Measurement of Focal Spots of X-ray Tubes Using a CT Reconstruction Approach on Edge Images of Large Holes and Comparison to Pinhole Imaging

The first Non-destructive testing (NDT) method which evolved in the industrial age was radiographic testing (RT) [1]. Among all NDT methods, RT is no exception, so there are still many issues for optimizations even today. One of them is the measurement of the focal spot of X-ray tubes [2]. The size of the focal spot is critical for imaging, because it determines the spatial resolution in the X-ray image. The classical way to evaluate focal spots of X-ray tubes is by pinhole imaging using a camera obscura [1]. But this method has a natural lower limit, which is defined by the diameter of the pinhole used (today min. 10 µm) [2]. Therefore, focal spot sizes lower than 50 µm diameter cannot be imaged and measured correctly. An alternative approach, which permits this, was investigated here using the edge unsharpness of holes much larger than the focal spot size. The results of both methods were compared using 3 different X-ray tubes.


Introduction
In conventional X-ray tube imaging, pinhole imaging methods are limited to focal spot sizes above 50 µm due to the minimum pinhole size of 10 µm [3].To address focal spot sizes below 50 µm, alternative imaging methods are necessary.The development of Computed Tomography (CT) algorithms offers a solution by using larger holes than the focal spot size, allowing measurement of edge unsharpness [2].This approach eliminates the lower limit on focal spot size, but computational challenges need addressing, and practical application parameters must be determined.The use of pinhole imaging methods requires specialized equipment, as outlined in standards such as ASTM E 1165-20 or EN 12543-2:2021 [3].These standards specify the determination of focal spot size and shape from pinhole images, emphasizing the need for a focal spot size significantly larger than the pinhole diameter to avoid additional unsharpness.Smaller pinhole diameters (<10 µm) are impractical due to insufficient X-ray contrast and photon statistics [1].Existing standards cover spot sizes from 5 µm to several millimeters, with ongoing efforts to establish standards for nano focus tubes, addressing inconsistencies in measurement methods.Proposed standards aim to provide internationally accepted methods for accurate spot size determination, replacing proprietary techniques used by equipment manufacturers [4].

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Optimization of the magnification factor depending on hole size and real focal spot size.

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Investigation of computational problems of the existing software and comparison of results.

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Comparison of results using EN12543-2 & prEN12543-7 on the same X-ray tube and identical focal spot settings.
• Determination of application ranges of the different techniques for practical focal spot measurement and summary

X-ray focal spot measurement for tube #1
This X-ray tube offers three focal spot sizes for three distinct X-ray power values, all of which were measured.Following the guidelines of EN12543-2 [3] and prEN12543-7 [6] standards, 75% of the maximum tube voltage was utilized for all measurements (169 kV).Focal spot measurements were conducted using the KowoSpot X pinhole camera, specifically designed for focal spot size measurement in accordance with ASTM E1165-20 and EN12543-2:2021 standards.Utilizing a Hamamatsu DDA with 20 µm pixel size and dedicated software, data acquisition and projection data evaluation were performed.Screen snapshots were also evaluated using "Isee!" software [7], with focal spot sizes calculated considering a magnification factor of 7, as summarized in Table 1.Subsequently, a 2 mm sharp hole gauge or the NxS gauge, developed in the NanoXSpot project [5], was employed alongside the Dexela NDT1512 DDA for gauge image acquisition.Both X-ray tubes #1 and #2 were measured again, with screenshots evaluated by the NxS tool [8] implementing methods from the prEN12543-7 standard draft.However, when the 2 mm sharp hole gauge was measured with the Hamamatsu DDA, a CNR (Contrast to Noise Ratio) below 20 was achieved, rendering the NxS tool unable to calculate the focal spot size.While the Hamamatsu DDA, used in the KowoSpot X pinhole camera system, provided suitable results for pinhole measurement method according to EN 12543-2, its application alongside the NxS gauge yielded images of insufficient quality for NxS tool evaluation.Hence, the Dexela DDA, with a pixel size of 75 µm and a thicker CsI scintillator screen, was employed for further measurements.The increased contrast sensitivity of the Dexela detector, due to its thicker CsI scintillator screen, ensured higher-quality images for evaluation.Magnification calculation variations were investigated in this study, with magnification calculated from measured distances according to Figure 2. The NxS tool measured magnification in the image using the given DDA pixel size and hole diameter, with three setups designed to achieve three different magnifications of 7, 11, and 25.All obtained results are presented in Table 1.Through analysis, it was evident that images acquired by the DDA Hamamatsu with the NxS gauge lacked sufficient Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) for evaluation, rendering these images nonevaluable (highlighted in orange in Table 1).Additionally, in accordance with prEN12543-7 standard requirements, the permissible range of gauge hole diameter should fall between 5 and 15 times the anticipated focal spot size (AFS), highlighted in green in Table 1.Hole diameters outside this standard range are marked in blue (larger) and yellow (smaller) in Table 1.
Considering the uncertainty considerations provided in chapter 3.2, an overall uncertainty of ±5% was derived for the results.To facilitate comparison between the two methods, the size of the X-ray focal spot measured by ISee! software (using the pinhole method) represents the standard EN 12543-2, while the remaining measurements with a large hole, measured by the NxS tool, represent the standard prEN 12543-7 (i.e., the reconstruction method).Furthermore, the pinhole method is deemed an acceptable standard measurement method for focal spot sizes above 50 µm.Hence, in this research, the pinhole method measurement with ISee! software serves as a reference value and is compared with the other results obtained using a large hole.Table 1 reveals that generally, as magnification increases, the differences between values decrease, indicating increased accuracy in measurements.It was observed that the difference in focal spot size calculated for the smallest focal spot size (at 50 W) ranged from -30% to -35%, while for the larger focal spot size (at 130 W), it ranged from 6% to +16%.For the largest focal spot size (at 200 W), the range was from +7% to +21%.Differences between values at varying diameters of the target hole were below the uncertainty threshold (<5%).

X-ray focal spot measurement for tube #2
The focal spots of the Comet MXC-450MF -MesoFocus 450 kV X-ray tube were measured, with results provided in Table 2.This tube offers the flexibility to select one of five different focal spot sizes depending on the X-ray power.All five sizes were measured across five power settings: 50 W, 100 W, 250 W, 350 W, and 450 W. As per EN12543-2 and prEN12543-7 standards, 75% of the maximum tube voltage (337 kV) was utilized for all measurements.However, to explore the influence of voltage on the focal spot size, four different voltages were used: 100 kV, 200 kV, 337 kV, and 450 kV.To measure the focal spots, the KowoSpot X pinhole camera with a 10 µm pinhole and the Hamamatsu DDA were employed as the reference method.Pinhole images were analyzed using ISee! software and the KowoSpot X software, with focal spot sizes calculated using the ILP method according to EN 12543-2:2021, as listed in Table 2.The minimal broadening of the focal spot image using a 10 µm pinhole on a 50 µm focal spot renders it negligible.

X-ray focal spot measurement for tube #3
Focal spots of the MicroFocus 240 kV X-RAY WorX -XWT-240 THE X-ray tube were measured and the obtained results are given in Table 3.This X-ray tube offers adjustable X-ray voltages and currents, contrasting with MesoFocus tubes which allow only voltage selection at fixed power settings (MXR-225MF: 20 to 225 kV at 50 W, 130 W, and 250 W fixed; MXC-450MF: 100 kV to 450 kV at 50 W, 100W, 250 W, 350 W, and 450 W fixed). Six power settings (5 W, 10 W, 15 W, 25 W, 50 W, and 80 W) of this MicroFocus X-ray tube were measured.The X-ray generator software adjusted the electron beam accordingly, resulting in different focal spot sizes for each power setting and X-ray voltage.Compliance with the prEN12543-7 standard draft necessitated using 75% of the maximum tube voltage for all measurements (150 kV).However, to assess the influence of X-ray voltage on focal spot size, one voltage setting lower than the standard (60 kV) and another higher (200 kV) were employed.Measurement of the focal spots utilized only the NxS gauge and Dexela DDA due to the small focal spot size of the MicroFocus X-ray tube.According to EN12543-2 standard regulations, the pinhole method cannot measure focal spot sizes below 50 µm, rendering the application of the pinhole camera impractical.The NxS gauge and magnified imaging were employed for measurement, as prescribed by new standard drafts prEN12543-6 [9] and prEN12543-7 [7].
All six power settings were evaluated by the NxS tool based on the methodology introduced in prEN12543-7.Focal spot sizes were measured at 60 kV, 150 kV, and 200 kV, with a magnification of 107 chosen for all measurements.Comparison between methods was facilitated by utilizing the simple edge evaluation method described in prEN12543-4 alongside focal spot reconstruction per prEN12543-7.Focal spot sizes were calculated using both methods, with the higher value chosen as the size of the focal spot in the former, and methods akin to those used for MesoFocus tubes employed in the latter.Results were consolidated in Table 3. Dexla DDA was consistently used for image acquisition, with the NxS gauge positioned as close as possible to the X-ray tube window.Analysis revealed defocusing of the focal spot at 60 kV for power exceeding 10W, resulting in larger focal spot sizes than expected from the X-ray power setting.Reconstruction of the focal spot image exhibited significant noise due to the low contrast-to-noise ratio (CNR) in the acquired image with a 30s exposure time.Compliance with prEN12543-7 dictated a gauge hole diameter between 5 and 15 times the Airy disk function size.The findings demonstrated that due to limitations on the X-ray generator tube current (maximum 1 mA) at 60 kV, a maximum power of 60 W could be used.P = I * U (1) P (at max point) = 1 mA (limited by X-ray generator) * 60 kV = 60 W The results indicate that focal spot sizes calculated through reconstruction methods are consistently smaller than those obtained from profile measurements utilizing edge unsharpness in identical images.At lower energies, the disparities can be substantial, with the largest differences reaching up to 940%, as depicted in Figure 4.However, as energy levels increase, this discrepancy diminishes.The disparity arises from the focal spot shape generated by the MicroFocus tube, characterized by a sharp center and a broader periphery.Using the edge profile and the 16%-84% method, the focal spot size measures 49 µm.Conversely, employing the first derivative of the displayed profile in the same image yields a focal spot size of 5 µm.This discrepancy represents a ninefold difference between the two measurements.The reconstruction method of the NxS tool uses a first derivative as the first step of reconstruction and measures therefore the focal spot size similar to Figure 5.

Uncertainty
The focal spot size d according to the ILP method as investigated here is calculated according to the following formula, which is not given in the standards [9] but in ASTM E 2903-18 for micro focus tubes: d = 1.47 *(P1 -P2) * p/(M-1) = 1,47 ΔP *p/(M-1) (2) with p -pixel size, M -Magnification, P1, P2 -the 14% and 86% points on the ILP profile, the factor of 1,47 to expand the 14%-and 86%-point difference to a 0% and 100% line.The pixel size p of the detector is not assumed to differ from its specified value, so it does not contribute to the uncertainty of this measurement.Therefore, the uncertainty consists of 2 independent contributions: the measurement error in the profile positions of the points P1 and P2 (1/1.47ΔP) and the measurement error in the magnification M (ΔM/M).because the above formula on the calculation of d is linear, both contributions add quadratically as a simplified approach.Therefore, the final uncertainty of the focal spot measurement is given by: Δd/d = [(ΔM/M) 2 + 1/(1.47*ΔP) 2 ] 1/2 (3) In our experiments we estimated the measurement uncertainty of the magnification M with 2%.The evaluated ILP profiles on the Dexela detector with 75 µm and a Magnification (M-1) = 14 for a focal spot size of 130 µm give a ΔP of 24 pixels and the 2 profile positions are evaluated with an error of one pixel caused by the digitization.Therefore, the final uncertainty for the focal spot size d is: Δd/d = [(0.02) 2 + 1/(1.47*24) 2 ] 1/2 = 0,0347 = 3.5% (4) For smaller focal spots than 130 µm, the uncertainty increases, because the number of pixels across the ILP profile ΔP is lower.Finally, an overall value of 5% for the total uncertainty of the focal spot measurements was considered in the graphs shown before.

Conclusions
In conclusion, this study aimed to compare focal spot measurement methods outlined in EN12543-2 (pinhole method) and prEN12543-7 (large hole method) across focal spot sizes ranging from 5 µm to 500 µm.Key findings are summarized as follows: 1) The pinhole camera measurement method according to EN12543-2 was successfully applied using the KowoSpot X pinhole camera with a 10 µm pinhole in a focal spot range between 60 µm to 430 µm and an X-ray voltage range between 60 kV and 450 kV.Using this camera and the MesoFocus 450 kV X-ray tube, a defocused X-ray focus was detected for a power higher than 200W at 100kV (minimal voltage of this tube) and for >400W at 200 kV.This is a side effect of the current limit of max. 2 mA of the generator.The generator firmware does not handle this limit correctly, and as a consequence a defocused focal spot with a larger size result in these settings.To measure correctly of focal spot sizes below 100 µm it is important to use the 10 µm pinhole and a sufficient magnification.Previous measurements with (M-1) = 3 were not acceptable (the uncertainty was too high) the measurements described here with (M-1) = 7 (20 µm pixel size, 50 µm focal spot) had an uncertainty of 4,5% using this 10 µm pinhole.Focal spot measurements up to 450 kV were possible without problems and the values obtained were used for comparison with the results of the hole measurements according to prEN 12543-7.
3) Analysis of MesoFocus tubes #1 and #2 revealed focal spot size differences between methods within the -25% to +36% range.For focal spots up to 0.5 mm, the prEN12543-7 method proved a reliable alternative to the EN12543-2 pinhole method.4) Higher magnification yielded reduced differences between methods.Maximum magnification is recommended for the prEN12543-7 method, albeit requiring longer exposure times for adequate CNR.
5) The acquisition of large hole images with the MicroFocus X-ray tube (no pinhole imaging was possible here) provides a set of images for several power settings.These images were evaluated by the profile edge unsharpness method of prEN12543-4 and the focal spot reconstruction according to prEN12543-7.Here both methods result in large differences up to factor 10, caused by the different processing of the long-range focal spot contributions of this X-ray tube.Whereas the edge unsharpness method of prEN12543-4 considers also the longrange focal spot contribution, the first derivate of the focal spot reconstruction according to prEN12543-7 reduces this long-range contribution below the noise level.Therefore, this contribution is not reconstructed and followingly the focal spot size is much lower than measured by the profile edge unsharpness method.

Statement
The presented work is based on the Master thesis of Seyedreza Hashemi entitled "Measurement of focal spots of X-ray tubes using a CT reconstruction approach on edge images of holes with a diameter larger than the focal spot and comparison to classical pinhole imaging", which was defended successfully at Dresden International University in November 2023.

Figure 1 -
Figure 1 -X-Ray focal spot sizes range covered by currently available standards and the new range extension by the European EURAMET project "NanoXSpot" below 5 µm [5].

Figure 2 -
Figure 2 -Different Magnification Set-ups with MXR-225MF tube a. Magnification 7 with the KowoSpot X pinhole camera (vertical), b.Magnification 11 with NxS gauge and Hamamatsu DDA, c. Magnification 25 with NxS gauge and Dexela DDA

Figure 4 -
Figure 4 -Focal spot evaluation by ISee! Software for the X-ray tube XWT-240 THE (Power: 25 W, Magnification: 107, Hole Diameter: 0.5mm, DDA: Dexela, Voltage: 240 kV), resulting focal spot size from edge unsharpness: 49 µm, this measurement does only poorly reflect the focal spot shape; a sharp contribution is accompanied by a very unsharp contribution (broad foot) as visible in the edge profile (red line in left window).

Table 2 . Comet MXC-450MF -MesoFocus 450kV
hole size smaller than requirement in standard prEN 12543-7 (Hole size less than 15x of focal spot) hole size larger than requirement in standard prEN 12543-7 (Hole size larger than 5x of focal spot) hole size is according to standard prEN 12543-7Defocused focal spot by generator current limitation (2mA) * Cannot be measured by NxS tool Analysis revealed limitations in the X-ray generator current (maximum 2mA) at 100 kV for power settings exceeding 200W, resulting in defocused focal spots (approximately 800 µm).Similar behavior was observed at 200 kV with power settings surpassing 400 W. A bug in the generator firmware was identified for specific settings: 100 kV and 250W, 350 W, and 450W, as well as 200 kV and 450 W. Consequently, users are advised against selecting any X-ray power requiring a current higher than 2 mA, despite potential allowances within the generator software.The defocused spots are highlighted in orange in Table2.According to prEN12543-7 standards, the permissible gauge hole diameter range should be between 5 and 15 times the anticipated focal spot size (AFS), highlighted in green in Table2, with deviations marked in blue or yellow.Instances of insufficient Contrast-to-Noise Ratio (CNR) render the NxS tool unable to calculate focal spot size via reconstruction procedure, denoted by *.Longer exposure times are suggested to improve CNR values.Differences between measurement results obtained via the NxS gauge and the pinhole method of EN 12543-2 standard, serving as the reference, are compared with results from the Reconstruction method (standard prEN 12543-7).Additionally, voltage variations beyond the EN 12543-2 standard requirement (75% of the maximum tube voltage, i.e., 337 kV) were explored, including 100 kV, 200 kV, and 450 kV.