General Description of Computed Tomography
Computed tomography (CT) is a radiographic inspection method that uses a computer to reconstruct an image of a cross sectional plane of an object. In conventional radiography, information on the slice plane P projects into a single line, A-A; whereas in the associated CT image, the full spatial information is preserved (see Figure 1). The CT image 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. 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.

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Computed tomography affords extensive capabilities for a variety of applications. 

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The systematic observations are a set of X-ray attenuation measurements made along a set of paths projected at different locations around the periphery of the test article. Figure 2a 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 is referred to as a single view. It is shown as f(x'), where x' denotes the linear position of the measurement. Figure 2b shows measurements taken at several other angles f(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). The next step to create the CT image is to backproject the views, which is also shown in Figure 2b. 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.

Figure 1 — CT image versus a conventional radiograph. 

 

Figure 2 — Schematic illustrations of backprojection.  

 

The resulting 2D cross sectional image is a quantitative map of the linear X-ray attenuation coefficient at each point in the slice plane of the test article. 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. The attenuation of the X-rays as they interact with matter is a well studied problem and is the result of several different interaction mechanisms. For industrial CT systems with peak X-ray energy below a few megaelectronvolts, all but a few minor effects can be accounted for in terms of the sum of just two interactions — photoelectric absorption and Compton scattering. 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.

One particularly important property of the total linear attenuation coefficient is that it is proportional to material density, which is a fundamental physical property of all matter. The fact that CT images are proportional to density is one of the principal virtues 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. However, this can be an oversimplification. The linear attenuation coefficient also carries an energy dependence that is a function of material composition. The energy dependence of the attenuation coefficient may or may not be more important than the density dependence, depending on the materials and the energies of the X-rays involved. Once the CT system is calibrated for density measurements (an algorithm for density calibration is defined in ASTM document E1935 Standard Test Method for Calibrating and Measuring CT Density), the linear attenuation coefficient of an unknown feature in an image can be measured from a determination of its mean CT value. Its density can then be extracted from a knowledge of its mass attenuation coefficient.

 

Types of Computed Tomography Scanners
Computed tomography scanners are identified by the mechanical equipment configuration which provides the relative motion between the test article, the source, and the detectors. It makes no difference, at least in principle, whether the test object is moved systematically relative to the source and detectors or if the source and detectors are moved relative to the test object. Physical considerations such as the weight or size of the test article should be the determining factors for the most appropriate motion to use.

The majority of scan geometries that have been employed can be classified as one of five generations. This classification is a legacy of the early, rapid development of CT in the medical arena, and these terms are still widely used. The various scan geometries are illustrated in Figure 3.

First generation CT systems (Figure 3a) are characterized by a single X-ray source and single detector that undergo both linear translation and rotational motions. The source and detector assembly is translated in a direction perpendicular to the X-ray beam. Each translation yields a single view, as shown in Figure 2. Successive views are obtained by rotating the test article and translating again. The advantages of this design are simplicity, good view to view detector matching, flexibility in the choice of scan parameters (such as resolution and contrast), and ability to accommodate a wide range of different object sizes. The disadvantage is a longer scanning time.

Figure 3 — Sketches illustrating the evolution of CT scan geometries, each a distinct generation of instrumentation; (a) first generation single pencil beam translate/rotate scanner; (b) second generation multiple pencil beam translate/rotate scanner; (c) third generation rotate/rotate fan beam scanner; (d) fourth generation rotate/stationary inverted fan beam scanner; (e) fifth generation cone beam cylindrical scanner.

Second generation CT systems (Figure 3b) use the same translate/rotate scan geometry as the first generation. The primary difference is that second generation systems use a fan beam of radiation and multiple detectors so that a series of views can be acquired during each translation, which leads to correspondingly shorter scan times. Like first generation systems, second generation scanners have the inherent flexibility to accommodate a wide range of different object sizes, which is an important consideration for some industrial CT applications.

Third generation CT systems (Figure 3c) normally use a rotate only scan geometry, with a complete view being collected by the detector array during each sampling interval. To accommodate objects larger than the field of view subtended by the X-ray fan, it is possible to include part translations in the scan sequence, but data are not acquired during these translations as during first or second generation scans. Typically, third generation systems are faster than their second generation counterparts; however, because the spatial resolution in a third generation system depends on the size and number of sensors in the detector array, this improvement in speed is achieved at the expense of having to implement more sensors than with earlier generations. Since all elements of a third generation detector array contribute to each view, rotate-only scanners impose much more stringent requirements on detector performance than do second generation units, where each view is generated by a single detector.

Fourth generation CT systems (Figure 3d) also employ a rotate-only scan motion. The difference between third generation and fourth generation systems is that a fourth generation CT system uses a stationary circular array of detectors and only the source moves. The test specimen is placed within the circle of detectors and is irradiated with a wide fan beam which rotates around the test article. A view is made by obtaining successive absorption measurements of a single detector at successive positions of the X-ray source. The number of views is equal to the number of detectors. These scanners combine the artifact resistance of second generation systems with the speed of third generation units, but they can be more complex and costly than first, second, or third generation machines. Furthermore, they require that the object fit within the fan of X-rays, and they are more susceptible to scattered radiation.

Fifth generation CT systems (Figure 3e) are different than the previous modes in that there is no mechanical motion involved. The scanner uses a circular array of X-ray sources, which are electronically switched on and off. The sources project onto a curved fluorescent screen, so that when an X-ray source is switched on, a large volume of the part is imaged simultaneously, providing projection data for a cone beam of rays diverging from the source. This method of data collection is essentially different from the other four, since a series of 2D projections of a 3D object is collected rather than a series of 1D projections of a 2D object. This scanning mode is appropriate for precise imaging of a rapidly moving part (typical application is imaging of heart or other moving organs).

 

Tradeoffs in CT Instrumentation
Currently, the selection of a CT system geometry is application specific. The generational differences are more or less suited to certain areas. A significant factor in driving medical CT systems to use rotate-only scan geometries was the requirement that scanning times be short compared to the length of time that a patient can remain motionless or that involuntary internal motion can be ignored (that is, seconds). These considerations are not as important for industrial applications in which scan times for specific production related items can typically be much longer (that is, minutes) and the dose to the object is often not an important factor. A second generation scan geometry is attractive for industrial applications in which a wide range of part sizes must be accommodated, since the object does not have to fit within the fan of radiation as it generally does with third or fourth generation systems. A third generation scan geometry is attractive for industrial applications in which the part to be examined is well defined and scan speed are important. To date, first, fourth, and fifth generation scan geometries have seen little commercial application, but there may be special situations for which they would be well suited.

 

Advantages and Disadvantages of CT Technique
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. And, with proper calibration, dimensional inspections and absolute density determinations can also be made very accurately.

As with any modality, CT has its limitations. The most fundamental is that potential objects for examination must be small enough to be accommodated by the handling system of the CT equipment available to the user and must be 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. 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 a 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.

 

Common Industrial Applications of CT
Computed tomography provides a nonsuperimposed visual image of the internal structures of a part and is fundamentally a nondestructive inspection tool. However, the industrial applications where CT has proven most valuable are in the areas of rapid prototyping, reverse engineering and metrology.

Rapid prototyping can be accomplished utilizing a class of manufacturing techniques where parts are built from computer models in a variety of materials. Stereolithography is one such technique that can utilize the information of CT to produce extremely accurate polymer parts. Taking multiple CT slices, the 2D images can be assembled to produce complete 3D representations of scanned components. The data is presented to the stereolithography system as full volume information or simply contour plots, allowing the generation of either filled or hollow polymer parts. The choice of data would be based on the rapid tooling techniques that are applied in the specific application area.

Computed tomography assisted reverse engineering methods are successful in enabling older designs without computer aided design (CAD) files to access the many available rapid tooling techniques currently available. In reverse engineering applications, as in rapid prototyping, the 2D images can be assembled to produce complete 3D representations of scanned components. There are many computational methods that allow the CT derived digital data to be transformed to CAD contours, which can be used to reverse engineer the part. The CAD contours produced from CT data have been determined to be accurate to within a few thousandths of an inch. Thus, CT data is similar to dimensional data from coordinate measuring machines except it provides a number of advantages — CT data is acquired without contacting the part, CT data not only provides surface information but also accurate measurements of all internal structure, and CT images can be formed of any object without special programming, regardless of its structural complexity.

Metrology of the CT data — evaluating dimensional measurements — can be accomplished using a number of techniques. The most accurate means is by reverse engineering the slice data. This method requires the generation of a point cloud — a collection of points in 3D space that represent the surface of the part — from the CT data and registering that with the CAD model of the part. The deviations between the inspection data and the design data are evaluated based on the necessary tolerances for the application.

Computed tomography affords extensive capabilities for a variety of applications. In addition to a nondestructive inspection technique for quality control, CT data is a record of the different material densities present in the part and feeds into other programs to provide rapid prototyping and reverse engineering capabilities.

 

Conclusion
Computed tomography 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, 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 nonmetallic specimens, solid and fibrous materials, and smooth and irregularly surfaced objects. 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, and, when used in conjunction with other NDT methods, such as ultrasound, CT data can provide evaluations of material integrity that cannot currently be provided nondestructively by any other means.

 

References
Herman, Gabor T., Image Reconstruction from Projections: The Fundamentals of Computerized Tomography, New York, Academic Press, 1980.

Newton, T.H., and D.G. Potts, Eds., Radiology of the Skull and Brain, Vol 5: Technical Aspects of Computed Tomography, C.V. Mosby Company, 1981.

* Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/MLLP, 2230 Tenth St., Wright-Patterson AFB, OH 45433, (937) 255-9795; fax (937) 255-9804; e-mail clandia.hughes@afrl.af.mil.

† ARACOR, 514 E. Dayton Yellow Springs Rd., Fairborn, OH 45324-6432; (937) 879-4200, X25; e-mail neel@oharacor.com.

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