In x-ray imaging, high resolution is essential, particularly in sectors such as medical and industries where the need for nondestructive defect detection is required. Previous research has shown that altering beam design and the number of gates offset holes has an impact on focal spot size (FSS). However, the specific effects of beam size and offset size were not thoroughly assessed. In the present study, the influence of beam size and gate offset size was evaluated by utilizing a cold cathode electron beam. Various beam sizes were employed to achieve a small FSS, and subsequently, the smallest beam was utilized to examine the impact of gate offset size. In doing so, the smallest FSS of 0.25 mm vertical and 0.33 mm horizontal was attained without the utilization of any additional focusing lens. This illustrates that by adjusting the beam size and gate offset size, it is possible to attain a small FSS, facilitating the development of an economically viable x-ray imaging beam.

X-ray radiography serves as a commonly employed technique for nondestructive inspection of samples, enabling the detection of internal flaws. This technology is crucial in medical diagnostics, industrial manufacturing, and scientific research. High-resolution x-ray imaging is essential for early tumor diagnosis and quality control in mass manufacturing. Advanced 3D computed tomography systems in healthcare require higher resolution microfocus x rays to detect defected tissue more effectively.1–5 

Adjusting the x-ray image magnification enables the acquisition of small particle x-ray images to check minor faults in objects. However, for micro-objects, this method may not provide a better resolution x-ray image. This is due to the magnification process, which can add a negative blurring impact on the x-ray images. A microfocus x-ray tube with an extremely small focused x ray is required to overcome this constraint.

In the high-resolution x-ray imaging system, electron sources are the most important parameter. Existing commercial microfocus x-ray sources generate electrons with thermionic emission, which emits electrons from heating filaments (hot cathodes).6 On the other hand, field emission offers a different method for electron extraction. This entails a quantum phenomenon where, influenced by a strong external field, the fermi level electrons pass through the energy barrier and hit on the anode. There are various intrinsic limitations of thermionic emission, such as poor response time, high cost, and short lifespan, due to high operating temperatures. Due to its reliance on quantum tunneling under high electrostatic field circumstances, field emission has significant benefits over thermionic emission, allowing for quick switching of x-ray dose. As a result, it is feasible to accurately limit the dose by eliminating unnecessary x rays during diagnosis; moreover, field emission electron sources have a long lifespan since temperature is not employed in this process.7–10 

Discovered in 1991, carbon nanotubes (CNTs) represent a unique form of carbon allotrope. The first validation of electron field emission using these allotropes occurred in 1995, leading to further research. Field emission sources based on carbon nanotubes have proven advantageous over traditional thermionic emission x-ray tubes, thanks to their distinctive features. These include sharp tips, high aspect ratios, and favorable electrical properties. Consequently, CNTs exhibit higher field enhancement factors and lower emission threshold fields compared to conventional emitters like lithography-fabricated Spindt-type tips11–14 In this study, the impact of beam size and gate offset size is explored using a cold cathode electron beam (C-beam), an electron beam based on vertically aligned carbon nanotubes (VACNTs). Focal spot size (FSS) management is significantly facilitated by VACNTs, presenting a distinct advantage over commercially available paste carbon nanotubes.15–20 

The FSS, representing the specific region affected by electrons on the anode’s surface, emerges as a crucial element for producing high-resolution images. Typically, achieving superior spatial images with higher resolutions entails the attainment of a smaller and more stable FSS in x-ray imaging.21–23 

Focusing lenses are widely used for focusing electron beams toward the anode to get a small FSS.24 This study aims to achieve small FSS without using an extra focusing lens instead of just modifying beam geometry and gate offset. The effect of beam geometry and beam offset can be examined by reducing the beam size and modifying the gate offset size of the C-beam;25 as a consequence, this technique allows for more efficient and cost-effective beam design. In a prior work, the smallest FSS of 0.25 × 0.41 mm was obtained by adjusting the number of gate offset holes and beam area; however, the exact effect of the size of the beam and offset size was not measured.25 Meanwhile, in the present study, the precise impact of both beam size and gate offset size is evaluated. The smallest FSS of 0.25 × 0.33 mm was achieved in this study.

To generate varying sizes of VACNT beams, we employed magnetron sputtering technology to apply a nickel thin coating onto an n-type Si wafer. Following that, a traditional photolithography method was used to create a dot pattern beam on the silicon wafer using positive photoresist. During the photolithography process, multiple beam sizes are generated using a homemade pattern. Then, using plasma-enhanced chemical vapor deposition, VACNTs were grown as an electron emitter with a 2.5 Torr chamber pressure. The mesh electrode used in this system was biased at a voltage of −300 V and the cathode was biased at a voltage of −600 V. At 850 °C, C2H2 and NH3 gases (65:453 SCCM) were introduced into the chamber. The schematic and SEM images for all VACNT growth beams with their magnified single islands’ SEM images are shown in Figs. 1 and 2. Precise conditions for the growth of VACNTs have been provided elsewhere.26 

FIG. 1.

VACNT electron source with various designs: (a)–(d) scanning electron microscopic (SEM) images of 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beams and (e) and (f) SEM images with magnified vertically aligned CNT.

FIG. 1.

VACNT electron source with various designs: (a)–(d) scanning electron microscopic (SEM) images of 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beams and (e) and (f) SEM images with magnified vertically aligned CNT.

Close modal
FIG. 2.

(a)–(d) Schematic diagram for 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beams.

FIG. 2.

(a)–(d) Schematic diagram for 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beams.

Close modal

1. Beam size variation using different emitter arrays

We evaluated the effect of beam size on the FSS of an x-ray. The entire beam is made up of 1 × 10, 1 × 8, 1 × 6, and 1 × 4 emitter arrays, each of which is made up of 280 × 280 μm2 single islands with the pitch of 500 μm. The single island is divided into four different subislands with a size of 100 × 100 μm2. The vertical dimensions of the beams 1 × 10, 1 × 8, 1 × 6, and 1 × 4 are 4.78, 3.78, 2.78, and 1.78 mm, respectively, while the horizontal dimension for all beams is 0.28 mm. For the entire beam alignment, the 1 × 10 gate mesh with a 400 × 400 μm2 hole size has been used. To examine the effect of beam size, as shown in Figs. 3(a)3(d), all different sizes of beams were aligned in a 1 × 10 gate mesh and the FSS for all beams was measured.

FIG. 3.

(a)–(d) 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beam alignments with 1 × 10 gate mesh. The electron source size of 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beams are varying from 4.78, 3.78, 2.78, and 1.78 mm, respectively.

FIG. 3.

(a)–(d) 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beam alignments with 1 × 10 gate mesh. The electron source size of 1 × 10, 1 × 8, 1 × 6, and 1 × 4 beams are varying from 4.78, 3.78, 2.78, and 1.78 mm, respectively.

Close modal

2. Gate offset variation using different gate meshes

The objective of this section is to study the impact of beam offset size, which is the distance between the emitter edge and the gate guide inner wall, on the FSS of a C-beam. According to Sec. III A, the 1 × 4 emitter array has the lowest FSS; therefore, it is constant in this phase, although the gate offset varies between 2.05, 1.55, 1.05, and 0.55 mm on each side of the beam. Other parameters, such as gate hole size and beam size, remain constant. Figures 4(a)4(d) depict the beam alignment for the 1 × 4 emitter array with different gate offsets.

FIG. 4

(a)–(d) 1 × 4 beam alignment with different gate offset sizes. The mesh offset varies from 2.05, 1.55, 1.05, and 0.55 mm on both sides of 1 × 4 beam.

FIG. 4

(a)–(d) 1 × 4 beam alignment with different gate offset sizes. The mesh offset varies from 2.05, 1.55, 1.05, and 0.55 mm on both sides of 1 × 4 beam.

Close modal

The x-ray imaging setup comprises a C-beam utilizing VACNTs based electron sources, accompanied by a gate mesh and an anode positioned in the x-ray chamber for x-ray image capturing. Following VACNT alignment in the triode module, these C-beam modules were placed in a custom-built x-ray chamber for imaging. Figures 5(a) and 5(b) depict an x-ray imaging system and its schematic representation. The distance between the C-beam module and the anode remained constant at 15 mm. The anode was angled 12° to emit x rays through the window. The window in the above arrangement was made of 98.5% high purity beryllium and had a thickness of 127 μm. A turbo-molecular pump was used to keep the chamber vacuum at 3.0 × 10−7 Torr constant.

FIG. 5.

(a) Experimental setup for x-ray imaging in which source to object distance is 120 mm and object to source distance is 240 mm. (b) schematic diagram for x-ray imaging setup in which the positive anode voltage (Va) is applied to the anode using the Spellman ST120P12.

FIG. 5.

(a) Experimental setup for x-ray imaging in which source to object distance is 120 mm and object to source distance is 240 mm. (b) schematic diagram for x-ray imaging setup in which the positive anode voltage (Va) is applied to the anode using the Spellman ST120P12.

Close modal

To capture x-ray images, we utilized the flat panel detector (VIVIX-S 1012 N), featuring 124 × 124 μm2 of pixel pitch and 2048 × 2560 pixels resolution. A tungsten cross wire is used between the source and detector for FSS resolution analysis. The magnification of 3 was kept constant for each x-ray image. To compute all FSS, the European standard EN 12543-5 approach was implemented. ImageJ software was used to calculate the FSS from the captured x-ray images of all beams.

In this experiment, the cathode was negatively biased using the negative bias technique, and the gate mesh was kept grounded. The biasing scheme is shown in Figs. 5(a) and 5(b). A negative voltage of −1.2 to −1.7 kV is given to the cathode using Keithley model 248. The gate current was monitored using a digital multimeter (Agilent model 34401A), and the anode voltage was set to positive 65 kVp using Spellman ST 120 P12. The anode current was 0.2 mA after applying a negative voltage to the cathode.27 

The tungsten cross wire had been used as an object for all measurements, and the European standard EN 12543-5 technique was followed to measure all FSS. This technique begins with capturing an x-ray image of the tungsten cross wire, followed by generating line profile graphs along both the vertical and horizontal lines of the tungsten cross wire using ImageJ software. Subsequently, the FSS is determined by calculating the 90 and 50 percentage values of the gray scale using these graphs and then the calculated value is divided by the magnification factor to get the focal spot size of the beam.28 As depicted in Figs. 5(a) and 5(b), the distance between the object and the source was set at 120 mm, and the distance between the object and the source was established at 240 mm, resulting in a constant magnification of 3.

In this study, we consistently refer to the long axis of the electron source (C-beam) as the vertical direction and the short axis as the horizontal direction. For instance, in a 1 × 10 beam, the 4.78 mm length represents the vertical axis, while the 0.28 mm length represents the horizontal axis.

In our experimental setup, the electron source is aligned perpendicular to the anode. Consequently, when x rays are captured, the vertical axis of the electron source corresponds to the longitudinal side of the x-ray image of the tungsten cross wire, while the horizontal axis corresponds to the transverse direction of the x-ray image of the tungsten cross wire. To facilitate comprehension, Figs. 7 and 10 illustrate which direction of the tungsten cross wire represents the vertical axis and which represents the horizontal axis.

Before obtaining x-ray images under uniform exposure circumstances, all C-beam current-voltage (I-V) properties were thoroughly investigated. This included a systematic sweep of the cathode voltage from 0 to −1700 V in −50 V increments while maintaining a gate mesh grounded and constant anode voltage of 5 kV. Figure 6(a) depicts the I-V curve of anode current as it relates to beam size variations, whereas Fig. 6(b) depicts the I-V curve of anode current as it relates to gate offset size variations. The electron emission current not much changed with design parameters and within the variation range of each design.

FIG. 6.

(a) Anode current I-V curve for all different beam sizes. Negative cathode voltage (−kV) vs anode current [Ia]. (b) Anode current I-V curve for all gate offset sizes. Negative cathode voltage (−kV) vs anode current [Ia].

FIG. 6.

(a) Anode current I-V curve for all different beam sizes. Negative cathode voltage (−kV) vs anode current [Ia]. (b) Anode current I-V curve for all gate offset sizes. Negative cathode voltage (−kV) vs anode current [Ia].

Close modal

As shown in Figs. 3(a)3(d), 1 × 10 gate mesh was constant in this phase, and the beam size was altered between 4.78, 3.78, 2.78, and 1.78 mm. Figures 7(a)7(d) show x-ray images of a tungsten cross wire along with a thickness of 1 mm. We studied the x-ray images with ImageJ software to develop a graphic representation of FSS and then calculate FSS using the European standard EN 12543-5 technique. In this method, the FSS was measured by generating line profiles using ImageJ software along both the vertical and horizontal axes of the tungsten cross wire x-ray image. In Fig. 8(a), it can be seen that the width of the line profile for the tungsten cross wire decreases as the vertical beam size reduces from 4.78 to 1.78 mm. Conversely, in the horizontal direction, the line profile graph was not found to be spreading which is shown in Fig. 8(b).

FIG. 7

(a)–(d) Tungsten cross wire x-ray images for all different size beams with denoting the horizontal and vertical axes of tungsten cross wire.

FIG. 7

(a)–(d) Tungsten cross wire x-ray images for all different size beams with denoting the horizontal and vertical axes of tungsten cross wire.

Close modal
FIG. 8.

Line profile graph plotted using ImageJ software distance vs gray scale with the arbitrary unit (a.u.): (a) vertical focal spot size comparison for 1 × 10 and 1 × 4 beams. As the vertical size of the beam is reduced from 1 × 10 to 1 × 4 beam, the line profile width is also reduced. (b) In horizontal FSS of different size beams, there is no change in horizontal FSS because all beams have the same horizontal size.

FIG. 8.

Line profile graph plotted using ImageJ software distance vs gray scale with the arbitrary unit (a.u.): (a) vertical focal spot size comparison for 1 × 10 and 1 × 4 beams. As the vertical size of the beam is reduced from 1 × 10 to 1 × 4 beam, the line profile width is also reduced. (b) In horizontal FSS of different size beams, there is no change in horizontal FSS because all beams have the same horizontal size.

Close modal

Each image was captured at 65 kVp anode voltage, with expose time and anode current kept constant at 0.2 s and 0.2 mA respectively, and the anode-to-gate distance remained constant at 15 mm. The calculated vertical FSS values for beam sizes of 4.78, 3.78, 2.78, and 1.78 mm were 0.49, 0.45, 0.41, and 0.37 mm, respectively, and the horizontal FSS was constant at 0.33 mm for all beam sizes.

The FSS comparison demonstrates that the horizontal FSS remains constant, but when the vertical size of a beam decreases, the FSS decreases, as seen in the Fig. 9. A consistent decrease in FSS is observed as the vertical beam size is reduced from 4.78 to 1.78 mm while maintaining a 1 mm gap. Across each measurement with a 0.04 mm gap, the vertical FSS decreases from 0.49 to 0.37 mm with a 24.5 percentage total reduction. This signifies a proportional reduction in FSS as the beam size decreases. The reduction in FSS is attributed to the decrease in beam size, where the geometrical factor of the beam contributes to making the FSS smaller. In simpler terms, as the beam size is reduced, the electron emission area also decreases, resulting in the observed reduction in FSS.

FIG. 9.

Summary graph for vertical and horizontal focal spot size of a different beam size in which vertical FSS is measured for different vertical sizes while the horizontal is constant (0.28 mm) in all measurements.

FIG. 9.

Summary graph for vertical and horizontal focal spot size of a different beam size in which vertical FSS is measured for different vertical sizes while the horizontal is constant (0.28 mm) in all measurements.

Close modal

Because the 1 × 4 (1.78 mm in vertical size) beam produced small FSS in the previous phase, the 1 × 4 beam is kept constant in this phase and the gate offset size, between the emitter edge and the gate guide inner wall distance, is adjusted from 2.05, 1.55, 1.05, and 0.55 mm on both sides of the 1 × 4 beam. The experimental conditions were kept consistent with the preceding part, which employed a negative voltage to the cathode and gate kept grounded. Figures 10(a)10(d) show the tungsten cross wire x-ray image at the anode voltage 65 kVp, anode current 0.2 mA, and expose time 0.2 s. The anode-to-gate distance was kept constant at 15 mm. Subsequently, using ImageJ software, we plotted the line profile graphs along the vertical and horizontal axes of the tungsten cross wire x-ray image. In Fig. 11(a), it can be observed that the width of the line profile is reduced as the gate offset size is decreased from 2.05 to 0.55 mm. However, as illustrated in Fig. 11(b), the horizontal offset size remained unchanged due to the horizontal offset size was constant for all beams. Following that, the European standard EN 12543-5 approach was used on these line profile graphs to measure FSS. The calculated vertical FSS values for gate offset sizes of 2.05, 1.55, 1.05, and 0.55 mm were 0.37, 0.33, 0.29, and 0.25 mm, respectively.

FIG. 10.

(a)–(d) Tungsten cross wire x-ray images for all different gate offset sizes with denoting the horizontal and vertical axes of tungsten cross wire.

FIG. 10.

(a)–(d) Tungsten cross wire x-ray images for all different gate offset sizes with denoting the horizontal and vertical axes of tungsten cross wire.

Close modal
FIG. 11.

Line profile graph plotted using ImageJ software distance vs gray scale with a.u.: (a) vertical focal spot size comparison for 2.05 and 0.55 mm gate offsets. As the offset size is decreased, the width of the line profile is also reduced. (b) In horizontal focal spot size comparison for different gate offset sizes, there is no change in the horizontal side due to the same offset was used for all measurements.

FIG. 11.

Line profile graph plotted using ImageJ software distance vs gray scale with a.u.: (a) vertical focal spot size comparison for 2.05 and 0.55 mm gate offsets. As the offset size is decreased, the width of the line profile is also reduced. (b) In horizontal focal spot size comparison for different gate offset sizes, there is no change in the horizontal side due to the same offset was used for all measurements.

Close modal

The change in FSS is brought about by adjusting the vertical offset size. This phenomenon occurs because when a larger offset is utilized; the beam divergence angle is increased, leading to a broader beam spread and larger FSS on the anode. Conversely, when a smaller offset size is employed, gate opening is reduced, resulting in a smaller beam divergence angle, thereby causing a smaller beam spread at the anode and a decrease in FSS.25 

A systematic decrease in gate offset size from 2.05 to 0.55 mm, with a constant 0.5 mm gap, corresponds to a consistent reduction in vertical FSS from 0.37 to 0.25 mm while maintaining a steady 0.04 mm gap. Figure 12 visually illustrates this correlation, showcasing the clear relationship between adjusting gate offset size and decreasing FSS. This connection is rooted in the idea that increasing the gate offset size leads to a larger angle of electron emission divergence, resulting in a larger FSS. The precision gained by adjusting the gate offset size significantly contributes to crafting a finer and more focused x-ray beam.25 This understanding underscores the critical role of fine-tuning the gate offset size, emphasizing its practical importance in enhancing x-ray imaging. It serves as a key element for improving diagnostic precision and achieving clearer imaging outcomes.

FIG. 12.

Vertical and horizontal focal spot sizes of a different gate offset in which vertical FSS is measured for different gate offsets while the horizontal beam size and offset are constant in all measurements.

FIG. 12.

Vertical and horizontal focal spot sizes of a different gate offset in which vertical FSS is measured for different gate offsets while the horizontal beam size and offset are constant in all measurements.

Close modal

In summary, our research aimed to enhance C-beam module resolution through the manipulation of beam and gate offset sizes. By reducing the beam size from 4.78 to 1.78 mm, we observed a consistent decrease in FSS from 0.49 to 0.37 mm, highlighting a direct relationship between smaller beam sizes and reduced electron emission areas. Additionally, our investigation into gate offset size revealed a significant impact on x-ray resolution, with the FSS decreasing from 0.37 to 0.25 mm as the gate offset size decreased from 2.05 to 0.55 mm. This demonstrated that a smaller gate offset size led to a decrease in FSS, emphasizing the role of electron emission angle divergence in influencing resolution. These findings suggest that x-ray resolution can be varied by adjusting beam and gate offset sizes without requiring extra focusing lenses. This approach not only enhances image quality but also allows for a reduction in the cost of the beam. It provides flexibility in managing the cost of the electron source according to specific needs.

This research was supported by the Project for Practical Use of Regional Science and Technology Performance of the Commercialization Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science & ICT (No. 1711198121, Kyung Hee University).

The authors have no conflicts to disclose.

Jaydip Sawant: Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Ketan Bhotkar: Formal analysis (equal); Investigation (equal). Yi Yin Yu: Resources (equal); Visualization (equal). Kyu Chang Park: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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