The Light Reflection Simulation in Geant4
Cláudio Silva, José Pinto da Cunha
Vitaly Chepel, Américo Pereira
Vladimir Solovov, Paulo Mendes
M. Isabel Lopes, Francisco Neves
The Light Reflection Simulation in Geant4 – p.1/28
.
The Light Reflection Simulation in
Geant4
Cláudio Silva LIP University of Coimbra
12th Geant4 Collaboration Workshop, Hebden House,
Hebden Bridge (UK), 13-19 September 2007
The Light Reflection Simulation in Geant4 – p.2/28
Introduction
•
The correct simulation of the reflectivity of the
detector’s inner surfaces is important to describe
the observed phenomena
•
Some materials exhibit a reflection profile involving
different types of reflection (specular, diffuse,
backscattering)
•
The reflection profile for each material depends of
the surface finish and the λ of the incident light
The Light Reflection Simulation in Geant4 – p.3/28
Overview
•
Measurements of the reflected VUV light for PTFE,
Copper and Glass
•
Simulation of the experimental results using
Geant4
•
Modeling the specular and diffuse reflection
•
The Fit to the experimental results
•
The proposed model to the Geant4 simulation
The Light Reflection Simulation in Geant4 – p.4/28
The Experiment
•
The incident light is from the xenon scintillation
light (λ = 175nm)
•
The measurements are performed in a controlled
environment (argon atmosphere)
•
Measurements were made for copper, glass and
PTFE
•
Data was taken changing the angles θi , θr and φr .
Pin Hole
Xenon
Gas 1 bar
+HV
1.3 kV
e−
α
α
U.V.
Light Source
90.6 mm
α
Quartz
Window
80.0 mm
Surface
Sample
θi
n θr
PMT
Slit
A
66.4 mm
50 mm
PMT
The Light Reflection Simulation in Geant4 – p.5/28
The Geant4 optical simulation
•
Geant4 has two different models Glisur and
Unified
•
The Glisur model has two parameters (polishment
and reflectance)
•
The Unified Model depends of the interface
•
•
Dielectric - Dielectric
Dielectric - Metal
The Light Reflection Simulation in Geant4 – p.6/28
The Dielectric - Metal Interface
•
The user introduces two parameter the reflectance
of the surface and the surface roughness
Reflectance
Independent of θi
Absorption
Reflection
Polished
θi = θ r
Rough
D(σα )
The Light Reflection Simulation in Geant4 – p.7/28
Reflectance R
The Dielectric - Metal Interface
10
The copper measurements
show a reflectance highly
dependent of θi
•
Geant4 assumes a
constant reflectance
•
Fresnel equations F (θ, n, κ)
are required
-1
a
10
•
-2
0
b
10
20
30
40
50
60
70
80
90
Incident Angle θi
a : n = 1.04 ± 0.02
κ = 0.439 ± 0.004
b : n = 0.972 ± 0.004 κ = 0.193 ± 0.003
a and b are for two different oxidations of the copper sample
The Light Reflection Simulation in Geant4 – p.8/28
The Dielectric - Dielectric Interface
•
The Geant4 simulation uses three parameters
n, WD /WL , σ
•
The values of the parameters were tunned so that
the Geant4 simulation approaches our
measurements
•
The predicted reflectance is given by the number
of reflected photons over to the number of incident
photons
The Light Reflection Simulation in Geant4 – p.9/28
The Dielectric - Dielectric Interface
PTFE Measurements
(a.u)
10
10
10
10
-2
-3
φr=0
65
45
30
-4
-5
-20
0
20
40
60
80
Reflection Angle θr
but the reflectance obtained from the Geant 4
simulation is not realistic:
θi
30◦
45◦
65◦
R
8%
10%
25%
PTFE is considered a very good reflector
The Light Reflection Simulation in Geant4 – p.10/28
The Dielectric - Dielectric Interface
MICROFACET NORMAL
n1 sin θr = n2 sin θt
sin θt > 1
Total Internal
Reflection
sin θt <1
0
Amplitude F θr , n
Refraction
Reflection
lobular
spike
lamb
The Light Reflection Simulation in Geant4 – p.11/28
The Dielectric - Dielectric Interface
I
I
verify effects such
ad
ow
Geant4 looks at I~ · n̂ < 0 to test
Sh
•
^n
but fails to
^
n
Ma
sk
•
In general R = R [F (θ, n, κ)]
•
The lambertian component is proportional to the
specular reflection
0
IL = L · F θr , n
The Light Reflection Simulation in Geant4 – p.12/28
Reflection Models in the Literature
• Oren Nayar:
diffuse reflection - caused by the
surface roughness
• Wolf:
diffuse reflection - caused by internal
scattering
• Torrance-Sparrow:
• Combined Model:
specular reflection
diffuse plus specular reflection
The Light Reflection Simulation in Geant4 – p.13/28
The Oran-Nayar Model
•
Is intended to describe the diffuse lobe
•
Models the surface as a set of V-shaped cavities
•
The width of each facet is small compared to its
length
•
The roughness of the surface is specified using a
probability distribution function for the facet slopes
•
The facet area is large enough compared with the
λ of the incident light
•
Reflection in each facet is purely lambertian
The Light Reflection Simulation in Geant4 – p.14/28
The Oran-Nayar Model
Lr (θi , θr , φr − φi , σ) = Li WπD
×(A + B · max {0, cos (φr − φi )}
× sin (γ) tan (β))
A =
B =
σ2
1.0 − 0.5 (σ2 +0.33)
0.45σ 2
(σ 2 +0.009)
γ = max {θi , θr }
β = min {θi , θr }
The Light Reflection Simulation in Geant4 – p.15/28
Combined Model for Diffuse
Reflection
•
Both models are complementary in their
applicability to surfaces with different roughness
properties
•
Surfaces with a intermediated roughness exhibits
a combination of effects produced by both internal
scattering and external roughness
•
The two models can be joined together making the
assumption that each V-groove micro-facet reflects
according the Wolf model replacing the factor A by
−1
0
0
C = A [1 − F (θi , n, κ)] × 1 − F (sin [(sin θr )/n ], 1/n )
The Light Reflection Simulation in Geant4 – p.16/28
The Torrance Sparrow Model
•
Planar micro-facets oriented according a
distribution D (αr , σr )
•
The reflection in each micro-facet is specular
0
•
The Fresnel Factor F (θr , n, κ) introduces
polarization dependence
•
The shadowing and masking effects are accounted
for by the geometrical attenuation factor, G
The Light Reflection Simulation in Geant4 – p.17/28
The Torrance Sparrow Model
0
F (θ , n, κ)G (θi , θr , φr ) D (αr , σ)
Lr = W s
0
4 cos θ
• Ws
is the weight factor for the specular lobe
0
• F (θ , n, κ)
are the Fresnel equations for the
absorbing media
• G (θi , θr , φr )
• D (αr , σr )
is the geometrical attenuation factor
is the micro-facet distribution function
The Light Reflection Simulation in Geant4 – p.18/28
The Combined Model
Lr
WD
π
× (C + B · max {0, cos (φr − φi )} × sin (γ) tan (β))
0
i ,θr ,φr )D(α,σr )
+Ws F (θ ,n,κ)G(θ
4 cos θ0
where C is:
C = A [1 − F (θi , n, κ)] × {1 − F (sin−1 [(sin θr )/n0 ], 1/n0 )}
the reflection distribution function depends of 5
parameters Lr = Lr (θi , θr , φr , κ, n, WD , WS , σr )
The Light Reflection Simulation in Geant4 – p.19/28
The Fit
x = [θi , θr , φr ]
p = [WD , WS , n, κ, σ]
min
X (I (x) − Lr (x, p))2
x
2
σI(x)
•
The results were fitted with this model
•
We used a genetic algorithm to find the minimum
The Light Reflection Simulation in Geant4 – p.20/28
The Fit
•
A global fit was performed
•
Number of data points used: 2439 x = {θi , θr , φr }
•
Number of fitted parameters: 5
p = {WD , WS , n, κ, σ}
•
The micro-facet distribution D (α, σr ) was
considered Lorentzian
D (α, σr ) =
α2 +
•
1
σr2
2
2
Fit results: p = {WD , WS , n, κ, σ} =
{0.00145, 0.032, 1.09, 0.41, 0.072} χ2 ' 10
The Light Reflection Simulation in Geant4 – p.21/28
-4
(a.u)
10
10
-3
0
10
10
40
60
-5
-5
-3
10
10
10 20 30 40 50 60 70 80 90
Reflection Angle θr
0
20
40
θr=45
φr=3
60
40
60
-20
10
-3
10
10
Reflection Angle θr
20
40
θr=45
φr=10
60
80
Reflection Angle θr
-5
0
10
10 20 30 40 50 60 70 80 90
0
-4
80
θr=30
φr=3
θr=65
φr=10
-4
Reflection Angle θr
-3
-5
-3
80
10
20
-2
Reflection Angle θr
-5
-4
10
10
0
10
10
10
-4
80
θr=30
φr=0
(a.u)
-4
Reflection Angle θr
-3
-4
10
10
60
θr=65
φr=3
-20
10
40
-3
80
-4
20
-2
Reflection Angle θr
(a.u)
(a.u)
20
θr=45
φr=0
0
10
10
10
-20
10
10
(a.u)
10
-3
θr=65
φr=0
(a.u)
10
-2
(a.u)
10
(a.u)
(a.u)
The Results
20
40
60
80
Reflection Angle θr
-3
-4
-5
θr=30
φr=10
10 20 30 40 50 60 70 80 90
Reflection Angle θr
The Light Reflection Simulation in Geant4 – p.22/28
Proposed model for the Geant4
simulation
Mirror reflections
•
For High Reflectances: R constant
•
For κ .
1
2π
•
For κ &
1
2π
h
i
0
: R F (θ , n)
h
i
0
: R F (θ , n, k)
The Light Reflection Simulation in Geant4 – p.23/28
Proposed model for the Geant4
simulation
specular lobe plus diffuse lobe
The user has to provide five parameters
p = {WD , WS , n, κ, σ}
the function Lr is sampled in the simulation,
Lr =
WD
π (C +0 B × max {0, cos (φr
i ,θr ,φr )D(α,σr )
+Ws F (θ ,n,κ)G(θ
4 cos θ0
− φi )} × sin (γ) tan (β))
The Light Reflection Simulation in Geant4 – p.24/28
Proposed model for the Geant4
simulation
Radiance L (θi , θr , φr , p)
Integration in (θr , φr )
Reflectance R (θ i )
R (θi , p) + A (θi , p) +
T (θi , p) = 1
Refraction or
Absorption
Reflection
L (θi , θr , φr , p)
Choose θr and θi
The Light Reflection Simulation in Geant4 – p.25/28
Preliminary results obtained with the
proposed model
(a.u)
10
10
10
10
-2
-3
φr=0
65
45
30
-4
-5
-20
0
20
40
60
80
Reflection Angle θr
The Light Reflection Simulation in Geant4 – p.26/28
Conclusions
•
Geant4 simulation was compared with our light
measurements.
•
A new model for reflection by rough surfaces was
considered.
•
The new model was added to the Geant4
simulation. It seems to describe closely our
measurements.
•
This work is still going on.
The Light Reflection Simulation in Geant4 – p.27/28
.
(a.u)
10
10
10
10
(a.u)
10
10
10
10
-2
-3
φr=0
65
45
30
-4
-5
-20
0
20
40
60
80
Reflection Angle θr
-2
-3
φr=0
65
45
30
-4
-5
-20
0
20
40
60
The Light Reflection Simulation in Geant4 – p.28/28
80
Reflection Angle θr