Research on the method for measuring the focal spot size of micro-focus X-ray sources using the JIMA resolution test card

Abstract

Background

Measuring an X-ray source's focal spot size is vital for Micro-CT resolution. Standard methods are often too complex or inaccurate. The popular JIMA resolution test card is simple to use but lacks a clear, quantitative formula to determine the actual focal spot size.

Objective

This study aims to create a reliable quantitative link between JIMA resolution and focal spot size using simulations and experiments.

Methods

We used Monte Carlo simulations and practical experiments to establish the relationship between JIMA resolution and focal spot size.

Results

We found that the focal spot size is twice the line pair width on the JIMA card when the image contrast (MTF) is at 10%. This method is highly accurate, with a maximum measurement error of less than 8.7% compared to a high-precision technique.

Conclusions

Our findings provide a simple, fast, and validated method for measuring focal spot size using the JIMA test card. This makes it a practical and reliable alternative to more complex procedures.

Keywords

focal spot size beam equivalent width resolution test card Monte Carlo method

Introduction

In the field of high-resolution digital imaging, micro-focus X-ray sources, boasting exceptional image resolution, have emerged as a pivotal technology in applications such as industrial non-destructive testing. Furthermore, Micro-Computed Tomography (Micro-CT) systems built with micro-focus X-ray sources have established themselves as indispensable tools in domains including non-destructive testing, biomedicine, and materials science.^1–3 As a core component of the Micro-CT system, the focal spot size of the micro-focus X-ray source stands as a critical factor governing the system's imaging performance and directly impacts the spatial resolution of the Micro-CT system. Precisely measuring the focal spot size holds significant practical value for enhancing the spatial resolution and imaging quality of Micro-CT systems.^4,5

Currently, measuring the focal spot size of X-ray sources hinges on the EN 12543 series standards formulated by the European Committee for Standardization. Common measurement methods encompass the pinhole method,⁶ slit method,⁷ and edge method.⁸ These methods excel in measuring larger focal spots but falter when gauging tiny ones, yielding inaccurate results.⁹ Per the EN 12543-5 standard,^10,11 micro-focus spot sizes exceeding 5μm can be measured, yet this method only captures the focal spot size in one dimension. Furthermore, the penumbra images based on filament edges are swayed by factors like magnification and filament diameter, inducing substantial errors in measurements. The newly proposed the Circular Edge Back-projection can reconstruct 2D images of the focal spot of micro-focus X-ray sources and quantify the focal spot size with high precision,¹² but it entails complex image processing algorithms. Methods involving converging line group patterns (e.g., Siemens star),¹³ coded masks,¹⁴ and annular patterns¹⁵ can pinpoint the distribution of focal spots and quantify their sizes via image deconvolution techniques. However, these deconvolution-based methods are prone to interference from noise and filtering technologies, leading to unstable measurement results and intricate data processing workflows.^14,15 In recent years, Convolutional Neural Network (CNN) technology has also been deployed to measure focal spot sizes,¹⁶ but the measurement accuracy of these methods is heavily influenced by datasets. Thus, in practice, the JIMA resolution test method remains widely adopted to assess the focal spots of micro-focus X-ray sources. Despite its straightforward and swift operation with intuitive results, it is an indirect measurement method. Additionally, there exists no rigorous quantitative relationship between JIMA imaging resolution and focal spot size, and the theoretical and systematic explanations are inadequate, which constrains the acceptance and credibility of this method.¹¹

This paper analyzes the measurement principle of the JIMA resolution test card, simulates the measurement process of micro-focus X-ray sources with varying focal spot sizes via the Monte Carlo method, and summarizes the quantitative relationship of the JIMA resolution test card method. Specifically, when the geometric magnification is greater than 50 and the image contrast (Modulation Transfer Function, MTF) is 10%, the focal spot size (a) is approximately twice the JIMA line pair width (D) (i.e., a≈2D). This systematically addresses the shortcomings of JIMA test charts in practice, namely the lack of a rigorous quantitative relationship as well as sufficient theoretical and systematic explanations. Moreover, through validation by comparative experiments against the Circular Edge Back-projection for focal spot measurement, it further confirms the accuracy and reliability of the JIMA resolution test card measurement method, furnishing a robust theoretical and experimental foundation for the rapid and intuitive measurement of the focal spot size of micro-focus X-ray sources.

Testing methods and principles for the focus of micro-focus X-ray sources

Micro-focus X-ray source and focus

The structure of a micro-focus X-ray source is depicted in Figure 1, incorporating core components like an electron gun, focusing coil, and X-ray conversion target. The electron beam, accelerated by high voltage, bombards the X-ray target, with X-rays generated via the bremsstrahlung effect. The region on the target where X-rays originate is typically termed the focal spot. The shape and size of the focal spot are shaped by multiple factors: filament dimensions, electron beam focusing performance, magnetic field strength, and target material, among others.

Figure 1.

Schematic diagram illustrating the core structure and operational principle of the micro-focus X-ray source.

Testing method for the focus of micro-focus X-ray sources

1. Fine filament method

The current EN 12543 standard recommends the thin filament method for measuring the focal spot size of micro-focus and small-focus X-ray tubes, with its schematic illustrated in Figure 2.¹⁷ With a geometric magnification of 20∼100, imaging is performed on a thin metal wire (such as tungsten) with a diameter of Φ1 mm. By capitalizing on the geometric blurring effect at the filament edge (as shown in Figure 2(b)), the focal spot size a can be indirectly computed via $a = (\bar{E F} + \bar{G H}) / m$ . Here, $\bar{E F}$ and $\bar{G H}$ denote the length from 50% to 90% of the air grayscale value (blurring of the filament edge induced by the focal spot), and m stands for the magnification. This method applies to measuring X-ray tube focal spot sizes ranging from 5μm to 300μm. Yet, it suffers from significant measurement errors due to the influence of factors like geometric magnification, X-ray energy, and image noise.

2. Circular Edge Back-projection

Figure 2.

Schematic diagram of focal size measurement using the thin filament method.

The principle of focal spot measurement using the Circular Edge Back-projection method is illustrated in Figure 3. X-rays penetrate a high-density metal plate featuring a circular aperture and project an image onto a flat-panel detector. The geometric blurring at the circular aperture's edge hinges on both the X-ray source's focal spot dimensions and the geometric magnification factor. Leveraging the known geometric magnification, the two-dimensional intensity distribution of the focal spot can be computationally reconstructed through back-projection, enabling precise quantification of the focal spot size. The workflow for measuring the focal spot size using this method is outlined in Figure 4: following image denoising, the radial Edge Spread Function (ESF) is extracted along the 360°circumference of the circular aperture (Figures 4(a, (b), (c))). Then, the derivative of the ESF in the 360°direction is obtained to obtain the corresponding Line Spread Function (LSF) to generate the sine graph (Figure 4 (e)). Finally, the two-dimensional image of the focal spot is reconstructed using the Filtered Back-Projection (FBP) algorithm.¹² Both theoretical and experimental results have proven that this method is suitable for measuring the focal spot size of micro-focus X-ray sources with high precision.¹² Therefore, this paper selects the Circular Edge Back-projection for comparative experiments.

3. IMA resolution test card imaging method

Figure 3.

Schematic diagram of the focus measurement principle using the circular edge back-projection.

Figure 4.

Flow of the circular edge back-projection for measuring focus size.

The JIMA resolution test card (depicted in Figure 5) is crafted using advanced semiconductor lithography, with line pairs of varying sizes—from tens of micrometers down to sub-micrometers—etched into a silicon substrate. In Figure 5(a), the black lines consist of tungsten with a line width D of 2μm, while the white lines are 2μm-wide SiO₂. As illustrated in Figure 5(b), the tungsten lines measure 1μm in thickness. Figure 5(c) shows the DR image of the JIMA resolution test card. When measuring the focal spot size of a micro-focus X-ray source, the finer the identifiable line pairs in the JIMA resolution test card image, the smaller the focal spot size.

Figure 5.

Schematic of the JIMA resolution test card.

The quantitative relationship between the imaging resolution of the JIMA resolution test card and the micro-focus spot size

As illustrated in Figure 6, during imaging with the JIMA resolution test card, the projected image q(x) of the test card is defined as the result of convolving the ideal projected image p(x) of the JIMA resolution test card with the system's point spread function (PSF) p_sf(x):

q (x) = p (x) \otimes p_{sf} (x),

(1)

Figure 6.

X-ray imaging schematic.

The PSF blurs X-ray images. This blurring stems predominantly from the combined impact of the light source's finite dimensions and signal crosstalk between detector pixels. The effective size of the point spread function these two factors generate at the object's center—termed the equivalent Beam Width (BW)¹⁸ —can be formulated as:

B_{W} = \frac{\sqrt{d^{2} + {[a (m - 1)]}^{2}}}{m},

(2)

Here, B_w denotes the equivalent beam width, a represents the source size, d stands for the detector pixel size, and m is the system's imaging magnification ratio.

Equation (2) for the equivalent beam width reveals that once the source's focal spot size and detector pixel size are fixed, B_w at any imaging magnification can be calculated. When the object is positioned near the X-ray source, B_w is dominated by the focal spot size: at large values of m, the smaller d/m becomes (and thus d/m is negligible), the assumption that B_w ≈ a holds true. Conversely, when the object is close to the detector, B_w is governed primarily by the detector: as m approaches 1, B_w ≈ d.

As shown in Figure 7, it illustrates the convolution result between the PSF function with a width of B_w and the JIMA resolution test card (featuring periodic details with a line width of D and an interval of 2D). When D = B_w/2, the effective contrast is zero, and the spatial resolution at this time is the cut-off frequency of the system.^18,19 From Equation (2), it can be seen that when m is large, the relationship between the focal spot size a and the width of the JIMA line pair satisfies a≈2D. When the resolution test card detects the optimal resolution of the system, the focal spot size can be estimated to be twice the line width corresponding to the optimal resolution.

Figure 7.

Convolutional calculations of P_SF function with width B_w and JIMA resolution test card¹⁹.

Set the intensity distribution of the light source to follow a Gaussian distribution with a Full Width at Half Maximum (FWHM) of Bw, then convolve it with the line-pair test card. Calculate the modulation coefficient after convolution (the ratio of effective contrast $Δ u_{e}$ to actual contrast $Δ u$ ) to explore the relationship between the focal spot and the line-pair test card. The relevant parameters and simulation results are presented in Table 1.

Table 1.

Theoretical simulation parameters and results.

FWHMBw/μm	Test card widthD/μm	The relationship between FWHM and the test card	Modulation degreeM/%
1	2	D = 2BW	99.099.0(±0.1)
1	1	D = BW	81.4(±0.1)
1	0.8	D = 0.8BW	64.7(±0.2)
1	0.6	D = 0.6BW	30.4(±0.2)
1	0.5	D = 0.5BW	9.1(±0.3)
1	0.4	D = 0.4BW	1.7(±0.3)

The simulation results reveal that when B_w = 2D the modulation degree reaches 9.1%. This phenomenon enables us to quantitatively investigate the relationship between focal spot size and line-pair width. Generally, whether the modulation degree exceeds 10% is adopted as the criterion for judging the resolvability of two details.¹⁹ As shown in Figure 8, we perform polynomial fitting on the simulation results, then take the resolution corresponding to a 10% modulation degree as the system's spatial resolution, yielding a calculated value of 990.8 lp/mm. At this point, the focal spot size measures 1.009 μm, which is twice the line-pair width, and the error relative to the theoretical value is 0.9%.

Figure 8.

MTF curve of simulation results.

Theoretical analysis and simulation results confirm that when the magnification surpasses 50 and the image modulation degree hits 10%, the line-pair width of the JIMA resolution test card and the focal spot size adhere to the relationship: a ≈ 2D.

Experiment

Monte Carlo simulation experiment

To verify the accuracy of the relationship between the JIMA resolution test card and the focal spot size proposed in the principle section, we employed BEAMnrc software²⁰ to conduct simulations based on the schematic diagram shown in Figure 6. BEAMnrc is a core software based on the Monte Carlo method,²¹ which is used to simulate the transport process of particles such as electrons and photons in media. In this study, it is employed to simulate the entire imaging process, including the emission of the X-ray source, the penetration of X-rays through the JIMA test card model, and the arrival of X-rays at the detector plane.

The X-ray source was set to a focal spot with a Gaussian distribution, operating at an energy of 100 keV, the average angular refractive index of the ray is 7.5° and a simulated particle count of 1 × 10⁹. A JIMA resolution test card model was positioned 0.3 cm from the X-ray source; after penetrating the card, the X-rays formed a photon detection plane 15 cm from the source, as depicted in Figure 9.

Figure 9.

Schematic diagram of simulation.

BEAMDP is a post-processing software used to process the phase-space files generated by BEAMnrc. In this study, we use BEAMDP software to process the phase-space files generated by BEAMnrc and extracted X-Y plane particle distribution scatter plot data. Analyzed multiple sets of simulation data for JIMA resolution test cards with known focus sizes a and varying line widths D, then computed the corresponding modulation degree (results are shown in Table 2). By transforming the JIMA test card’ s physical parameter D into spatial resolution, combining spatial resolution with modulation degree, and applying polynomial fitting, we obtained the Modulation Transfer Function (MTF) of the system for different focal spot sizes.

Table 2.

Different combinations of focus size and line width and simulation tuning regime.

Focal spot sizea/μm	Line widthD/mm	Resolution /(lp·mm-1)	Modulation degreeM/%	Focal spot sizea/μm	Line widthD/mm	Resolution /(lp·mm-1)	Modulation degreeM/%
20	8	62.5	0	10	4	125	0
20	10	50	10.12(±0.2)	10	5	100	10.2(±0.2)
20	15	33.33	33(±0.2)	10	7	71.43	28.9(±0.2)
20	20	25	53.4(±0.1)	10	10	50	52.8(±0.1)
20	30	16.67	70.1(±0.1)	10	15	33.33	71(±0.1)
4	1.5	333.33	0	2	0.8	625	0
4	2	250	9.94(±0.2)	2	1	500	10.1(±0.2)
4	3	166.67	30.6(±0.2)	2	1.5	333.33	31.8(±0.2)
4	4	125	49.1(±0.1)	2	2	250	52.4(±0.1)
4	6	83.33	69.5(±0.1)	2	3	166.67	70.7(±0.1)

As shown in Table 2, when the focal spot size satisfies the condition a = 2D, the modulation degrees from the simulation results all fluctuate around 10%, which is consistent with the theoretical simulation result of 9.1%. Fitting the data in Table 2 yields the CT system's MTF curve, allowing us to pinpoint the spatial resolution corresponding to a 10% modulation degree (Figure 10) and further calculate the focal spot size.

Figure 10.

Simulated modulation regime and MTF fitting curves for different combinations of focal size and line width.

As shown in Table 3, extract the spatial resolution at the 10% modulation degree from the fitted curves, compute the corresponding focus sizes, and compare them against theoretical values. The results demonstrate that the measurement error of the JIMA resolution test card-based focal spot measurement simulation experiment is below 1%. This confirms that the JIMA resolution test card method for focal spot measurement can precisely quantify focal spot sizes.

Table 3.

The error value between the simulated and theoretical focus dimensions.

Focal spot sizea/μm	Modulation degree/(lp·mm-1)	Simulated focal spot sizea/μm	Error /%	Focal spot sizea/μm	Modulation degree/(lp·mm-1)	Simulated focal spot sizea/μm	Error /%
20	49.52	20.19	0.95	10	99.19	10.08	0.8
4	248.38	4.03	0.75	2	494.36	2.02	1.0

Actual imaging experiment

As shown in Figure 11, we employed an open-tube X-ray source from WorX and set its energy to 100 keV. We then positioned the JIMA resolution test card close to the source and imaged it with a 0.1mm pixel detector. Next, we measured the focal spot size of the X-ray source using both the JIMA resolution test card method and the Circular Edge Back-projection.²²

Figure 11.

Layout of the focal spot measurement experiment.

In an open-tube X-ray source, adjusting the focusing current modulates the focal spot size. We used a JIMA RT RC-02 resolution test card to measure focal spot sizes across different focusing currents. At a focusing current of 630 mA, line pairs of 15μm, 10μm, and 7μm are clearly resolved, as shown in Figure 12.

Figure 12.

X-ray images of the JIMA resolution test card.

In Experiments 1, 2, and 3, the focusing current was adjusted such that the modulation degrees of the 15 μm, 10 μm, and 7 μm line pairs reached approximately 10%, indicating that the focal spot sizes were respectively adjusted to 30 μm, 20 μm, and 14 μm. Then, we deployed both the JIMA resolution test card method and the Circular Edge Back-projection to measure and compare the focal spot sizes under these conditions.

The experimental results are presented in Figure 13. In Experiment 1, with a focusing current of 647.5 mA, the modulation degree of the 15 μm line pairs reached 10.3%. In Experiment 2, at a focusing current of 641.5 mA, the modulation degree of the 10 μm line pairs registered 10.8%. In Experiment 3, with a focusing current of 638.5 mA, the modulation degree in at 10.6%. The experimental results reveal that the line pair resolution in the y-direction is significantly lower than in the x-direction. This confirms the focal spot is non-circular, with the x-direction focal spot being smaller than its y-direction counterpart. Consequently, this paper focuses on analyzing only the x-direction focal spot size to streamline quantitative analysis.

Figure 13.

Focus measurement results from the JIMA resolution test card.

Under the same parameters as the three experiments above, the JIMA resolution test card shown in Figure 11 was swapped out for a 1.5 mm-diameter metal circular hole. The Circular Edge Back-projection was deployed to measure the focal spot size, yielding the results depicted in Figure 14. The focal spot sizes measured by the two methods were then collated into Table 4.

Figure 14.

Measurement results using the circular edge back-projection.

Table 4.

Focal spot size measurement results.

Number	JIMA resolution test card for focal spot measurement/μm	Circular Edge Back-projection for focal spot measurement/μm	Absolute error/μm	Relative error/%
1	30.0	29.68	0.32	1.1
2	20.0	21.77	1.77	8.1
3	14.0	15.33	1.33	8.7

The deviations in focal spot sizes measured by the JIMA resolution test chart method and the Circular Edge Back-projection, as shown in Table 4, are both small. The relative errors of the three sets of experimental results (with the measurements from the Circular Edge Back-projection serving as reference values) stay below 8.7%. These findings validate that the JIMA resolution test card method is practically viable for micro-focal spot measurement tasks: it enables real-time and intuitive tracking of focal spot changes, thereby better facilitating the adjustment and maintenance of ray tube parameters.

In both simulation and actual experiments, we validated the effectiveness of the JIMA resolution test card for evaluating focal spot size under magnifications exceeding 50x. Results demonstrate that at a 10% modulation degree, the focal spot size approximates twice the line pair width of the JIMA resolution test card. This method boasts advantages such as straightforward operation and high measurement precision, delivering reliable estimates of focal spot size. However, it only enables indirect evaluation of focal spot size and cannot precisely quantify the specific shape of the focal spot.

Conclusion

This paper examines the quantitative relationship in measuring the focal spot size of micro-focus X-ray sources using the JIMA resolution test card, and validates the method's effectiveness through theoretical analysis, Monte Carlo simulations, and physical experiments. Results demonstrate that with magnification exceeding 50 and 10% modulation degree on the JIMA chard, the corresponding focal spot size approximates twice the JIMA line width. Compared to techniques like the Circular Edge Back-projection, the JIMA-based approach eliminates the need for complex image processing and analysis, offering straightforward operation and high measurement precision. Through theoretical analysis and physical experiments, this paper systematically establishes the quantitative relationship between JIMA card imaging resolution and focal spot size, strengthening the method's acceptance and credibility while providing robust theoretical and experimental foundations for its widespread application.

Footnotes

Acknowledgments

This work is supported by the National Key Research and Development Program of China (No. 2022YF0706400); Fund Project of State Key Laboratory of Shock Wave Physics and Detonation Physics (No. 2024CXPJGFJJ06411); Chongqing Postgraduate Research Innovation Project (No. CYB240015).

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the the National Key Research and Development Program of China, Chongqing Postgraduate Research Innovation Project, Fund Project of State Key Laboratory of Shock Wave Physics and Detonation Physics, (grant number 2022YF0706400, CYB240015, 2024CXPJGFJJ06411).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ORCID iD

Li Fengxiao

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