ASTM E1441-19

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1441 − 19
Standard Guide for
Computed Tomography (CT)
This standard is issued under the fixed designation E1441; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope* 2. Referenced Documents
2.1 ASTM Standards:
1.1 CT is a radiographic examination technique that gener-
ates digital images in three dimensions of an object, including E746Practice for Determining Relative Image Quality Re-
sponse of Industrial Radiographic Imaging Systems
the interior structure. Because of the relatively good penetra-
bilityofX-rays,CTpermitsthenondestructivephysicaland,to E1316Terminology for Nondestructive Examinations
a limited extent, chemical characterization of the internal E1570Practice for Fan Beam Computed Tomographic (CT)
structureofmaterials.Also,sincethemethodisX-raybased,it Examination
applies equally well to metallic and non-metallic specimens, E1695Test Method for Measurement of Computed Tomog-
solid and fibrous materials, and smooth and irregularly sur- raphy (CT) System Performance
faced objects. E1935Test Method for Calibrating and Measuring CT
Density
1.2 This guide is intended to satisfy two general needs for
E2698Practice for Radiographic Examination Using Digital
users of industrial CT equipment: (1) the need for a tutorial
Detector Arrays
guide addressing the general principles of X-ray CT as they
E2736Guide for Digital Detector Array Radiography
applytoindustrialimaging;and(2)theneedforaconsistentset
2.2 ISO Standards:
of CT performance parameter definitions, including how these
ISO 15708-1:2017-02 International Standard for Non-
performance parameters relate to CT system specifications.
destructive Testing - Radiation Methods for Computed
1.3 ThisguidedoesnotspecifyCTexaminationtechniques,
Tomography - Part 1: Terminology
such as the best selection of scan parameters, the preferred
ISO 15708-2:2017-02 International Standard for Non-
implementation of scan procedures, or the establishment of
destructive Testing - Radiation Methods for Computed
accept/reject criteria for a new object.
Tomography - Part 2: Principles, Equipment and Samples
ISO 15708-3:2017-02 International Standard for Non-
1.4 Units—No units are mentioned in this document.
However,forCT,valuesaretypicallystatedinSIunitsandare destructive Testing - Radiation Methods for Computed
Tomography - Part 3: Operation and Interpretation
regarded as standard.
ISO 15708-4:2017-02 International Standard for Non-
1.5 This standard does not purport to address all of the
destructive Testing - Radiation Methods for Computed
safety concerns, if any, associated with its use. It is the
Tomography - Part 4: Qualification
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
3. Terminology
mine the applicability of regulatory limitations prior to use.
3.1 Definitions—In addition to terms defined in Terminol-
1.6 This international standard was developed in accor-
ogy E1316, the following terms are specific to this standard.
dance with internationally recognized principles on standard-
3.1.1 Throughout this guide, the term “X-ray” is used to
ization established in the Decision on Principles for the
denote penetrating electromagnetic radiation; however, elec-
Development of International Standards, Guides and Recom-
tromagnetic radiation may be either X-rays or gamma rays.
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
3.2 Definitions of Terms Specific to This Standard:
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
This guide is under the jurisdiction of ASTM Committee E07 on Nondestruc- contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
tive Testing and is the direct responsibility of Subcommittee E07.01 on Radiology Standards volume information, refer to the standard’s Document Summary page on
(X and Gamma) Method. the ASTM website.
Current edition approved July 1, 2019. Published August 2019. Originally Available from International Organization for Standardization (ISO), ISO
approved in 1991. Last previous edition approved in 2011 as E1441–11. DOI: Central Secretariat, BIBC II, Chemin de Blandonnet 8, CP 401, 1214 Vernier,
10.1520/E1441-19. Geneva, Switzerland, http://www.iso.org.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1441 − 19
3.2.1 CT detectability, n—the extent to which the presence Section 10 identifies some CT system processes for quantita-
of a feature or indication can be reliably inferred from a tive measurements to compare the relative performance of
tomographic examination image. different CT systems and calibrate for densitometric informa-
3.2.1.1 Discussion—CT detectability is dependent on the tion.NotethatISO15708Parts1-4havebeenupdatedandthis
spatialresolutionandcontrastresolutionoftheimage.Features guide has been harmonized with the recent publications.
may be detectable even if they are too small to be resolved,
5. Significance and Use
provided their contrast after blurring is still sufficient.
5.1 Computed tomography (CT) is a radiographic recon-
3.2.2 CT slice, n—a tomogram or the object cross-section
struction method that provides a sensitive technique whenever
corresponding to it.
the primary goal is to locate and size planar and volumetric
3.2.2.1 Discussion—Thesliceplaneistheplane,determined
detail in three dimensions.
by the focal spot and linear array of detectors or a single line
5.2 CTprovidesquantitativevolumeimagesasafunctionof
of an area array, around which each measurement of a planar
density and element number (attenuation coefficient) by means
tomographic scan is centered. Each such scan also has a slice
of computer-processed combinations of many X-ray measure-
thickness, which is the distance normal to the slice plane over
whichchangesinobjectopacitywillsignificantlyinfluencethe ments taken from different angles to produce cross-sectional
images of specific areas of a scanned object, allowing the user
measurements; typically, an average value based on the aper-
ture function is used to characterize this parameter. When toseeinsidetheobjectwithoutcutting.CTisconsideredmuch
easier to interpret than conventional radiographic data due to
three-dimensional CT-density maps have been reconstructed, a
slice may be formed on an arbitrary plane or other surface, not the elimination of overlapping structures. The new user can
learn quickly to read CT data because the images correspond
just on slice planes.
more closely to the way the human mind visualizes three-
3.2.3 CT view/projection, n—a set of X-ray opacity projec-
dimensional structures than conventional projection radiogra-
tion values (derived from measurements or by simulation)
phy. Further, because CT slices and volumes are digital, they
grouped together for processing purposes, especially for the
may be enhanced, analyzed, compressed, archived, input as
convolution and backprojection steps of computing a tomo-
data into performance calculations, compared with digital data
graph.
from other NDE modalities, or transmitted to other locations
3.2.3.1 Discussion—The set of line integrals resulting from
for remote viewing.
a scan of an object can be grouped conceptually into subsets
referred to as views. Each view corresponds to a set of ray
6. Computed Tomography (CT) Overview
paths through the object from a particular direction.The views
6.1 CT is a radiographic examination method that uses a
are also referred to as projections or profiles, while each
computer to reconstruct an image of one or more cross-
individual datum within a given projection is referred to as a
sectional plane (slice(s)) through an object. The result is a
sample or often simply a data point
quantitative map of the linear X-ray attenuation coefficient, µ,
3.2.4 detector aperture function, n—a three-dimensional
at each point in the plane. The linear attenuation coefficient
function centered on the axis from the radiation source to a
characterizes the local instantaneous rate at which X-ray
detector element, giving the sensitivity of the detector to the
photons are attenuated during the scan, by scatter or
presence of attenuating material at each position.
absorption,fromtheincidentradiationasitpropagatesthrough
the object.
3.2.4.1 Discussion—The detector aperture function gives
the extent and intensity distribution of each ray around and
6.2 One particularly important property of the total linear
along the length of its central line. The function is determined
attenuation coefficient is that it is dependent upon atomic
by the size and shape of the radiation source and of the active
number and is proportional to material density, which is a
region of the detector, and by relative distance to the source
fundamental physical property of all matter. The fact that CT
and the detector. The average width of this function in the
images are proportional to density is perhaps the principal
regionoftheobjectbeingexaminedisanimportantlimitonthe
virtue of the technology and the reason that image data are
spatial resolution of a CT scan.
often thought of as representing the distribution of material
3.2.5 sinogram, n—a two-dimensional array of position
density within the object being examined; however, the linear
within view versus view angle, which can be stacked into a
attenuationcoefficientalsocarriesanenergydependencethatis
volume for volumetric reconstruction techniques. a function of material composition (atomic number). This
feature of the attenuation coefficient may or may not (depend-
4. Summary of Guide ingonthematerialsandtheenergiesoftheX-raysinvolved)be
more important than the basic density dependence. In some
4.1 This guide provides a tutorial introduction to the tech-
instances, this effect can be detrimental, masking the density
nology and principles of CT and is divided into six main
differences in a CT image; in other instances, it can be used to
sections. Section 5 discusses the significance of CT compared
advantage, enhancing the contrast between different materials
to conventional radiography. Section 6 provides a brief over-
of similar density.
viewofCT.Section7describesthebasichardwareelementsof
CT systems. Section 8 outlines the general principles of CT 6.3 The fundamental difference between CT and conven-
imaging. Section 9 outlines CT system performance factors tional radiography is shown in Fig. 1. In conventional
used in characterizing the system performance and images. radiography, information on the slice plane “P” projects into a
E1441 − 19
tion are typically collected by rotating the sample (or source
and detector around the sample) at least 180° plus opening
angleofthefanbeam.Withthiskindofgeometry,asingleslice
of object can be reconstructed. The object may be translated
along the rotation axis to collect other slices.
6.6.1.1 Slice thickness is set by the X-ray optics of the
system.Itisafunctionoftheobjectposition(themagnification
of the scan geometry) and the effective sizes (normal to the
scan plane) of the focal spot of the source and the acceptance
aperture of the detector. The effective size of the focal spot is
determined by its physical size and any source-side collima-
tion. The maximum thickness is achieved with the maximum
effectivefocalspotsizeandthemaximumeffectiveacceptance
aperture. The minimum thickness is achieved with the mini-
mum focal spot size permitted and the minimum effective
acceptance angle permitted. Due to the collimation (tube and
detector)oftenusedinthisgeometry,theinfluenceofscattered
radiation, which disturbs the reconstruction process signifi-
cantly (artifacts), is minimal. Multiple slices along the axis of
FIG. 1 A CT Image Versus a Conventional Radiograph rotation may be stacked into a 3-D data set and rendered as a
3-D image. Two types of scan motion geometries are most
common: translate-rotate motion and rotate-only motion.
single line, “A-A;” whereas with the associated CT image, the
6.6.1.2 Translate-rotate Motion—The object is translated in
fullspatialresolutionoftheplaneispreserved.CTinformation
adirectionperpendiculartothedirectionandintheplaneofthe
is derived from a large number of systematic observations at
X-ray beam. Full data sets are obtained by rotating the test
differentviewingangles,andanimageofthesliceplaneisthen
object between translations by the fan angle of the beam and
reconstructed with the aid of a computer. The image is
again translating the object until a minimum of 180° of data
generated in a matrix of voxels.The resultant map is an image
have been acquired. The main advantage of this design is
of the object under examination. Thus, by using CT, one can,
ability to accommodate a wide range of different object sizes
in effect, slice open the object under examination, examine its
includingobjectstoobigtobesubtendedbytheX-rayfan.The
internal features, record the different attenuations, perform
disadvantageislongerscantime.Ifthetestobjectislargerthan
dimensional measurements, and identify any material or struc-
the prescribed field of view (FOV), either by necessity or by
tural anomalies that may exist.
accident, unexpected and unpredictable artifacts or a measur-
6.4 From Fig. 1, it can be appreciated readily that if an
able degradation of image quality can result.
internal feature is detected in conventional projection
6.6.1.3 Rotate-only Motion—A complete view is collected
radiography, its position along the line-of-sight between the
by the detector array during each sampling interval. A rotate-
source and the film is unknown. Somewhat better positional
onlyscanhaslowermotionpenaltythanatranslate-rotatescan
information can be determined by making additional radio-
and is attractive for industrial applications where the part to be
graphs from several viewing angles and triangulating. This
examinedfitswithinthefanbeamandscanspeedisimportant.
triangulation is a rudimentary, manual form of tomographic
If the test object is larger than the prescribed field of view
reconstruction. In essence, a CT image is the result of trian-
(FOV), either by necessity or by accident, unexpected and
gulating every point in the plane from many different direc-
unpredictable artifacts or a measurable degradation of image
tions.
quality can result.
6.5 As with any modality, CT has its limitations. Candidate
6.6.2 Cone Beam CT (3D CT)—Inasystemwhichisableto
objects for examination must be small enough to be accom-
perform a 3D-CT (or cone beam CT), an area scan detector,
modatedbythehandlingsystemoftheCTequipmentavailable
typically a digital detector array (DDA), is used, where each
totheuserandradiometricallytranslucentattheX-rayenergies
row of the area array “acts” like a linear array.The projections
employed by that particular system. In addition, the detector
needed for a reconstruction are typically collected by rotating
cannotbesaturatedinanyview.ThisrequirementcanlimitCT
the sample (or source and detector around the sample) at least
as compared to 2D radiography where one may saturate parts
180° plus opening angle of the cone beam. With this kind of
of the detected image in order to obtain proper signal through
geometry, a volume with multiple slices of object can be
an area of interest where for CT, for a given view/projection
reconstructed, Feldkamp reconstruction (a reconstruction pro-
image, the detector can only be saturated in an area outside the
cess that reconstructs 3D data directly to a 3D image), with a
part.
single rotation of the object. Compared to the fan beam
6.6 Types of CT: geometry, scattered radiation within the used cone cannot be
6.6.1 Fan Beam CT (2D-CT)—In a system which is able to reduced by collimation. Usually the image quality of the slices
perform a 2D-CT (or fan beam CT), a linear detector array produced is worse in quality compared to the fan beam
(LDA) is being used. The projections needed for a reconstruc- geometry. Additionally, the cone beam geometry produces
E1441 − 19
another artifact, which depends on the opening angle of the toconebeamCT,HelicalCTavoidstheFeldkampconeartifact
cone parallel to the rotation axis.This artifact is widely known since all measured object details will pass the central plane.
asFeldkampartifact(see9.7.6).TheinfluenceoftheFeldkamp The acquisition process for larger volumes is less time con-
artifact can be reduced by minimizing the opening angle of the sumingthanfanbeamCT.HelicalCTcantheoreticallybeused
cone,whichshouldbenolargerthan11°intotalifFeldkamp’s
to measure infinitely long objects, like those produced in
reconstruction algorithm is used.The scanning and acquisition extrusion processes.
process for larger volumes is typically less time consuming
6.6.4 Computed Laminography (Planar CT, Tomosynthesis,
than fan beam CT.
Coplanar Translational, Coplanar Rotational
6.6.2.1 Mathematically only 180° plus the fan angle is
Laminography)—Laminography is a radiographic technique in
required for CT reconstruction of the described method. It is,
which the relative motion of the source, detector, and object
however, best practice to acquire a full 360° of data as this
show a specific plane more clearly. Some systems will utilize
provides redundant information which fills in for detector
a reconstruction algorithm to assist in the image development.
defects (for example, bad pixels) and reduces artifacts. This
This method is especially suitable for large or flat objects that
also allows for checking the first versus the last image as a
are either difficult to rotate or have geometries that make
check for object motion during the scan.
penetration from some angles impossible.
6.6.2.2 Extended Field of View/Offset Scanning—Another
6.6.5 Irregular (Optimized) Geometries for CT—The qual-
method for increasing the width of the FOV while using a
ity of a CTvolume is highly influenced by the geometry of the
smallerareadetectoristooffsetthepositionofthedetector(or
part. Due to the circular trajectories being used in most CT
shift rotation axis, or a combination of both), collimate the
geometries unfavorable transmission directions are produced
beamasymmetrically,andscantheobject.Eachprojectionwill
duringthescan.Lackofpenetrationinthesepositionscanlead
beviewingalittlemorethanhalfthetotaldiameterofthefield
to unwanted artifacts in the reconstruction. Collecting the
ofview.Foroffsetscanning,thecenterofrotationmustalways
projections on an arbitrary path (for example, optimized based
be within each projection (Fig. 2). This method requires 360°
on the object geometry) can avoid the unfavorable positions
of data for mathematical sufficiency.
and therefore reduce artifacts. To make use of the arbitrary
6.6.3 Helical CT—In a system which is able to perform
geometries, special reconstruction methods are necessary. In
Helical CT (or Spiral CT), a multi-row LDA or an area scan
most cases, algebraic reconstruction is used, which can deal
detectorisbeingused.Theprojectionsneededforareconstruc-
with any kind of geometry.
tion are typically collected by rotating the sample (or source
and detector around the sample) combined with a linear
7. Basic Hardware Configuration
movement along the rotation axis. With this kind of geometry,
a volume with multiple slices of object can be reconstructed 7.1 CT systems are composed of a number of subsystems,
withmultiplerotationsoftheobject.Comparedtothefanbeam typically those shown in Fig. 3. The choice of components for
thesesubsystemsdependsonthespecificapplicationforwhich
geometry, scattered radiation within the cone cannot be re-
duced by collimation. Usually the quality of the slices pro- thesystemwasdesigned;however,thefunctionservedbyeach
duced is worse in quality compared to the fan beam geometry subsystem is common in almost all CT scanners. These
but improved compared to the cone beam geometry. Contrary subsystems are:
FIG. 2 Method of Acquiring an Extended FOV Using a DDA; (A) Conventional Geometric Arrangement Whereby the Central Ray of the
X-ray Beam From the Focal Source is Directed Through the Middle of the Object to the Center of the DDA; (B) Alternate Method of
Shifting the Location of the DDA (Multiple Positions Can be Used) and Collimating the X-ray Beam Laterally to Extend the FOV Object
E1441 − 19
FIG. 3 Typical Components of a Computed Tomography (CT) System
7.2 Source of Penetrating Radiation—Therearethreerather 7.2.2 Isotope Sources—Isotope sources are attractive for
broadtypesofradiationsourcesusedinindustrialCTscanners: someapplications.TheyofferanadvantageoverX-raysources
(1)X-raytubes,(2)accelerators,and(3)isotopes.Thefirsttwo in that problems associated with beam hardening are reduced
broad energy spectra are polychromatic (or Bremsstrahlung) or nonexistent for these monoenergetic/discrete energies type
electrical sources; the third is approximately monoenergetic sources. They have the additional advantages, which are
radioactive sources. The choice of radiation source is dictated important in some applications, that they do not require bulky
bythesamerulesthatgovernthechoiceofradiationsourcefor and energy-consuming power supplies, and they have an
conventional radiographic imaging applications. inherently more stable output intensity. The intensity of avail-
7.2.1 X-ray Sources—While the CT systems may utilize able isotopic sources, however, is limited by specific activity
either gamma-ray or X-ray generators, the latter is used for (decays per second per mass of 1 gram). The intensity affects
mostapplications.Foragivenfocalspotsize,X-raygenerators signal-to-noise ratio, and, even more importantly, the specific
(that is, X-ray tubes and linear accelerators) are several orders activitydeterminessourcespotsizeandthusspatialresolution.
of magnitude more intense than isotope sources. Most X-ray Both of these factors tend to limit the industrial application of
generatorsareadjustableinpeakenergyandintensityandhave isotopic scanners. Nevertheless, they can be used in some
the added safety feature of discontinued radiation production applicationsinwhichscanningtimeorresolutionisnotcritical.
when switched off; however, the polychromaticity of the 7.2.3 Source Setup—Caution is advised against applying
energy spectrum from an X-ray source causes artifacts such as practices developed for projection radiography. Except at very
beam hardening (the anomalous decreasing attenuation toward high energies, mass attenuation differences between materials
the center of a homogeneous object) in the image if uncor- (signal contrasts) tend to decrease as the mean X-ray energy is
rected. increased; whereas, X-ray production and penetrability (signal
E1441 − 19
levels) tend to increase under the same condition. Therefore, area of the DDAcan be used to reduce scattered radiation and
the optimum source energy for a given part is not determined good practice is to collimate to the FOV needed for a given
by the lowest possible X-ray energy that provides adequate
object. For uniform scintillator screens (Gd O S plastics, for
2 2
penetration but rather by the X-ray energy that produces the example), the thickness of the scintillator screen will reduce
maximum signal-to-noise ratio (SNR).When a part consists of
theresolutionwhenitexceedsthepixelsizeastheunsharpness
a single material or several materials with distinct physical
from internal light scatter becomes bigger than the pixel size.
density differences or different atomic numbers, or both, the
However, a thinner scintillator converts less X-ray quanta—
best SNR may be obtained at a high source energy. In such
especially for higher energies—which results in a much lower
cases, the decreased image noise at higher energies is more
SNR so use of a thicker scintillator or conversion screen, or
important than the increased contrast at lower energies. When
both, may be desirable even though it reduces resolution. It
chemically different components have the same or similar
should also be noted that in some instances a collimated 2D
physical densities, the best discrimination of materials may be
scintillator like CsI may mitigate this issue, particularly at
obtained at a low source energy. In such cases, the increased
lower energies. LDAs bypass this constraint by using single
contrast at lower energies may be more important than the
collimated pixels which allows for much thicker scintillators
decreased image noise at higher energies. Use of beam filters
without resolution reduction. A DDA creates an area view;
near the source is a common way of optimizing the beam,
after rotating of the object by 360° a 3D volume image is the
similar to 2D radiography
result.FormoreinformationaboutthepropertiesofDDAs,and
their constraints, refer to Guide E2736.
7.3 Radiation Detection Systems—Thedetectionsystemisa
transducer that converts the transmitted radiation containing 7.3.4 The application ranges of the three different technolo-
information about the test object into an electronic signal gies differ due to the pros and cons. For very high energies
suitableforprocessing.MostsystemsconvertX-raystovisible
(>>MeV) where a very high collimation is required for scatter
light in a scintillator and then detect the light with photo prevention, many high energy CT systems are equipped with
diodes. The detection system may consist of a single sensing
LDA detectors. Due to the higher scintillator efficiency and
element (single pixel detector), a linear detector array (LDA)
physical reduction of scatter by the fan beam and collimation
of sensing elements, or a digital detector array (DDA) of
slit, LDA CT systems usually offer a better image quality
sensing elements. The more detector pixels used at the same
compared to CT systems with DDAs; LDAs are commonly
time, the faster the required scan data can be collected; but
used in the energy range from 0.4 to 20 MeV. When possible,
there are important tradeoffs to be considered. Single pixel
DDAs are preferred because they deliver 3D scans within a
detectors are used for parallel and fan-beam geometry. LDAs
muchshortertime.Itisalsobecomingincreasinglycommonto
are used with fan-beam CT systems where the beam is
build a system with both an LDAand DDAto allow for either
collimated to a small slit to reduce scatter radiation. DDAs are
option.
used with cone-beam CT systems which can get a 3D volume
7.4 Mechanical Scanning Equipment—The mechanical
image much faster than parallel and fan-beam geometry
equipmentprovidestherelativemotionbetweenthetestobject,
systems but are prone to scatter radiation which can be
the source, and the detectors. It makes no difference, at least in
corrected by software.
principle, whether the test object is moved systematically
7.3.1 A single pixel detector provides the least efficient
relative to the source and detectors, or if the source and
method of collecting data but entails minimal complexity,
detectors are moved relative to the test object. Physical
eliminates detector cross talk and detector matching, and
considerations such as the weight or size of the test object
allows for collimation in two directions just to the active area.
should be the determining factors for the most appropriate
Avery efficient scintillator for very high energy can be used as
motion to use.
there is only a single pixel. This type of detector needs a
mechanical movement and an exposure for each pixel of a
7.5 Computer Systems—The computer system performs the
projection, whereas an LDA needs only one exposure per
tasks of Operator Interface, acquisition, reconstruction,
projection. The CT result is a one slice image of the object.
visualization, and storage.
7.3.2 Linear Detector Arrays (LDAs) have reasonable scan
7.5.1 The Operator Interface is the primary control of the
times at moderate complexity, acceptable cross talk and detec-
system and the test examination, including controls for
tor matching, and a flexible architecture (length of the detector
acquisition, reconstruction, visualization, and storage.
and width of the collimator slit) that typically accommodates a
7.5.1.1 Acquisition refers to the control of the mechanical
collimation in one direction.Ahighly efficient scintillator with
handling system and electronic controls for the data collection
a large thickness compared to the pixel size can be used.Also,
for the specific examination.This includes controlling the scan
forhighenergiessufficientX-rayquantaareconvertedtolight.
motion, source operation, and data acquisition functions.
An LDA generates one scanline per exposure. Rotating the
7.5.1.2 Reconstruction refers to the parameters and math-
object creates the sinogram.The CTresult is a one slice image
ematical operations for creation of the resultant slice or
of the object. A 3D image could be created by generating
volume.
multiple slices.
7.3.3 DDAsasareaimagingdevicescancapturemuchmore 7.5.1.3 Visualization includes the image display and pro-
cessingofthereconstructeddata.Imagedisplayandprocessing
information in a single exposure than an LDA using the cone
beam of the X-ray source. Collimation smaller than the active are subfunctions of the computer system that provide a degree
E1441 − 19
of image interaction not available with conventional radiogra- along a line corresponding to the direction in which the
phy. The mapping between the pixel linear attenuation coeffi- projection data were collected. The backprojections, when
cientandthedisplayedintensityofthepixelcanbechangedto enough views are employed, form a faithful reconstruction of
accommodate the best viewing conditions for a particular the object. Even in this simple example, with only four
feature. Image processing functions such as statistical and projections, the concentration of backprojected rays already
densitometricanalysescanbeperformedonanimageorgroup begins to show the relative size and position of features in the
of images. The digital nature of the image allows major original object.
advances in the way data are processed, analyzed, and stored.
8.2 Radon Transform—The theoretical mathematical foun-
7.5.1.4 Storage—Storage includes the archiving require- 4
dationunderlyingCTwasestablishedin1917byJ.Radon (1).
mentsfortheCTexamination.Informationsuchasimagedata,
Radon established that if the infinite set of line integrals of a
operating parameters, part identification, operator comments,
function, which is finite over some region of interest and zero
slice orientation, and other data is usually archived in a
outside it, is known for (parallel) ray paths through the region
computer-readable, digital format on some type of storage
alongallangles,thenthevalueofthefunctionoverthatregion
medium. An advantage of saving this material in computer-
can be uniquely determined. A particular function and its
readableformat(ratherthaninsimplehardcopy)isthatoldand
associated set of line integrals form a transform pair; the set of
new data sets can be compared directly, and subsequent
integrals is referred to as the Radon transform of the function.
changes in reconstruction or analysis procedures can be reap-
Radon demonstrated the existence of an inverse transform for
plied to saved data or images.
recovering a function from its Radon transform, providing an
important existence theorem for what later came to be called
8. General Principles of CT/Main CT Process Steps
CT.
8.1 Mathematical Basis of CT—CT is the science of recov-
8.2.1 Theessentialtechnologicalrequirementisthatasetof
ering an estimate of the internal structure of an object from a
systematically sampled line integrals of the parameter of
systematic indirect measurement of a physical property, such
interestaremeasuredoverthecross-sectionoftheobjectunder
as the linear attenuation coefficient by means of X-ray projec-
examination and that the geometrical relationship of these
tion images.This is performed by measuring a complete set of
measurements to one another be well known. Within this
line integrals involving the physical parameter of interest over
constraint, many different methods of collecting useful data
the designated cross-section and then using an algorithm to
exist. However, the quality of the resulting reconstruction
recover an estimate of the spatial variation of the parameter
depends on at least three major factors: (1) how finely the
over the desired slice.
object is sampled, (2) how accurately the individual measure-
8.1.1 A set of X-ray attenuation measurements is made
ments are made, and (3) how precisely each measurement can
along a set of paths projected at different locations around the
be related to an absolute frame of reference.
periphery of the test object. The first part of Fig. 4 illustrates a
8.2.2 Sampling the Radon Transform—For monoenergetic
set of measurements made on a test object containing two
X-rays, attenuation in matter is governed by Lambert’s law of
attenuating disks of different diameters. The X-ray attenuation
absorption (2), which holds that each layer of equal thickness
measurement made at a particular angle, φ , is referred to as a
attenuates an equal fraction of the radiation that traverses it.
single projection. It is shown as f (x'), where x' denotes the
φ1
Mathematically, this can be expressed as the following:
linear position of the measurement. The second part of Fig. 4
dI
shows measurements taken at several other angles f (x'). Each
φi 52µdx (1)
I
of the attenuation measurements within these projections is
digitized and stored in a computer, where it is subsequently
where:
conditioned (for example, normalized and corrected) and
I = the intensity of the incident radiation,
filtered (convolved). The next step in image processing is to dI
⁄I = the fraction of radiation removed from the flux as it
backproject the views, which is also shown in the second part
traverses a small thickness, dx, of material, and
ofFig.4.Backprojectionconsistsofprojectingeachviewback
µ = the constant of proportionality.
In the physics of X-ray attenuation, µ is referred to as the
linear attenuation coefficient. Eq 1 can be integrated easily to
describe X-ray attenuation in the following perhaps more
familiar form:
2µx
I 5 I e (2)
o
where:
I = the intensity of the unattenuated radiation, and
o
I = theintensityofthetransmittedfluxafterithastraversed
a layer of material of thickness x.
The boldface numbers in parentheses refer to a list of references at the end of
FIG. 4 Schematic Illustrations of How CT Works this standard.
E1441 − 19
8.2.2.1 IfX-rayspenetrateanon-homogeneousmaterial,Eq available that require only a limited set of views; however,
2 must be rewritten in the more general form: there is greater uncertainty in the resultant slice volume and
artifacts may be present in the data. Therefore, as with any
2*µ~s!ds
I 5 I e (3)
o
technique, the user must learn to recognize and be able to
where the line integral is taken along the direction of propa-
discount common artifacts subjectively.
gation and µ(s) is the linear absorption coefficient at each
point on the ray path. In CT, the fractional transmitted
(1)For Feldkamp based reconstruction algorithms, the
I
intensity, ⁄Io , is measured for a very large number of ray π
number of independent views (projections) should be V$ ·M
paths through the object being examined and then the loga-
rithm is applied to obtain a set of line integrals for input to
with an uneven number of projections for 360° to avoid star
the reconstruction algorithms. Specifically, the primary
artifacts (see 9.7.7). For practical applications the number of
measurements, I and I , are processed to obtain the neces-
o
π
views is typically reduced to V5 · M, since most algorithms
sary line integrals:
of filtered back projection have a smoothing effect at higher
I
µ s ds52ln (4)
* ~ ! S D
spatial frequencies
I
o
8.3 Reconstruction: Inverting the Radon Transform—The
8.2.3 Forthereconstructionproblemthesetoflineintegrals
reconstruction task can be defined as follows: given a set of
mustrepresentasystematicsamplingoftheentireobject.Ifthe
systematic transmission measurements corrupted by various
circle of reconstruction is inscribed in an M by M image
known and unknown sources of error, determine the best
matrix, this implies (π/4) M unknowns and a need for at least
estimate of the cross-section of the object associated with that
(π/4) M linearly independent measurements. Since the pres-
data. There are three broad classes of reconstruction algo-
ence of random noise corrupts the data, and due to strong
rithms: (1) matrix inversion methods, (2) finite series-
correlation between consecutive X-ray images with small
expansion methods, and (3) transform methods. Today, matrix
angular increment, the minimum sampling requirement is
inversion and finite series-expansion are not in typical usage;
greater than for noise-free data as well as to be sensitive to the
transform methods are conventionally used today in CT.
algorithm employed. Typically, data set sizes are on the order
8.3.1 Transform methods are based on analytical inversion
of one to three times the minimal amount, depending on the
systemandtheapplication.Arbitrarilycomplexobjectsrequire formulas. The two primary types of transform methods are (1)
the convolution-backprojection algorithm or filtered backpro-
more data than objects with simple geometrical shapes or
highlydevelopedsymmetries.Thenumberofsamplesperview jection algorithm and (2) the direct Fourier algorithm.
is generally more important than the number of views, and the 8.3.2 Backprojection Methods—Backprojection can be
relative proportion of views and samples should reflect this thought of as reversing the data collection process. Each
principle. In addition, each line integral must be accurately sample within a given projection represents the fractional
known, as well as referenced accurately to a known coordinate transmittance of a narrow beam of X-rays through the object,
system. This places strict requirements on the data acquisition which is assumed to be sufficiently well approximated by
and mechanical handling systems. small, discrete voxels of constant attenuation. Conceptually,
8.2.3.1 Sampling—Fan-Beam reconstruction algorithms, in backprojectioncanbethoughtofassmearingeachprofileback
generalrequireatleast180°ofrotationaldataplusfananglebe across the image in the direction of the radiation propagation.
collected by the scanner; however, there is the potential for Filtered backprojection is used to reduce the “smearing” effect
artifacts in the data. Cone beam reconstructions require 180° of each profile; a filter is applied (convolution with the data
plus fan angle but commonly acquire 360° of rotational data, profiles) that preserves the essential response of the detector to
and an uneven number of projections; the exact number of the presence of the point object but adds a negative tail to
projections needed depends on the shape of the object and the reduce the falloff that occurs with pure back-projection. See
reconstruction algorithm. There are reconstruction algorithms Fig. 5. Backprojection method is the method used by virtually
FIG. 5 Filtered Convolution Backprojection
E1441 − 19
all commercial CT systems. 9.2.1 Mathematically, the MTF is the modulus of the
8.3.3 Direct Fourier Algorithm—The direct Fourier algo- one-dimensional Fourier Transform (Magnitude) of the Line
rithm is based on the underlying fact that the one-dimensional Spread Function (LSF). The LSF may be described as the
Fourier transform of a CT projection of an object corresponds one-dimensional profile across the image of a line.This profile
toaspokeinFourierspaceofthetwo-dimensionaltransformof is not accessible to a direct measurement since there is no real
that object (the so-called Central-Section Theorem or physical implementation of such (one-dimensional) line.
Projection-Slice Theorem (3)). Thus, in theory, all that is However,theLSFisthefirstderivativeoftheone-dimensional
required in order to obtain an image by this method is to profile across the image of a sharp edge, the Edge Response
transform each projection as it is collected; place it along its Function (ERF). These three steps are illustrated in Fig. 6.
proper spoke in two-dimensional Fourier space; and when all
9.3 Contrast Discrimination Function (CDF)—The ability
the views have been processed, take the inverse two-
todiscriminateacontrastingfeatureofsize Dinmmorsize D*
dimensional Fourier transform to obtain the final image. This
in voxels from the base, at a certain noise level, can be
only works for parallel beam data.
described, approximately, by a single curve, called the CDF.
8.3.4 Feldkamp Reconstruction Algorithm—The Feldkamp
The CDF describes the influence of image noise on the
algorithm is applied to cone-beam generated datasets. The key
detectability (contrast sensitivity) of a feature in an elsewhere
to the Feldkamp algorithm is that all slices in the cone beam
homogeneous material neighborhood as a function of the size
geometry except the center one violates Tuy’s (4) sufficiency
D* of this feature in voxels. If it is multiplied by a physiologi-
condition that any plane through any voxel must intersect the
cal factor c it represents the ability of human observers to
source path. What Feldkamp observed was that if you do
recognize indications with larger than size D at a smaller
backprojection along a cone with shallow enough angle the
Contrast Noise Ratio (CNR), if the unsharpness can be
reconstruction works with minimal artifacts in spite of this.
neglected.
This angle is usually stated as a 5° or 6° half angle (10° or 12°
9.3.1 Calculation of CDF—To calculate the CDF, it is
fullangle)butslightartifactswillstillbeseenonsomepartsat
necessarytodeterminethenoiseintheimage.Theimagenoise
the top and bottom (5-7). The main advantages of this
at the center of a uniform cylinder of material is characterized
reconstruction algorithm are the possibility of using partial
by measuring the standard deviation in the mean σ , for
m
detection coverage and high computational efficiency.
different areas of interest. The process for determining σ
m
8.4 Reconstruction Matrix Size—The reconstruction matrix begins by selecting a Region of Interest (ROI). Each ROI is
size governs the number of views and data samples in each made of a series of tiles of squares of voxels from 1x1, 2x2,
view that must be acquired. The higher the resolution, the upto kxkvoxels.EachtilewithintheROIhasthemeanvalue
smallerthepixelsizeandthelargerthepixelmatrixforagiven of the voxel values within it. See Test Method E1695. First, a
region of interest on the test object. The reconstruction matrix tomographic slice image of a homogenous object (cylinder) is
sizeaffectsthenumberofscansandlengthoftimenecessaryto densely covered with m square tiles T of side length D*.
i
examine an object. Withineachtile,withintheROI,themeanvoxelvalue µ ofall
i
*2
n = D voxel values x{T is defined by:
i
9. CT System Performance Overview
*
µ ~D ! 5 Σ x (5)
i
9.1 CT System Performance—As a CT system can never
n
x{T
i
exactly duplicate the object that is scanned, the ability of a CT
where:
system to image thin cross-sectional areas of interest through
D = length in mm;
an object is dictated largely by the competing influences of the
∆v = voxel to voxel distance; and
spatial resolution, the statistical noise, and the artifacts of the
D
D* =
*
imaging system. This section will define and derive the issues
length in number of voxels D 5
∆v
associated with a CT system performance, including Modula-
9.3.2 The ROI is then moved to an adjacent non-
tion Transfer Function (MTF), Contrast Discrimination Func-
overlapping location and the measurement is repeated. This
tion (CDF), and Contrast-Detail-Diagram (CDD). The CDD is
procedureiscontinueduntilenoughindependentdatahasbeen
generated from the
...