Significance and Use
This guide provides a tutorial introduction to the theory and use of computed tomography. This guide begins with a overview intended for the interested reader with a general technical background. Subsequent, more technical sections describe the physical and mathematical basis of CT technology, the hardware and software requirements of CT equipment, and the fundamental measures of CT performance. This guide includes an extensive glossary (with discussion) of CT terminology and an extensive list of references to more technical publications on the subject. Most importantly, this guide establishes consensus definitions for basic measures of CT performance, enabling purchasers and suppliers of CT systems and services to communicate unambiguously with reference to a recognized standard. This guide also provides a few carefully selected equations relating measures of CT performance to key system parameters.
General Description of Computed Tomography—CT is a radiographic inspection method that uses a computer to reconstruct an image of a cross-sectional plane (slice) through an object. The resulting cross-sectional image is a quantitative map of the linear X-ray attenuation coefficient, μ, at each point in the plane. The linear attenuation coefficient characterizes the local instantaneous rate at which X-rays are removed during the scan, by scatter or absorption, from the incident radiation as it propagates through the object (See 7.5). The attenuation of the X-rays as they interact with matter is a well-studied problem (1) and is the result of several different interaction mechanisms. For industrial CT systems with peak X-ray energy below a few MeV, all but a few minor effects can be accounted for in terms of the sum of just two interactions: photoelectric absorption and Compton scattering (1). The photoelectric interaction is strongly dependent on the atomic number and density of the absorbing medium; the Compton scattering is predominantly a function of the electron density of the material. Photoelectric attenuation dominates at lower energies and becomes more important with higher atomic number, while Compton scattering dominates at higher energies and becomes more important at lower atomic number. In special situations, these dependencies can be used to advantage (see 7.6.2 and references therein).
One particularly important property of the total linear attenuation coefficient is that it is proportional to material density, which is of course a fundamental physical property of all matter. The fact that CT images are proportional to density is perhaps the principal virtue of the technology and the reason that image data are often thought of as representing the distribution of material density within the object being inspected. This is a dangerous oversimplification, however. The linear attenuation coefficient also carries an energy dependence that is a function of material composition. This feature of the attenuation coefficient may or may not (depending on the materials and the energies of the X-rays involved) be more important than the basic density dependence. In some instances, this effect can be detrimental, masking the density differences in a CT image; in other instances, it can be used to advantage, enhancing the contrast between different materials of similar density.
The fundamental difference between CT and conventional radiography is shown in Fig. 1. In conventional radiography, information on the slice plane “P” projects into a single line, “A-A;” whereas with the associated CT image, the full spatial information is preserved. CT information is derived from a large number of systematic observations at different viewing angles, and an image is then reconstructed with the aid of a computer. The image is generated in a series of discrete picture elements or pixels. A typical CT image might consist of a 512 by 512 or 1024 by 1024 array of attenuation values for a single cross-sectional slice through a test specimen. This resultant two-dimensional map of the slice plane is an image of the test article. Thus, by using CT, one can, in effect, slice open the test article, examine its internal features, record the different attenuations, perform dimensional inspections, and identify any material or structural anomalies that may exist. Further, by stacking and comparing adjacent CT slices of a test article, a three dimensional image of the interior can be constructed.
From Fig. 1, it can be appreciated readily that if an internal feature is detected in conventional projection radiography, its position along the line-of-sight between the source and the film is unknown. Somewhat better positional information can be determined by making additional radiographs from several viewing angles and triangulating. This triangulation is a rudimentary, manual form of tomographic reconstruction. In essence, a CT image is the result of triangulating every point in the plane from many different directions.
Because of the volume of data that must be collected and processed with CT, scans are usually made one slice at a time. A set of X-ray attenuation measurements is made along a set of paths projected at different locations around the periphery of the test article. The first part of Fig. 2 illustrates a set of measurements made on a test object containing two attenuating disks of different diameters. The X-ray attenuation measurement made at a particular angle, ϕ1, is referred to as a single view. It is shown as fϕ1(x′), where x′ denotes the linear position of the measurement. The second part of Fig. 2 shows measurements taken at several other angles fϕi(x′). Each of the attenuation measurements within these views is digitized and stored in a computer, where it is subsequently conditioned (for example, normalized and corrected) and filtered (convolved), as discussed in more detail in Section 7. The next step in image processing is to backproject the views, which is also shown in the second part of Fig. 2. Backprojection consists of projecting each view back along a line corresponding to the direction in which the projection data were collected. The backprojections, when enough views are employed, form a faithful reconstruction of the object. Even in this simple example, with only four projections, the concentration of backprojected rays already begins to show the relative size and position of features in the original object.
System Capabilities—The ability of a CT system to image thin cross-sectional areas of interest through an object makes it a powerful complement to conventional radiographic inspections. Like any imaging system, a CT system can never duplicate exactly the object that is scanned. The extent to which a CT image does reproduce the object is dictated largely by the competing influences of the spatial resolution, the statistical noise, and the artifacts of the imaging system. Each of these aspects is discussed briefly here. A more complete discussion will be found in Sections 8 and 9.
Spatial Resolution—Radiographic imaging is possible because different materials have different X-ray attenuation coefficients. In CT, these X-ray coefficients are represented on a display monitor as shades of gray, similar to a photographic image, or in false color. The faithfulness of a CT image depends on a number of system-level performance factors, with one of the most important being spatial resolution. Spatial resolution refers to the ability of a CT system to resolve small details or locate small features with respect to some reference point.
Spatial resolution is generally quantified in terms of the smallest separation at which two points can be distinguished as separate entities. The limiting value of the spatial resolution is determined by the design and construction of the system and by the amount of data and sampling scheme used to interrogate the object of interest. The precision of the mechanical system determines how accurately the views can be backprojected, and the X-ray optics determine the fineness of the detail that can be resolved. The number of views and the number of single absorption measurements per view determine the size of the reconstruction matrix that can be faithfully reconstructed. Reducing pixel size can improve spatial resolution in an image until the inherent limit set by these constraints is reached. Beyond this limit, smaller pixels do not increase the spatial resolution and can induce artifacts in the image. However, under certain circumstances, reconstructing with pixels smaller than would otherwise be warranted can be a useful technique. For instance, when performing dimensional inspections, working from an image with pixels as small as one-fourth the sample spacing can provide measurable benefit.
It can also be shown that a given CT image is equivalent to the blurring (convolution) of the ideal representation of the object with a smooth, two-dimensional Gaussian-like function called the point-spread-function (PSF). The specification of the PSF of a system is an important characterization of a CT system and can be derived fairly accurately from the parameters of the CT system. The effect of the PSF is to blur the features in the CT image. This has two effects: (1) small objects appear larger and (2) sharp boundaries appear diffuse. Blurring the image of small objects reduces resolution since the images of two small point-like objects that are close together will overlap and may be indistinguishable from a single feature. Blurring sharp edges reduces the perceptibility of boundaries of different materials for the same reason. This effect is especially important at interfaces between materials, where the possibility of separations of one type or another are of the greatest concern. Thus, knowledge of the PSF of a CT system is crucial to the quantitative specification of the maximum resolution and contrast achievable with that system.
It should be noted, since it is a common source of misunderstanding, that the smallest feature that can be detected in a CT image is not the same as the smallest that can be resolved. A feature considerably smaller than a single pixel can affect the pixel to which it corresponds to such an extent that it will appear with a visible contrast relative to adjacent pixels. This phenomenon, the “partial-volume effect,” is discussed in 7.6. The difference between the resolution of a small feature and the resolution of its substructure is of fundamental importance for CT.
Scope
1.1 Computed tomography (CT) is a radiographic method that provides an ideal examination technique whenever the primary goal is to locate and size planar and volumetric detail in three dimensions. Because of the relatively good penetrability of X-rays, as well as the sensitivity of absorption cross sections to atomic chemistry, CT permits the nondestructive physical and, to a limited extent, chemical characterization of the internal structure of materials. Also, since the method is X-ray based, it applies equally well to metallic and non-metallic specimens, solid and fibrous materials, and smooth and irregularly surfaced objects. When used in conjunction with other nondestructive evaluation (NDE) methods, such as ultrasound, CT data can provide evaluations of material integrity that cannot currently be provided nondestructively by any other means.
1.2 This guide is intended to satisfy two general needs for users of industrial CT equipment: (1) the need for a tutorial guide addressing the general principles of X-ray CT as they apply to industrial imaging; and (2) the need for a consistent set of CT performance parameter definitions, including how these performance parameters relate to CT system specifications. Potential users and buyers, as well as experienced CT inspectors, will find this guide a useful source of information for determining the suitability of CT for particular examination problems, for predicting CT system performance in new situations, and for developing and prescribing new scan procedures.
1.3 This guide does not specify test objects and test procedures for comparing the relative performance of different CT systems; nor does it treat CT inspection techniques, such as the best selection of scan parameters, the preferred implementation of scan procedures, the analysis of image data to extract densitometric information, or the establishment of accept/reject criteria for a new object.
1.4 Standard practices and methods are not within the purview of this guide. The reader is advised, however, that examination practices are generally part and application specific, and industrial CT usage is new enough that in many instances a consensus has not yet emerged. The situation is complicated further by the fact that CT system hardware and performance capabilities are still undergoing significant evolution and improvement. Consequently, an attempt to address generic examination procedures is eschewed in favor of providing a thorough treatment of the principles by which examination methods can be developed or existing ones revised.
1.5 The principal advantage of CT is that it nondestructively provides quantitative densitometric (that is, density and geometry) images of thin cross sections through an object. Because of the absence of structural noise from detail outside the thin plane of inspection, images are much easier to interpret than conventional radiographic data. The new user can learn quickly (often upon first exposure to the technology) to read CT data because the images correspond more closely to the way the human mind visualizes three-dimensional structures than conventional projection radiography. Further, because CT images are digital, they may be enhanced, analyzed, compressed, archived, input as data into performance calculations, compared with digital data from other NDE modalities, or transmitted to other locations for remote viewing. Additionally, CT images exhibit enhanced contrast discrimination over compact areas larger than 20 to 25 pixels. This capability has no classical analog. Contrast discrimination of better than 0.1 % at three-sigma confidence levels over areas as small as one-fifth of one percent the size of the object of interest are common.
1.6 With proper calibration, dimensional inspections and absolute density determinations can also be made very accurately. Dimensionally, virtually all CT systems provide a pixel resolution of roughly 1 part in 1000 , and metrological algorithms can often measure dimensions to one-tenth of one pixel or so with three-sigma accuracies. For small objects (less than 100 mm (4 in.) in diameter), this translates into accuracies of approximately 0.1 mm (0.003 to 0.005 in.) at three-sigma. For much larger objects, the corresponding figure will be proportionally greater. Attenuation values can also be related accurately to material densities. If details in the image are known to be pure homogeneous elements, the density values may still be sufficient to identify materials in some cases. For the case in which no a priori information is available, CT densities cannot be used to identify unknown materials unambiguously, since an infinite spectrum of compounds can be envisioned that will yield any given observed attenuation. In this instance, the exceptional density sensitivity of CT can still be used to determine part morphology and highlight structural irregularities.
1.7 In some cases, dual energy (DE) CT scans can help identify unknown components. DE scans provide accurate electron density and atomic number images, providing better characterizations of the materials. In the case of known materials, the additional information can be traded for improved conspicuity, faster scans, or improved characterization. In the case of unknown materials, the additional information often allows educated guesses on the probable composition of an object to be made.
1.8 As with any modality, CT has its limitations. The most fundamental is that candidate objects for examination must be small enough to be accommodated by the handling system of the CT equipment available to the user and radiometrically translucent at the X-ray energies employed by that particular system. Further, CT reconstruction algorithms require that a full 180 degrees of data be collected by the scanner. Object size or opacity limits the amount of data that can be taken in some instances. While there are methods to compensate for incomplete data which produce diagnostically useful images, the resultant images are necessarily inferior to images from complete data sets. For this reason, complete data sets and radiometric transparency should be thought of as requirements. Current CT technology can accommodate attenuation ranges (peak-to-lowest-signal ratio) of approximately four orders of magnitude. This information, in conjunction with an estimate of the worst-case chord through a new object and a knowledge of the average energy of the X-ray flux, can be used to make an educated guess on the feasibility of scanning a part that has not been examined previously.
1.9 Another potential drawback with CT imaging is the possibility of artifacts in the data. As used here, an artifact is anything in the image that does not accurately reflect true structure in the part being inspected. Because they are not real, artifacts limit the user's ability to quantitatively extract density, dimensional, or other data from an image. Therefore, as with any technique, the user must learn to recognize and be able to discount common artifacts subjectively. Some image artifacts can be reduced or eliminated with CT by improved engineering practice; others are inherent in the methodology. Examples of the former include scattered radiation and electronic noise. Examples of the latter include edge streaks and partial volume effects. Some artifacts are a little of both. A good example is the cupping artifact, which is due as much to radiation scatter (which can in principle be largely eliminated) as to the polychromaticity of the X-ray flux (which is inherent in the use of bremsstrahlung sources).
1.10 Depending on the technology of the CT system, complete three-dimensional CT examinations can be time consuming. Thus, less than 100 % CT examinations are often necessary or must be accommodated by complementing the inspection process with digital radiographic screening. One partial response to this problem is to use large slice thicknesses. This leads to reduced axial resolution and can introduce partial volume artifacts in some cases; however, this is an acceptable tradeoff in many instances. In principle, this drawback can be eliminated by resorting to full volumetric scans using planar detectors instead of linear detectors (see (1) under 6.5.1.5).
1.11 Complete part examinations demand large storage capabilities or advanced display techniques, or both, and equipment to help the operator review the huge volume of data generated. This can be compensated for by state-of-the-art graphics hardware and automatic examination software to aid the user. However, automated accept/reject software is object dependent and to date has been developed and employed in only a limited number of cases.
1.12 Units—The values stated in SI units are to be regarded as standard. The values given in parentheses are mathematical conversions to inch-pound units that are provided for information only and are not considered standard.
1.13 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
