x-ray image of your daughters broken arm is really a picture
of shadows. If the image is caught on film, dense material like
bone will appear lighter because it absorbs more of the x rays
than organs or soft tissue. The x ray, or radiograph, easily reveals
the broken bone, showing where it needs to be reset.
obtain the image, the technician places your daughters arm
between the radiation source (x-ray machine) and a detector, which
may be film or a digital device. The end result is that three
dimensions are compressed to produce a two-dimensional image of
your daughters arm. There will be a bit of blur, but the
image meets the doctors needs just fine.
Computed tomography (CT)
takes the radiography process several steps further. A tomograph,
whether made for a medical, industrial, or scientific application,
starts out as radiographic viewsas many as 1,000 of themtaken
a given plane. The measurements in those two-dimensional radiographic
projections are mathematically reconstructed into a three-dimensional
volume of data. When the reconstruction is complete, doctors or
researchers can view individual cross-sectional planes of the
object with all other planes eliminated.
Medical radiographs and
tomographs are concerned with contrastthe degree of difference
between dark and light in imagesas well as the shape and
location of bone, internal organs, tumors, and so on. But many
and the National Nuclear Security Administrations Stockpile
Stewardship Programto preserve the reliability and safety
of nuclear weaponsrequire more than contrast and geometry.
Many stockpile stewardship applications require reconstructed
tomographs that researchers can use to determine the density of
an object and accurately identify minute voids and other changes.
The data produced by current radiographic methods and tomographic
reconstruction techniques have just not been good enough to meet
For useful tomographic
reconstructions, researchers must be able to model and simulate
the radiography process to provide good data for the reconstructions.
Right now, researchers can simulate two-dimensional radiographs
for Livermore applications to about a 10-percent accuracy. Future
applications will require an accuracy of about 1 percent, that
is, differences in image contrast as small as 1 percent should
be perceptible. Tomographic reconstruction is also problematic.
The best reconstruction software available today cannot calculate
the blurring effects caused by the detector and the radiation
source; the software accounts for blurring after the fact, through
a deconvolution process. X rays come in a spectrum of energies
that attenuate differently in different materials, but current
reconstruction methods ignore the differences. Noise, artifacts
from x-ray scatter, and the spectrum of x rays from the source
further diminish tomographic results. With current limitations,
the accuracy of computed tomography is typically about 15 percent.
To attain 1-percent accuracy,
Livermores Center for Nondestructive Characterization set
up a team headed by physicist Harry Martz to achieve that goal.
The teams first order of business was to improve the radiographic
imaging process to get the best data possible for tomographic
reconstructions. Martz and team members improved the
data acquisition system of Livermores 9-megaelectronvolt
linear accelerator, changing it to better account for radiation
scattering and blur from the radiation source. Equally important,
they modeled the detector using a Monte Carlo code so they would
understand detector response and be able to reduce or eliminate
blur caused by the detector.
Then they began to develop
software that incorporates the real effects of blur, attenuation
differences, noise, and artifacts at the front end of a reconstruction
to achieve the tomographic accuracy that Livermore needs.
of the HADESCCG tomographic reconstruction process.
Items with a purple background are operations that CCG performs.
Items with a gray background are operations that HADES performs.
All results are passed between the codes using shared files.
view of eight-layer test object.
a pure material, we cannot get a perfect radiograph or tomographic
reconstruction, says Martz. So it is hardly surprising
that we cannot get high-quality reconstructions of objects made
of several different kinds of materials.
One challenge is that for
some tomographic reconstructions, only a limited amount of data
is available, sometimes as few as 4 to 20 radiographic views.
The manner in which we do tomographic reconstruction is
different with a smaller number of views, says Morry Aufderheide,
creator of HADES, a ray-tracing code for simulating the radiographic
projections. Martz, Aufderheide, and the rest of the team members
are working on coupling HADES with an optimization algorithm to
perform tomographic reconstruction with a limited number of radiographic
named HADES for the Greek underworld, where the dead were sometimes
referred to as shadows. HADES can accurately simulate the radiographic
processfrom radiation source to image formation and detection.
With the recent huge increase in computing power, HADES can include
radiographic physicsblur from both the detector and the
radiation source, differing energy attenuations, and noisein
its calculations. HADES incorporates detailed models of various
radiation sources and detectors to understand blur, noise, and
HADES can also operate
with an optimization algorithm known as constrained conjugate
gradient (CCG), developed by Livermore engineer Dennis Goodman
several years ago. CCG has been used for adaptive optics systems
on large telescopes and was first applied to tomographic reconstruction
a few years ago. Goodman took a standard conjugate gradient code
and modified it so that a researcher can specify constraints.
For example, in a tomographic reconstruction, totally opaque portions
of an object can be ignored. The code also performs well with
limited data sets.
Reconstructing a CT image
entails solving a large matrix equation that relates simulations
of the object being reconstructed to the many radiographic projections
taken of it. First, CCG creates a model of the object, which may
be based on some known data or may simply be all zeros. HADES
then simulates a radiograph of this modeled object. The CCG search
algorithm compares the simulated radiograph to an actual measured
radiographic projection, seeking what is known as a maximum likelihood
solution. This search continues iteratively, efficiently modifying
the model using conjugate gradients and user-specified constraints,
until the difference between the actual measured radiographs and
the simulated or calculated radiographs is satisfactorily small.
This reconstruction technique also minimizes, but does not eliminate,
the possibility of introducing spurious features.
CCG and HADES are both
complex codes, created and maintained separately. Attempting to
actually merge the two codes would be time-consuming and inefficient.
Merging them could also make maintenance and upgrades to either
code more difficult. The most effective solution so far has been
to run them in parallel and exchange information between them
in shared files.
Reconstruction of eight-layer test object with neutrons and
(b) reconstruction of eight-layer test object with x rays.
Martz and his team have
performed several experiments to test their new capability in
experimental and simulation radiography as well as the new CT
image reconstruction technique. They used a variety of test objects
because each one tests a different aspect of the simulation and
tomographic reconstruction process.
In one experiment, they
imaged two copper step wedges to quantify their improvements to
the radiography experimental and simulation process. The experiment
showed that new collimators have indeed reduced scattering at
the detector. It also showed a better agreement with simulations
by accounting for the response of the digital amorphous-silicon
detector, which they had modeled with a Monte Carlo code and incorporated
into HADES. Of the experiments with these test objects, fabricated
of a single pure material, a pleased Martz says, We got
between 1- and 2-percent radiographic accuracy.
the evaluation of the new radiography modeling process, the team
tested a more complicated object, a disk made of eight layers
of five different materials. The first experiment used neutron
radiography (see S&TR, May
Hidden Defects with Neutrons) and was performed at the Ohio
University Accelerator Laboratory, one of the few neutron sources
in the country. The team took 64 radiographic images of the disk.
One radiographic image and a two-dimensional reconstruction of
its radiographic projection are shown in the figure (a) above.
The quality of the reconstruction is remarkable, considering that
it was made with just one rather than all or even several of the
64 images. When few projections are available, the quality of
the input data must be as high as possible. The high quality of
the CT reconstruction is also a measure of the effectiveness of
the HADES-CCG reconstruction process.
When the same disk was
tested using Livermores 9-megaelectronvolt x-ray source,
the results were quite different, as shown in the figure (b) above.
The x rays could not penetrate as far as the neutrons, just to
the fourth or fifth layer of the disk, producing only noise beneath
those layers. However, in the layers they did penetrate, the x
rays provided better contrast than neutron imaging. Neutron and
x-ray imaging complement each other to provide more complete tomographic
The team has just begun
working on full three-dimensional tomographic reconstructions
of objects made from multiple materials. This most complex version
of the tomographic process is what Livermore really needs for
stockpile stewardship and other projects. Its a long way
from the radiograph of your daughters arm.
computed tomography, constrained conjugated gradient (CCG), HADES,
radiographic modeling, radiography, Stockpile Stewardship Program.
information contact Harry Martz (925) 423-4269 (firstname.lastname@example.org).