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Refractive index of silica aerogel:
uniformity and dispersion law
Tito BellunatoINFN Sezione di Milano–Bicocca
RICH 2007 Trieste – October 18th, 2007
Outline
• Silica aerogel
– Physical and optical properties
• Refractive index measurement
– Minimum deflection
• Refractive index uniformity
– Laser deflection: monochromatic
– Charged particle beam: Cherenkov spectrum
• Wide spectrum dispersion measurement
– UV lamp + Monochromator
RICH 2007 Trieste – October 18th, 2007 2 Tito Bellunato
Silica Aerogel
– Silica aerogel is a linked network of SiO2
nanocrystals, 2 − 5 nm in diameter.
– Tunable density ( ρ ∼ 0.15 g/cm3) → tunable
refractive index n
– We tested tiles with dimension 200 × 200 × 50
mm3 and n ' 1.03 produced by the Boreskov
Institute in Novosibirsk.
The refractive index is measured with
the minimum deviation method. Ne-He Laser
Filters L
x
CCD
Aerogel
Φθout
Turning Table
θin
n =
sin
„
Φ + θout
2
«
sin
„
Φ
2
«
RICH 2007 Trieste – October 18th, 2007 3 Tito Bellunato
Refractive Index Inhomogeneity
– The refractive index of aerogel depends on the
density according to n(λ) = 1 + k(λ)ρ with
k ' 0.21 at λ = 400 nm
– local density fluctuations lead to variations of
the refractive index within the tile
– these variations contribute to the θC Cherenkov
angle accuracy
Two methods developed to evaluate the homogeneity
– laser beam deflection
– Cherenkov angle measurement
LHCb requirement:
Max variation σ(n − 1)/(n − 1) < 1%
corresponding to σi(θC) ' 1.17 mrad
when σtot(θC) ' 2.6 mrad
RICH 2007 Trieste – October 18th, 2007 4 Tito Bellunato
Refractive Index Inhomogeneity
Electromagnetic radiation bends if there is a refractive
index gradient transverse to the direction of propagation
t
Aerogel block
δ
He-Ne Laser
∆z
CCDy
L
Laser Beam Method
Assuming parallel faces for the tile,
the deviation angle δ is proportional
to the refractive index gradient
dn
dy' n
δ(y)
t⇒ ∆n(y) =
n
t
Z y
y0
δ(y)dy
RICH 2007 Trieste – October 18th, 2007 5 Tito Bellunato
Refractive Index Inhomogeneity
Laser Aerogel CCD camera
Y axis
Sample measurement with
gradient towards the sides:
100 × 100 × 41 mm3
0
0.05
0.1
0.15
0.2
x 10-2
0 20 40 60 80 100
Y (mm)
∆n(y
)
A=0.9558C=0.0060 µm4/cm
– fast feed–back method
– one wavelength at a time can be monitored
– extrapolation to the full wavelength range
σ(n − 1)/(n − 1) ∼ 1.3%
RICH 2007 Trieste – October 18th, 2007 6 Tito Bellunato
APACHE
Aerogel Photographic Analysis by CHerenkov Emission
� table–top RICH detector with b/w film as photon detector
� 500 MeV electrons from the DAΦNE Beam Test Facility in Frascati
� scanning the beam entrance point along the aerogel surface
N2
Film
Aerogel
Mirror
e- beam
Photons
Aerogel Holder
Spherical MirrorFilm
Beampipe
Aerogel200 × 200 × 50 mm3
RICH 2007 Trieste – October 18th, 2007 7 Tito Bellunato
APACHE
– Cherenkov ring width dominated by
chromaticity n = n(λ)
aerogel ring
N2 ring
GEANT4
RICH 2007 Trieste – October 18th, 2007 8 Tito Bellunato
APACHE
– Cherenkov ring width dominated by
chromaticity n = n(λ)
aerogel ring
N2 ring
DATA
RICH 2007 Trieste – October 18th, 2007 9 Tito Bellunato
APACHE
– 25 entrance points measured (a 200 × 200 × 50 mm3 tile tested)
– retracking algorithm to build the distribution of reconstructed θC
– resolution: ∼ 0.3 mrad, including systematics (GEANT4)
RICH 2007 Trieste – October 18th, 2007 10 Tito Bellunato
APACHE
– 25 entrance points measured (a 200 × 200 × 50 mm3 tile tested)
– retracking algorithm to build the distribution of reconstructed θC
– resolution: ∼ 0.3 mrad, including systematics (GEANT4)
RICH 2007 Trieste – October 18th, 2007 11 Tito Bellunato
APACHE
– 25 entrance points measured (a 200 × 200 × 50 mm3 tile tested)
– retracking algorithm to build the distribution of reconstructed θC
– resolution: ∼ 0.3 mrad, including systematics (GEANT4)
0
500
1000
1500
2000
2500
3000
x 10 3
0 0.05 0.1 0.15 0.2 0.25 0.3
θC (rad)
Ligh
t Int
ensit
yA=0.9558C=0.0060 µm4/cm
RICH 2007 Trieste – October 18th, 2007 12 Tito Bellunato
APACHE
– 25 entrance points measured (a 200 × 200 × 50 mm3 tile tested)
– retracking algorithm to build the distribution of reconstructed θC
– resolution: ∼ 0.3 mrad, including systematics (GEANT4)
0
500
1000
1500
2000
2500
3000
x 10 3
0 0.05 0.1 0.15 0.2 0.25 0.3
θC (rad)
Ligh
t Int
ensit
yA=0.9558C=0.0060 µm4/cm
Surface plot of n − n̄
02468
101214161820
0 2 4 6 8 10 12 14 16 18 20
-0.4
-0.2
0
0.2
0.4
x 10-3
X (cm)
Y (c
m)
σ(n − 1)/(n − 1) = (0.76 ± 0.01)%
The very promising results from the APACHE runs show that large transverse size
aerogel tiles now available comply with the homogeneity requirements of LHCbRICH 2007 Trieste – October 18th, 2007 13 Tito Bellunato
Dispersion law
– Chromatic dispersion is often the source of the dominant contribution to σθ
in RICH detectors with silica aerogel as radiator
– A correct parameterisation of n(λ) is essential for a realistic simulation of the
detector and a more performing pattern recognition
– There are several heuristic models, based on the Lorentz-Lorenz law:
n2− 1
n2 + 2= cf (Eγ) with c =
4πa30ρNA
3M
– f(Eγ) can be parameterised in terms of a multi–pole Sellmeier function as:
f (E) =N∑
j=1
Fj
E2j − E2
γ
RICH 2007 Trieste – October 18th, 2007 14 Tito Bellunato
Dispersion - Setup
Usual prism method with some important modifications:
– A UV lamp coupled to a monochromator provides a monochromatic source,
an objective allows to have parallel rays at the output
– The refracted beam stops on a fine mesh screen
– Centre of gravity of the spot is calculated taking a picture of the screen with
a digital camera
– Measurements taken at fixed angle instead of minimal deviation condition,
hard to find at short wavelengths
We were able to take data in the range 350–700 nm, well matched to the spectrum
of detected photons from the aerogel in LHCb.
Below 350 nm the transmission of the objective is too poor.
RICH 2007 Trieste – October 18th, 2007 15 Tito Bellunato
Dispersion
– A one–pole Sellmeier function fits well the data
– Two superimposed poles are found in a two–poles fit
As a function of λ:
n2(λ) − 1 =a0λ
2
λ2− λ2
0
The pole is found at 83.2 nm. The den-
sity dependent coefficient is consistent
with the one calculated from the mea-
sured density of the aerogel sample.Wavelength (nm)
300 350 400 450 500 550 600 650 700 750
Refra
ctive
Inde
x
1.0280
1.0282
1.0284
1.0286
1.0288
1.0290
1.0292
1.0294
1.0296
/ ndf 2χ 5.534 / 15 0a 4.383e-05± 0.05639 0λ 1.246± 83.22
/ ndf 2χ 5.534 / 15 0a 4.383e-05± 0.05639 0λ 1.246± 83.22
Dispersion Law
RICH 2007 Trieste – October 18th, 2007 16 Tito Bellunato
Comparison of different parameterisations
The esperimental points are compared to various parameterisations, all properly
scaled to match the laser measurement n(632.8 nm) = 1.0282.
The same n(λ) laws are compared in simulations.– n1 is the unphysical approximation
n=constant.
– n2 is the fitted one–pole Sellmeier
function
– n3 is the curve derived from SiO2
data (the stars) and the Clausius–
Mossotti equation for binary mix-
tures.
– n4 is a two–pole Sellmeier function
for the aerogel used in the LHCb sim-
ulation
Wavelength (nm)300 350 400 450 500 550 600 650 700 750
Refra
ctive
Inde
x
1.0280
1.0285
1.0290
1.0295
1.0300
1.0305
1.0310
n(632.8)=1.02823
1n
2n
3n
4n
Dispersion Law
RICH 2007 Trieste – October 18th, 2007 17 Tito Bellunato
MonteCarlo analysis
The APACHE simulation package has been run four times, each time with a dif-
ferent ni(λ), as previously defined. The results are summarized in the table below.
The plot shows the log–scale distribution of the reconstructed Cherenkov angle for
the constant n and the one–pole Sellmeier.
Mean Cherenkov angle θC and sin-
gle photon resolution σθ (mrad)
for 10 GeV/c pions.
θC (mrad) σθ (mrad)
n1 234.3 0.5
n2 236.3 2.8
n3 236.1 2.0
n4 236.4 3.5Cherenkov Angle (rad)
0.22 0.23 0.24 0.25 0.26 0.27
Entri
es
10
210
310
410
510
1n
2n
CθReconstructed Cherenkov Angle
RICH 2007 Trieste – October 18th, 2007 18 Tito Bellunato
Conclusions
– Complete characterization of the aerogel for the LHCb experiment
– It has been verified both with measurement at fixed λ and with a dedicated
Cherenkov detector that the material is well inside the specifications for the
homogeneity of the refractive index σ(n − 1)/(n − 1) < 1%
– The refractive index has been measured in the range 350 to 700 nm and a
one–pole Sellmeier function fits the data very well
– This information is essential for the simulation and the performance of an
aerogel–based RICH detector
RICH 2007 Trieste – October 18th, 2007 19 Tito Bellunato
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