minimized, as shown by an integrated circuit magnified at 1.25× (b), 20× (c), and 40× (d).
Rockwell International
Reduction of Scattering. Another advantage of placing the testpiece closer to the source is a reduction of secondary
(scattered) radiation. When the magnification factor, M, in Eq 9 is greater than 3, the build-up factor, 1 + I
S
/I
D
, approaches
1 (Ref 2).
Distortion. As long as the plane of a two-dimensional object and the plane of the imaging surface are parallel to each
other, the image will be undistorted regardless of the angle at which the beam of radiation impinges on the object. In
addition, the degree of enlargement at different points in a given image is constant because the ratio L
i
/L
o
is invariant.
However, as shown in Fig. 23(b), if the plane of the object and the plane of the recording surface are not parallel, the
image will be distorted because the degree of enlargement is different between rays passing through any two points on the
surface of the object. This is the main reason radiographic images almost always present a distorted picture of testpiece
features; the shape of most testpieces is such that one or more of its features is not parallel to the imaging surface. The
degree of distortion is directly related to the degree of nonparallelism; small amounts of nonparallelism produce small
degrees of distortion, and large amounts produce large degrees of distortion.
Although there is no distortion of images of features that are parallel to the imaging surface, spatial relationships among
testpiece features are distorted, with the amount of distortion being directly related to the cosine of the angle of the beam
to the imaging surface. For example, two circular features that are parallel to the imaging surface but at different object-
to-detector distances may produce two separate circular images, or one noncircular image because two images overlap, as
shown in Fig. 23(c), depending on the direction of the radiation beam. In most actual radiographs, regions where images
of different features overlap will appear as regions of greater or lesser contrast than adjacent regions where the images do
not overlap, depending on whether the features absorb less radiation or more radiation than portions of the testpiece
surrounding the features. For example, overlapping images of voids or cavities will appear darker on film or brighter on
fluorescent screens in regions of overlap because less radiation is absorbed along paths intersecting overlapping voids
than along paths that intersect only one void.
Geometric Unsharpness. In reality, any radiation source is too large to be approximated by a point. Conventional x-
ray tubes have focal spots between 2 by 2 mm (0.08 by 0.08 in.) and 5 by 5 mm (0.2 by 0.2 in.) in size, while microfocus
x-ray systems have focal-spot sizes as small as 5 m (0.2 mil). Even high-energy sources have focal spots of appreciable
size, although seldom exceeding 2 mm (0.08 in.) in diameter. Gamma-ray sources vary widely in size, depending on
source strength and specific activity, but are seldom less than about 2.5 mm (0.1 in.) in diameter.
Radiographic definition varies according to the geometric relationships among source size, source-to-object distance, and
object-to-image distance. When radiation from a source of any finite size produces a shadow, that portion of the image
that is in shadow for radiation emanating from all points on the surface of the source is a region of complete shadow
known as the umbra. Portions of the image that are in shadow for radiation emanating from any portion of the source, but
not in shadow for radiation from some portion, are regions of partial shadow known as the penumbra. The degree of
geometric unsharpness is equal to the width of the penumbra. Mathematically, the geometric unsharpness, U
g
, is
determined from the laws of similar triangles, as illustrated in Fig. 23(d), and can be expressed as:
(Eq 10)
where F is the size of the focal spot -ray source, t is the object-to-image distance, and L
o
is the source-to-object
distance. In most cases, t is considered to be the difference between the source-to-image distance, L
i
, and the source-to-
object distance, L
o
; therefore, Eq 10 can be alternatively expressed as:
(Eq 11)
The size of the penumbra, or the geometric unsharpness, can be reduced by lengthening the source-to-object distance, by
reducing the size of the focal spot, or by reducing the object-to-image distance. In practice, the source size is determined
by the characteristics of a given x-ray tube or by the physical dimensions of a radioactive pellet, and the object-to-image