ASNT NDT Handbook Volume 4 Infrared and Thermal Testing

1. Cesium iodide can be formed into phosphor material on these same detector
needles on top of the diode structure structures. The fiber optic scintillator
to direct the light to the photodiodes structure and the hybrid analogs (Fig. 3)
without significant light scatter. The provide a similar light guiding capability,
needles are separated by small air gaps provide high X-ray absorptivity without
and the high refractive index sensitivity to moisture and permit control
mismatch between the cesium iodide of afterglow17-19 but are not as bright an
needles and air ensures a high total X-ray converter as is the cesium iodide.
internal reflection of the light as it is
directed to the photodiode. Because the gain in the fiber optic
scintillators materials is not as high as in
2. The needle structure enables thick cesium iodide, a potential secondary
phosphor layers, which improves quantum sink is possible especially in a
X-ray absorption. lens based charge coupled device system.
This lower gain will clearly lead to a
3. The cesium iodide has a high effective higher noise level for a given exposure or
atomic number (Z) which also to a much longer exposure time to
contributes to good X-ray absorption generate similar statistics. If the detection
efficiency. system used leads to a strictly quantum
limited configuration for any of the
One disadvantage of the thallium phosphor systems mentioned, then they
activated cesium iodide material is that it all should provide similar image quality,
is sensitive to moisture and this assuming the resulting signal levels are
hygroscopic nature can degrade the high enough above the noise floor of the
spatial resolution of the phosphor and detection system to render the detector
therefore the device over time if allowed noise negligible.
to be in contact with ambient humid
conditions. Manufacturers of cesium On the other hand, if a phosphor is
iodide based systems provide sealed too bright under a range of X-ray
enclosures. A sealed enclosure may conditions, then it is possible for the
typically add 20 percent or more to the diodes to be filled too quickly and a
cost relative to other phosphors and may mottled image can result simply because
reduce the robustness of the system. of the low number of X-ray photons
Another disadvantage is that the actually transmitting the part. One way to
phosphor is prone to afterglow and solve this problem is to use a lower gain
potential variations in light output as a phosphor or the fiber optic scintillators
function of increasing X-ray dose. and use an extended exposure in a single
frame. Another way is to average multiple
Nevertheless, the thallium activated frames with the faster phosphor until the
cesium iodide phosphor has shown desired image quality is produced.
increasing use on the amorphous silicon
detector,13 the charge coupled device To summarize, the selection of the
detector and the linear array detector. phosphor is as important as the selection
Other inorganic phosphor materials, such of the readout electronics and image
as terbium activated gadolinium acquisition software. All three have to be
oxysulfide (Gd2O2S:Tb),14 high density considered together in the design and
glass fiber optic scintillators (FOSs)15 and purchase of a system, as well as in the
hybrid combinations of gadolinium operation of the system.
oxysulfide and fiber optic scintillators16
have also been used successfully as X-ray The selenium photoconductive
material has been the photoconductive
FIGURE 2. Photograph of cesium iodide material of choice as a direct means of
fibers grown onto a photodiode array. converting X-rays directly into charged
carriers and avoiding the production of
light.3 This is described in more detail
elsewhere. The obvious advantage here is
that the image forming carriers can be
more effectively and efficiently directed to
the electrode structure than is possible
with light. The image sharpness and speed
that results can be very high. The
modulation transfer function can in
principle be higher than that of phosphor
based systems for a given pixel pitch. The
disadvantage of the selenium material,
however, is that it does not have as high
an atomic number as cesium iodide or
gadolinium oxysulfide. For nondestructive
testing applications where the X-ray
energy is typically above 50 kV, to obtain
similar X-ray sensitivity to the higher Z
phosphor materials, the selenium layer

290 Radiographic Testing

needs to be substantially thicker than the signal-to-noise ratio. This problem has
phosphor material. This means that the been corrected through reduction of gain
X-ray energy will be deposited in a thicker amplification during electronic readout.
region than in these phosphor
configurations. The downfall here is that Clearly, the debate of photoconductor
X-ray scatter and the diverging X-ray versus phosphor will remain an
beam can reduce the resulting spatial interesting topic for discussion and both
resolution in the image, reducing some of approaches will continue to be used
the benefit of the electrostatic transfer. successfully. If system noise or other
artifacts in the system begin to compete
A problem for the selenium approach with statistical noise, then in addition to
in the 1990s was that the speed of the proper selection of the converter, the
selenium process was too high in some detection system electronics needs to be
circumstances and the pixels were filled carefully evaluated. The systems discussed
with charge at a relatively low X-ray here have a wide range of system noise
exposure. This overcharging resulted in values, some from different sources and
quantum mottling and a reduced some not necessarily correctable. As a

FIGURE 3. Hybrid scintillator — phosphor attached to fiber optic scintillator.

(a)

Scintillating fiber optics
Phosphor layer

Coupling fluid

(b)

Radiation (X-rays) Phosphor
particles
Extramural absorption material
Phosphor
layer

Scintillating
fiber optics
Cladding
material
Fibers
Light

Digital Radiographic Imaging 291

final check, it is best to test the system for selected goes down, the percentage of
the application at hand. X-ray information in the radiation beam
will diminish and poor image contrast
Spatial Resolution will result.
Considerations
To compensate for this image
The efficiency of the energy conversion degradation, the conversion material can
process relates to the speed of the test, the be made thicker or, if time permits, a
throughput and the tradeoff with contrast longer total exposure time can be selected
sensitivity (the ability to detect a small to capture more X-ray quanta. Making the
change in thickness or density). conversion layer thicker can impact the
spatial resolving power of the device
Detector Resolution because both X-ray cross talk and signal
(light or electron hole carriers) cross talk
The spatial resolution of the detector will yield a breakdown in the modulation
determines if features in the object are of the signal somewhere in the spatial
detectable from a pixel sampling frequency range of the detector.
consideration. The selection of the spatial
resolution of the detector is also Modulation Transfer Function
important in designing or selecting a
detection system. From the aspect of A good measure of the spatial resolution
image contrast and spatial resolution, it is therefore is the modulation transfer
desirable to have the largest pixel that will function (MTF). The modulation transfer
allow detection of the features of interest function measures the signal modulation
in the radiographic examination. For as a function of spatial frequency and is
example, it is not necessary to select a typically computed using a fourier
39 µm pixel pitch if the application is for transform of a line spread function
the detection of large foreign objects left acquired on an angled tungsten edge
behind in an engine nacelle. Similarly, placed directly on the detector.13 Figure 4
fatigue crack detection is probably not shows the power of a modulation transfer
going to be too successful with a pixel function for revealing a breakdown in
pitch of 200 µm or larger. spatial resolution throughout the spatial
frequency regime of the detector. If the
Pixel Pitch spatial resolution drops near the 0 line
pairs per millimeter spatial frequency
The predominant factor that governs the regime, this drop can be interpreted as a
spatial resolution of a detector is the pixel severe degradation in image contrast and
pitch. The pixel size of a number of digital will result in poor density discrimination.
detectors is provided in Table 1. The If the modulation transfer function is low
selection of the X-ray conversion screen at high spatial frequencies, near the
then becomes important. Here the sampling limit of the detector, this
architecture of the X-ray conversion
material will dictate to what degree the FIGURE 4. Examples of modulation transfer function curves,
full spatial resolution of the detector can showing localized variations in modulation transfer function
be realized. curve in some regions of spatial frequency domain.
Maximum spatial resolution for detector is 10 line pairs per
As the pixel pitch is reduced to increase millimeter.
resolution, the total number of pixels in
the image increases for a constant field of Modulation transfer function 1 Scintillating fiber
view. The file sizes for typical images run (ratio, log scale) optic plates
from 2 to 8 megabytes. However, for
digital images at radioscopic (real time) Low
frame rates of 30 frames per second, the frequency
image size must be closer to about 0.1 drop (light
1 megabyte at current technology. scatter within
Therefore tradeoffs are made in selecting scintillator)
larger pixels for smaller fields of view for
digital radioscopy. Phosphor screen
reduces spatial
The selection of a high atomic number resolution
X-ray conversion material that can
provide a signal gain sufficient to not 0.01 2 4 6 8 10
allow secondary quantum sinks following 0 Spatial resolution (line pairs per millimeter)
absorption is critical. Forming this
material into a shape that directs the
signal onto a single pixel, as is done with
cesium iodide, is then crucial to
maintaining good image detail. As the
atomic number of the conversion material

292 Radiographic Testing

indicates that the conversion material is damage is a general term that can refer to
not a good choice for detection of the fine any range of damage to a component in
features that the system was designed to the detection chain. The damage can lead
detect. Another choice should be selected. to subtle changes in performance, all the
Balancing the spatial resolving powers of way to failure. Most digital detectors are
a conversion material with its quantum designed so that the electronic
efficiency has been an active area of components behind the X-ray conversion
research and development in digital material are either shielded from the
radiography since 1985. X-rays (for example, by the conversion
material itself or by fiber optic transfer
Gain and Offset Correction components behind it) or are sufficiently
thin to absorb only a small portion of the
Imagery from digital detectors are X-rays that impinge on the component.
frequently normalized for pixel-to-pixel The damage that occurs in the electronic
gain variations and also adjusted to circuitry can result in an increase in the
subtract out the background or offset. The electronic noise of the device and
offset or background signal is usually a eventually to failure as the accumulated
small percentage of the maximum signal dose to the component increases. Each
and is common to all digital detectors. It manufacturer uses proprietary circuitry
is important to subtract this background and various forms of shielding elements
signal to provide a wider linear range and to prevent these effects. Each system is
to subtract any latent images on the different, so the reader is referred to a
detector. In performing a gain correction, general text on radiation effects on silicon
not only are pixel-to-pixel variations circuitry.20
reduced but also variations in the optical
components feeding these pixels will be The X-ray conversion material, being
diminished. Performing this gain the primary X-ray absorption component,
correction can also be used to flatten the is exposed to the highest levels of
radiation intensity distribution across the radiation within the imaging chain.
detector panel. Making the radiation Phosphors such as cesium iodide and
beam intensity more uniform across the photoconductive materials such as
detector can result in wider latitude selenium have discontinuity centers
(viewable thickness range) in the image. within their band structures that will trap
This normalization is really not possible electron and hole carriers produced by the
with film radiography. ionizing radiation. In many
circumstances, thermally released carriers
The gain correction is accomplished by from these traps will yield a delayed
taking an image with a radiation luminescence or a delayed release of
technique similar to that planned for charge. This form of radiation damage
production but without an object in the known as afterglow or lag usually increases
beam (an air image) and with a much as a function of radiation dose until an
reduced X-ray intensity. By simply equilibrium occurs where the number of
performing an image division by the gain carriers being trapped equals the number
factor on a pixel-by-pixel basis, the offset being thermally released.
corrected air image is then used to correct
each subsequent image of an object. Another form of radiation damage to
Following gain and offset correction, X-ray conversion materials that occurs is
detection sensitivity improves in relation when the carriers are permanently
to an image that does not have this trapped in deep centers within the band
correction. For the air image, it is critical gap. This trapping is sometimes associated
that the image be free of transient latent with a darkening of the conversion
images, have the correct intensity and material and usually results in a rapid
also not contain an object of any sort decrease in signal that can only be healed
(such as a fixture) in the beam. If any of by heat annealing of the material or by
these occur, then every subsequent slow thermal release at room temperature.
corrected object image will contain This form of damage is known as a gain
artifacts and the correction will do more decrease. In other materials, it is possible
damage than good. to observe a rapid signal gain increase as a
function of increased radiation dose.
Radiation Damage Although the mechanism of gain decrease
is not widely understood, both gain
In digital imaging devices, there are changes can impart spatial artifacts into a
numerous elements of the detector current image created by the variation in
assembly that can be damaged by the radiation intensity across a prior specimen
ionizing radiation. Every component in image. In most cases these gain changes
the imaging chain not shielded are not long term or permanent. If the
appropriately from X-rays or gamma rays system is prone to these radiation induced
can be damaged. The term radiation gain changes, it is important to
continually update gain and offset data,
even if the actual examination is not

Digital Radiographic Imaging 293

changing, so that these artifacts can be possible because larger pixels can produce
reduced. If the problem becomes severe it a higher signal-to-noise ratio for a given
might warrant a new phosphor. X-ray exposure. Larger pixels will also
allow a lower exposure for a constant
The storage phosphor used in signal-to-noise ratio. Larger pixels permit
computed radiography systems, europium thicker X-ray conversion materials, again
activated barium fluorobromide potentially adding speed to the test.
(BaFBr:Eu), inherently has discontinuity Finally larger pixels will result in a larger
centers when prepared under certain overall field of view (larger throughput).
reducing conditions in the presence of a For example, a four million pixel array of
partial pressure of hydrogen (H2) gas in an 200 µm pixels will have 16× the field of
otherwise inert atmosphere.4,21,22 In this view of a four million pixel array of
phosphor, this radiation damage has been 50 µm pixels. As mentioned earlier, the
used in a novel way by storing these size of the detector and the size of the
charge carriers in the phosphor material pixel still go hand in hand using today’s
and then later reexciting those carriers technology. It is be possible to have a
(with red light emitting diodes or a 10 000 × 10 000 pixel array of 25 µm
helium neon laser) to produce a delayed pixels resulting in a 250 × 250 mm device.
luminescence. In storage phosphors, this That said, if a smaller pixel device is
radiation damage is beneficial but, in selected, it might be possible to average
promptly emitting materials such as pixels into larger superpixels to enhance
cesium iodide, is to be avoided if possible. speed and part throughput. The minor
drawbacks of such superpixels is that the
Selection of Systems to X-ray conversion material may not be of
Match Application optimal thickness for the larger size pixel
and the percent of active pixel (because
Some of the key characteristics that might the amorphous silicon approach may be
be considered in the selection of a digital summing four field effect transistors) may
radiographic imaging system are the not be as great as if the pixel were
following: (1) detection precision and designed with a single set of readout
accuracy; (2) system speed to match that circuitry. Finally, the noise of averaging
of manufacturing and test processes; four pixels is a little higher than the noise
(3) area of the detector to match of a similar detector element of the same
manufacturing throughput needs; size.
(4) volume of the device for access to
tight locations in an assembly; For tight locations, small detectors
(5) presence of artifacts that can impact based on charge coupled device or
detection capability. complementary metal oxide silicon
technology can be used. Some of these
If a large area detector is needed and devices are being used for dental
there is a requirement to work at real time radiography and they are beginning to
frame rates of 30 frames per second, then find application in nondestructive testing.
an amorphous silicon detector or charge
coupled device based detector should be Where the requirement is to simply
selected.23 Note that technology in 2002 replace film in favor of a lower cost digital
may limit digital radioscopy frames to solution, then storage phosphors can be
about one million pixels. If static imaging used quite successfully. However, if access
is required but the highest spatial is not an issue, then the other digital
resolution is needed and the object size is approaches may be more cost effective
not large, then a system using a low noise over the long term because they are more
phosphor or charge coupled device should amenable to high speed mechanized
be selected. For this same application, a automation of the detector and X-ray tube
large area flat panel detector operating in to scan about a part or conversely for the
static mode can also be selected if used in part to be scanned through the stationary
combination with a microfocus X-ray tube tube and detector configuration.
but only if the application can withstand
the longer exposure times associated with Linear arrays can be used in an
magnification radiography.24 assembly line configuration, as can the
real time flat panel and charge coupled
If super high resolution is required, for device detector based systems. Line
example, very tight small crack detection, scanners offer the advantage of reduced
then magnification may be required with sensitivity to X-ray scatter in relation to
the high resolution charge coupled device area array systems.22
devices.
The scanning beam, reversed geometry
As mentioned above, it is important to system has shown promise in reduced
have the largest pixel that can be accepted access applications. This detector is
from a feature detection (spatial natural because the detector module is
resolution) standpoint. This parameter quite small. The reversed geometry system
then provides the highest throughput is probably the best system for reduced
sensitivity to X-ray scatter because the
detector is essentially a point based

294 Radiographic Testing

sensor. However, it is important to note
that the detector is typically much larger
than an X-ray tube focal spot. Because of
the effective focal spot size of the system,
there may be some geometric constraints
placed on this system in terms of image
unsharpness.

Artifacts have been prevalent in digital
radiographic systems. The presence of
artifacts, therefore has to be evaluated
almost on a detector-to-detector basis.

Digital Radiographic Imaging 295

PART 4. X-Ray Detector Technology

Amorphous Silicon speed and synchronized process. Each
Detectors23 charge is digitized by an analog to digital
converter and then stored in a precise
Most new amorphous silicon designs are memory location in the image processing
based on a flat glass panel that has computer. Once every transistor is
undergone a deposition process resulting sampled and read out, a complete image
in a coating on one side that contains will be displayed on the viewing monitor.
several million amorphous silicon
transistors. These transistors are arranged With regard to flat panel receptors, a
in a precise array of rows and columns. pixel is the area of one transistor and one
Bias and control lines are brought to the photo diode.24 Typically these pixels
edge of the panel for each individual range is size from 100 × 100 µm
transistor. The length and makeup of
these control lines play a role in how fast FIGURE 6. Circuitry of amorphous silicon
image data can be scanned out of the detector array.
array. On large receptors the control lines
are typically brought out from the middle Read amplifiers One pixel
to both sides of the panel to minimize the
track lengths. Row drivers

Figure 5 illustrates a cutaway view of a Thin film Bias supply
typical panel design. This configuration is transistor
typical of a receptor incorporating a
phosphor conversion layer. The phosphor switch
layer converts the X-ray photons to light
photons. The light photons are in turn Photodiode
converted to electrons by the amorphous
silicon array and the readout electronics. FIGURE 7. Photomicrograph of amorphous silicon detector
circuitry.
The next layer of the assembly (shown
in Fig. 5) is the amorphous silicon Data Bias
transistor array. Deposited on a glass line line
substrate to provide a rigid and very flat
surface, this layer converts the light Row
photons, from the phosphor, into line Thin film
electrons that can be read out, amplified,
digitized and stored as an image. Each transistor
element of the amorphous silicon array is switch
made up of a transistor and a photo
diode. See Fig. 6 for a schematic
representation of a small section of the
receptor. The light from the phosphor is
captured by the photodiode and then read
out through the transistor in a very high

FIGURE 5. Scintillator attached to amorphous silicon array.

Scintillator

Photodiode

Transistor array

Glass One pixel
substrate

296 Radiographic Testing

(0.004 × 0.004 in.) to 400 × 400 µm each pixel and the connections used to
(0.016 × 0.016 in.). A typical pixel is get the image data out.
shown in Fig. 7.
The high resolution view of an
Figure 8 shows a cross sectional view of aluminum tube weld in Fig. 10 was
an amorphous silicon receptor that uses a obtained with an amorphous silicon panel
cesium iodide scintillator. This view originally acquired at 4× geometric
suggests the path taken by the X-ray beam magnification with a microfocus X-ray
as it exits the object being tested and source. In the lower portion of the image
enters the input of the receptor. Figure 9 is the placement of a 75 µm (0.003 in.)
shows an image receptor assembly with thick ASTM aluminum plaque image
the electronics folded out from behind quality indicator. The central hole in this
the panel during assembly and testing. plaque is 250 µm (0.010 in.) in diameter
The large dark area at the right center of and is clearly visible through the thin
the picture is the amorphous silicon array. aluminum walls, about 1.25 mm
Around the edges of the array are all the (0.050 in.) thick. This image illustrates
electronics required to control and read that very small diameter porosity can be
out the image data. detected in these structures: comparing
the gray scale and size of the pores in the
The micrograph in Fig. 7 shows the weld with the holes of the image quality
mechanical makeup of the amorphous indicator reveals porosity much smaller in
silicon layer. The bias and data lines diameter than the 1T (250 µm [0.010 in.])
provide the ability to properly control hole. Figure 10b provides a high pass filter
rendition of this image. Once filtered,
FIGURE 8. Schematic cross section of photodiode X-ray contrast may be added to the image so
detector using amorphous silicon receptor with cesium that high contrast can be observed across
iodide scintillator. the entire thickness range of the object.
This now provides information on the
X-rays weld almost to the tangent point and
assists the operator in identifying
Cesium Visible photons discontinuities over a wider range of
iodide thickness in a single view.

Bias Most flat panel receptors available
Output today are designed to provide
radiographic acquisition capability at a
Photodiode Row select rate of one image about every 5 to 10 s.
Some designs take more or less time to
put the image on the monitor but most
fall into this range. This speed is certainly

FIGURE 9. Photograph of amorphous silicon FIGURE 10. Aluminum tube weld image acquired with
detector with electronics mounted to side of amorphous silicon detector with 4X geometric
panel in position where they can be magnification. (a) porosity as small as 125 µm (0.005 in.)
shielded from X-rays. can be detected in gray scale image; (b) high pass filter
provides high contrast over wider thickness range in single
view, making porosity evident almost to tangent point of
weld.

(a) (b)

Digital Radiographic Imaging 297

much faster than what can be achieved field lines. Because the field lines are
with film cassettes. This technology parallel to the incident X-ray beam (other
represents an advance in practicality since than for oblique angles), the field
the 1990s. prevents the charge from lateral scattering
and thus there is virtually no blur.
Amorphous Selenium Intuitively, this would seem to suggest
Detectors that the amorphous selenium conversion
layer (excluding the pixel electrodes)
In flat panel arrays using an amorphous should exhibit extremely high resolution.
selenium converter (or other In fact, measurements prove this to be the
photoconductors), the X-ray to electrical case.
charge conversion process is referred to as
direct because no intermediate steps are Charge Coupled Device
required. As shown in Fig. 11, the high Radiographic Systems
voltage bias field applied to an
amorphous selenium layer creates vertical Charge coupled devices are used in X-ray
imaging systems in combination with
FIGURE 11. Schematic cross section of amorphous selenium X-ray phosphors or scintillators without
X-ray detector.12 the need for electronic image
intensification. A charge coupled device is
Top bias electrode Positive voltage an integrated circuit formed by depositing
a series of electrodes, called gates on a
Field lines Amorphous selenium semiconductor substrate to form an array
of metal oxide semiconductor (MOS)
Trapped holes capacitors. By applying voltages to the
gates, the material below is depleted to
Pixel electrode Pixel electrode form charge storage wells. These store
charge injected into the charge coupled
Drain ++++ Drain Source device or generated within the
Insulator semiconductor by photoelectric
absorption of optical quanta. If the
Source voltages over adjacent gates are varied
appropriately, the charge can be
Gate Glass substrate Gate transferred from well to well under the
gates, much in the way that boats will
move through sets of locks as the
potential (water heights) are adjusted.12

FIGURE 12. Charge couple device based X-ray detector: (a) X-rays directly excite charge
coupled device through phosphor (phosphor does not provide enough shielding); (b) fiber
optic scintillator coupled directly to charge couple device provides shielding to sensor.

(a)

Phosphor layer, 0.05 to 0.20 mm
(0.002 to 008 in.) thick

Charge couple device array

(b)

Fiber optic protection plate or fiber optic X-rays
scintillator, 1 to 25 mm (0.04 to 1.0 in.) thick

Charge couple device array

298 Radiographic Testing

In the simplest charge coupled device surface. Fiber optic tapers thereby increase
systems, the charge coupled device is the field of view, provide efficient light
rapidly scanned to provide television collection (with respect to a lens), offer
frame rates with typical exposures per shielding of the charge coupled device
frame of 33 ms. In this mode, the signal from direct X-ray hits and can yield a
captured can be very low and the compact, light weight rigid design. Fiber
resulting signal-to-noise ratio will optic tapers have now been incorporated
therefore also be low because of the small with a 100 × 100 mm (4.0 × 4.0 in.) active
number of photons impinging on the area.25
phosphor in the time allotted and the
high noise level of the charge coupled A lens as an optical coupling device has
device. The noise of the device increases the drawback that it is a very inefficient
as a function of the square root of the light collection device. Relative to a fiber
readout speed and is quite high at real optic taper a lens system is less efficient
time frame rates. The image quality can by a factor roughly of ten or more. This
be improved by averaging multiple frames inefficiency can lead to secondary
in a digital processor but the high noise of quantum sinks and additional noise in
the device operating at these speeds does the image. Secondly, the lens does not
not provide film quality images. provide adequate shielding to the charge
coupled device, so an additional shielding
The better way to improve glass is needed directly in front of the
signal-to-noise ratio using charge coupled charge coupled device to reduce direct
devices, is to integrate the charge X-ray hits on the device. In addition, a
produced by light from the phosphor mirror can be used to move the camera
directly on the charge coupled device out of the radiation beam. The charge
cells. The wells generated by the readout coupled device can then be shrouded in
approach can be sufficiently deep to lead to reduce excitation by tangentially
capture three to four orders of magnitude scattered X-rays. One advantage of a lens
in equivalent light levels. Because the is the increased flexibility it offers to
exposure times are now much slower than
the real time rates of traditional charge FIGURE 13. Coupling of light from phosphor to charge couple
coupled device video cameras, the readout device in X-ray detector system: (a) lens coupling; (b) fiber
speed can be reduced to obtain lower optic coupling.
camera noise levels. On a frame-by-frame
basis, the signal levels have been (a)
increased while the additive noise from
the camera has been decreased. In this Fiber optic scintillator or
mode, further electrostatic image phosphor or both
intensification is not needed.
Shielding glass Lens
Charge coupled devices are now Cooled charge coupled
available with image formats as large as (b) device camera
4096 × 4096 pixels and 16 bits. Some
devices have been made as large as Scintillating X-ray shield
60 × 60 mm (2.4 × 2.4 in.). A phosphor fiber optics
screen can be coupled directly to the
charge coupled device itself but even if Fiber optic Charge
the phosphor has good X-ray quantum taper coupled
efficiency, those X-ray photons not device
absorbed by the phosphor (even if it is a Phosphor layer camera
small percentage) can still be absorbed in X-ray and light shield
the silicon layer of the charge coupled
device and yield a significant direct
excitation speckle noise in the image. To
avoid this noise a fiber optic image
transfer plate or a scintillating fiber optic
plate may be used16 to absorb the
transmitted X-rays before being absorbed
in the silicon (see Fig. 12).

The field of view of the charge coupled
device based X-ray systems can be
expanded with a fiber optic taper or a lens
system. These configurations are shown in
Fig. 13.

Fiber optic tapers are fiber optic face
plates in which the size of each fiber in
the face plate is reduced so that an image
deposited at the input surface may be
transferred to a smaller device such as a
charge coupled device at the output

Digital Radiographic Imaging 299

adjust the field of view for testing of both FIGURE 15. X-radiographic images of barrels and contents
large and small objects. made with linear detector arrays: (a) first barrel; (b) second
barrel.
The amorphous silicon, the amorphous
selenium (Fig. 14) and the charge coupled (a) (b)
device approach each provides image
characteristics of interest. Charge coupled
devices can provide high resolution with
a small field of view whereas the larger
amorphous detectors will provide
moderate resolution with a large field of
view.

Linear Detector Arrays

The linear detector array based systems
are ideally suited for production
environments. Many industries —
including automotive manufacture, cargo
transport, food inspection, munitions,
security and nuclear waste containment
— use linear arrays of X-ray detectors for
their inspection needs. Thousands of
these units have been installed. Figure 15
shows images of various objects
suspended in barrels and detected with
linear arrays.

FIGURE 14. Radiographic image of nickel
alloy bucket blade with enlarged view of
finning effect. Image was acquired with
400 kV exposure of 350 × 430 mm
(14 × 17 in.) field of view with part on
amorphous selenium detector.

300 Radiographic Testing

References

1. Nondestructive Testing Handbook, 9. Winfree, W.P., N.A. Cmar-Mascis and
second edition: Vol. 3, Radiography and F.R. Parker. “Enhanced Imaging of
Radiation Testing. Columbus, OH: Corrosion in Aircraft Structures with
American Society for Nondestructive Reverse Geometry X-Ray ®.” Paper
Testing (1985). 7C2. Third Joint Conference on Aging
Aircraft [Albuquerque, NM]. Arlington,
2. Janesick, J. and T. Elliot. “History and VA: Galaxy Scientific, for the Federal
Advancement of Large Area Array Aviation Administration,
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(March 1990): p 326-327.
14. Weisfeld, R.L., M.A. Hartney,
7. Koskinen, J. “LDA Technology Today R.A. Street and R.B. Apte. “New
and Possibilities in the Future.” Paper Amorphous-Silicon Image Sensor for
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and R.A. Betz. “Solid State X-Ray
Imaging Methodology.” Final Report,
Contract No. F33615-89-C-5617,
WL-TR-92-4003. Wright-Patterson Air
Force Base, OH: Wright Laboratory,
Materials Directorate, Air Force
Systems Command (March 1992).

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16. Placious, R.C., D. Polansky, H. Berger, Bibliography
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17. Bueno, C., R.L. Rairden, R.A. Betz, ASTM E 1453-93, Standard Guide for Storage
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1997).

302 Radiographic Testing

12

CHAPTER

Computed Tomography

Richard H. Bossi, The Boeing Company, Seattle,
Washington
Paul Burstein, Skiametics Incorporated, Winchester,
Massachusetts
James M. Nelson, The Boeing Company, Seattle,
Washington

PART 1. Introduction to Computed Tomography

Standard radiography uses superposition pattern, so long as one plane remains in
of information to create two-dimensional focus.
images of three-dimensional objects. For a
great many objects, this effect is This approach has not been widely
acceptable. However, in complicated applied for industrial objects, although
objects this superposition can cause there has been interest in the electronics
difficulty in interpretation. It is desirable industry for circuit board inspection.
in such cases to be able to view interior Multiple applications of synchronous
regions of interest without interference. motion are required to focus on different
The term tomography comes from the planes in the object. With the application
Greek τοµοσ, tomos, “cut” or “slice.” of digital imaging, however, it is possible
Several techniques of tomographic to generalize the technique as shown in
imaging have been developed to slice or Fig. 2. By using a digital imager and
section an object radiographically. collecting multiple data sets at different
projection views from the source, the data
Classical body scan tomography has may be reconstructed digitally to create a
been used for many years in the medical series of focused planes through the
field. In this technique the source, object object. Again, the position of the source,
and detector planes can be manipulated object and detector may be manipulated
during the imaging process in a in a number of ways, so long as
synchronous manner such that a single registration is maintained for digital
plane of interest remains in focus while focusing on a plane of interest. This
other planes in the object are blurred. technology is sometimes referred to as
Figure 1 is a simple schematic of the laminography or tomosynthesis. Commercial
approach where the object remains equipment can be purchased to perform
stationary while the source and image this data acquisition and reconstruction.
plane detector are moved synchronously, The reconstruction can include not only
keeping one plane of the object in focus. the laminar planes but other
The source and image plane need not reconstruction surfaces as desired.
necessarily be moved in a linear fashion
but may have a circular or other motion Computed tomography (CT) is a
powerful digital data reconstruction
technique for radiographic information

FIGURE 1. Classical body scan tomography method where source and image detector are moved synchronously such that one
plane of interest remains in focus: (a) early in scan; (b) interrogating beam normal to plane of interest; (c) late in scan.
(a) (b) (c)

Source

Focus plane

Object

Image plane

304 Radiographic Testing

that was conceived in the early 1960s. X-ray beam is collimated to a narrow slit
Computed tomography uses and aligned with a detector array to
measurements of X-ray transmission from define a computed tomographic slice
many angles about a component to plane in the component. The slit
compute the relative X-ray linear collimation reduces scatter and improves
attenuation coefficient of small volume the signal-to-noise ratio in the image. For
elements and presents them in cross 100 percent coverage of an object,
sectional image maps (tomograms). multiple, contiguous slices must be taken
Computed tomography can provide over the entire component. It is possible
quantitative information about the to perform volume computed tomography
density or constituents and dimensions of or cone beam computed tomography,
the features imaged. where the source is uncollimated and the
entire cone of radiation passing through
Computed tomography is used for both the object is measured using an area
medical and industrial applications. detector. This is potentially a higher
Medical systems are designed for high throughput technique than the standard
throughput and low dosages specifically single slice, high collimation technique,
for humans and human sized objects. although there are limitations in the
These systems can be applied to industrial reconstruction and an increase in scatter
objects that have low atomic number and signal level.
are less than 0.5 m (20 in.) in diameter.
FIGURE 3. Computed tomography using a collimated fan
Industrial computed tomographic beam and linear detector array data acquisition to
systems do not have dosage and size reconstruct cross section of object.
constraints. They are built in various sizes
for applications ranging from evaluation Detector
of small (millimeter scale) material array
samples using low energy X-ray sources,
to the inspection of small jet engine Objects on Z
turbine blades using medium energy turntable X-ray source
(hundreds of kilovolt) X-ray sources, to
the inspection of large intercontinental Data transfer Collimator
ballistic missiles requiring high (megavolt
scale) X-ray energies.

A typical computed tomographic
configuration is shown in Fig. 3. The

FIGURE 2. Digital laminographic method where 1 to n images
are taken with various orientations of source object and
detector, allowing multiple focus planes in part to be
reconstructed from data set.

View 1 View 2 View n Computer reconstructed
map of slice through
Source the object from multiple
X-ray projections
Y
X

Feature

Example plane of
reconstruction

Object

Detector
Image 1 feature location
Image 2 feature location
Image n feature location
Reconstructed image
aligns features at plane
reconstruction

Computed Tomography 305

PART 2. Laminography

In the body scan tomography or Tomosynthesis
laminographic technique as shown in
Fig. 1, at any given position a standard The basic form of classical tomography
radiograph consisting of a summation of can be accomplished with digital
feature effects along the projected lines of radiography, in which case, the plane of
sight to the film is made. If, however, the interest is specified and the response
source and detector are moved image is calculated. This technique,
simultaneously about a pivot point referred to as laminography or digital
located in a plane of interest in the test tomosynthesis, has the advantage of
specimen, only that plane will remain in allowing multiple planes of interest to be
focus on the film. Everything above or calculated from a few digital images. A
below the focal plane blurs. The number of variations of digital
information outside the plane of interest laminography or tomosynthesis have been
contributes to the overall noise in the developed by various researchers.2,3,5-10
image of the plane but does not add any Figure 5 shows the generalized
small scale (that is, high spatial mathematical solution to the problem of
frequency) information. In this classical tomosynthesis on any plane.
tomography, all features in the test
specimen are present in the image but in Equation 1 shows the notational
a blurred form. The farther away the convention for vectors, unit vectors and
features are from the plane of interest, the their components in the following
more blurred they are. equations.

Classical tomography is a strictly Equations 2 to 22 refer to variables and
mechanical technique. It does not rely on coordinates diagrammed in Fig. 5.4
computation, except insofar as the Vector R represents the XYZ coordinate
mechanical registration of source and system fixed with respect to the part
detectors with respect to the plane is being inspected:
calculated.
FIGURE 4. Scanned beam laminography system.
The technique has been applied to
electronic multiplayer circuit boards by Scanning electron
using a combination of a moving source beam system
and radioscopic imaging system. In
particular, by using a scanning electron Electron beam Focus coils
beam source and radioscopic imaging X-rays
system a very fast system can be X-ray generating target
developed as shown in Fig. 4.1 The circuit Object
board is inspected by mounting it on an
XYZ table and positioning the region of Fluorescent
interest in the field of view. The scanning screen
beam source rotates in a circular motion, Mechanically
synchronous with a rotating motion of rotating
the mirror system. The radiographic mirror system
image of the object is detected by the Radioscopic
fluorescent screen and subsequently camera imager
captured by the camera detector. High
speed rotation (600 rotations per minute
for example) causes a narrow plane of
interest in the object to be in focus based
on the geometry of the system.
Movement of the object in the Z direction
will cause planes of interest to be brought
into focus. Objects with high contrast,
uniform size and shape and laminar in
nature are good candidates for the
technique.

306 Radiographic Testing

X R rr21  (6) V = R p3 – R p1
Y  R 
(1) R =  , r= = 

Z  r3  (7) W = V – (V ⋅ u)u

The view image raster is (I + 1) × (J + 1) Then solve the 3 × 3 system of Eqs. 8 to
pixels. The laminogram image raster is 10 for RB:
(M + 1) × (N + 1) pixels, where I,J and M,N
represent the horizontal and vertical sizes, ( )(8) m = ⋅ u
respectively, of each image in units of M RB – Rp1 U
pixel spacings. The laminography
integration steps are as follows. First, pick ( )(9) n = ⋅ w
a destination pixel in the laminogram N RB – Rp1 W
(m,n), then solve Eqs. 2 to 4 for the
constants c1, c2 and c3:

(2) Zp1 = c1 ∗ Xp1 + c2 ∗Yp1 + c3 (10) ZB = c1∗ XB + c2 ∗YB + c3

(3) Zp2 = c1 ∗ Xp2 + c2 ∗Yp2 + c3 Continuing with reference to variables
and dimensions in Fig. 5, the remaining
(4) Zp3 = c1 ∗ Xp3 + c2 ∗Yp3 + c3 steps are performed for each image (k of
Define U, V and W: K). Solve 3 × 3 Eqs. 11 to 13 for ei:
(5) U = Rp2 – Rp1 (11) Zd1 = e1 ∗ Xd1 + e2 ∗Yd1 + e3

FIGURE 5. Generalized laminography mathematical solution.4 (12) Zd2 = e1 ∗ Xd2 + e2 ∗Yd2 + e3

X-ray tube (XSk, YSk, ZSk) (13) Zd3 = e1 ∗ Xd3 + e2 ∗Yd3 + e3
S
Define T:

(14) T = RA − RS

(Xp3, Yp3, Zp3) Solve 4 × 4 Eqs. 15 and 16 for RA and d:

Part being inspected (15) RA = RS + dt

Z (16) ZA = e1 ∗ XA + e2 ∗YA + e3
Then compute the vectors:
B Y (17) F = Rd2 – Rd1
mn X
(Xp1, Yp1, Zp1) (Xp2, Yp2, Zp2)

(Xd3k, Yd3k, Zp3k) (18) G = Rd3 – Rd1

iA (19) H = G – (G ⋅ f ) f

(Xd1k, Yd1k, Zd1k) j (Xd2k, Yd2k, Zd2k)

Radiographic detector array Finally, calculate the indices of the image
pixel to be summed:

( )(20) = ⋅ f
Legend i I RA − Rd1 F
A = point in detector surface
B = point in laminographic focus plane ( )(21) = h
d = subscript designating detector j J RA − Rd1 ⋅ H
i,j = position in detector surface
k = subscript designating source/detector configuration

m,n = position in laminographic focus plane
p = subscript designating corner points of laminographic focus plane
S = radiation source

X,Y,Z = cartesian coordinates

Computed Tomography 307

And perform the sum into the completed field is created. Computed tomography is
laminogram L: the limiting case for the effective slice
thickness through the object. The
(22) L(m,n) = L(m,n) + Ik(i, j) resulting images from the techniques
show an increase in contrast sensitivity
Implementation of Laminographic for features as the depth of field is
Techniques narrowed.

Laminography of this type can be Figure 7 is an example of
performed in a variety of ways. Computed laminographic reconstruction from only
tomography (see below) is one technique
where the geometry is known because of FIGURE 7. Digital laminographic reconstructions of pocket
precision of the stage mechanisms. By army knife: (a) first layer; (b) second layer; (c) third layer.10
using the digital radiographic imaging
mode of computed tomographic scanning Phillips screwdriver
systems a series of digital images at
various geometric locations can be (a)
obtained and reconstructed for the data
set.6 The computed tomographic system Small blade
provides precise encoding of the geometry
locations for the reconstruction. It is Tweezers
possible however to simply use fiducials
in the image to generate the required (b) Ring holder
geometry data and reconstruction.7
Techniques of laminography using a Large blade
object motion apparatus with fixed source
and detector positions have been (c) Awl with hole
devised.8,9 These techniques provide a
relatively simple implementation of the Openers
methodology.
FIGURE 8. Digital tomosynthesis
The key issue for laminography is the reconstructions of weld shows vertical
effective image aperture. Figure 6 reconstructions through pores and notch to
demonstrates how the position of the determine depth information: (a) plan view;
X-ray source affects the aperture. In the (b) vertical view through both pores;
case of the single source position of a (c) vertical view through notch.10
conventional radiograph, the image can
be considered to have an effective infinite (a)
depth of field and the entire object is the
slice (compression of all information into Inclusions
one plane). As the angles of the
laminographic data acquisition become Pores
larger, an effectively narrower depth of

FIGURE 6. Graphical representation of effective apertures: Notch
(a) radiography; (b) laminography; (c) computed
tomography.45

(a) (b) (c)

(b)

Slice 16.08 mm
(0.633 in.)

Slice

(c)

3.99 mm(0.157 in.)

308 Radiographic Testing

eight digital images.10 In this example,
several layers of a pocket knife are imaged
by focusing on the several different
depths in the object. Figure 8 is an
example of a weld radiograph with two
digital tomosynthesis reconstructions. By
reconstructing a series of laminographic
planes through the object, the volume
information on the part is obtained.
Tomosynthesis of any arbitrary surface
through that volume is now possible. In
Fig. 8 two vertical planes have been
reconstructed to demonstrate the ability
to obtain depth information on features.

Computed Tomography 309

PART 3. Principles of Computed Tomography

Background on the sky — strip integrations that
provided measurements of a number of
The development of modern computed point sources but integrated over these
tomography hinges on advances in a apertures. Bracewell solved this problem
number of different fields. X-rays had using fourier transforms for a relatively
been known since before the turn of the small number of sources and passes. The
century. Medical X-ray films were important point, however, is that he had
routinely made as early as 1900. As the found a transformation that worked.
technology improved, these projection Bracewell deconvolved the data and was
radiographs became better and better, able to derive the positions of the
with reasonably good diagnostic quality multiple point radio sources in his data.
being reached in the 1930s. The images
returned by those medical systems In the period from 1957 to 1963,
contained useful information but much Alan M. Cormack, a mathematical
information was obscured by tissue and physicist, was struck by the fact that the
bone on either side of the region of child of a friend had died of a brain
interest. This was especially true in tumor that was inoperable, perhaps
making images of the brain and other because it could not be detected or
interior sections of the skull. Early delimited by conventional X-ray
medical researchers reasoned, that if a projection radiography. Cormack,
series of X-ray absorption measurements convinced that he could provide a
could be made around the periphery of solution, proposed a set of mathematical
the head, the X-ray density of the interior basis functions — the jacobi polynomials.
could be reconstructed. This would Cormack actually conducted a crude
remove the superposition difficulties experiment, tabulated the results by hand
inherent in projection radiography. The and reconstructed a crude line of voxels
problem could be viewed as a giant matrix in a phantom. The seminal papers
of equations; however, solving the appeared in 1963 and almost escaped
equation matrix for useful spatial notice.11,12
resolution would require too much
computation unless an algorithm could be In the late 1960s Geoffrey Hounsfield
found. built a computed tomographic system.
Hounsfield was very much a hands-on
The existence theorem for that experimenter who was absolutely
algorithm was proved by J.H. Radon in convinced that he could provide a
1917. He showed that an arbitrary reconstruction means, whether rigorously
distribution of material can be mathematical or not. Before the
reconstructed on a point-by-point basis by convolve-and-backproject technique was
measuring the line integrals — that is, generally used, Hounsfield experimented
summing the elements of the distribution with algebraic reconstruction and other
along a series of lines through the iterative solutions. Hounsfield’s original
distribution — and plugging them into a instrument is the basis of all modern
formula. Unfortunately, although Radon medical computed tomography.13
proved the existence of the formula, he (Cormack and Hounsfield shared the
needed a mathematical transformation Nobel Prize in Medicine for their work on
that would make the problem tractable. computed tomographic scanning.)

Although this existence theorem for The two main drivers for computed
computed tomography had been known tomography are development of good
since World War I, there was no impetus mathematical algorithms for
to find a technique of reconstruction, reconstruction and inexpensive
because it was clear that whatever computers. The combination of the
technique was used, the number of availability of both was what allowed the
calculations would be staggering. In the field to develop technically. The promise
mid-1950s, however, the impetus to find a of a strong United States market for
set of basis functions for the practical computed tomographic equipment is
solution to the problem came from radio what prompted the sponsors to provide
astronomy. Ronald N. Bracewell had taken the capital. Much work on codes has
a series of radioastronomy measurements. evolved at various institutions for all sorts
These amounted to long, narrow apertures of specialized applications. But what gave
scientific experimenters access to

310 Radiographic Testing

nonmedical computed tomography was multiple view data collected. This
the availability of codes in the public reconstructed image is a two-dimensional
domain. These codes, such as SNARK or presentation of a two-dimensional cross
the Berkeley Donner Laboratory package, sectional cut through the object. A
could be run on a general purpose primary benefit of computed tomography
minicomputer.14,15 These codes allowed is that features are not superimposed in
anybody who wanted the opportunity a the image, thus making it easier to
chance to try computed tomography. interpret than radiographic projection
images. The image data points are small
The other successful implementations volumetric measurements directly related
of reconstructive schemes are positron to the X-ray attenuation coefficient of the
emission tomography (PET) and nuclear material present in the volume elements
magnetic resonance imaging (MRI). defined by the slice thickness and the
Positron emission tomography uses an image plane resolution of the computed
injected radioactive chemical that is tomographic system. The computed
metabolized in certain organs. The degree tomographic image values and locations
of uptake of that chemical in the body provide quantitative data for dimensional
depends on how well (or poorly) the measurements and measurements of
organ functions. The radioactive tracer material density and constituents.
element undergoes a decay, resulting in a
positron electron pair product. The The computed tomography process is
positron goes only a short distance before fundamentally different from other forms
annihilating by collision with another of radiographic imaging. Ordinary
electron, emitting two 511 keV photons. projection radiography makes intuitive
Positron emission tomography detects sense. It is relatively straightforward to
these photons. The algorithms are imagine X-rays coming off an anode or a
somewhat different, because the source is gamma source, being absorbed and
distributed. Some algorithms look for scattered by the test specimen and finally
single 511 keV photons; some look only interacting in a film. The image on film is
for coincidences. All require a a projection of everything along the line
reconstructive geometry along line of sight between the source and the film.
integrals. You can imagine the film to be a kind of
murky image, with objects close to the
Nuclear magnetic resonance imaging is film being clearer than those farther away.
really a radio frequency measurement that All the associated details of projection
uses gradient alternating magnetic fields radiography — for example, geometric
superimposed on a static magnetic field at unsharpness due to finite source
right angles. The nuclear magnetic size — make good sense.
moment of atoms will allow absorption
and subsequent decay only at certain What happens when the depth
frequencies. Following excitation the location of a feature found in a
atoms will emit radio waves at specific radiograph is important? The most
frequencies dependent on their common technique for discovering the
gyromagnetic constant and the strength position along the line of sight where the
of the magnetic field. By proper feature lies is to use triangulation. This
manipulation of magnetic fields it is consists of obtaining a second film of the
possible to effectively measure line area in question but with the source in a
integrals representing the presence of different angular position relative to the
specific atoms (for example, hydrogen) in test specimen than was obtained on the
an object. These integrals may be treated first exposure. The geometry is carefully
similarly to computed tomographic data laid out on a piece of paper; measured
for image reconstruction. positions of source, test specimen
anomalous feature on the films are noted;
Physical Principles and the position of the anomalous feature
along the intersecting lines of sight is
Computed tomography differs from determined as shown in Fig. 9. Distances
conventional radiographic imaging in from discontinuities to the image plane
that it uses X-ray transmission are calculated by using triangulation as
information from numerous angles about shown in Eqs. 23 and 24.
an object to computer reconstruct cross
sectional images (that is, slices) of the (23) h1 = dδ1
interior structure. To generate a computed s + δ1
tomographic image, X-ray transmission is
measured by an array of detectors (see (24) h2 = dδ2
Fig. 3). Data are obtained by translating s + δ2
and rotating the object so that many
viewing angles about the object are used. Triangulation is a rudimentary
A computer mathematically reconstructs tomographic reconstruction that contains
the cross sectional image from the

Computed Tomography 311

the essentials elements of computed plane in the object. The slit collimation
tomography. The first step is to recognize reduces scatter, improving the signal to
the features of interest. When more than noise in the image. Data are obtained by
one image is used, the mind can detect translating and rotating the object so that
and locate these features as being many viewing angles about the object are
somehow different. The eye-and-brain acquired.
system filters out the other information,
so that the mind is left only with the Figure 10a shows how a data projection
features of interest in both radiographs. can be taken through a part. The
The second step is to correlate the test transmitted X-ray intensity at each
specimen, the source position the detector element position in the detector
radiographic image together for both array is converted to a digital output level
exposures. This correlation in space allows and transmitted to a computer as a
the information from the two exposures projection for the particular angle
to be overlaid constructively. Finally, the through the object. The projection data
third step is to note the position of the are analogous to a series of slit
attenuation corresponding to the radiographs taken at numerous
anomalous feature to project it back to orientations (projections) about the
the source along the original attenuation object. The resulting slit radiographs yield
line. This backprojection is performed for an attenuation that is an average over the
each exposure and the combined effects slit thickness.
of these two backprojections is the
constructive interference of the two FIGURE 10. Computed tomography data acquisition and back
attenuation patterns. projection reconstruction: (a) source-object-detector
geometry; (b) back projection reconstruction from multiple
In computed tomography the basic views.
methodology can be considered in a
similar manner. The X-ray beam is (a) Object Detector array Pq
collimated to a narrow slit and aligned
with a solid state X-ray detector array to X-ray beam
define a computed tomographic slice

FIGURE 9. Example of triangulation as basis for computed
tomography: (a) first image, with line of interrogation
normal to sensor plane; (b) second image, with line of
interrogation oblique to sensor plane.

(a) (b)

Source s

(b) Pq2 Transmitted
intensity
Pq1
Pq3

d

Object h2
Image h1
plane

δ1
δ2

Image 1 Image 2

Legend Pq4
d = distance from source to image plane
h1 = distance from round discontinuity to image plane Legend
h2 = distance from square discontinuity to image plane p = projection
s = source travel distance q = subscript that designates angle
δ1 = apparent travel distance of round discontinuity in image plane
δ2 = apparent travel distance of square discontinuity in image plane

312 Radiographic Testing

When a series of projections are taken The measured intensity at the detector
from many angles about a part, the is normalized based on the calibration of
projection data can be backprojected as the detector array and the measured
shown in Fig. 10b to create an image. As intensity for no object in the beam. By
the number of projections increase, the taking the logarithm of the normalized
ability to more exactly reconstruct the intensity, the value of the projection Pq(r)
object increases. In a computed is proportional to the linear attenuation
tomographic system, the projections are coefficient:
actually subjected to an incredible
amount of mathematical massaging but ( )(27) Pq R = ln I ∝µ
the steps are effectively the same as Io
involved in the manual triangulation.
where Pq is the projection at angle q and R
The computed tomography image, the is the position of the ray along that
cross sectional representation of the projection (see Fig. 10b).
densities within an object, depends on the
three basic processes: (1) convolution or The backprojection of the data will
filtering of the data with special therefore create an image distribution
mathematical operators; (2) correlation of where the values in the image are
the projection data in an absolute space; proportional to the linear attenuation
(3) backprojecting the convolved coefficient. The backprojection is given by
attenuation data along its original spatial Eq. 28:
vectors. The mathematics of the image
reconstruction can be found in a number ∫(28) bq(x,y) = Pq(R)
of references.4,16-18
× δ(xcos q + y sin q − R) dR
The intensity of an attenuated X-ray
beam passing through an object is given
by the line integral:

∫ ∫ { [ ]}(25) I = where δ is the dirac delta function. This
Io (E)exp −µ(E,x)dx dE equation effectively distributes the values

where I is the beam intensity at the of the projections Pq(R) to all points (X,Y)
detector, Io(E) is the beam intensity with that lie on the projection line. By
no object, E is energy of the X-rays, µ(E,x)
is the linear attenuation coefficient and x integrating over angle q the total
is the transmitted distance through the
object. Most computed tomographic reconstructed image will be formed:
systems use X-rays generated by a
bremststrahlung source that creates a ∫∫(29) f (x,y) = Pq(R) × δ (xcosq
broad spectrum defined here as IO(E). The
transmitted intensity is an integration )+ y sin q − R dR dq
over the energy spectrum and along the
ray path through the object as a function This reconstruction is crude because,
of the distribution of linear attenuation intuitively, a point object (or delta
coefficient µ(E,x). For predictive purposes, function) will be reconstructed with the
it is useful to change Eqs. 25 to 26: crossing of radial lines creating a star
effect. This is evident in Fig. 10b and is
[ ]( )(26) I = Io exp −µ Eeff x shown in Fig. 11. This point response can
be shown to be a 1·r–1 blurring of the
where Eeff is an effective energy and a image points (where r is the distance from
uniform material is assumed. The effective the point). Reconstructions must therefore
energy is that specific energy, where the use filtering to remove this effect.
transmitted intensity of a monoenergetic
beam would be equivalent to that of an The filtering is usually performed by a
integrated spectrum. The effective energy convolution function C(R) such that:
is influenced by the type and amount of
material penetrated because, as the ∫ ∫(30) f (x,y) = Pq(R) ∗ CR
attenuation or path length increases, the
lower energy photons are preferentially ( )× δ xcos q + y sin q − R dRdq
attenuated, resulting in higher effective
energies or harder beams. In computed Each projection is convolved with a
tomographic applications, attenuations of function and the result is backprojected.
104 and higher are not uncommon, Figure 11 demonstrates the benefit of the
although attenuations of 101 to 102 are filtering. The convolution function C(R) is
preferred. a filtering operation that can be selected
to enhance various characteristics of the
image. Innumerable filters are possible for
use in the convolution. The two most
popular (and extreme) filters are the
ramachandran filter, used to emphasize
sharpness, and the shepp and logan filter,

Computed Tomography 313

used to emphasize contrast. It is also data be taken before reconstruction,
convenient in some cases to perform the whereas filtered backprojection has the
filtering by fast fourier transforming the advantage of allowing reconstruction to
projection, multiplying by a filter begin on each projection data set. The
function, inverse transforming and iterative reconstruction technique
backprojecting. The mathematics of the assumes a solution for the image matrix
filtering is easier to visualize in the and iteratively compares projections
frequency domain but is equivalent to the through the image to the measured
convolution technique of Eq. 30. projection data. With each iteration the
image matrix is altered until a match of
Alternative reconstruction techniques the calculated and measured projections
to the filtered backprojection technique are within an acceptable accuracy. This
are available including fourier transform technique is useful when limited angles
techniques and iterative reconstruction. are available but can become very time
The fourier transform technique fills a consuming for data taken from many
two-dimensional frequency space with the angles.
transform of each projection. A
two-dimensional inverse transform is X-ray computed tomography can be
required to create the reconstructed considered the high end application of
image. The two-dimensional fourier radiation measurements because the data
transform technique requires that all the obtained are quantitative measures
(directly related to the X-ray linear
FIGURE 11. Filtering of back projection: (a) backprojection of attenuation coefficient) for each volume
original profiles: (b) backprojection of filtered profiles. element throughout an object. The
computed tomographic image is digital
(a) with an image intensity value assigned to
each pixel of the image. The pixel is
Pq2 actually a voxel because it represents the
Pq3 two-dimensional cross section plus a third
dimension (depth) defined by the slice
Pq1 thickness. The medical field uses the
hounsfield notation for the image data:
(b) Pq2 Pq4
Pq3 (31) H = 1000 µ − µw
Pq1 µw

where H is the hounsfield number, µ is
the measured attenuation coefficient and
µw is the attenuation number coefficient
for water. Using this scale, water takes on
the value of zero, vacuum (or air) is –1000
and bone is 1000. This range used in
medical computed tomographic scanners
corresponds to a density range of about
0 to 2.0 g·cm–3. A change of one integer
in the hounsifeld scale is a 0.1 percent
change in attenuation value. Medical
facilities maintain a regular calibration
schedule of their equipment to maintain
proper hounsfield readings. Table 1 shows
a numerical scale for hounsfield units.
Medical scanners can be used for higher

TABLE 1. Hounsfield units.

Material Hounsfield Value

Pq4 Air – 1000

Water 0

Bone 1000

Acrylic 110

Carbon 580

Legend Aluminum 1900
p = projection
q = subscript that designates angle Iron 24 000

314 Radiographic Testing

density materials than bone but readings
beyond 4000 hounsfield units are usually
not suitable.

Industrial computed tomographic
systems do not use the hounsfield scale
but use the numerical values from their
reconstructions. For most scanners the
data will be 16 bit or represent an image
gray scale range from 0 to 64 000 K values
(K values being increments of blackness in
the image). Calibration of the
reconstructed values to true density must
be performed by scanning a standard.

Computed Tomography 315

PART 4. Resolution and Contrast

The basic resolution of a computed the resolution of details on either side of
tomographic system is determined by the the object.
effective beam width of the X-ray beam in
the object. The effective beam is a Figure 12c shows the case of a very
function of the source and detector small source (microfocus) and larger
dimensions and the position of the object detector. By using projection
with respect to them. The vertical magnification, very fine resolution may
resolution of the slice volume will be be possible in the object. The resolution
determined by the effective slice thickness can be estimated by taking an average of
of the collimation apertures. the effective beam size in millimeter
(mm), multiplying by two and inverting
Figure 12 shows the configuration of a to obtain resolution values in line pairs
source and detector for the horizontal per 1 mm.
resolution of a computed tomographic
slice through an object. In Fig. 12a, a The number N of data points necessary
source and detector of equivalent aperture to achieve the highest resolution from a
size have an object positioned midway particular scanner geometry can be
between them. With this configuration estimated from the effective beam width.
the effective beam width is minimized at If the field of view (circle of
the center. At the edges of the object the reconstruction) has a diameter D, then
effective beam width will be slightly larger the number of data points in each
and the resolution is decreased. When the projection across the object should be:
source and detector apertures differ in
size, as shown in Fig. 12b, the best (32) N = 2D
resolution will be off center. In this case w
the rotation of the computed
tomographic system, whether 180 or where w is the effective beam width. This
360 degrees, could make a difference on allows two samples per beam width. The
number of projection views is estimated
FIGURE 12. Examples of source-object-detector configurations by allowing a ray through each beam
and effective beam widths (w): (a) source and detector of width on the outer radius of the field of
equivalent aperture size; (b) source larger than detector; view:
(c) source smaller than detector.
(33) v = π D
(a) Object Collimated w
w detector
Source The total number of data points used for
the computed tomographic data
(b) Object acquisition will be 2π D2·w–2.
Manufacturers of computed tomographic
Source Collimated systems may use a variation on the above
detector assumptions to establish the number of
projections and data points per projection
(c) Object Detector used for their equipment.

Microfocus The slice thickness is the third
source dimension that defines the inspection
volume. The operator will normally select
this value. Increasing the slice thickness
will allow more photons for better
imaging statistics or greater scanning
speed. However it will increase the
smearing of sloping edges on objects or
features and decrease sensitivity to details
that may be thinner than the slice
thickness. Narrowing the slice provides
finer detail sensitivity to axial variations
in the object but at the cost of scan time
and increased statistical noise.

316 Radiographic Testing

The contrast sensitivity in computed large object size are mutually exclusive,
tomographic images is inherently high requiring compromise in system design.
because each reconstructed volume
element is composed of backprojected Because of the high signal-to-noise
rays from many orientations about the ratio in any voxel, computed tomography
object. Equation 34 shows an estimate of can detect features below the resolution
the signal-to-noise ratio (SNR) in a voxel limit of the image. For features that are
element as a function of various larger than a single voxel the contrast
computed tomographic system sensitivity improves by the square root of
characteristics for a reconstruction of the number of pixels making up the
cylindrical object:19 feature. For a feature smaller than a pixel,
the apparent density is averaged over the
( )(34) SNR = 0.665 µw1.5 vnt exp −2π R image voxel and therefore the signal for
∆p that image voxel is reduced. This is called
a partial volume effect. Although the
In this equation, µ is the linear signal is reduced by the partial volume
effect, the feature may still be detected.
attenuation coefficient, w is the X-ray This is a significant point about the
application of computed tomography
beam width, v is the number of views, n is because very often relatively large image
voxels (compared to very fine
the photon intensity rate at the detector, discontinuities) may be used — the very
small features are still detected but not
t is the integration time of the detectors, necessarily resolved.
∆p is the ray spacing and R is the radius of
the object. The contrast ratio will be given

by:

(35) Contrast ratio = 6
SNR × Z

where Z is the number of pixels over
which the contrast is observed. Table 2
shows an example of calculations based
on Eqs. 34 and 35. Computed
tomographic systems often provide
contrast sensitivity measurements in the
range of 0.1 to 1.0 percent. What the
equations show is that the signal-to-noise
ratio improves with increases in computed
tomographic system characteristics of
X-ray beam width, number of views,
X-ray beam intensity and integration
time. The signal-to-noise ratio will also be
improved by decreasing the ray spacing
and object diameter. These computed
tomographic system characteristics reflect
the tradeoffs in optimizing a computed
tomographic system. Fast scan times, fine
resolution, high contrast sensitivity and

TABLE 2. Computed tomography contrast ratio calculation.

Parameter Symbol Quantification

Object diameter D 150 mm (6.0 in.)
Attenuation coefficient µ 0.24 cm–1
Beam width w 0.08 mm (0.003 in.)
Number of views v 588
Photon rate n 108 s–1
Integration time t 10 ms
Ray spacing ∆p 2 mm (0.08 in.)
Signal to noise ratio SNR 324
Number of pixels Z9
Contrast ratio CR 0.0062 = 0.62 percent

Computed Tomography 317

PART 5. Computed Tomographic Systems

The computer reconstructed computed The entire test specimen can be
tomographic image is a two-dimensional covered if the procedure is repeated n
image of a two-dimensional plane in the times where n = 180·θ–1 in theory (in
object. The data in the image is composed practice, 360 rather than 180 is
of information in small voxel units that sometimes required.)
are composed of the X,Y reconstruction 2. Second generation geometry uses the
matrix element sizes and averaged over same principle as first generation
the slice thickness of the computed geometry. The difference is that
tomographic collimation scheme. By instead of having only a single
taking a series of contiguous computed detector, there is typically a bank of
tomographic slices through the object a detectors arranged to subtend a fan
volumetric data set can be created from beam of the source. (The fan beam is
which cross section images in any plane collimated so that the fan lies in the
through the object may be extracted. The plane of interest.) Thus the central
slice thickness used determines the detector acquires the same data on a
vertical resolution of the volume data set. single traverse as the first generation
The horizontal resolution is determined system described above. The next
by the effective X-ray beam size in the detector might be placed so that its
object and the reconstruction matrix size. center as seen from the source focal
spot is displaced by angle θ from the
Computed tomography requires more central detector. Simultaneously with
sophisticated equipment for data the first traverse, that next detector
acquisition and reconstruction than gathers the identical information that
conventional radiography. The total time would, in a first generation
required to inspect an object configuration, be gathered
volumetrically can also be relatively long, sequentially on the second traverse. In
making computed tomography a fact, second generation geometry lets
significantly more expensive inspection. all views in the fan angle of the source
However, for many structures computed be obtained on the same traverse.
tomography provides unique information. After traversing the fan, the object
rotates the number of degrees of the
System Configurations fan and transverses back across the fan
beam. Rotations continue until 180 or
Computed tomography has several 360 degrees have been covered.
variations from its basic concept of Fig. 3. 3. Third generation geometry uses a
Figure 13 shows four generations of single source and a bank of detectors
computed tomographic system that span the test specimen as seen
configurations. from the source. The detectors provide
a single view simultaneously of a series
1. The essential characteristics of first of fan shaped measurements rather
generation geometry are a single than parallel ray measurements. By
source and a single detector. The continuously turning the test
source and detector are locked specimen and taking data, many fan
together (or at least their relative views are acquired for reconstruction.
positions are constant) and the entire In third generation scanning each
source and detector unit made to detector will not see all of the object
traverse the test specimen. A single as in second generation. Thus detector
traverse yields a series of attenuation imbalance causes ring artifacts in the
measurements (recall that each image.
attenuation measurement is a ray and 4. Fourth generation geometry uses a
that the series across the test specimen single moving source and a bank of
is a view), thus generating a single stationary detectors configured into a
view. The most important circular ring. As the source rotates
characteristic of this view is that it is a inside the detector ring, a single view
series of parallel rays. If the test might be made at one time; instead,
specimen is rotated by an angle θ and the view data is constructed from
another such traverse is made, another simultaneous positions of the source
view of attenuation data but displaced with respect to a single detector. Like
by angular rotation θ will be made.

318 Radiographic Testing

the third generation geometry, this with a single detector; this presents an
fourth generation configuration uses a advantage over third generation
fan beam view structure. The main geometry where searching for changes
reason for using the fourth generation in small scale signals is frequently
geometry is that each view is made overwhelmed with interdetector
normalization problems. The fourth
FIGURE 13. Computed tomographic system generations: generation use of one detector for
(a) first generation; (b) second generation (rotate and each view obviates interdetector
translate); (c) third generation (rotate only); (d) fourth detector normalization problem.
generation.
The most useful forms for industrial
(a) Object computed tomography are second
generation and third generation. Both
Source Detector techniques use a collimated fan beam of
X-rays and one-dimensional array of
(b) Object Detector detectors.
MOVIE.
Second Source Rotate-and-Translate
generation Configuration Advantages
(rotate and
translate). The second generation scheme, the
rotate-and-translate scheme, is commonly
(c) Detector used for industrial objects because objects
MOVIE. larger than the X-ray beam fan angle can
Third Source be accommodated. The main reasons for
generation this implementation are three:
(rotate only).
1. The spatial resolution is determined by
(d) Detector the spacing between sampling
positions and is not dependent on the
ring number of detectors or the
Object interdetector spacing.
Source
2. The problems of false large scale radial
density variations (cupping or capping
— very common in third generation
geometry) are largely avoided. Hence,
true absolute densities, an important
factor for nondestructive test systems,
especially for composites, are easily
obtained.

3. The interdetector normalization
requirements compared with third
generation systems are relaxed by a
factor of about 100.

This last point is especially important
because, in gathering the series of ray
measurements necessary for a single view
(one-dimensional projection), it is the
small scale variations in response that
determine the visibility of any particular
feature. In second generation geometry, a
view is made by successive measurements
with the same detector element.

Third Generation Configuration

In third generation geometry, a view is
made by the simultaneous measurements
of all the detector elements. Thus,
variations in response between adjacent
detectors can mimic the response of a
small feature present in the object. In
third generation systems, complex
smoothing algorithms usually are used to
mitigate the effects of the second and
third objections.

The third generation, or rotate only,
scanning approach is used on small
industrial objects because it is faster than

Computed Tomography 319

second generation. Both the second and relying on strictly mechanical motions.
third generation techniques only image in The penalty is in a more complex
a single computed tomography scan one interface between motion subsystems and
slice location through the part. That slice the control computer and in a more
inspection volume is the size of the fan computationally intensive algorithm for
beam height collimation. arriving at a reconstructed image.

Other Configurations Mechanical handling system tolerance
budgets are almost always expressed in
Volume Computed Tomgraphy. Another terms of the spatial resolution. For second
technique, volume computed tomography generation geometry, the total stacking
or cone beam computed tomography, uses tolerance is given as 0.25× to 0.33× the
a two-dimensional area detector and an spatial resolution. Thus, for a resolution
uncollimated cone of radiation such that corresponding to good spatial
the entire object may be inspected in one discrimination of adjacent pixels of size
scan. This technique sacrifices some detail 1.0 mm (0.04 in.) the nominal tolerance
in the image quality for a higher stackup would be 0.33 mm (0.013 in.).
throughput when the entire object must This means that all the imprecisions in
be inspected with computed tomography the individual mechanical components
and has limitations on the applicable part must, when added together, be less than
size. It also generally works well only for this absolute tolerance. This applies to
relatively small objects. random errors — for example, runout in a
bearing. The limit for systematic errors
Limited Angle Tomography. Limited tends to be about ten times more
angle, tangential and annular stringent although each individual
reconstruction computed tomography are contributor must be analyzed separately.
also techniques that can be beneficial to Because the reconstruction process adds
large composite structure. Limited angle data taken from many different positions
computed tomography does not require a systematic error produces an artifact
that the computed tomographic data be that is characteristic of the selective
taken from all angles completely about reinforcement of the particular error.20
the part. This can be particularly
advantageous for large planar composite System Design
structure. Tangential and annular
reconstruction offer advantages for large Because computed tomographic systems
cylindrical structures where information is require more precise equipment and data
only needed along annular rings, processing than traditional nondestructive
particularly near the outside of the evaluation hardware, it is important to
structure. consider the components in a computed
tomographic system and discuss their
Mechanical Handling ramifications.

The primary technical considerations for Figure 14 shows a generic design of
computed tomographic system computed tomographic system
configurations are X-ray source, detectors, components. The major subsystems that
computer processing hardware and go into a computed tomographic system
software, algorithms, speed and visibility include the mechanical handling
of anomalous conditions. Mechanical subsystem, the data acquisition subsystem
handling systems for computed and the computer interface and software
tomographic systems are mature. The subsystem. These major subsystems
advent of microprocessor control, high categories can be further broken down
resolution encoder and feedback systems into components and characteristics that
and the ability to use fire-on-position data are essential for a computed tomographic
acquisition rather than a freerunning system to operate for the desired output.
clock have actually eased the mechanical The selection of certain component
handling tasks. attributes or system characteristics will
affect the selection of other components
Mechanical handling has been eased or the overall performance and cost of a
because the smoothness of motion and computed tomographic system.
accuracy of position required of previous
era systems have been supplanted by Table 3 lists key attributes of a
knowledge-of-position systems. In many computed tomographic system and the
modern computed tomographic systems ramifications of selections of the
for nondestructive testing, especially attributes on system component selection.
those that are designed with a range of In the selection of a computed
applications, incorporation of the tomographic system to perform
knowledge of position is done routinely nondestructive inspections it is important
and results in considerably more to be able to define the desired inspection
flexibility than is possible with systems characteristics, particularly specimen (size,
type, weight), inspection parameters

320 Radiographic Testing

FIGURE 14. Generic computed tomographic system components.

X-ray beam precollimator Test X-ray
X-ray specimen detectors
source Detector
electronics

Motion
hardware
Position
encoding

X-ray bay

X-ray intensity Motion Detector Data Specialized Memory Control room
and processor processor acquisition processors Main bus

frequency signal

Host Disk storage Operator’s Image Hard copy Archives Signal
central console processor output
processing
Image
unit display

TABLE 3. Computed tomography system attributes and their major ramifications.

Attribute Ramifications

Test specimen size, weight and shape mechanical handling equipment, loading and unloading
Test specimen X-ray penetrability X-ray source
Spatial resolution X-ray detector type
Contrast sensitivity dynamic range of detector and front end electronics
Artifact level accuracy of mechanical handling equipment
Speed of computed tomographic process configuration of source, object and detector
source and detector aperture size
Number of pixels in image strength of X-ray source
Slice thickness range integration time
Operator interface reconstruction algorithm software
accuracy of mechanical handling equipment
Archival requirements size of object
X-ray source strength
number and configuration of detectors
bus structure
speed and architecture of processors
mechanical hardware — motors, brakes and others
number and configuration of detectors
amount of data acquired
choice of computer and hardware
detector configuration
system dynamic range
instrument control panel
image processing system
control software
interface to remote workstation
choice of computer and hardware

Computed Tomography 321

(spatial resolution, contrast sensitivity, part might have a 0.01 mm (0.0004 in.)
slice thickness, time for inspection) and beam width.
the operator interface (system control
panel, image display, processing functions It is of course possible, and routinely
and data archiving). performed, to reconstruct the 1024 × 1024
matrix over subregions of a component so
The most significant point of Table 3 is that a higher resolution beam width finer
how the specimen to be inspected than 1 part in 1000 of the object can be
determines many of the principle used effectively. However, the scan must
characteristics of the computed still cover the full size of the part. As the
tomographic system. For this reason, part size increases, the distance from
different computed tomographic systems source to detector increases and X-ray
are designed for different sized objects. intensity at the detector falls off
The object size and X-ray penetrability quadratically. Thus, it is impractical to use
determines the mechanical handling a very small beam width on large parts
characteristics. As the object becomes because of the very long scan time that
larger, higher energy X-ray sources and will result. Practical resolutions for
larger mechanical systems are required. computed tomographic systems that
The result of this is higher cost for the handle large components greater than
computed tomographic system. Figure 15 0.30 m (12 in.) in diameter are in the
shows the effect of object size and energy range of 1 to 2 line pairs per 1 mm (25 to
on the cost of a computed tomographic 50 line pairs per 1.0 in.). For components
system. less than 300 mm (12 in.) diameter, 2 to 4
line pairs per 1 mm (50 to 100 line pairs
The sensitivity to fine detail of per 1.0 in.) can be obtained. For higher
computed tomographic systems is a resolution, greater than 4 line pairs per
function of resolution and contrast 1 mm (100 line pairs per 1.0 in.) and
sensitivity. The computed tomographic feature sensitivity on the order of
resolution is fundamentally determined 0.125 mm (0.005 in.), the computed
by the beam width of the X-ray optics tomographic systems are designed to
design and is driven by the selection of handle objects of only 30 or 40 mm
source and detector aperture sizes and the (about 1 or 2 in.) in size.
source, object and detector distances. The
beam width, size of the object computed Figure 16 shows how the size and
tomographic image reconstruction matrix detail sensitivity of computed
must all be considered in a system design. tomographic systems are related by the
design. Each type of system (A though D)
A typical reconstruction matrix size for represents a range of capability that can
computed tomography at the turn of the found in commercially available
century was 1024 × 1024. A first computed tomographic systems but no
approximation would make the resolution one computed tomographic system can
limit roughly one part in 1000 and the provide both large object inspection and
system would be designed to match the very fine resolution.
X-ray optics to 0.001× the size of the part.
For example, a system designed to handle FIGURE 16. Computed tomographic system size versus
a 0.5 m (20 in.) size part might allow for sensitivity to detail.
0.5 mm (0.02 in.) size beam width and a
system designed for a 10 mm (0.4 in.) size

FIGURE 15. Computed tomographic system size versus cost. 2.0 (80)
1.8 (72)
Size, m (in.)3.0 (120) 9 1.6 (64) Type D
Energy (MV)2.5 (100) 8 1.4 (56)
2.0 (80) 7 1.2 (48)
Object size, m (in.)1.5 (60)61.0 (40)
1.0 (40) Size 5 0.8 (32) Type C
0.5 (20) 4 0.6 (24)
0 Energy 3 0.4 (16) Type B
1 1.5 2 2.5 2 0.2 (8)
0.5 Cost (millions of dollars in 2001) 1 0 Type A
0
3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
(4) (8) (12) (16) (20) (24) (28) (32) (36) (40)

Resolution, mm (10–3 in.)

322 Radiographic Testing

PART 6. Applications of Computed Tomography

Computed tomographic data allows Present computed tomographic
accurate evaluation of dimensions, technology is relatively expensive. The
locations in three-dimensional object value of computed tomography is
space or material density (as related to therefore realized in applications where
X-ray linear attenuation coefficient) to be the objects are of critical value or
performed in any orientation throughout adequate measurements cannot be made
the volume of an object that has been by other means. A primary example is
scanned with the computed tomographic rocket motors. Computed tomography is
system. Table 4 summarizes computed used extensively on rocket motors because
tomography’s capability and typical the objects are very valuable and are used
sensitivity ranges and limitations. in critical applications, so that the cost of
computed tomography remains a small
In general, the benefit of X-ray fraction of the overall mission value.
computed tomography over alternative Complex, high value turbine blades are
nondestructive evaluation methodologies another example where computed
is its ability to map the relative X-ray tomography is worth the cost because of
linear attenuation coefficient of small dimensional accuracy better than that
volume elements throughout a from other techniques.
component, permitting the extraction of
dimensional and material characteristics Beyond these few examples, computed
of features and anomalies. With these tomography is not routinely applied to
characteristics, derived from the objects as a final inspection process.
computed tomographic data, engineers Rather, computed tomography is applied
can perform a variety of analyses to arrive as an engineering tool and enabling
at quantitative measurements of technology to support product
parameters to improve the overall development activities, speeding products
product. For objects that fit the to market. Table 5 summarizes cost
constraints of size and shape for proper effective applications for computed
computed tomographic examination, the tomography.
computed tomographic data offer
unparalleled capability for feature The application of computed
detection and measurement. As tomography as a measurement tool for
complexity of design increases, the value engineering and manufacturing provides a
of computed tomographic measurement cost benefit to a number of processes.
capability increases. Computed tomography is used by
engineers on prototypes to fully

TABLE 4. Capabilities of computed tomography. Technical Capability
Point of Interest

Volumetric Measurement volumetric feature detection and configuration control
Quantitative features digital; three-dimensional
Data must have separation
Disbond detection
large structures: typically 0.5 mm (0.02 in.) features are resolved, smaller high contrast features can be detected
Detail Sensitivity small structures, <250 mm (10 in.): typically 0.002 to 0.004 parts per thousand are resolved
Resolution multiple materials must differ in X-ray linear attenuation coefficients (density and atomic number) for detection

Density measurement (0.01 to 0.1 percent for large areas, >1.0 mm (0.04 in.) diameter
large aspect ratios cause streak artifacts (>15:1 is difficult)
Artifacts detail sensitivity in low density material near high density features is compromised

Parts Handling X-ray transmission is limited by size, density and atomic number of the part and by the available X-ray energy
Penetration Access to 360 degrees around the part
Size and shape

Computed Tomography 323

characterize the object. Computed analysis rather than qualitative inspection
tomography measurements can be standards has considerable potential for
performed on test articles to validate reducing scrap and increasing component
prototypes and models before testing, reliability. Maintenance, repair and failure
during certain types of testing and post analysis activities benefit from computed
testing, including noninvasive tomography measurements by providing
micrographic evaluations. Computed information for making decisions on
tomography permits geometry acquisition irreversible steps and/or eliminating
(often referred to as reverse engineering), disassembly or destructive testing to
providing a direct cost saving over obtain critical data. The long range value
traditional approaches to translating of computed tomography technology is
existing components into digital models that it closes the loop between the
in computer aided design (CAD) engineering and the manufacturing
workstations and computer aided operations by providing quantitative data
engineering (CAE) workstations. that can be accessed by engineers at their
Computed tomography is particularly workstations.
effective during product failure analysis
by noninvasively inspecting the interior Because the output of computed
condition of articles, including scans tomography is a digitized, quantitative
under various operational conditions. map of the density, the computed
Computed tomography evaluation of tomographic image can be analyzed by
materials also is useful in performance quantitative, computer based techniques.
prediction based on the measurements Subtle deviations in density from a host
obtained from the computed tomographic density can be identified and measured
data. This is where engineering and much more precisely than with any other
nondestructive evaluation need to means. The important point about
collaborate to create the most cost computed tomography is its data
effective products. presentation: a clear, unambiguous image
in digital, computer readable format.
Computed tomography can be an Although traditional projection
important tool in the manufacturing and radiography does deliver an image,
process development stages of product life foreground and background material can
cycles by providing feature and anomaly obscure the clarity of the image in the
location, configuration control and the region of interest. Computed tomography
direct measurement of dimensions for provides great sensitivity to the most
engineering acceptance. The value of subtle variations in density; typically,
computed tomographic evaluation is high computed tomography provides 10 to 100
for ensuring a development process has times greater sensitivity to density than
been brought into control. For routine projection radiography. Compared to
production quality control the application other inspection modalities, computed
of computed tomographic depends on the tomography works best in complex, thick
relation between the object value, objects. Figure 17 and Table 6 show how
computed tomographic scanning cost and object geometry influences the test
the cost of alternatives. The more technique.
complex and costly an assembly, the more
likely that computed tomography can be The major disadvantage to
a cost effective tool. conventional computed tomography lies
in having to make X-ray measurements
Ultimately computed tomography can over the entire periphery of a test
allow the acceptance of a product on the specimen for each slice. Thus, as shown in
basis of quantitative measurements and Fig. 17, graphic slices that do not have to
engineering criteria. Such an engineering penetrate through much material present
the best computed tomographic images;
TABLE 5. Beneficial application areas for computed computed tomographic slices that suffer
tomography. massive amounts of absorption do not
provide images as good as those taken
Field Application with projection radiographs taken from a
different perspective where the path is not
Engineering prototype evaluation so heavily absorbed, as shown in the flat
Manufacturing geometry acquisition pancake shape of Fig. 17.
failure analysis
performance prediction An important point, usually
process development overlooked, is illustrated by the pancake
feature and anomaly location shape: computed tomographic images and
configuration control projection radiography images that
acceptance by engineering criteria present substantially the cross sectional
picture are taken from entirely different
perspectives. In this case, the projection
radiography would be taken with the
source above and the recording film
below (or vice versa) so that the X-ray

324 Radiographic Testing

paths are essentially perpendicular to the larger assembly, such as rocket nozzles,
pancake plane. The computed and (3) computed tomographic sampling
tomographic image would be acquired yields information as an engineering tool
with source and detectors confined to the for process control, such as geometry
pancake plane and relative motion would acquisition for dimensional control.
be induced between them so that the
X-ray paths are always within the plane. Because computed tomography is a
direct, full imaging mode, many
The test specimen diversity in sizes, developed systems, especially those
materials, anomalies and time constraints conceived with a more general use,
of industrial objects is such that no single provide the capability for inspections
X-ray computed tomographic system is based on techniques derivative of
appropriate for even a major fraction of computed tomography. Among these
the range of applications. Thus, the capabilities are laminography and other
investment required in the development techniques based on reconstructive
of a single computed tomographic system imaging, such as limited angle
design for nondestructive testing cannot, (incomplete views) computed tomography
in general, be amortized over a variety of or high resolution annular computed
applications. Computed tomographic tomography.
systems are slow and expensive. With
several exceptions, nondestructive testing Other nonimaging modes peculiar to
computed tomography has been the particular problem at hand are also
developed in several very specific sets of possible — for example, precise
circumstances: (1) the finished product is measurement of an internal seal
very expensive, such as a ballistic clearance. Indeed, such computed
missile,21 (2) a relatively inexpensive tomography derivative techniques may
component becomes a critical item in a present the most fruitful of approaches for
solving specific inspection problems.
FIGURE 17. Object shapes referred to in Why? In most nondestructive testing
comparison of computed tomography with problems, there is a great deal of a priori
conventional radiography: (a) oblong knowledge and anomalies tend to fall in
cylinder; (b) regular cylinder; (c) short and very narrow, well defined categories. Thus,
wide cylinder; (d) flat or pancake cylinder. digital signal processing of nonimaged
See Table 6. signature data may provide quick,
efficient schemes for specific kinds of
(a) anomalies that traditional computed
tomographic imaging cannot provide.
Some of these applications are discussed
below.

Computed Tomography
Examples

Figures 18 to 21 show examples of
computed tomographic images of
materials and structures.

The detailed evaluation of complex
castings is an excellent application of
computed tomographic technology.22-26
(b) Figure 18 shows a comparison of
computed tomography with conventional

TABLE 6. Shape inspectability by computed tomography
versus conventional radiography. See Fig. 17.

___R_a_d__io_g__r_a_p_h_i_c_T_e_c_h__n_iq__u_e___
(c) _________O_b__je_c_t__S_h_a_p_e_________ Computed Conventional

Description Figure Tomography Radiography

Cylinder, oblong 17a satisfactory a satisfactory

Cylinder, regular 17b excellent poor

(d) Cylinder, short and wide 17c excellent poor

Cylinder, flat (pancake) 17d poor excellent

a. With sensor plane parallel to test object.

Computed Tomography 325

radiography for a turbine blade casting. FIGURE 19. Computed tomographic image of
The part contains a complex internal graphite epoxy woven J stiffener showing
geometry. The radiograph is unable to ply condition and consolidation.31
evaluate the internal cross sectional
configuration of the part. The computed 13 mm (0.5 in.)
tomographic slice shows the wall
thickness of the casting directly and will
show discontinuities in the cast material if
they are present at the location of the
slice plane.

The ability of computed tomographic
images to show internal material
variations is particularly advantageous for
composite material inspection.27-33
Figure 19 shows a computed tomographic
image of a composite J stiffener, where the
variations in the consolidation and the
ply layups can be evaluated, particularly
at T junctions.

FIGURE 18. Computed tomographic
evaluation of casting turbine blade with
400 kV computed tomographic system
showing internal feature condition and wall
thickness measurement: (a) digital
radiograph; (b) computed tomographic
slice.
(a)

FIGURE 20. Cruise missile engine: (a) projection radiograph
showing complex superposition of information;
(b) longitudinal computed tomographic slice along axis of
engine obtained with 2.5 MV computed tomographic
system showing internal details.49
(a)

(b) 1.0 m (40 in.)

5 mm (0.2 in.) (b)

326 Radiographic Testing

Figure 20 shows a radiograph and a MOVIE. MOVIE.
longitudinal computed tomographic slice Electronic Image slices of
through a cruise missile engine using a device on device, top to
9 MV X-ray source. This example turntable. bottom.
demonstrates the power of computed
tomography for complex structure MOVIE. MOVIE.
evaluation overcoming superposition Images of Slices show
common in radiography to reveal superior electronic delaminations
information about the internal device. in composite
configuration of systems. fastener hole.

Figure 21 is an example of volumetric
computed tomographic scanning.

FIGURE 21. Volumetric computed tomographic system data of
small single battery flashlight data by using area array
detector. Multiple slice reconstruction and three-dimensional
surface rendering are possible: (a) digital radiograph;
(b) horizontal slices; (c) vertical slice; (d) three-dimensional
surface rendering.49,50

(a) (c)

MOVIE. MOVIE.
Tomographic Transverse
data image of image of
electronic delaminations
device. in fastener hole.

(b) (d)

Computed Tomography 327

PART 7. Reference Standards for Computed
Tomography

Background The phantoms used in medical computed
tomographic evaluation have various
The initial developments of computed components that test these parameters.
tomography were directed at medical
diagnostic applications. The medical The theory of image quality considers
community has generated comprehensive the modulation transfer function (MTF)
literature on the theory and performance and the noise power spectrum as the
of computed tomography for biomedical essential defining characteristics of
applications. The basic references on the imaging systems.39 These principles have
fundamentals of computed tomography been applied to medical computed
come from medical users. tomographic imaging. Judy describes
using the line spread function40 to obtain
Medical computed tomographic system the modulation transfer function and
performance measurement requirements Bischof and Ehrhardt describe the point
have been described with the spread function18 to obtain it. Hanson41
development of appropriate phantoms. describes the noise power spectrum
McCullough and others,34 Payne and measurement. Hansen considers
others35 and Bergstrom51 discuss probability distributions to indicate signal
measurements for performance detection probabilities in computed
evaluation, for acceptance testing and for tomographic imaging. Resolution and
ongoing quality assurance of computed noise can be combined in detectability
tomographic scanning systems. They limit curves that plot contrast needed to
discuss possible phantom types that can detect an object versus the object size for
be constructed to test parameters of different dose levels of medical imaging.
interest. Goodenough and others36 and These are referred to as contrast detail
White and others37 describe the dose (CDD) curves. Bergstrom51 shows an
developments of phantoms to be used in example contrast detail dose curve from
measuring various parameters. The research data and discusses the difficulties
American Association of Physicists in in creating a phantom for such
Medicine (AAPM) also describes a measurement. Cohen and Di Bianca42 use
phantom.38 Table 7 indicates the the contrast detail dose diagram to
parameters, generally agreed on in the evaluate a computed tomographic
literature, that require evaluation in scanner.
medical computed tomographic systems.
As computed tomography has
expanded from the medical to industrial

TABLE 7. Parameters of interest for computed tomography standards.

Parameter Notes
Alignment image artifacts caused by mechanical alignment; dimensional

Slice thickness and geometry accuracy
vertical coverage; alignment and uniformity of computed
Spatial uniformity
Noise tomographic plane in object
variation of computed tomography measurement across scan plane
Low contrast sensitivity random variation in attenuation measurements (measured by
Spatial resolution
statistical variation or noise power spectrum)
Modulation transfer function ability to detect small contrast changes (mainly limited by noise)
Effective energy and linearity of ability to distinguish two objects as separate (measurement

tomography numbers should be under noise free conditions)
Accuracy and precision quantitative measurement of high contrast spatial resolution
Dose monochromatic photon energy that would give result equivalent

to results from polychromatic spectrum used
reliability and stability of computed tomography measurements
patient exposure (for medical computed tomography)

328 Radiographic Testing

applications, industrial users have Resolution
discussed the issue of standards. Dennis43
describes computed tomographic Resolution refers to the ability to sense
fundamentals and the image quality that two features are distinct.
parameters from an industrial computed Measurements of resolution with a
tomography perspective. The American phantom can be performed in a wide
Society for Testing and Materials (ASTM) variety of ways. Holes in a uniform
CT Standardization Committee E7.01.03 material of either fixed diameter and
has also developed a document describing changing separation, or decreasing
the basic principles of industrial diameter with separations that also
computed tomography and advocates the decrease accordingly, are very common.
modulation transfer function and contrast The resolution is defined as the minimum
detail dose for measurement of system separation detectable.
performance.44-46 For industrial
applications, the contrast detail dose Plates of alternating high and low
curve is referred to the contrast density material (that is, plastic to air,
discrimination curve (CDC). Sivers and metal to air or metal to plastic) can be
Silver have described the theoretical used to make line pair gages. The
background and experimental results of resolution limit is determined by the
using modulation transfer function ability to see the line pairs. The loss in
measurements and contrast sensitivity is due to a loss of modulation
discrimination curves on industrial between the high and low density features
computed tomographic systems.47 Jacoby of the line pairs as the plate thickness
and Lingenfelter describe the use of a test becomes smaller. This can be monitored
phantom for monitoring industrial numerically by a data trace across the
computed tomographic system image of the line pairs to measure the
performance over time.48 modulation as a function of line pair size.
A plot of the modulation values as a
The parameters listed in Table 7 may be function of the line pair value is the
measured from data taken by a phantom square wave response of the system. This
that contains features that represent the is related but not equivalent to the
parameter. A single phantom unit may modulation transfer function.
contain a variety of subsections that will
measure various parameters. The The modulation transfer function is
parameters themselves are not defined for a sinusoidal varying test
independent but often are different pattern; however, such a pattern is very
manifestations of the fundamental difficult to construct for use with X-rays.
performance characteristics of the system. Because of the definition of the
Table 8 lists some key categories for a modulation transfer function, it can be
phantom and potential techniques of measured by mathematical calculation of
obtaining the measurements. the fourier transform of the
one-dimensional line spread function
TABLE 8. Phantom categories and measurement (LSF) or the two-dimensional point spread
technique. function (PSF). The line spread function
and/or point spread function is obtained
Type Construction or Technique by measurement of the spreading of the
image from a delta function input such as
Resolution holes a pin or wire. If the pin is small enough
squares the point spread function is given directly.
line pairs If not, the size of the pin must be
pins and wires deconvolved from the results. Because of
calculation of modulation transfer function the problem of finding an adequate line
or point source phantom, the line spread
Contrast signal to noise in a uniform material sample function is very often measured by
small density variation differentiation of the edge spread function
(ESF). The edge spread function is readily
Material and density various solids obtained from a data trace across a sharp
liquids of different mixture percentages edge in the image.
porous material compaction
The modulation transfer function
Dimensional accuracy pin sets output is a curve of the response of a
and distortion hole sets system as a function of frequency. It is
often useful to have a single numeric
Slice thickness pyramids value to be used for relative comparison
cones of performance. In the case of the
slanted edges modulation transfer function an arbitrary
spiral slit value from the curve may be taken, such
as the frequency at which the modulation
is decreased to 10 percent. The width of
the line spread function or point spread

Computed Tomography 329

function can also be used as a single assembly is bolted together and the line
numeric value for comparison of pair plates can be changed if additional or
resolution. By measuring the full width at a different range of line pairs is desired.
half maximum (FWHM) of the line spread After computed tomography scanning the
function a relative value that is related to reconstructed image is analyzed by
the system resolution is obtained. measuring the modulation of the
computed tomography numbers obtained
Resolution is most commonly from a trace across the line pairs. The
measured in the computed tomographic modulation at each line pair set is
image, which is a slice through the object. measured as a percentage, where the
However, computed tomographic data are modulation measured between the 3 mm
fundamentally volumetric in nature, (0.12 in.) thick metal and 3 mm (0.12 in.)
multiple contiguous computed thick acrylic steps is taken to be
tomographic slices result in a volume data 100 percent. The resolution phantom has
base. Depending on the use of the data, it been fabricated in two forms: (1) steel and
may be important to consider the acrylic and (2) aluminum and acrylic. The
resolution in the axial orientation of the steel and acrylic phantom is for systems
computed tomographic data acquisition. of 300 kV and up, the aluminum and
This resolution will be for the most part acrylic phantom is for systems under
determined by the effective slice thickness 300 kV.
and axial step spacing used in the
scanning sequence and may be quite Figure 23 shows a computed
different from the individual slice tomographic image of the steel resolution
resolution. In addition, the effective slice phantom obtained from a relatively high
thickness often will vary over the field of resolution computed tomographic system.
view, leading to additional resolution The computed tomographic image density
characterization requirements. In the case contour line across the phantom indicates
of direct volume computed tomographic modulation for the respective line pair
imaging using cone beam geometries, the measurements at about 82 percent at
data are usually taken and reconstructed
so that resolution is about the same in all FIGURE 23. Computed tomography of line pair phantom:
directions in the volume. (a) tomographic image; (b) density trace evaluation.

Figure 22 is a photograph of a line pair (a)
resolution phantom. The phantom
consists of sets of metallic and acrylic
plates of specified thickness. Line pairs of
0.5, 1, 2 and 4 line pairs per 1 mm
(12, 25, 50 and 100 line pairs per 1.0 in.)
are formed by the phantom. The entire

FIGURE 22. Photograph of line pair phantom.

(b) A B Computed
C DE tomographic
4000 scan
3500
3000 Magnitude (counts) Density
2500 trace
2000
1500 30 60 90 120 150 180
1000 Distance (pixels)

500
0
0

Legend
A. Reference bar.
B. 0.5 line pairs per 1 mm (13 line pairs per 1 in.).
C. 1 line pairs per 1 mm (25 line pairs per 1 in.).
D. 2 line pairs per 1 mm (50 line pairs per 1 in.).
E. 4 line pairs per 1 mm (100 line pairs per 1 in.).

330 Radiographic Testing

0.5 line pairs per 1 mm (12 line pairs per function — and detector cross talk are all
1.0 in.), 46 percent at 1 line pair per possible causes.
1 mm (25 line pairs per 1.0 in.), 4 percent
at 2 line pairs per 1 mm (50 line pairs per The modulation transfer function may
1.0 in.) and 0 percent at 4 line pairs per be calculated directly from the
1 mm (100 line pairs per 1.0 in.). asymmetric line spread function or the
line spread function may be processed to
The modulation transfer function form a symmetric function. Figure 25
provides a measurement of the resolution shows three possible modulation transfer
of a system by plotting the signal functions for System D data. By taking the
modulation that the system can provide line spread function and mirroring it at
as a function of frequency. The the peak, symmetric line spread functions
modulation transfer function are generated for the air and aluminum
characterization can be obtained by halves of the edge spread function. Figure
different techniques. One of the easiest 25 shows that modulation transfer
techniques is to calculate the modulation function curves for each of these three
transfer function from line trace data approaches to handling the System D data
across the edge of a phantom. In the will create significantly different curves.
following, the edges used for the
measurement are from the contrast Figure 26 shows the results of
sensitivity disk phantom discussed in modulation transfer function
below. The process involves using measurements for several computed
multiple traces across the edge of the disk tomographic systems. The modulation
from numerous angles. This provides edge transfer function measurements were
traces from all orientations in the
computed tomographic image. These FIGURE 25. Modulation transfer function of system D,
traces are averaged to form the edge showing effects of asymmetric and symmetric line spread
spread function, then differentiated to functions.
form the line spread function and finally
fourier transformed to generate the 1.2
modulation transfer function.
Modulation transfer function 1
Figure 24 shows the line spread Air half
function for each of three different
computed tomographic systems. The 0.8
shape of the line spread function is an
important characteristic of the system. 0.6 Total
The full width at half maximum (FWHM)
of the line spread function is a measure of 0.4
the relative resolution capability of each 0.2 Aluminum half
system. The shape of the line spread
function should be symmetric. In Fig. 24 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
data System I is symmetric, System K is 0 (13) (25) (38) (50) (63) (75) (88) (100)
slightly asymmetric and System D is very
asymmetric. The asymmetry may be due Frequency, line pairs per 1 mm (per 1 in.)
to a variety of causes. Aliasing in the data
acquisition — that is, under sampling,
truncating or clipping the edge spread

FIGURE 24. Line spread function for three computed FIGURE 26. Modulation transfer function measurements of
tomographic systems. several computed tomographic systems.

0.12 System D Modulation transfer function 1.2
0.1
Normalized response 0.08 K
0.06 1B
0.04
0.02 A
0 0.8
–0.02
System K 0.6
–0.2 System I
(–0.08) 0.4

0.2 H D

I

–0.1 0 0.1 0.2 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
(–0.04) (0.04) (0.08) 0

(13) (25) (38) (50) (63) (75) (88) (100)

Position, mm (in.) Frequency, line pairs per 1 mm (per 1 in.)

Computed Tomography 331

analyzed by obtaining an average edge FWHM values of the line spread functions
spread function, using a three point are also listed. The modulation transfer
running average over the curve, functions are less than 1 line pair per
differentiating, repeating a three point 1 mm (25 line pairs per 1.0 in.) for lower
running average and then taking the resolution systems, typically for test
fourier transform. For Systems B and D, objects greater than 750 mm (30 in.) in
the line spread function has been diameter. The higher resolution systems
modified to be symmetric by mirroring (B and D) are designed for smaller test
the aluminum side of the edge spread objects, that is, 150 to 300 mm (6 to
function. One system demonstrates 12 in.) in diameter.
modulation transfer function values
greater than expected, which can be Contrast Sensitivity
caused by frequency enhancement in the
reconstruction algorithms. Contrast sensitivity refers to the
graininess in an image. The best way to
Table 9 tabulates the modulation measure contrast sensitivity is to obtain a
transfer function values for 5, 10 and histogram of pixel values in a region of
20 percent contrast from the two sets of uniform density of a test specimen.
modulation transfer function calculations Contrast sensitivity is then defined as the
of Fig. 26. Five percent contrast is usually fractional standard deviation of the
considered the limit of resolution. The distribution. The inverse of this contrast
sensitivity value is also commonly
TABLE 9. Modulation transfer function frequency for 5, 10 referred to as a signal-to-noise
and 20 percent contrast. measurement of the system. The best
contrast sensitivity phantom is an
Frequency (line pairs per Full Width at absolutely featureless uniform disk
composed of a material whose X-ray
_____1_m__m__)_f_o_r__C_o_n_t_r_a_s_t_L_e_v_e__ls_____ _H_a_l_f_M__a_x_i_m__u_m__ absorption and density mimic those of
the actual class of inspection objects.
System 5 percent 10 percent 20 percent mm (in.)
In practice it is of interest to measure
A 0.84 0.77 0.67 1.10 0.043 the contrast sensitivity as a function of
B 1.41 1.28 1.05 0.60 0.024 the feature size. Materials of very close but
D 2.10 1.93 1.31 0.30 0.012 differing densities can be used for this.
H 0.80 0.70 0.56 1.10 0.043 Normally plugs of slightly different
I 0.70 0.58 0.51 1.30 0.051 densities are inserted into a background
K 1.08 1.00 0.92 0.80 0.031

FIGURE 27. Probability distribution analysis for feature detection.

∆µ

Relative probability pσm qσm

Background Signal

σm

FN FP
µc

Signal amplitude (relative scale)
Legend

FN = false negative
FP = false positive
p = FP level units of σm
q = FN level units of σm
∆µ = contrast discrimination
µc = signal threshold in decision process
σm = standard deviation of mean over some specified feature size

332 Radiographic Testing

material. The size of the plugs is a computed tomographic slice of the large
variable. Evaluators then determine which aluminum contrast sensitivity phantom
level of contrast they can detect as a with the corresponding density trace.
function of feature size. This type of
phantom can cause a contrast The measurement of contrast
discrimination curve. By plotting the size sensitivity is obtained by taking a region
of feature with its percentage contrast for in the center of the reconstructed image
detectability, the curve is generated. and determining the average and standard
Numerous samples, however, may be deviation for all computed tomographic
required. The contrast detectability will numbers in the region. A typical region
change with exposure and multiple curves size of 10 mm (0.4 in.) diameter is used.
are created as a function of the patient (or Readings are usually taken at the center of
object) dose. The visual perception of the the disk. The ratio of the average to the
detectability of features will be different standard deviation is used as a signal to
for different individuals. Thus a large noise measurement. The inverse is a
number of interpreters should be used to measure of contrast sensitivity. The
develop a curve where, for example, measurement of signal to noise for the
50 percent of the interpreters sense the image shown in Fig. 28 is about 6.
contrast level for detection of various
feature sizes. The signal-to-noise ratio is an
important measure of system
An alternative technique to obtain the performance. The values improve with
contrast discrimination curve is to higher signal strengths. Large slice
calculate it on the basis of noise thickness and longer scan times will also
measurements as a function of region of improve signal to noise. The
interest size in a uniform phantom and signal-to-noise ratio will also improve
weight the curve for loss of contrast as a with smoothing algorithms in the
function of resolution by using the reconstruction; however, this will decrease
modulation transfer function. The the resolution. Thus, the signal-to-noise
contrast required to detect a feature will ratio and resolution must be considered
depend on the statistical confidence, in together in assessing performance.
terms of false positive or false negatives,
that one is willing to accept. Figure 27 FIGURE 28. Computed tomographic image of aluminum
shows the statistical variation in the contrast sensitivity phantom: (a) slice image; (b) density
background and signal that could be trace.
observed in an image. The contrast
discrimination ∆µ necessary for detection (a)
depends on the values of acceptable false
positive (FP) and false negative (FN), (b) 40 Magnitude (counts)
respectively, where σm is the standard
deviation of the mean over some specified 30 100 200 300 400 500 600
feature size, p is the false positive, q is the 20 Distance (pixels)
FN level in units of σm and µc is the 10
critical value used in the decision process
to decide if a signal is present or not. A 0
contrast discrimination curve can be –10
created for any combination of false –20
positive and false negative values by
multiplying the σm values in the noise 0
curve by the sum of p and q and dividing
by the modulation transfer function
modulation. The contrast discrimination
curve determines the minimum contrast
that a feature must have to be detectable
at the statistical discrimination levels
selected. The exposure level is a variable
in data acquisition, which is a factor in
the noise measurements as a function of
feature size.

A contrast sensitivity phantom can be
made from a uniform disk of material
such as aluminum, 25 mm (1.0 in.) thick.
Different sizes such as 140 mm (5.5 in.) in
diameter and 70 mm (2.8 in.) in diameter
may be appropriate for different
computed tomographic systems. The
smaller diameter size is used on systems
with small fields of view or low kV.
Figure 28 shows an example of a

Computed Tomography 333

A means of combining signal-to-noise scan time dependent. Thus scanning
ratio and resolution is the contrast longer or with larger slice thickness
discrimination curve. The contrast should drive the curves lower. The
discrimination is affected by the feature systems shown in this figure, of course,
size. Low contrast changes are easier to have been operated at different scan
detect over larger areas than in small areas times, slice thicknesses and X-ray energies
where they are easily masked by noise. or intensities that are appropriate for the
This effect can be calibrated by measuring goal of that particular computed
the statistical variations in the values of tomographic system design.
the means of the computed tomographic
numbers as a function of the size of the Figure 31 shows the effects of the false
region of interest. Figure 29 plots the error positive and false negative discrimination
in the mean of the computed levels on the contrast discrimination
tomographic value (standard deviation σm curve.
of the mean) for a number of readings as
a function of the feature size (size of the Material Density
region of interest) on several computed
tomographic systems. An important phantom function is to
establish the correlation between
From this curve and the modulation computed tomographic value and
transfer function, it is possible to generate material density. Such a phantom can be
the contrast discrimination curve as quite difficult to manufacture because it is
discussed above. The conversion of difficult to change density significantly
modulation transfer function line pair
values to the feature size is obtained by Contrast discrimination (percent)FIGURE 30. Contrast discrimination curves for several
multiplying the line pair per millimeter computed tomographic systems (A, B, H, I, K) at 10 percent
by two and inverting to provide false positive and false negative values.
modulation as a function of feature size.
100
Figure 30 shows the contrast I
discrimination curve for five computed
tomographic systems. The contrast 10
discrimination curves are plotted for B
10 percent false positive and false negative
discrimination levels. The lower the H A
contrast discrimination value on the 1 K
curve, the easier it should be to detect
features. Thus, systems such as H and K 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
would be most likely to detect low 0 (0.02) (0.04) (0.06) (0.08) (0.10) (0.12) (0.14) (0.16) (0.18)
contrast changes in an object. It is
interesting that system K, a medical Feature size, mm (in.)
scanner, has excellent contrast
discrimination. Medical systems can play
a useful role in industrial computed
tomography for components that can be
penetrated with the lower kV and that fit
within the medical gantry system size.
The contrast discrimination curve data are

FIGURE 29. Standard deviation σm of mean of computed FIGURE 31. Contrast discrimination curves at 1, 10 and
tomographic readings, as function of feature size. 30 percent false positive and false negative values.

10 100
System B Contrast discrimination (percent)
Error in mean (percent) 9 System A 10

8 1.0 1 1 percent
7 System D (0.04) 10 percent

6 10 0.1 30 percent
(0.4) 0
5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
(0.04)(0.08)(0.12)(0.16)(0.20) (0.24)(0.28) (0.32)(0.36)(0.40)
4
3 System I
2 System H

1
0 System K
0.1
(0.004)

Feature size, mm (in.) Feature size, mm (in.)

334 Radiographic Testing

without changing atomic number. The isopropyl alcohol or dilutions of
X-ray attenuation coefficient is dependent potassium iodide. These can be used to
on both density and atomic number. At create steps of density over a very narrow
high X-ray energies where the compton range. Various polymers, such as acrylic
effect dominates the attenuation, the and nylon, have also been used. They
calibration is not difficult. At low have inherent manufacturing variations
energies, where photoelectric effects are that will result in differing attenuation
involved in the attenuation, it is a real measurements between samples that can
problem. The range of high or low energy be used to develop a phantom.
depends on the material being tested. At Carbon-to-carbon composite specimens
medical computed tomographic energies can be manufactured to varying levels of
of 80 keV effective, carbon materials can densification in the range of about 1.3 to
be used for density calibration. At 150 keV 1.8 g·cm–3, which makes a useful
effective for a 300 kV X-ray system, even phantom for low density calibration.
magnesium and aluminum may distort Densification of ceramic powders is also
the density calibration. feasible for ranges of about 60 percent to
full densification.
The traditional density phantoms used
in medical computed tomography have A phantom that consists of differing
been liquid mixtures, such as glycerin and materials of significant density variation
for a wide range of industrial material
FIGURE 32. Example of material density phantom: (a) top applications may be fabricated. However,
view; (b) side view. Each density phantom is a cylinder the evaluation of the results from such a
measuring 13 mm (0.05 in.) diameter x 25 mm (1.0 in.) phantom must consider the X-ray energy
±0.0025 mm (0.001 in.). and the atomic elements involved when
extrapolating to other materials not
(a) included in the phantom.

13 mm (0.5 in.) diameter An example material calibration
phantom is shown in Fig. 32. It consists
2 1 of an acrylic disk of 140 mm (5.5 in.)
3 10 diameter with inserts of ten various
4 materials. The inserts are machined to
44 mm 9 specific tolerances and weighed to obtain
5 (1.75 in.) 140 mm the density. The accuracy of the density
(5.5 in.) value is estimated to be better than one
(b) percent. The acrylic disk is 50 mm
8 (2.0 in.) thick but the inserts are only
25 mm (1.0 in.) long, which leaves in the
7 phantom a uniform acrylic disk area that
6 can be used for other measurements, such
as the modulation transfer function and
25 mm the contrast detail dose.
(1.0 in.)
A computed tomographic scan of the
50 mm material calibration phantom is shown in
(2.0 in.) Fig. 33. The computed tomographic
numbers for each insert from the
Legend reconstructed image are plotted against
1. Air gap. the measured densities to serve as a
2. High molecular weight polyethylene, density 0.95 g·cm–3. calibration curve for the system. The
3. Nylon, density 1.16 g·cm–3. insert materials vary in atomic number
4. Nylon, lubricant filled, density 1.17 g·cm–3. that adds another variable in the process
5. Acrylic plexiglas (core material), density 1.19 g·cm–3. when the X-ray energy is such that the
6. Acetal homopolymer, density 1.51 g·cm–3. photoelectric effects are significant. The
7. Magnesium, density 1.78 g·cm–3. phantom is useful for generating a general
8. Fluorocarbon resin, density 2.18 g·cm–3. density calibration curve for a computed
9. Aluminum, density 2.70 g·cm–3. tomographic system. Figure 34 shows a
plot of material density versus computed
10. Titanium, density 4.42 g·cm–3. tomographic density for one system.

Other Functions of
Phantoms

Numerous phantoms of all sizes and
shapes have been made to evaluate
various characteristics of a system. Most
commonly, pyramids or slanting edges of
some type or other have been used to

Computed Tomography 335

assess the slice plane thickness and field phantoms are necessary to monitor
uniformity of computed tomographic artifacts, although pin phantoms are
systems. Phantoms that represent actual normally used for mechanical system
parts that are discontinuity free or have alignment. The artifact pattern generated
anomalies of known dimensions are from the pin is used to adjust the
excellent for monitoring inspection computed tomographic system
sensitivity day to day and should be configuration for minimal artifacting.
implemented if possible.
Extraction of positional and
Artifacts are features present in the dimensional information from complex
image that are not present in the object. assemblies represents an important
All imaging systems, even the human eye, application of X-ray computed
will have artifacts at some level. Artifacts tomography. Examples include
in computed tomographic systems range noninvasively measuring gaps and
from those associated with the particular measuring deformations under
computed tomographic configuration mechanical load. Such information is
such as circular rings in third generation extracted also where no photogrammetry
(rotate-only computed tomography) to or mechanical technique is possible to
those that are computed tomographic produce accurate, dimensioned
process dependent such as partial volume representations of assemblies.
streaks. Beam hardening is a primary
source of artifacts from polychromatic A basic assumption made in these
sources. Mechanical inaccuracies, material calculations is the absolute equivalence of
densities and partial voluming effects can the computed tomographic image frame
also produce artifacts. It is important to of reference and the scanned object frame
be able to recognize an artifact as such of reference. Because this equivalence
and to understand the limitation the depends on a variety of factors including
artifact places on the recognition of mechanical, motion, physical element,
anomalies or measurement of some analysis techniques, software
critical characteristic. Artifacts must not implementation and calibration
mask the presence of anomalies for techniques, this assumption of
unambiguous interpretation. This is equivalence may introduce significant
accomplished if the artifact noise level errors. A dimensional measurement
can be kept below the required signal phantom (DMP) is needed to establish
level for anomaly detection. No particular precision of a computed tomographic
imaging system.
FIGURE 33. Computed tomographic scan of material density
phantom49. An example of a dimensional
measurement phantom consists of a
1 16.5 mm (0.65 in.) thick disk, 200 mm
(7.87 in.) in diameter with forty-nine
10 8.6 mm (0.34 in.) diameter precision
drilled holes forming a rectangular matrix
at equal spacings of 20.0 mm (0.787 in.)
plus or minus 0.006 mm (2.5 × 10–4 in.).
Three additional, precisely located, small
holes were drilled adjacent to two corners
of the large hole matrix, two at one

Measured density (g·cm–3)FIGURE 34. Plot of material density versus computed
tomographic density for material density phantom.
Legend
1. Most dense. 5
System I
10. Least dense.
4

3

2

1

0

–1
0 500 1000 1500 2000 2500 3000 3500 4000
Computed tomographic density (arbitrary scale)

336 Radiographic Testing

corner and one at the adjacent corner to It probably overstates the inaccuracy for
serve as reference points during image system L that had a forced offset because of
analysis. Figure 35 shows a computed probable slight misalignment and the
tomographic scan of the dimensional calibration technique used. The accuracy
measurement phantom in the nominal determined for the other two systems falls
orientation used for the measurements well within the uncertainty in part
discussed below. dimension that would be associated with
FIGURE 36. Dimensional phantom metric Γ: (a) image;
The dimensional phantom provides a (b) object; (c) example Γ map for particular test.
metric for the precise dimensional (a)
analysis of scanned parts. Figure 36 and
Eq. 36 show the concept of the metric Γ, Y
which measures distortion.
X
  ∂X ∂X  2
(b) y
(36) Γ =  det  ∂x ∂y  − 1
 ∂Y ∂Y  x
 ∂x ∂ y 
(c)
The metric uses the local jacobian of the
transformation matrix between the part
and its computed tomographic image
representation to provide a quantitative
means of assessing the inherent geometric
accuracy of any given computed
tomographic system.

Table 10 summarizes the outcome of
phantom measurements for three
computed tomographic systems. The first
column identifies the system. The second
shows the mean value of the dimensional
distortion metric (Γij) measured for each
of the systems. This index of the overall
image distortion shows that it was
extremely small. The third column gives
the ratio of the 6σ width of the deduced
distribution of principal diagonal
measurements ratioed to the nominal
dimension. It is a measure of system
precision. The last column indicates
system accuracy. It is the offset of the
peak of the probability distribution for the
diagonal length from the nominal value.

FIGURE 35. Computed tomographic image of
dimensional metric phantom.

TABLE 10. Summary of dimensional fidelity measurements
metric on dimensional measurement phantom.

Average Dimensional Maximum Dimensional
Distortion G* Precision,
System (dimensionless) Inaccuracy in
6 σ (percent)
____1_7_0__m_m___(_6_.7__i_n_._)___
µm (10–3 in.)

A 4.0 × 10–6 0.93 15.2 0.6
H 3.5 × 10–6 0.04 2.54 0.1
L 4.2 × 10–6 0.05 55.9 2.2

Computed Tomography 337

normal temperature variations in the
working environment, ±6 °C (±10 °F), for
a coefficient of thermal expansion of
aluminum of 1.22 × 10–5.

The methodology adopted in this study
should be easily transportable to other
systems for which an inherent geometry
accuracy (IGA) is desired. Location of the
centers of an array of precision machined
holes in the computed tomographic
image of a test article for comparison with
the location of the holes in the part itself
is an excellent means of deriving the
elements of the local transformation
matrix for inherent geometry accuracy
determination. The success of the
technique relies on the fact that the hole
center location is insensitive to the
criterion used for finding the hole edge,
particularly because the hole center
coordinates are highly overdetermined.
Techniques that rely on precise
determination of edges (for example,
finding the absolute diameter of the test
article) will be less successful because they
are sensitive to the definition of an edge
in the image.

338 Radiographic Testing

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