0032] Formula 6:

[0033] Furthermore, the specific process of step 4 is as follows:

[0034] Step 41: Obtain the height and width of the original image and calculate the center coordinate value of the image;

[0035] Step 42: Define the inner and outer diameters of all the rings to be sliced;

[0036] Step 43: On the basis of excluding the inner circle, the mask of the image is calculated by looping, and the mask is applied to the original image, and finally the sub-images after all the slices are displayed.

[0037] Furthermore, the specific process of step 5 is as follows:

[0038] Extending the one-dimensional Lanczos interpolation to the two-dimensional case, we get the Lanczos kernel function and the weighted average weight value as follows:

[0039] Formula 7: L(x,y) = L(x)·L(y)

[0040] Formula 8:

[0041] Where: L(x,y) is the Lanczos function, a represents the order of the Lanczos function, x and y are the positions to be interpolated, i and j are the existing sampling positions, s ij is the pixel value at the current position, and S(x,y) is the interpolation result at position i.

[0042] Furthermore, the specific process of step 6 is as follows:

[0043] Step 61: reinitialize the stretched image, initialize all pixels, and set the color channel value of each pixel to 0; the length and width of the new image are the sum of the length and width of the original image and the stretched length of twice the radius, specifically expressed as:

[0044] Formula 9: S c =r outn -r out

[0045] Formula 10: H n =H+S c *2

[0046] Formula 11: W n =W+S c *2

[0047] Where: S c Indicates the required change in radius after the image edge stretching operation, H n Indicates the image height after stretching the image, W n Indicates the width of the image after stretching the image, r outn Represents the outer radius length of the stretched image, r out Indicates the length of the outer radius of the original ring;

[0048] Step 62: Traverse all pixels of the original image, and the pixel coordinates are expressed as (x k ,y k );

[0049] Step 63: Calculate the corrected length l in the x-axis direction k , and calculate the angle λ between the current pixel point and the center of the circle in the coordinate system:

[0050] Formula 12: C n =[H n / 2,W n / 2]

[0051] Formula 13:

[0052] Formula 14:

[0053] Where: [·] means rounding the value; C n Indicates the center coordinates of the stretched image;

[0054] Step 64: Determine the area where the pixel is located, and recalculate the pixel value and radial position. The specific operations are as follows:

[0055] If l k ≤r in , r in represents the length of the inner radius of the original ring, then:

[0056] Formula 15:

[0057] Among them: x and O y Represents the recalculated pixel value, C x and C y Indicates the center position value of the image;

[0058] If r in <l k ≤r outn , then the linear interpolation method is used:

[0059] Formula 16:

[0060] Formula 17:

[0061] Formula 18:

[0062] Where: S r represents the interpolation coefficient, D o Indicates the new radial position.

[0063] Furthermore, the specific process of step 7 is as follows:

[0064] Step 71: extracting the circular ring features of the first corrected minimum circular sub-image, and mapping the circular ring features to the second corrected circular sub-image to form a new sub-image Image_new(1+2);

[0065] Step 72: extract the annular feature in the Image_new(1+2) image, and map the annular feature to the third corrected annular sub-image to form a new sub-image Image_new(1+2+3);

[0066] Step 73: Repeat the above steps until all the corrected annular sub-images are stitched together to form a final corrected image.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] The surface image correction method of the curved optical element can effectively correct the original image with distortion effect. As the number of image slices increases, the image correction effect is better. When the number of slices approaches infinity, the image is basically restored, which can not only accurately correct the shape and size of the surface defects of the curved optical element, but also significantly reduce or even eliminate the interference of the distortion effect on defect detection, thereby providing more accurate and reliable detection results. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The figure is a flow chart of the method of the present invention.

[0070] Figure 2 The schematic diagram of circular sub-image slicing.

[0071] Figure 3 Schematic diagram of edge stretching operation.

[0072] Figure 4 This is the image slicing effect.

[0073] Figure 5 Zoom in to the center.

[0074] Figure 6 This is the edge stretching effect diagram.

[0075] Figure 7 Re-stitch the image.

[0076] Figure 8 This is a comparison chart of the original image and the rectified image. DETAILED DESCRIPTION

[0077] In order to have a clearer understanding of the technical features, purposes and beneficial effects of the present invention, the technical solution of the present invention is now described in detail below, but it should not be construed as limiting the applicable scope of the present invention.

[0078] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0079] An embodiment of the present invention provides a method for correcting an image on a curved optical element surface, the flow chart of which is as follows: Figure 1 As shown, the method comprises the following steps:

[0080] Step 1: Annular sub-image segmentation, specifically: divide the half-section image of the curved optical element into equal parts with the center of the circle as the reference point to form multiple annular sub-image slices; by calculating the length of each arc segment and its projection length in the x-axis direction, the radius difference between the kth circular ring and the k-1th circular ring is finally obtained.

[0081] Figure 2 This is the principle diagram of slicing curved optical elements. Figure 2 (a) shows a half-section view of a curved optical element, where is the original arc on the surface of the half-section image, and O' is the center of the original arc of the half-section image. First, the half-section image is decomposed into n equal parts with the center O' as the reference point, corresponding to the arc in the figure The original center angle of the half-section is θ, and the center angle corresponding to each arc length is Figure 2 (b) shows the axonometric view of the curved optical element, the area is the smallest unit sector area divided, and similarly the smallest unit sector area is divided into Figure 2 By dividing in the way (a), we can get point x k (k=1,2,……n), corresponding to Figure 2 Points x0, x1, ... x in (a) n , the smallest unit sector area is divided into n equal arc lengths as the corresponding contour lines. The contour line diagram after division is as follows Figure 2 As shown in (b).

[0082] The length and The length of each arc is:

[0083] Formula 1:

[0084] Formula 2:

[0085] Among them: r represents The radius length; δ(·) means rounding the function value;

[0086] Known point x k The coordinates of (k=1,2,……n) are The projection length of each arc length in the x-axis direction is obtained through iterative calculation. The specific calculation method is as follows: By analogy, we get:

[0087] Formula 3:

[0088] It follows that the radius difference between the kth ring and the k-1th ring is:

[0089] Formula 4:

[0090] Step 2: Calculate the correction factor of the annular sub-image, specifically: for each annular sub-image slice, calculate its correction factor in the x-axis direction to correct the distortion of the three-dimensional image in the x-axis direction.

[0091] exist Figure 2 In (a), in order to correct the distortion problem of the 3D image in the x-axis direction, the original 2D image is corrected. For each arc length, the length of the image in the x-axis direction needs to be corrected to That satisfies the following equation:

[0092] Equation 5: Δx k ·T k = l k

[0093] Where: T k is the correction factor required for each arc length, Δx k is the radius difference between the kth circle and the k-1th circle, l k is the corrected length in the x-axis direction;

[0094] Convert Equation 5 into an equivalent matrix as follows:

[0095] Formula 6:

[0096] Formula 7:

[0097] From this we can calculate T k The value of

[0098] Step 3: Calculate the center magnification factor and edge stretching factor, specifically: calculate the center magnification factor and edge stretching factor of each circular ring according to the correction factor of the circular sub-image.

[0099] For Δx1, the correction factor is Center magnification factor The edge stretch coefficient E1 = 0, which is decomposed into a ring without inner diameter, i.e. a small circle. For Δx2, the correction factor is After Δx1 correction Corrected before The central magnification factor of Δx2 is calculated as follows:

[0100] Formula 8: C2x1=x1'

[0101] Formula 9:

[0102] For Δx2, the center magnification correction After correction The edge stretch coefficient of Δx2 is calculated as follows:

[0103] Formula 10:

[0104] Similarly, for Δx k The correction factor The center magnification factor is calculated as follows:

[0105] Formula 11:

[0106] The edge stretch factor calculation is as follows:

[0107] Formula 12:

[0108] Step 4: Slicing of the annular sub-image, specifically: after calculating all the parameters required for image slicing, the original image is actually sliced ​​to obtain the sliced ​​annular sub-image. The difference between this step and step 1 is that step 1 is a theoretical slicing division, while this step is an actual operation process.

[0109] The specific operations are as follows:

[0110] Step 41: Obtain the height and width of the original image and calculate the center coordinate value of the image;

[0111] Step 42: Define the inner and outer diameters of all the rings to be sliced;

[0112] Step 43: On the basis of excluding the inner circle, the mask of the image is calculated by looping, and the mask is applied to the original image, and finally the sub-images after all the slices are displayed.

[0113] Step 5: center enlargement, specifically: using the Lanczos interpolation method to enlarge the center area of ​​each annular sub-image.

[0114] The principle of image center magnification is the same as that of image magnification. Both use the interpolation principle to enlarge or reduce the image. For the interpolation function, Lanczos kernel interpolation is an interpolation method used for image processing and signal processing. It is based on the Lanczos function, which is a smooth window function used to limit the bandwidth of interpolation. Lanczos interpolation is often used for image scaling and resampling because it can reduce the jagged effect while maintaining image details. The basic idea of ​​Lanczos interpolation is to use the Lanczos function as a weight function to perform weighted averaging on the original data points to obtain the value of the interpolation point. The shape of the Lanczos function depends on its order, and a 2nd or 3rd order Lanczos function is usually used. The higher the order, the smoother the interpolation result, but the greater the amount of calculation. The weight L(x) at different positions is:

[0115] Formula 13:

[0116] Wherein, x is the position to be interpolated; a represents the order of the Lanczos function. When a=2, the algorithm is suitable for image reduction interpolation; when a=3, the algorithm is suitable for image enlargement interpolation; get:

[0117] Formula 14:

[0118] After calculating the weights of the 16 points, take the weighted average of the 16 values. The formula is as follows:

[0119] Formula 15:

[0120] Where: x is the position to be interpolated, i is the existing sampling position, s i is the pixel value at the current position, and S(x) is the interpolation result at position i.

[0121] Extending the one-dimensional Lanczos interpolation to the two-dimensional case, the Lanczos kernel function and the weighted average weight value are:

[0122] Formula 16: L(x,y) = L(x)·L(y)

[0123] Formula 17:

[0124] Where: L(x,y) is the Lanczos interpolation function, x and y are the positions to be interpolated, i and j are the existing sampling positions, s ij is the pixel value at the current position, and S(x, y) is the interpolation result at position i obtained by interpolation. In the present invention, a single sub-circle needs to be enlarged, so the Lanczos function with a=3 is used for interpolation, and the image interpolation changes more smoothly.

[0125] Step 6: Image edge stretching, specifically: stretching the edge area of ​​each annular sub-image to keep the inner diameter area of ​​the annular image unchanged, and stretching the area from the inner diameter to the outer diameter to a specified length.

[0126] like Figure 3 The figure shows the edge stretching operation diagram, where height and weight represent the height and width of the original image, and the height and width values ​​are represented by H and W respectively; Radius_inner represents the inner radius length of the original ring, and is represented by r in Indicates; Radius_outer_original indicates the outer radius length of the original ring, expressed as r out Original_image_boundary represents the edge of the original image; Radius_outer_new represents the length of the outer radius of the stretched image, expressed as r outn Indicates; New_image_boundary indicates stretching the image edge. According to the edge stretching coefficient, all the circular areas except the area in the innermost circle need to be stretched. The specific operation is:

[0127] Step 61: Reinitialize the stretched image, initialize all pixels, and the color channel value of each pixel is 0, that is, the image is a black image. The length and width of the new image are the sum of the length and width of the original image and the twice radius stretching length, specifically expressed as:

[0128] Formula 18: S c =r outn -r out

[0129] Formula 19: H n =H+S c *2

[0130] Formula 20: W n =W+S c *2

[0131] Where: S c Indicates the required change in radius after the image edge stretching operation, H n Indicates the image height after stretching the image, W n Indicates the width of the image after stretching it.

[0132] Step 62: traverse all the pixels of the original image. The operation is: traverse all the pixels of all the rows of the image in order. The pixel coordinates are expressed as (x k ,y k ).

[0133] Step 63: Calculate the corrected length l in the x-axis direction k , and calculate the angle λ between the current pixel point and the center of the circle in the coordinate system:

[0134] Formula 21: C n =[H n / 2,W n / 2]

[0135] Formula 22:

[0136] Formula 23:

[0137] Where: [·] means rounding the value; C n Indicates the center coordinates of the stretched image.

[0138] Step 64: Determine the area where the pixel is located, and recalculate the pixel value and radial position. The specific operations are as follows:

[0139] If l k ≤r in , then:

[0140] Formula 24:

[0141] Among them: x and O y Represents the recalculated pixel value, C x and C y Indicates the center position value of the image.

[0142] If r in <l k ≤r outn , then the linear interpolation method is used:

[0143] Formula 25:

[0144] Formula 26:

[0145] Formula 27:

[0146] Where: S r represents the interpolation coefficient, D o Indicates the new radial position.

[0147] Step 7: Re-stitching the images, specifically: re-stitching all the corrected and processed annular sub-images to form a final corrected image.

[0148] The specific splicing process is as follows:

[0149] Step 71: extract the circular ring features of the first corrected minimum annular sub-image, and map the annular features to the second corrected annular sub-image to form a new sub-image Image_new(1+2).

[0150] Step 72: extract the annular features in the Image_new(1+2) image, and map the annular features to the third corrected annular sub-image to form a new sub-image Image_new(1+2+3).

[0151] Step 73: Repeat the above steps until all the corrected annular sub-images are stitched together to form a final corrected image.

[0152] In the embodiment of the present invention, after obtaining the original image, the above steps 1-7 are performed. The image slicing effect is as follows Figure 4 The center magnification effect is as shown. Figure 5 The edge stretching effect is shown in Figure 6 The image re-stitching effect is shown in Figure 7 As shown. The comparison between the original image and the rectified image is Figure 8 As shown in the figure, it can be seen that the surface defect characteristics of the curved optical element are restored, avoiding the influence of the distortion effect on the image defect characteristics.

[0153] The above are only preferred embodiments of the present invention. It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention. These should also be regarded as the protection scope of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent.

Claims

1. A method for correcting an image on a curved optical element surface, characterized in that: The following steps are involved: Step 1: segmenting the annular sub-image, specifically: dividing the half-section image of the curved optical element into equal parts with the center of the circle as the reference point to form multiple annular sub-image slices; by calculating the length of each arc segment and its projection length in the x-axis direction, finally obtaining the radius difference between the kth annular ring and the k-1th annular ring; Step 2: Calculate the correction factor of the annular sub-image, specifically: for each annular sub-image slice, calculate its correction factor in the x-axis direction to correct the distortion of the three-dimensional image in the x-axis direction; Step 3: Calculate the center magnification factor and edge stretching factor, specifically: calculate the center magnification factor and edge stretching factor of each circular ring according to the correction factor of the circular sub-image; Step 4: Slicing the annular sub-image, specifically: performing an actual slicing operation on the original image to obtain a sliced ​​annular sub-image; Step 5: center enlargement, specifically: using the Lanczos interpolation method to enlarge the center area of ​​each annular sub-image; Step 6: Image edge stretching, specifically: stretching the edge area of ​​each annular sub-image to keep the inner diameter area of ​​the annular image unchanged, and stretching the area from the inner diameter to the outer diameter to a specified length; Step 7: Re-stitching the images, specifically: re-stitching all the corrected and processed annular sub-images to form a final corrected image.

2. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 1 is as follows: Decompose the half-section of the curved optical element into n equal parts with the center O' as the reference point to obtain the arc The original center angle of the half-section is θ, and the center angle corresponding to each arc length is Define the area is the smallest unit sector area divided, and the point x is obtained by dividing it k (k=1,2,……n); The length and The length of each arc is: Formula 1: Formula 2: Among them: r represents The radius length; δ(·) means rounding the function value; Known point x k The coordinates of (k=1,2,……n) are The projection length of each arc length in the x-axis direction is obtained through iterative calculation, and the radius difference between the kth circle and the k-1th circle is obtained as follows: Formula 3:

3. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 2 is as follows: For each arc length, the length of the image in the x-axis direction is corrected to That satisfies the following equation: Formula 4: Δx k ·T k = l k Where: T k is the correction factor required for each arc length, Δx k is the radius difference between the kth ring and the k-1th ring, l k is the length corrected in the x-axis direction; after converting Equation 4 into an equivalent matrix, T is calculated k The value of 4. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 3 is as follows: Δx k Correction factor The center magnification factor is calculated as follows: Formula 5: The edge stretch factor calculation is as follows: Formula 6:

5. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 4 is as follows: Step 41: Obtain the height and width of the original image and calculate the center coordinate value of the image; Step 42: Define the inner and outer diameters of all the rings to be sliced; Step 43: On the basis of excluding the inner circle, the mask of the image is calculated by looping, and the mask is applied to the original image, and finally the sub-images after all the slices are displayed.

6. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 5 is as follows: Extending the one-dimensional Lanczos interpolation to the two-dimensional case, we get the Lanczos kernel function and the weighted average weight value as follows: Formula 7: L(x,y) = L(x)·L(y) Formula 8: Where: L(x,y) is the Lanczos function, a represents the order of the Lanczos function, x and y are the positions to be interpolated, i and j are the existing sampling positions, s ij is the pixel value at the current position, and S(x,y) is the interpolation result at position i.

7. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 6 is as follows: Step 61: reinitialize the stretched image, initialize all pixels, and set the color channel value of each pixel to 0; the length and width of the new image are the sum of the length and width of the original image and the stretched length of twice the radius, specifically expressed as: Formula 9: S c =r outn -r out Formula 10: H n =H+S c *2 Formula 11: W n =W+S c *2 Where: S c Indicates the required change in radius after the image edge stretching operation, H n Indicates the image height after stretching the image, W n Indicates the width of the image after stretching the image, r outn Represents the outer radius length of the stretched image, r out Indicates the length of the outer radius of the original ring; Step 62: Traverse all pixels of the original image, and the pixel coordinates are expressed as (x k ,y k ); Step 63: Calculate the corrected length l in the x-axis direction k , and calculate the angle λ between the current pixel point and the center of the circle in the coordinate system: Formula 12: C n =[H n / 2,W n / 2] Formula 13: Formula 14: Where: [·] means rounding the value; C n Indicates the center coordinates of the stretched image; Step 64: Determine the area where the pixel is located, and recalculate the pixel value and radial position. The specific operations are as follows: If l k ≤r in , r in represents the length of the inner radius of the original ring, then: Formula 15: Among them: x and O y Represents the recalculated pixel value, C x and C y Indicates the center position value of the image; If r in <l k ≤r outn , then the linear interpolation method is used: Formula 16: Formula 17: Formula 18: Where: S r represents the interpolation coefficient, D o Indicates the new radial position.

8. The method for correcting the surface image of a curved optical element according to claim 1, characterized in that: The specific process of step 7 is as follows: Step 71: extracting the circular ring features of the first corrected minimum circular sub-image, and mapping the circular ring features to the second corrected circular sub-image to form a new sub-image Image_new(1+2); Step 72: extract the annular feature in the Image_new(1+2) image, and map the annular feature to the third corrected annular sub-image to form a new sub-image Image_new(1+2+3); Step 73: Repeat the above steps until all the corrected annular sub-images are stitched together to form a final corrected image.

Images