IAPS, University of Latvia COST 529, April 12-16, Madeira, Portugal Modelling of spectral line shapes in electrodeless discharge lamps G. Revalde 1 , N. Denisova 2 , A.Skudra 1 1 High-resolution spectroscopy and light source technology laboratory, Institute of Atomic Physics and Spectroscopy, University of Latvia 2 Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia E-mail: [email protected]Web: http://www.atomic-physics.lv
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Modelling of spectral line shapes in electrodeless discharge lamps
Modelling of spectral line shapes in electrodeless discharge lamps. G. Revalde 1 , N. Denisova 2 , A.Skudra 1 1 High-resolution spectroscopy and light source technology laboratory, Institute of Atomic Physics and Spectroscopy, University of Latvia - PowerPoint PPT Presentation
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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
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
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
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.