~ radiograph is a two-dimensional representa-1.1 tion of a three-dimensional object. To obtain

the maximal value from a radiograph, a clinician musthave a clear understanding of normal anatomy andthen mentally reconstruct a three-dimensional image ofthe anatomic structures of interest from one or moreof these two-dimensional views. Using high-quality radi-ographs greatly facilitates this task. The principles ofprojection geometry describe the effect of focal spotsize and position (relative to the object and the film)on image clarity, magnification, and distortion. Clini-cians use these principles to maximize image clarity,minimize distortion, and localize objects in the imagefield.

Several geometric considerations contribute to imageclarity, particularly image sharpness and resolution.Sha7pness measures how well a boundary between twoareas of differing radiodensity is revealed. Image spatialresolution measures how well a radiograph is able toreveal small objects that are close together. Althoughsharpness and resolution are two distinct features, theyare interdependent, being influenced by the same geo-metric variables. For clinical diagnosis it is desirable tooptimize conditions that will result in images with highsharpness and resolution.

When x rays are produced at the target in an x-raytube, they originate from all points within the area ofthe focal spot. Because these rays originate from dif-ferent points and travel in straight lines, their projec-tions of a feature of an object do not occur at exactlythe same location on a film. As a result, the image ofthe edge of an object is slightly blurred rather than

sharp and distinct. Fig. 5-1 shows the path of photonsthat originate at the margins of the focal spot andprovide an image of the edges of an object. The result-ing blurred zone of unsharpness on an image causes aloss in image clarity by reducing sharpness and resolu-tion. The larger the focal spot area, the greater the lossof clarity.

Three methods exist for minimizing this loss ofimage clarity and improving the quality of radiographs:1. Use as small an effective focal spot as practical. Dental

x-ray machines should have a nominal focal spotsize of 1.0mm or less. Some tubes used in extraoralradiography have effective focal spots measuring0.3 mm, which greatly adds to image clarity. X-raytube manufacturers use as small an effective focalspot size as is consistent with the requirements forheat dissipation. As described in Chapter 1, the sizeof the effective focal spot is a function of the angleof the target with respect to the long axis of the elec-tron beam. A large angle distributes the electronbeam over a larger surface and decreases the heatgenerated per unit of target area, thus prolongingtube life. However, this results in a larger effectivefocal spot and loss of image clarity (Fig. 5-2). A smallangle has a greater wearing effect on the target butresults in a smaller effective focal spot, decreasedun sharpness, and increased image sharpness andresolution. This angle of the face of the target to thecentral x-ray beam is usually between 10 and 20

degrees.2. Increase the distance between the focal spot and the object

by using a long, open-ended cylinder: Fig. 5-3 shows howincreasing the focal spot-to-object distance reducesimage blurring by reducing the divergence of the x-ray beam. The longer focal spot-to-object distanceminimizes blurring by using photons whose paths

86

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87PROJECTION GEOMETRYCHAPTER 5

Focal spotAnodeare almost parallel. The benefits of using a long focalspot-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 film. Fig.5-4 shows that as the object-to-film distance isreduced, the unsharpness decreases, resulting inenhanced image clarity. This is the result of mini-mizing the divergence of the x-ray photons.

~

Object

Image size distortion (magnification) is the increasein size of the image on the radiograph compared withthe actual size of the object. The divergent paths ofphotons in an x-ray beam cause enlargement of theimage on a radiograph. Image size distortion resultsfrom the relative distances of the focal spot-to-film andobject-to-film (see Figs. 5-3 and 5-4). Accordingly,increasing the focal spot-to-film distance and decreas-ing the object-to-film distance minimizes image magni-fication. The use of a long, open-ended cylinder as an

Image

ceptor

'to:

i+Unsharpness-'t-; i+

Density

FIG. 5-1 Photons originating at different places on the focalspot result in a zone of unsharpness on the radiograph. Thedensity of the image changes from a high background valueto a low value in the area of an edge of enamel, dentin, or bone.

Imagereceptor

Imagereceptor

"IIIIIIIIIIII ..(-II

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:~i~ ~III,

~ unsnarpness~

FIG. 5-2 Decreasing the angle ot the target perpendicular to the long axis ot the electronbeam decreases the actual focal spot size and decreases heat dissipation and thereby tubelife. It also decreases the effective focal spot size, thus increasing the sharpness of the image.

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,88 PART IV IMAGING PRINCIPLES AND TECHNIQUES

~

d

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FIG. 5-3 Increasing the distance between the focal spot and the object results in animage with increased sharpness and less magnification of the object.

1m",'~'pw'

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FIG. 5-4 Decreasing the distance between the object and the film increases the sharp-ness and results in less magnification of the object.

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aiming device OIY an x-ray machme thus reduces themagnification of images on a periapical view. Further-more, as mentioned above, this technique alsoimproves image clarity by increasing the distancebetween the focal spot and object.

~

FIG. 5-6 Elongation of a radiographic image results whenthe central ray is perpendicular to the object but not to the film.

Image shape distortion is the result of unequal magni-fication of different parts of the same object. This situ-ation arises when not all the parts of an object are atthe same focal spot-to-object distance. The physicalshape of the object may often prevent its optimal ori-entation, resulting in some shape distortion. Such aphenomenon is seen by the differences in appearanceof the image on a radiograph compared with the trueshape. To minimize shape distortion, the practitionershould make an effort to align the tube, object, and filmtarefully, using the following guidelines:1. Position the film parallel to the long axis of the object.

Image shape distortion is minimized when the longaxes of the film and tooth are parallel. Fig. 5-5 showsthat the central ray of the x-ray beam is perpendi-cular to the film, but the object is not parallel to thefilm. The resultant image is distorted because of theunequal distances of the various parts of the objectfrom the film. This type of shape distortion is calledforeshortening because it causes the radiographicimage to be shorter than the object. Fig. 5-6 shows

4

me sltuauon wnen me x-ray oeam IS onentea at ngntangles to the object but not to the film. This resultsin elongation, with the object appearing longer on thefilm than its actual length.

2. Orient the central ray perpendicular to the object and film.Image shape distortion occurs if the object and filmare parallel but the central ray is not directed at rightangles to each. This is most evident on maxillarymolar projections (Fig. 5-7). If the central ray is ori-ented with an excessive vertical angulation, thepalatal roots appear disproportionately longer thanthe buccal roots.The practitioner can prevent distortion errors by

aligning the object and film parallel with each otherand the central ray perpendicular to both.

Paralleling and BisectIng-Angie

Techniquesrrom me earllt:lil UitYli VI U\::lllitl litUIV~litpIlY, it LIlIlIL"1

objective has been to produce accurate images of dentalstructures that are normally visually obscured. An earlymethod for aligning the x-ray beam and film with theteeth and jaws was the bisecting-angle technique (Fig. 5-8).In this method the film is placed as close to the teethas possible without deforming it. However, when thefilm is in this position, it is not parallel to the long axesof the teeth. This arrangement inherently causes

III'ayt:receptor

h oiy 5 ~O.,.,.".,.,.,.,.,...

1-1l.J. ~-~ I-oresnorrenlng or CI rCluluyrClfJlllL IIIIQ!:jt: 1t:~Ull~when the central ray is perpendicular to the film but theobject is not parallel with the film.

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\IMAGING PRINCIPLES AND TECHNIQUESPART IV90

\ Central axis of tooth

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FIG. 5-7 The central ray should be perpendicular to thelong axes of both the tooth and the film. When the direc-tion of the x-ray beam is not at right angles to the long axisof the tooth, the appearance of the tooth is distorted, as seenby apparent elongation of the length of the palatal roots.Additionally, distortion of the relationship of the height ofthe alveolar crest relative to the cementoenamel junction(CEJ) occurs. In this case the buccal alveolar crest appears tolie superior to the palatal CEJ.

FIG. 5-9 In the paralleling technique the central ray isdirected at a right angle to the central axes of the object and

the film.

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mandible. Even though the projected length of a toothis correct, the image is still distorted because the filmand object are not parallel and the x-ray beam is notdirected at right angles to them. This distortion tendsto increase along the image toward the apex.

When the central ray is not perpendicular to thebisector plane, the length of the image of a projectedtooth changes. If the central ray is directed at an anglethat is more positive than perpendicular to the bisector,the image of the tooth is foreshortened. Likewise, if it isinclined with more negative angulation to the bisector,the image is elongated. In recent years, the bisecting-angle technique has been used less frequently forgeneral periapical radiography as use of the parallelingtechnique has increased.

The paralleling technique is the preferred method formaking intraoral radiographs. It derives its name as theresult of placing the film parallel with the long axis ofthe tooth (Fig. 5-9). This procedure minimizes imagedistortion and best incorporates the imaging principlesdescribed in the first three sections of this chapter.

To achieve this parallel orientation, the practitioneroften must position the film toward the middle of theoral cavity, away from the teeth. Although this allows theteeth and film to be parallel, it results in some imagemagnification and loss of definition by increasingunsharpness. As a consequence, the paralleling tech-nique also uses a relatively long open-ended aimingcylinder ("cone") to increase the focal spot-to-object

FIG. 5-8 In the bisecting-angle technique the central rayis directed at a right angle to the imaginary plane that bisectsthe angle formed by the film and the central axis of theobject. This method results in an image that is the samelength as the object.

distortion. Nevertheless, by directing the central rayperpendicular to an imaginary plane that bisects theangle between the teeth and the film, the practitionercan make the length of the tooth's image on the filmcorrespond to the actual length of the tooth. This anglebetween a tooth and the film is especially apparentwhen teeth are radiographed in the maxilla or anterior

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~lI'KUjtLllUN (.,tUMtIKY'-MAl" I:K ;)

dIstance. thiS dIrects Only me most central ana paral-lel rays of the beam to the film and teeth and reducesimage magnification while increasing image sharpnessand resolution. The paralleling technique has bene-fited from the development of fast-speed film emul-sions, which allow relatively short exposure times inspite of an increased target-to-object distance.

Because it is desirable to position the film near themiddle of the oral cavity with the paralleling technique,film holders should be used to support the film in thepatient's mouth. Chapter 8 discusses film-holdinginstruments and techniques for intraoral radiographyusing the paralleling technique.

radIograph, the dentIst may take an occlusal projectionto identify its mediolateral position. The occlusal filmmay reveal a calcification in the soft tissues located lat-erally or medially to the body of the mandible. Thisinformation is important in determining the treatmentrequired. The right-angle (or cross-section) techniqueis best for the mandible. On a maxillary occlusal pro-jection the superimposition of features in the anteriorpart of the skull may frequently obscure the area ofinterest.

The second method used to identify the spatial posi-tion of an object is the tube shift technique. Other namesfor this procedure are the buccal object rule and Clark'srule (Clark described it in 1910). The rationale for thisprocedure derives from the manner in which the rela-tive positions of radiographic images of two separateobjects change when the projection angle at which theimages were made is changed.

Fig. 5-11 shows two radiographs of an object exposedat different angles. Compare the position of the objectin question on each radiograph with the referencestructures. If the tube is shifted and directed at the ref-erence object (e.g., the apex of a tooth) from a moremesial angulation and the object in question also movesmesially with respect to the reference object, the objectlies lingual to the reference object.

Alternatively, if the tube is shifted mesially and theobject in question appears to move distally, it lies on the

In cimIcal practIce, the dentIst must otten derIve troma radiograph three-dimensional information concern-ing patients. The dentist may wish to use radiographs,for example, to determine the location of a foreignobject or an impacted tooth within the jaw. Twomethods are frequently used to obtain such three-dimensional information. The first is to examine twofilms projected at right angles to each other. Thesecond method is to employ the so-called tube shift

technique.Fig. 5-10 shows the first method, in which two projec-

tions taken at right angles to one another localize an objectin or about the maJcilla in three dimensions. In clinicalpractice the position of an object on each radiographis noted relative to the anatomic landmarks. This allowsthe observer to determine the position of the objector area of interest. For example, if a radiopacity isfound near the apex of the first molar on a periapical

A

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FIG. 5-11 The position of an object may be determinedwith respect to reference structures using the tube shift tech-nique. In A, an object on the lingual surface of the mandiblemay appear apical to the second premolar. When anotherradiograph is made of this region angulated from the mesial,B, the object appears to have moved mesially with respectto the second premolar apex ("same lingual" in the acronym

SLOB).

g

FIG. 5-10 A, The periapical radiograph shows impactedcanine lying apical to roots of lateral incisor and first pre-molar. S, The vertex occlusal view shows that the canine liespalatal to the roots of the lateral incisor and first premolar.

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,

92 PART IV IMAGING PRINCIPLES AND TECHNIQUES

landmarks with respect to the teeth helps identifychanges in horizontal or vertical angulation. Fig. 5-13shows the inferior border of the zygomatic processof the maxilla over the molars. This structure liesbuccal to the teeth and appears to move mesially as thex-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 theteeth.

buccal aspect of the reference object (Fig. 5-12). Theserelations can be easily remembered by the acronymSLOB: Same Lingual, Opposite Buccal. Thus if theobject in question appears to move in the same direc-tion with respect to the reference structures as does thex-ray tube, it is on the lingual aspect of the r~ferenceobject; if it appears to move in the opposite directionas the x-ray tube, it is on the buccal aspect. If it doesnot move with respect to the reference object, it lies atthe same depth (in the same vertical plane) as the ref-erence object.

Examination of a conventional set of full-mouthfilms with this rule in mind demonstrates that the inci-sive foramen is indeed located lingual (palatal) to theroots of the central incisors and that the mentalforamen lies buccal to the roots of the premolars. Thistechnique assists in determining the position ofimpacted teeth, presence of foreign objects, and otherabnormal conditions. It works just as well when the x-ray machine is moved vertically as horizontally.

The dentist may have two radiographs of a regionof the dentition that were made at different angles,but no record exists of the orientation of the x-raymachine. Comparison of the anatomy displayed on theimages helps distinguish changes in horizontal orvertical angulation. The relative positions of osseous

A

A

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~FIG. 5-13 The position of the maxillary zygomaticprocess in relation to the roots of the molars can help in iden-tifying the orientation of projections. In A, the inferior borderof the process lies over the palatal root of the first molar,whereas in B, it lies posterior to the palatal root of the firstmolar. This indicates that when A was made, the beam wasoriented more from the posterior than when B was made.The same conclusion can be reached independently byexamining the roots of the first molar. In A, the palatal rootlies behind the distobuccal root, but in B, it lies between thetwo buccal roots.

BFIG. 5-12 The position of an object can be determinedwith respect to reference structures using the tube shift tech-nique. In A, an object on the buccal surface of the mandiblemay appear apical to the second premolar. When anotherradiograph is made of this region angulated from the mesial,B, the object appears to have moved distally with respect tothe second premolar apex ("opposite buccal" in the

acronym SLOB).

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93CHAPTER 5 PROJECTION GEOMETRY

BIBLIOGRAPHY Khabbaz MG, Serefoglou MH: The application of the buccalobject rule for the determination of calcified root canals,Int Endod] 29:284-7,1996.

Ludlow ]B: The Buccal Object Rule, Dentomaxillofac Radiol28:258, 1999.

Reader A: A teaching model for the buccal object rule,] DentEduc 48:469-72, 1984.

BUCCAL OBJECT RULE

Chenail B, Aurelio ]A, Gerstein H: A model for teaching theBuccal Object Moves Most Rule,] Endod 9:452-3, 1983.

Clark CA: A method of ascertaining the relative position ofunerupted teeth by means of film radiographs, Proc R SocMed Odontol Sect 3:87,1910.

Goerig AC, Neaverth E]: A simplified look at the buccal objectrule in endodontics,] Endod 13:570,1987.Jacobs

SG: Radiographic localization of unerupted teeth:further findings about the vertical tube shift method andother localization techniques, Am ] Orthod DentofacialOrthop 118:439-47, 2000.

Jacobs SG: Radiographic localization of unerupted maxillaryanterior teeth using the vertical tube shift technique: thehistory and application of the method with some casereoorts. Am T Orthod Dentofacial Orthop 116:415-23, 1999.

PARALLELING TECHNIQUEForsberg], Halse A: Radiographic simulation of a periapical

lesion comparing the paralleling and the bisecting-angletechniques, Int Endod] 27:133-8, 1994.

Forsberg]: A comparison of the paralleling and bisecting-angle radiographic techniques in endodontics, Int Endod] 20:177-82,1987.

Schulze RK, d'Hoedt B: A method to calculate angular dis-parities between object and receptor in "paralleling tech-nique," Dentomaxillofac Radiol 31:32-8, 2002.

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