om calibration and thin metal film theory

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


Outline

1 OM Calibration

2 Thin metal film theory



Set-up of the experiment

The black box:1m × 1m × 2m

The robot:all positionsall incidences

The light source:absolute calibrationmonitoring



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




Linearity range




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




Linearity range




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




Linearity range






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







Qin pC =10(Qpeak

ADC−QpedADC)C

fR


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







Qin pC =10(Qpeak

ADC−QpedADC)C

fR


charge

-500 -400 -300 -200 -100 0 100

1

10

210

310

410

510



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



First results





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



First results





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



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



Next steps



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



Next steps



Perform other scans



Outline

1 OM Calibration

2 Thin 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



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.



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



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


S component

r s12 =

n1 cos θ1 − n2 cos θ2


ts12 =

2n1 cos θ1


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.



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.



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

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0.4

0.5

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0.7

0.8

0.9

1



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].



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


om calibration and thin metal film theory

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