Dual-moment X-ray backlighting imaging system and method based on a single laser beam

By setting up a focus optical device, a primary target and a secondary target in the laser X-ray photography system, and using a single beam of laser to generate multiple X-ray sources, the problem of difficulty in achieving multi-time and multi-angle photography in the prior art is solved, and efficient dual-time X-ray backlight photography is achieved, and economic costs are reduced.

CN116300293BActive Publication Date: 2025-05-27LASER FUSION RES CENT CHINA ACAD OF ENG PHYSICS
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Patent Information

Application Number
CN202310140160.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-02-20
Publication Date
2025-05-27
Estimated Expiration
2043-02-20

AI Technical Summary

Technical Problem

In the existing laser X-ray photography methods, a single beam laser target can only generate one X-ray source at a time, making it difficult to achieve efficient photography at multiple times and multiple angles. Increasing the number of lasers to shoot will increase the system scale and complexity, bringing high economic costs.

Method used

By setting up a focus optical device, a primary target and a secondary target, a single beam of laser is used to generate a primary X-ray source and a secondary X-ray source, and a coaxial or biaxial dual-time X-ray backlight photography is achieved.

Benefits of technology

Two-time X-ray backlight photography based on single-beam laser is realized, reducing the demand for the number of lasers, reducing economic costs, and improving the spatial resolution and energy utilization of the photography.

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Abstract

The present invention relates to the fields of laser fusion research and X-ray detection technology, and in particular to a dual-time X-ray backlight photography system and method based on a single laser beam, wherein the backlight photography method includes generating a primary X-ray source based on the first focusing of a single laser beam acting on a primary target; transmitting the transmitted laser that does not act on the primary target from the outside of the primary target to a focusing optical device, and using the focusing optical device for secondary focusing to reduce the focal spot of the transmitted laser; generating a secondary X-ray source based on the secondary focused transmitted laser acting on a secondary target; and realizing backlight photography using an image acquisition device. The purpose is to solve the technical problem that a single laser beam acting on a target can only generate one X-ray source at a time in the existing laser X-ray photography method, and to achieve the technical effect of dual-time X-ray backlight photography based on coaxial or biaxial single laser beams.
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Description

Technical Field

[0001] The present invention relates to the fields of laser fusion research and X-ray detection technology. Specifically, it relates to a two-moment X-ray backlighting imaging system and method based on a single laser beam. Background Art

[0002] Currently, perspective imaging technology based on the high penetration ability of X-rays is used to obtain internal structure information of objects and has been widely applied in fields such as industrial non-destructive testing, medical diagnosis, and scientific research. Traditional X-ray sources include radioactive sources, X-ray machines, accelerator X-ray sources, etc. With the progress of high-power laser engineering technology, various new types of ultrafast and ultra-high-intensity X-ray sources have been generated based on high-power lasers. Since the power density after focusing of high-energy picosecond lasers and femtosecond lasers exceeds the relativistic intensity (about 10 18 W / cm 2 ), a large number of MeV high-energy electrons can be generated during target shooting, and thus a high-brightness and high-energy X-ray source can be generated. The pulse width of the above new type of X-ray source is usually shorter than 0.1 ns. When applied to transient imaging of objects moving at high speeds (speed 1 - 1000 km / s), the image blur caused by motion can be reduced to less than 0.1 mm. Combining the advantages of a small focal spot of the laser X-ray source, high-resolution X-ray imaging can be achieved. Therefore, ultrafast high-energy X-ray imaging based on laser X-ray sources has been widely applied in fields such as high-energy density physics and inertial confinement fusion.

[0003] When applying ultrafast high-energy X-ray imaging based on laser X-ray sources, it is difficult to obtain multi-moment and multi-angle imaging images simultaneously due to limitations in the number of laser X-ray sources, the high-speed motion characteristics of the object, and the limited time resolution of the image recording system. It faces very difficult engineering and scientific problems to rotate the object moving at high speed to achieve multi-angle imaging and improve the time resolution of a large-area image recording system to the ps level.

[0004] In the prior art, by increasing the number of picosecond laser beams, the number of laser X-ray sources can be increased, and multi-angle and multi-moment ultrafast high-energy X-ray imaging applications can be achieved by changing the laser target shooting moment, such as Compton imaging applications for inertial confinement fusion, etc. However, in the above technical solutions, a single laser beam can only generate one X-ray source when acting on the target once. This scheme of increasing the number of laser beams for target shooting will increase the system scale and complexity and bring extremely high economic costs. Therefore, we propose a two-moment X-ray backlighting imaging system and method based on a single laser beam. Summary of the Invention

[0005] The object of the present invention is to provide a dual - moment X - ray backlighting imaging system and method based on a single - beam laser, so as to solve the technical problem in the prior art that only one X - ray source can be generated when a single - beam laser acts on a target once, and to achieve the technical effect of dual - moment X - ray backlighting imaging based on co - axial or bi - axial single - beam laser.

[0006] The technical solution of the first aspect of the present invention provides a dual - moment X - ray backlighting imaging system based on a single - beam laser, including a focusing optical device, an object to be measured, and an image acquisition device arranged at intervals in sequence. Two focal points are provided on the side of the focusing optical device close to the object to be measured, and a primary target and a secondary target are respectively arranged on the two focal points.

[0007] Further, the cross - sectional size of the primary target is configured to be smaller than the focal spot of the incident laser.

[0008] Further, the primary target is a micro - wire target or a micro - sphere target.

[0009] Further, the secondary target is one of a micro - wire target, a micro - sphere target, and a planar target.

[0010] Further, the focusing optical device adopts an ellipsoidal focusing mirror.

[0011] The technical solution of the second aspect of the present invention provides a dual - moment X - ray backlighting imaging method based on a single - beam laser, including the following steps:

[0012] Based on the first - time focusing of a single - beam laser on the primary target to generate a primary X - ray source;

[0013] The transmitted laser that does not act on the primary target is transmitted from the outside of the primary target to the focusing optical device, and the focusing optical device is used for secondary focusing to make the focal spot of the transmitted laser smaller;

[0014] Based on the transmitted laser after secondary focusing acting on the secondary target to generate a secondary X - ray source;

[0015] Use the image acquisition device to achieve backlighting imaging.

[0016] Further, the method further includes:

[0017] By changing the position between the object to be measured and the two focal points of the focusing optical device, and then adjusting the imaging angle, co - axial imaging or bi - axial imaging is achieved;

[0018] By adjusting the parameters of the focusing optical device or the distance between the object to be measured and the two focal points of the focusing optical device, and then adjusting the imaging moment, co - axial dual - moment imaging or bi - axial dual - moment imaging is achieved.

[0019] Further, the coaxial photography is specifically achieved by changing the position between the object to be measured and the two foci of the focusing optical device, and then adjusting the photography angle, which specifically includes:

[0020] The object to be measured is configured to be placed on the extension line of the connection line between the two foci of the focusing optical device, so that the object to be measured and the two foci are collinearly distributed, thereby achieving coaxial photography.

[0021] Further, the biaxial photography is specifically achieved by changing the position between the object to be measured and the two foci of the focusing optical device, and then adjusting the photography angle, which specifically includes:

[0022] The object to be measured is configured to be placed on the side of the connection line between the two foci of the focusing optical device and away from the focusing optical device, so that the object to be measured and the two foci are triangularly distributed, thereby achieving biaxial photography.

[0023] Further, the method further includes:

[0024] The cross-sectional size of the secondary target is configured to be smaller than the spot diameter after secondary focusing to improve the spatial resolution of the X-ray source; or, the cross-sectional size of the secondary target is configured to be larger than the spot diameter after secondary focusing to improve the laser energy utilization rate.

[0025] The beneficial effects of the present invention include:

[0026] 1. By providing a focusing optical device and combining a primary target and a secondary target, the present invention realizes two X-ray sources, namely a primary X-ray source and a secondary X-ray source, generated by a single laser shot on a target; on the other hand, by changing the position between the object to be measured and the two foci of the focusing optical device, the technical effect of dual-moment X-ray backlighting photography based on a single laser coaxial or biaxial is achieved by using an image acquisition device; compared with the prior art, the requirement for the number of lasers for realizing dual-moment photography is reduced, and the economic cost is lowered. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required to be used in the embodiments of the present invention. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can also be obtained based on these drawings without creative efforts.

[0028] Figure 1 It is a schematic structural diagram of the backlighting photography system provided by the embodiment of the present invention;

[0029] Figure 2 It is a schematic structural diagram of coaxial dual-moment backlighting photography provided by the embodiment of the present invention;

[0030] Figure 3Schematic structural diagram of dual-axis dual-moment backlight photography provided by an embodiment of the present invention;

[0031] Figure 4 Schematic flow chart of the backlight photography method provided by an embodiment of the present invention.

[0032] Icons: 100 - focusing optical device, 110 - secondarily focused transmitted laser, 200 - object to be measured, 300 - image acquisition device, 400 - primary target, 410 - transmitted laser, 420 - primary X-ray source, 500 - secondary target, 510 - secondary X-ray source, 600 - incident laser. Specific embodiments

[0033] Next, the technical solutions in the embodiments of the present invention will be described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0034] It should be noted that: similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of the present invention, terms such as "first", "second", etc. are only used for distinguishing descriptions and cannot be construed as indicating or implying relative importance.

[0035] Please refer to Figure 1 As shown, the technical solution of the first aspect of the present invention provides a dual-moment X-ray backlight photography system based on a single laser beam, including a focusing optical device 100, an object to be measured 200, and an image acquisition device 300 that are sequentially arranged at intervals. On one side of the focusing optical device 100 close to the object to be measured 200, there are two focal points, and a primary target 400 and a secondary target 500 are respectively arranged on the two focal points;

[0036] Preferably, the cross-sectional size of the primary target 400 is configured to be smaller than the focal spot of the incident laser 600; the primary target 400 can adopt a microfilament target or a microsphere target with a micron-level diameter. For example, it can be a tungsten wire target with a diameter of 5 - 10 μm, or a gold ball target with a diameter of 5 - 10 μm. In actual use, high-power laser acting on the primary target 400 will generate a large number of high-energy electrons, and the high-energy electrons will generate a primary X-ray source 420 in the primary target 400; it should be noted that the size of the primary target 400 should be determined according to the actual requirements in actual use, specifically according to the size requirements of the focal spot of the primary X-ray source 420;

[0037] For example, selecting a primary target 400 with a small size can generate a primary X-ray source 420 with a small focal spot. The primary X-ray source 420 with a small focal spot can achieve high-resolution photography. It can be understood that in this backlight photography system, part of the laser that does not act on the primary target 400 will transmit through the outside of the primary target 400 to generate transmitted laser 410. The smaller the size of the primary target 400, the larger the share of its transmitted laser 410, and more transmitted laser 410 will transmit through the outside of the primary target 400.

[0038] Preferably, the focusing optical device 100 uses an ellipsoidal focusing mirror. Based on the characteristics of the ellipsoidal focusing mirror itself, the light emitted from one of the two focal points of the ellipsoidal focusing mirror will be focused on the other focal point. Therefore, the reduction of the optical focal spot can be achieved. The primary target 400 and the secondary target 500 are respectively placed at the two focal points of the ellipsoidal focusing mirror. Based on the parameter settings (major axis length and minor axis length) of the ellipsoidal focusing mirror, the focal spot of the transmitted laser 410 after secondary focusing on the ellipsoidal focusing mirror is smaller than the focal spot of the original transmitted laser, so that the power of the transmitted laser 410 after secondary focusing is high enough to generate a secondary X-ray source 510.

[0039] Preferably, the secondary target 500 can be one of a microfilament target, a microsphere target, and a planar target with a micron-level diameter. In actual use, the above-mentioned transmitted laser 410 acts on the secondary target 500 after secondary focusing by the ellipsoidal focusing mirror to generate a secondary X-ray source 510. The size of the secondary target 500 should also be determined according to the requirements in actual use.

[0040] For example, if in order to generate a secondary X-ray source 510 with a micro focus, the size of the secondary target 500 can be configured to be smaller than the diameter of the spot after secondary focusing, so as to improve the spatial resolution of the secondary X-ray source. If in order to improve the spatial resolution of the secondary X-ray source 510, the size of the secondary target 500 can be configured to be larger than the diameter of the spot after secondary focusing, thereby improving the utilization rate of laser energy.

[0041] The dual-moment X-ray backlight photography system based on a single laser beam provided by the present disclosure realizes two X-ray sources, namely a primary X-ray source 420 and a secondary X-ray source 510, by setting a focusing optical device 100 and combining a primary target 400 and a secondary target 500. Compared with the prior art, it reduces the requirement for the number of lasers to achieve dual-moment photography and reduces the economic cost.

[0042] Please refer to Figure 4 As shown, the technical solution of the second aspect of the present invention provides a dual-moment X-ray backlight photography method based on a single laser beam, including the following steps:

[0043] Step S1: Generate a primary X-ray source 420 based on the first focusing effect of a single laser beam on a primary target 400;

[0044] Among them, the single laser beam can be a picosecond or femtosecond pulsed laser with an energy of dozens to thousands of joules, and the laser focal spot can be configured to be dozens of micrometers; the single laser beam can be first focused using an existing off-axis parabolic mirror, and the angle between the incident angle of the single laser beam and the primary target 400 (this angle can change the optical path) can be determined according to actual needs;

[0045] Step S1 further includes configuring the focusing optical device 100 so that the power density of the transmitted laser 410 reaching the surface of the focusing optical device 100 is between 10 14 W / cm 2 and 10 15 W / cm 2 . The purpose is that the power density in the above range can generate a plasma mirror on the surface of the focusing optical device 100 to achieve a high laser reflectivity of the focusing optical device 100; it should be noted that too low or too high power density will reduce the laser reflectivity, which is not conducive to the generation of subsequent X-ray sources;

[0046] Step S2: The transmitted laser 410 that does not act on the primary target 400 is transmitted from the outside of the primary target 400 to the focusing optical device 100, and the focusing optical device 100 is used for secondary focusing to reduce the focal spot of the transmitted laser 410;

[0047] Step S3: Generate a secondary X-ray source 510 based on the transmitted laser 410 after secondary focusing acting on a secondary target 500;

[0048] Step S4: Use the image acquisition device 300 to achieve backlighting photography;

[0049] Preferably, the above backlighting photography method further includes:

[0050] By changing the position between the object under test 200 and the two focal points of the focusing optical device 100, and then adjusting the photography angle, coaxial photography or biaxial photography is achieved;

[0051] Preferably, by changing the position between the object under test 200 and the two focal points of the focusing optical device 100, and then adjusting the photography angle, as shown in Figure 3 as well. Specifically, achieving coaxial photography includes: configuring the object under test 200 to be placed on the extension line of the connection between the two focal points of the focusing optical device 100. It can be understood that at this time, the object under test 200 and the two focal points of the focusing optical device 100 are collinear, and coaxial photography is achieved at this time;

[0052] Preferably, by changing the position between the two foci of the object under test 200 and the focusing optical device 100, and then adjusting the photographing angle, as also shown in Figure 2 The realization of dual-axis photographing specifically includes: configuring the object under test 200 to be placed on one side of the line connecting the two foci of the focusing optical device 100 and away from the focusing optical device 100. It can be understood that at this time, the object under test 200 and the two foci of the focusing optical device 100 are in a triangular distribution, and dual-axis photographing is realized at this time;

[0053] Preferably, by adjusting the parameters of the focusing optical device 100 or the distance between the object under test 200 and the two foci of the focusing optical device 100, and then adjusting the photographing time, coaxial dual-time photographing or dual-axis dual-time photographing is realized; in this embodiment, the adjustment of the photographing time should be determined according to the actual position of the object under test 200;

[0054] For example, as shown in Figure 2 When applied to dual-axis dual-time backlight photographing, the above image acquisition device 300 can be configured as a time-integrating imaging plate, film, X-ray CCD, scintillator-coupled CCD, scintillator-coupled CMOS and other X-ray image recording devices, and can also be a photon-counting semiconductor detector with time resolution ability, X-ray framing camera;

[0055] For example, as shown in Figure 3 When applied to coaxial dual-time backlight photographing, the above image acquisition device 300 can be configured as an existing device such as an X-ray framing camera with time resolution ability;

[0056] For example, when the object under test 200 is placed on the extension line of the line connecting the two foci of the focusing optical device 100 or on the perpendicular bisector of the two foci of the focusing optical device 100, the adjustment of the photographing time is determined by the specific parameters of the focusing optical device 100;

[0057] For example, different from the above embodiment, when the position of the object under test 200 is on the intersection line of the axes of the primary target 400 and the secondary target 500, the photographing time is not only determined by the specific parameters of the focusing optical device 100, but also related to the specific position of the object under test 200 on the intersection line; specifically, by changing the specific distance between the object under test 200 and the primary target 400 and the secondary target 500, changing the optical path of the secondary focusing of the focusing optical device 100, and then adjusting the photographing time of the X-ray source to realize dual-time photographing;

[0058] Preferably, the method further includes: configuring the cross-sectional size of the secondary target 500 to be smaller than the spot diameter after secondary focusing to improve the spatial resolution of the X-ray source; or configuring the cross-sectional size of the secondary target 500 to be larger than the spot diameter after secondary focusing to improve the laser energy utilization rate;

[0059] The following provides an embodiment to elaborate on the above backlight photography method in detail:

[0060] In this embodiment, first, a primary target 400 is placed at the first focus of the ellipsoidal focusing mirror. The energy of the incident single laser beam is selected to be 100 J, the pulse width is 1 ps, and it is incident after being first focused by an off-axis parabolic mirror with an F number of 2.5. The size of the focused spot is 30 μm, and the power density after focusing is 9×10 18 W / cm 2 ;

[0061] Among them, the primary target 400 is configured as a wire target with a diameter of Φ10 μm, and the material is gold. The angle between the incident single laser beam and the axis of the wire target is 50°; since the laser focal spot is larger than the primary target 400, only about 36 J of laser energy will act on the primary target 400, which can generate a primary X-ray source 420 with an energy greater than 10 keV, and the number of photons of the primary X-ray source 420 reaches 9×10 11 pieces;

[0062] Among them, the parameters of the ellipsoidal focusing mirror are configured as follows: the major axis is 16.8 mm, and the minor axis is 12 mm; the angle between the incident single laser beam and the line connecting the two foci of the ellipsoidal focusing mirror is configured to be 20°. At this time, the spot of the transmitted laser 410 reaching the ellipsoidal focusing mirror will diverge to a diameter of about 10 mm, and the corresponding laser power density is about 10 15 W / cm 2 , and at this power density, the reflectivity of the ellipsoidal focusing mirror to the transmitted laser 410 is approximately 50%. At this time, 32 J of laser will be secondarily focused;

[0063] Furthermore, after calculation according to the imaging formula of the ellipsoidal focusing mirror, the laser focal spot reaching the secondary target 500 will be reduced by 0.38 times to 11.4 μm, and the laser power density reaching the secondary target 500 after secondary focusing will reach 2×10 19 W / cm 2 ;

[0064] Among them, the secondary target 500 at the second focus of the ellipsoidal focusing mirror is configured as a gold wire target with a diameter of 10 um, and the angle of the transmitted laser 410 incident on the secondary target 500 is configured to be 50°. At this time, the number of photons with an energy greater than 10 keV in the generated energy can reach 1×10 12 pieces; Through the above steps, two X-ray sources are generated by using a single laser beam acting on the primary target 400 and the secondary target 500;

[0065] Then, place the object 200 to be measured at the intersection of the axes of the primary target 400 and the secondary target 500; at this time, when observing from the direction of the object 200 to be measured, it is a point-like X-ray source photography with two 10 μm, and thus the spatial resolution of 10 μm in two directions can be obtained; in this setting, the distance from the primary target 400 to the object 200 to be measured is configured to be 18.5 mm, and the distance from the secondary target 500 to the object 200 to be measured is configured to be 14.5 mm; at this time, the total optical path difference including the optical path difference brought by the focusing optical device 100 is 29.6 mm, corresponding to a time delay of 98.6 ps.

[0066] Finally, place a multi-layer imaging plate in the direction of the two-source photography to achieve two-axis and two-time photography. In this embodiment, a single picosecond laser is incident on a double gold wire target system including an ellipsoidal focusing mirror, realizing two-axis and two-time X-ray backlight photography. The photography resolution of each axis reaches 10 μm, and the time delay of the two times is about 100 ps. This can be used for the research on the evolution process of high-speed objects with a speed greater than 100 km / s. For example: the dynamic research of the imploding pellets in inertial confinement fusion.

[0067] In summary, the two-time X-ray backlight photography method based on a single laser beam provided by the present disclosure realizes the technical effect of two-time X-ray backlight photography based on a single laser beam coaxial or biaxial by changing the position between the object 200 to be measured and the two focal points of the focusing optical device 100, and can obtain information from two perspectives of the shell to be measured. The photographic visibility can be flexibly adjusted according to requirements.

[0068] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A dual - moment X - ray backlighting imaging system based on a single - beam laser, characterized in that, it includes a focusing optical device, an object to be measured, and an image acquisition device that are sequentially arranged at intervals. On one side of the focusing optical device close to the object to be measured, there are two foci, and a primary target and a secondary target are respectively arranged on the two foci. The cross - sectional size of the primary target is configured to be smaller than the focal spot of the incident laser.

2. The dual - moment X - ray backlighting imaging system based on a single - beam laser according to claim 1, characterized in that, the primary target is a micro - wire target or a micro - sphere target.

3. The dual - moment X - ray backlighting imaging system based on a single - beam laser according to claim 1, characterized in that, the secondary target is one of a micro - wire target, a micro - sphere target, and a planar target.

4. The dual - moment X - ray backlighting imaging system based on a single - beam laser according to any one of claims 1 to 3, characterized in that, the focusing optical device uses an ellipsoidal focusing mirror.

5. A dual - moment X - ray backlighting imaging method based on a single - beam laser, characterized in that, it includes the following steps: Based on the first - time focusing of a single - beam laser on the primary target, a primary X - ray source is generated; The transmitted laser that is not acting on the primary target is transmitted from the outside of the primary target to the focusing optical device, and the focusing optical device is used for secondary focusing to make the focal spot of the transmitted laser smaller; Based on the transmitted laser after secondary focusing acting on the secondary target, a secondary X - ray source is generated; Using the image acquisition device to achieve backlighting imaging.

6. The dual - moment X - ray backlighting imaging method based on a single - beam laser according to claim 5, characterized in that, this method further includes: By changing the position between the object to be measured and the two foci of the focusing optical device, and then adjusting the imaging angle, co - axial imaging or bi - axial imaging is achieved; By adjusting the parameters of the focusing optical device or the distance between the object to be measured and the two foci of the focusing optical device, and then adjusting the imaging moment, co - axial dual - moment imaging or bi - axial dual - moment imaging is achieved.

7. The dual - moment X - ray backlighting imaging method based on a single - beam laser according to claim 6, characterized in that, The specific process of achieving co - axial imaging by changing the position between the object to be measured and the two foci of the focusing optical device and then adjusting the imaging angle includes: The object to be measured is configured to be placed on the extension line of the connection line of the two foci of the focusing optical device, so that the object to be measured and the two foci are collinearly distributed to achieve co - axial imaging.

8. The dual - moment X - ray backlighting imaging method based on a single - beam laser according to claim 6, characterized in that, The specific process of achieving bi - axial imaging by changing the position between the object to be measured and the two foci of the focusing optical device and then adjusting the imaging angle includes: The object to be measured is configured to be placed on the side of the connection line of the two foci of the focusing optical device and far from the focusing optical device, so that the object to be measured and the two foci are triangularly distributed to achieve bi - axial imaging.

9. The dual - moment X - ray backlighting imaging method based on a single - beam laser according to any one of claims 6 to 8, characterized in that, this method further includes: Configure the secondary target cross-sectional size to be smaller than the spot diameter after secondary focusing to improve the spatial resolution of the X-ray source; or configure the secondary target cross-sectional size to be larger than the spot diameter after secondary focusing to improve the laser energy utilization rate.

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