Nondestructive Evaluation and Quality Control (1998) Part 9 pot

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 dens

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 radiography 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 engine turbine blade (nickel alloy precision casting) from an industrial

region-of-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-point 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:

where I is the intensity of the beam transmitted through the absorber, I0 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 = I0 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 I0 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:

(Eq 12)

for one dimension, or

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:

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 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

two-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, fb, can be represented by the convolution of the true image,

f, with the blurring function, 1/r, or:

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:

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

48 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, Indian J Pure Appl Phys., Vol 9, 1971, p 997

53 L.A Shepp and B.F Logan, The Fourier Reconstruction of a Head Section, Trans IEEE, Vol NS-21, 1974,

p 21-43

54 R Gordon, R Bender, and G.T Herman, Algebraic Reconstruction Techniques (ART) for

Three-Dimensional Electron Microscopy and X-Ray Photography, J Theor Biol., Vol 29, 1970, p 471-481

55 P Gilbert, Iterative Methods for the Three-Dimensional Reconstruction of an Object From Projections, J Theor Biol., Vol 36, 1972, p 105-117

56 G.T Herman and A Lent, Iterative Reconstruction Algorithms, Comput Biol Med., Vol 6, 1976, p

273-294

Industrial Computed Tomography

Michael J Dennis, General Electric Company, NDE Systems and Services

Appendix 2: Computed Tomography Glossary

• 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

• 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

• 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

• 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

• 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)

• 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

• 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

• 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

• Point spread function (PSF)

• The image response of a system to a very small, high-amplitude object; the image blurring function

• 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

• 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

• 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

• 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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23 D.H Maylotte, P.G Kosky, C.L Spiro, and E.J Lamby, "Computed Tomography of Coals," U.S DOE Contract DE-AC21-82MC19210, 1983

24 A.R Lowrey, K.D Friddell, and D.W Cruikshank, "Nondestructive Evaluation of Aerospace Composites Using Medical Computed Tomography (CT) Scanners," Paper presented at the ASNT Spring Conference, Washington, D.C., American Society for Nondestructive Testing, March 1985

25 R.G Buckley and K.J Michaels, "Computed Tomography: A Powerful Tool in Solid Motor Exit Cone Evaluation," Paper presented at the ASNT Spring Conference, Washington, D.C., American Society for Nondestructive Testing, March 1985

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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

1 H Berger, Ed., Practical Applications of Neutron Radiography and Gaging, STP 586, American Society for

Testing and Materials, 1976

2 Neutron Radiography Issue, At Energy Rev., Vol 15 (No 2), 1977, p 123-364

3 N.D Tyufyakov and A.S Shtan, Principles of Neutron Radiography, Amerind Publishing, 1979 (translated

from the Russian)

4 P Von der Hardt and H Rottger, Ed., Neutron Radiography Handbook, D Reidel Publishing, 1981

5 J.P Barton and P Von der Hardt, Ed., Neutron Radiography, D Reidel Publishing, 1983

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

Vol 3, American Society for Nondestructive Testing, 1985

7 "Standard Practices for Thermal Neutron Radiography of Materials," E 748, Annual Book of ASTM Standards, American Society for Testing and Materials

8 J.P Barton, G Farny, J.L Person, and H Rottger, Ed., Neutron Radiography, D Reidel Publishing, 1987

9 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

Table 1 Characteristics of neutron radiography at various neutron-energy ranges

Type of

neutrons

Energy range, J (eV)

Thermal 1.6 × 10-21 to 8.0

× 10-20 (0.01 to 0.5)

Good discrimination between materials, and ready availability of sources

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 10-5times 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

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 collimator, is a significant geometric

factor that determines the angular divergence of the beam and the neutron intensity at the inspection plane

Collimation is necessary for thermal-neutron radiography because there are no useful point sources of low-energy neutrons Good collimation in thermal-neutron radiography is comparable to small focal-spot size in conventional radiography; the images of thick objects will be sharper with good collimation On the other hand, it should be noted that available neutron intensity decreases with increasing collimation

Nuclear Reactors. Many types of reactors have been used for thermal-neutron radiography The high neutron flux generally available provides high-quality radiographs and short exposure times Although truck-mounted reactors are technically feasible, a reactor normally must be considered a fixed-site installation, and testpieces must be taken to the reactor for inspection Investment costs are generally high, but small medium-cost reactors can provide good results When costs are compared on the basis of available neutron flux (typically, 1012 n/cm2 · s flux is often available at collimator entrance, and 106 to 107 n/cm2 · s flux is available at the film plane), reactor sources can be less costly than other sources

Accelerators. The accelerators most often used for thermal-neutron radiography are:

• The low-voltage type employing the reaction + + , a (d,T) generator, where n, d, and

T represent the neutron, deuteron (the nucleus of a deuterium atom, D or , that consists of one neutron and one proton), and tritium ( ), respectively

• High-energy x-ray machines, in which (x,n) reactions are used, where x represents x-ray radiation

• Van de Graaff accelerators

• More recently, high-energy linear accelerators and cyclotrons to generate neutrons by charged-particle reactions on beryllium or lithium targets

Low-Voltage Accelerators. A (d,T) generator provides fast-neutron yields in the range of 1010 to 1012 n/s Target lives in sealed neutron tubes are reasonable (100 to 1000 h, depending on yield), and the sealed-tube system presents a source similar to that of certain types of x-ray machines

High-Energy X-Ray Machines. An (x,n) neutron source is a high-energy x-ray source such as a linear accelerator that can be converted for the production of neutrons by adding a suitable secondary target for example, beryllium X-rays having energies above an energy threshold level cause the secondary target to emit neutrons; in beryllium, the threshold x-ray energy for neutron production is 2.67 × 10-13 J (1.66 MeV) Useful neutron radiography has been performed with an 8.8 × 10-13 J (5.5 MeV) linear accelerator having an x-ray output of 0.17 C/kg · min (650 R/min) at 1 m (3 ft) Changeover time from neutron emission to x-ray emission for this source was only 1 h Beam intensities for neutron radiography with this source were about 5 × 104 n/cm2 · s with reasonable beam collimation

Van de Graaff Accelerators. Much higher beam intensities have been obtained by the acceleration of deuterons onto

a beryllium target in a 3.2 × 10-13 J (2.0 MeV) Van de Graaff generator An intensity of 1.2 × 106 n/cm2 · s was achieved (with medium collimation), and it is estimated that an acceleration voltage of 4.8 × 10-13 J (3.0 MeV) would improve beam intensity by a factor of approximately six

The principle of the Van de Graaff machine is illustrated in Fig 3 A rotating belt transports the charge from a supply to a high-voltage terminal An ion source within the terminal is fed deuterium gas from a reservoir frequently located within the terminal A radio-frequency system ionizes the gas, and positive ions are extracted into the accelerator tube The terminal voltage of about 3 MV is distributed by a resistor chain over about 80 gaps forming the accelerator tube, all of which is enclosed in a pressure vessel filled with insulating gas (N and CO at 2.0 MPa, or 290 psi)

Fig 3 Cross section showing Van de Graaff principle as it is applied to neutron radiography Source: Ref 6

The particle beam is extracted along flight tubes In a typical neutron reaction, the beam bombards a water-cooled beryllium target in the center of the water moderator tank, which also serves as a partial shield The higher-energy accelerators indicated above can provide neutron yields of 1013 n/s and moderated, well-collimated beam intensities of the order of 106 n/cm2 · s

A few 4.8 × 10-13 J (3.0 MeV) Van de Graaff generators have recently been placed in service for thermal-neutron radiography In one such Van de Graaff system designed for neutron radiography, deuterons (4.8 × 10-13 J, or 3 MeV; 280 A) are accelerated onto a disk-shaped, water-cooled beryllium metal target Neutrons in the range of 3.2 to 9.6 × 10-13 J (2 to 6 MeV) are emitted preferentially in the forward direction and are moderated in water The 4 (solid angle) yield of

5 × 1011 n/s produces a peak thermal neutron flux of 2 × 109 n/cm2 · s At a collimator ratio of 36:1, the typical exposure time for high-quality film (3 × 109 n/cm2) is about 2 h

The accelerator tank for the 4.8 × 10-13 J (3 MeV) machine measures 5.2 m (17 ft) in length and 1.5 m (5 ft) in diameter The weight is 6100 kg (13,500 lb) The dimensions of the water tank are approximately 1 m (3 ft) on each side Neutron beams can be extracted through three horizontal beam collimators Unlike reactors, subcritical multipliers, or (d, T) accelerators, the Van de Graaff accelerators utilize no radioactive source material and sometimes require less stringent license processes

Other acceleration machines or reactions can be used for thermal-neutron radiography However, those described above have been most widely used

Radioactive Sources. There are many possible radioactive sources The characteristics of several radioisotopes that are commonly used are summarized in Table 3

Table 3 Properties and characteristics of several radioisotopes used for thermal-neutron radiography

Radioisotope Neutron reaction Half-life Characteristics

124

Sb-Be ( , n) 60 days Short half-life, high -ray background, low neutron energy easily thermalized,

low cost, high neutron yield

Long half-life, small size, low neutron energy easily thermalized, high neutron yield

Radioisotopes offer the best prospect for a portable neutron-radiographic facility, but it should be recognized that the thermal-neutron intensity is only about 10-5 of the total fast-neutron yield from the source Consequently, neutron radiography using a radioisotope as a neutron source normally requires long exposure times and fast films For example, a typical 3.7 × 1011 Bq (10 Ci) source would provide a total fast-neutron yield of the order of 107 n/s The radiographic intensity would be about 102 n/cm2 · s, and a typical exposure time using a fast film/converter-screen combination would

be about 1 h Californium-252, usually purchased in the form shown in Fig 4, has been the most frequently used radioactive source for neutron radiography

Fig 4 Cross section of doubly encapsulated 252 Cf source Source: Ref 6

Subcritical Assembly. Another type of source that has received some attention is a subcritical assembly This type of source is similar to a reactor, except that the neutron flux is less and the design is such that criticality cannot be achieved

A subcritical assembly offers some of the same neutron multiplication features as a reactor It is somewhat easier to operate, and safety precautions are less stringent, because it is not capable of producing a self-sustaining neutron chain reaction

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

Attenuation of Neutron Beams

Unlike electrons and electromagnetic radiation, which interact with orbital electrons surrounding an atomic nucleus, neutrons interact only with atomic nuclei Usually, neutrons are deflected by interaction with the nuclei, but occasionally

a neutron is absorbed into a nucleus When a neutron collides with the nucleus of an atom and is merely deflected, the neutron imparts some of its kinetic energy to the atom Both the neutron and the atom move off in different directions from the original direction of motion of the neutron This process, known as scattering, reduces the kinetic energy of the neutron and the probability that the neutron will pass through the object (testpiece) in a direction that will permit it to be detected by a device placed behind the object

True absorption of neutrons occurs when they are captured by nuclei The capture of a neutron transforms the nucleus to the next-higher isotope of the target nucleus and sometimes produces an unstable nucleus that then undergoes radioactive decay The probability that a collision between a neutron and a nucleus will result in capture is known as the capture cross section and is expressed as an effective area per atom (The capture cross section is usually measured in barns, 1 barn equaling 10-24 cm2 or 1.6 × 10-25 in.2.) The capture cross section varies with neutron energy, atomic number, and mass number For thermal neutrons (energy of about 4.0 × 10-21 J, or 0.025 eV), the average capture cross section varies randomly with atomic number, being high for certain elements and relatively low for other elements The cross section actually varies by isotope rather than element However, radiographers usually consider an average cross section for an element For intermediate neutrons (energies of 8.0 × 10-20 to 1.6 × 10-15 J, or 0.5 eV to 10 keV) and for fast neutrons (energies exceeding 1.6 × 10-15 J, or 10 keV), the capture cross section is normally smaller than that for thermal neutrons, and there is much less variation with atomic number For fast neutrons, most elements are similarly absorbing, and scattering is the dominant process of attenuation

In relation to other types of penetrating radiation, many materials interact less with neutrons Therefore, neutrons can sometimes be used to inspect greater thicknesses than can be conveniently inspected with electromagnetic radiation The combined effect of scattering and capture can be expressed as a mass-absorption coefficient; this coefficient is used to determine the exposure factor for the neutron radiography of a given object (testpiece) For a given material, attenuation varies exponentially with thickness, and the basic law of radiation absorption (discussed in the article "Radiographic Inspection" in this Volume) applies to neutron attenuation as well as to the attenuation of electromagnetic radiation

Neutron Radiography

Harold Berger, Industrial Quality, Inc

Neutron Detection Methods

Detection methods for neutron radiography generally use photographic or x-ray films In the so-called direct-exposure method, film is exposed directly to the neutron beam, with a conversion screen or intensifying screen providing the secondary radiation that actually exposes the film (Fig 5a) Alternatively, film can be used to record an autoradiographic image from a radioactive image-carrying screen in a technique called the transfer method (Fig 5b)

Fig 5 Schematics of neutron radiography with film using the direct-exposure method (a) and the transfer

method (b) The cassette is a light-tight device for holding film or conversion screens and film in close contact during exposure

Direct-Exposure Method. Conversion screens of thin gadolinium foil or a scintillator have been most widely used in the direct-exposure method When bombarded with a beam of neutrons, some of the gadolinium atoms absorb some of the neutrons and then promptly emit -rays The -rays in turn produce internal conversion electrons that actually expose the film; these are directly related in intensity to the intensity of the neutron beam Scintillators, on the other hand, are fluorescent materials often made of zinc sulfide crystals that also contain a specific isotope, such as or In a neutron beam, these isotopes react with neutrons as follows:

The particles emitted as a result of these reactions cause the zinc sulfide to fluoresce, which in turn exposes the film Gadolinium oxysulfide, a scintillator originally developed for conventional radiography, is now widely used for neutron radiography

Scintillators provide useful images with total exposures as low as 5 × 105 n/cm2 The high speed and favorable relative neutron/gamma response of scintillators make them attractive for use with nonreactor neutron sources For high-intensity sources, gadolinium screens are widely used Gadolinium screens provide greater uniformity and image sharpness (high-contrast resolution of 10 m, or 400 in., has been reported), but an exposure about 30 or more times that of a scintillator

is required, even with fast films Excessive background radiation should be kept to a minimum because it can have a detrimental effect on image quality

In the transfer method, a thin sheet of metal called a transfer screen, which is usually made of indium or dysprosium, is exposed to the neutron beam transmitted through the specimen Neutron capture by the isotope or

induces radioactivity, indium having a half-life of 54 min and dysprosium a half-life of 2.35 h The intensity of radioactive emission from each area of the transfer screen is directly related to the intensity of the portion of the transmitted neutron beam that induced radioactivity in that area The radiograph to be interpreted is made by placing the radioactive transfer screen in contact with a sheet of film The particle and -ray emissions from the transfer screen expose the film, with film density in various portions of the developed image being proportionally related to the intensity

of radioactive emission

The transfer method is especially valuable for inspecting a radioactive specimen Although the radiation emitted by the specimen (especially -rays) causes heavy film fogging during conventional radiography or direct-exposure neutron radiography, the same radiation will not induce radioactivity in a transfer screen Therefore, a clear image of the specimen can be obtained even when there is a high level of background radiation

In comparing the two primary detection methods, the direct-exposure method offers high speed, unlimited integration time, and the best spatial resolution The transfer method offers insensitivity to the -rays emitted by the specimen and greater contrast because of lower amounts of scattered and secondary radiation

image-Real-time imaging, in which light from a scintillator is observed by a television camera, can also be used for neutron radiography Because of low brightness, most real-time neutron radiographic images are enhanced by an image-intensifier tube, which may be separate or integral with the scintillator screen This method can be used for such applications as the study of fluid flow in a closed system or the study of metal flow in a mold during casting The lubricants moving in an operating engine have been observed with the real-time neutron imaging method

Neutron Radiography

Harold Berger, Industrial Quality, Inc

Applications

Various applications concerning the inspection of ordnance, explosive, aerospace, and nuclear components are discussed

in Ref 1, 2, 3, 4, 5, 6, 7, 8, 9 The presence, absence, or correct placement of explosives, adhesives, O-rings, plastic components, and similar materials can be verified Nuclear fuel and control materials can be inspected to determine the distribution of isotopes and to detect foreign or imperfect material Ceramic residual core in investment cast turbine blades can be detected Observations of corrosion in metal assemblies are possible because of the excellent neutron sensitivity to the hydrogenous corrosion product Hydride deposition in metals and diffusion of boron in heat treated boron-fiber composites can be observed The following examples illustrate the application of neutron radiography to the inspection of radioactive materials and several assemblies of metallic and nonmetallic components

Example 1: Thermal-Neutron Radiography Used to Determine Size of Highly Radioactive Nuclear Fuel Elements

Highly radioactive nuclear fuel elements required size measurements to determine the extent of dimensional changes that may have occurred during irradiation Generally, inspection is done in a hot cell, but because hot-cell inspection is a relatively long, tedious, and costly procedure, neutron radiography was selected

The fuel elements to be inspected consisted of 6.4 mm ( in.) diam cylindrical pellets of UO2-PuO2; the plutonium content was 20%, and the uranium was enriched in 235U The pellets had been irradiated to 10% burnup, which resulted in

a level of radioactivity of 3 × 10-2 C/kg · h (10 KR/h) at 0.3 m (1 ft)

Five elements were selected for inspection A neutron radiograph was taken by activating 0.25 mm (0.010 in.) thick dysprosium foil with a transmitted beam of thermal neutrons An autoradiograph of the activated-dysprosium transfer screen on a medium-speed x-ray film yielded the result shown in the positive print in Fig 6

Fig 6 Positive print of a thermal-neutron radiograph of five irradiated nuclear fuel elements, taken to

determine if dimensional changes occurred during irradiation Radiograph was made using a dysprosium transfer-screen method Dark squares in middle element are voids

Both 235U and plutonium have high attenuation coefficients for thermal neutrons The high contrast of the fuel pellets made it possible to measure pellet diameter directly from the neutron radiographs These measurements were both repeatable and statistically significant within 0.013 mm (0.0005 in.) Later, radiographic measurements were compared with physical measurements made in a hot cell The two sets of values corresponded within 0.038 mm (0.0015 in.)

Example 2: Indium-Resonance Technique for Determining Internal Details of Highly Radioactive Nuclear Fuel Elements

The five nuclear fuel elements inspected for dimensional changes in Example 1 were further inspected for internal details This was necessary because the thermal-neutron inspection procedure did not reveal any internal details; it only shadowed the pellets, as shown by the positive print in Fig 6

To inspect for internal details, an indium-resonance technique, which utilizes epithermal neutrons, was used In this technique, a collimated neutron beam was filtered by 0.5 mm (0.02 in.) of cadmium to remove most of the thermal neutrons Filtering produced a neutron beam with a nominal average energy somewhat above thermal The epithermal-neutron beam passed through the fuel elements and activated a sheet of indium foil Neutrons with an energy of about 2.34 × 10-19 J (1.46 eV), which is the resonance-absorption energy for indium, were primarily involved in activation The positive print of a radiograph made with epithermal neutrons shown in Fig 7 reveals considerable internal details, in contrast to the lack of internal details in Fig 6

Fig 7 Positive print of a neutron radiograph of the same five nuclear fuel elements shown in Fig 6 Radiograph

was made with epithermal neutrons and an indium-resonance technique, and it reveals internal details not shown in the thermal-neutron radiograph in Fig 6

With epithermal neutrons, there was less attenuation by the fuel elements than with thermal neutrons Therefore, internal details that were not revealed by thermal-neutron radiography such as cracking or chipping of fuel pellets, and dimensional features of the central void in the fuel pellets (including changes in size and accumulation of fission products) were revealed with the indium-resonance technique

Example 3: Use of Conventional and Neutron Radiography to Inspect an Explosive Device for Correct Assembly

Small explosive devices assembled from both metallic and nonmetallic components required inspection to ensure correct assembly The explosive and the components made of paper, plastic, or other low atomic number materials, which are less transparent to thermal neutrons than to x-rays, could be readily observed with thermal-neutron radiography Metallic components were inspected by conventional x-ray radiography

A positive print of a thermal-neutron, direct-exposure radiograph of a 50 mm (2 in.) long explosive device is shown in Fig 8(a) The radiograph was made on Industrex R film (Eastman Kodak), using a gadolinium-foil screen Total exposure was 3 × 109 n/cm2, which was achieved with an exposure time of 4 to 5 min At the top in Fig 8(a), just inside the stainless steel cap, can be seen a line image that corresponds to a moisture absorbent made of chemically treated paper Below the paper is a mottled image, which is the explosive charge Below the explosive charge are plastic components and, at the very bottom, epoxy

Fig 8 Comparison of positive prints of a thermal-neutron radiograph (a) and a conventional radiograph (b) of a

50 mm (2 in.) long explosive device Neutron radiograph reveals details of paper, explosive compound, and plastic components not revealed by x-rays

A conventional radiograph of the same device is shown in Fig 8(b) The metallic components, which were poorly delineated in the thermal-neutron radiograph, are more clearly seen in Fig 8(b) Together, the two radiographs verified that both metallic and nonmetallic components were correctly assembled

Example 4: Use of Neutron Radiography to Detect Corrosion in Aircraft Components

Aluminum honeycomb components are extensively used for aircraft construction The aluminum material is subject to corrosion if exposed to water or humid environments Thermal-neutron radiography is an excellent method of detecting hidden corrosion in these assemblies The corrosion products are typically hydroxides or water-containing oxides; these

corrosion products contain hydrogen, a material that strongly attenuates thermal neutrons The aluminum metal, on the other hand, is essentially transparent to the neutrons Therefore, a thermal-neutron radiograph of a corroded aluminum honeycomb assembly shows the corrosion product and other attenuating components such as adhesives and sealants Figure 9 depicts a thermal-neutron radiograph of an aluminum honeycomb assembly showing the beginnings of corrosion The white line image across the middle of the radiograph represents the adhesive coupling together two core sections The faint white smears in the upper half of the image and the double dot in the lower left area are images of corrosion as disclosed by the thermal-neutron radiograph Developmental work has shown that thermal-neutron imaging techniques are capable of detecting the corrosion product buildup represented by an aluminum metal loss of 25 m (1000 in.) The neutron method, therefore, is a very sensitive technique for the detection of corrosion

Fig 9 Thermal-neutron radiograph of aluminum honeycomb aircraft component showing early evidence of

hydrogen corrosion See text for discussion Courtesy of D Froom, U.S Air Force, McClellan Air Force Base

Example 5: Use of Neutron Radiography to Detect Corrosion in Bonded Aluminum Honeycomb Structures

Adhesive-Aluminum corrosion of aircraft surfaces has plagued both military and civilian aircraft Identification of this corrosion has been difficult, at best, usually being detected after the corrosion has caused the part to fail Of the nondestructive testing methods used to detect aluminum corrosion, thermal neutron radiography has proved the most sensitive method to date

The detection of aluminum corrosion is based on the attenuation properties of hydrogen associated with the corrosion products rather than aluminum and aluminum oxide with their low attenuation coefficients Depending on the environment, the corrosion products include aluminum trihydrates, monohydrates, and various other aluminum salts Because the linear attenuation coefficient for aluminum is similar to that of water and about 28 times greater than that for aluminum, a 0.13 mm (0.005 in.) corrosion layer should be detectable under optimum conditions

The sensitivity standard plate for aluminum corrosion fabricated by the Aeronautical Research Laboratories (Australia) contains corrosion products varying from 0.13 to 0.61 mm (0.005 to 0.024 in.) thick (Fig 10)

Fig 10 Standard plate for aluminum corrosion detection contains 0.13 to 0.61 mm (0.005 to 0.024 in.) thick

corrosion products Courtesy of R Tsukimura, Aerotest Operations Inc

Aluminum corrosion of honeycomb structures is complicated by the bonding adhesives that may appear similar in a neutron radiograph (Fig 11a) (see the article "Adhesive-Bonded Joints" in this Volume) Tilting of the honeycomb structure will alleviate this problem by allowing adhesive found along the bond lines to be distinguished from the randomly distributed corrosion products (Fig 11b)

Fig 11 Effect of bonding adhesives on the quality of neutron radiographs obtained when checking for

aluminum corrosion in honeycomb structures Radiograph taken (a) normal to specimen surface and (b) tilted

at any angle other than 90° to specimen surface Courtesy of R Tsukimura, Aerotest Operations Inc

Example 6: Use of Neutron Radiography to Verify Welding of Dissimilar Materials (Titanium and Niobium)

Exotic metal welded joints are a product of the extremely cold environment of space and man's desire to explore the vast emptiness of space For space vehicles, attitude control rockets provide the fine touch for proper vehicle alignment

For one application, a titanium-niobium welded joint was required between the light-weight propellant tank and the nozzle section Attempts to verify weld integrity using conventional radiography were not productive

Thermal neutron radiography provided the image required to ensure quality welds This defect standard weld shows the porosity at the seam and the similar thermal neutron attenuation for both titanium (Ti) and niobium (formerly known as columbium, Cb) (Fig 12a) For comparison, the x-ray radiograph image is also shown (Fig 12b)

Fig 12 Comparison of thermal neutron (a) and x-ray (b) radiographs of a titanium-niobium welded joint

Courtesy of R Tsukimura, Aerotest Operations Inc

Example 7: Use of Neutron Radiography to Detect Core Material Still Remaining

in the Interior Cooling Passages of Air-Cooled Turbine Blades

Investment casting of turbine blades using the lost wax process results in relatively clean castings As the demand for higher-powered turbine engines has increased, the interior cooling passages for air-cooled turbine blades have become more and more complex Concurrently, the removal of the core material has become increasingly more difficult Incomplete removal of the core results in restricted flow through the cooling passages and possible failure of the overheated blade

Previously, visual inspection was the nondestructive inspection method of choice for residual core detection However, current designs preclude the use of borescopes and other visual means for the interior passages X-radiography has proved rather ineffective in detecting residual core material Thermal neutron radiography is the nondestructive testing method of choice, especially when gadolinium oxide (Gd2O3) is used to dope the core material (1 to 3% by weight) (Fig 13) prior to casting the blade

Fig 13 Residual core material in a gas-cooled aircraft-engine turbine blade as detected by thermal neutron

radiography The excess core material, tagged with 1.5% Gd 2 O 3 , is shown circled in the second photo from the right Courtesy of R Tsukimura, Aerotest Operations Inc

When concerns about the possible detrimental effects of Gd2O3 during the casting process prevents its use in the core material, a procedure was developed to tag the residual core material after the core removal process The castings are dipped in a gadolinium solution [Gd(NO3)2 in solution] to impregnate any residual core, which is then imaged and subsequently detected by neutron radiography

The blades shown in Fig 14 have been tagged The neutron radiograph shows any residual core material greater than 0.38

mm (0.015 in.) in diameter Figure 15 is a schematic of typical core fragments in investment cast turbine blades detected

by thermal neutron radiography Image clarity of gadolinium tagged or doped cores is much greater than that of normal cores

Fig 14 Thermal neutron radiograph of 12 turbine blades tagged with Gd2O3 solution One of the 12 blades (located in the top row and second from the left) contains residual core material in its upper right-hand corner

cooling passage Courtesy of R Tsukimura, Aerotest Operations Inc

Fig 15 Schematic of turbine blade core standards: gadolinium [Gd(NO3 ) 3 in solution] tagged core, normal core (no gadolinium tagging or doping), and Gd2O3 doped core Typical core fragments of various thicknesses are shown Source: R Tsukimura, Aerotest Operations Inc

Example 8: Use of Neutron Radiography to Verify Position of Explosive Charges and Seating of O-Ring Seals in Explosive Bolt Assemblies

There are many critical applications of explosive release devices in aircraft, space, and missile systems Nondestructive testing is an important step in the quality control portion of the production cycle for these units Thermal neutron radiography has proved an indispensable tool in the nondestructive testing arsenal, particularly for thick-walled, metal devices, such as explosive bolts (Fig 16)

Fig 16 Schematic showing location of critical components that comprise an explosive bolt Source: R

Tsukimura, Aerotest Operations Inc

The inner details of explosive bolts can be imaged only by thermal neutron radiography methods (Fig 17) This particular type of bolt from a missile system is activated from the bottom by actuating the firing pin onto the primer The short section of mild detonating cord carries the energy to the output charge, which fractures the bolt and allows the bolt to be severed

Fig 17 Thermal neutron radiograph showing two sample bolts identical to the workpiece shown schematically

in Fig 16 Courtesy of R Tsukimura, Aerotest Operations Inc

In addition to the explosive charges, the internal O-ring seals, including the concentric pair around the firing pin and for the body are readily visible For safety's sake, determining the presence of the shear pin can also be accomplished through the use of thermal neutron radiography

Example 9: Application of Neutron Radiography to Determine Potting Fill Levels

in Encapsulated Electronic Filters

Electronic filters are an integral component of all space and satellite systems Because the cost of these satellites is very high and the cost to repair them even more prohibitive, high reliability filters are necessary

A common mode of filter failure is that caused by inadequate potting of the internal components and the subsequent physical breakdown of the filter during periods of high vibration, such as that encountered during vehicle launch Thermal neutron radiography is the method of choice for determining potting fill levels in encapsulated filters

The potting material attenuates the thermal neutrons and appears as the light density area Voids in the potting material, the fill level, and the distribution can readily be detected with neutron radiography

References cited in this section

1 H Berger, Ed., Practical Applications of Neutron Radiography and Gaging, STP 586, American Society for

Testing and Materials, 1976

2 Neutron Radiography Issue, At Energy Rev., Vol 15 (No 2), 1977, p 123-364

3 N.D Tyufyakov and A.S Shtan, Principles of Neutron Radiography, Amerind Publishing, 1979 (translated

from the Russian)

4 P Von der Hardt and H Rottger, Ed., Neutron Radiography Handbook, D Reidel Publishing, 1981

5 J.P Barton and P Von der Hardt, Ed., Neutron Radiography, D Reidel Publishing, 1983

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

Vol 3, American Society for Nondestructive Testing, 1985

7 "Standard Practices for Thermal Neutron Radiography of Materials," E 748, Annual Book of ASTM Standards, American Society for Testing and Materials

8 J.P Barton, G Farny, J.L Person, and H Rottger, Ed., Neutron Radiography, D Reidel Publishing, 1987

9 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

References

1 H Berger, Ed., Practical Applications of Neutron Radiography and Gaging, STP 586, American Society

for Testing and Materials, 1976

2 Neutron Radiography Issue, At Energy Rev., Vol 15 (No 2), 1977, p 123-364

3 N.D Tyufyakov and A.S Shtan, Principles of Neutron Radiography, Amerind Publishing, 1979

(translated from the Russian)

4 P Von der Hardt and H Rottger, Ed., Neutron Radiography Handbook, D Reidel Publishing, 1981

5 J.P Barton and P Von der Hardt, Ed., Neutron Radiography, D Reidel Publishing, 1983

6 L.E Bryant and P McIntire, Ed., Radiography and Radiation Testing, in Nondestructive Testing Handbook, Vol 3, American Society for Nondestructive Testing, 1985

7 "Standard Practices for Thermal Neutron Radiography of Materials," E 748, Annual Book of ASTM Standards, American Society for Testing and Materials

8 J.P Barton, G Farny, J.L Person, and H Rottger, Ed., Neutron Radiography, D Reidel Publishing, 1987

9 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

10 A Ridal and N.E Ryan, in Neutron Radiography, Proceedings of the Second World Conference (Paris, June 1986), J.L Barton et al., Ed., D Reidel Publishing, 1987, p 463-470

Thermal inspection is applicable to complex shapes or assemblies of similar or dissimilar materials and can be used in the one-sided inspection of objects Moreover, because of the availability of infrared sensing systems, thermal inspection can also provide rapid, noncontact scanning of surfaces, components, or assemblies

Thermal inspection does not include those methods that use thermal excitation of a test object and a nonthermal sensing device for inspection For example, thermally induced strain in holography or the technique of thermal excitation with ultrasonic or acoustic methods does not constitute thermal inspection

Thermal Inspection

Grover Hardy, Wright Research and Development Center, Wright-Patterson Air Force Base; James Bolen, Northrop Aircraft Division

Principles of Thermal inspection

The basic principle of thermal inspection involves the measurement or mapping of surface temperatures when heat flows from, to, or through a test object Temperature differentials on a surface, or changes in surface temperature with time, are related to heat flow patterns and can be used to detect flaws or to determine the heat transfer characteristics of a test body For example, during the operation of a heating system, a hot spot detected at a joint in a heating duct may be caused by a hot air leak Another example would be a hot spot generated when an adhesive-bonded panel is uniformly heated on one side A localized debonding between the surface being heated and the substructure would hinder heat flow to the substructure and thus cause a region of higher temperature when compared to the rest of the surface Generally, the larger the imperfection and the closer it is to the surface, the greater the temperature differential

Heat Transfer Mechanisms. Heat will flow from hot to cold within an object by conduction and between an object and its surroundings by conduction, convection, and radiation Within a solid or liquid, conduction results from the random vibrations of individual atoms or molecules that is transferred via the atomic bonding to neighboring atoms or molecules In a gas, the same process occurs but is somewhat impeded by the greater distance between the atoms or molecules and the lack of bonds, thus requiring collisions to transfer the energy When a gas or liquid flows over a solid, heat is transferred by convection This occurs from the collisions between the atoms or molecules of the gas or liquid with the surface (conduction) as well as the transport of the gas or liquid to and from the surface Convection depends upon the velocity of the gas or liquid, and cooling by convection increases as the velocity of the gas or liquid increases

Radiation is the remaining mechanism for heat transfer Although conduction and convection are generally the primary heat transfer mechanisms in a test object, the nature of thermally induced radiation can be important, particularly when temperature measurements are made with radiation sensors

Electromagnetic radiation is emitted from a heated body when electrons within the body change to a lower energy state Both the intensity and the wavelength of the radiation depend on the temperature of the surface atoms or molecules For a blackbody, the radiation wavelength and spectral emission power vary as a function of temperature, as shown in Fig 1 At

300 K (27 °C), the temperature of a warm day, the dominant wavelength is 10 m (400 in.), which is in the infrared region (Fig 2) A surface would have to be much hotter for the dominant wavelength to fall in the visible region below