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OM CalibrationThin metal film theory
OM calibration and thin metal film theory
Lucien Gauchet1, Alexandre Creusot1,2, Darko Veberic2,3
and the Antares APC group.
1AstroParticules et Cosmologie, Paris2University of Nova Gorica, Nova Gorica
3J. Stefan Institute, Ljubljana
Antares meeting, Moscow, June 2011
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Outline
1 OM Calibration
2 Thin metal film theory
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Set-up of the experiment
The black box:1m × 1m × 2m
The robot:all positionsall incidences
The light source:absolute calibrationmonitoring
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Set-up of the experiment
The black box:1m × 1m × 2m
The robot:all positionsall incidences
The light source:absolute calibrationmonitoring
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Set-up of the experiment
The black box:1m × 1m × 2m
The robot:all positionsall incidences
The light source:absolute calibrationmonitoring
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Light source calibration
Linearity range
Large amplitude⇒ 2 and 3 pe signalscounted as 1 pe signal?
Low amplitude⇒ statistic limit
Still to doabsolute calibration· · ·
NIST power [nW]0 20 40 60 80 100
rati
o o
f d
etec
ted
tri
gg
ers
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Light source calibration
Linearity range
Large amplitude⇒ 2 and 3 pe signalscounted as 1 pe signal?
Low amplitude⇒ statistic limit
Still to doabsolute calibration· · ·
NIST power [nW]0 20 40 60 80 100
ratio
ofde
tected
trigge
rs
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Light source calibration
Linearity range
Large amplitude⇒ 2 and 3 pe signalscounted as 1 pe signal?
Low amplitude⇒ statistic limit
Still to doabsolute calibration· · ·
NIST power [nW]0 1 2 3 4 5 6 7 8 9
rati
o o
f d
etec
ted
tri
gg
ers
0
0.01
0.02
0.03
0.04
0.05
0.06
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Light source calibration
Linearity range
Large amplitude⇒ 2 and 3 pe signalscounted as 1 pe signal?
Low amplitude⇒ statistic limit
Still to doabsolute calibration· · ·
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Acquisition system calibration
Developped atCEA-Saclay (E.Delagnes)and LAL-Orsay(D.Breton)
First mode:waveformoffline analysis
Second mode:charge online analysisin ADC counts
Qin pC =10(Qpeak
ADC−QpedADC)C
fR
with C = 0.61 mV/ADC,f = 1.6·109 s−1 andR = 50 Ω
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Acquisition system calibration
Developped atCEA-Saclay (E.Delagnes)and LAL-Orsay(D.Breton)
First mode:waveformoffline analysis
Second mode:charge online analysisin ADC counts
Qin pC =10(Qpeak
ADC−QpedADC)C
fR
with C = 0.61 mV/ADC,f = 1.6·109 s−1 andR = 50 Ω
time0 20 40 60 80 100 120 140 160 180 200 220 240
sig
nal
am
plit
ud
e
-35
-30
-25
-20
-15
-10
-5
0
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Acquisition system calibration
Developped atCEA-Saclay (E.Delagnes)and LAL-Orsay(D.Breton)
First mode:waveformoffline analysis
Second mode:charge online analysisin ADC counts
Qin pC =10(Qpeak
ADC−QpedADC)C
fR
with C = 0.61 mV/ADC,f = 1.6·109 s−1 andR = 50 Ω
charge
-500 -400 -300 -200 -100 0 100
1
10
210
310
410
510
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
First results
Parallel beam scan:289 pointssteps of 1cm106 triggers per point
below 0.45% of eventscharge histogram
Statistical error below1.5%
fluctuations about 20%
x [mm]
250300
350400
450y [mm]
100
150
200
250
300
350
z [
mm
]
020406080
100120140
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
First results
Parallel beam scan:289 pointssteps of 1cm106 triggers per point
below 0.45% of eventscharge histogram
Statistical error below1.5%
fluctuations about 20%
x [mm]300 320 340 360 380 400 420 440 460z [mm]
160180
200220
240260
280300
320
rati
o
00.0005
0.0010.0015
0.0020.0025
0.0030.00350.004
0.0045
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
First results
Parallel beam scan:289 pointssteps of 1cm106 triggers per point
below 0.45% of eventscharge histogram
Statistical error below1.5%
fluctuations about 20%
rati
o
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
x [mm]300 320 340 360 380 400 420 440 460
z [
mm
]
160
180
200
220
240
260
280
300
320
rati
o
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Next steps
Define the angularresolution
Increase the number ofpoints
Perform other scans
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
x [mm]376 377 378 379 380 381 382 383 384
z [
mm
]
254
255
256
257
258
259
260
261
262
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Next steps
Define the angularresolution
Increase the number ofpoints
Perform other scans
x [mm]
300 320 340 360 380 400 420 440 460 480y [m
m]
180200
220240
260280
300320
340360
z [
mm
]
020406080
100120
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Next steps
Define the angularresolution
Increase the number ofpoints
Perform other scans
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Outline
1 OM Calibration
2 Thin metal film theory
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Generalities
Two crucial points
Wave:due to the thickness of the film and to the multiple reflexions,the path length in the film is longer in average than theintrinsic thickness. Exiting waves can also add coherently.
Particle:the photon get absorbed in the metal. The probabilitydepends on the path length in the metal
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Formalisms
Physicist convention:
~E (~r , t) = ~E0ei(~k·~r−ωt)
Engineer convention:
~E (~r , t) = ~E0ei(ωt−~k·~r)
Crucial when applying Maxwell equations and Snell-Descarteslaw for an absorbing media.
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Formalisms
Physicist convention:
~E (~r , t) = ~E0ei(~k·~r−ωt)
Engineer convention:
~E (~r , t) = ~E0ei(ωt−~k·~r)
Crucial when applying Maxwell equations and Snell-Descarteslaw for an absorbing media.
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Formalisms
Physicist convention:
~E (~r , t) = ~E0ei(~k·~r−ωt)
Engineer convention:
~E (~r , t) = ~E0ei(ωt−~k·~r)
Crucial when applying Maxwell equations and Snell-Descarteslaw for an absorbing media.
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Complex index of refraction
From Maxwell equations
Physicist convention
n = η + iηκ
Engineer convention
n = η − iηκ
ref. Born, Wolf, principles of Optics, 7th edition, Cambridge University Press, 1999.
η and κ both positiveref. M.E. Moorhead, N.W. Tanner, Nucl. Instr. and Meth. A 378 (1996) 162
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Fresnel equations
From the continuity of the tangential component of ~E and ~B
P component
rp12 =
n2 cos θ1 − n1 cos θ2
n2 cos θ1 + n1 cos θ2
tp12 =
2n1 cos θ1
n2 cos θ1 + n1 cos θ2
S component
r s12 =
n1 cos θ1 − n2 cos θ2
n1 cos θ1 + n2 cos θ2
ts12 =
2n1 cos θ1
n1 cos θ1 + n2 cos θ2
for both formalisms.The same equations can be written between media 2 and 3.
ref. Born, Wolf, principles of Optics, 7th edition, Cambridge University Press, 1999.
ref. H.A. Macleod, Thin-Film Optical Filters, third edition, Institute of Physics Publishing, Bristol, 2001.
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Snell-Descartes law
In order to solve Fresnel equations, we get
θ2 from n2 sin θ2 = n1 sin θ1
θ3 from n3 sin θ3 = n2 sin θ2
Physicist convention
Im[θ3] < 0
Engineer convention
Im[θ3] > 0
θ3 can not be extracted from n1 sin θ1 = n3 sin θ3.
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Theoritical results
nenv = 1.34n1 = 1.49
n2 = 2.7 + i1.56n3 = 1.00h = 20 nm
R,T,A
]° [θcos 0 10 20 30 40 50 60 70 80 90
Rat
ios
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Theoritical results
nenv = 1.34n1 = 1.49
n2 = 2.7 + i1.56n3 = 1.00h = 20 nm
R,T,A
]° [θcos 0 10 20 30 40 50 60 70 80 90
Rat
ios
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
]° [θcos 0 10 20 30 40 50 60 70 80 90
Rat
ios
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Im[θ3] = 0.
]° [θcos 0 10 20 30 40 50 60 70 80 90
Rat
ios
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
−Im[θ3].
creusot OM calibration and thin metal film theory
OM CalibrationThin metal film theory
Conclusions
OM calibration:test bench ready and already in acquisitionstill needs some small improvementspossibility to test all kind of optical detector
Thin film:theory well understoodcode implementation done (among other characteristics)comparison with the OM calibration to perform
creusot OM calibration and thin metal film theory