SPECIAL FEATURES IN RADIOGRAPHY ACCESSED BY 3D
MONTE CARLO MODEL
Gerd-RUdiger Tillack and Carsten Bellon
Federal Institute for Materials Research and Testing (BAM), Unter den Eichen 87,
12205 Berlin, Germany
ABSTRACT. Standard radiography simulators are based on the attenuation law complemented by
built-up-factors (BUF) to describe the interaction of radiation with material. The assumption of BUF
implies that scattered radiation reduces only the contrast in radiographic images but does not image
object structures itself. This simplification holds for a wide range of applications like weld inspection
as known from practical experience. But only a detailed description of the different underlying interaction mechanisms is capable to explain effects like mottling or others that every radiographer has
experienced in practice. The application of the N-Particle Monte Carlo code MCNP is capable to handle primary and secondary interaction mechanisms contributing to the image formation process like
photon interactions (absorption, incoherent and coherent scattering including electron-binding effects,
pair production) and electron interactions (electron tracing including X-Ray fluorescence and Bremsstrahlung production). Additionally it opens up possibilities like the separation of influencing factors
and the understanding of the functioning of intensifying screen used in film radiography. The paper
intends to discuss the opportunities in applying the Monte Carlo method to investigate special features
in radiography in terms of selected examples. It is important to note that the use of Monte Carlo
methods is a laboratory type of technique for basic investigations because of the enormous computing
power that is needed. For in-field applications such as for inspection planing simplified models are of
much greater importance and increasingly in use.
INTRODUCTION
In recent years the availability of computing power on PC-platforms allows the
modeling of complex processes and physics that control the X-ray image formation. This
development in computer hardware allows the implementation of NDE measurement models that are capable to predict the signals seen in NDE inspections and that can be used to
quantitatively study the effects of various parameters on those signals. The link between
NDE models and CAD provides the ability to quantitatively evaluate complex inspection
procedures. Depending on the formulated inspection problem or the influencing factor that
should be accessed by modeling an appropriate physical model has to be chosen to handle
the underlying interaction mechanisms.
Scattered radiation generated by a specimen can significantly influence the flaw
sensitivity by reducing the relative contrast of the flaw indication [1]. This statement holds
if the scattered radiation produces a uniform intensity distribution in the film or detector
plane, i.e. it is non-image forming while contributing to the radiographic projection. The
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
537
introduction of built-up factors yields a sufficient description of the reduction of the relative contrast in the radiographic image [1]. Accordingly radiography simulators are widely
used that are based on the attenuation law to describe the primary radiation and a BUF
model to count for scattered radiation. These models have a wide application range as
known from practice. But if the specimen covers a large range of material thickness (e.g.
castings) this simplification can not been used any more because the distribution of the
scattered radiation becomes non-uniform, i.e. it is influenced by the object structure itself.
In this case the underlying physical mechanisms have to be treated as an X-ray or photon
transport problem based on a Boltzmann type equation. There are several attempts known
to solve this problem for X-ray NDE applications such as moment approximation methods
[2,3], solution of the integral transport equation [4,5], and the Monte Carlo method [6-8].
The Monte Carlo approach is capable to count for primary and secondary interaction
mechanisms contributing to the image formation process like photon interactions (absorption, incoherent and coherent scattering including electron-binding effects, pair production)
and electron interactions (electron tracing including X-Ray fluorescence and Bremsstrahlung production). It is a powerful tool to separate different influencing factors and to
understand special features of detector systems, e.g. the functioning of intensifying screen
used in film radiography. On the other hand this approach is restricted applicable due to the
required computing time or the need of using parallel computing capabilities.
This paper intends to discuss exemplary the use of standard Monte Carlo packages
like MCNP [9] to derive fast empirical models counting for the contribution of scattered
radiation and to analyze the impact of lead screen on the image formation in industrial radiography.
PHYSICAL BACKGROUND
The Monte Carlo code MCNP [9] used for the investigations presented here includes
neutron, photon, and electron interactions. For the studies elaborated here photon and electron interactions have to be considered as shown in Fig. 1. The physics treatment for the
photon transport includes the photoelectric effect, coherent and Compton scattering, and
pair production. In detail it accounts for fluorescent photons after photoelectric absorption.
Additionally form factors are used with coherent and incoherent scattering to account for
electron binding effects.
The photoelectric effect consists of the absorption of the incident photon with energy £, with the consequent emission of fluorescent photons and the ejection or excitation
of an orbital electron of binding energy e<E, giving the electron a kinetic energy of E-e. Up
to two fluorescent photons are emitted. Only emitted photons with energy greater than
1 keV are considered. Each fluorescent photon born is assumed to be emitted isotropically
and transported.
To model Compton scattering the angle 6 of scattering, the new energy £" of the
photon, and the recoil kinetic energy of the Compton electron E-E' are determined. The
differential cross section is assumed as product of the Klein-Nishina cross section and the
scattering form factor counting for electron binding effects.
The coherent scattering involves no energy loss. It is only a photon process that
cannot produce electrons for further transport. Only the scattering angle 6 is computed. The
differential cross section includes the form factor to modify the energy-dependent Thompson cross section.
This investigation includes only photons with energy smaller 1 MeV such that pair
production does not occur.
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incident photon
scattering
Rayleigh scattering
Compton
electron
scattered
photon
electron
escape
photon
escape
I
photoelectric
absorption
incident photon
scattering
I
photoelectric absorption
photo electron
X-ray fluorescence
production of
conduction band
electrons
phonons
photon escape
light photons
electron escape
FIGURE 1. Photon and electron interaction mechanisms.
The transport of electrons or other charged particles is fundamentally different from
the transport of uncharged particles like neutrons or photons. The long-range Coulomb
force, resulting in a large number of possible interactions, dominates the transport of the
electrons. The energy loss of the electron by multiple interaction is considered such as the
production of Bremsstrahlung, K-shell electron impact ionization, Auger transition, and
scattering of an electron by an electron. The trace of the electrons is only used for the investigation of the lead screens.
APPLICATION OF MONTE CARLO METHOD
Contribution of Scattered Radiation to the Image Formation
The contribution of scattered radiation to the image formation is discussed here in
terms of two examples. The first example (see Fig. 2) shows the distribution of scattered
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FIGURE 2. Scattered photon flux for (a) steel and (b) Aluminum plate (thickness 10 mm, 80 keV photons).
radiation for a plate of 100x100 mm with a thickness of 10 mm made of steel (Fig. 2a) and
Aluminum (Fig. 2b) using a monochromatic source with 80 keV. In case of steel the mean
free path of the photons is 7.1 mm, i.e. smaller than the thickness of the plate. It is assumed
that the main contribution to a point in the detector plane is given by photons being scattered in within a half sphere of radius equal to the mean free path / of the photons. As a result three regions can be distinguished. If an arbitrary position is chosen with a distance
larger than / from the edge of the plate the integration volume is constant yielding a uniform distribution of the scattered photons in this region. If coming closer to the edge the
corresponding integration volume is reduced up to a factor of 4 yielding a reduction of the
scattered flux. For positions outside the area covered by the plate the morphology of the
problem is changed. Here angle-selective contributions to the scattered scalar flux are
found. The smaller the angle of the photon path relative to the edge of the plate the more it
contributes to the flux in the film plane because the total path length of the photon through
the material is decreased. This results in an increase of the flux that is overlaid by the divergence of the beam yielding a maximum as shown in Fig. 2a. If the material is changed to
Aluminum the mean free path of the photons is 21.7 mm, i.e. / is larger than the thickness
of the plate. In this case no increase of the photon flux is found for positions outside the
plate because the integration volume does not change here. Here only a decrease of the flux
is found due to beam divergence (see Fig. 2b).
The second example investigates the distribution of scattered radiation in case of
projection radiography for pipes. Fig. 3 shows the geometrical setup together with two
profiles of the scattering contribution for two different wall thicknesses. As seen in the figure, the Lorentz function fits the scattered distribution over a range of about two orders of
magnitude. This function can be used as an empirical model to describe the contribution of
scattered radiation for pipes. The Monte Carlo calculations are used to determine the parameters a and b of the Lorentz function over the expected application range of this projection technique. By introducing this approximation to standard X-ray simulators instead of
the simple BUF model, the accuracy of these simulators is considerably increased without
increase of calculation expenses. A comparison of the BUF model and the Lorentz approximation is shown in Fig. 4. The total photon flux is given by the primary radiation calculated from the attenuation law plus the contribution of scattered radiation.
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(b)
(a)
io-9
io-1
-200
——H
0
position [mm]
400
FIGURE 3. Geometrical setup for projection radiography (a) and profile of scattered radiation in the detector
plane (b) together with Lorentz fit.
2.5
>> 2.0
1
•9
<d
0
^.^
—— ^
/^/^
!'5
U
1.0
"^NTX
N
.......... I /
y BUF
\\
l^^^
0.5
0.0
.
— —- Lorentz approximation
^—— Built up Factor approximation
3.0
Lorentzfit
primary radiation
-100
-50
0
50
100
position [mm]
FIGURE 4. Comparison BUF and empirical scattering model.
Heavy Metal Intensifying Screens
Radiographic screens are employed to utilize more fully the X- or gamma ray energy reaching the film. When an X- or gamma ray beam strikes a film, usually less than one
percent of the energy is absorbed. Since the formation of the radiographic image is primarily governed by the absorbed radiation, more than 99 percent of the available energy in the
beam performs no useful photographic work. Any means of utilizing this unused energy
without complicating the technical procedure is highly desirably. Two types of radiographic screens are in use to achieve this goal: lead and fluorescence screen. For radiography in the range 150 to 400 kV, lead screens in direct contact with both sides of the film are
used. Lead screen has three principle effects: (i) it increases the photographic action on the
film mainly by reason of the electrons emitted and partly by the secondary radiation generated in the lead (see Fig. 5), (ii) it absorbs the longer wavelength scattered radiation more
541
incident photons
photoelectric f
absorption ft
film
FIGURE 5. Principle of intensification by lead screens.
than the primary, and (Hi) it intensifies the primary radiation more than the scattered radiation. The aim of this investigation was to understand the intensification effect of lead
screens because of the production of electrons and to study the influence of the screen
thickness on the intensifying factor. Additionally the effect of secondary radiation produced
in the screen is evaluated.
As shown in Fig. 5, two interaction mechanisms are to be considered here that produce electrons, namely the photoelectric absorption and the Compton scattering. If these
electrons reach the film emulsion they will be absorbed and contribute to the formation of
the latent image. The secondary radiation, i.e. the Compton photon and the X-ray fluorescence radiation, also reaches the film and contributes to the latent image. But again more
than 99 percent of its energy stays unused. Fig. 6 gives the distribution of scattered photons
and fluorescence photon for a monochromatic photon source of 310 keV producing a pencil
beam. Here lead screens of 0.027 and 0.100 mm thickness are investigated as commonly
used in Europe. Comparing the photon flux reaching the film it turn out that the fluorescence flux is about one order of magnitude smaller than the Compton scattered flux. Additionally these results can be used to determine the contribution of scattered photons to the
inner unsharpness, i.e. to determine a point spread function. As the thickness of the screen
increases the more scattering occurs and the distribution becomes wider.
The distribution of electrons produced in the lead screen is shown in Fig. 7. The
width of the electron distribution is not very much influenced by the thickness of the
2.5
310 keV monochromatic X-i
needle beam
I
310 keV monochromatic X-rays
needle beam
1.0
t
0.0 6**
-0.10
-0.05
0.00
position [mm]
0.05
0.10
0.10
FIGURE 6. Distribution of scattered (left) and fluorescence (right) photons for monochromatic source and pencil
beam.
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310 keV monochromatic X-rays
needle beam
0.027 mm Pb
0.100 mmPb
10
T3
5
-0.05
0.00
position [mm]
0.05
0.10
FIGURE 7. Distribution of electron flux in the film plane.
30
1.40
100 keV monochromatic X-rays
needle beam
7cd
300 keV monochromatic X-rays
needle beam
25
T? 1-35
1
20
1.30
15
1.25
13
1
10
0.00
0.02
0.04 0.060.08
1.20'—
0.00
0.05
0.10 0.15
thickness of lead screen [mm]
thickness of lead screen [mm]
FIGURE 8. Total electron yield as function of screen thickness for 100 keV (left) and 300 keV (right) incident photons.
screen. The total electron yield can be used as a measure for the intensification. A series of
calculation have been carried out to study the influence of the screen thickness on the total
electron yield for various incident photon energies. As an example the results for 100 keV
and 300 keV incident photons are given in Fig. 8. A clear maximum of the total electron
yield can be found. This maximum is shifted to greater screen thicknesses as the energy of
the photons is increased. Additionally it can be seen from the plots, that the form of the
curve is changed. With increasing photon energy the tail of the distribution becomes longer
and does not decrease as fast as for smaller energies. The reason for this behavior is the increased kinetic energy of the produced electrons such that their mean free path in the screen
material is also increased. The conclusion can be drawn that for higher energy photons the
correct choice of the optimal screen thickness is not that important as for lower energy
photons. If the total electron yield is taken as a measure for the effect of intensification its
maximum can be chosen as optimal screen thickness. The results are plotted in Fig. 9. As a
result follows, that with increasing photon energy thicker screens are preferable as it is
suggested by the European standards for film radiography.
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0.25
monochromatic X-rays
needle beam
0.20
0.15
0.10
0.05
0.00
0
150
300
450
600
photon energy [keV]
FIGURE 9. Screen thickness as function of incident photon energy.
CONCLUSIONS
State-of-the-art radiography simulators have a broad application range. These
simulators are based on the attenuation law to describe the primary radiation. The BUF is
used to simulate the contribution of the scattered radiation yielding a reduction of the radiographic contrast. Empirical detector models based on transfer functions are implemented
to describe the recording of the radiation in the film or detector plane. To handle inner unsharpeness and detector noise a point spread function and Gaussian distributed white noise
is introduced.
In cases where a detailed description of the radiation physics is required, Monte
Carlo packages can be applied. These models include the interaction mechanisms for photons and electrons. With the help of Monte Carlo models complex problems can be simulated like the intensifying effect of heavy metal screens. On the other hand these models
can be used to derive empirical models for the contribution of scattered radiation to the image forming process to increase the accuracy of simplified radiographic simulators.
REFERENCES
1. Halmshaw, R., Industrial Radiology, Chapman & Hall, London, 1995
2. Tillack, G.-R., Bellon, C, and Nockemann, C., in Review of Progress in QNDE9 Vol. 14,
eds. D. O. Thompson and D. E. Chimenti, Plenum Press, New York, 1995, pp. 665-672
3. Tillack, G.-R., Artemiev, V. M., and Naumov, A. O., JNDE 20 4, 153 (2001)
4. Inane, F. and Gray, J. N., in Review of Progress in QNDE, Vol. 10, eds.
D. O. Thompson and D. E. Chimenti, Plenum Press, New York, 1991, pp. 355-362
5. Inane, F. and Gray, J.N., Applied Radiation and Isotopes 48 10-12, 1299(1997)
6. Bell, Z. W., in Review of Proggress in QNDE, Vol. 10, eds. D. O. Thompson and
D. E. Chimenti, Plenum Press, New York, 1991, pp. 347-353
7. Aerts, W., De Meester, J. R., and Bollen, R., Mat. Eval. 40 9, 1071 (1982)
8. Inane, F., in Review of Progress in QNDE, Vol. 22, eds. D. O. Thompson and
D. E. Chimenti, AIP, New York, to be published
9. Briesmeister, J. F. (ed.), MCNP-A General Monte Carlo N-Partide Transport Code,
LANL Report LA-13709-M, Los Alamos, 2000
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