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
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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
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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.
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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
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10
0
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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,
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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.
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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.
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