An Image Center Positioning Optimization Method

Abstract

The present invention provides an image center positioning optimization method. The method comprises: extracting the pixel-level edge and sub-pixel-level edge of the target image according to the grayscale features of the sample photo to be tested, determining the first center point coordinates of the first target image within the pixel-level edge using the grayscale weighted centroid method, and then determining the first weighting coefficient of the first center point coordinates in combination with the grayscale features of the first target image, determining the second center point coordinates of the second target image within the sub-pixel-level edge using the ellipse center fitting method, and then determining the second weighting coefficient of the second center point coordinates in combination with the roundness features of the second target image, and finally performing weighted summation on the first center point coordinates and the second center point coordinates to obtain the center point coordinates of the target image. The whole method greatly improves the accuracy and robustness of image center positioning under extreme measurement conditions such as target contamination or poor measurement angles, thereby making the accuracy of later photo splicing and solution higher and the measurement accuracy attenuation smaller.

Description

Technical Field

[0001] The invention belongs to the fields of computer vision and computer graphics, and relates to an image center positioning optimization method. Background Art

[0002] Digital photogrammetry is an image-based measurement technology. After taking photos of the sample to be tested at each camera station, the three-dimensional coordinates of the target are obtained by locating the image center point of the target in the photo of the sample to be tested, and subsequent measurements are carried out on this basis. The center point of the target image in the photo of the sample to be tested is mainly analyzed based on the image features of the photo, where the image features of the photo mainly refer to the grayscale distribution and roundness of the target image corresponding to the target on the photo of the sample to be tested during the shooting and measurement process.

[0003] Generally speaking, locating the image center point of the target in the photo of the sample to be tested mainly includes two processes: edge extraction and image center positioning. Edge extraction generally uses gradient operators (such as Sobel operator, Prewitt operator, LoG operator and Cany operator, etc.) to first determine the pixel-level edge of the target image in the photo of the sample to be tested, and then further determine the sub-pixel edge of the target image according to the gray gradient of the pixel-level edge. There are two main methods for image center positioning: grayscale weighted centroid method and ellipse center fitting method. Both methods are based on the grayscale distribution and circularity of the target image to perform center positioning. Among them, the grayscale weighted centroid method only needs to obtain the pixel-level edge of the target image, and is not sensitive to the circularity of the target. The positioning accuracy is mainly affected by the grayscale level and gradient distribution characteristics of the target. The ellipse center fitting method requires the sub-pixel edge of the target image to be ellipse fitted before positioning the center. The positioning accuracy is mainly affected by the circularity of the target and the grayscale distribution of the image edge.

[0004] Under extreme measurement conditions such as target contamination or poor measurement angle, the target image will have image distortions such as abnormal grayscale distribution or distorted roundness features. At this time, using conventional image center positioning methods (i.e., using the grayscale weighted centroid method or ellipse center fitting method alone) to locate the image center will result in a large positioning error of the center point of the same target in all photos, which will lead to low accuracy in subsequent photo stitching and solution, and a significant attenuation of measurement accuracy. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides an image center positioning optimization method, comprising:

[0006] Acquire image features of a photo of a sample to be tested, wherein the image features include grayscale features;

[0007] Extracting pixel-level edges and sub-pixel-level edges of the target image according to the grayscale features;

[0008] Determining the coordinates of a first center point of the first target image within the pixel-level edge using a grayscale weighted centroid method;

[0009] Determining a first weighting coefficient of the first center point coordinates according to the grayscale features of the first target image;

[0010] Determining the coordinates of a second center point of the second target image within the sub-pixel edge using an ellipse center fitting method;

[0011] Determining a second weighting coefficient of the second center point coordinates according to the roundness feature of the second target image;

[0012] The center point coordinates of the target image are determined according to the first center point coordinates, the first weighting coefficient, the second center point coordinates, and the second weighting coefficient.

[0013] Furthermore, the determining the coordinates of the first center point of the first target image within the pixel-level edge by using the grayscale weighted centroid method includes:

[0014] Acquire the position coordinates and grayscale value of each pixel contained in the first target image within the pixel-level edge;

[0015] Determining the grayscale centroid coordinates of the first target image using a grayscale weighted centroid method according to the position coordinates and grayscale values ​​of each pixel included in the first target image;

[0016] The grayscale centroid coordinates are determined as the first center point coordinates of the first target image.

[0017] Further, the determining the grayscale centroid coordinates of the first target image by using a grayscale weighted centroid method according to the position coordinates and grayscale values ​​of each pixel included in the first target image includes:

[0018] The grayscale centroid coordinates of the first target image are determined by the following formula:

[0019]

[0020] Among them, x 0 and 0 is the grayscale centroid coordinate of the first target image, x i and i is the position coordinate of the ith pixel contained in the first target image, f i is the grayscale value of the i-th pixel contained in the first target image, i is an integer greater than or equal to 1 and less than or equal to n, and n is the number of pixels contained in the first target image.

[0021] Further, the determining of the first weighting coefficient of the first center point coordinate according to the grayscale feature of the first target image includes:

[0022] According to the grayscale features of the first target image, obtaining the grayscale value of the first center point corresponding to the first center point coordinates and the edge grayscale value of the pixel-level edge;

[0023] Determining a grayscale distribution level according to the grayscale value of the first center point and the edge grayscale value;

[0024] The grayscale distribution level is normalized to obtain a first weighting coefficient of the first center point coordinate.

[0025] Furthermore, the determining the coordinates of the second center point of the second target image within the sub-pixel edge by using an ellipse center fitting method includes:

[0026] Performing ellipse least squares fitting on all pixel points constituting the sub-pixel edge to obtain a fitted ellipse;

[0027] Determining the center coordinates of the fitted ellipse according to the parameters of the ellipse equation corresponding to the fitted ellipse;

[0028] Determine whether the plane where the target on the sample to be tested is located is parallel to the target image;

[0029] If the plane where the target on the sample to be tested is located is parallel to the target image, the center coordinates of the fitted ellipse are determined as the second center point coordinates of the second target image within the sub-pixel edge.

[0030] Furthermore, determining the center coordinates of the fitted ellipse according to the parameters of the ellipse equation corresponding to the fitted ellipse includes:

[0031] The center coordinates of the fitted ellipse are determined by the following formula:

[0032]

[0033] Among them, x' 0 and y' 0 are the center coordinates of the fitted ellipse, and B, C, D, and E are all parameters of the ellipse equation corresponding to the fitted ellipse.

[0034] Furthermore, the method further comprises:

[0035] If the plane where the target on the sample to be tested is located is not parallel to the target image, the target center projection offset compensation amount is determined according to the angle between the plane where the target on the sample to be tested is located and the target image, the target diameter of the target on the sample to be tested, the focal length of the lens used to photograph the sample to be tested, the radial offset of the target on the target image, the lateral offset of the target relative to the optical axis, and the distance from the target to the lens projection center;

[0036] The center coordinates of the fitting ellipse are offset compensated according to the target center projection offset compensation amount to obtain the second center point coordinates of the second target image within the sub-pixel edge.

[0037] Further, the target center projection offset compensation amount is determined according to the angle between the plane where the target on the sample to be tested is located and the target image, the target diameter of the target on the sample to be tested, the focal length of the lens used to photograph the sample to be tested, the radial offset of the target on the target image, the lateral offset of the target relative to the optical axis, and the distance from the target to the lens projection center, including:

[0038] The target center projection offset compensation is determined by the following formula:

[0039]

[0040] Among them, e' is the target center projection offset compensation, r m is the radial offset of the target on the target image, c is the focal length of the lens used to photograph the sample to be tested, and R m is the lateral offset of the target relative to the optical axis, Z m is the distance from the target to the projection center of the lens, d is the target diameter of the target on the sample to be tested, and α is the angle between the plane where the target on the sample to be tested is located and the target image.

[0041] Further, the determining the second weighting coefficient of the second center point coordinate according to the roundness feature of the second target image includes:

[0042] Obtaining the major axis length and the minor axis length of the fitted ellipse;

[0043] Determine the ratio of the major axis length to the minor axis length as a coefficient to be adjusted;

[0044] The coefficient to be adjusted is normalized to obtain a second weighting coefficient of the second center point coordinate.

[0045] The beneficial effects of the present invention are as follows: the first center point coordinates are obtained by using the grayscale weighted centroid method, and then the first weighting coefficient of the first center point coordinates is determined in combination with the grayscale features of the first target image, the second center point coordinates are obtained by using the ellipse center fitting method, and then the second weighting coefficient of the second center point coordinates is determined in combination with the roundness features of the second target image, and finally the first center point coordinates and the second center point coordinates are respectively weighted and summed accordingly to obtain the center point coordinates of the target image, which greatly improves the accuracy and robustness of image center positioning under extreme measurement conditions such as target contamination or poor measurement angles, thereby making the accuracy of later photo stitching and solution higher and the measurement accuracy attenuation less. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0047] Figure 1 A schematic diagram of a flow chart of an image center positioning optimization method provided by an embodiment of the present invention;

[0048] Figure 2 It is a schematic diagram of the grayscale interpolation principle;

[0049] Figure 3 is a schematic diagram showing an example of the relative position of the target plane and the target image;

[0050] Figure 4 A geometrical schematic diagram of an offset compensation model corresponding to when the plane where the target is located is not parallel to the target image provided by an embodiment of the present invention;

[0051] Figure 5 A schematic diagram for comparing the center point, the first center point, and the second center point of a target image provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] In view of the deficiencies in the prior art, an embodiment of the present invention provides an image center positioning optimization method. Figure 1 The flowchart of an image center positioning optimization method provided by an embodiment of the present invention is exemplarily shown. Figure 1 As shown, the specific steps include:

[0054] 101: Obtain image features of the photograph of the sample to be tested.

[0055] Among them, the image features include grayscale features.

[0056] Specifically, the grayscale feature represents the grayscale value of each pixel.

[0057] 102: Extract pixel-level edges and sub-pixel-level edges of the target image according to the grayscale features.

[0058] Specifically, there are many ways to extract pixel-level edges and sub-pixel-level edges of the target image, which are not specifically limited in the embodiment of the present invention.

[0059] 103: Determine the coordinates of a first center point of the first target image within the pixel-level edge by using a grayscale weighted centroid method.

[0060] Specifically, the pixel-level edge of the target image is used as the edge of the first target image, that is, the pixel-level edge of the target image is used as the grayscale weighted boundary.

[0061] Furthermore, the coordinates of the first center point of the first target image within the pixel-level edge may be determined by using the grayscale weighted centroid method specifically through the following steps:

[0062] Step 1: Obtain the position coordinates and grayscale value of each pixel contained in the first target image within the pixel-level edge.

[0063] Step 2: According to the position coordinates and grayscale values ​​of each pixel contained in the first target image, the grayscale weighted centroid method is used to determine the grayscale centroid coordinates of the first target image.

[0064] Furthermore, the grayscale centroid coordinates of the first target image can be determined by formula (1):

[0065]

[0066] In formula (1), x 0 and 0 is the grayscale centroid coordinate of the first target image, x i and i is the position coordinate of the i-th pixel contained in the first target image, f i is the grayscale value of the i-th pixel contained in the first target image, i is an integer greater than or equal to 1 and less than or equal to n, and n is the number of pixels contained in the first target image.

[0067] Step three, determining the grayscale centroid coordinates as the first center point coordinates of the first target image.

[0068] Figure 2 The schematic diagram of grayscale interpolation principle is shown as an example. Figure 2 As shown, the pixel-level edge of the target image is used as the grayscale weighted boundary, and the pixel position is weighted by the grayscale value of the first target image pixel, and then the grayscale centroid of the target is obtained as the center of the target. Figure 2 In the above equation, (i, j) represents the position coordinates of the pixel where the center of the target is located, (i+1, j-1) represents the position coordinates of the lower left neighboring pixel where the center of the target is located, and (i-1, j+1) represents the position coordinates of the upper right neighboring pixel where the center of the target is located. 1 Indicates the starting value of the target grayscale gradient direction angle, α 2 Indicates the end value of the direction angle of the target gray gradient.

[0069] 104: Determine a first weighting coefficient of the first center point coordinates according to the grayscale feature of the first target image.

[0070] Specifically, the first weighting coefficient of the first center point coordinates can be determined by the following steps:

[0071] Step 1: According to the grayscale features of the first target image, the grayscale value of the first center point corresponding to the first center point coordinates and the edge grayscale value of the pixel-level edge are obtained.

[0072] The edge gray value represents the average gray value of each pixel on the edge.

[0073] Step 2: Determine the grayscale distribution level according to the grayscale value of the first center point and the edge grayscale value.

[0074] Specifically, the grayscale distribution level=(grayscale value of the first center point−edge grayscale value) / 255.

[0075] If the value of the grayscale distribution level is relatively large, it means that the target exposure is reasonable, bright enough and not overexposed, and it is suitable to use the grayscale weighted centroid method to determine the center.

[0076] Step three, normalize the grayscale distribution level to obtain the first weighting coefficient of the first center point coordinates.

[0077] Specifically, the normalization process means converting the value of the grayscale distribution level into a decimal between 0 and 1.

[0078] 105: Determine the coordinates of a second center point of the second target image within the sub-pixel edge by using an ellipse center fitting method.

[0079] Specifically, the sub-pixel edge of the target image is used as the edge of the second target image.

[0080] Furthermore, the coordinates of the second center point of the second target image within the sub-pixel edge may be determined by the following steps:

[0081] Step 1: Perform ellipse least squares fitting on all pixel points constituting the sub-pixel edge to obtain a fitted ellipse.

[0082] The general equation of a plane ellipse can be expressed by formula (2):

[0083] x 2 +2Bxy+Cy 2 +2Dx+2Ey+F=0 Formula (2)

[0084] In formula (2), B, C, D, E and F all represent the parameters of the ellipse equation corresponding to the fitted ellipse. These parameters can be solved by least squares fitting to obtain the expression of the fitted ellipse.

[0085] Step 2: Determine the center coordinates of the fitted ellipse based on the parameters of the ellipse equation corresponding to the fitted ellipse.

[0086] Specifically, after determining the parameters of the ellipse equation corresponding to the fitted ellipse, the center coordinates of the fitted ellipse can be determined by formula (3):

[0087]

[0088] In formula (3), x' 0 and y' 0 is the center coordinate of the fitted ellipse, and B, C, D, and E are the parameters of the ellipse equation corresponding to the fitted ellipse.

[0089] Step three, determine whether the plane where the target on the sample to be tested is located is parallel to the target image.

[0090] For example, Figure 3 An example schematic diagram of the relative position of the target plane and the target image is shown as an example. Figure 3 As shown, O' is the position of the camera, C is the center of the target plane, τ is the distance between the target center and the image center. When the target plane is parallel to the image plane, the center C' of the imaging is the same as the center E' of the fitted ellipse, and there is no projection offset compensation (i.e., e'=0). When the target plane is not parallel to the image plane, there is a certain projection deviation between the center C' of the imaging and the center E' of the algorithm-fitted ellipse, i.e., e'. The size of the deviation is related to the angle between the planes.

[0091] Step 4: If the plane where the target on the sample to be tested is located is parallel to the target image, the center coordinates of the fitted ellipse are determined as the second center point coordinates of the second target image within the sub-pixel edge.

[0092] Step five, if the plane where the target on the sample to be tested is located is not parallel to the target image, determine the target center projection offset compensation amount according to the angle between the plane where the target on the sample to be tested is located and the target image, the target diameter of the target on the sample to be tested, the focal length of the lens used to shoot the sample to be tested, the radial offset of the target on the target image, the lateral offset of the target relative to the optical axis, and the distance from the target to the projection center of the lens.

[0093] Furthermore, the target center projection offset compensation amount can be determined by formula (4):

[0094]

[0095] In formula (4), e' is the target center projection offset compensation, r m is the radial offset of the target on the target image, c is the focal length of the lens used to shoot the sample to be tested, R m is the lateral offset of the target relative to the optical axis, Z m is the distance from the target to the center of the lens projection, d is the target diameter of the target on the sample to be tested, and α is the angle between the plane where the target on the sample to be tested is located and the target image.

[0096] Figure 4 The geometric diagram of the offset compensation model corresponding to the case where the plane where the target is located is not parallel to the target image provided by the embodiment of the present invention is exemplarily shown. Figure 4 As shown, the angle between the circular target on the sample to be tested and the image plane is α, and the distance from the circular target to the projection center of the lens is Z m , the lateral offset of the circular target relative to the optical axis is R m , the focal length of the lens used to photograph the sample to be tested is c, and the radial offset of the circular target on the target image is r m , the projection of the target center point and the image center projection offset is e'.

[0097] Step six, offset compensation is performed on the center coordinates of the fitted ellipse according to the target center projection offset compensation amount to obtain the second center point coordinates of the second target image within the sub-pixel edge.

[0098] 106: Determine a second weighting coefficient of the second center point coordinates according to the roundness feature of the second target image.

[0099] Specifically, the second weighting coefficient of the second center point coordinates may be determined in the following manner:

[0100] First, obtain the length of the major axis and the minor axis of the fitted ellipse.

[0101] Then, the ratio of the major axis length to the minor axis length is determined as the coefficient to be adjusted.

[0102] Generally speaking, the ratio of the major axis length to the minor axis length can be used to evaluate the roundness of the fitted ellipse. The closer the roundness is to 1, the closer the fitted ellipse is to a perfect circle, and it is more suitable to use the ellipse center fitting method to determine the center.

[0103] Finally, the coefficient to be adjusted is normalized to obtain the second weighting coefficient of the second center point coordinate.

[0104] The normalization process refers to converting the value of the coefficient to be adjusted into a decimal between 0 and 1.

[0105] 107: Determine the center point coordinates of the target image according to the first center point coordinates, the first weighting coefficient, the second center point coordinates, and the second weighting coefficient.

[0106] Specifically, the first center point coordinate and the second center point coordinate are respectively multiplied by the corresponding first weighting coefficient and the second weighting coefficient, and then the products are summed to obtain the center point coordinate of the target image.

[0107] Figure 5 A schematic diagram showing a comparison of the center point, the first center point, and the second center point of a target image provided by an embodiment of the present invention is exemplarily shown. Figure 5 As shown, the center point of the target image is shown as the center point of the weighted algorithm in the figure, the first center point is shown as the center point of algorithm 1 in the figure, the second center point is shown as the center point of algorithm 2 in the figure, and the first weighting coefficient is the weighting coefficient γ 1 , the second weighting coefficient is the weighting coefficient γ 2 .

[0108] The beneficial effects of the present invention are as follows: the first center point coordinates are obtained by using the grayscale weighted centroid method, and then the first weighting coefficient of the first center point coordinates is determined in combination with the grayscale features of the first target image, the second center point coordinates are obtained by using the ellipse center fitting method, and then the second weighting coefficient of the second center point coordinates is determined in combination with the roundness features of the second target image, and finally the first center point coordinates and the second center point coordinates are respectively weighted and summed accordingly to obtain the center point coordinates of the target image, which greatly improves the accuracy and robustness of image center positioning under extreme measurement conditions such as target contamination or poor measurement angles, thereby making the accuracy of later photo stitching and solution higher and the measurement accuracy attenuation less.

[0109] The present invention has been described in detail above in conjunction with specific implementations and exemplary examples, but these descriptions cannot be understood as limiting the present invention. Those skilled in the art understand that, without departing from the spirit and scope of the present invention, a variety of equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its implementation methods, all of which fall within the scope of the present invention. The scope of protection of the present invention shall be subject to the attached claims.

Claims

1. An image center positioning optimization method, It is characterized in that include: Acquire image features of a photo of a sample to be tested, wherein the image features include grayscale features; Extracting pixel-level edges and sub-pixel-level edges of the target image according to the grayscale features; Determining the coordinates of a first center point of the first target image within the pixel-level edge using a grayscale weighted centroid method; Determining a first weighting coefficient of the first center point coordinates according to the grayscale features of the first target image; Determining the coordinates of a second center point of the second target image within the sub-pixel edge using an ellipse center fitting method; Determining a second weighting coefficient of the second center point coordinates according to the roundness feature of the second target image; Determining the center point coordinates of the target image according to the first center point coordinates, the first weighting coefficient, the second center point coordinates, and the second weighting coefficient; The method of determining the coordinates of the first center point of the first target image within the pixel-level edge by using the grayscale weighted centroid method includes: Acquire the position coordinates and grayscale value of each pixel contained in the first target image within the pixel-level edge; Determining the grayscale centroid coordinates of the first target image using a grayscale weighted centroid method according to the position coordinates and grayscale values ​​of each pixel included in the first target image; Determining the grayscale centroid coordinates as the first center point coordinates of the first target image; The step of determining the first weighting coefficient of the first center point coordinate according to the grayscale feature of the first target image includes: According to the grayscale features of the first target image, obtaining the grayscale value of the first center point corresponding to the first center point coordinates and the edge grayscale value of the pixel-level edge; Determining a grayscale distribution level according to the grayscale value of the first center point and the edge grayscale value; Normalizing the grayscale distribution level to obtain a first weighting coefficient of the first center point coordinate; The method of determining the coordinates of the second center point of the second target image within the sub-pixel edge by using the ellipse center fitting method includes: Performing ellipse least squares fitting on all pixel points constituting the sub-pixel edge to obtain a fitted ellipse; Determining the center coordinates of the fitted ellipse according to the parameters of the ellipse equation corresponding to the fitted ellipse; Determine whether the plane where the target on the sample to be tested is located is parallel to the target image; If the plane where the target on the sample to be tested is located is parallel to the target image, the center coordinates of the fitted ellipse are determined as the second center point coordinates of the second target image within the sub-pixel edge; The determining, according to the roundness feature of the second target image, a second weighting coefficient of the second center point coordinates comprises: Obtaining the major axis length and the minor axis length of the fitted ellipse; Determine the ratio of the major axis length to the minor axis length as a coefficient to be adjusted; The coefficient to be adjusted is normalized to obtain a second weighting coefficient of the second center point coordinate.

2. The method according to claim 1, It is characterized in that Determining the grayscale centroid coordinates of the first target image by using a grayscale weighted centroid method according to the position coordinates and grayscale values ​​of each pixel included in the first target image includes: The grayscale centroid coordinates of the first target image are determined by the following formula: Among them, x 0 and 0 is the grayscale centroid coordinate of the first target image, x i and i is the position coordinate of the ith pixel contained in the first target image, f i is the grayscale value of the i-th pixel contained in the first target image, i is an integer greater than or equal to 1 and less than or equal to n, and n is the number of pixels contained in the first target image.

3. The method according to claim 1, It is characterized in that The step of determining the center coordinates of the fitted ellipse according to the parameters of the ellipse equation corresponding to the fitted ellipse comprises: The center coordinates of the fitted ellipse are determined by the following formula: Among them, x ’ 0 and ’ 0 are the center coordinates of the fitted ellipse, and B, C, D, and E are all parameters of the ellipse equation corresponding to the fitted ellipse.

4. The method according to claim 1, It is characterized in that The method further comprises: If the plane where the target on the sample to be tested is located is not parallel to the target image, the target center projection offset compensation amount is determined according to the angle between the plane where the target on the sample to be tested is located and the target image, the target diameter of the target on the sample to be tested, the focal length of the lens used to photograph the sample to be tested, the radial offset of the target on the target image, the lateral offset of the target relative to the optical axis, and the distance from the target to the lens projection center; The center coordinates of the fitting ellipse are offset compensated according to the target center projection offset compensation amount to obtain the second center point coordinates of the second target image within the sub-pixel edge.

5. The method according to claim 4, It is characterized in that The method of determining the target center projection offset compensation amount according to the angle between the plane where the target on the sample to be tested is located and the target image, the target diameter of the target on the sample to be tested, the focal length of the lens used to photograph the sample to be tested, the radial offset of the target on the target image, the lateral offset of the target relative to the optical axis, and the distance from the target to the lens projection center, comprises: The target center projection offset compensation is determined by the following formula: Among them, e' is the target center projection offset compensation, r m is the radial offset of the target on the target image, c is the focal length of the lens used to photograph the sample to be tested, and R m is the lateral offset of the target relative to the optical axis, Z m is the distance from the target to the projection center of the lens, d is the target diameter of the target on the sample to be tested, and α is the angle between the plane where the target on the sample to be tested is located and the target image.

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