CN111879799B - Manual testing method for spatial resolution of optical system - Google Patents
Manual testing method for spatial resolution of optical system Download PDFInfo
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Abstract
A method for manually testing the spatial resolution of an optical system, comprising: manufacturing a die body to be tested by a mechanical processing means; carrying out CT scanning on the two test blocks which are attached together to obtain CT images corresponding to the sections of the two test blocks; randomly framing one test block or the inner areas of two test blocks in the CT image, and calculating the mean value of the gray values in the framed area; making a line segment L which is vertical and equally divides the centers of two circles of the line segment in the CT image; extracting the gray distribution on the line segment, and finally drawing a gray distribution curve; drawing a straight line with the gray value K on the gray distribution curve, wherein the straight line is intersected with the gray value on the line segment L at two points; calculating the distance between the two intersected points; thereby calculating the minimum identification gap a; and calculate outTheI.e. the corresponding line logarithm under MIF-10%. The method has the advantages of low processing difficulty of the test die body, visual test result, simple test process and easy realization.
Description
Technical Field
The invention relates to the technical field of optical system performance testing, in particular to a manual testing method for the spatial resolution of an optical system.
Background
The industrial CT detection technology is a practical nondestructive detection means developed on the X-ray detection technology, is a special optical system, has the advantages of visual imaging, accurate quantification, positioning and qualitative determination, and can be widely applied to the fields of industrial nondestructive inspection, medical treatment and health care and the like. The performance evaluation of the industrial CT system is required to be involved in the processes of development, production, acceptance, use, debugging, maintenance and the like of the CT equipment, so that a performance evaluation method of the industrial CT system, which is convenient and fast to test, high in precision and strong in practicability, is urgently required for manufacturers and users.
Spatial resolution is one of the important indicators for performance evaluation of industrial CT systems, and represents a measure of how fine details are resolved by a CT system, and is generally a quantitative representation of the minimum separation between two details that can be resolved. At present, the spatial resolution test method mainly includes a fringe (circular hole) phantom measurement method and a modulation transfer function method. The fringe (round hole) die body measuring method adopts a series of structures (line pairs, round holes, square holes and the like) with different periodicities to scan and reconstruct a die body, a CT image is observed, the minimum period capable of distinguishing fringe or round hole patterns is used as the limit resolution, the resolution of a CT system can be conveniently and visually obtained, but the measuring result has subjectivity and is inaccurate, the precision of the measuring result is determined according to the periodic structure interval of the processed die body, the processing difficulty is high, and the cost is extremely high; the modulation transfer function method is a curve of the relationship between the modulation degree and the input spatial frequency, and is numerically equal to the fourier transform of the point spread function, and generally, the line logarithm corresponding to 10% of the modulation degree on the MTF curve is taken as the limit resolution of the CT system. The modulation transfer function method can be divided into a point spread function method (PSF), a line spread function method (LSF) and an edge spread function method (ESF), has low requirements on a die body and large noise influence, can be used for comparing spatial resolution between devices and under process conditions, gives a normalized quantization result which is not visual, and can be compared with an actual line card result only by equivalent conversion.
Further improvements are therefore desirable.
Disclosure of Invention
The invention aims to solve the technical problem of providing a manual testing method for the spatial resolution of an optical system, which has the advantages of low processing difficulty of a testing die body, visual testing result, simple testing process and easiness in realization, aiming at the current situation of the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows: a manual test method for the spatial resolution of an optical system is characterized in that: the method is used for manually measuring the limit spatial resolution in a linear array industrial CT system or an area array industrial CT system, and comprises the following steps:
step 2, the two test blocks in the step 1 are attached together, and CT scanning is carried out on the two attached test blocks to obtain CT images corresponding to the sections of the two test blocks;
step 4, recording the centers of two circles in the CT image as A 1 And A 2 Making a vertical and equally divided line segment A 1 A 2 A line segment L of (A);
step 5, extracting the gray distribution on the line segment L and drawing a gray distribution curve;
step 6, drawing a straight line P with the gray value K on the gray distribution curve in the step 5, wherein the straight line P and the gray value on the line segment L are intersected at two points B1 and B2;
step 7, calculating the distance h (unit: millimeter) between the two points B1 and B2;
and 8, calculating to obtain a minimum identification gap a (unit is: mm) according to the diameter d (unit is: mm) of the test block and the distance h in the step 7, wherein the calculation formula is as follows:
step 9, calculating the minimum identification gap a obtained in the step 8TheI.e. the corresponding line pair number under the MTF of 10%, which is the ultimate spatial resolution.
Specifically, the area framed in step 3 is smaller than two thirds of the corresponding circular cross section of the test block.
Preferably, the area selected in step 3 is circular or rectangular.
As an improvement, the value range of K in the step 6 is 50-55% T.
Preferably, the value of K in step 6 is 52% T.
Compared with the prior art, the invention has the advantages that: the test die body of the test method has the advantages of simple structure, small processing difficulty and low cost, and the manual test method has the advantages of simple test process, low data processing difficulty, easy realization and higher use value; and the test result is the physical quantity of the size, so that the test is more visual.
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FIG. 1 is a CT image of two test blocks corresponding to cross-sections according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a circular region inside two test blocks selected from the CT image of FIG. 1;
FIG. 3 is a schematic diagram of a line segment L drawn in the CT image of FIG. 1;
FIG. 4 is a schematic diagram of the gray-level distribution of the line segment L in FIG. 3;
FIG. 5 is a schematic view of FIG. 4 taken along line P;
FIG. 6 is a schematic diagram of a dual-circle mold according to an embodiment of the present invention;
FIG. 7 is a CT image of a cross-section of a line-to-line card and the two test blocks of FIG. 1 according to an embodiment of the present invention;
FIG. 8 is a diagram illustrating the results of a line-to-card test in an embodiment of the present invention;
Detailed Description
The invention is described in further detail below with reference to the following examples of the drawings.
A manual test method of optical system spatial resolution is used for manually measuring the limit spatial resolution in a linear array industrial CT system or an area array industrial CT system, and comprises the following steps:
step 2, the two test blocks in the step 1 are attached together, and CT scanning is carried out on the two attached test blocks to obtain CT images corresponding to the sections of the two test blocks; as shown in fig. 1;
the selected area is circular or rectangular, and the selected area is less than two thirds of the corresponding circular section of the test block; in this embodiment, the region corresponding to any one of the test blocks in the CT image may be selected by frame, or the two test blocks may be selected by frame, as shown in fig. 2; the difference between the gray value mean values calculated by the three methods after frame selection is small;
step 4, recording the centers of two circles in the CT image as A 1 And A 2 Making a vertical and equally divided line segment A 1 A 2 The line segment L of (a); as shown in fig. 3;
wherein, the length of the line segment L is more than 1.5 times of the diameter of the test block;
step 5, extracting the gray distribution on the line segment L and drawing a gray distribution curve; as shown in fig. 4, the abscissa is the position coordinate of each pixel in the CT image, and the ordinate is the gray value;
step 6, drawing a straight line P with the gray value K on the gray distribution curve in the step 5, wherein the straight line P and the gray value on the line segment L are intersected at two points B1 and B2; as shown in fig. 5;
wherein the value range of K is 50-55% T; in this embodiment, for convenience of calculation, the value of K is 52% T;
step 7, calculating the distance h (unit: millimeter) between the two points B1 and B2;
and 8, calculating to obtain a minimum identification gap a (unit is: mm) according to the diameter d (unit is: mm) of the test block and the distance h in the step 7, wherein the calculation formula is as follows:
step 9, calculating the minimum identification gap a obtained in the step 8The device isI.e. the corresponding line pair number at MTF 10%, which is the ultimate spatial resolution.
In order to verify the test result of the manual test method for the spatial resolution of the optical system and the spatial resolution test in GB/T35389-2017' guide rule for nondestructive testing X-ray digital imaging detectionThe result is consistent, the method of the invention is used for positioning a measuring straight line P at the position with the gray scale of 50% T-55% T on the curve, and the straight line P and the gray scale value on the line segment L are intersected at B 1 And B 2 Two points, B is obtained by calculation 1 And B 2 The minimum identification gap a is obtained by calculation according to the h, 1/2a is compared with the spatial resolution value under the 10% modulation degree (MTF) obtained by calculation in the GB/T35389-2017 method, and the result that the 1/2a is basically consistent with the result of the spatial resolution value under the 10% modulation degree (MTF) obtained by calculation in the GB/T35389-2017 method is obtained by experiments.
Calculated in step 9The proof process of the corresponding line logarithm under the MTF of 10% is as follows:
modulation degree M T Can be expressed as
The periodic bar-shaped mode can be expressed as a rectangular pulse function, and then the peaks p (x) and the troughs q (x) in the line pair card mode can be expressed as:
wherein: n is equal to Z, 2a i The rectangular pulse width of the wave crest (wave trough) in the line pair card module body is defined as the unit step signal of epsilon (x)
The industrial CT imaging system is a linear time-invariant system, a contrast reduction model caused by the imaging process can be approximated to a Gaussian degradation function model g (x), and then the imaging process is simplified to be convolution of an input function and a Gaussian degradation function:
similarly, the trough is shown after imaging
Without taking noise into account, the maximum peak I max Necessarily at x ═ 0:
substituting (6) into formula (1) to obtain modulation M after line-to-line card (5 line pairs) CT imaging T The expression is as follows:
analysis was performed using a double circle variable pitch model: two calibration cylinders (spheres) with the same nominal diameter (D) are used, which are brought into point contact with each other on a line (one point), the image of the contact region being distorted by the CT reconstruction, the extent of the distortion region decreasing with increasing spatial resolution of the CT system. Therefore, the mold body can be used as a rectangular wave test card with continuously-changed slit width.
As shown in fig. 6, the distance between two adjacent circular mold bodies parallel to the circle center line segment can be written as follows:
the gray distribution function with the distance h from the circle center line segment can be expressed as
In the formula, a h The width of the trough between the double circles is h away from the line segment of the circle center. Note that f (x, a) h ) Represents a normalized gray value, and 0 ≦ f (x, a) h )≤1。
Substituting x-0 for formula (9) can obtain the gray distribution on the lower central axis with different spacing, some
Because the integral of the normal distribution function g (x) has no analytic solution, the g (x) integral approximate calculation formula is introduced
By substituting (11) into the formula (10) and simplifying the process, the compound
Wherein W is more than or equal to 1;
according to the equivalent analysis of the double-circle variable pitch and periodic structure (line pair): let a gaussian degradation function model g (x) of the industrial CT imaging process be:
from the standard normal distribution, the integral function of g (x) is about 99.73% of the whole in the interval of 3 times the standard deviation. When the line pair width a i Is equal to the standard deviationIn this case, 3 sets of line pairs were included in a 3-fold standard deviation interval, and M in this case T The value is about 1.1%. When the content of M is less than or equal to 1.1 percent T When the peak value is less than or equal to 100 percent, the maximum peak value I max Can be approximated as:
substituting it into formula (7), introducing the g (x) integral approximate calculation formula and simplifying, then M T Can be expressed as:
the smallest line pair that can be resolved on a CT image is the line pair width at a modulation of 10%, so M is the number of lines T Substitution of 10% for formula (13) and simplification
The polynomial is rooted to a real solution greater than 1 in equation (14), W ≈ 2.81049.
Substituting W.apprxeq. 2.81049 into equation (12) to obtain
f(a h )≈0.5249 (15)
Thus, the CT system can resolve the spatial resolution as
The corresponding line-to-line spatial frequency freq (unit: line-to-card/mm) can be expressed as
And due to step 8In the formula (8)Namely: a is 2a h Thus in formula (17)The calculation in step 9 can be obtainedI.e. the corresponding log line number at MTF of 10%.
In this embodiment, two cylindrical test blocks with a diameter d equal to 8mm are processed, a line pair card and the cylindrical test blocks are scanned together to obtain a CT image, the CT image is shown in fig. 7, two circular inner regions are framed to obtain a mean gray value T equal to 94, and gray distribution on the central axis of two centers of circles is extracted; a measurement straight line P is positioned at the position of 47 gray levels on the curve, and the straight line P and the gray level value on the line segment L are intersected at B 1 And B 2 Two points, B is obtained by calculation 1 And B 2 The distance h between them is 1.952 mm. Substituting the diameter d of 8mm and the distance h of 1.952mm into a formula to calculate the minimum recognizable gap a of the industrial CT system;
the test results were compared with a line-to-line card having line widths of 0.5/0.4/0.3/0.25/0.2/0.1mm, respectively. Drawing a measuring line in the middle of the line-to-card, extracting the gray distribution on the line, and as shown in fig. 8, the measuring result is basically consistent with the line-to-card method.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, it is possible to make various improvements and modifications without departing from the technical principle of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention.
Claims (5)
1. A manual test method for the spatial resolution of an optical system is characterized in that: the method is used for manually measuring the limit spatial resolution in a linear array industrial CT system or an area array industrial CT system, and comprises the following steps:
step 1, manufacturing a die body to be tested by a mechanical processing means; the die body to be tested is two cylindrical or spherical test blocks with the same material and size;
step 2, the two test blocks in the step 1 are attached together, and CT scanning is carried out on the two attached test blocks to obtain CT images corresponding to the sections of the two test blocks;
step 3, randomly framing one test block or the internal area of two test blocks in the CT image, and calculating the gray value mean value T in the framed area;
step 4, recording the centers of two circles in the CT image as A 1 And A 2 Making a vertical and equally divided line segment A 1 A 2 A line segment L of (A);
step 5, extracting the gray distribution on the line segment L and drawing a gray distribution curve;
step 6, drawing a straight line P with the gray value K on the gray distribution curve in the step 5, wherein the straight line P and the gray value on the line segment L are intersected at two points B1 and B2;
and 7, calculating the distance h between the two points B1 and B2, wherein the unit is as follows: millimeter;
step 8, calculating the minimum recognition gap a according to the diameter d of the test block and the distance h in the step 7, wherein the units of d and a are as follows: millimeter, the calculation formula is:
2. The method for manually testing the spatial resolution of an optical system according to claim 1, wherein: and the area framed and selected in the step 3 is less than two thirds of the corresponding circular section of the test block.
3. The method for manually testing the spatial resolution of an optical system according to claim 1, wherein: the area selected by the frame in the step 3 is circular or rectangular.
4. A method for manual testing of the spatial resolution of an optical system according to claim 1, wherein: the value range of K in the step 6 is 50-55% T.
5. The method for manually testing the spatial resolution of an optical system according to claim 4, wherein: and the value of K in the step 6 is 52% T.
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