Welcome to the 7th issue of XCT Mastery Monthly! In this issue, I will be diving into the fascinating and fundamental concept of resolution. While it may sound like a simple term, understanding resolution is crucial for anyone working with X-ray computed tomography (XCT). We will explore what resolution truly means in the context of XCT, how it is measured, and why it is so critical for obtaining accurate and meaningful data. Join us as we decode this core concept and help you achieve mastery in your XCT applications.

1. The quest for clarity in XCT

Resolution stands as a paramount determinant of image quality in XCT, fundamentally influencing the utility and reliability of the acquired data across a plethora of applications. In the medical domain, high resolution is indispensable for accurate diagnosis, enabling the visualisation of minute anatomical details such as bone trabeculae or the early detection of small lesions, which can be critical for tumour identification. For industrial applications, resolution is equally crucial, underpinning the precise characterisation of materials by revealing features like cracks, pores, and complex microstructures that are otherwise undetectable. Beyond mere visualisation, resolution directly impacts the precision of quantitative analyses, including dimensional measurements, surface texture assessment, and porosity quantification, particularly for small-scale structures within dense materials.

The ability of an XCT system to deliver high-fidelity images directly translates into actionable insights, influencing critical clinical decisions and optimising industrial processes. Enhanced resolution can facilitate the early detection of defects or pathologies, leading to improved outcomes, reduced costs, and accelerated research and development cycles. This issue aims to provide a comprehensive exploration of XCT resolution, distinguishing between its various forms, dissecting the intricate factors that influence it, and examining the cutting-edge methodologies employed for its optimisation and enhancement.

2. Understanding the fundamentals: voxel size vs. spatial resolution

The concept of resolution in XCT is often discussed in two distinct yet interrelated forms: voxel size resolution and spatial resolution. While both are crucial for image quality, they describe different aspects of an imaging system's capability.

  • Definingvoxel size resolution: the digital representation

Voxel size resolution refers to the physical dimensions of the smallest discrete volume element, or voxel (volumetric pixel), that constitutes the reconstructed three-dimensional CT image (Fig. 1). It defines the digital sampling grid upon which the continuous physical information of the scanned object is mapped. The voxel dimensions are fundamentally determined by the detector pixel size divided by the geometric magnification factor of the XCT system. For example, if an XCT system employs a detector with 50 µm pixels and operates at a geometric magnification of 5X, the resulting voxel size in the reconstructed image would be 10 µm.


Figure 1 - From 2 2-dimensional pixel to 3-dimensional voxel

It is fundamental to recognise that voxel size primarily represents a digital sampling parameter. While a smaller voxel size allows for a finer digital representation of the object, simply reducing the voxel size artificially – for instance, through interpolation or by computationally dividing existing voxels into smaller sub-pieces – does not inherently improve the true spatial resolution of the system. This distinction is crucial for accurate interpretation of image quality; a finer digital grid cannot recover information that was never captured by the physical imaging process.

  • DefiningSpatial Resolution: the true measure of detail

Spatial resolution, in contrast, is a more comprehensive and fundamental metric. It quantifies the ability of an imaging system to distinguish between two adjacent structures or to differentiate small, closely spaced objects. This metric reflects the system's genuine capacity to render fine details of the scanned object.

Unlike voxel size, spatial resolution is not solely a digital parameter. It is profoundly influenced by the interplay between the voxel resolution and the Point Spread Function (PSF) of the entire imaging system (Fig. 2). The PSF, discussed in detail in the subsequent section, encapsulates the inherent blurring characteristics of the system. Furthermore, the actual spatial resolution achieved in an XCT image is significantly affected by other critical image quality parameters, including the contrast between different features, the Signal-to-Noise Ratio (SNR), and the presence of various image artefacts.


Figure 2 - Interplay of real object with the PSF with the final resulting image

The relationship between voxel size and spatial resolution is one of causal dependency and interrelation. While voxel size establishes the maximum possible spatial resolution that can be achieved, constrained by the Nyquist limit, the actual spatial resolution is frequently limited by the system's inherent blurring, as characterised by its PSF, and by other important image quality factors such as contrast and noise. This means that merely employing a tiny voxel size is insufficient to guarantee high spatial resolution if the underlying physical image is fundamentally blurred or obscured by noise. The digital sampling rate must be appropriate for the physical image quality; sampling an already blurry image more finely will not sharpen it, but rather may just represent the blur with more pixels.

  • TheNyquist criterion: Sampling for information capture

The Nyquist criterion, a direct application of the Nyquist-Shannon Sampling Theorem from information theory, is a foundational principle in digital imaging. It stipulates that to accurately resolve a feature, the sampling frequency (which is the inverse of the sampling distance or voxel size) must be at least twice the highest spatial frequency present in the object or image. In practical terms, this translates to a requirement that the pixel or voxel size needs to be half or smaller than the smallest feature size one intends to image.

At the UCL Centre for Correlative X-ray Microscopy, we have 4 XCT scanners available, varying in maximum spatial resolution achievable:


The UCL Centre for Correlative X-ray Microscopy suite resolution range (approximated)

This criterion determines the minimum sampling density necessary to capture all available information from the object into the digital image. Failure to adhere to this principle, a condition known as undersampling (where the sampling distance exceeds the Nyquist distance), leads to irreversible information loss and the introduction of "aliasing artefacts". These artefacts can manifest as jagged edges, often referred to as staircasing, or as artificial fringes in the image, both of which are notoriously difficult to remove post-acquisition.

A crucial aspect of this principle is that the ideal sampling rate, or "critical sampling distance," is intrinsically linked to the system's "bandwidth," which is itself determined by the Point Spread Function. This connection underscores the profound interdependency among sampling, the system's inherent blurring, and the fundamental limits of information capture. The Nyquist criterion is not simply a technical guideline; it is a fundamental principle of information theory. It defines the minimum sampling rate required to avoid irreversible loss of information from the system's bandwidth, which is directly characterised by the PSF. In our Nikon XTH 225, for example, we have a PerkinElmer 1620 detector with 2028 * 2028 pixels available. The ideal number of projections is 3185. This is given by the following relation:

(# PixelDetector * π)/2

or

(2028 * 3.14159265359)/2 = 3185

Consequently, achieving high spatial resolution necessitates a dual approach:

  1. First, theimaging system must produce a sharp physical image, implying a narrow PSFand high bandwidth;

  2. Second,the digital acquisition must sample that image sufficiently finely,meaning a voxel size small enough to meet the Nyquist requirement.

Disregarding the Nyquist criterion can lead to artefacts that either mimic real features or obscure them, thereby fundamentally compromising image integrity and potentially leading to erroneous interpretations. The issue with undersampling is particularly severe because it introduces irreversible errors, making the lost information permanently unrecoverable and the resulting image potentially misleading.

3. Point spread function (PSF) and Line spread function (LSF)

The clarity and detail observed in an XCT image are fundamentally governed by the system's inherent blurring characteristics, which are quantitatively described by the Point Spread Function (PSF) and its related metrics.

  • PointSpread Function (PSF): characterising system response and image blurring

The Point Spread Function (PSF) is a cornerstone concept in imaging science, serving as the fundamental descriptor of an imaging system's response to an ideal point source or object. Conceptually, if an infinitesimally small, perfectly bright point of X-rays were to pass through the system, the PSF would delineate the "shapeless blob" that appears in the reconstructed image due to the system's inherent imperfections and spreading effects.

More formally, the PSF is the system's impulse response function (IRF) in the spatial domain, representing how the system "spreads" or "blurs" an ideal input. The formation of any image in a linear imaging system, which XCT largely approximates, can be mathematically understood as a convolution of the true object with the system's PSF. This mathematical operation precisely describes how the PSF blurs the observed image, effectively distributing the details of the object across neighbouring pixels or voxels.

The extent of spreading or blurring represented by the PSF is a direct measure of the imaging system's quality. A narrower, more concentrated PSF indicates a sharper image and, consequently, higher spatial resolution. For an ideal circular aperture, the PSF theoretically takes the form of an Airy disk (Fig. 3), which defines the diffraction limit of resolution.


Figure 3 - Airy disk

The PSF in an XCT system is not a singular entity but a composite effect, resulting from the convolution of blurring contributions from multiple sources within the X-ray path. Key contributors include the X-ray source's focal spot size and any associated drift, the intrinsic PSF of the detector itself, the PSF of the scintillator (in indirect conversion detectors), and the PSF of any lens system present in the optical path. Furthermore, properties inherent to the sample, such as refractive index mismatches, can distort the PSF, causing it to become elongated or asymmetrical, with the distortion often increasing with imaging depth. This cumulative blurring from various components is the primary physical limitation to spatial resolution, regardless of how finely the image is sampled digitally.

The ability to accurately measure or model this complex, composite PSF is critical, not only for understanding system performance but also for enabling computational resolution enhancement techniques like deconvolution. Deconvolution is a powerful computational method that, by mathematically "undoing" the convolution process, can bring the acquired microscopy image closer to the true object, thereby improving both resolution and signal-to-noise ratio. The fact that the PSF can be distorted by sample properties, such as refractive index mismatch, highlights the complexity of real-world XCT. This suggests that a single, theoretical PSF might not be sufficient for optimal deconvolution in all cases, potentially necessitating adaptive or experimentally measured PSFs to achieve the best image restoration.

  • LineSpread Function (LSF): A Practical Derivative of PSF

The Line Spread Function (LSF) is closely related to the PSF and offers a more practical approach to characterising resolution, especially in systems where a perfect point source is difficult to realise. The LSF describes the spreading behaviour of X-rays or light from a theoretical line object. In practice, it can be measured by imaging a very thin wire or a sharp edge, which serves as an approximation of an ideal line.

The LSF can be directly calculated as the derivative of the Edge Spread Function (ESF), which measures the variation in pixel values across a sharp edge. This method is commonly employed in quality assurance protocols and for general system characterisation. By fitting the experimentally derived LSF with a suitable mathematical function, such as a double Gaussian, quantitative parameters related to the lateral resolution can be extracted. The LSF provides a practical and repeatable method for assessing system blur in a quantifiable manner.

  • KeyMetrics: Full Width at Half Maximum (FWHM) and Full Width at Tenth Maximum(FWTM)

From the LSF (or PSF) curve, several quantitative metrics are derived to express resolution:

  1. FullWidth at Half Maximum (FWHM): This widely usedmetric quantifies the width of the LSF or PSF curve at which the intensityhas dropped to one-half of its maximum value. A smaller FWHM indicates amore concentrated, sharper point or line, and thus signifies betterresolution. It is a common measure of the effective spread of the system'sresponse.

  2. FullWidth at Tenth Maximum (FWTM): Similar toFWHM, the FWTM measures the width of the LSF or PSF curve where theintensity has dropped to one tenth of its maximum value. FWTMprovides a broader assessment of the blur, including the "tails"of the spread function, which can be important for detecting faint signalsor distinguishing features with low contrast.

  • ModulationTransfer Function (MTF): Quantifying Resolution in the Frequency Domain

While PSF and LSF describe resolution in the spatial domain, the Modulation Transfer Function (MTF) quantifies it in the frequency domain. The MTF expresses the fidelity with which object information is transferred to the image as a function of spatial frequency in the object. It is a powerful tool for objectively comparing the resolution performance of different imaging systems.

The MTF is mathematically defined as the magnitude of the Fourier Transform of the Line Spread Function (LSF). Alternatively, it can be derived from the Edge Spread Function (ESF) by differentiation to obtain the LSF, followed by a Fourier Transform. This process allows for a quantifiable and repeatable assessment of how well small structures (high spatial frequencies) are preserved in the image.

In an ideal imaging system, the MTF would remain at a value of 1 (or 100%) across all spatial frequencies, indicating perfect transfer of all details. However, in real systems, the MTF curve typically decreases as spatial frequency increases, reflecting the system's inability to perfectly reproduce very fine details (Fig. 4). Small image structures correspond to high spatial frequencies, while large structures correspond to low frequencies. A system with higher resolution will exhibit higher MTF values at higher spatial frequencies, meaning it can differentiate more bar patterns in a resolution phantom.


Figure 4 - Modulation transfer Function

The MTF provides a more objective and quantitative measure of resolution compared to direct observation methods using bar patterns, which can be subjective and dependent on the observer. By scanning a thin wire, for instance, and taking its Fourier Transform, the MTF can be accurately determined, providing a standardised metric for system performance.

4. Sources of unsharpness and blurring in XCT

Image blurring and unsharpness in XCT can arise from various physical and computational factors, each contributing to the degradation of spatial resolution. Understanding these sources is crucial for effective mitigation and optimisation.

  • GeometricUnsharpness (Penumbra)

Geometric unsharpness, often referred to as the "penumbra effect," describes the blurring at the edges of a scanned object due to the finite size of the X-ray source's focal spot and the geometric arrangement of the source, object, and detector. A penumbra appears as a less-defined, blurred area at the object's edges (Fig. 5). Minimising this effect is essential for producing clear, reliable images, particularly for identifying nonconformities or verifying dimensions in industrial radiography.


Figure 5 - Penumbra effect (edge blurring)

Three primary geometric factors influence the degree of unsharpness:

  1. X-raySource Focal Spot Size: The size of the X-raysource's focal spot has a direct relationship with geometric unsharpness.A smaller focal spot size significantly enhances image resolution,resulting in greater sharpness and clarity by reducing the penumbraeffect. Conversely, larger focal spots produce images with more geometricunsharpness and reduced spatial resolution. For example, nanoCT systems,with their micron-sized focal spots, demonstrate clear advantages inproducing sharp edges and revealing finer details compared to microCTimages.

  2. Source-to-ObjectDistance (SOD): The SOD is the distancebetween the X-ray source and the test object. It has an inverserelationship with geometric unsharpness; increasing the SOD reducesunsharpness and improves image definition.

  3. Object-to-DetectorDistance (OID): The OID is the distancebetween the test object and the imaging detector. This distance has adirect relationship with geometric unsharpness, meaning that minimisingthe OID improves image sharpness. However, increasing the OID can lead tohigher geometric magnification, which might be desirable for resolvingsmall features, but it necessitates a longer exposure time or more intenseradiation to maintain image visibility.

The basic formula for calculating geometric unsharpness (Ug) is: Ug = f * b / a, where 'f' is the source size, 'b' is the object thickness, and 'a' is the object-to-detector distance.  

  • Detector-InducedBlur

The detector panel itself introduces blur, imposing a fundamental limit on the achievable resolution. This blur arises from several factors inherent to the detector's design and operation:

  1. DetectorPixel Size: The physical size of the detectorpixels directly influences the minimum achievable voxel size and,consequently, the spatial resolution. While a smaller pixel size isgenerally desirable for higher resolution, it is only one component of theoverall system PSF.

  2. ScintillatorProperties: In indirect conversion detectors,X-rays are first converted into visible light by a scintillator layer,which is then detected by a photodiode array or CCD. The properties of thescintillator, such as its thickness and material, significantly affect thedetector's PSF. Thinner scintillating crystals generally provide betterintrinsic resolution, but at the cost of reduced sensitivity. Theeffectiveness of the scintillator material in converting X-ray energy intolight photons and its emission spectrum's compatibility with the detectorare critical.

  3. DetectorCross-Talk: Energy from one sensor pixel canleak into neighbouring sensor pixels, a phenomenon known as detectorcross-talk. This leakage causes additional blur and reduces imagecontrast.

  • MotionBlur

Motion blur occurs when there is relative movement between the X-ray source, the object, and the detector during the image acquisition process. This movement can be caused by vibrations in the sample stage or imaging equipment, or by patient movement in medical applications. Motion blur reduces image sharpness and clarity, making it difficult to resolve fine features and accurately estimate physical distances between image features. Mitigating motion blur is critical for applications requiring precise dimensional metrology or the detection of small features like tumours.

Strategies to minimise motion blur typically involve reducing exposure times, stabilising the sample and imaging equipment, and, in some cases, using specialised software or hardware solutions designed for dynamic imaging.

  • Reconstruction-InducedBlur and Artefacts

Image reconstruction is a mathematical process that transforms the acquired X-ray projection data into tomographic images. The choice of reconstruction method and its parameters can significantly impact image quality, including spatial resolution and noise.

  1. ReconstructionKernels (Filters): In filtered backprojection(FBP), the most common analytical reconstruction method, a 1D filter (orkernel) is applied to the projection data. The selection of this kernelpresents a fundamental trade-off between spatial resolution and noise. Asmoother kernel generates images with lower noise but at the expense ofreduced spatial resolution. Conversely, a sharper kernel produces imageswith higher spatial resolution but increases image noise. The optimalkernel choice depends on the specific clinical or industrial application.

  2. SliceThickness: This parameter controls the spatialresolution in the longitudinal (z-axis) direction and also influences thetrade-offs among resolution, noise, and radiation dose. Thinner slicesgenerally offer better axial resolution but may increase noise and dose.

  3. BeamHardening Artefacts: X-ray beams used in CTare typically polychromatic, meaning they consist of a range of X-rayenergies. As these X-rays pass through an object, lower-energy photons arepreferentially absorbed, causing the beam's average energy to increase, aphenomenon known as "beam hardening". Most reconstructionalgorithms, however, assume a monochromatic (single-energy) X-ray beam.This mismatch between the assumption and reality leads to artefacts thatappear as cupping (varying grey levels within a uniform density object) orstreaks in the reconstructed images, significantly reducing image qualityand mimicking blurring. These artefacts can distort attenuationcoefficients, leading to systematic errors in CT numbers.

  4. IterativeReconstruction (IR): Unlike FBP, iterativereconstruction methods can more accurately incorporate important physicalfactors such as focal spot and detector geometry, photon statistics, X-raybeam spectrum, and scattering into the reconstruction process. This allowsIR to yield images with lower noise and higher spatial resolution comparedto FBP, and it can also reduce artefacts like beam hardening and metalartefacts. However, IR-reconstructed tomograms may have a differentnoise texture, and their local spatial resolution can be highlydependent on the contrast and noise of surrounding structures due to thenon-linear regularisation terms used in the optimisation process.

5. Optimising and enhancing XCT Resolution

Achieving optimal resolution in XCT involves a multifaceted approach, combining careful system configuration, advanced software techniques, and the adoption of cutting-edge hardware innovations.

  • SystemConfiguration and Scan Parameter Optimisation

Strategic choices in setting up the XCT system and defining scan parameters are fundamental to maximising resolution:

  1. GeometricMagnification: Increasing geometricmagnification by adjusting the source-to-object distance (SOD) andobject-to-detector distance (OID) allows for the projection of a largerimage of the object onto the detector, effectively reducing the effectivepixel size and thus the voxel size. This is a primary method for achievinghigher resolution, especially in X-ray microscopes. However, maximisingmagnification often requires a very small source-to-object distance, whichcan limit the working distance available for high-resolution analysis andconstrain the sample size. The size of the PSF is proportional tomagnification, meaning that while the relative blur might not worsen, theabsolute blur can increase.

  2. X-raySource Focal Spot Size: As discussedpreviously, a smaller focal spot size is directly correlated with reducedgeometric unsharpness and improved spatial resolution. Optimising thefocal spot size, often by adjusting the X-ray tube current, is a criticalstep in configuration.

  3. Voltage(kVp) and Current (mA): These parametersinfluence the X-ray beam's energy spectrum and intensity, respectively.Higher kVp (voltage) can improve penetration through dense materials butmay reduce contrast in low-density areas and affect beam hardening. Thecurrent (mA) affects the X-ray flux, which impacts the signal-to-noiseratio and, consequently, the effective resolution. Optimising theseparameters is a balance between achieving sufficient penetration,maintaining contrast, and minimising noise.

  4. Filters: Filters can be used to modify the X-ray spectrum, forinstance, to intentionally cause beam hardening (pre-harden the X-rays)and increase the X-ray peak energy, which can be beneficial forpenetrating denser materials. However, denser and thicker filters reduceX-ray intensity, potentially increasing data collection time and reducingsignal-to-noise ratio. Filters can also be used to mitigate beam hardeningartefacts by shaping the beam.

The optimisation of these parameters often involves trade-offs. For example, while a smaller focal spot improves sharpness, it may reduce the X-ray flux, requiring longer exposure times or higher currents, which can generate more heat and potentially broaden the focal spot or cause drift. A comprehensive understanding of these interdependencies is essential for selecting the optimal scan parameters for a given sample and desired resolution.

  • AdvancedSoftware Techniques

Software advancements play an increasingly vital role in enhancing XCT resolution, often mitigating the need for costly hardware modifications.

  1. Deconvolution: This is a powerful computational technique that aims toreverse the blurring effect introduced by the system's Point SpreadFunction (PSF). By mathematically modelling the PSF as a convolution ofthe true image, deconvolution algorithms can restore lost imageinformation, bringing the acquired image closer to the true object andsignificantly improving resolution and signal-to-noise ratio.Deconvolution can be applied to projection images to reduce focal spotblur, even restoring surface structures that might have been lost in theoriginal measurement. However, its effectiveness can be limited by severeimage noise, large image sampling distances, and significant initial imageblurring.

  2. IterativeReconstruction (IR): IR methods represent asignificant leap beyond traditional filtered backprojection (FBP)algorithms. They iteratively refine the reconstructed image byincorporating more accurate physical models of the X-ray acquisitionprocess, including factors like focal spot and detector geometry, photonstatistics, and beam spectrum. This allows IR to produce images with lowernoise and higher spatial resolution, and it is particularly effective atreducing common artefacts such as beam hardening and metal artefacts.While computationally more intensive, IR can lead to high-quality imagereconstruction with significantly shorter data collection times comparedto conventional FBP.

  3. ArtificialIntelligence (AI) and Deep Learning (DL): AI,particularly deep learning models, is rapidly transforming XCT imageprocessing and reconstruction. DL methods can be integrated into variousstages of the reconstruction workflow, from preprocessing topost-processing, offering software-based solutions for noise reduction andsuper-resolution without requiring hardware upgrades. AI-driven approacheshave demonstrated substantial improvements in noise reduction, artefactremoval, and real-time optimisation of imaging parameters, therebyenhancing diagnostic accuracy and potentially reducing radiation doses.For instance, deep learning models can effectively learn and correct fordeformation patterns like shrinkage and local distortions in additivemanufacturing, significantly improving registration accuracy between CADmodels and XCT data and reducing computational time from days to minutes.AI also holds promise for optimising acquisition protocols and improvingthe overall efficiency of XCT workflows.

  • Cutting-EdgeHardware Innovations

Advancements in X-ray sources and detector technologies are continuously pushing the boundaries of achievable resolution and imaging capabilities.

  • Next-GenerationX-ray Sources:

  1. NanofocusSealed Tube Transmission X-ray Sources: Thesesources combine high power and spatial resolution with maintenance-freeoperation, enabling sub-micron resolution (e.g., 0.5 µm spatial resolutionwith 70 nm minimum voxel size) even on large samples. https://www.sigray.com/apex-xct-150/

  2. LiquidMetal Jet Targets: A transformativetechnology, liquid metal jet X-ray tubes replace conventional solid-metalanodes with a continuously regenerated liquid-metal jet. This designovercomes the classical power limits of solid anodes, as the material isalready molten and constantly replenished, preventing damage from theelectron beam. This allows for significantly higher electron-beam powerand, consequently, higher X-ray flux and unprecedented brightness atmicron spot sizes. Such sources can enable a major increase in imageacquisition speed while maintaining resolution, or improve measurementthroughput with better precision and accuracy. They can achieve up to 27xhigher brightness than classical solid anode sources in the microfocusrange. https://www.excillum.com/products/metaljet/

  3. StructuredAnodes (e.g., Rotating Targets): Rotatingreflection targets, commonly used in medical and increasingly inindustrial CT, allow for increased electron flux without damaging thetarget by dissipating heat over a larger, moving area. This continuousregeneration of cooler anode material at the focal spot enables higherpower and stability, contributing to better resolution.

  • AdvancedDetector Technologies:

  1. Photon-CountingDirect Conversion Detectors (PCD-CT): Thistechnology represents a significant leap forward, overcoming limitationsof conventional energy-integrating detectors (EIDs). PCDs usesemiconductor materials (e.g., cadmium telluride, cadmium zinc telluride,silicon) to directly count individual X-ray photons while simultaneouslyresolving their energy levels. This energy-resolving capability ensuresequal weighting of low- and high-energy photons, eliminates electronicnoise, and enables material-specific imaging. The absence of physicalsepta, which are used in EIDs to prevent light photon cross-talk, resultsin smaller effective detector pixels in PCD-CT, enhancing detectionefficiency and spatial resolution. These innovations collectively lead tosuperior spatial and contrast resolution, spectral imaging capabilities,and significant noise reduction, all while enabling substantial radiationdose reduction.

  • EmergingImaging Modalities

Beyond conventional techniques, new imaging modalities are being developed to push the boundaries of XCT resolution.

  1. StructuredIllumination XCT: Drawing inspiration fromoptical microscopy, structured illumination techniques involve usingnon-uniform, patterned X-ray excitation light. By creating an overlapbetween the high-frequency organisation of the object and the highfrequency of the illumination patterns, lower-frequency patterns aregenerated that can be more easily collected by the objective. Thisapproach can significantly improve spatial resolution, potentiallydoubling it over wide-field microscopy, achieving resolutions ofapproximately 100 nm laterally and 250 nm axially. Recent researchcombines dark-field X-ray microscopy (DFXM) with structured illuminationto achieve precise 3D imaging of ordered materials at sub-micrometrelength scales without requiring sample rotation. This method encodes depthinformation along the diffracted beam by modulating intensity with a codedaperture, leading to a more stable and time-efficient imaging modality,particularly for in-situ experiments.

  2. PhaseContrast X-ray Imaging: Traditional XCT relieson the attenuation (absorption) of X-rays as they pass through a sample.Phase-contrast X-ray imaging, however, leverages the fact that differentmaterials also induce different phase shifts in the X-ray beam. Bytransforming these phase shifts into intensity variations that can berecorded by a detector, images with significantly enhanced contrast,particularly for low-Z elements and soft tissues, can be obtained. Thistechnique is especially useful for enhancing the contrast of surfaces andinterfaces that would be invisible using absorption contrast. Whilechallenging to implement due to the need for highly coherent X-ray beamsand specialised instrumentation, synchrotron facilities enable highspatial resolution phase contrast tomography, allowing for 3Dreconstruction of the real part of the refractive index. Ptychography,a lens-insensitive coherent diffraction imaging technique, is a promisingphase-contrast method that reconstructs high-resolution images byanalysing overlapping diffraction patterns, effectively solving the"phase problem" and providing quantitative images of bothabsorption and phase.

  3. Multi-scaleResolution: Many applications, particularly inmaterials science and electronics, require imaging features across a widerange of length scales, from millimetres down to tens of nanometers. Amulti-scale approach, which involves using imaging techniques with severalresolution ranges, is often necessary to fully characterise complexobjects. This can involve combining different XCT tools, such as microCTfor larger features and nanoCT for sub-micron or even sub-50 nm resolutionon smaller regions of interest. The development of two-stage magnificationapproaches and advanced X-ray optics like multilayer Laue lenses (MLL) forX-ray microscopes is enabling higher resolution at larger workingdistances or for smaller samples.

  4. Dynamic(4D) CT: This emerging diagnostic tool extends3D imaging by adding a fourth dimension: time. 4D CT involves acquiring aseries of 3D images over a period, allowing for the assessment of dynamicprocesses, such as joint movement in orthopaedics or fluid flow inmaterials. While offering invaluable information about dynamic pathologynot visible in static imaging, 4D CT protocols require careful managementof slice thickness, acquisition intervals, and radiation dose. The abilityto capture volumetric data throughout a movement series provides a uniqueperspective on functional changes and dynamic interactions within asample.

6. Conclusion: the future of XCT resolution

The pursuit of enhanced resolution in X-ray Computed Tomography is a continuous endeavour, driven by the ever-increasing demand for finer detail, greater accuracy, and more comprehensive insights across diverse fields. As explored in this issue, resolution in XCT is a complex concept, extending beyond simple voxel size to encompass the intricate interplay of system components, physical phenomena, and advanced computational techniques.

A fundamental understanding of the distinction between voxel size (a digital sampling parameter) and spatial resolution (the true measure of discernible detail, influenced by the system's Point Spread Function) is paramount. The Nyquist criterion underscores the critical importance of adequate sampling to capture the information bandwidth defined by the system's inherent blurring. The PSF, as the fundamental characteristic of an imaging system's blurring behaviour, is a composite of contributions from the X-ray source, detector, and even the sample itself, highlighting the need for a holistic approach to resolution optimisation. Metrics like LSF, FWHM, FWTM, and MTF provide the quantitative tools necessary to measure and compare system performance objectively.

The trajectory of XCT resolution points towards increasingly sophisticated systems capable of delivering sub-micron to nanometer-scale details across larger fields of view and with faster acquisition times. These continuous advancements will undoubtedly expand the applicability of XCT, enabling earlier detection of subtle features, more precise quantitative analyses, and deeper insights into the structural and functional properties of materials and biological systems. The future of XCT promises even greater clarity, pushing the boundaries of what is observable and measurable.

I hope you enjoyed this issue of XCT Mastery Monthly. Please like, comment and subscribe and forward the link to whoever might be interested in the fantastic world of XCT.

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