a calibration code based on optical method for the jet polarimeter

P. Gaudio 1 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012

A calibration code based on optical method for the JET Polarimeter P. Gaudio1, M. Gelfusa1, A. Murari2, A. Boboc3, M. Brombin2, F.P. Orsitto4, E. Giovannozzi4 and

JET EFDA Contributors*

1 Associazione EURATOM-ENEA - University of Rome “Tor Vergata” , 2 Consorzio RFX Associazione EURATOM-ENEA per la Fusione3 EURATOM/CCFE Fusion Association, Culham Science Centre4 Associazione EURATOM-ENEA – CR. ENEA Frascati

*See the Appendix of F. Romanelli et al., Fusion Energy Conference 2008 (Proc. 22nd Int. FEC Geneva, 2008) IAEA, (2008)

Frascati – Italy - 26-28 March 2012Frascati – Italy - 26-28 March 2012


Outline

• Polarimetry measurements– Description of measurements– Polarimeter setup

• Current calibration– Hardware Calibration procedure– Why a calibration is needed?– Why a new calibration procedure is needed?

• New Calibration optical method based– Ideas of use ray tracing method to reproduce laser

beam path– Optical scheme

• Some results and comparison


Polarimetry measurements

• Measurements are based on polarization laser beam that crosses a magnetised plasma area

• Two effects are observed:– A change of polarization of the laser beam known

as Faraday effect described by follow equation

– A change of ellipticity of the laser beam know as Phase shift effet described by the following equation

dzBne 2

dzBne 23


Polarimeter Set-up

Laser DCN

λ= 195 μm

Phase sensitiveanalog electronics

Gs

Gai

n co

ntro

lled

ampl

ifier

Gs

Gai

n co

ntro

lled

ampl

ifier

PLASMA

GratingWheel

Wire Grid(WG1)

HWP1

H - detector

V - detectorp(t)

100kHz beat signal

i(t)

100kHz beat signal

HWP2

Beam splitter

Recombinationplate

DieletricWaveguide

Mirror

Mirror

Freq

uenc

y of l

ight

incr

ease

d by

ω=1

00 k

Hz

Wire Grid(WG2)

BPF(80-120 kHz)

BPF(80-120 kHz)

RMSRMPPSDPSP

Wire Grid(WG3)

Pre-amplifier

Pre-amplifier

tEtEtp yy 00

0 cossincos

tEtEti xx 00

0 coscoscos

i’(t) ≈ Ex,0 sin (ωt) is generated by phase shifting i(t)

RMS = < i(t) x i(t) > PSD = < p(t) x i(t) >

RMP = < i’(t) x i’(t) > PSP = < p(t) x i’(t) >

RMSPSD

RRMPRMS

PSPR

'

RR

arctg'

'RRCarctg 2


Hardware Calibration procedure

Faraday

Deg

rees

Time (s)D

egre

esTime (s)

Phase Shift

• Currently, the procedure of calibration is the following:– the half-wave plate, located at the entrance of the vacuum vessel, is

rotated (via a step-motor) of a well-known angle () and the phase shift () is recorded at each angle, while the Faraday rotation (2) is equal to twice the half-wave plate angle.

Current calibration code fit the phase shift data at the aim to determinate the “spurious ellipticity angle to use for to interpreter experimental data.

Laser DCN

λ= 195 μm

Phase sensitiveanalog electronics

Gs

Gai

n co

ntro

lled

ampl

ifier

Gs

Gai

n co

ntro

lled

ampl

ifier

PLASMA

GratingWheel

Wire Grid(WG1)

HWP1

H - detector

V - detectorp(t)

100kHz beat signal

i(t)

100kHz beat signal

HWP2

Beam splitter

Recombinationplate

DieletricWaveguide

Mirror

Mirror

Freq

uenc

y of l

ight

incr

ease

d by

ω=1

00 k

Hz

Wire Grid(WG2)

BPF(80-120 kHz)

BPF(80-120 kHz)

RMSRMPPSDPSP

Wire Grid(WG3)

Pre-amplifier

Pre-amplifier


Current calibration

• Why a calibration is needed?– Polarimeter measurements are affected by:

• “Spurious phase shift” induced by not well identified optical component along laser path. Then a calibration procedure is needed at the aim to evaluate this effect and take it in account in final result of polarimetry measurements

• What are the problem?:– Current calibration is not able to determinate fit

parameter for every JET operation regime– Current calibration algorithm does not separate the

optical and the electronics effect• How to resolve the problem?

– To analyzed and check electronic components– To simulate the laser beam path through a series of

optical components which are represented with a matrix formalism.


Electronics bench testThe tests to check the reliability of the electronic cards used on polarimetry have mainly consisted on acquiring the raw data after the detectors, process them via software (Simulink/Matlab) and then compare the obtained outputs with the ones given by from the polarimeter electronics.

Gaudio P.. et al., Modelling of the signal processing electronics of JET interferometer-polarimeter, NIMA 623, 660-663, 2010


Laser DCN

λ= 195 μm

PLASMA

HWP1

H - detector

V - detector

Wire Grid

Retarder 1

Retarder 2

1000

0220

0220

0001

cossin

sincos

M

11

11

00

00

0010

0001

1

cossin

sincos

M

New Calibration code

22 22 RMRM'

1000

0220

0220

0001

11

111

cossin

sincos

R

yx

yx

yxyx

yxyx

xT

pp

pp

pppp

pppp

pM

2000

0200

00

002222

2222

2

yx

yx

yxyx

yxyx

yR

pp

pp

pppp

pppp

pM

2000

0200

00

002222

2222

2

WGxp cos WGyp sin

11 11 RMRM'

shiftphase1 retarderangle1


New calibration code

After the analyser, the laser beam is divided in two parts and the corresponding Stokes vectors are given by:

01 12SMMMMS TT

''

,

01 12SMMMMS RR

''

,

Therefore, it is possible to know the polarisation angle and the phase shift, given by:

2

3

SS

arctag

1

2

2

1

SS

arctag

Gaudio P.. et al., New calibration code for JET polarimeter, RSI, 81, 053507 (2010)

Overall the code depends on five adjustable parameters: .

To estimate these parameters an optimization routine has been written. The routine finds the values of

these five quantities which allow to best fit the calibration curves.

1 1 2 2 WGand


New calibration code: results

Calibration curveCalibration

Shot: 67677 chord #3

Using the better fit, the five adjustable parameters

are found!


Deg

rees

Black line: HWP

Red line : New Cal

Time (s)

Faraday

Theta (Degrees)

Deg

rees

Black diamond: New cal

Red Asterisk : Raw data

Phase Shift

Time (s)

Faraday

Rad

ian

s

Time (s)

Phase Shift

Deg

rees

Legend:Blue line: New calibration

Red line: PPF signalGreen asterisk: Stokes Model

1 1 2 2 WGand

In the plot Green spots represent numerical

simulation of full propagation code based on Stokes model


New calibration code: results



Faraday Phase Shift

Faraday Phase Shift

Rad

ian

sR

adia

ns

Time (s) Time (s)

Time (s) Time (s)D

egre

esD

egre

es




Alcoholλ= 119 μm

Laser DCN

λ= 195 μm

PLASMA

BS

BS

BS

RPBS

MM

MM

M

M

M

M

MM

M

WG2

M

WG1

HWP

HWP

HWP

GW

GW

5kHz

100kHz

M

V – detector

p(t)

H – detectori(t)

LEGEND

M : MirrorHWP: Half –Wave Plate

BS : Beam SplitterRP : Recombination Plate

GW : Grating Wheel

BS

Polarimeter scheme: lateral channels

1000

0220

0220

0001

cossin

sincos

M

180


New calibration code: lateral chords



Rad

ian

sR

adia

ns

Faraday

Faraday

Phase Shift

Phase Shift

Time (s)Time (s)

Time (s) Time (s)

Deg

rees

Deg

rees

Rad

ian

sR

adia

ns




Conclusions

JET polarimeter has been analyzed to understand and to solve the problems posed by the spurious ellipticity induced by the instrument optical components.

A simulator has been developed to verify the proper operation of the signal processing electronics. The analysis shows a good agreement between the simulation outputs and the experimental data.

A new calibration code has been written and tested for many shots acquired in different campaigns. The experimental data, calibrated with this code, has been compared with the rigorous numerical solution of the Stokes equations.

The developed model for the calibration is valid for all configurations of the diagnostic (any operation regime at JET).

a calibration code based on optical method for the jet polarimeter

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