High-energy high-dose microfocus X-ray computed tomography driven by high-average-current photo-injector

Abstract

High-energy, high-dose, microfocus X-ray computed tomography (HHM CT) is one of the most effective methods for high-resolution X-ray radiography inspection of high-density samples with fine structures. Minimizing the effective focal spot size of the X-ray source can significantly improve the spatial resolution and the quality of the sample images, which is critical and important for the performance of HHM CT. The objective of this study is to present a 9 MeV HHM CT prototype based on a high-average-current photo-injector in which X-rays with about 70μm focal spot size are produced via using tightly focused electron beams with 65/66μm beam size to hit an optimized tungsten target. In digital radiography (DR) experiment using this HHM CT, clear imaging of a standard 0.1 mm lead DR resolution phantom reveals a resolution of 6 lp/mm (line pairs per mm), while a 5 lp/mm resolution is obtained in CT mode using another resolution phantom made of 10 mm ferrum. Moreover, comparing with the common CT systems, a better turbine blade prototype image was obtained with this HHM CT system, which also indicates the promising application potentials of HHM CT in non-destructive inspection or testing for high-density fine-structure samples.

Keywords

Digital radiography (DR)Microfocus X-ray computed tomography (CT)non-destructive inspection X-ray source X-ray focal spot

1 Introduction

For half a century, X-ray computed tomography (CT) has been attracting growing interest in the manufacturing industry, clinical application and other non-destructive testing (NDTs), since it allows both the external geometrical and internal features of an object to be measured [1 –4]. In many scenarios, such as the precise and fast detection of a large workpiece with high density and fine structures, high spatial resolution, high penetrating power, and high-dose of an X-ray CT are required simultaneously. Unfortunately, such an ideal X-ray CT with all these merits has not been created to date.

Several methods have been explored to improve the overall performance of X-ray CT. Among them, low-energy microfocus X-ray CT [5, 6] can achieve excellent resolution due to small focal spot size, even less than 1μm [7, 8], but the penetrability is limited by low beam energy (equipped with X-ray tubes with a few tens of to hundreds of kV). Therefore, it is mainly used to detect low density or small size objects such as biological bodies [9] or circuit chips. The high-energy X-ray CT, with a MeV X-ray source generated by the linear accelerators (LINAC), has much more industrial applications to detect high-density objects [10]. The biggest challenge of high-energy industrial CT is to get high-resolution for the large and high-density objects. At present, the typical focal spot of high energy X-ray CT is 1.5–2.0 mm [11], which limits the spatial resolution to 1.5–2 lp/mm and hinders its applications. The spatial resolution is determined by the X-ray source focal spot size, the detector pixel size, and the magnification factor of the imaging system [12]. However, high-energy X-ray CT radiation detectors are limited by detect quantum efficiency, machining performances, etc., which means its pixel size is difficult to improve significantly [13, 14]. Therefore, high-energy, high-dose, microfocus X-ray computed tomography (HHM CT) becomes one of the most effective methods for high-resolution X-ray radiography inspection of high-density samples with fine structures.

In addition, new attempts to minimize the focal spot size of X-ray source have been carried out recently, including minimizing the bremsstrahlung target to about 100μm [15, 16], using bremsstrahlung or all-optical inverse Compton scattering driven by laser-accelerated electron beams [17 –20] with ultra-small focal spot size, and so on. These efforts improve the resolution of high-energy CT significantly, but none of them could provide a high dose rate enough. To achieve a high dose rate, bremsstrahlung with high average current electron beams is always preferred. Moreover, the electron source should have low emittance, low energy spread, and low peak current to be strongly focused to micron-scale to generate microfocus X-rays. Thus, Rhodotron [21 –23] and photo-injector with high-average-current [24] are suitable for the electron source of HHM CT. In particular, the photo-injector used to drive a high average power free electron laser can generate the highest quality electron beam [25 –28].

In this paper, we explore the feasibility of a 9 MeV HHM CT based on a novel high-average-current photo-cathode injector, which holds great promise to generate dream X-rays with high dose and micron-scale focal spot size. In Sec. II, we report the detailed design and implementation of a 9 MeV HHM CT prototype based on the beamline of Chengdu CAEP Terahertz Free Electron Laser (CTFEL) facility [29]. In Sec. III, we present the proof-of-principle imaging experiments carried out with this HHM CT. Discussion of these results and future plan of HHM CT system are given in Sec. IV.

2 Design and implement of high-energy high-dose microfocus X-ray CT

In a CT system, the cutoff frequency f_co [lp/mm] = (BW [mm]) ^-1, where BW is the equivalent beam width, which represents the spatial resolution and can be written as [30, 31]:

$BW = \frac{\sqrt{d^{2} + {[a (M - 1)]}^{2}}}{M}$ (1)

where d is the pixel size of the detector, a is the focal size of X-ray source, and M is the geometric magnification. M is defined as M = D_SD/D_SO, where D_SD and D_SO represent the distance between the source and the detector and the distance between the source and the object, respectively. The optimized geometric magnification corresponding to the best resolution is: $M |_{B W_{min}} = 1 + {(d / a)}^{2} . ∥$ (2)

By taking Equation (2) into Equation (1), the best resolution BW with optimized magnification factor can be derived as: $BW = \frac{\sqrt{d^{2} + {[a (M - 1)]}^{2}}}{M} = \frac{\sqrt{d^{2} + [a {(1 + d / a)}^{2} - 1)]^{2}}}{1 + {(d / a)}^{2}} = \frac{d \sqrt{1 + (d / a})^{2}}{1 + {(d / a)}^{2}}$ (3)

When d ⪡ a, M|_{BW
_min} ∼ 1, BW ∼ d, meaning that the resolution is determined by the detector’s pixel size. For most low-energy micro-focus X-ray CT, d ⪢ a, M|_{BW
_min} ∼ ∞ , BW ∼ a, the resolution is mainly determined by the X-ray source focal size. In normal situations of common high energy X-ray CT machines, it is difficult to satisfy neither d ⪡ a nor d ⪢ a, then the spatial resolution of CT system is jointly determined by both two factors of the detector’s pixel size and the X-ray source focal size. A straightforward conclusion can be reached from Equation (3) that the smaller the X-ray focal spot size or the detector’s pixel size is, the better the spatial resolution can be obtained. For the high-energy X-ray CT system, the detector’s pixel size is difficult to reduce significantly. Microfocus with much smaller X-ray source focal size will be a good solution to reach a better spatial resolution.

As mentioned above, the development of high-energy, high-dose, microfocus X-ray sources has imposed stringent requirements on electron sources, such as high-flux, low emittance, high energy, and low energy spread. The well-developed high-average-current photo-injectors can fulfill these requirements and are suitable to drive HHM CT. Therefore, we design and implement an HHM CT on the base of the CTFEL photo-injector. The whole layout of HHM CT is present in Fig. 1, which is mainly composed of four sections, including photo-injector section, beam diagnostic section, beam matching section as well as X-ray imaging section.

Fig. 1

Schematic diagram of the HHM CT driven by CTFEL photo-injector. Note: not to scale.

The high-average-current photo-injector composes a high-voltage photocathode DC gun [32], solenoids, a normal-conducting RF buncher and a 2×4 cell superconducting linac [33]. Electron beams are generated by illuminating a drive laser pulse on the GaAs photocathode and accelerator to 320 keV in the DC gun. Solenoid at the exit of the DC gun is for emittance compensation as well as envelope control. The buncher is to compress the pulse duration of electron bunches to avoid large energy spread in the main accelerator. The super-conducting linac is to boost beam energy to 9 MeV. Parameters of the electron beams produced by the photo-injector are listed in Table 1.

Table 1

Parameters of electron beams in CTFEL

Parameters	Values
Beam energy	4–9 MeV
Beam average current	1.5 mA
Normalized emittance	< 10 mm. mrad
Bunch length	10 ps
Energy spread	0.1%

The diagnostic section uses the combination of a YAG scintillator and a CCD camera to detect the transverse profile while uses a dipole magnet to measure the energy and energy spread of the electron beams. The beam matching section is made up of three quadrupole magnets (i.e., triplet) to achieve a strong focusing of the electron beam. A removable YAG screen measures the final focus of the electron beam (on the target position) with 10μm resolution. An optimized tungsten target is to produce high-energy, high-flux X-rays via bremsstrahlung. The object to be tested is mounted on a rotating platform, 476 mm downstream of the tungsten target. A flat panel detector with 2048×2048 pixels, 0.2 mm pixel size, and DRZ + scintillators is employed to collect the transmitted X-rays. The X-ray detector is about 2000 mm downstream of the target, forming a magnification factor of 4.2. Design considerations of microfocus electron beams, efficient X-ray conversion targets, and other limiting factors are present in the following subsections.

2.1 Microfocus electron beams

Behavior of an electron beam focused by a strong focusing element can be analogous to the focusing of light by a strong convex lens, where larger initial beam size and shorter focal length are helpful for a smaller final beam size achievable. However, the existence of space charge forces makes focusing of electron beams more complicated. A good estimation of beams’ transverse dimension evolution after the focusing triplet can be realized by the well-known envelope equation [34]: $R^{″} - \frac{2 I_{b}}{I_{A} β^{3} γ^{3}} \frac{1}{R} - \frac{ɛ_{n}^{2}}{β^{2} γ^{2}} \frac{1}{R^{3}} = 0$ (4)

where, R is the envelope, I_b is the beam current, I_A ≈ 17KA is the Alfven current, γ is the Lorentz factor, β is the speed in the unit of light speed and ɛ _ n is the normalized transverse emittance. Physically, the second and third term in Equation (4) represent the envelope expansion induced by space charge effect and transverse emittance, respectively.

Knowing the initial value of R and R′, the above differential equation can be solved numerically. By employing thin-lens approximation, R₀ is the beam size at entrance of the triplet and does not change within the triplet, while R₀^′ ≈ R₀/f, with f being the focal length. Then we can calculate the beam envelope evolution between the triplet and the tungsten target using electron beam parameters listed in Table 1. Simulation results are shown in Fig. 2(a), where larger initial beam size and short focal length is beneficial for obtaining < 100μm electron spot size on target.

Fig. 2

(a) Simulated beam envelope after focusing triplet with varying initial beam size and focal length. (b) Measured transverse profile of focused electron beam on target place with < 70μm lateral size (x: horizontal direction, y: vertical direction).

In practical experiments, a strong focusing triplet is located about 25 cm ahead of the tungsten target. By finely tuning the initial beam size R₀ and the focusing strength of three quadrupoles, a minimum beam size of 70μm (full-width-half-maximum, FWHM) can be obtained, as shown in Fig. 2(b). Since the X-ray source dimension is partly determined by the electron beam size on the target, obtaining of < 100μm microfocus electron beam paved the way for generating microfocus X-rays.

2.2 Target thickness analysis

With a specified electron beam energy, the conversion efficiency of the X-ray is determined by the thickness of the tungsten. With too thick target, the X-ray conversion efficiency will be reduced due to self-absorption of bremsstrahlung photons by the target, while the conversion efficiency is still low for too thin target, with less energy deposited by electron beam power inside the target. Therefore, the thickness of the tungsten target should be carefully optimized.

Following deductions in Ref [35], where considered energy loss of electrons and self-absorption of produced X-ray, a best thickness of the target d₀ can be estimated by: $d_{0} = \frac{l_{R}}{1 - μ \cdot l_{R}} \cdot ln (\frac{1 + 800 / (Z \cdot E_{0})}{μ \cdot l_{R} + 800 / (Z \cdot E_{0})})$ (5) where, μ is the single-energy X-ray absorption coefficient of equivalent energy (unit: 1/cm), l _ R is the electron radiation length, Z is the atomic number and E₀ is the beam energy. By calculation, the best thickness of the tungsten target for maximum conversion efficiency is about 2 mm with 9 MeV electron beam energy. Additionally, target thickness is also related to the energy spectrum of bremsstrahlung photons. Considering these two aspects, Monte Carlo simulations are carried out to simulate the X-ray energy spectrum and photon yield of 9 MeV incident electrons at different thicknesses, as shown in Fig. 3. Simulation results showed that the conversion efficiency is highest at 2 mm thickness, in agreement with our estimations, and it will drop a little with thicker target. On the other side, the mean energy of X-ray will shift to high energy end with thicker target, as seen from Fig. 3(b), where the calculated mean energy is 1.21 MeV, 1.27 MeV and 1.32 MeV for 1 mm, 2 mm, 3 mm target thickness, respectively. Moreover, another advantage of using thicker target is that the less transmitted electrons will easier to handle, thus minimizing the impact on subsequent X-ray imaging system. Therefore, we choose a 3 mm thick tungsten target in our HHM CT.

Fig. 3

Simulated X-ray photon yield (a) and energy spectrum (b) of 9 MeV electrons with tungsten target of different thicknesses.

Also, the dose and dose rate of HHM CT should be taken into consideration. The maximum exposure at one meter position after the target can be estimated using following empirical formula [36, 37]: $X (rem) = 1.1 \times 10^{- 3} \cdot I (kA) \cdot τ (ns) \cdot E^{2.8} (MeV)$ (6)

The absorbed dose D in the air is: $D (Gy) = X \cdot 8.733 \times 10^{- 3} (J / kg) .$ (7)

The corresponding dose rate within one minute can be written as: $D (mGy / \min) = D (J / kg) \cdot f (Hz) \cdot 6 \times 10^{4}$ (8)

The calculation results of dose rate of 9 MeV electron beam with tungsten target are listed in

2.3 Focal spot size widening by thick target

Once the microfocus electron beam has been obtained, focal spot size widening caused by scattering of electrons by the thick target needs to consider. The scattering and the focal spot size widening of the 9 MeV electron beam are simulated by CASINO [38], as shown in Fig. 4. Simulated results showed that, compared with the initial electron distribution, widening of focal spot size of 9 MeV electrons by 3 mm thick tungsten target is not obvious. Only a small portion of electrons are scattered to outer region of initial lateral size of electrons. The statistical data analysis showed that the focal spot size is increased from 100μm to about 110μm, indicating that a near 100μm X-ray source can be obtained in our HHM CT system.

Fig. 4

Focal spot widening of electron beams by target scattering.

3 Experiments and results

To investigate the effectiveness of the high-energy high-dose microfocus X-ray source described in above section, DR images of a standard X-ray resolution test phantom are acquired to evaluate the resolving power. The spatial resolution is calibrated by identifying the smallest distinguishable line pair in the original images. Next, the imaging mode is shifted to CT mode of the resolution phantom, where to measure the spatial resolution of our HHM CT system. Last, a representative test object in an industrial CT-turbine blade prototype is imaged in CT mode to evaluate the practical performance of our HHM CT. By comparing imaging results with common high energy industrial CT and low energy microfocus CT, the superiority of such an HHM CT is perfectly showcased.

3.1 DR experiment for spatial resolution calibration

Following the standard procedure in the X-ray imaging community, DR experiment of a resolution phantom is carried out to evaluate the spatial resolution of the HHM CT. Here, a test phantom made of 0.1 mm lead and containing eight groups of line-pairs is chosen. It can generate following spatial frequencies (in lp/mm): 3.4, 3.7, 4.0, 4.3, 4.6, 5.0, 5.5, 6.0, where the spatial frequency is determined by the line-pair slit width ω as f = 1/2ω. Once the DR image has been acquired, the modulation transfer function (MTF) can be measured by calculating the line profile in terms of gray-scale level along the line perpendicular to the line-pair region. The spatial resolution can be defined as the smallest achieved line-pair, which corresponds to MTF value of 10%.

In this DR experiment, using microfocus X-rays as listed in Table 2, a clear image of the resolution phantom is obtained with a total exposure time of 64 seconds (i.e. 64 frames average, one second per frame), as shown in Fig. 5(a). The measured line profile in Fig. 5(b) showed that the MTF value at 5 lp/mm is 24.6%, which is much better than the criteria of 10%. Though the MTF value drops as spatial frequency increases, this value at the highest 6 lp/mm is still 17.1%, thus indicating a lower limit of 6 lp/mm for spatial resolution in DR mode.

Table 2
The calculation results of the dose rate with 3 mm tungsten target and 9 MeV electrons

Parameters Values

Atomic number Z 74

Mass number A 184

Density ρ 19.3 g/cm³

Electron radiation length l_R 0.3504 cm

Macro pulse current I 1.5 mA

Macro pulse frequency f 1 Hz

Macro pulse width τ 5 ms

Dose rate D 219.3 cGy/min

Parameters	Values
Atomic number Z	74
Mass number A	184
Density ρ	19.3 g/cm³
Electron radiation length l_R	0.3504 cm
Macro pulse current I	1.5 mA
Macro pulse frequency f	1 Hz
Macro pulse width τ	5 ms
Dose rate D	219.3 cGy/min

Fig. 5

DR image of the resolution phantom: (a) original DR image; (b) line profile of the left four line-pairs in (a), indicated by the red line.

3.2 CT experiment of resolution phantom

Apart from the DR experiment, a CT experiment of another resolution phantom is also carried out with the HHM CT. This resolution phantom consists of four groups of line-pairs, including 2 lp/mm, 3 lp/mm, 4 lp/mm and 5 lp/mm. The material of this resolution phantom is ferrum, while the thickness is 10 mm. The CT resolution phantom is scanned in 1000 views over 360 degree, within a whole scan time of 1000 seconds. The CT experiment results are shown in Fig. 6. As can be seen from Fig.6(a), the CT slice imaging result shows that the line-pair of 5 lp/mm is clearly distinguished. The MTF curve of the resolution phantom is shown in Fig. 6(c), in which the MTF of 5 lp/mm line-pair is as high as 30%. These results indicate that a conservative estimation of 5 lp/mm spatial resolution can be achieved in the HHM CT, in well agreement with the DR imaging results. To our best knowledge, this is the first time that spatial resolution of 100μm has been demonstrated when using a MeV high-energy, high-dose, microfocuse X-ray CT.

Fig. 6

CT image of the resolution phantom. (a) the CT slice imaging result; (b) the CT 3D result; (c) the gray distribution curve of the CT image and the measured MTF.

3.3 Turbine blade prototype experiment

Finally, the practical performance of the HHM CT is checked with the CT experiment of a turbine blade prototype [39]. The main system parameters of this HHM CT, 450 kV CT and conventional high energy CT are listed in Table 3. The turbine blade is scanned in 1000 views over 360 degrees, with a scanning period of only 16.67 minutes. Reconstruction of the turbine blade is realized using the Feldkamp-Davis-Kress (FDK) [40] algorithm. Here, the resolving power of the HHM CT on this turbine blade is calibrated by measuring the edge response function (ERF) and the corresponding point spread function (PSF) of the inner arc region of the blade, which is a key part that determines the image quality of the turbine blade prototype, as indicated by the red short line in Fig.7(a). With this HHM CT, boundaries of the blade are clearly identified in CT image, while the calibrated PSF is 261μm. In comparison, though the CT image of the blade using a 450 kV microfocus X-ray CT is measured to hold a spatial resolution of 364μm, the blade cannot be fully penetrated, leaving certain parts indistinguishable, see Fig. 7(c). Moreover, CT image of the turbine blade is also obtained with a conventional high-energy industrial X-ray CT, as shown in Fig. 7(e). Obviously, the boundary of the blade is severely blurred due to the large focal spot size of the X-ray, and the calculated PSF indicates a much poorer resolution of 857μm. In this sense, considerable advantages, including high spatial resolution as well as high penetration power provided by this HHM CT can be taken of, to significantly promote the detection capabilities of such sophisticated workpieces.

Table 3
The main parameters of HHM CT, 450 kV CT and conventional high energy CT

Parameters HHM CT 450 kV CT conventional high energy CT

Beam energy 9 MeV 450 kV 9 MeV

Focal spot size 0.1 mm 0.4 mm 1.5 mm

Pixel size 0.2 mm 0.2 mm 0.2 mm

CT resolution 5 lp/mm 3.5 lp/mm 2 lp/mm

Scan directions 1000 1000 1000

Scan period 16.67 min 16.67 min 16.67 min

Geometric magnification 4.2 1.6 1.17

PSF of the turbine blade prototype 261μm 364μm 857μm

Parameters	HHM CT	450 kV CT	conventional high energy CT
Beam energy	9 MeV	450 kV	9 MeV
Focal spot size	0.1 mm	0.4 mm	1.5 mm
Pixel size	0.2 mm	0.2 mm	0.2 mm
CT resolution	5 lp/mm	3.5 lp/mm	2 lp/mm
Scan directions	1000	1000	1000
Scan period	16.67 min	16.67 min	16.67 min
Geometric magnification	4.2	1.6	1.17
PSF of the turbine blade prototype	261μm	364μm	857μm

Fig. 7

Turbine blade CT images: (a) CT image of the HHM CT, (b) the edge response function (ERF) (blue line) and the PSF (orange line) of the HHM CT image in the red line, (c) image of the 450 kV CT, (d) the ERF (blue line) and the PSF (orange line) of the 450 kV CT image in the red line, (e) image of the common high energy CT, (f) the ERF (blue line) and the PSF (orange line) of the common high energy CT image in the red line.

4 Discussion

This study provides a comprehensive design, implement and experimental verification of a HHM CT prototype on the base of CTFEL high-average-current photo-injector. Realization of microfocus X-ray source is achieved by a strongly focused < 70μm electron beam spot on the tungsten target. The target thickness is carefully optimized, with an overall consideration of photon yielding, energy spectrum and spot size widening effect. Experimental investigations of resolution phantoms are performed with the HHM CT, in both DR and CT imaging mode. Imaging results of resolution phantoms show that a DR spatial resolution of up to 6 lp/mm and a CT spatial resolution better than 5 lp/mm can be readily obtained. Moreover, the practical performance of the HHM CT is checked with the imaging of a turbine blade prototype, where the blade is fully penetrated and clearly imaged with a quite good resolution of 261μm. By comparing imaging results with conventional low energy microfocus X-ray CT and high energy industrial X-ray CT, the superiority of such an HHM CT with simultaneously obtainable high resolution power and high penetration power is well established. Success of this HHM CT prototype should pave the way to standard HHM CT machine in the future.

5 Conclusion

In summary, this study paves the way to the development of HHM CT driven by a high-average-current photo-injector. This technology may become an important means of high-energy metrology CT. More importantly, successful imaging of the turbine blade using this HHM CT should have a major impact on non-destructive testing and non-destructive evaluation of high-density fine-structured components, such as those used in aviation, aerospace, ships, automobiles, etc.

Footnotes

Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC Grants No.11975218, 11905210, 11805192, 12005211 and 11605190), and by the Innovation Foundation of CAEP with grant (No.CX2019036, CX2019037).

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

References

Hounsfield

G.N.

Computerized transverse axial scanning (tomography): Part 1. Description of system, The British Journal of Radiology 46 (1973), 1016–1022.

Ambrose

Computerized transverse axial scanning (tomography): Part 2. Clinical application, The British Journal of Radiology 46 (1973), 1023–1047.

De Chiffre

, Carmignato

, Kruth

J.P.

, Khan

I.U.

, et al., Industrial applications of computed tomography, CIRP Annals 63 (2014), 655–677.

Khan

S.U.

, Khan

I.U.

, Ullah

, et al., A review of airport dual energy X-ray baggage inspection techniques: image enhancement and noise reduction, Journal of X-ray Science and Technology 28 (2020), 481–505.

Heo

S.H.

, Ihsan

, Cho

S.O.

Transmission-type microfocus x-ray tube using carbon nanotube field emitters, Applied Physics Letters 90 (2007), 183109.

Kruth

, Bartscher

, Carmignato

, et al., Computed tomography for dimensional metrology, CIRP Annals 60 (2011), 821–842.

de Paiva

R.F.

, Bisiaux

, Lynch

, et al., High resolution x-ray tomography in an electron microprobe, Review of Scientific Instruments 67 (1996), 2251–2256.

Roth

, He

, Paul

, “Inspection of miniaturised interconnections in IC packages with nanofocus x-ray tubes and nanoCT,” in 2008 10th Electronics Packaging Technology Conference (IEEE, 2008) pp. 644–649.

Paulus

M.J.

, Gleason

S.S.

, Kennel

S.J.

, et al., High resolution x-ray computed tomography: an emerging tool for small animal cancer research, Neoplasia 2 (2000), 62–70.

10.

Izumi

, Kamata

, Satoh

, Miyai

, High energy x-ray computed tomography for industrial applications, IEEE Transactions on Nuclear Science 40 (1993), 158–161.

11.

Zhang

, Guo

, Zhang

, et al., Industrial CT technology and principle [M]. Beijing: http://www.sciencep.com, 2009: P40.

12.

Abe

, Fujimoto

, Sato

, Takatsuji

, “Evaluation of resolution performance of high energy x-ray CT,” in International Conference on Optical and Photonic Engineering (icOPEN 2015), Vol. 9524, edited by A. K. Asundi and Y. Fu, International Society for Optics and Photonics (SPIE, 2015) pp. 459–462.

13.

Hoshino

, Uesugi

, Yagi

, Development of an x-ray imaging detector for high-energy x-ray microtomography, Journal of Synchrotron Radiation 27 (2020), 934–940.

14.

Romano

, Altana

, Cosentino

, et al., A new X-ray pinhole camera for energy dispersive X-ray fluorescence imaging with high-energy and high-spatial resolution, Spectrochimica Acta Part B: Atomic Spectroscopy 86 (2013), 60–65.

15.

Sato

, Makoto

, Takatsuji

, Development of high-energy and high-resolution x-ray CT, Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology 54 (2018), 276–283.

16.

Sato

, Abe

, Takatsuji

, “Characterization of resolution performance of novel high energy X-CT: eXTRA CT,” in 9th Conference on Industrial Computed Tomography (2019) pp. 1–3.

17.

Y.C.

, Zhu

, Li

, et al., Towards high-energy, high-resolution computed tomography via a laser driven micro-spot gamma-ray source, Scientific Reports 8 (2018), 15888.

18.

Yang

, Wu

Y.C.

, Li

, et al., Design and characterization of high energy micro-CT with a laser-based x-ray source, Results in Physics 14 (2019), 102382.

19.

, Hua

, Liu

, et al., Region-of-interest micro-focus computed tomography based on an all-optical inverse Compton scattering source, Matter and Radiation at Extremes 5 (2020), 064401.

20.

Underwood

C.I.D.

, Baird

C.D.

, Murphy

C.D.

, et al., Development of control mechanisms for a laser wakefield accelerator-driven bremsstrahlung x-ray source for advanced radiographic imaging, Plasma Physics and Controlled Fusion 62 (2020), 124002.

21.

Defrise

, Abs

, Genin

, Jongen

, Technical status of the first industrial unit ofthe 10 Mev, 100 Kw rhodotron, Radiation Physics & Chemistry 46 (1995), 473–476.

22.

, Yang

, Liao

, et al., “A proposal of using improved Rhodotron as a high dose rate micro-focused X-ray source,” in 13th Symposium on Accelerator Physics (SAP’17), Jishou, China, 28–30 August 2017 (2018) pp. 143–145.

23.

Yang

, He

, Li

, et al., “Electromagnetic, Thermal, Structural Analysis for the RF-cavity ofa Rhodotron Accelerator,” in 13th Symposium on Accelerator Physics (SAP’17), Jishou, China, 28–30 August 2017 (2018) pp. 165–168.

24.

Bartnik

, Gulliford

, Bazarov

, et al., Operational experience with nanocoulomb bunch charges in the cornell photoinjector, Physical Review Special Topics-Accelerators and Beams 18 (2015), 083401.

25.

Williams

, FAR-IR/THz radiation from the Jefferson laboratory, energy recovered linac, freeelectron laser, Review of Scientific Instruments 73 (2002), 1461–1463.

26.

Geloni

, Saldin

, Samoylova

, et al., Coherence properties of the European XFEL, New Journal of Physics 12 (2010), 035021.

27.

Gul

, Farrukh

, Basim Kakakhel

, et al., Measurement of 6MV small field beam profiles –comparison of micro ionization chamber and linear diode array with Monte Carlo code, 655–, Journal of X-ray Science and Technology 27 (2019), 664.

28.

Decking

, Abeghyan

, Abramian

, et al., A mhz-repetitionratehard X-ray free-electron laser driven by a superconducting linear accelerator, Nature Photonics 14 (2020), 391–397.

29.

, Li

, Yang

, et al., First lasingof the CAEP THz FEL facility driven by a superconducting accelerator, Conference Series 1067 (2018), 032010.

30.

Yester

M.V.

, Barnes

G.T.

, “Geometrical Limitations Of Computed Tomography (CT) ScannerResolution,” in Application of Optical Instrumentation in Medicine VI, Vol. 0127, edited byJ.E. Gray andW.R. Hendee, International Society for Optics and Photonics (SPIE, 1977) pp.296–303.

31.

Kalender

W.A.

, Computed tomography: fundamentals, system technology, image quality, applications(John Wiley & Sons, 2011).

32.

Wang

, Li

, et al., “A gaas photoemission dc gun for caephigh-average-power thz fel,” in Proceeding of FEL’ in Proceeding of FEL’14 (2014) pp. 318–321.

33.

Luo

, Lao

, Zhou

, et al., Design and fabrication of the 2x4-cell superconducting linac modulefor the free-electron laser, Accelerators, Spectrometers, Detectors and Associated Equipment 871 (2017), 30–34.

34.

Lee

E.P.

, Cooper

R.K.

, General envelope equation for cylindrically symmetric charged particle beams, Particle Accelerators 7 (1976), 83–95.

35.

, Bremsstrahlung Convertor for 5MeV/150kW Irradiation Accelerator, Master’s thesis, China Academy of Machinery Science and Technology (2011).

36.

Martin

, “Determination of bremsstrahlung production efficiencies from data obtained on phermex at 27 mev.” Tech. Rep. (Sandia Labs., Albuquerque, N. Mex., 1969).

37.

Tang

, Low energy accelerators for cargo inspection, Reviews of Accelerator Science and Technology 08 (2015), 143–163.

38.

Drouin

, Couture

A.R.

, Joly

, et al., Casino v2. 42—a fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users, The Journal of Scanning Microscopies 29 (2007), 92–101.

39.

Lakshmi

, Mondal

, Jadhav

, et al., Overview of ndt methodsapplied on an aero engine turbine rotor blade, Insight-Non-Destructive Testing and Condition Monitoring 55 (2013), 482–486.

40.

Feldkamp

L.A.

, Davis

L.C.

, Kress

J.W.

, Practical cone-beam algorithm, Journal of the Optical Society of America A 1 (1984), 612–619.