High-resolution X-ray CT (Computed Tomography) is a completely nondestructive technique for visualizing features in the interior of opaque solid objects, and for obtaining digital information on their 3-D geometries and properties. It is useful for a wide range of materials, including rock, bone, ceramic, metal and soft tissue. High-resolution X-ray CT differs from conventional medical CAT-scanning in its ability to resolve details as small as a few tens of microns in size, even when imaging objects made of high density materials.
The following overview is excerpted and adapted from several works, with the principal one being:
Ketcham, R.A. and Carlson, W.D., 2001. Acquisition, optimization and interpretation of X-ray computed tomographic imagery: Applications to the geosciences. Computers and Geosciences, 27, 381-400. [PDF]
Essentials of Computed Tomography
Acquisition of CT data
Resolution and Size Limitations
Artifacts and Partial-Volume Effects
“Tomos” is the Greek word for “cut” or “section”, and tomography is a technique for digitally cutting a specimen open using X-rays to reveal its interior details. A CT image is typically called a slice, as it corresponds to a slice from a loaf of bread. This analogy is apt, because just as a slice of bread has a thickness, a CT slice corresponds to a certain thickness of the object being scanned. Therefore, whereas a typical digital image is composed of pixels (picture elements), a CT slice image is composed of voxels (volume elements).
The gray levels in a CT slice correspond to X-ray attenuation, which reflects the proportion of X-rays scattered or absorbed as they pass through each voxel. X-ray attenuation is primarily a function of X-ray energy and the density and atomic number of the material being imaged. A CT image is created by directing X-rays through the slice plane from multiple orientations and measuring their resultant decrease in intensity. A specialized algorithm is then used to reconstruct the distribution of X-ray attenuation in the slice plane. By acquiring a stacked, contiguous series of CT images, data describing an entire volume can be obtained, in much the same way as a loaf of bread can be reconstructed by stacking all of its slices.
First developed for widespread use in medicine for the imaging of soft tissue and bone, X-ray CT was subsequently extended and adapted to a wide variety of industrial tasks. These latter developments, which demanded imagery of denser objects across a range of size classes and resolution requirements, provided key advances that greatly enhanced the potential for application of this technology to geological investigations.
To maximize their effectiveness in differentiating tissues while minimizing patient exposure, medical CT systems need to use a limited dose of relatively low-energy X-rays (<140 keV). They must also acquire their data rapidly because the patient should not move during scanning. To obtain the best data possible given these requirements, they use relatively large (mm-scale), high-efficiency detectors, and X-ray sources with a high output, requiring relatively large (mm-scale) focal spots.
Because industrial CT systems image only non-living objects, they can be designed to take advantage of the fact that the items being studied don't move and aren't harmed by X-rays. They employ the following optimizations: (1) Use of higher-energy X-rays, which are more effective at penetrating dense materials; (2) Use of smaller X-ray focal spots, providing increased resolution at a cost in X-ray output; (3) Use of finer, more densely packed X-ray detectors, which also increases resolution at a cost in detection efficiency; (4) Use of longer exposure times, increasing the signal-to-noise ratio to compensate for the loss in signal from the diminished output and efficiency of the source and detectors.
Essentials of Computed Tomography
Because industrial X-ray CT scanners are typically custom-built, no detailed description of their principles and operation will apply in all cases. Instead, we provide here a description of each component of the CT-scanning process, both in general terms and as specifically applied at the University of Texas High-resolution X-ray CT Facility. The material presented in this and subsequent sections is a combination of information provided with the UT system by the manufacturer (Bio-Imaging Research, Inc., of Lincolnshire, Illinois), insights gained from experience, and general principles derived from the literature. For a more complete technical overview of CT, we recommend ASTM publication E1441-92a (ASTM, 1992) as an excellent starting point. Very readable, if somewhat dated, synopses of medical CT and its components and history can be found in Hendee (1979) and Newton and Potts (1981).
The simplest common elements of X-ray radiography are an X-ray source, an object to be imaged through which the X-rays pass, and a series of detectors that measure the extent to which the X-ray signal has been attenuated by the object (Fig. 1). A single set of X-ray intensity measurements on all detectors for a given object position and scanner geometry is termed a view. The fundamental principle behind computed tomography is to acquire multiple views of an object over a range of angular orientations. By this means, additional dimensional data are obtained in comparison to conventional X-radiography, in which there is only one view.
First- through fourth-generation computed tomography systems utilize only rays in a single plane: the scan plane. In first-generation CT (Fig. 1a) this is done by directing a pencil beam through the object to a single detector, translating the source-detector pair across the extent of the object in the scan plane, then repeating the procedure from a number of angular orientations. Second-generation CT (Fig. 1b) uses the same scanning procedure, but a fan beam replaces the pencil beam and the single detector is replaced by a linear or arcuate series of detectors, leading to a higher rate of data acquisition. In typical third-generation CT (Fig. 1c), the fan beam and detector series are wide enough to encompass the entire object, and thus only rotation of the object or the source-detector combination is required. One variation of third-generation scanning offsets the sample from the center of the fan beam so that a part of it is outside of the beam, but the center of rotation is within it (Fig. 1d). As the object rotates, all of it passes through the fan beam, which permits reconstruction of a complete image. This technique allows larger objects to be scanned and permits smaller objects to be moved closer to the source into a narrower section of the fan beam, leading to increased resolution through enhanced utilization of detectors to image smaller subsections of the object in any one view. Third-generation scanning tends to be much faster than second-generation, as X-rays are utilized more efficiently. Most modern medical scanners are fourth-generation devices, consisting of a fixed complete ring of detectors and a single X-ray source that rotates around the object being scanned. In first- through third-generation scanners the motion between the object being scanned and the source-detector pair is relative, and can be accomplished either by keeping the object stationary and moving the source-detector pair, as is done in medical CT systems, or vice versa as is more common in industrial systems.
In volume CT, a cone beam or highly-collimated, thick, parallel beam is used rather than a fan beam, and a planar grid replaces the linear series of detectors. This allows for much faster data acquisition, as the data required for multiple slices can be acquired in one rotation. However, it is also computationally more intensive, prone to distortion, and in many cases provides lower-resolution images. Whereas volume CT has been largely perfected for some of the most advanced medical systems, and is ideally suited for tomography using parallel-beam synchrotron radiation, for industrial scanners it does not yet provide the same quality of imagery as single-slice arrangements.
|Figure 1: Schematic illustration of different generations of X-ray CT scan geometries. Solid arrows indicate movements during data collection, dashed arrows indicate movement between sequences of data collection. The solid lines passing from the sources to the detectors are ray paths, and each set of solid lines from a single angular orientation constitutes a view. These illustrations show the source and detectors moving around a stationary object, as is the case with medical scanners. The motion is relative, however, and in many industrial scanners the object moves while the source and detectors are stationary. In all cases, the axis of rotation is the center of the circle. A. First-generation, translate-rotate pencil beam geometry. B. Second-generation, translate-rotate fan beam geometry. C. Third-generation, rotate-only geometry. D. Third-generation offset-mode geometry.|
The important variables that determine how effective an X-ray source will be for a particular task are the size of the focal spot, the spectrum of X-ray energies generated, and the X-ray intensity. The focal-spot size partially defines the potential spatial resolution of a CT system by determining the number of possible source-detector paths that can intersect a given point in the object being scanned. The more such source-detector paths there are, the more blurring of features there will be. The energy spectrum defines the penetrative ability of the X-rays, as well as their expected relative attenuation as they pass through materials of different density. Higher-energy X-rays penetrate more effectively than lower-energy ones, but are less sensitive to changes in material density and composition. The X-ray intensity directly affects the signal-to-noise ratio and thus image clarity. Higher intensities improve the underlying counting statistics, but often require a larger focal spot.
Many conventional X-ray tubes have a dual filament that provides two focal-spot sizes, with the smaller spot size allowing more detailed imagery at a cost in intensity. Medical CT systems tend to have X-ray spot sizes that range from 0.5 mm to 2 mm. The high-resolution system at the UT CT Facility utilizes a dual-spot 420-kV X-ray source (Pantak HF420), with spot sizes of 0.8 and 1.8 mm. The small spot has a maximum load of 800 W (i.e., 2 mA at 400 kV), whereas the large spot has a maximum load of 2000 W. The 200 kV tube used for ultra-high resolution work (Feinfocus FXE-200.20) has an adjustable focal spot with a minimum size of <10 µm at 8 W total load, but at higher loads the spot size is automatically increased to prevent thermal damage to the target. In most cases a slightly “defocused” beam (larger spot size) can be used to improve counting statistics with little cost in resolution. Both sources have tungsten targets.
The energy spectrum generated is usually described in terms of the peak X-ray energy (keV or MeV), but actually consists of a continuum in which the level with maximum intensity is typically less than half of the peak (Fig. 2). The total "effective" spectrum is determined by a number of factors in addition to the energy input of the X-ray source itself, including autofiltering both by absorption of photons generated beneath the surface of a thick target (Silver, 1994) and by passage through the tube exit port; other beam filtration introduced to selectively remove low-energy X-rays; beam hardening in the object being scanned; and the relative efficiency of the detectors to different energies. As discussed below, changes in the X-ray spectrum caused by passage through an object can lead to a variety of scanning artifacts unless efforts are made to compensate for them.
|Figure 2: Theoretical energy spectra for a 420-kV X-ray source with a tungsten target, calculated combining 5-keV intervals. The spectra consist of continuous Bremsstrahlung and characteristic K-series peaks at 57-59 keV and 67-69 keV. The upper spectrum is modified only by inherent beam filtration by 3 mm of aluminum at the tube exit port. The mean X-ray energy is 114 keV. The lower curve represents a spectrum that has also passed through 5 cm of quartz. The preferential attenuation of low-energy X-rays causes the average energy to rise to 178 keV.|
As the X-rays pass through the object being scanned, the signal is attenuated by scattering and absorption. The basic equation for attenuation of a monoenergetic beam through a homogeneous material is Beer's Law:
where I0 is the initial X-ray intensity, µ is the linear attenuation coefficient for the material being scanned (units: 1/length), and x is the length of the X-ray path through the material. If the scan object is composed of a number of different materials, the equation becomes:
where each increment i reflects a single material with attenuation coefficient µi over a linear extent xi. To take into account the fact that the attenuation coefficient is a strong function of X-ray energy, the complete solution would require solving the equation over the range of the effective X-ray spectrum:
However, such a calculation is usually problematical for industrial CT, as the precise form of the X-ray spectrum, and its variation at off-center angles in a fan or cone beam, is usually only estimated theoretically rather than measured. Furthermore, most reconstruction strategies solve equation (2), insofar as they assign a single value to each pixel rather than some energy-dependent range.
There are three dominant physical processes responsible for attenuation of an X-ray signal: photoelectric absorption, Compton scattering, and pair production. Photoelectric absorption occurs when the total energy of an incoming X-ray photon is transferred to an inner electron, causing the electron to be ejected. In Compton scattering, the incoming photon interacts with an outer electron, ejecting the electron and losing only a part of its own energy, after which it is deflected in a different direction. In pair production, the photon interacts with a nucleus and is transformed into a positron-electron pair, with any excess photon energy transferred into kinetic energy in the particles produced.
In general for geological materials, the photoelectric effect is the dominant attenuation mechanism at low X-ray energies, up to approximately 50-100 keV. Compton scatter is dominant at higher energies up to 5-10 MeV, after which pair production predominates. Thus, unless higher-energy sources are used, only photoelectric absorption and Compton scattering need to be considered. The practical importance of the distinction between mechanisms is that photoelectric absorption is proportional to Z4-5, where Z is the atomic number of an atom in the attenuating material, whereas Compton scattering is proportional only to Z (Markowicz, 1993). As a result, low-energy X-rays are more sensitive to differences in composition than higher-energy ones.
The best way to gain insight into what one might expect when scanning a geological sample is to plot the linear attenuation coefficients of the component materials over the range of the available X-ray spectrum. These values can be calculated by combining experimental results for atomic species (e.g., Markowicz, 1993). Alternatively, mass attenuation coefficients can be obtained from the XCOM database managed by NIST. Mass attenuation coefficients must be multiplied by mass density to determine linear attenuation coefficients. To illustrate, Figure 3 shows curves for four minerals: quartz, orthoclase, calcite, and almandine garnet. Quartz and orthoclase are very similar in mass density (2.65 g/cm3 vs. 2.59 g/cm3), but at low energy their attenuation coefficients are quite different because of the presence of relatively high-Z potassium in the feldspar. With rising X-ray energy, their attenuation coefficients converge, and at approximately 125 keV they cross; above ~125 keV quartz is slightly (but probably indistinguishably) more attenuating, owing to its higher density. Thus, these two minerals can be differentiated in CT imagery if the mean X-ray energy used is low enough, but at higher energies they are nearly indistinguishable (Fig. 4). Calcite, though only slightly denser (2.71 g/cm3) than quartz and orthoclase, is substantially more attenuating, owing to the presence of calcium. Here the divergence with quartz persists to slightly higher energies, indicating that it should be possible to distinguish the two even on higher-energy scans. High-density, high-Z phases such as almandine are distinguishable at all energies from the other rock-forming minerals examined here.
|Figure 3: Linear attenuation coefficient as a function of X-ray energy for four rock-forming minerals. Such curves, when combined with the X-ray spectrum utilized for scanning (Fig. 2), allow prediction of the ability to differentiate between minerals in CT images.|
|Figure 4: A core of graphic granite imaged at various energy conditions. The field of view diameter for each image is 22 mm, and the slice thickness is 100 µm. Scan (A) was created using an X-ray energy of 100 keV and no beam filtration; scan (B) was acquired with an X-ray energy of 200 keV and a 1/8" brass filter. Both scans employed a "self-wedge" calibration.|
Detectors for CT scanners make use of scintillating materials in which incoming X-rays produce flashes of light that are counted. Detectors influence image quality through their size and quantity, and through their efficiency in detecting the energy spectrum generated by the source. The size of an individual detector determines the amount of an object that is averaged into a single intensity reading, while the number of detectors determines how much data can be gathered simultaneously. In third-generation scanning, the number of detectors also defines the degree of resolution possible in a single view, and thus in an image overall. The film used in conventional X-ray radiography is an excellent detector in that it consists, in essence, of a very large number of small and sensitive detectors. Unfortunately, it is not amenable to quickly producing the digital data needed for computed tomography.
The efficiency of scintillation detectors varies with X-ray energy, precisely because higher-energy X-rays are more penetrative than lower-energy ones, indicating that they are more capable of traveling through materials without interactions. This factor must be taken into account when determining the level of expected signal after polychromatic X-rays pass through materials.
The high-resolution system at UT has two separate detectors. The P250D detector consists of a linear array of 512 discrete cadmium tungstate scintillators with dimensions 0.25 mm x 5.0 mm x 5.0 mm, packed in a comb to prevent crosstalk between channels, and each connected to a Si photodiode. Its channel-to-channel pitch is 381 µm, and its total horizontal extent is 195 mm. The RLS (Radiographic Line Scanner) detector consists of a single 0.25 mm-thick gadolinium oxysulfide scintillator screen connected to a 2048-channel linear photodiode array using a fiber optic taper. The detector spacing is 50 µm, and the total detector extent is approximately 100 mm. The ultra-high-resolution scanner uses a 9-inch image intensifier (Toshiba AI-5764-HVP) as a detector. The image intensifier consists of a partial sphere of cesium iodide scintillators attached to a photocathode. The signal from the photocathode is electronically focused onto a phosphor screen, producing a real-time X-ray image. The image on the phosphor is converted to digital data using a 1024x1024 CCD video camera. The video signal, consisting of scan lines divided into pixels, is used to create a set of 1024 virtual detectors by software.
Acquisition of CT Data
Strictly speaking, the only preparation that is absolutely necessary for CT scanning is to ensure that the object fits inside the field of view and that it does not move during the scan. Because the full scan field for CT is a cylinder (i.e., a stack of circular fields of view), the most efficient geometry to scan is also a cylinder. Thus, when possible it is often advantageous to have the object take on a cylindrical geometry, either by using a coring drill or drill press to obtain a cylindrical subset of the material being scanned, or by packing the object in a cylindrical container with either X-ray-transparent filler or with material of similar density. For some applications the sample can also be treated to enhance the contrasts that are visible. Examples have included injecting soils and reservoir rocks with NaI-laced fluids to reveal fluid-flow characteristics (Wellington and Vinegar, 1987; Withjack, 1988), injecting sandstones with Woods metal to map out the fine-scale permeability, and soaking samples in water to bring out areas of differing permeability, which can help to reveal fossils (Zinsmeister and De Nooyer, 1996).
Calibrations are necessary to establish the characteristics of the X-ray signal as read by the detectors under scanning conditions, and to reduce geometrical uncertainties. The latter calibrations vary widely among scanners; as a rule flexible-geometry scanners such as the one at the University of Texas require them, whereas fixed-geometry scanners geared towards scanning a single object type may not.
The two principal signal calibrations are offset and gain, which determine the detector readings with X-rays off, and with X-rays on at scanning conditions, respectively. An additional signal calibration, called a wedge, used on some third-generation systems (including the UT facility) consists of acquiring X-rays as they pass through a calibration material over a 360º rotation. The offset-corrected average detector reading is then used as the baseline from which all data are subtracted. If the calibration material is air, the wedge is equivalent to a gain calibration. A typical non-air wedge is a cylinder of material with attenuation properties similar to those of the scan object. Such a wedge can provide automatic corrections for both beam hardening and ring artifacts, and can allow utilization of high X-ray intensities that would saturate the detectors during a typical gain calibration. Although widely employed in medical systems, which use phantoms of water or water-equivalent plastic to approximate the attenuating properties of tissue, the wedge calibration is relatively uncommon in industrial systems.
The principal variables in collection of third-generation CT data are the number of views and the signal-acquisition time per view. In most cases, rotation is continuous during collection, and each rotation is for a full 360º, although for some systems smaller rotations may be used. At the UT CT Facility, the number of views used ranges from 600 to 3600 or more. Each view represents a rotational interval equal to 360º divided by the total number of views. The raw data are displayed such that each line contains a single set of detector readings for a view, and time progresses from top to bottom. This image is called a sinogram, as any single point in the scanned object corresponds to a sinusoidal curve. Second-generation CT data are collected at a small number of distinct angular positions (such as 15 or 30), but the progression of relative object and source-detector position combinations allows these data to complete a fairly continuous sinogram.
Reconstruction is the mathematical process of converting sinograms into two-dimensional slice images. The most widespread reconstruction technique is called filtered backprojection, in which the data are first convolved with a filter and each view is successively superimposed over a square grid at an angle corresponding to its acquisition angle. The primary convolution filter used at UT is the Laks filter (Ramachandran and Lakshminarayanan, 1970), which is preferred when high-resolution images are desired; also available is the Shepp-Logan filter (Shepp and Logan, 1974), which is used more frequently in medical systems and reduces noise at some expense in spatial resolution (ASTM, 1992).
During reconstruction, the raw intensity data in the sinogram are converted to CT numbers or CT values that have a range determined by the computer system. Most medical and older industrial systems use a 12-bit scale, in which 4096 values are possible, while most more recent systems use a 16-bit scale, which allows values to range from 0 to 65535. On most industrial scanners, these values correspond to the grayscale in the image files created or exported by the systems. Although CT values should map linearly to the effective attenuation coefficient of the material in each voxel, the absolute correspondence is arbitrary. Medical systems generally use the Hounsfield Unit (HU), in which air is given a CT number of -1000 and water is given a value of 0, causing most soft tissues to have values ranging from -100 to 100 and bone to range from 600 to over 2000 (Zatz, 1981). Industrial CT systems are sometimes calibrated so that air has a value of 0, water of 1000, and aluminum of 2700, so the CT number corresponds roughly with density (Johns and others, 1993). The calibration of CT values is straightforward for fixed-geometry, single-use systems, but far less so for systems with flexible geometry and scanning modes, and multiple uses each requiring different optimization techniques.
Although a link to a reference scale can be useful in some circumstances, the chemical variability of geological materials and the wide range of scanning conditions used precludes any close correspondence to density in most cases. Furthermore, because material components can range from air to native metals, a rigid scale would be counterproductive. Given the finite range of CT values, a single scale may be insufficiently broad if there are large attenuation contrasts, or needlessly desensitize the system if subtle variations are being imaged. For geological purposes, it is commonly more desirable to select the reconstruction parameters to maximize the CT-value contrast for each scanned object. This can be done by assigning arbitrary low and high values near the limits of the available range to the least and most attenuating features in the scan field. In general we try to ensure that no CT value is generated beyond either end of the 16-bit range, lest some dimensional data be lost. For example, the boundary of an object being scanned in air is usually taken to correspond to the CT-value average between the object and air. If air is assigned to a CT value below zero, the apparent boundary of the object may shift inward.
Resolution and Size Limitations
Industrial scanners can accomodate objects with a wide range of sizes, shapes, and materials. Just as variable is the range of objectives for scanning, which can range from making precise measurements to observing gross features. Successful scanning will rely on all of these factors. In this section we discuss briefly the
The spatial resolution in a CT image is determined principally by the size and number of detector elements, the size of the X-ray focal spot, and the source-object-detector distances. In the UT instrument, the source-to-detector distance and the sizes of the detector elements are fixed. In this situation, maximum in-plane resolution is achieved by minimizing the source-to-object distance to give maximum magnification. By using offset geometries, in which the axis of rotation for the specimen is not in the center of the X-ray fan beam, higher magnification is achieved, though at a slight cost in image quality because fewer X-rays penetrate each volume element in the sample than is the case in a centered geometry.
As a rule of thumb, a CT image should have about as many pixels in each dimension as there are detector channels providing data for a view. For example, a 1024-channel linear detector array justifies a 1024x1024 pixel reconstructed image; if an offset scaning mode is used, up to a 2048x2048 pixel image may be justified.
Slice thickness, which governs the resolution in the third dimension, is determined by varying the thickness of linear apertures (slits) in front of the detectors. (Systems that use image intensifiers as detectors accomplish the same effect by selecting video lines (from the video signal) surrounding the midplane of the fan beam in smaller or larger numbers.)
Because both X-ray generation and the scattering events that produce attenuation within the object are stochastic processes, the X-ray signal is inherently noisy; the detector and its amplification electronics contribute additional noise. Thus, variations in the X-ray signals arising from these effects can obscure the variations arising from the sample itself. This noise in the intensity measurements limits the scanner's ability to differentiate between nearby volume elements with closely similar attenuation, thereby degrading the resolution of the image. Increasing the X-ray flux and/or the counting time for each intensity measurement will bolster the signal-to-noise ratio and improve the resolution.
Because decreasing slice thickness correspondingly decreases the the X-ray flux on each detector element, attempts to gain improved resolution by using thinner slices are eventually thwarted by the need to maintain sufficient X-ray flux to generate satisfactory counting statistics. Increasing the intensity of the incident beam can help, but insofar this will tend to also increase the focal spot size, additional blurring can result. Increasing the duration of each intensity measurement can compensate without this compromise, but can prove prohibitively costly or simply impractical if the required times are excessively long.
Conventional medical CT instruments provide resolution on the order of 1-2 mm for meter-scale to decimeter-scale objects. "High-resolution" instruments, including the high-energy subsystem of the UT instrument and common industrial CT systems, provide resolution on the order of 100-200 micrometers for decimeter-scale to centimeter-scale objects. "Ultra-high-resolution" instruments, like the microfocal subsystem of the UT instrument, provide resolution on the order of a few tens of microns for centimeter-scale to millimeter-scale objects. Micro-tomgraphy is perfomed using dedicated beamlines at synchrotron facilities; with such techniques, micron-scale resolution is possible within objects at millimeter to submillimeter scale (cf. Flannery et al., 1987; Kinney et al., 1993).
The ability to differentiate materials depends on their respective linear attenuation coefficients. In practical terms, successful imaging will depend on innate material properties of density and atomic composition, and on the machine parameters of the X-ray spectrum utilized and the signal-to-noise ratio. Materials with very divergent densities and/or atomic constituents are easy to differentiate. In favorable circumstances, modern CT instruments are capable of discriminating between values of µ that differ by as little as 0.1%, but only if the regions being tested are relatively large, spanning many voxels, and if there is sufficient X-ray flux to keep image noise low. As a result, spatial and density/attenuation resolution are linked: if materials are very different in their attenuation propoerties, very fine details or very small particles can be imaged, but if they are similar only larger-scale details and/or particles can be reliably distinguished.
Apart from the obvious constraint imposed by the size of the instrument's sample holder (50 cm diameter on the UT high-energy subsystem, and ~10 cm on the ultra-high-resolution subsystem), the maximum size of objects that can be examined by CT is determined by the need to acquire a sufficiently strong signal from the beam after it has been attenuated by passage though the object. If the object is too thick, it will absorb too much energy, resulting in low X-ray flux and poor image quality. A 420 kV X-ray tube generate beams capable of imaging geologic materials (objects with average densities close to those of common silicate minerals) with maximum dimensions up to perhaps 30-40 cm. Larger or denser objects can be imaged with special CT instruments that use very high-energy sources (e.g., linear accelerators or radioactive 60Co) capable of far greater penetration.
Artifacts and Partial-Volume Effects
Although the output of computed tomography is visual in nature and thus lends itself to straightforward interpretation, subtle complications can render the data more problematic for quantitative use. Scanning artifacts can obscure details of interest, or cause the CT value of a single material to change in different parts of an image. Partial-volume effects, if not properly accounted for, can lead to erroneous determinations of feature dimensions and component volume fractions. In this section we discuss commonly encountered problems, and some approaches for solving them.
The most commonly encountered artifact in CT scanning is beam hardening, which causes the edges of an object to appear brighter than the center, even if the material is the same throughout (Fig. 5a). The artifact derives its name from its underlying cause: the increase in mean X-ray energy, or "hardening" of the X-ray beam as it passes through the scanned object. Because lower-energy X-rays are attenuated more readily than higher-energy X-rays, a polychromatic beam passing through an object preferentially loses the lower-energy parts of its spectrum. The end result is a beam that, though diminished in overall intensity, has a higher average energy than the incident beam (Fig. 2). This also means that, as the beam passes through an object, the effective attenuation coefficient of any material diminishes, thus making short ray paths proportionally more attenuating than long ray paths. In X-ray CT images of sufficiently attenuating material, this process generally manifests itself as an artificial darkening at the center of long ray paths, and a corresponding brightening near the edges. In objects with roughly circular cross sections this process can cause the edge to appear brighter than the interior, but in irregular objects it is commonly difficult to differentiate between beam hardening artifacts and actual material variations.
Beam hardening can be a pernicious artifact because it changes the CT value of a material (or void) depending upon its location in an image. Thus, the attempt to utilize a single CT number range to identify and quantify the extent of a particular material can become problematic. One measure that is sometimes taken is to remove the outer edges of the image and analyze only the center. Although this technique removes the worst part of the problem, the artifact is continuous and thus even subsets of the image are affected. Furthermore, if the cross-sectional area of the object changes from slice to slice, the extent of the beam-hardening artifact also changes, making such a strategy prone to error.
There are a number of possible remedies for beam hardening, ranging from sample and scanning preparation to data processing. The simplest approach is to use an X-ray beam that is energetic enough to ensure that beam hardening is negligible, and can thus be ignored. Unfortunately, most materials of geological interest are attenuating enough that beam hardening is noticeable unless the sample is quite small. Furthermore, higher-energy beams are less sensitive to attenuation contrasts in materials, and thus may not provide sufficient differentiation between features of interest. Another possible strategy is to pre-harden (or post-harden) the X-ray beam by passing it through an attenuating filter before or after it passes through the scanned object (Fig. 5c). Filters are commonly flat or shaped pieces of metal such as copper, brass or aluminum. The drawback to beam filtration is that it typically degrades the X-ray signal at all energies to some degree, thus leading to greater image noise unless longer acquisition times are used. It is also characteristically only partially effective. Another method is to employ a wedge calibration using a material of similar attenuation properties to the object (Fig. 5d), as discussed above. To be effective, the wedge material should be cylindrical, and the scanned object should either be cylindrical or packed in an attenuating material (ideally the wedge material) to achieve an overall cylindrical form. If the latter is necessary, images may be noisier because of the additional X-ray attenuation caused by the packing material. The wedge material in the images also commonly interferes with 3-D analysis of the object of interest, in which case it must be eliminated during image processing.
Beam hardening is characteristically more difficult to alleviate at the data-processing stage, and such measures are usually available only in special circumstances. If the scanned object is materially uniform, a correction can be applied to the raw scan data that converts each reading to a non-beam-hardened equivalent before reconstruction takes place; unfortunately, the requirement of uniformity is more often met in industrial applications than geological ones. If the object is cylindrical and fairly uniform (i.e., a rock core), it may be possible to construct an after-the-fact wedge correction by compiling a radial average of CT values for a stack of slices. A Fourier filter that removes long-wavelength variations in CT value has also been effective in some circumstances.
|Figure 5: Scans through a 6-inch-diameter column of saprolite encased in PVC pipe, showing scanning artifacts and the results of various strategies for remedying them. The scans all represent 1-mm-thick slices collected with the X-ray source at 420 kV and acquisition times of 3 minutes. Scan (A) shows both ring and beam-hardening artifacts. The latter is visible most obviously as the bright ring around the outer part of the PVC. Image (B) is the result of a software correction of the ring artifacts in (A). If the grayscale fluctuations caused by the rings are smaller than for the features of interest, this approach can be very successful. However, in this case some fractures close to the center have been obscured or altered. Image (C) shows the result of pre-filtering the X-ray beam by passing it through 6.35 mm of brass. Beam-hardening and ring artifacts have been reduced markedly but not totally, and image noise has increased considerably. The scan shown in (D) was done using a self-wedge calibration through a relatively homogeneous portion of the column. The bright rim on the left was caused by imperfect centering of the column; the image of the saprolite itself, however, has only very minor ring artifacts and no beam hardening. Note that although the centers of images (B) and (D) are similar, the edges of the saprolite are brighter in image (B). Thus it is evident that the beam hardening artifact in image (B) was not confined strictly to the edge of the PVC casing, but was a continuous feature within the saprolite as well. Also, the y-intersection of fractures just to the upper-left of center (indicated by arrows) appears discontinuous in the software-corrected image (B). Sample courtesy of Dr. Gerilynn Moline, Oak Ridge National Laboratory.|
Ring artifacts occur in third-generation scanning, appearing as full or partial circles centered on the rotational axis (Fig. 5a). They are caused by shifts in output from individual detectors or sets of detectors, which cause the corresponding ray or rays in each view to have anomalous values; the position of a ring corresponds to the area of greatest overlap of these rays during reconstruction. A number of factors can cause such a shift, all of which have their basis in detectors responding differently to changes in scanning conditions. Some factors, such as change in temperature or beam strength, can be overcome by carefully controlling experimental conditions or by frequent recalibrations. A more problematic source of detector divergence is differential sensitivity to varying beam hardness. If the detector response calibration (gain or wedge) is taken through air, the relative response of the detectors can change if the hardness of the X-ray beam is sufficiently affected by passage through the scanned object. If the object is uneven then different views can reflect different degrees of hardening, in which case only partial rings may occur, possibly obscuring their nature as artifacts.
Because of their link to beam hardening, ring artifacts can be addressed at the scanning stage with many of the same methods: by use of a filtered or sufficiently high-energy X-ray beam, or employing a wedge calibration through a material of similar attenuating properties to the scanned object.
Ring artifacts are somewhat more amenable to software remedies than beam hardening. A series of anomalous readings from a single detector appears on a sinogram as a vertical line, and thus it can potentially be detected and removed before reconstruction. Similarly, a reconstructed image can be converted to polar coordinates, vertical lines detected and removed, and converted back (Fig. 5b). A drawback of these strategies, particularly the latter, is that any roughly linear feature in the scanned object that is tangential to a circle centered on the rotational axis may be erased, blurred, or otherwise altered, even if it does not coincide with a ring. This can constitute a serious flaw in some applications, such as detecting sutures in fossils or tracing fractures.
In second-generation scanning, readings from an anomalous detector traverse the entire scan subject, so no rings are developed. Instead, detector drift is manifested by increased image noise.
A variety of other artifacts can arise in certain situations. If a highly attenuating object is noncircular in cross-section, streaks that traverse the longest axes of the object can occur. For example, a scanned cube of a dense material may have dark streaks connecting opposite corners. These streaks can intensify ring artifacts where they overlap, making remediation more difficult. If the scanned material includes features that are of much higher density than the surrounding matrix, a "starburst" artifact can form in which bright streaks emanate from the object for a short distance into nearby material, potentially obscuring features. In several instances we have found that fossils have been repaired with steel pins, resulting in severe artifacts. Similar artifacts have been caused by crystals of sulfide or oxide minerals.
Because each pixel in a CT image represents the attenuation properties of a specific material volume, if that volume is comprised of a number of different substances then the resulting CT value represents some average of their properties. This is termed the partial-volume effect. Furthermore, because of the inherent resolution limitations of X-ray CT, all material boundaries are blurred to some extent, and thus the material in any one voxel can affect CT values of surrounding voxels. Although these factors can make CT data more problematic to interpret quantitatively, they also represent an opportunity to extract unexpectedly fine-scale data from CT images. For example, medical CT data have long been used to trace two-phase fluid flow in soil and sedimentary rock cores (Wellington and Vinegar, 1987; Withjack, 1988), even though the fluids themselves appear only as subtle attenuation changes in the matrix they are passing through. Partial-volume effects have also been used to measure crack sizes cracks in crystalline rocks (Johns and others, 1993) and pores in soil columns (Peyton and others, 1992) down to a scale that is considerably finer than even the pixel dimensions.
The interpretation of CT values in voxels containing multiple components is not necessarily straightforward. Wellington and Vinegar (1987) utilize the approximation that the CT value in a voxel containing two components is equal to a linear combination of the CT values of the two end-members according to their volumetric proportions, which provides a reasonable solution if their attenuation values are fairly close (Pullan and others, 1981). If the end-member attenuation values are far apart, as is the case for rock and void space, significant errors of 10% or more can result from this approximation if their boundary is nearly parallel with the scan plane. However, in most cases where randomly oriented voids are studied, this error is significantly lower, and is commonly neglected without large consequence (Johns and others, 1993; Kinney and others, 1993; Wellington and Vinegar, 1987).
An example of the possible utility of partial-volume effects is shown in Figure 6. A core of limestone from the lower Ismay member of the Paradox Formation was scanned and subsequently cut for petrographic analysis (Beall and others, 1996). Individual fractures that appear on the scan were measured petrographically and found to have widths that were significantly smaller than the pixel dimensions. The fracture width can be estimated using partial-volume calculations similar to those used by Johns and others (1993), although at least one additional step is required to take fracture dip into account.
|Figure 6: 100-µm slice through fractured limestone from the lower Ismay member of the Paradox Formation. Scan field of view is 21.5 mm, and individual pixels are 42 µm on a side. After scanning the entire volume, the sample was cut and fractures were measured in thin section. Fractures are visible despite being considerably thinner than the pixel width, because of partial volume effects. Sample and measurements courtesy of Dr. Brenda Kirkland George, University of Texas at Austin.|
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