IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Modelling of spectral line shapes in electrodeless discharge lamps
G. Revalde1, N. Denisova2, A.Skudra1
1 High-resolution spectroscopy and light source technology laboratory, Institute of Atomic Physics and Spectroscopy, University of Latvia2 Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia
E-mail: [email protected]: http://www.atomic-physics.lv
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Electrodeless lamps:
Bright radiators in the broad spectral range (VUV - IR);
Filled with a gas or metal vapor+buffer gas;
No electrodes – long working life
Inductive coupled/ capacitatively coupled;
Hf, Rf Electromagnetic field excitation;
Different designs and types in dependence on application
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Our experience and technology:
manufacturing of electrodeless lamps containing such elements as Sn, Cd, Hg, Zn, Pb, As, Sb, Bi, Fe, Tl, In, Se, Te, Rb, Cs, I2, H2, He, Ne, Ar, Kr, Xe as well as combined Hg-Cd, Hg-Zn, Hg-Cd-Zn, Se-Te etc (also isotope fillings, as example Hg202) etc.
for different applications
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Examples
300 400 500 600 7000
1000
2000
3000
4000
Inte
nsity
, rel
. un.
Wavelength, nm
He
200 300 400 500 600 700 8000
1000
2000
3000
4000
Inte
nsity
, rel
. un.
Wavelength, nm
Hg
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Spectral line profile is important
• to control self-absorption or radiation trapping for design consideration of low pressure lamps for lighting
application - resonance radiation of Hg at 185 nm and 254 nm
in all cases when narrow spectral line is necessary – for atomic absorption, optical pumping, quantum standards, for spectral reference
• to get important plasma parameters (such as gas temperature, lower state density, collisional broadening)
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Example of atomic absorption spectrometry
• Narrow, not self-absorbed spectral line is neccessary -- >
to get high differential cross section of atomic absorption --> low limits of detection
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
• But with self-absorption dependent on– working regime– filling pressure,– filling content– lamp geometry– excitation geometry
Possibilty to avoid the self-absorption – optimisation of all parameters
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Capillary
Lamp
Capillary
Monochromator
Power supply
Fabry – Perrot interferometerPhotomultiplierComputer
LensLens
Vacuum chamberAmplifier
Line profile measurements
High-resolution scanning Fabry-Perrot interferometer
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
High-resolution scanning Zeeman spectrometer for resonance lines
Hme
c
41
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Hg 253,7 nm• Natural filling Hg 202 isotope
In dependence on the Tcold spot
On the working regime
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Line shape modeling
Observed spectral line profile: f x f x y f y dy x( ) `̀ ( ) (̀ ) ( )
,
where f ’(x) - real profile, f’’(x) - instrumental function, (x) - function characterising random errors. Task –to get real spectral line profile and parameters characterising plasma by means of a quite universal program for spectral line shape fitting. Model include:
1)
G I
T
G
G
( ) exp ln
,
0 00
2
7
4 2
7 16 10 1
; Gaussian shape
2) L L
L
( )
0
02 24
,
where L =nat+coll+res. Lorentzian shape
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
3) Voigt profile
V a a y dya y
( , ) exp( )( )
2
2 2 , where yG
( ) ln 2 ,
aL
G
ln 2 ,
2 20( ) ln G
4) self-absorption drdxxnxvPsrvPrnIvIr
aaee
)(),(exp),()()( 0
, where ;)()(a
aa N
rnrn e
ee N
rnn )(
; N n r dra a
12
( ) ; N n r dre e
( ) , We can assume )(),(),( vPlvPlvP ae ,
drdxxnwPwP
srnwPIvIr
ae
)()()(
exp)()()(0
0
Excitation function E yn rn r
e
a
( )( )( )
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
;)()(2
)(
1
n
raae dxxnrnnrn E y
n y y
ny y
n
n( )
,
( ) ,
20 1
22 1 2
1
1 , y n x dxar
( ) - relative
number of atoms capable of absorbing the line present per unit cross-section between the point under consideration and the outside of the source
1) )0()(;
!2!)()( 0
0
2
0 PPlk
njnePII
j
j
(Cowan and Dieke)
n Z , P()V() by a=const, k0l - optical density
2) , if n=1 homogenous radiation source
II P
k lk l P
P( )
( )exp ( )
( )
0
002
10
3) if n completely inhomogeneous radiation source
I I P k l PP
( ) ( )exp ( )( )
0 0 0 ,
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
5) Manifold of HFS and isotope components having intensities I1, I2,,...,Ik
and respective shifts 1 2.. k 6) Convolution of the self-absorbed Voigt profile with an instrument function
a) for Fabry-Perrot I IRR
0
22
1
1 41 2( )
sin,
2
, - opt. diff. of
interfering rays, R- effective refraction coefficient b) absorption profile (Gaussian or Voigt) for Zeeman spectrometer c) numerical or other
7) Generation of random errors (x).
8) Fitting of the modelled function to the experimental using
2
1
2
N
ii criterion
by means of multi-parameter fitting procedure, where ii
i iyy f x
1
( ) are
deviations of the experimental data yi from the theoretical values f(xi) at the position of xi, weighted by the experimental errors yi . 9) Results G (gas temperature), L, (collisions), k0l (nlower), n, instrum, and intensities and shifts
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Zeeman spectrometer Fabry-Perrot spectrometer
Necessity to take into account the instrument function, also by a small FWHM value of instrument profile due to the influence on the self-reversal
Examples of experimental and modeled profiles
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,0
0,2
0,4
0,6
0,8
1,0
Inte
nisi
ty, r
el. u
n.
Wavenumber, cm-1
Experimental Theoretical Real
Hg202+Ar
253.7 nm,i=160 mA,without cooling
0,0 0,2 0,4 0,6 0,8 1,00,0
0,2
0,4
0,6
0,8
1,0
Inte
nisi
ty, r
el. u
n.Wavenumber, cm-1
Experimental Calculated Real
Hg202+Ar, 10 Torr253.7 nm
i=160 mAt=45oC
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
0,0
0,2
0,4
0,6
0,8
1,0
Inte
nsity
, re.
un.
Wavenumber, cm-1
Experimental Theoretical Real
Hg202 - 90% +Ar (2 Torr)253.7 nm,i=140 mAwithout thermostabilisation
Optical density 6.8
dopl = 0,044 cm-1(T=488 K)Reff= 0,84%
Hg202/Ar(2 Torr) experimental and modeled profiles of 253.7 nm line, spherical discharge
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
160 mA, Tc.spot.=72oC
50 mA, Tc.spot.=72oC
Example, Hg 202 (99.8 %) 253,7 nm line
Distribution of the intensitites other isotopic components (0.2 %) also fitted
0,0 0,2 0,4 0,6 0,8 1,0
0,0
0,2
0,4
0,6
0,8
1,0
model experimental real
Inte
nsity
, arb
.un.
Wavenumber, cm-1
0,0 0,2 0,4 0,6 0,8 1,0-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
Inte
nsity
, rel
. un.
Wavenumber, cm-1
experimental model real
20 30 40 50 60 70 800
50
100
150
200
160 mA
50 mA
Opt
ical
den
sity
, k0l
Temperature, oC
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Hg202/Ar capillary
0,0 0,2 0,4 0,6 0,8 1,0
0
5
10
15
20
25
25oC 45oC
Inte
nisi
ty, r
el.u
n.
Wavenumber, cm-1
253. 7 nm
Hg202+Ar, capillary, 10 Torri=160 mA
65oC
0,0 0,5 1,0 1,5 2,0
0,0
0,2
0,4
0,6
0,8
1,0
Inte
nsity
, rel
. un.
Wavenumber, cm-1
experimental theoretical real
Hg 202 +Ar 10 Torr
20 25 30 35 40 45 50 55 60 65 70 75 80
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
160 mA 100 mA
Opt
ical
den
sity
Cold spot temperature, oC
Experiment
Reff = 0,8% (ninstr =0,071 cm-1).
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Hg202/Ar (10 Torr) capillary, 253.7 nm line, Tcold spot= 25oC
80 90 100 110 120 130 140 150 160 170360
380
400
420
440
460
480
500
520
540
560
580
600
620
HF generator current, mA
Tem
pera
ture
, K
80 90 100 110 120 130 140 150 160 1700,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
Opt
ical
den
sity
80 90 100 110 120 130 140 150 160 1700,116
0,118
0,120
0,122
0,124
0,126
0,128
0,130
0,132
Tota
l FW
HM
, cm
-1
The estimated optical density in the line center
The total experimental spectral line FWHM as a function of the HF generator current
The estimated temperature of the emitting atoms
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Hg202/Ar (2 Torr) capillary, 253.7 nm line, Tcold spot= 65oC
80 100 120 140 160 180 2003
4
5
6
7
8
9
10
11
12
13
14
Opt
ical
den
sity
HF generator current, mA
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Comparison- spherical and capillary
0,6 0,8 1,0 1,2 1,4
0,0
0,2
0,4
0,6
0,8
1,0
Inte
nsity
, rel
.un.
Wavenumber, cm-1
spherical capillary
160 mA and T cold spot =25oC, pAr=10 Torr
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Hg visible triplett
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,350,0
0,2
0,4
0,6
0,8
1,0
Inte
nsity
, rel
.un.
Wavenumber, cm-1
40 mA 100 mA 140 mA
404.7 nm
Experimental 404.7 nm line shapes in dependence on the HF generator current for a HF isotope electrodeless lamp
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35
0,0
0,2
0,4
0,6
0,8
1,0
Inte
nsity
, rel
. un.
Wavenumber, cm-1
experimental theoretical real
404.7 nm, Hg
Example of the line shape fitting of Hg 404.7 nm line, HF generator current i=100 mA. Fitted parameters wG=0,032 cm-1; wL=0,002 cm-1; R=0,72, kol=1,8, n=13, using the model of Cowan and Dieke
40 60 80 100 120 140
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
300
400
500
600
700
800
900
1000
Opt
ical
den
sity
HF generator current, mA
Temperature, oC
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Experimental radial distributions of Hg 404.7 nm line intensity, emitted from HF electrodeless lamp by two different discharge power values.
-1,0 -0,5 0,0 0,5 1,0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
220000
240000
260000
Inte
nsity
, rel
. un.
r/r0
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35
0,0
0,2
0,4
0,6
0,8
1,0
In
tens
ity, r
el.u
n.
Wavenumber, cm-1
experimental theoretical real
546.1 nm, Hg
Example of the line shape fitting of 546.1 nm Hg line, i=140 mA. Fitted parameters wG=0,033 cm-1; wL=0,002 cm-1; R=0,8; kol=35; with taking into account the measured distributions.
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Helium example
Optical density in the line center in dependence on the HF generator current estimated for 501,6 nm and 567,8 nm lines in the helium electrodeless discharge using the model of uniformly excited source.
80 100 120 140 160 180
0,5
0,6
0,7
0,8
0,9
Opt
ical
den
sity
Generator current, mA
501,6 nm 567,8 nm
0 1 2
1
2
3
4
5
6
Inte
nsity
, rel
.un.
Radiuss, cm
28,0 W58,3 W
587.6 nm He
Experimental radial distributions of He 587,6 nm line intensity, emitted from helium HF electrodeless lamp by two different discharge power values.
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
Thank you for your attention!
IAPS,University of Latvia
COST 529, April 12-16, Madeira, Portugal
0 50 100 150 200 250
1E-3
0.01
0.1
1
10
100
pHg,
torr
Tcold spot, oC
p Hg vapor, Torr