CN115060747A - Method for quantifying size of focus of X-ray source for industrial CT system - Google Patents
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Abstract
The invention relates to a method for quantifying the size of a focus of an X-ray source for an industrial CT system, which is characterized by comprising the following steps: step 1, preparing a sphere from a high-density material; step 2, opening the X-ray source and the detector to obtain a sphere projection image; step 3, carrying out binarization processing on the sphere projection image, and extracting a sphere projection contour position from the binarized sphere projection image; step 4, calculating coordinates of the center T of the sphere projected on the sphere projection image; step 5, obtaining an edge expansion function f (x) of the focus; step 6, fitting the edge spread function f (x) of the focus obtained in the step 5, and calculating a Gaussian function of the fitted edge spread function; and 7, acquiring a standard deviation of the Gaussian function, and taking a result of multiplying the standard deviation by the preset minimum distance n on the focal plane as the focal size. The method has the advantages of low processing difficulty of the ball mould body, high reliability and capability of realizing accurate quantification of the size of the focus.
Description
Technical Field
The invention relates to the technical field of performance evaluation of an X-ray source for an industrial CT system, in particular to a method for quantifying the focal spot size of the X-ray source for the industrial CT system.
Background
X-ray inspection is one of the most widely used techniques in non-destructive inspection. The X-ray source is mainly used for generating X-rays, and the X-rays can penetrate through a detected workpiece to perform projection imaging on the internal structure and the defects of the detected workpiece, so that nondestructive detection of the internal defects is realized. The focus of the X-ray source is a key parameter influencing the defect detection capability, and the smaller the focus of the X-ray source is, the smaller the detectable internal defect of the workpiece is. Therefore, ray machine manufacturers are dedicated to developing small-focus, high-energy industrial X-ray sources. At present, ray machines with micron-sized focus are commercially available, and especially the focus size of 225kV ray sources can be generally about 4-8 microns. It is very important how to accurately and quantitatively evaluate the performance of the X-ray source for the micron-sized focus.
At present, common methods for measuring the focus size of an X-ray source for an industrial CT system are divided into a direct method and an indirect method, wherein the direct method refers to the method of directly observing the shape and the size of a focus, and the common method mainly adopts a pinhole method; the indirect method is to calculate the focal size by observing a point spread function or a line spread function due to the focal size, and common methods include a knife edge method, a slit method, and a ball target method. The pinhole method is to realize the projection of the size and shape of a focus by using a classical pinhole imaging principle, the definition of the focus projection depends on the size of a pinhole, the smaller the pinhole is, the higher the definition of the focus projection is, and the micron-sized focus needs to be manufactured with a small number of pinholes. In addition, because the X-ray belongs to electromagnetic waves with extremely strong penetrating power, the baffle made of materials with high attenuation coefficients such as tungsten needs to be used for punching, and the ultrahigh hardness of the tungsten also increases the difficulty in manufacturing small holes. In addition, the edge method adopts a tungsten block to form a straight edge in an image, observes the degradation analysis of the edge, calculates a line spread function by adopting a derivation method, is an improved edge method, uses a tungsten cylindrical block to replace the tungsten block, namely adopts an arc surface with a certain radius to replace a flat surface, is easy to realize the centering of the device, and directly influences the measurement effectiveness of a focus by the identification precision of an edge direction angle; the slit method adopts the parallel arrangement of two tungsten blocks, and a slit is formed between the tungsten blocks to directly obtain a line spread function, and has higher requirements on the distance between the slits and the parallelism of the tungsten blocks; the ball target method is to adopt high-density material to make into the spheroid, carry on its projection method to gather the picture, gather the marginal degradation function on the circumference of the ball, calculate the point spread function, the centre of sphere positioning accuracy is superior to the line positioning accuracy.
British Standard BS EN 12543-5, measurement of effective Focus size of miniature and miniature focus x-ray tubes, recommends a method for measuring the Focus size by the ball target method, which uses the unclear edge width of the projected image of the ball at the magnification to calculate the Focus size, and the standard clearly requires that the diameter of the ball be between 0.9mm and 1.1mm, the magnification be between 20 and 100 times, the tube voltage be less than 200kV, and indicates that the focus measurement error which is not in this range is large. Further improvements are needed for this purpose.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for quantifying the size of the focus of an X-ray source for an industrial CT system, which aims at the prior art and has low processing difficulty of a spherical die body, high reliability and high measurement precision.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for quantifying the size of a focus of an X-ray source for an industrial CT system is characterized by comprising the following steps:
step 2, placing the sphere in the step 1 in an industrial CT system at the central position of a rotary table, adjusting the rotary table to be close to an X-ray source, turning on the X-ray source and a detector, setting a detection process for measuring the focal size of the X-ray source, and obtaining a sphere projection image which is a gray scale image;
step 3, performing binarization processing on the sphere projection image to obtain a binarized sphere projection image, extracting a sphere projection contour position from the binarized sphere projection image, and forming a sphere projection contour point set I by the sphere projection contour position;
step 4, obtaining an edge expansion function f (x) of the focus; wherein x is the distance from any point K1 on the focal point to the focal point center position v; (x) is the gray scale value of any point K1 in the focus;
the method comprises the following specific steps:
step 4-1, randomly selecting a point I in the sphere projection contour point set I 0 And in the projection image of the sphereThe point i is extracted 0 The gray value distribution curve W on the line segment TI formed by the center T of the sphere i0 (x′)；
Wherein i 0 The serial numbers of the projection contour points in the sphere projection contour point set I are obtained; x' is the distance from any point on the line segment TI to the sphere center T on the sphere projection image;
step 4-2, selecting a focus K, a sphere center T and a point I in a sphere projection contour point set I of the X-ray source 0 Forming a KIT profile including a focal point K and a point i 0 A line segment KI, a line segment TI and a line segment KT are formed between the focus K and the sphere center T; making a line segment JT perpendicular to the line segment KI from the sphere center T, wherein the intersection point of the line segment JT and the line segment KI is a point J;
and the gray value distribution curve W on the line segment TI in the step 4-1 i0 (x') projecting the curve onto line JT to obtain the gray value distribution curve W on line JT i0 (j)；W i0 (j) The calculation formula of (2) is as follows:
W i0 (j)＝W i0 (x′*t i0 )；
wherein j is the distance from any point on the line segment JT to the sphere center T; t is t i0 Correction coefficient for line segment TI
JT | is the length of line JT; l TI | is the length of the line segment TI;
step 4-3, the gray value distribution curve W on the line segment JT i0 (j) Projecting the gray value distribution curve on the focal point to obtain a gray value distribution curve on the focal point;
the method comprises the following specific steps: let d denote the distance from any point on the line JT to point J j The distance from any point on the focal point to the focal point center position v is denoted as d n ，d n And d j Approximately satisfies the following formula:
wherein r is the radius of the sphere;
and according toFormula (II): d j Obtaining any point I in the sphere projection contour point set I 0 Distribution curve of gray values projected on the focal point
Step 4-4, extracting a gray value distribution curve on a line segment formed by each point and the sphere center T in the sphere projection contour point set I according to the same method in the step 4-1, and extracting a gray value distribution curve of each point projected on a focus in the sphere projection contour point set I according to the same method in the steps 4-2 and 4-3;
step 4-5, setting a minimum distance n on a focal plane, and carrying out sampling interpolation on a gray value distribution curve on the focal point by using the minimum distance n to obtain a gray value of each point on the focal point; when the same point on the focus has a plurality of gray values, taking the average value of the gray values of all the gray values as the gray value of the point on the focus;
step 4-6, calculating the gray value W of each point on the focus obtained in the step 4-5 i0 (d n ) And the distance d between the corresponding point and the focal point center position v n Substituting into the edge expansion function f (x) of the focus to obtain the edge expansion function f (x) of the focus;
wherein x ═ d n ；f(x)＝W i0 (d n )；
Step 5, fitting the edge spread function f (x) of the focus obtained in the step 4, and calculating a Gaussian function of the fitted edge spread function;
and 6, acquiring a standard deviation of the Gaussian function, and taking a result of multiplying the standard deviation by a preset minimum distance n on a focal plane as the focal size.
Preferably, the specific method for binarization in step 3 is as follows:
acquiring a gray value distribution graph of any line segment A positioned on the sphere in the sphere projection image, acquiring a gray value at a% height in the gray value distribution graph, and performing binarization processing on the sphere projection image by using the gray value as a threshold value; wherein a% ∈ (0%, 100%), and the maximum value of the gray value is at 100% height in the gray value distribution diagram; the minimum value of the gray value is at 0% height in the gray value profile.
Preferably, the value range of a% is: 40 to 60 percent.
Further, the specific calculation method of the coordinates of the center of sphere T in the step 4-2 is as follows:
calculating coordinates of a point M farthest from a central point O of a sphere projection image and a point N closest to the central point O in a sphere projection contour point set I, forming a line segment MN by the point M and the point N, and calculating a coordinate of a point S farthest from the line segment MN in the sphere projection contour point set I; and simultaneously calculating the vertical center coordinate from the point S to the line segment MN, wherein the vertical center coordinate corresponds to the coordinate projected on the sphere projection image by the sphere center T of the sphere.
Further, the calculation process of the length | JT | of the line JT in step 5-2 is as follows:
according to the Helen formula, we obtain:
|JT|＝2S/|KI|
where | KT | is the length of the line segment KT,
(x O ，y O ) Coordinates of a central point O of the sphere projection image; (x) T ，y T ) Is the coordinate of the center of sphere T; SDD is the distance from the focus K to the center point O of the sphere projection image;
(x i ，y i ) Projecting points I in the set of contour points I for a sphere 0 The coordinates of (a); the | KI | is the length of the line segment KI;
compared with the prior art, the invention has the advantages that: the method does not need precise requirements on the size and the placement position of the sphere, the actual amplification ratio is calculated by analyzing the projection edges of the sphere at different angles, different resolutions of edge expansion functions at different angles are different due to different amplification ratios at different angles, and oversampling interpolation and average noise reduction of the edge expansion functions are realized by utilizing the characteristics. The method has the advantages of low processing difficulty of the ball mould body, high reliability and capability of realizing accurate quantification of the size of the focus.
Drawings
FIG. 1 is a schematic view of a sphere for spot size quantification of an X-ray source in an embodiment of the present invention;
FIG. 2 is a schematic illustration of the projection imaging of the sphere of FIG. 1;
FIG. 3 is a projection image of a sphere obtained by imaging the sphere projection of FIG. 1;
FIG. 4 is a gray-scale distribution diagram of line A in FIG. 3;
FIG. 5 is a three-dimensional schematic view of the projection of FIG. 2;
FIG. 6 is a cross-sectional view of the KIT of FIG. 5;
FIG. 7 is a schematic view of mapping point J of the KIT profile of FIG. 6 to a focal point;
FIG. 8 is a schematic view of a test spherical mold body according to an embodiment of the present invention;
FIG. 9 is an image obtained by projection imaging of FIG. 8;
fig. 10 is a diagram illustrating the effect of extracting and fitting the edge spread function to the image of fig. 9.
Detailed Description
The invention is described in further detail below with reference to the accompanying examples.
The method for quantifying the focal spot size of the X-ray source for the industrial CT system in the embodiment comprises the following steps:
the sphere in this embodiment suggests the use of pure tungsten material; in addition, in order to realize the support of the sphere and simultaneously not influence the imaging of the sphere, as shown in fig. 1, a support rod for supporting the sphere is made of a low-density material, and the support rod is made of carbon fiber;
the step also comprises the step of calibrating the diameter of the sphere by adopting a three-coordinate measuring machine, and when the size of the detected focus is smaller, the sphere with smaller diameter is used;
step 2, placing the sphere in the step 1 in an industrial CT system at the central position of a rotary table, adjusting the rotary table to be close to an X-ray source, turning on the X-ray source and a detector, setting a detection process (tube voltage and tube current) for measuring the focal size of the X-ray source, and obtaining a sphere projection image which is a gray scale image;
the schematic diagram of the test of the sphere of fig. 1 is shown in fig. 2, the projection image of the sphere is shown in fig. 3, and the reason for the low density of the support rods is that it is negligible when imaging; where point O in fig. 3 is the center point position of the sphere projection image (imaged on the detector); because the X-ray sources and the detectors of all CT devices are coaxial, a sphere is generally selected to be larger, the sphere is larger and has higher precision, and the point O is in a sphere projection image; t is the projection position of the sphere center of the sphere on the detector;
step 3, performing binarization processing on the sphere projection image to obtain a binarized sphere projection image, extracting a sphere projection contour position from the binarized sphere projection image, and forming a sphere projection contour point set I by the sphere projection contour position;
the threshold value selection method for the binarization processing comprises the following steps:
acquiring a gray value distribution graph of any line segment A passing through the sphere in the sphere projection image, wherein the line segment A cannot be a tangent of the sphere projection image and two intersection points are required to be arranged between the line segment A and the sphere projection image, the gray value distribution graph on the line segment A in FIG. 3 is shown in FIG. 4, the gray value at a% height in the gray value distribution graph is acquired, the gray value is used as a threshold value, and finally the threshold value is used for carrying out binarization processing on the sphere projection image; a% ∈ (0%, 100%), and the maximum value of the gray value at 100% height in the gray value distribution graph; the position of 0% height in the gray value distribution diagram is the minimum value of the gray value; in the embodiment, the content of a is 50%;
step 4, obtaining an edge expansion function f (x) of the focus; wherein x is the distance from any point K1 on the focal point to the focal point center position v; (x) is the gray scale value of any point K1 in the focus;
the method comprises the following specific steps:
step 4-1, randomly selecting a point I in the sphere projection contour point set I 0 And extracting the point i from the projection image of the sphere 0 The gray value distribution curve W on the line segment TI formed by the center T of the sphere i0 (x′)；
Wherein i 0 The serial numbers of the projection contour points in the sphere projection contour point set I are obtained; x' is the distance from any point on the line segment TI to the sphere center T on the sphere projection image;
step 4-2, selecting a focus K, a sphere center T and a point I in a sphere projection contour point set I of the X-ray source 0 Forming a KIT cross-sectional view including a focus K and a point i 0 A line segment KI, a line segment TI and a line segment KT are formed between the focus K and the sphere center T; making a line segment JT perpendicular to the line segment KI from the sphere center T, wherein the intersection point of the line segment JT and the line segment KI is a point J;
and the gray value distribution curve W on the line segment TI in the step 4-1 i0 (x') projecting the curve onto the line JT to obtain the gray value distribution curve W on the line JT i0 (j)；W i0 (j) The calculation formula of (2) is as follows:
W i0 (j)＝W i0 (x′*t i0 )；
wherein j is the distance from any point on the line segment JT to the sphere center T; t is t i0 Correction coefficient for line segment TI
JT | is the length of line JT; l TI | is the length of the line segment TI;
the specific calculation method of the coordinates of the sphere center T comprises the following steps:
calculating coordinates of a farthest point M and a nearest point N from a central point O of a sphere projection image in a sphere projection contour point set I, forming a line segment MN by the point M and the point N, and calculating a coordinate of a farthest point S from the line segment MN in the sphere projection contour point set I; meanwhile, the vertical center coordinate from the point S to the line segment MN is calculated, and the vertical center coordinate is the coordinate of the projection of the sphere center T of the sphere on the sphere projection image;
wherein a two-dimensional plane x-y (corresponding to the projection on the detector) is established for the sphere projection image, and the coordinate of the central point O of the sphere projection image is (x) O ，y O ) Distance (x) in the set of sphere contour points I 0 ，y 0 ) Coordinate (x) of nearest point N N ，y N ) And the coordinate (x) of the farthest point M M ，y M ) The calculation formula is as follows:
wherein (x) i ，y i ) Projecting the coordinates of the ith point in the contour point set I in the two-dimensional image for the sphere, (x) i ，y i )∈I：
The formula is calculated according to the coordinates (x, y) of each point on the line segment MN as follows:
(y M -y N )x+(x M -x N )y+x M y N -x N y M ＝0
projection contour point set I of any point (x) of sphere i ，y i ) The distance L to the line segment MN is calculated as:
coordinate (x) of point S farthest from line segment MN in sphere projection contour point set I S ，y S ) Is calculated byThe formula is as follows:
vertical center coordinate (x) from point S to line segment MN T ，y T ) The calculation formula of (2) is as follows:
the length | JT | of the line segment JT is calculated as:
according to the Helen formula, we obtain:
|JT|＝2S/|IK|
where | KT | is the length of the line segment KT,
(x O ，y O ) Coordinates of a central point O of the sphere projection image; (x) T ，y T ) Is the coordinate of the center of sphere T; the SDD is the distance from the focus K to the central point O of the sphere projection image, and the SDD value can be read by industrial CT system software;
(x i ，y i ) Projecting points I in the set of contour points I for a sphere 0 The coordinates of (a); the | KI | is the length of the line segment KI;
the projected three-dimensional schematic diagram is shown in fig. 5, | OK | ═ SDD;
additionally, a cross-sectional view of KIT is shown in fig. 6;
the theoretical basis for mapping the gray value distribution on the line segment TI to the line segment JT is as follows: according to the triangle formed by the point J, the point T and the point I:
thus obtaining:
the gray-value distribution curve W on the line segment TI is thus adapted i0 (x') projecting the curve onto the line JT to obtain the gray value distribution curve W on the line JT i0 (j)；
Step 4-3, the gray value distribution curve W on the line segment JT i0 (j) Projecting the gray value distribution curve on the focal point to obtain a gray value distribution curve on the focal point;
assuming that the focal point is a circle in fig. 6, regardless of its size, it is thought that this size becomes the following fig. 7. The focus K is a plane with a certain width, and the focus center is set as v, and v-C-J is on a line. The overall idea is to project the gray value distribution on the line JT to the focus to form the point spread function of the focus, and then estimate the size of the focus.
The reason why the gray value distribution on the line segment TI is mapped onto the line segment JT is that vCh (h is the center of the sphere) and vJT share the same angle, and the radius r of the sphere (obtained by calibrating the diameter of the sphere using the coordinate measuring machine in step 1) and the length of the line segment JT are known according to the relationship between the radius r and the length of the sphere
And since | VC | + | CJ | ═ VJ |, then:
mapping the gray value distribution on the line segment JT to a focus by using the relational expression;
the method comprises the following specific steps: let d denote the distance from any point on the line JT to point J j The distance from any point on the focal point to the focal point center position v is denoted as d n ，d n And d j Approximately satisfies the following formula:
wherein r is the radius of the sphere;
and according to the formula: d j Obtaining any point I in the sphere projection contour point set I 0 Distribution curve of gray values projected on the focal point
4-4, extracting a gray value distribution curve on a line segment formed by each point and the sphere center T in the sphere projection contour point set I according to the same method in the step 4-1, and extracting a gray value distribution curve of each point projected on a focus in the sphere projection contour point set I according to the same method in the steps 4-2 and 4-3;
step 4-5, setting a minimum distance n on a focal plane, and carrying out sampling interpolation on a gray value distribution curve on the focal point by using the minimum distance n to obtain a gray value of each point on the focal point; when the same point on the focus has a plurality of gray values, taking the average value of the gray values of all the gray values as the gray value of the point on the focus;
since a large number of point set gray values are projected onto the focus, an edge expansion function of the focus can be formed by adopting an oversampling interpolation and average noise reduction method;
step 4-6, calculating the gray value W of each point on the focus obtained in the step 4-5 i0 (d n ) And the distance d between the corresponding point and the focal point center position v n Substituting into the edge expansion function f (x) of the focus to obtain the edge expansion function f (x) of the focus;
wherein x ═ d n ；f(x)＝W i0 (d n )；
Step 5, fitting the edge spread function f (x) of the focus obtained in the step 4, and calculating a Gaussian function of the fitted edge spread function;
and 6, acquiring a standard deviation of the Gaussian function, and taking a result of multiplying the standard deviation by a preset minimum distance n on a focal plane as the focal size.
Because the central axis of the sphere is not necessarily perpendicular to the central axis of the detector and the focus, the projection of the sphere is oblique; in the invention, 3 times of projection mapping is utilized, firstly, the projection of a sphere on a detector plane is utilized to form edge degradation gray value analysis, wherein an I point set is an edge contour point, and the gray value distribution near the I point; secondly, projecting the I point set to the J point, so that the gray value distribution near the I point is changed into the gray value distribution near the J point; and finally, projecting the J point to a v point (focal plane), and projecting the gray value distribution of the points near the J point set to a focal point near the v point. Therefore, the accurate position of the circle center of the circular oblique projection is calculated, the slight change of the amplification ratio is caused by the different oblique projection angles of each side of the circle, the amplification ratio of each edge is obtained through calculation, the edge expansion functions with different resolutions are obtained on the basis, and then the over-sampling interpolation and the mean value noise reduction are carried out, so that the high-precision focus size quantification is realized.
To verify the utility of the present invention, the test was performed on a three-dimensional cone-beam micro-focal-plane-array CT system with a focal spot size of between about 5 and 9 microns as provided by the X-ray machine manufacturer. A spherical die body as shown in fig. 8 was used, the sphere diameter being 2 mm.
The spherical phantom is erected on a turntable, is as close as possible to an X-ray source, and DR images are acquired by respectively adopting different detection processes (specifically shown in table 1) (note that the focal size of the ray machine is generally in positive correlation with the power during use, namely the power is larger, and the focal point is larger).
TABLE 1 different detection Processes
| Serial number | Tube voltage | Tube current |
| 1 | 60kV | 60uA |
| 2 | 60kV | 90uA |
| 3 | 60kV | 120uA |
The integration time was 1000ms, the SDD value was set to 480mm, and a DR image was acquired as shown in FIG. 9.
The minimum distance n calculated by setting the focus is 0.0005 mm. It is subjected to edge spread function extraction and a gaussian function is calculated by iterative approximation fitting, as shown in fig. 10.
And calculating a Gaussian function (which can be obtained by derivation) corresponding to the fitted edge extension function, calculating to obtain the standard deviation of the Gaussian function, and multiplying the standard deviation value by the minimum distance n to obtain the focus size.
TABLE 2 Focus size measurement results
| Serial number | Standard deviation of gaussian function | Size of |
| 1 | 15.2371 | 7.01234 |
| 2 | 16.9274 | 7.65257 |
| 3 | 18.339 | 8.6678 |
As can be seen from the experimental results shown in table 2, the larger the power, the larger the focal spot size, which is consistent with the reality.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the technical principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A method for quantifying the size of a focus of an X-ray source for an industrial CT system is characterized by comprising the following steps:
step 1, preparing a sphere from a high-density material;
step 2, placing the sphere in the step 1 in an industrial CT system at the central position of a rotary table, adjusting the rotary table to be close to an X-ray source, turning on the X-ray source and a detector, setting a detection process for measuring the focal size of the X-ray source, and obtaining a sphere projection image which is a gray scale image;
step 3, performing binarization processing on the sphere projection image to obtain a binarized sphere projection image, extracting a sphere projection contour position from the binarized sphere projection image, and forming a sphere projection contour point set I by the sphere projection contour position;
step 4, obtaining an edge expansion function f (x) of the focus; wherein x is the distance from any point K1 on the focal point to the focal point center position v; (x) is the gray scale value of any point K1 in the focus;
the method comprises the following specific steps:
step 4-1, randomly selecting a point I in the sphere projection contour point set I 0 And extracting the point i from the projection image of the sphere 0 The gray value distribution curve W on the line segment TI formed by the center T of the sphere i0 (x′)；
Wherein i 0 The serial numbers of the projection contour points in the sphere projection contour point set I are obtained; x' is the distance from any point on the line segment TI to the sphere center T on the sphere projection image;
step 4-2, selecting a focus K, a sphere center T and a point I in a sphere projection contour point set I of the X-ray source 0 Forming a KIT profile including a focal point K and a point i 0 A line segment KI, a line segment TI and a line segment KT are formed between the focus K and the sphere center T; making a line segment JT perpendicular to the line segment KI from the sphere center T, wherein the intersection point of the line segment JT and the line segment KI is a point J;
and the gray value distribution curve W on the line segment TI in the step 4-1 i0 (x') projecting the curve onto the line JT to obtain the gray value distribution curve W on the line JT i0 (j)；W i0 (j) The calculation formula of (c) is:
W i0 (j)＝W i0 (x′*t i0 )；
wherein j is the distance from any point on the line segment JT to the sphere center T; t is t i0 Correction coefficient for line segment TI
JT | is the length of line JT; l TI | is the length of the line segment TI;
step 4-3, the gray value distribution curve W on the line segment JT i0 (j) Projecting the gray value distribution curve on the focal point to obtain a gray value distribution curve on the focal point;
the method comprises the following specific steps: let d denote the distance from any point on the line JT to point J j The distance from any point on the focal point to the focal point center position v is denoted as d n ，d n And d j Approximately satisfies the following formula:
wherein r is the radius of the sphere;
and according to the formula: d j Obtaining any point I in the sphere projection contour point set I 0 Distribution curve of gray values projected on the focal point
4-4, extracting a gray value distribution curve on a line segment formed by each point and the sphere center T in the sphere projection contour point set I according to the same method in the step 4-1, and extracting a gray value distribution curve of each point projected on a focus in the sphere projection contour point set I according to the same method in the steps 4-2 and 4-3;
step 4-5, setting a minimum distance n on a focal plane, and carrying out sampling interpolation on a gray value distribution curve on the focal point by using the minimum distance n to obtain a gray value of each point on the focal point; when the same point on the focus has a plurality of gray values, taking the average value of the gray values of all the gray values as the gray value of the point on the focus;
step 4-6, calculating the gray value W of each point on the focus obtained in the step 4-5 i0 (d n ) And the distance d between the corresponding point and the focal point center position v n Substituting into the edge expansion function f (x) of the focus to obtain the edge expansion function f (x) of the focus;
wherein x ═ d n ；f(x)＝W i0 (d n )；
Step 5, fitting the edge spread function f (x) of the focus obtained in the step 4, and calculating a Gaussian function of the fitted edge spread function;
and 6, acquiring a standard deviation of the Gaussian function, and taking a result of multiplying the standard deviation by a preset minimum distance n on a focal plane as the focal size.
2. The method of claim 1, wherein the method comprises: the specific method of binarization in the step 3 is as follows:
acquiring a gray value distribution graph of any line segment A positioned on the sphere in the sphere projection image, acquiring a gray value at a% height in the gray value distribution graph, and performing binarization processing on the sphere projection image by using the gray value as a threshold value; wherein a% ∈ (0%, 100%), and the maximum value of the gray value is at 100% height in the gray value distribution diagram; the minimum value of the gray value is at 0% height in the gray value profile.
3. The method of claim 2, wherein the method comprises: the value range of a% is as follows: 40 to 60 percent.
4. The method of claim 1, wherein the method comprises: the specific calculation method of the coordinates of the sphere center T in the step 4-2 comprises the following steps:
calculating coordinates of a point M farthest from a central point O of a sphere projection image and a point N closest to the central point O in a sphere projection contour point set I, forming a line segment MN by the point M and the point N, and calculating a coordinate of a point S farthest from the line segment MN in the sphere projection contour point set I; and simultaneously calculating the vertical center coordinate from the point S to the line segment MN, wherein the vertical center coordinate corresponds to the coordinate projected on the sphere projection image by the sphere center T of the sphere.
5. The method of claim 4, wherein the method comprises: the calculation process of the length | JT | of the line JT in step 4-2 is as follows:
according to the Helen formula, we obtain:
|JT|＝2S/|KI|
where | KT | is the length of the line segment KT,
(x O ，y O ) Coordinates of a central point O of the sphere projection image; (x) T ，y T ) Is the coordinate of the center of sphere T; SDD is the distance from the focus K to the center point O of the sphere projection image;
(x i ，y i ) Projecting points I in the set of contour points I for a sphere 0 The coordinates of (a); the | KI | is the length of the line segment KI;
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