https://orcid.org/0000-0003-1117-4287
Figures
Abstract
This study aims to evaluate the measurement accuracy of computed tomography (CT) systems, focusing on the necessity of using calibration phantoms for enhanced precision. Both clinical CT and micro-CT systems were evaluated using a specially designed two-ball phantom, which provides a reliable reference for spatial resolution and geometric accuracy. The study involved scanning the phantom with two micro-CT devices (the oversize micro-CT SkyScan 1173 and the high-resolution micro-CT SkyScan 1272) and a clinical CT device, a third-generation dual-source CT scanner (SOMATOM Force), measuring the distance between the centres of two ruby balls. The results showed significant differences in measurement accuracy between the devices. The high-resolution micro-CT provided the most consistent measurements with minimal variance, indicating its superiority in applications requiring high precision. In contrast, the oversize micro-CT exhibited larger errors, particularly at smaller voxel sizes, suggesting that internal calibration affected its accuracy. The dual source CT system had the smallest mean error but a larger standard deviation, indicating less consistency compared to micro-CT systems. Calibration with the two-ball phantom improved measurement accuracy across all devices. This improvement underscores the importance of using calibration phantoms to ensure accurate measurements, especially in fields that require high precision, such as clinical diagnostics and materials science. We concluded that routine calibration with phantoms is essential to achieve high measurement accuracy in CT imaging, thereby increasing the reliability of CT-based analyses in various disciplines.
Citation: Scherberich J, Windfelder AG, Steinbart J, Krombach GA (2025) Measurement accuracy of CT systems: The importance of calibration phantoms. PLoS One 20(9): e0332263. https://doi.org/10.1371/journal.pone.0332263
Editor: Christopher Njeh,, Indiana University, UNITED STATES OF AMERICA
Received: December 10, 2024; Accepted: August 28, 2025; Published: September 25, 2025
Copyright: © 2025 Scherberich et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: An Excel-datasheet is available from the OSF database (https://osf.io/5rsgj/ with the DOI: 10.17605/OSF.IO/5RSGJ).
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Computed tomography (CT) represents a gold standard in imaging procedures for a multitude of clinical issues. The scan data obtained is often used to measure various structures non-invasively and in high resolution. In particular, micro-computed tomography (micro-CT) has demonstrated its value in a number of fields, offering the ability to visualise smaller samples in high resolution. Such common imaging indications include clinical applications such as bone or tooth analysis [1–7] and forensics [8], as well as also material sciences [9–15], mineral and soil sciences [16–19], life sciences [20–22] and the visualisation and measurement of various animal models [23–30].
In both types of scanners, namely the dual-source CT and the micro-CT, X-rays are emitted from a cathode in the beam direction towards a detector. The dimensions of the sample observed on the detector are contingent upon its position between the X-ray source and the detector itself. A series of projection images is captured from varying angles, which can then be used to generate cross-sectional images. The resulting size of the three-dimensional pixels (voxels) is typically determined by the calibration of the respective devices [31]. It is anticipated by device users that scans will be highly accurate, produced by factory-calibrated scanners without the use of further phantoms [25,32–34]. Typical pre-scan calibration steps only include stage alignment and flat-field corrections [35], however the usage of calibration objects is recommended [36,37].
This raises a critical question regarding the metrological accuracy of measurements derived from CT or micro-CT scans. While users often trust the factory-calibrated settings of their devices, the actual accuracy may vary. It is therefore crucial to determine if further improvements are necessary through scans of a calibrated phantom. It is important to distinguish metrological accuracy—the correctness of a length measurement—from spatial resolution, which is the ability to distinguish fine details and is often tested with different tools like line-pair phantoms. The objective of this study is therefore to examine the measurement accuracy of different CT devices and to determine the necessity and effectiveness of using a calibration phantom to correct for systematic errors. The use of a ruby two-ball phantom, manufactured for the evaluation of spatial resolution and overall precision in CT imaging, allows for the empirical determination of the differences in performance of the systems (Fig 1). By establishing a fixed distance between the two spheres, the phantom serves as a reliable point of reference for calibrating the system’s spatial resolution and geometric precision. A different phantom, which measures the distance from edge to edge, would exhibit either softer or harder edges, which would depend on the windowing adjustment in the scan reconstruction (Fig 1B). As a result, the measured length would be different. This would also entail a change in the distance to be measured. Consequently, a two-ball phantom is employed. The distance between the centres of the balls is measured, as this distance is not affected by the windowing. It is anticipated that the highest level of measurement accuracy will be observed in micro-CT devices, while a greater degree of measurement inaccuracy will be evident in clinical CT, primarily due to the inferior resolution.
(A) 3D rendering and (B) schematic image of a two-ball phantom. (C) For calibration purposes, the distance between the centre of the balls is used, as the outer edge may appear smaller or larger depending on the windowing in the image reconstruction (black arrows). The distance between the two spheres can be measured in 2D (D) or in 3D using matching spheres (E).
Materials and methods
Two-ball phantom
A two-ball phantom with a nominal 20 mm separation (ICT calibration sphere 20 mm 18040105, Goekeler Messtechnik GmbH, Lenningen, Germany) was utilised to assess the measurement accuracy of the CT systems. The phantom is composed of two high-precision ruby spheres, each with a diameter of 2 mm, connected by a CFRP rod (Fig 1). Ruby was chosen due to its ideal properties for X-ray tomography: it is extremely hard and chemically stable, and its high density and uniform composition provide excellent contrast and sharply defined edges in the resulting images. The definitive distance between the centres of the spheres is 19.89221 mm, a value certified by the German Accreditation Service (DAkkS; certificate: 49520) with a measurement uncertainty of only 0.0008 mm at a standard temperature of 20°C. This extremely low uncertainty confirms the phantom as a reliable gold standard for our study, ensuring that any measured deviations originate from the CT systems, not the phantom itself. The phantom was fixed in place using parafilm and styrofoam (for details see [38]).
CT scanning and reconstruction
The two-ball phantom was scanned in two micro-CTs (the tabletop oversize micro-CT SkyScan 1173 & the tabletop high-resolution micro-CT SkyScan 1272, Bruker, Kontich, Belgium) and a clinical system, a third-generation dual-source CT scanner (SOMATOM Force, Siemens Healthineers, Forchheim, Germany) (Table 1). Scans were conducted at an ambient temperature of approximately 20°C to match the phantom’s certification conditions and minimize any potential for thermal expansion artifacts.
In each case, a central and a peripheral position were selected. For the micro-CT scans, the voxel size was divided into three positions, designated as near, middle, and far, by positioning the sample holder (Table 2). Each combination was measured seven times, resulting in a total of 98 scans. The X-ray projection images were saved in 16-bit TIFF (micro-CT) format or as DICOM (dual-source CT). Reconstructed cross-sectional images were stored in 8-bit PNG format using the software NRecon (NRecon 1.7.5.0, Bruker).
Analysis of scan data
The two-ball phantom scans were analysed in two and three dimensions. The 3D analysis was conducted using Amira-Avizo 2022.1 (Amira-Avizo 2022.1, ThermoFischer Scientific, Waltham, USA). The two ruby spheres were segmented using either a grey threshold of 80–255 (dual-source CT scans) or Otsu partitioning (micro-CT scans) and then marked with a fitted sphere. The centre-to-centre distances of the spheres were calculated for each scan (Fig 1E). For 2D evaluation, the scans were first aligned in the DataViewer software (DataViewer 1.7.0.1, Bruker) and an image in which both spheres were positioned at the centre was saved for further evaluation. The distances between the centres of the spheres in the 2D image were then measured in the Fiji/ImageJ software (Fiji 2.15.1, National Institutes of Health, USA) using a circle selection (Fig 1D) [39]. Furthermore, to assess the scan sharpness in the centre or at the edge of the device measurement field, the grey values were measured for each sphere using a line of 50 pixels (25 pixels for scans of the dual-source CT), which was drawn over the edge of the sphere to the centre in Fiji/ImageJ (n = 112). A fit curve (Rodbard) was created for this grey value line and its gradient was calculated in the grey value range between 60–140. Scans of the phantom made by the dual-source CT were measured in sagittal and coronal plane. For measurements in the axial plane the scans were resliced using Analyze (Analyze 14.0, AnalyzeDirect, Overland Park, United States) from 97x97x400 µm voxels to 97x97x97 voxels to be processed without distortion in the DataViewer.
Statistical analysis
Statistical analysis was conducted using PAST software (version 4.16c, [40]). Given the non-normal distribution of the data, medians were compared using the Kruskal-Wallis test followed by Dunn’s post hoc test.
Results
To determine the measuring accuracy of clinical and micro-CT systems a calibrated two-ball phantom was scanned in a central or peripheral position using near, middle and far distances to the X-ray source.
Measurement accuracy
With an average measurement difference of −0.329 mm (±0.056 mm) in the 2D image and −0.334 mm (±0.055 mm) in the 3D image, the oversize micro-CT had the largest error of the three devices compared to the phantom size of 19.89221 mm (±0.0008 mm measurement uncertainty). The measurement results of the oversize micro-CT were significantly lower compared to the high-resolution micro-CT (p: < 0.001) and the dual-source CT (p: < 0.001). However, measurements of the phantom with the high-resolution micro-CT had a lower measurement deviation of 0.091 mm (±0.012 mm) in the 2D image and 0.088 mm (±0.011 mm) above the expected value. Measurements using the dual-source CT scans had an average deviation of 0.094 mm (±0.116 mm) in the 2D image and −0.045 mm (±0.111 mm) in the 3D image, but also the largest standard deviation of the measured values (Fig 2). The most accurate measurement of all device/position combinations was the 2D measurement of the dual-source CT (centre position, coronal plane) with a distance of 19.895 mm (±0.047 mm), corresponding to an error of 0.013%. In contrast, the largest error of 2.02% was found with the oversize micro-CT (at 11 µm voxel size, positioned at the edge of the field of view). Varying the phantom position between the centre and the margin of the measuring field did not result in significant differences in the measurement of the sphere distance in any device. Changing the sample holder position (near, centre and far from the X-ray source) also showed no significant differences in any of the devices tested. However, there are clear increments between the sample holder distances, especially in the oversize micro-CT (2D measurement in the central position: 19.499 ± 0.008 mm in the near range, 19.567 ± 0.012 mm in the middle range and 19.628 ± 0.012 mm in the far range, Fig 2). The results are summarized in Table 3.
CT scans of a calibrated 19.89221 mm (±0.0008 mm) two-ball phantom (blue line) were analysed in (A) 2D cross-sections and (B) 3D volume renderings and shown as violin plots (median, quartiles and distribution). Scans taken with the oversize micro-CT were below the correct phantom length and scans taken with the high-resolution micro-CT were above the correct phantom length. Dual-source CT scans were analysed in the sagittal plane in addition to the coronal plane.
By calibrating the CT scan data with the two-ball phantom for each position and distance setting using the mean values, the measurement result can be improved (Fig 3). After adjusting the averages to the size of the phantom (19.89221 mm), very accurate measurement values were obtained for the micro-CTs. The measured values of the oversize micro-CT were in the range between 19.877 mm and 19.899 mm (0.021 mm difference) and those of the high-resolution micro-CT were in the range between 19.884 mm and 19.900 mm (0.016 mm difference) in the 3D image. The range of measurements for the dual-source CT scans was between 19.763 mm and 20.076 mm (0.313 mm difference) and was therefore larger than for micro-CT. The range of the measurements for the 2D image showed a similar picture but was slightly higher than that for the 3D image. For the oversize micro-CT, the values were in the range between 19.875 mm and 19.910 mm (0.035 mm difference), for the high-resolution micro-CT in the range between 19.873 mm and 19.908 mm (0.034 mm difference) and for the dual-source CT in the range between 19.732 mm and 20.146 mm (0.414 mm difference).
Measurement results after adjustment of the mean values to the size of the calibrated two-ball phantom of 19.89221 mm (blue line) in (A) 2D cross-sections and (B) 3D volume renderings. The corrected results show a good representation of the actual phantom size. Measurement of scans taken with the SOMATOM Force showed a greater scatter of data compared to the micro-CTs.
To visually demonstrate the impact of calibration, the uncalibrated measurement error can be compared directly against the corrected measurement. After applying the calculated correction factor, the adjusted measurement (Fig 4) accurately reflects the true phantom geometry.
An overlay on a 2D slice from the oversize micro-CT shows the uncalibrated measured distance (red line and overlay), which is visibly shorter than the actual center-to-center distance. After applying the correction factor derived from the phantom, the calibrated measurement (blue line) accurately aligns with the centers of the two ruby spheres, demonstrating the effectiveness of the calibration.
Scan sharpness
In each CT scan, a profile line was placed over the outer edge of the ruby spheres in the 2D view. The slope of the profile line (Fig 5A) corresponds to the transition of the image from the background (black) to the radiopaque ruby ball (white). A decrease in the clarity of the edge of the phantom results in a corresponding decrease in the gradient of the profile line (Figs 5 and 6, S1 Fig). No significant differences were identified between the phantom positions (centre, margin) and the various measurement distances (near, middle and far) for scans conducted with the oversize micro-CT and the dual-source CT. Scans with the high-resolution micro-CT were significantly sharper in the near position (6 µm voxel size) (p central/margin: 0.003/0.001) than in the far position (23 µm voxel size). The scans obtained with the high-resolution micro-CT exhibited the greatest gradient of the profile line in the near position (central: 15.21 ± 2.12 grey values/µm, margin: 16.35 ± 3.82 grey values/µm). The scans performed on the dual-source CT exhibited the lowest gradient of the profile line, with values of 0.34 ± 0.05 grey values/µm for the central coronal scan and 0.29 ± 0.07 grey values/µm for the outer coronal scan. The differences in quality of the various voxel sizes are also evident in the FFT conversion of the respective sphere images (Fig 6). At far measurement positions, clear ring-shaped gradations are visible in the FFT display, which are caused by softer image edges.
A profile line of 50 pixels (25 pixels for SOMATOM Force scans) was placed over the outer edge of the ruby ball in each CT scan in the 2D view to determine the gradient of the grey values. (A) The slope of the fit curves (Rodbard fit) with a grey value between 60 and 140 (grey box) was determined for the profile lines and shown as an example for a scan in the high-resolution micro-CT (11 µm voxel size, central position) in red and the oversize micro-CT (20 µm voxel size, central position) in green. (B) Comparison of the slope of the profile lines (B). In the micro-CTs, scans with smaller voxel sizes have steeper profile lines. The steepest profile lines were measured in the high-resolution micro-CT scans.
A cross-sectional view of the top ruby sphere of the phantom is presented in the 2D view with differing scan parameters (left) and the corresponding FFT conversion (right). Positions and voxel sizes were varied. For better interpretation, a computer-generated virtual phantom was added as an idealized reference case (bottom right image pair). This virtual image was created with a defined, slight blur at the edge to serve as a benchmark. The FFT of this virtual phantom produces a characteristic checkered pattern, which serves as a reference for how a blurred edge is represented in the frequency domain. In comparison, the FFTs of the real scans with larger voxel sizes (e.g., 23 µm) and consequently lower edge sharpness show ring-shaped gradations, indicating greater image blur. Scale: 3 mm.
Discussion
In this study, the measurement accuracy of CT systems using a two-ball phantom is compared to assess whether it is necessary to check measurements with these devices by means of a further calibration scan with a phantom. While factory-calibrated settings provide a baseline accuracy, additional calibration with a phantom, such as the two-ball phantom used in this study, can significantly improve measurement precision. This is particularly crucial for applications requiring high accuracy, such as in clinical diagnostics, biological research and material sciences.
Accuracy of the CT systems
Micro-CT systems are renowned for their high resolution, which is vital for comprehensive imaging of minute structures. The findings of this study demonstrate that the high-resolution micro-CT yielded the most uniform results with minimal variance, a conclusion supported by other research that underscores the superiority of micro-CT in visualising intricate details. [21]. This consistency is essential for applications that are dependent on high precision.
It was surprising to find that measurement errors of up to 2% (~0.3 mm below the expected value) could occur depending on the distance of the phantom with the oversize micro-CT. The results demonstrated that the errors were not randomly distributed but rather exhibited consistency, albeit dependent on the voxel size utilized. In this context, the smallest voxel size (best resolution) exhibited the greatest measurement error, while the largest voxel size (poorer resolution) demonstrated the most accurate measurement. This stepwise gradation of the measurement results is likely due to the internal calibration of the device, which estimates the size of the projected image on the detector. The oversize micro-CT, although less accurate than the high-resolution micro-CT, still provided reliable measurements within a narrow range after calibration.
Clinical CT systems, such as the dual-source CT, are designed to facilitate imaging of larger structures, including the human body. These systems typically have larger voxel sizes (e.g., 97.7 µm), which limits their resolution and precision in comparison to micro-CT systems. Notwithstanding, the dual-source CT exhibited a small average deviation of 0.094 ± 0.116 mm in 2D and 0.045 ± 0.111 mm in 3D images in comparison to micro-CT systems. However, this was accompanied by a larger standard deviation, indicating less consistency. The variability in measurement accuracy observed in the dual-source CT is consistent with the findings of Saxena et al. [41], who noted that clinical CT protocols can have difficulty discriminating fine details, such as nasal cartilage boundaries, in comparison to micro-CT. Nevertheless, the measurements of scans with the dual-source CT are remarkably accurate. This is also in line with measurements by Windfelder et al., who were able to measure and distinguish different pore sizes starting from 0.6 mm with an increment of 0.2 mm very consistently in a Derenzo phantom [23] in the same system.
Recalibration of the factory settings
Systematic errors in CT measurements can arise from various sources, including inaccuracies in the measurement of distances between the X-ray source and the sample or detector. The utilisation of two-ball phantoms for the calibration of length measurements in CT systems, both dual-source CT and micro-CT, is a crucial practice to ensure the accuracy and precision of measurements. Calibration with a two-ball phantom is an important step in achieving high accuracy in CT measurements, as it provides a reliable reference for spatial resolution and geometric accuracy. Zemek et al. [31,42] constructed a self-designed two-ball phantom comparable to the phantom employed in this study, albeit with 0.3 mm ruby spheres, for the calibration of minute field of views in micro-CT scanners. The measurement of center-to-center distances between two spheres is minimally affected by edge detection and beam hardening, making it a robust method for voxel size calibration [43]. This is particularly important in micro-CT systems, where even small deviations can significantly impact measurement accuracy due to the high resolution involved. Once the error factor (the average measurement deviation against the phantom length of 19.89221 mm) had been taken into account, it was found that all devices were capable of measuring with great precision (Fig 3). (The standard deviation of the micro-CT was found to be no greater than 0.005 mm, while that of the dual-source CT was 0.067 mm in relation to the expected value).
Influence of the phantom position on the resolution
The sharpness of edges in CT phantoms is of paramount importance for accurate imaging and analysis. It is indicated that the modulation transfer function (MTF) varies significantly across the field of view (FOV), suggesting that edges may indeed be sharper in the center compared to the periphery. MTF measurements of Sari et al. [44] showed a sharpness decrease as the FOV increases, with a notable difference in MTF values (10% and 50%) between smaller and larger FOVs, indicating sharper edges at the center. The study highlights that noise levels decrease with larger FOVs, which may contribute to perceived edge sharpness [44]. The profile lines across the edges of the phantom in this study demonstrated no statistically significant differences in their slope when positioned centrally or at the margin. A smaller voxel size, on the other hand, led to a significantly steeper slope of the profile lines. In contrast, a reduction in voxel size resulted in a markedly more pronounced slope of the profile lines. Consequently, in the context of micro-CTs, the voxel size appears to exert a greater influence on image sharpness than the positioning within the central field of view.
Sources of measurement error and the role of calibration
Our results reveal that while all CT systems provide solid measurements, their inherent accuracy and precision vary significantly. Systematic errors, as seen prominently in the oversize micro-CT, can arise from multiple sources. The stepwise gradation of error with changing voxel size in the oversize micro-CT strongly suggests an inaccuracy in the system’s internal geometric calibration model, which estimates object size based on the projection geometry. This model may be less robust when extrapolating across the full range of possible sample magnifications. Crucially, our study demonstrates that such systematic, device-specific errors can be effectively corrected by applying a correction factor derived from a simple phantom scan.
The higher variability (i.e., larger standard deviation) observed in the dual-source clinical CT has different origins. It is primarily attributable to its much larger voxel size (e.g., 97.7 µm x 97.7 x 400 µm) compared to the micro-CT systems. These large voxels lead to more significant partial volume effects at the curved surface of the spheres, making the precise determination of the sphere’s geometric center less consistent across repeated measurements.
Beyond voxel size, the fundamental differences in hardware and software between the micro-CT systems and the clinical dual-source CT significantly contribute to the observed variations in measurement accuracy. The system components are optimized for vastly different applications. The micro-CT systems utilize high-density flat-panel sensors (e.g., 4096x4096 pixels) paired with a very small X-ray focal spot size (< 5 µm), which is fundamental for achieving high intrinsic spatial resolution. In contrast, the clinical SOMATOM Force detector (StellarInfinity) is optimized for rapid, low-dose acquisitions over a large anatomical field of view, which typically involves larger detector elements. This inherently limits its ability to resolve fine details with the same fidelity as a micro-CT detector. The reconstruction parameters also diverge based on their primary goal. The clinical CT employed a tin filter for spectral shaping, a technique used to optimize image quality and dose in advanced clinical protocols like dual-energy imaging. Such spectral filtering, combined with the sophisticated iterative reconstruction algorithms common in modern clinical scanners, is designed to manage noise and enhance diagnostic contrast in patient scans. This approach differs significantly from the simpler aluminum filtration and the cone-beam reconstruction algorithms (e.g., NRecon software) used for the micro-CTs, which are primarily aimed at achieving high geometric fidelity. Collectively, these differences in detector technology, X-ray spot size, reconstruction strategy, and acquisition geometry explain why the micro-CT systems, while exhibiting systematic errors that necessitate calibration, offer higher intrinsic precision for metrological tasks. The clinical CT, on the other hand, is optimized for patient safety, speed, and diagnostic image quality over ultimate measurement precision.
It is also important to acknowledge the limitations of the two-ball phantom used in this study. While excellent for calibrating linear distance and voxel size, it does not assess more complex, non-linear geometric distortions across the field of view, such as barrel or pincushion distortion. For such comprehensive geometric characterization, alternative phantoms like 3D grid phantoms would be required. Nevertheless, for a vast number of applications based on linear measurements, the two-ball phantom provides a robust, accessible, and highly effective method for accuracy correction.
Conclusion
In conclusion, this study demonstrates that relying solely on factory calibrations for CT and micro-CT systems can lead to significant and systematic measurement errors. The necessity of user-performed calibration was confirmed, as applying a correction factor derived from a simple two-ball phantom dramatically improved measurement accuracy across all tested devices. Our findings show that the high-resolution micro-CT provides the most consistent measurements, making it superior for applications requiring high precision. For micro-CT measurements in particular, where errors can be dependent on the voxel size setting, probes should ideally be measured at a consistent voxel size, and a corresponding correction factor from a phantom scan should be applied for each measurement series. However, even less precise systems can yield highly accurate data once calibrated. Therefore, we conclude that the routine use of calibration phantoms is an essential and effective procedure to ensure measurement accuracy. We recommend that such a calibration be performed regularly (e.g., quarterly) and after any system maintenance or software update to guarantee the reliability of CT-based metrology in both research and clinical applications.
Supporting information
S1 Fig. Phantom edge profile curves in pixel.
A profile line of 50 pixels (25 pixels for scans of the SOMATOM Force) was placed over the outer edge of the ruby spheres in each CT scan in the 2D view. This was done to determine the gradient of the grey values. The slope of the fit curves (Rodbard fit) was determined for the profile lines and compared with each other. The steepest profile lines were measured in the scans of the high-resolution micro-CT.
https://doi.org/10.1371/journal.pone.0332263.s001
(TIF)
Acknowledgments
We would like to thank Dr. Markus J. Heneka for discussions regarding technical aspects.
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