Ray tracing to model time of flight effect in square based pyramid scintillators
Contact: [email protected]
J Rice, L Wilson and D Neely*
Central Laser Facility, STFC Rutherford Appleton
Laboratory, Oxfordshire, OX11 0QX, UK
P McKenna
Department of physics, University of Strathclyde,
SUPA, Glasgow G4 0NG, UK
*
R Deas
Security Sciences Department, DSTL, Fort
Halstead, Sevenoaks, Kent, TN14 7BP, UK
Z (m)
0.02
Method:
The scintillator was positioned aligned along the yaxis as shown in Figure 1. To simulate the X-ray
absorption process, the photons were randomly
allocated an interaction location and then given an
energy value (according to the material’s
absorption coefficient for the nominal incident
photons energy), which effectively accounts for the
deposition process. For the X-rays of interest (10,
14, 50, 100 and 2000KeV), the corresponding mass
attenuation coefficient for a plastic scintillator
material (BC422Q) was used, to ensure that the
code correctly estimated the energy deposition as
shown in Figure 2.
This simulation model assumes that a single
“optical equivalent” photon transports all the
nominal optical energy, as this was found to be the
Image of an
inversed square
based pyramid.
The dimensions
are variables.
X: 0.01
Y: 0.08
Z: -0.01
0.01
0
-0.01
X: -0.01
Y: 0.08
Z: -0.01
-0.02
0.08
X: 0.005
Y: 0
Z: -0.005
0.06
Detector
plane
0.04
Y (m)
0.02
0.01
0.02
Y axis (m)
0
0
-0.01
-0.02
X (m)
X axis (m)
X-ray photons
Optical photon
is formed and
given a vector.
The photon
reflects until it
passes through
the detector.
0.02
0.01
Z (m)
Introduction:
The aim of this project was to model the temporal
signal generated at the output of an “ideal”
scintillator. By “ideal”, we assume for the sake of
simplicity that there is no delay between the
incident X-ray photon exciting the scintillator and
the optical emission. We also assume that the
scintillator has negligible lifetime so that we are
only examining the effects of the detector geometry
and boundary scattering/reflection/absorption on
the temporal output of the system. The ideal
scintillator shape would give high sensitivity and a
small amount of afterglow, which allows the
scintillator to produce higher time resolution
outputs. Optimisation can be done by modelling the
optical photons paths and comparing different
geometries and surface coatings.
X: 0.01
Y: 0.08
Z: 0.01
X-ray photons
Z axis (m)
Abstract:
Scintillators are regularly used to convert high
energy photons into optical emission, which can
then be readily detected. Most scintillator based
systems are designed for high collection efficiency
so that the energy of the incident photon can be
resolved. However, in this study we have examined
time of flight aspects using a ray tracing model. As
new ways of generating ever shorter x-ray pulses
become available, measuring the duration of such
beams is becoming a critical issue.
0
-0.01
-0.02
0.08
0.06
0.02
0.04
Y (m)
0.01
0
0.02
-0.01
0
-0.02
X (m)
Figure 1. A schematic of the geometry for an inversed
square based pyramid. Upper image shows how the
scintillator is positioned, which direction the x-rays are
incident from and the plane the optical photons are
detected through. In the lower image, the red line indicates
a typical path the photons travels to reach the detector.
simplest coding algorithm. As each equivalent
photon is reflected, it’s value is then appropriately
reduced by each reflection off the scintillators
walls, until it passes into the detector where the
time it takes the photon to reach this point is found
by the distance travelled accounting for the
refractive index of the material. The temporal
energy output graph indicates how the reflected
photons decrease the temporal resolution.
8000
Number of photons * energy per photon per mm into scintillator
14000
10keV μ 190
14keV μ 78
50keV μ 19.6
100keV μ 16.7
2MeV μ 4.94
7000
12000
Energy output
(Arb.)
Energy output
6000
8000
6000
4000
2000
0
0
0.01
0.02
0.03
0.04
0.05
Distance into scintillator (m)
0.06
0.07
5000
4000
3000
(a) Black
2000
1000
0
0.08
0
1
2
3
4
5
Time (s)
Time (ns)
Figure 2. Energy deposited into scintillator per mm
from a million tests
6
-9
8000
Results:
Tests were performed using 3 different coatings
dielectric boundary (clear scintillator), scattering
(Reflective random, rough) and black (absorbent).
For each coating, a cuboid 2x2x8 cm scintillator
was tested for 5 different incident X-ray energies of
10, 14, 50, 100 and 2000KeV.
Black Coating:
The black coating scintillator absorbs all photons
that collide with the walls of the scintillator, so the
temporal resolution is very sharp. The output is
much lower than most of the simple boundary and
random coating output values.
Dielectric boundary:
A dielectric boundary (assuming a refractive index
of 1.58) increases the decay time due to photons
being reflected in the scintillator but it does not
significantly affect the peak.
Random coating:
With random coatings, the temporal resolution is
much worse than either of the other coatings due to
the photons reflecting in any direction, resulting in
a similar peak to the other systems but an
exponentially decreasing tail.
Discussion:
From these tests it has been shown that black
coated scintillators have the shortest decay time
and so best temporal resolution. The boundary and
random scattering coatings primarily act to add to
the tail of the signal which does not aid in
measuring the emission duration.
Conclusions:
The simple model has been used to demonstrate
that an absorbing coating gives the best temporally
resolved output for a rectangular scintillator
geometry. Further work examining the trade-off
between detection efficiency, scintillator shape and
temporal resolution will now be undertaken.
Energy Energy
output
(Arb.)
output
7000
6000
5000
4000
(b) Dielectric boundary
3000
2000
1000
0
0
1
2
3
4
5
6
5
6
Time (ns)
8000
7000
Energy
output
Energy
output (Arb.)
Energy Deposited
10000
6000
5000
4000
(c) Random coating
3000
2000
1000
0
0
1
2
3
Time (ns)
4
Figure 3. a) Black coating, b) Simple boundary, c) Random
coating. All of size X and Z width’s 2cm and Y of 8cm with
a million tests run for each x-ray energy level.
Acknowledgements:
We would like to acknowledge the support of
CALTA.