CHAPTER 6 Projection Geometry OUTLINE Image Sharpness and Resolution Image Size Distortion Image Shape Distortion Paralleling and Bisecting-Angle Techniques A conventional radiograph is made with a stationary x-ray source and displays a two-dimensional image of a part of the body. Such images are often called plain or projection views (in contrast to ultrasound, computed tomography [CT], magnetic resonance imaging, or nuclear medicine). In plain views, the entire volume of tissue between the x-ray source and the image receptor (digital sensor or film) is projected onto a two-dimensional image. To obtain the maximal value from a radiograph, a clinician must have a clear understanding of normal anatomy and mentally reconstruct a three-dimensional image of the anatomic structures of interest from one or more of these two-dimensional views. Using high-quality radiographs greatly facilitates this task. The principles of projection geometry describe the effect of focal spot size and relative position of the object and image receptor (digital sensor or film) on image clarity, magnification, and distortion. Clinicians use these principles to maximize image clarity, minimize distortion, and localize objects in the image field. IMAGE SHARPNESS AND RESOLUTION Several geometric considerations contribute to image sharpness and spatial resolution. Sharpness measures how well a boundary between two areas of differing radiodensity is revealed. Image spatial resolution measures how well a radiograph is able to reveal small objects that are close together. Although sharpness and resolution are two distinct features, they are interdependent, being influenced by the same geometric variables. For clinical diagnosis, it is desirable to optimize conditions that result in images with high sharpness and resolution. When x rays are produced at the target in an x-ray tube, they originate from all points within the area of the focal spot. Because these rays originate from different points and travel in straight lines, their projections of a feature of an object do not occur at exactly the same location on an image receptor. As a result, the image of the edge of an object is slightly blurred rather than sharp and distinct. Figure 6-1 shows the path of photons that originate at the margins of the focal spot and provide an image of the edges of an object. The resulting blurred zone of unsharpness on an image causes a loss in image sharpness. The larger the focal spot area, the greater the unsharpness. There are three means to maximize image sharpness: 1. Use as small an effective focal spot as practical. Dental x-ray machines preferably should have a effective focal spot size of 0.4 mm because this greatly adds to image clarity. As described 84 Object Localization Eggshell Effect in Chapter 1, the size of the effective focal spot is a function of the angle of the target with respect to the long axis of the electron beam. A large angle distributes the electron beam over a larger surface and decreases the heat generated per unit of target area, thus prolonging tube life; however, this results in a larger effective focal spot and loss of image clarity (Fig. 6-2). A small angle has a greater wearing effect on the target but results in a smaller effective focal spot and increased image sharpness. 2. Increase the distance between the focal spot and the object by using a long, open-ended cylinder. Figure 6-3 shows how increasing the focal spot-to-object distance reduces image blurring by reducing the divergence of the x-ray beam. A longer focal spot-to-object distance minimizes blurring by using photons whose paths are almost parallel. The benefits of using a long focal spot-to-object distance support the use of long, open-ended cylinders as aiming devices on dental x-ray machines. 3. Minimize the distance between the object and the image receptor. Figure 6-4 shows that, as the object-to-image receptor distance is reduced, the zone of unsharpness decreases, resulting in enhanced image clarity. This is the result of minimizing the divergence of the x-ray photons. IMAGE SIZE DISTORTION Image size distortion (magnification) is the increase in size of the image on the radiograph compared with the actual size of the object. The divergent paths of photons in an x-ray beam cause enlargement of the image on a radiograph. Image size distortion results from the relative distances of the focal spot-to-image receptor and object-to-image receptor (see Figs. 6-3 and 6-4). Increasing the focal spot-to-image receptor distance and decreasing the objectto-image receptor distance minimizes image magnification. The use of a long, open-ended cylinder as an aiming device on an x-ray machine thus reduces the magnification of images on a periapical view. As previously mentioned, this technique also improves image sharpness by increasing the distance between the focal spot and the object. IMAGE SHAPE DISTORTION Image shape distortion is the result of unequal magnification of different parts of the same object. This situation arises when not all the parts of an object are at the same focal spot-to-object C H A P T E R 6 Projection Geometry Anode Large focal spot Anode 85 Small focal spot FIGURE 6-1 Photons originating at different places on the focal spot (red) result in a zone of unsharpness on the radiograph. The density of the image changes from a high background value to a low value in the area of an edge of enamel, dentin, or bone. On the left, a large focal spot size results in a wide zone of unsharpness compared with a small focal spot size on the right, which results in a sharper image (narrow zone of unsharpness). Object Image receptor Unsharpness Unsharpness Density Density Electron beam Electron beam Anode Anode Actual focal spot Actual focal spot Object Effective focal spot FIGURE 6-2 As the angle of the target becomes closer to perpendicular to the long axis of the electron beam (as shown on the right) the actual focal spot becomes smaller, which decreases heat dissipation and tube life. The more perpendicular angle also decreases the effective focal spot size, increasing the sharpness of the resulting image. Image receptor Unsharpness distance. The physical shape of the object may often prevent its optimal orientation, resulting in some shape distortion. Such a phenomenon is seen by the differences in appearance of the image on a radiograph compared with the true shape. To minimize shape distortion, the practitioner should make an effort to align the tube, object, and image receptor carefully according to the following guidelines: 1. Position the image receptor parallel to the long axis of the object. Image shape distortion is minimized when the long axes of the image receptor and tooth are parallel. Figure 6-5 shows that the central ray of the x-ray beam is perpendicular to the image receptor, but the object is not parallel to the image receptor. The resultant image is distorted because of the unequal distances of the various parts of the object from the image receptor. This type of shape distortion is called foreshortening because it causes the radiographic image to be shorter than the object. Figure 6-6 shows the situation when the x-ray beam is oriented at right angles to the object but not to the image receptor; this results in elongation, with the object appearing longer on the image receptor than its actual length. 2. Orient the central ray perpendicular to the object and image receptor. Image shape distortion occurs if the object and image receptor are parallel, but the central ray is not directed at right angles to each. This distortion is most evident on maxillary molar views (Fig. 6-7). If the central ray is oriented with an excessive vertical angulation, the palatal roots appear disproportionately longer than the buccal roots. 86 PART II Imaging Anode FIGURE 6-3 Increasing the distance between the focal spot and the object results in an image with increased sharpness and less magnification of the object as seen on the right. Anode Image receptor Anode Anode FIGURE 6-4 Decreasing the distance between the object and the image receptor increases the sharpness and results in less magnification of the object as seen on the left. Image receptor 0 The practitioner can prevent shape distortion errors by aligning the object and image receptor parallel with each other and the central ray perpendicular to both. PARALLELING AND BISECTING-ANGLE TECHNIQUES From the earliest days of dental radiography, a clinical objective has been to produce accurate images of dental structures that are normally visually obscured. An early method for aligning the x-ray beam and image receptor with the teeth and jaws was the bisectingangle technique (Fig. 6-8). In this method, the image receptor is 5 10 15 20 0 5 10 15 20 25 placed as close to the teeth as possible without deforming it. However, when the image receptor is in this position, it is not parallel to the long axes of the teeth. This arrangement inherently causes distortion. Nevertheless, by directing the central ray perpendicular to an imaginary plane that bisects the angle between the teeth and the image receptor, the practitioner can make the length of the tooth’s image on the image receptor correspond to the actual length of the tooth. This angle between a tooth and the image receptor is especially apparent when teeth are radiographed in the maxilla or anterior mandible. Although the projected length of a tooth is correct, these images display a distorted image of the C H A P T E R 6 Projection Geometry 87 Anode 10 5 0 Image receptor 0 5 10 FIGURE 6-5 Foreshortening of a radiographic image results when the central ray is perpendicular to the image receptor but the object is not parallel with the image receptor. FIGURE 6-7 The central ray should be perpendicular to the long axes of both the tooth and the image receptor. If the direction of the x-ray beam is not at right angles to the long axis of the tooth, the appearance of the tooth is distorted, typically by apparent elongation of the length of the palatal roots of upper molars and distortion of the relationship of the height of the alveolar crest relative to the cementoenamel junction. Central axis of tooth Anode Imaginary bisector 5 10 0 5 10 15 20 25 0 FIGURE 6-6 Elongation of a radiographic image results when the central ray is perpendicular to the object but not to the image receptor. FIGURE 6-8 In the bisecting-angle technique, the central ray is directed at a right angle to the imaginary plane that bisects the angle formed by the image receptor and the central axis of the object. This method produces an image that is the same length as the object but results in some image distortion. position of alveolar crest with respect to the cementoenamel junction of a tooth. In recent years, the bisecting-angle technique has been used less frequently for general periapical radiography as use of the paralleling technique has increased. The paralleling technique is the preferred method for making intraoral radiographs. It derives its name as the result of placing the image receptor parallel to the long axis of the tooth (Fig. 6-9). This procedure minimizes image distortion and best incorporates the imaging principles described in the first three sections of this chapter. To achieve this parallel orientation, the practitioner often must position the image receptor toward the middle of the oral cavity, away from the teeth. Although this allows the teeth and image receptor to be parallel, it results in some image magnification and loss of sharpness. To overcome these limitations, the paralleling technique also uses a relatively long open-ended aiming cylinder (“cone”) to increase the focal spot-to-object distance. This “cone” directs only the most central and parallel rays of the beam to the image receptor and teeth and reduces image magnification, while increasing image sharpness. Because it is desirable to position image receptors near the middle of the oral cavity with the paralleling technique, image receptor holders should be used to support the image receptor in the patient’s mouth (see Chapter 7). OBJECT LOCALIZATION In clinical practice, the dentist often must derive from a radiograph three-dimensional information concerning patients. For example, 88 PART II Imaging the dentist may wish to use radiographs to determine the location of a foreign object or an impacted tooth within the jaw. Three methods are frequently used to obtain such three-dimensional information. The first is to examine two images projected at right angles to each other. The second method is to use the tube-shift technique employing conventional periapical views. Third, in recent years, the advent of cone-beam imaging has provided a new tool for obtaining three-dimensional information. In this chapter, we discuss the first two of these methods. These techniques are valuable because cone-beam CT may not be available or even necessary if the dentist already has multiple periapical views of the region of interest. Cone-beam CT is discussed in Chapters 11-13. Figure 6-10 shows the first method, in which two views made at right angles to one another localize an object in or about the maxilla in three dimensions. In clinical practice, the position of an object on each radiograph is noted relative to the anatomic landmarks; this allows the observer to determine the position of the object or area of interest. For example, if a radiopacity is found near the apex of the mandibular first molar on a periapical Central axis of tooth radiograph, the dentist may take a mandibular occlusal view to identify its mediolateral position. The occlusal film may reveal a calcification in the soft tissues located laterally or medially to the body of the mandible. This information is important in determining the treatment required. The right-angle (or cross section) technique is best for the mandible (see Figs. 22-8, A, 22-15, and 22-23, B). On a maxillary occlusal view, the superimposition of features in the anterior part of the skull frequently obscures the area of interest. The second method used to identify the spatial position of an object is the tube-shift technique. Other names for this procedure are the buccal-object rule and Clark’s rule (Clark described this method in 1910). The rationale for this procedure derives from the manner in which the relative positions of radiographic images of two separate objects change when the projection angle at which the images were made is changed. Figure 6-11 shows two radiographs of an object exposed at different angles. Compare the position of the object in question on each radiograph with the reference structures. If the tube is shifted and directed at the reference object (e.g., the apex of a tooth) from a more mesial angulation and the object in question also moves mesially with respect to the reference object, the object lies lingual to the reference object. Alternatively, if the tube is shifted mesially and the object in question appears to move distally, it lies on the buccal aspect of the reference object (Fig. 6-12). These relationships can be easily remembered by the acronym SLOB: same lingual, opposite buccal. Thus if the object in question appears to move in the same direction with respect to the reference structures as does the x-ray tube, it is on the lingual aspect of the reference object; if it appears to move in the opposite direction as the x-ray tube, it is on the buccal aspect. If it does not move with respect to the reference object, it lies at the same depth (in the same vertical plane) as the reference object. FIGURE 6-9 In the paralleling technique, the central ray is directed at a right angle to the central axes of the object and the image receptor. This technique requires a device to support the film in position. A B A B FIGURE 6-10 A, Periapical radiograph shows impacted canine lying apical to roots of lateral incisor and first premolar. B, Vertex occlusal view shows that the canine lies palatal to the roots of the lateral incisor and first premolar. FIGURE 6-11 The position of an object may be determined with respect to reference structures with use of the tube shift technique. A, A radiopaque object on the lingual surface of the mandible (black dot) may appear apical to the second premolar. B, When another radiograph is made of this region angulated from the mesial, the object appears to have moved mesially with respect to the second premolar apex (“same lingual” in the acronym SLOB). C H A P T E R 6 Projection Geometry 89 A B A FIGURE 6-12 The position of an object can be determined with respect to reference structures with use of the tube shift technique. A, An object on the buccal surface of the mandible may appear apical to the second premolar. B, When another radiograph is made of this region angulated from the mesial, the object appears to have moved distally with respect to the second premolar apex (“opposite buccal” in the acronym SLOB). Examination of a conventional set of full-mouth images with this rule in mind demonstrates that the incisive foramen is located lingual (palatal) to the roots of the central incisors and that the mental foramen lies buccal to the roots of the premolars. This technique assists in determining the position of impacted teeth, the presence of foreign objects, and other abnormal conditions. It works just as well when the x-ray machine is moved vertically as horizontally. The dentist may have two radiographs of a region of the dentition that were made at different angles, but no record exists of the orientation of the x-ray machine. Comparison of the anatomy displayed on the images helps distinguish changes in horizontal or vertical angulation. The relative positions of osseous landmarks with respect to the teeth help identify changes in horizontal or vertical angulation. Figure 6-13 shows the inferior border of the zygomatic process of the maxilla over the molars. This structure lies buccal to the teeth and appears to move mesially as the x-ray beam is oriented more from the distal. Similarly, as the angulation of the beam is increased vertically, the zygomatic process is projected occlusally over the teeth. EGGSHELL EFFECT Plain images—images that project a three-dimensional volume onto a two-dimensional receptor—may produce an eggshell effect of corticated structures. Figure 6-14, A, shows a schematic view of an egg being exposed to an x-ray beam. The top photon has a tangential path through the apex of the egg and a much longer path through the shell of the egg than does the lower photon, which strikes the egg at right angles to the surface and travels through two thicknesses of the shell. As a result, photons traveling through the periphery of a curved surface are more attenuated B FIGURE 6-13 The position of the maxillary zygomatic process in relation to the roots of the molars can help in identifying the orientation of views. A, The inferior border of the zygomatic process lies over the palatal root of the first molar. B, The inferior border of the zygomatic process lies posterior to the palatal root of the first molar. This difference in position of the zygomatic process in relation to the palatal root indicates that when the image in A was made, the beam was oriented more from the posterior than when the image in B was made. The same conclusion can be reached independently by examining the roots of the first molar. The palatal root lies behind the distobuccal root in the image in A, but it lies between the two buccal roots in the image in B. than photons traveling at right angles to the surface. Figure 6-14, B, shows an expansile lesion on the buccal surface of the mandible on an occlusal view. The periphery of the expanded cortex is more opaque than the region inside the expanded border. The cortical bone is not thicker on the cortex than over the rest of the lesion, but rather the x-ray beam is more attenuated in this region because of the longer path length of photons through the bony cortex on the periphery. This eggshell effect accounts for why normal structures such as the lamina dura, the border of the maxillary sinuses and nasal fossa, and abnormal structures, including the corticated walls of cysts and benign tumors, are well demonstrated on plain images. Soft tissue masses, such as the nose and tongue, do not show an eggshell effect because they are uniform rather than being composed of a dense layer surrounding a more lucent interior. 90 PART II A Imaging B C FIGURE 6-14 Eggshell effect. A, Radiograph of a hard-boiled egg. Note how the rim of the eggshell is opaque even though it is uniform in thickness. B, Schematic view of the egg being exposed to an x-ray beam. The top photon has a tangential path through the apex of the egg and a longer path through the shell of the egg than the lower photon. As a result, photons traveling through the periphery of a curved surface are more attenuated than the photons traveling at right angles to the surface. C, An expansile lesion on the buccal surface of the mandible on an occlusal view. The expanded cortex is more opaque than the region inside the border as a result of the eggshell effect. BIBLIOGRAPHY Buccal-Object Rule Clark CA: A method of ascertaining the relative position of unerupted teeth by means of film radiographs, Proc R Soc Med Odontol Sect 3:87–90, 1910. Gutmann JL, Endo C: Clark’s rule vis a vis the buccal object rule: its evolution and application in endodontics, J Hist Dent 59(1):12–15, 2011. Jacobs SG: Radiographic localization of unerupted maxillary anterior teeth using the vertical tube shift technique: the history and application of the method with some case reports, Am J Orthod Dentofac Orthop 116:415–423, 1999. Jacobs SG: Radiographic localization of unerupted teeth: further findings about the vertical tube shift method and other localization techniques, Am J Orthod Dentofac Orthop 118:439–447, 2000. 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