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39.

P.M. Joseph, Artifacts in Computed Tomography, Phys. Med. Biol., Vol 23, 1978, p 1176-1182
40.

R.H. Brooks, et al., Aliasing: A Source of Streaks in Computed Tomograms, J. Comput. Asst. Tomgr.,
Vol
3 (No. 4), 1979, p 511-518
41.

D.A. Chesler, et al., Noise Due to Photon Counting Statistics in Computed X-Ray Tomography,
J. Comput.
Asst. Tomgr., Vol 1 (No. 1), 1977, p 64-74
42.

K.M. Hanson, Detectability in Computed Tomographic Images, Med. Phys., Vol 6 (No. 5), 1979
43.

W.D. McDavid, R.G. Waggener, W.H. Payne, and M.J. Dennis, Spectral Effects on Three-
Dimensional
Reconstruction From X-Rays, Med. Phys., Vol 2 (No. 6), 1975, p 321-324
44.

P
.M. Joseph and R.D. Spital, A Method for Correcting Bone Induced Artifacts in Computed Tomography
Scanners, J. Comput. Asst. Tomogr., Vol 2 (No. 3), 1978, p 100-108
Industrial Computed Tomography
Michael J. Dennis, General Electric Company, NDE Systems and Services

Special Features

The components that constitute a CT system often allow for additional flexibility and capabilities beyond providing the
cross-sectional CT images. The x-ray source, detector, and manipulation system provide the ability to acquire
conventional radiographic images. The acquisition of digital images along with the computer system facilitates the use of
image processing and automated analysis. In addition, the availability of the cross-sectional data permits three-
dimensional data processing, image generation, and analysis.
Digital Radiography. One of the limitations of CT inspection is that the CT image provides detailed information only
over the limited volume of the cross-sectional slice. Full inspection of the entire volume of a component with computed
tomography requires many slices, limiting the inspection throughput of the system. Therefore, CT equipment is often used
in a DR mode during production operations, with the CT imaging mode used for specific critical areas or to obtain more
detailed information on indications found in the DR image. Digital radiography capabilities and throughput can be
significant operational considerations for the overall system usage.
Computed tomography systems generally provide a DR imaging mode, producing a two-dimensional radiographic image
of the overall testpiece. The high-resolution detector of the rotate-only systems normally requires a single z-axis
translation (Fig. 25) to produce a high-quality DR image. For even higher resolution, interleaved data can be obtained by
repeating with a shift of a fraction of the detector spacing. For large objects, a scan-shift-scan approach can be used. The
translate-rotate systems are typically less efficient at acquiring DR data because the wider detector spacing requires
multiple scans, with shifts to provide adequate interleaving of data. If the width of the radiographic field does not cover
the full width of the object, the object can be translated and the sequence repeated.

Fig. 25 Digital ra
diography mode. The component moves perpendicular to the fan beam, and the radiographic
data are acquired line-by-line.
The capabilities and use of these DR images are generally the same as discussed for radiographic inspection. The method
of data acquisition is different on the CT systems; the data are acquired as a sequence of lines or line segments. The use of
a thin fan beam with a slit-scan data acquisition is a very effective method of reducing the relative amount of measured
scatter radiation. This can significantly improve the overall image contrast (Fig. 26). In addition, the data acquisition
requirements for CT systems provide for a high sensitivity and very wide dynamic range detector system.

Fig. 26 Digital radiograph of an aircraft e
ngine turbine blade (nickel alloy precision casting) from an industrial

CT system
Image Processing and Analysis. Because the DR and CT images are stored as a matrix of numbers, the computer
can be used as a tool to obtain specific image information, to enhance images, or to assist in analyzing image data.
Display Features. A number of display features are used to obtain or present specific image information. A region-of-
interest program defines a portion of the image and provides information on the pixel values within the region, such as
minimum, maximum, and average CT number values; the standard deviation of the CT numbers; or the area or number of
pixels contained in the region. A histogram plot can display the relative frequency of occurrence of CT number values.
Cursor functions can be used to point to specific features, to annotate the images, and to determine coordinate locations,
distances between points, or angles between lines. A plot or profile can be generated from the CT numbers along a
defined line.
Image Processing. The image itself can be processed to enhance boundaries and details or to smooth the image to
reduce noise. Linear operators or filters used to sharpen the image, however, will increase the image noise, and smoothing
filters that reduce noise also blur or decrease the sharpness of the image. These processing steps, however, can assist in
improving the visibility of specific types of structures. Nonlinear processing techniques can be used to enhance or smooth
the image while minimizing the detrimental effects of the processing. Nonlinear techniques include median filtering and
smoothing limited to statistically similar pixel values; both techniques reduce the image noise while maintaining sharper
boundary edges. These nonlinear techniques, however, typically require more computation and can be difficult to
implement in fast array processors.
Image Analysis. Digital images can be analyzed for specific features or to measure definable parameters contained in
the image data. Where the image-processing capabilities are generic for any image, automated image analysis software is
written to analyze specific features in specific components. The software can verify the presence of specific necessary
components or can search for defined indications. Automated analysis is generally computational intensive, and
identifying a broad range of indications is a highly complex task. Consequently, the automated analysis of flaw
indications has generally been limited to a few, narrowly scoped analysis tasks.
The automated measurement of specific design parameters of components can be more readily defined and implemented.
The cross-sectional presentation of the component structure in the CT image allows for the measurement of critical
dimensions, wall thicknesses, cord lengths, and curvatures. The automated measurement of critical wall thicknesses on
complex precision castings is a standard feature on CT systems used in the manufacture of aircraft engine turbine blades
(Fig. 10).
Planar and Three-Dimensional Image Reformation. Having a stack of adjacent cross-sectional CT slices

characterizes the density distribution within the scanned volume in three dimensions. With this set of data in the
computer, alternate planes through the object can be defined, and the CT image data corresponding to these planes can be
assembled. These CT planar reformations allow the presentation of CT images in planes other than the planes in which
the data were originally acquired, including planes that CT data acquisition would not be feasible because of component
size and shape (Fig. 27). The CT image data can also be presented along other nonplanar surfaces. The CT data that
correspond to a conical surface on a rocket exit cone or along other structures can be presented. The data can also be
reformatted to alternate coordinates, such as presenting the data for a tubular section with the horizontal axis of the
display corresponding to an angular position and with the radial distance along the vertical axis of the display.

Fig. 27
CT image (a) across a sample helicopter tail rotor blade showing outer fiberglass airfoil and center
composite spar
. (b) Planar reformation through the composite spar from a series of CT slices. The dark vertical
lines are normal cloth layup boundaries, while the mottling at the top is due to interplanar waviness of the cloth
layup.
Structures within a scanned object can also be specifically characterized. Three-dimensional surface imaging identifies
the surface of a structure in a stack of CT images, defines surface tiles corresponding to this surface, and produces a
computer-assisted design perspective display of the structure, as shown in Fig. 11 (Ref 45). Because the CT images also
display interior surfaces, the computer can be used to slice open these surface models to display interior features. These
capabilities hold the potential for improving the component design cycle by documenting the configuration of physical
prototypes and operational components.
Computed tomography can also be used to define actual components, including their internal density distribution, as a
direct input for finite-element analysis (FEA). Automated meshing techniques are being analyzed that could significantly
reduce the time required to generate FEA models. In addition, this direct FEA modeling of actual components could assist
in the nondestructive analysis and characterization of components that are to be failure tested and may allow improved
calibration of the engineering models from the test data.
Dual Energy Imaging. In the range of x-ray energies used in industrial computed tomography, attenuation of the x-ray
photons predominantly occurs by either photoelectric absorption or Compton scattering. The probability of attenuation
due to photoelectric absorption decreases more rapidly than the probability of attenuation due to Compton scattering.
Consequently, photoelectric absorption predominates at low energies, and Compton scattering is the primary interaction

for high-energy photons. In addition, the probability for attenuation by photoelectic absorption is highly dependent on the
atomic number of the absorber, while Compton scattering is relatively independent of atomic number.
These differences between photoelectric and Compton attenuation cause difficulties in correcting x-ray transmission data
for beam hardening in structures having multiple materials. This difference in the attenuation process can be used,
however, to obtain additional information on the composition of the scanned object (Ref 46). If the object is scanned at
two separate energies, the data can be processed to determine a pair of images corresponding to the photoelectric and
Compton attenuation differences. The pair of images can be a photoelectric and Compton image or can correspond to
physical density and effective atomic number. This pair of basic images can be combined to form a CT image without
beam hardening variations.
The data for the basis images are a result of the differences in the high- and low-energy scans and are highly sensitive to
random variations. As a consequence, these basis images tend to have a very high noise level. The image noise level for
the combined pseudo-monoenergetic image, however, is equivalent to or lower than the noise in either of the original
single energy images. Accurate implementation of dual energy processing requires consistent data between the high- and
low-energy scans and characterization of the differences, such as that due to the detection of Compton scatter. Dual
energy imaging can also be implemented with the DR data to determine the basis data corresponding to the sum along the
measured ray paths.
Partial Angle Imaging. All of the CT imaging techniques discussed have considered the ability to obtain transmission
data from all angles in the plane of the cross-sectional slice. This is highly suitable for objects that can be readily
contained within a tight cylindrical workspace, but it can be impractical for large planar structures. Other components,
such as large ring and tubular structures, can be conventionally scanned given a large enough workspace, but it is
advantageous to minimize the source-to-detector distance and to image through a single wall in order to have reasonable
x-ray intensities and inspection throughput.
Methods have been investigated for medical imaging for reconstruction from partial data sets. Industrial imaging has the
advantage, however, in being able to apply a priori information from the component design or from measured external
contours to compensate for the missing data (Ref 47).
Another related approach is to use methods based on the focal-plane tomography or laminography techniques developed
in the early 1920s. Focal-plane tomography involves moving the x-ray source and film relative to the object such that
features in the object are blurred, except for the features in the focal plane. This method does not necessarily eliminate all
of the structures outside of the focal plane as in computed tomography, however, the data are obtained without circling
the object.

The capabilities of the conventional focal-plane tomography approach can be enhanced by using digital processing
techniques. With a series of digital radiographs, the images can be shifted and combined within the computer to yield a
series of focal planes at different levels in the object from one set of data. In addition, image filtering can be applied,
similar to the filtering in the filtered-backprojection CT reconstruction, to enhance the features in the focal plane and to
improve the elimination of out of plane structures.

References cited in this section
45.

H.E. Cline, W.E. Lorensen, S. Ludke, C.R. Crawford, and B.C. Teeter, Two Algorithms for the Three-
Dimensional Reconstruction of Tomograms, Med. Phys., Vol 15 (No. 3), 1988, p 320-327
46.

R. E. Alvarez and A. Macovski, Energy Selective Reconstructions in X-
Ray Computerized Tomography,
Phys. Med. Biol., Vol 21, 1976, p 733-744
47.

K.C. Tam, Limited-Angle Image Reconstruction in Non-Destructive Evaluation, in
Signal Processing and
Pattern Recognition in Nondestructive Evaluation of Materials,
C.H. Chen, Ed., NATO ASI Series Vol
F44, Springer-Verlag, 1988
Industrial Computed Tomography
Michael J. Dennis, General Electric Company, NDE Systems and Services

Appendix 1: CT Reconstruction Techniques
Computed tomography requires the reconstruction of a two-dimensional image from the set of one-dimensional radiation
measurements. It is useful to know some of the basic concepts of this process in order to understand the information
presented in the CT image and the factors that can affect image quality.

The reconstruction process consists of two basic steps:
•
The conversion of the measured radiation intensities into projection data that correspond to the sum or
projection of x-ray densities along a ray path
• The processing of the projection data with a reconstruction algorithm to determine the point-by-poin
t
distribution of the x-ray densities in the two-dimensional image of the cross-sectional slice
The development of projection data is common to all CT reconstruction techniques, while the reconstruction algorithm
can be approached by one of several mathematical methods (Ref 48, 49, 50).
Of the various reconstruction algorithms developed for computed tomography, there are two basic methods: transform
methods and iterative methods. Transform methods are based on analytical inversion formulas of the projection data
values given by Eq 9. Transform methods are fast compared to iterative methods and produce good-quality images. The
two main types of transform methods are the filtered-backprojection algorithm and the direct Fourier algorithm. The
filtered-backprojection technique is the most commonly used method in industrial CT systems.
Projection Data
The first step in the reconstruction of a CT image is the calculation of projection data. The measured transmitted intensity
data are normalized by the expected unattenuated intensity (intensity without the object). A logarithm is taken of these
relative intensity measurements to obtain the projection data. The projection data values correspond to the integral or sum
of the linear attenuation coefficient values along the line of the transmitted radiation. The reconstruction process seeks to
determine the distribution of linear attenuation coefficients (or x-ray densities) in the object that would produce the
measured set of transmission values.
The projection data values for a narrow monoenergetic beam of x-ray radiation can be theoretically modelled by first
considering Lambert's law of absorption:
I = I
0
exp(- s)


(Eq 6)
where I is the intensity of the beam transmitted through the absorber, I

0
is the initial intensity of the beam, s is the
thickness of the absorber, and is the linear attenuation coefficient of the absorber material. The linear attenuation
coefficient corresponds to the fraction of a radiation beam per unit thickness that a thin absorber will attenuate (absorb
and scatter). This coefficient is dependent on the atomic number of the materials and on the energy of the x-ray beam and
is proportional to the density of the absorber.
If instead of a single homogenous absorber there were a series of absorbers, each of thickness s, the overall transmitted
intensity would be:
I = I
0
exp[(
1
+
2
+
3
. . . +
i
)s]


(Eq 7)
where
i
is the linear attenuation coefficient of the ith absorber.
Considering a two-dimensional section through an object of interest, the linear attenuation coefficients of the material
distribution in this section can be represented by the function, (x, y), where x and y are the Cartesian coordinates
specifying the location of points in the section. Using the integral equivalent to Eq 7, the intensity of radiation transmitted
along a particular path is given by:

(Eq 8)
where ds is the differential of the path length along the ray. The objective of the reconstruction program in a CT system is
to determine the distribution of (x, y) from a series of intensity measurements through the section. Dividing both sides of
Eq 8 by I
0
and taking the natural logarithm of both sides of the equation yields the projection value, p, along the ray:


(Eq 9)
Equation 9, known as the Radon transformation of (x, y), is a fundamental equation of the CT process. It states that
taking the logarithm of the ratio of the unattenuated intensity to the transmitted intensity yields the line integral along the
path of the radiation through the two-dimensional distribution of linear attenuation coefficients. The inversion of Eq 9
was solved in 1917, when Radon demonstrated in principle that (x, y) could be determined analytically from an infinite
set of these line integrals. Similarly, given a sufficient number of projection values (or line integrals) in tomographic
imaging, the cross-sectional distribution, (x, y), can be estimated from a finite set of projection values.
The projection value as determined by Eq 9 is based on several assumptions that are not necessarily true in making
practical measurements. If an x-ray source is used, the x-ray photon energies or spectra range from very low energies up
to energies corresponding to the operating voltage of the x-ray tube. The energy of a beam can be characterized by an
effective or average energy. The effective energy, as well as the associated linear attenuation coefficients of the material,
will vary with the amount of material of filtration through which the beam passes. The increase in effective energy caused
by the preferential absorption of the less penetrating, lower-energy photons when passing through increasing thicknesses
of material is referred to as beam hardening. Beam hardening can cause nonlinearities in the measured projection values
relative to Eq 9 and can cause shading artifacts in the image. With knowledge of the type of material in the object being
imaged, corrections can be made to minimize this effect.
Other variations may also, occur in measuring the transmitted intensity values and determining the projection values.
These include the measurement of scatter radiation, the stability of the x-ray source, or any intensity or time-dependent
nonlinearities of the detector. To the extent that these systemic variations can be characterized or monitored, they can be
corrected in the data processing. Another variance that cannot be eliminated is the statistical noise of the measurement
due to the detection of a finite number of photons.

Direct Fourier Reconstruction Technique
The direct Fourier reconstruction technique utilizes the Fourier transformation of projection data. A Fourier transform is a
mathematical operation that converts the object distribution defined in spatial coordinates into an equivalent sinusoidal
amplitude and phase distribution in spatial frequency coordinates. The one-dimensional Fourier transformation of a set of
projection data at a particular angle, , is described mathematically by:


(Eq 10)
where r is the spatial position along the set of projection data and is the corresponding spatial frequency variable.
Fourier reconstruction techniques (and the filtered-backprojection method) are based on a mathematical relationship
known as the central projection theorem or central slice theorem. This theorem states that the Fourier transform of a one-
dimensional projection through a two-dimensional distribution is mathematically equivalent to the values along a radial
line through the two-dimensional Fourier transform of the original distribution. For example, given one set of projection
data measurements (Eq 9) through an object at a particular angle, taking the one-dimensional Fourier transform (Eq 10) of
this data profile provides data values along one spoke in frequency space (Fig. 28). Repeating this process for a number of
angles defines the two-dimensional Fourier transform of the object distribution in polar coordinates (Fig. 28b). Taking the
inverse two-dimensional Fourier transform of this polar data array yields the object distribution in spatial coordinates.

Fig. 28
Data points in (a) direct space and (b) frequency space. The data points obtained in the orientation
shown in (a) correspond to the data points on one spoke in the two-dimensional Fourier transform space (b).
Although the direct Fourier technique is potentially the fastest method, the technique has not yet achieved the image
quality of the filtered-backprojection method, because of interpolation problems. Typical computer methods and display
systems are based on rectangular grids rather than polar distributions, and several variations of the direct Fourier
reconstruction technique exist for interpolating the data from polar coordinates to a Cartesian grid (usually interpolating
the data in the spatial frequency domain). The interpolation techniques can be complex, and the quality of the images
from measured data have generally been poorer than some of the other reconstruction methods. Interesting results have
been obtained in industrial multiplanar microtomography research, but this method is not typically used in commercial
systems (Ref 51).
Filtered-Backprojection Technique

The filtered-backprojection technique is the most commonly used CT reconstruction algorithm. Before discussing this
method, a brief discussion of filtering and the simple backprojection method is provided.
Convolutions and Filters. A convolution is a mathematical operation in which one function is smeared by another
function. Mathematically it can be defined as:
g(x) = f(x) * h(x)


(Eq 11)


(Eq 12)
for one dimension, or
g(x,y) = f(x,y) * h(x,y)


(Eq 13)


(Eq 14)
for two dimensions where * is the symbol for the convolution operation. If the system is a digital system with a discrete
number of samples, the corresponding equation to Eq 12 is:


(Eq 15)
and two-dimensional equivalent to Eq 13 is:


(Eq 16)
Convolutions are a common physical operation in data acquisition and imaging systems whether or not the term
convolution is used. All imaging systems have limitations in their ability to reproduce an object faithfully. One method of

quantifying the quality of an image is to define its point spread function or blurring function. A measured image is the
convolution of the object function with this blurring function (Fig. 29). This is represented in Eq 13, in which g(x, y) is
the resultant image formed by convoluting the object function f(x, y) with the blurring function h(x, y). If the object
function was an infinitely small target or a point, then f(x, y) is a delta function with a value of zero everywhere but at one
location, and the image g(x, y) will be equal to the PSF, h(x, y). This is how the point spread function is defined and
measured.

Fig. 29 Convolution operation (*) in which a distribution f(x) is blurred by a function h(x
) to form the blurred
distribution g(x). The function h(x
) is analogous to the PSF of an image system or a smoothing convolution
filter in image processing.
Convolutions can also be used in image processing to smooth (Fig. 29) or sharpen (Fig. 30) an image. Smoothing
convolution filters are typically square (averaging) or bell shaped, while sharpening convolution filters often have a
positive value in the center, with adjacent values being negative.

Fig. 30 Convolution operation with the sharpening filter h'(x). This sharpening of g(x) [or a restoration of f(x
)
with the "inverse" of h(x
)] is analogous to image process filtering or to the filtering of the projection data in the
filtered-backprojection reconstruction technique.
Reference has already been made to Fourier transforms, as in Eq 10, and to their ability to transform spatial data into
corresponding spatial frequency data. Filtering operations, such as image smoothing or sharpening, can be readily
performed on the data in the spatial frequency domain. According to the convolution theorem, convolution operations in
the spatial domain correspond to simple function multiplications in the spatial frequency domain (Fig. 31), that is:
g(x) = f(x) * h(x)


(Eq 17)
is equivalent to

G( ) = F( ) H( )


(Eq 18)
where G( ), F( ), and H( ) are the Fourier transformed functions of g(x), f(x), and h(x), where is the spatial frequency
conjugate of x. The functional multiplication in Eq 18 is simply the multiplication of the values of F( ) and H( ) at every
value of . The two-dimensional convolution of Eq 13 has its counterpart to Eq 18 where the functions G, F, and H are
the two-dimensional Fourier transforms of g(x, y), f(x, y), and h(x, y). Note that the spatial frequency variable, , has units
of 1/distance.

Fig. 31
The process of filtering according to the convolution theorem. Filtering operations can be performed as
a convolution (*) of the spatial functions, (top) or as a multiplication (×) of
the Fourier transform of these
functions (bottom). Either technique can be used in the filtered-backprojection reconstruction process.
Because the blurring or convolution process is represented in the spatial frequency domain as a simple functional
multiplication, the blurred image conceptually can be easily restored to a closer representation of the original object
distribution. If the Fourier transform of the image, G( ), is filtered by multiplying by the function H'( ) where H'( ) =
1/H( ), the result is the original object frequency distribution, F( ). In practice, this restoration is limited by the
frequency limit of H( ) leading to division by zero, and by the excessive enhancement of noise along with the signal at
frequencies with small H( ) values. This restoration process or "deconvolution" of the blurring function can likewise be
performed as a convolution in the spatial domain as illustrated in Fig. 30.
Backprojection is the mathematical operation of mapping the one-dimensional projection data back into a two-
dimensional grid. This is done intuitively by radiographers in interpreting x-ray films. If a high-density inclusion or
structure is visible in two or more x-ray films taken at different angles, the radiographer can mentally backproject along
the corresponding ray paths to determine the intersection of the rays and the location of the structure in space.
Mathematically, this is done by taking each point on the two-dimensional image grid and summing the corresponding
projection value from each angle from which projection data were acquired. This backprojection process yields a
maximum density at the location of the structure where the lines from the rays passing through this structure cross (Fig.
3a). The resultant image is not an accurate representation of the structure, however, in that these lines form a star artifact

(Fig. 3a) extending in all directions from the location of the high-density structure. For a very large number of projection
angles, the density of this structure is smeared over the entire image and decreases in amplitude with 1/r, where r is the
distance from the structure. This simple backprojected image, f
b
, can be represented by the convolution of the true image,
f, with the blurring function, 1/r, or:
f
b
(r, ) = f(r, ) * (1/r)


(Eq 19)
With ideal data, this blurring function can be removed by a two-dimensional deconvolution or filtering of the blurred
image. The appropriate filtering function can be determined by using the convolution theorem to transform Eq 19 into its
frequency domain equivalent of:
F
b
( , ) = F( , ) (1/ )


(Eq 20)
where the function (1/ ) is the Fourier transform of 1/r in polar coordinates. Dividing both sides by (1/ ) yields:
F( , ) = F
b
( , )


(Eq 21)
Therefore, the corrected image, f, can be obtained by determining a simple backprojection, f
b

, taking its Fourier
transform, filtering, and then taking the inverse Fourier transform to get back into spatial coordinates. Alternatively, the
filter function, , can be transformed into spatial coordinates, and the backprojected image can be corrected by a two-
dimensional convolution operation. Equations 19, 20, and 21 become somewhat more complex when evaluated in
rectangular coordinates rather than as represented in polar coordinates.
This approach tends to produce poor results with actual data. Filtering out this blurring function from the projection data
prior to backprojection, however, is quite effective and is the basis for the most commonly used reconstruction method,
the filtered-backprojection reconstruction technique.
Filtered-Backprojection Reconstruction. According to the central slice theorem discussed in the section "Direct
Fourier Reconstruction Technique" in this Appendix, the Fourier transform of the one-dimensional projection data
through a two-dimensional distribution is equivalent to the radial values of the two-dimensional Fourier transform of the
distribution. Consequently, the filtering operation performed in Eq 21 can be performed on the projection data prior to
backprojection. This is the conceptual basis for the filtered-backprojection reconstruction technique (Ref 52, 53), and it is
illustrated schematically in Fig. 3(b).
As with other filtering operations, this correction can be implemented as a convolution in the spatial domain or as a
functional multiplication in frequency domain. Fourier filtered backprojection is performed by taking the measured
projection data, Fourier transforming it into the frequency domain, multiplying by the ramp-shaped filter (which
enhances the high spatial frequencies relative to the low frequencies), taking the inverse Fourier transform of this
corrected frequency data, and then backprojecting the filtered projection data onto the two-dimensional grid.
If the filtering is performed in the spatial domain by convoluting the measured projection data with a spatial filter
equivalent to the inverse Fourier transform of , the process is often referred to as the convolution-backprojection
reconstruction method. The frequency filter has the shape of a ramp, enhancing the high frequency (or sharp detail
information) of the projection data. Therefore, the convolution function, or kernel, has the expected shape for a
sharpening filter. The positive central value is surrounded by negative values that diminish in magnitude with distance
from the center. Because of the similar results obtained by Fourier filtering and convolution filtering and the uncertainty
with which the filtering approach is often implemented on specific systems, the terms filtered-backprojection
reconstruction and convolution-backprojection reconstruction are sometimes used interchangeably.
The filtered-backprojection reconstruction technique is the method that is commonly used in both medical and industrial
tomography systems. The method is more tolerant of measured data imperfections than some of the other techniques.
Filtered-backprojection reconstruction provides relatively fast reconstruction times and permits the processing of data

after each view is acquired. With appropriate computational hardware, the displayed image can be available almost
immediately after all the data have been acquired.
Variations in the filter functions used result from the physical limitations encountered with actual data (particularly its
finite quantity) and the boundary assumptions made in the calculations. Additional windowing filters are sometimes
combined with the theoretically derived filter to smooth or sharpen the image with no additional processing time.
Another variation used in special situations consists of combinations of the reconstruction techniques, such as performing
a filtered-backprojection reconstruction followed by iterative processing. This may be beneficial in cases where the data
set is limited and additional known information on the object's shape and content can be applied through the iterative
steps to provide an improved image.
Iterative Reconstruction Techniques
Another broad category of methods is the iterative reconstruction algorithms. With this approach, an initial guess is made
of the density distribution of the object. This initial guess may result from knowledge of the nominal design of the object
or may assume a homogenous cylinder of some density. The computer then calculates the projection data values that
would be measured for this assumed object. Each calculated value is compared to the corresponding measured projection
data value, and the difference between these values is used to adjust the assumed density values along this ray path. This
correction to the assumed distribution is applied successively for each measured ray. An iteration is completed when the
image has been corrected along all measured rays, and the process begins again with the first ray. With each iteration, the
approximated distribution (or reconstructed image) improves its correspondence to the object distribution.
There are numerous variations of iterative processing that may be additive or multiplicative, weighted or unweighted,
restricted or unrestricted, and may specify the order in which the projection data are processed. Some of the more
common techniques are the iterative least squares technique, the simultaneous iterative reconstruction technique, and the
algebraic reconstruction technique (Ref 54, 55, 56).
Iterative reconstruction techniques are rarely used. They require all data to be collected before even the first iteration can
be completed, and they are very process intensive. Iterative techniques may be beneficial for selected situations where the
data set is limited or distorted. Iterative techniques can be effective with incomplete sets of projection data or with
irregular data collection configurations. Known information about the object, such as the design, material densities, or
external contours, can be used, along with optimization criteria, to aid in determining the solution. This can allow the
reconstruction process to be less sensitive to missing or inaccurate projection data. In addition, reconstruction-dependent
corrections can be incorporated into these techniques, such as spectral correction for multiple materials or attenuation
corrections in emission computed tomography (SPECT) of radionuclide distributions.

References cited in this section
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R. Brooks and G. DiChiro, Principles of Computer Assisted Tomography (CAT) in Radiographic and
Radioisotopic Imaging, Phys. Med. Biol., Vol 21, 1976, p 689-732
49.

G.T. Herman, Image Reconstruction From Projections: Implementation and Applications, Springer-
Verlag,
1979
50.

G.T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography,

Academic Press, 1980
51.

B.P. Flannery, H.W. Deckman, W.G. Roberge, and K.L. D'Amico, Three-Dimensional X-
Ray
Microtomography, Science, Vol 237, 18 Sept 1987, p 1439-1444
52.

G.N. Ramachandran and A.V. Laksh-minarayanan, Three-
Dimensional Reconstruction From Radiographs
and Electron Micrographs: III. Description and Application of the Convolution Method,
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294
Industrial Computed Tomography
Michael J. Dennis, General Electric Company, NDE Systems and Services

Appendix 2: Computed Tomography Glossary
• Afterglow
• A detrimental property of a scintillator in which the emission of light continues for a period of time after
the exciting radiation has been discontinued.
• Algorithm
• A procedure for solving a mathematical problem by a series of operations. In computed tomography, the
mathematical process used to convert the transmission measurements into a cross-sectional image. Also
known as reconstruction algorithm.
• Aliasing
• An artifact in discretely measured data caused by insufficient sampling of high-frequency data, with this
high-frequency information falsely recorded at a lower frequency. See Nyquist sampling frequency.

• Aperture, collimator
• The opening of the collimator enabling variations in the shape of the measured x-ray beam.
• Archival storage
• Long-term storage of information. In computed tomography, this can be accomplished by storing the
information on digital magnetic tape, on optical disk, or as images on x-ray film.
• Array, data
• An ordered set or matrix of numbers.
• Array, detector
• An ordered arrangement of individual detector elements that operates as a unit, such as a linear detector
array.
• Array processor
• A special-purpose computer processor used to perform special functions at high speeds.
• Artifact
• An error or false structure in an image that has no counterpart in the original object.
• Attenuation of x-rays
• Absorption and scattering of x-rays as they pass through an object.
• Backprojection
• The process of mapping one-dimensional projection data back into a two-dimensional image array. A
process used in certain CT reconstruction algorithms.
• Beam hardening
• The increase in effective energy of a polyenergetic (for example, x-ray) beam with increasing attenuation
of the beam. Beam hardening is due to the preferential attenuation of the lower-energy, or soft, radiation.
• Capping
• Artifact characterized by dark shading or lowering of pixel values toward edges; opposite of cupping.
Sometimes caused by an overcompensating beam hardening correction to the data.
• CAT
• See computed tomography.
• Collimator
• The x-ray system component that confines the x-ray beam to the required shape. An additional collimator
can be located in front of the x-ray detector to further define the portion of the x-ray beam to be

measured.
• Computed tomography (CT)
• The collection of transmission data through an object and the subsequent reconstruction of an image
corresponding to a cross section through this object. Also known as computerized axial tomography,
computer-assisted tomography, or CAT scanning.
• Contrast-detail-dose diagram
• A plot of the minimum percent contrast needed to resolve a feature versus the feature size. The ability to
visualize low-contrast structures tends to be limited by image noise, while small high-contrast structures
are resolution limited.
• Contrast scale
• The change of CT number that occurs per given change in linear attenuation coefficient. Contrast scale is
dependent on the x-ray beam energy and the scaling parameters in the reconstruction process.
• Contrast sensitivity
• The ability to differentiate material density (or linear attenuation coefficient) differences with respect to
the surrounding material.
• Convolution
• A mathematical process used in certain reconstruction algorithms. An operation between two functions in
which one function is blurred or smeared by another function.
• Coronal plane
• A medical term for a plane that divides the body into a front and back section. A y-z planar presentation,
which may be mathematically constructed from a series of cross-sectional slices. See sagittal plane and
reformation, planar.
• Crosstalk, detector
• The unwanted pickup of the signal associated with neighboring detector elements. Crosstalk may be
caused by radiation scatter or electronic interference.
• CT numbers
• The numbers used to designate the x-ray attenuation in each picture element of the CT image.
• Cupping
• Artifact characterized by dark shading in the center of the field of view. May be caused by beam
hardening.

• Data acquisition system (DAS)
• The components of a CT system used to collect and digitize the detected x-ray signal.
• Density resolution
• The measure of the smallest density difference of an image structure that can be distinguished.
• Detectability, low contrast
• The minimum detectable object size for a specified percent contrast between the object and its
surroundings as measured with a test phantom.
• Detective quantum efficiency (DQE)
• The fraction of the beam intensity needed to produce the same signal-to-noise ratio as a particular
detector if it were replaced with an ideal detector. Also known as the quantum detection efficiency.
• Detector aperture
• The physical dimensions of the active area of the detector, including any restriction by the detector
collimation. Used in particular for the detector dimension in the plane of the CT scan.
• Detector, x-ray
• Sensor array used to measure the x-ray intensity. Typical detectors are high-pressure gas ionization,
scintillator-photodiode detector arrays, and scintillator-photomultiplier tubes.
• Digital radiography (DR)
• Radiographic imaging technology in which a two-dimensional set of x-ray transmission measurements is
acquired and converted to an array of numbers for display with a computer. Computed tomography
systems normally have DR imaging capabilities. Also known as digital radioscopy.
• Display resolution
• Number of picture elements (pixels) per unit distance in the object.
• Dual energy imaging
• The process of taking two identical scans (DR or CT) at two different x-ray energies and processing the
data to produce alternate images that may be insensitive to beam hardening artifacts or may be
particularly sensitive to physical density, or the effective atomic number of the materials contained in the
object.
• Dynamic range
• The range of operation of a device between its upper and lower limit. This range can be given as a ratio
(example 100:1) of the upper to lower limits, the number of measurable steps between the upper and

lower limits, the number of bits (needed to record this number of measurable steps), or the minimum and
maximum measurable values.
• Edge enhancement
• A mathematical manipulation in which rapid density changes are enhanced or sharpened by means of
differentiation or high-pass filters. This operation will also increase image noise.
• Effective atomic number
• For an element, the number of protons in the nucleus of an atom. For mixtures, an effective atomic
number can be calculated to represent a single element that would have attenuation properties identical to
those of the mixture.
• Effective x-ray energy
• The monoenergetic beam energy that is attenuated to the same extent by a thin absorber as is the given
polyenergetic x-ray beam.
• Field-of-view (FOV)
• The maximum diameter of an object that can be imaged. Also known as scan FOV. The object dimension
corresponding to the full width of a displayed image (display FOV).
• Focal spot
• The area of the x-ray tube from which the x-rays originate. The effective focal-spot size is the apparent
size of this area when viewed from the detector.
• Fourier transformation
• A mathematical process for changing the description of a function by giving its value in terms of its
sinusoidal spatial (or temporal) frequency components instead of its spatial coordinates (or vice versa).
• Full width at half maximum (FWHM)
• A parameter that can be used to describe a distribution such as the point spread function.
• Geometries, CT
• The geometrical configuration and mechanical motion to acquire the x-ray transmission data. Typically,
parallel beam data are acquired from translate-rotate data acquisition, and fan beam data are obtained
from rotate-only movement of the object (or of the source and detector about the object).
• Histogram
• A plot of frequency of occurrence versus the measured parameter. In a CT image, the plot of the number
of pixels with a particular CT number value versus CT number.

• Histogram equalization
• An image display process in which an equal number of image pixels is displayed with each displayable
gray shade or color.
• Hysteresis
• Dependence of a measured signal on the previous measurement history.
• Intensity
• The energy per unit area per unit time incident on a surface.
• Ionization
• The process in which neutral atoms become charged by gaining or losing an electron.
• Iterative reconstruction
• A method of reconstruction that produces an improving series of estimated images that is repeated until a
suitable quality level is obtained.
• Kernel
• A function that is convoluted with a data function. The kernel in the convolution-backprojection
reconstruction algorithm can be modified to enhance sharpness or reduce noise. Also known as
convolution kernel.
• Kiloelectron volt (keV)
• A unit of energy usually associated with individual particles. The energy gained by an electron when
accelerated across 1000 V.
• Linear attenuation coefficient
• The fraction of an x-ray beam per unit thickness that a thin object will absorb or scatter (attenuate). A
property proportional to the physical density and dependent on the atomic number of the material and the
energy of the x-ray beam.
• Linearity, detector
• A measure of the consistency in detector sensitivity versus the radiation intensity level.
• Matrix
• An array of numbers arranged in two dimensions (rows and columns).
• Megaelectron volt (MeV)
• A unit of energy usually associated with a particle. The energy gained by an electron accelerated across
1,000,000 V.

• Modulation transfer function (MTF)
• A measure of the spatial resolution of an imaging system that involves the plot of image contrast (system
response) versus the spatial frequency (line pairs per millimeter) of the contrast variations on the object
being imaged. A plot of these two variables gives a curve representing the frequency response of a
system. The MTF can also be determined from the Fourier transform of the point spread function.
• Noise
• Salt-and-pepper appearance of an image caused by variations in the measured data. Image noise can be
affected by choice of reconstruction algorithm and by image processing, such as sharpening and
smoothing operations.
• Noise, quantum (or photon)
• Noise due to statistical variations in the number of x-ray photons detected. An increase in the number of
photons measured decreases the relative quantum noise.
• Noise, structural
• Unwanted detail of an object from overlying structures or due to granularity or material structure.
• Noise, structured
• Nonrandom noise, such as due to reconstruction algorithm filtering or systemic errors in the
measurements.
• Nyquist sampling frequency
• The ability to characterize a signal from a series of discrete samples requires that the signal be sampled at
a minimum of twice the frequency of the highest frequency contained in the signal. The undersampling of
a signal causes the high-frequency signals to mimic or appear as lower-frequency signals, an effect
termed aliasing.
• Partial volume artifact
• Streaking or shadowing artifacts caused by high-density structures partially intercepting the finite-sized
measured x-ray beam. The effect is due to the summation of multiple ray paths in an inhomogenous
mixture.
• Partial volume effect
• The effect of measuring a density lower than the true structure density due to the fact that only a part of
the structure is within the measured voxel, that is, within the full slice width or resolution element.
• Phantom

• A test object used to measure the response of the CT system. Phantoms can be used to calibrate the
system or to measure performance parameters.
• Photodiode
• A semiconductor device that permits current flow proportional to the intensity of light striking the diode
junction.
• Photomultiplier tube (PMT)
• A light-sensitive vacuum tube with multiple electrodes providing a highly amplified electrical output.
• Photon
• A quantum, or particle, of electromagnetic radiation (such as light or x-rays).
• Pixel
• Shortened term for picture element. A pixel is the smallest displayable element of an image; a single
value of the image matrix. A pixel corresponds to the measurement of a volume element (voxel) in the
object.
• Point spread function (PSF)
• The image response of a system to a very small, high-amplitude object; the image blurring function.
• Polychromatic
• Photons with a mixture of colors, or energies. Same as polyenergetic.
• Polychromatic artifacts
• Image distortion such as image shading or low-density bands between high-density structures caused by
the polychromatic x-ray beam. When an x-ray beam travels a longer path or through a high-absorption
region, the low-energy components of the polychromatic beam are preferentially absorbed, resulting in a
higher effective beam energy and creating artifacts in the image.
• Polychromatic x-ray spectra
• An x-ray beam that consists of a range of x-ray energies. The maximum amplitude and effective energy
of an x-ray beam are always less than the corresponding voltage applied to the tube. The maximum
energy of an x-ray beam corresponds to the peak x-ray tube voltage.
• Projection
• A set of contiguous measured line integrals (projection data points) through an object. May be parallel ray
or divergent (fan) ray projection data set. Also called a view.
• Projection data

• The logarithm of the normalized transmitted intensity data. The line integral of the linear attenuation
coefficient through an object.
• Quantum detection efficiency
• See detective quantum efficiency.
• Radionuclide
• A specific radioactive material.
• Reconstruction
• The process by which raw digitized detector measurements are transformed into a cross-sectional CT
image.
• Reformation, planar
• A displayed image comparable to a measured CT image, but along a planar section that cuts across a
series of measured CT slices. The computer selects the data corresponding to the selected plane from a
stack of CT slices through a volume of the object.
• Reformation, 3-D surface
• A perspective display of a structure; an image that appears as a photograph of the structure.
• Resolution, high contrast
• A measure of the ability of an imaging system to present multiple high-contrast structures and fine detail;
measurements made with line pair gage or bar resolution phantom. See spatial resolution.
• Resolution, low contrast
• The minimum detectable spacing between specified objects for a specified percent contrast between the
objects and their background as measured with a test phantom.
• Sagittal plane
• A medical term for a plane that divides the body into left and right sides. A y-z planar presentation, which
can be mathematically constructed from a series of cross-sectional slices. See coronal plane and
reformation, planar.
• Scan
• The operation of acquiring the data for a CT or DR image. Sometimes used in reference to the CT or DR
image.
• Scattering of x-rays
• One of the two ways in which the x-ray beam interacts with matter and the transmitted intensity is

diminished in passing through object. The x-rays are scattered in a direction different from the original
beam direction. Such scattered x-rays falling on the detector do not add to the radiological image.
Because they reduce the contrast in that image, steps are usually taken to eliminate the scattered
radiation. Also known as Compton scatter.
• Scintillator
• A material that produces a rapid flash of visible light when an x-ray photon is absorbed. The scintillator is
coupled with a light-sensitive detector to measure the x-ray beam intensity.
• Sharpening
• Image-processing technique that enhances edge contrast and increases image noise. The opposite of
smoothing.
• Slice
• The cross-sectional plane through an object that is scanned to produce the CT image. See also
tomographic plane.
• Slice thickness
• The height or z-axis dimension of the measured x-ray beam normally measured at the center of the object.
The slice thickness along with the image resolution defines the size of the measured volume
corresponding to a pixel CT value.
• Slit-scan radiography
• Method of producing an x-ray image in which a thin x-ray beam produces the image one line at a time. A
method used to reduce measured scatter radiation. The DR mode of most CT systems uses a slit-scan
technique with a linear detector array.
• Smoothing
• Image-processing technique that averages the image data, reducing edge sharpness and decreasing image
noise. Opposite of sharpening.
• Spatial resolution
• A measure of the ability of an imaging system to represent fine detail; the measure of the smallest
separation between individually distinguishable structures. See resolution, high contrast, point spread
function, and modulation transfer function.
• Spectrum, x-ray
• The plot of the intensity or number of x-ray photons versus energy (or wavelength).

• Test phantom
• See phantom.
• Tomographic plane
• A section of the part imaged by the tomographic process. Although in CT the tomographic plane or slice
is displayed as a two-dimensional image, the measurements are of the materials within a defined slice
thickness associated with the plane.
• Tomography
• From the Greek "to write a slice or section." The process of imaging a particular plane or slice through an
object.
• View
• A set of measured parallel or fan beam data for a particular angle through the center of the object. Also
known as a profile or projection.
• Voxel
• Shortened term for volume element. The volume within the object that corresponds to a single pixel
element in the image. The box-shaped volume defined by the area of the pixel and the height of the slice
thickness.
• Window, display
• The range of CT values in the image that are displayed. The display window can normally be adjusted
interactively by the operator to view different density ranges in the reconstructed image data.
Industrial Computed Tomography
Michael J. Dennis, General Electric Company, NDE Systems and Services
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Neutron Radiography
Harold Berger, Industrial Quality, Inc.

Introduction
NEUTRON RADIOGRAPHY is a form of nondestructive inspection that uses a specific type of particulate radiation,
called neutrons, to form a radiographic image of a testpiece. The geometric principles of shadow formation, the variation
of attenuation with testpiece thickness, and many other factors that govern the exposure and processing of a neutron
radiograph are similar to those for radiography using x-rays or -rays. These topics are extensively covered in the article
"Radiographic Inspection" in this Volume and will not be discussed here.
This article will deal mainly with the characteristics that differentiate neutron radiography from x-ray or -ray
radiography, as discussed in Ref 1, 2, 3, 4, 5, 6, 7, 8, 9. Neutron radiography will be described in terms of its advantages
for improved contrast on low atomic number materials, the discrimination between isotopes, or the inspection of
radioactive specimens.

References
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H. Berger, Some Recent Developments in X-Ray and Neutron Imaging Methods, in Nondestructive Testing,

Vol 1, J.M. Farley and R.W. Nichols, Ed., Pergamon Press, 1988, p 155-162
Neutron Radiography
Harold Berger, Industrial Quality, Inc.

Principles of Neutron Radiography
Neutron radiography is similar to conventional radiography in that both techniques employ radiation beam intensity
modulation by an object to image macroscopic object details. X-rays or -rays are replaced by neutrons as the
penetrating radiation in a through-transmission inspection. The absorption characteristics of matter for x-rays and
neutrons differ drastically; the two techniques in general serve to complement one another.
Neutrons are subatomic particles that are characterized by relatively large mass and a neutral electric charge. The
attenuation of neutrons differs from the attenuation of x-rays in that the processes of attenuation are nuclear rather than
ones that depend on interaction with the electron shells surrounding the nucleus.
Neutrons are produced by nuclear reactors, accelerators, and certain radioactive isotopes, all of which emit neutrons of
relatively high energy (fast neutrons). Because most neutron radiography is performed with neutrons of lower energy
(thermal neutrons), the sources are usually surrounded by a moderator, which is a material that reduces the kinetic energy
of the neutrons.
Neutron Versus Conventional Radiography. Neutron radiography is not accomplished by direct imaging on film,
because neutrons do not expose x-ray emulsions efficiently. In one form of neutron radiography, the beam of neutrons
impinges on a conversion screen or detector made of a material such as dysprosium or indium, which absorbs the
neutrons and becomes radioactive, decaying with a short half-life. In this method, the conversion screen alone is exposed
in the neutron beam, then immediately placed in contact with film to expose it by autoradiography. In another common
form of imaging, a conversion screen that immediately emits secondary radiation is used with film directly in the neutron
beam.
Neutron radiography differs from conventional radiography in that the attenuation of neutrons as they pass through the
testpiece is more related to the specific isotope present than to density or atomic number. X-rays are attenuated more by
elements of high atomic number than by elements of low atomic number, and this effect varies relatively smoothly with

atomic number. Thus, x-rays are generally attenuated more by materials of high density than by materials of low density.
For thermal neutrons, attenuation generally tends to decrease with increasing atomic number, although the trend is not a
smooth relationship. In addition, certain light elements (hydrogen, lithium, and boron), certain medium-to-heavy elements
(especially cadmium, samarium, europium, gadolinium, and dysprosium), and certain specific isotopes have an
exceptionally high capability of attenuating thermal neutrons (Fig. 1). This means that neutron radiography can detect
these highly attenuating elements or isotopes when they are present in a structure of lower attenuation.

Fig. 1 Mass attenuation coefficients for the elements as a function of atomic number for thermal (4.0 × 10
-21
J,
or 0.025 eV) neutrons and x-rays (energy
125 kV). The mass attenuation coefficient is the ratio of the linear
attenuation coefficient, , to the density, , of the absorbing material. Source: Ref 6
Thermal (slow) neutrons permit the radiographic visualization of low atomic number elements even when they are present
in assemblies with high atomic number elements such as iron, lead, or uranium. Although the presence of the heavy
metals would make detection of the light elements virtually impossible with x-rays, the attenuation characteristics of the
elements for slow neutrons are different, which makes detection of light elements feasible. Practical applications of
neutron radiography include the inspection of metal-jacketed explosives, rubber O-ring assemblies, investment cast
turbine blades to detect residual ceramic core, and the detection of corrosion in metallic assemblies.
Using neutrons, it is possible to detect radiographically certain isotopes for example, certain isotopes of hydrogen,
cadmium, or uranium. Some neutron image detection methods are insensitive to background -rays or x-rays and can be
used to inspect radioactive materials such as reactor fuel elements. In the nuclear field, these capabilities have been used
to image highly radioactive materials and to show radiographic differences between different isotopes in reactor fuel and
control materials. The characteristics of neutron radiography complement those of conventional radiography; one
radiation provides a capability lacking or difficult for the other.

Reference cited in this section
6.

L.E. Bryant and P. McIntire, Ed., Radiography and Radiation Testing, in Nondestructive Testing Handbook,

Vol 3, American Society for Nondestructive Testing, 1985
Neutron Radiography
Harold Berger, Industrial Quality, Inc.

Neutron Sources
The excellent discrimination capabilities of neutrons generally refer to neutrons of low energy, that is, thermal neutrons.
The characteristics of neutron radiography corresponding to various ranges of neutron energy are summarized in Table 1.
Although any of these energy ranges can be used for radiography, this article emphasizes the thermal-neutron range,
which is the most widely used for inspection.
Table 1 Characteristics of neutron radiography at various neutron-energy ranges
Type of
neutrons
Energy range, J
(eV)
Characteristics
Cold <1.6 × 10
-21

(<0.01)
High-absorption cross sections decrease transparency of most materials, but also increase
efficiency of detection. An advantage is reduced scatter at energies below the Bragg cutoff,
where neutrons can no longer undergo Bragg reflection.
Thermal 1.6 × 10
-21
to 8.0
× 10
-20
(0.01 to
0.5)

Good discrimination between materials, and ready availability of sources
Epithermal 8.0 × 10
-20
to 1.6
× 10
-15
(0.5 to
10
4
)
Excellent discrimination for particular materials by working at energy of resonance. Greater
transmission and less scatter in samples containing materials such as hydrogen and enriched
reactor fuels
Fast 1.6 × 10
-15
to 3.2
× 10
-12
(10
4
to
2.0 × 10
7
)
Good point sources are available. At low-energy end of spectrum, fast-neutron radiography
may be able to perform many inspections done with thermal neutrons, but with a panoramic
technique. Good penetration capability because of low-absorption cross sections in all materials.
Poor material discrimination

In thermal-neutron radiography, an object (testpiece) is placed in a thermal-neutron beam in front of an image detector.

The neutron beam may be obtained from a nuclear reactor, a radioactive source, or an accelerator. Several characteristics
of these sources are summarized in Table 2. For thermal-neutron radiography, fast neutrons emitted by these sources must
first be moderated and then collimated (Fig. 2). The radiographic intensities listed in Table 2 typically do not exceed 10
-5

times the total fast-neutron yield of the source. Part of this loss is incurred in moderating the neutrons, and the remainder
in bringing a collimated beam out of a large-volume moderator.
Table 2 Properties and characteristics of thermal-neutron sources
Type of source Typical
radiographic
intensity,
n/cm
2
·s
Spatial
resolution
Exposure
time
Characteristics
Radioisotope 10
1
to 10
4
Poor to medium Long
Stable operation, low-to-medium investment cost,
possibly movable
Accelerator 10
3
to 10
6

Medium Average
On-off operation, medium cost, possibly movable
Subcritical
assembly
10
4
to 10
6
Good Average
Stable operation, medium-to-high investment cost,
movement difficult
Nuclear reactor 10
5
to 10
8
Excellent Short Medium-to-high investment cost, movement difficult


Fig. 2
Thermalization and collimation of beam in neutron radiography. Neutron collimators can be of the
parallel-
wall (a) or divergent (b) type. The transformation of fast neutrons to slow neutrons is achieved by
moderator materials such as paraffin,
water, graphite, heavy water, or beryllium. Boron is a typically used
neutron-absorbing layer. The L/D ratio, where L
is the total length from the inlet aperture to the detector
(conversion screen) and D is the effective dimension of the inlet of the coll
imator, is a significant geometric
factor that determines the angular divergence of the beam and the neutron intensity at the inspection plane.