A Characterisation of the Wavelength Modulated Diode Laser Absorption Spectrometry Technique in Graphite Furnace

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Part  A: A Description of the 
Wavelength Modulated Diode 
Laser Absorption Spectrometry 
Technique in Graphite Furnace 
(WM – DLAS – GF) 
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2. Properties and Performances of the WM 
– DLAS – GF Technique 
The ability to detect trace elements in gas phase using laser spectro-
scopic techniques can often be increased using various modulation tech-
niques [1, 2]. The general approach is to modulate the laser light frequency 
(or wavelength) before the beam interacts with the atoms. The analytical 
signal is then extracted from the modulated detector signal with a suitable 
technique, usually using a lock-in. This modulation process reduces greatly 
the noise by moving the detection to higher frequencies. The modulation has 
also the advantage that it removes the constant and linear part of the 
background. 
The wavelength modulated (WM) spectroscopy is the most used tech-
nique to increase the ability to detect trace elements by means of absorption 
[1]. The most common procedure is to detect at 2f, that is to modulate the 
laser wavelength at the frequency f
m
 and then detect the light absorption 
using a lock in whose reference signal has double frequency, 2f
m 
[3]. 
Sensitivities of 10
-4
-10
-5
 (relative absorption) have been observed [2]. 
This work constitutes of a part of the general development of the WM – 
DLAS – GF technique for detection of trace concentrations and trace 
amounts of species in liquid or solid samples, performed in the Laser 
Physics Group at Umeå University 
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3. Experimental Apparatus 
In addition to a high sensitivity, so as to allow the detection of analytes 
at very low concentrations, important requirements of modern techniques 
for trace species detection are a low cost and small dimensions. Using a 
semiconductor laser together with the wavelength modulation technique is a 
good compromise among these requirements. 
Sine
Modulation
 
Fig. 3.1 The experimental apparatus used in the WM – DLAS – GF technique 
The experimental apparatus can be divided in three parts: light genera-
tion and modulation, interaction with the sample, detection and extraction of 
the signal. We will examine here these three parts in details.  
3.1 The Laser 
A commercial laser diode is connected to a temperature and a current 
controller. The working temperature is slowly changed to reach the desired 
wavelength, and, once reached that particular temperature, is kept constant. 
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The modulation process is controlled by a lock-in amplifier. The input 
channel of the current driver is connected to the reference output of the 
lock-in amplifier, generating a sine modulation. The same lock-in is then 
used to detect the signal. A constant current value is added to this modula-
tion to determine the central (mean) working frequency. 
In the experiments, we used different diode lasers with powers between 
10 and 50 mW, working at the wavelength of 780 nm. 
3.1.1 Advantages and Disadvantages of the Laser Diode 
The advantages of using a laser light source instead of a hollow cathode 
lamp such as in traditional techniques, are well known and given in detail in 
ref. [4]. The semiconductor laser has been chosen because it is small and 
cheap, following the general requirements of modern techniques. 
Unfortunately, the semiconductor lasers have some disadvantages. First 
of all, virtually all diode lasers produce light at wavelengths above 600 nm, 
not allowing the analysis of most atoms, which have absorption lines in the 
blue or ultraviolet range of the electromagnetic spectrum. 
W
a
v
e
l
e
n
g
t
h
Current
1 nm
100 pm
 
Fig. 3.2 The wavelength as function of the input current in a semiconductor 
laser 
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1
2
3
4
Secondly, even if the atomic absorption line is in the accessible part of 
the spectrum, it is not always possible to reach it. The reason is that the laser 
wavelength response to current modulation is not continuous but shows 
some steps, due to a jump of the frequency of the laser light from one cavity 
mode to another (Fig. 3.2). This is referred as mode hops. Nevertheless, 
varying the temperature changes the frequency at which the mode hops take 
place, which thereby gives a fairly good chance of finding the desired 
wavelength. Since techniques for frequency doubling of the laser light have 
been developed in the last years and will be furthermore developed in the 
future, it should therefore be possible to detect a large variety of atoms. 
3.2 The Graphite Furnace 
Differently from other atomisers, for example flames or plasmas, the 
graphite furnace (GF) does not need a continuous flux of the sample to 
analyse, allowing the measurement of very small amounts of substance. 
We used in all the measurements a commercial model of furnace, pro-
duced by Perkin Elmer Co. termed THGA (Transversely Heated Graphite 
Atomiser) that is suitable to measure volumes between 5 and 50 µ l (Fig. 
3.3) 
By sending a high current through the contact tubes (1) and (2) the GF is 
heated by the thermoelectric 
effect. It is possible to reach 
temperature up to about 2300 °C 
before the graphite starts to 
decompose. The sample is 
introduced through the dosing 
hole (3) and put on a platform 
connected with the tube (4) 
through which the laser beam is sent. Since the atomisation takes place on 
the platform that is not directly heated by the current the sample atomises 
Fig. 3.3 The graphite furnace 
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later than without platform. This implies that the walls are hot enough to 
minimise condensation. Moreover, the furnace temperature will be stable 
simplifying the developing of a mathematical model of the absorption 
process. The furnace is pyrolitically coated to avoid memory effects that 
would affect the accuracy of the measurements working at high concentra-
tions. 
The control system uses a photo-diode to measure the temperature of the 
GF. Due to the small mass of the furnace, the temperature may change very 
quickly (Fig. 3.4).  
0
500
1000
1500
2000
2500
0 0.5 1 1.5 2 2.5 3
T
e
m
p
e
r
a
t
u
r
e
 
(
°
C
)
Time (s)
 
Fig. 3.4 Heating process of the graphite furnace 
As the graphite would burn if it would react with oxygen, the furnace is 
continuously flushed with argon. A water cooling system prevents the 
furnace from overheating. 
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3.3 Signal Detection and Elaboration 
A photo-diode located just after the furnace in the optical path of the 
laser beam converts the light to an electric signal. We used a photo-diode 
instead of others detectors because it has a linear response, it is cheap and 
small. 
The signal is then amplified and processed using a lock-in that multiplies 
it with a reference signal to extract a Fourier component, usually the second 
(2f) or the fourth (4f). 
The signal corresponding to the chosen harmonic is digitalised and 
stored in a numeric format using a PC. The same PC runs the program 
controlling the furnace. 
3.4 The Rubidium Atom 
Even if the technique discussed is suitable to analyse quantitatively sev-
eral atomic species all the measurements in this thesis are carried out on 
rubidium atoms, more exactly a mixture of 72% of 
85
Rb and 28% of 
87
Rb 
which is the natural abundance of Rb. 
The central frequency of the laser is set to excite the transition 5s
2
S
1/2
 
→  5p
2
P
3/2
 at a wavelength of 780 nm. Due to hyperfine interaction, both 
the ground and the excited level of rubidium are split into sub-levels; 
moreover, the two isotopes, having different mass, show absorption lines 
slightly shifted. Given this and applying the selection rules we end up with 
an absorption spectrum that is the convolution of 12 peaks, as is shown in 
the insert in Fig. 3.5 
Working at atmospheric pressure and high temperature the hyperfine 
structure and the isotopic shift, 1-2 GHz wide, are significantly smaller than 
the Doppler and collision broadening, 5-10 GHz wide. At atomisation 
conditions, the 12 peaks will overlap collapsing in only one, much 
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broadened and slightly asymmetric peak, as is shown by the solid line in the 
upper part of Fig. 3.5 
The harmonic signal is strongly dependent on the shape of the absorp-
tion profile. For example, the characteristic form of the 4f component, as is 
shown in Fig. 4.1 in the next section, is due to the asymmetry mentioned 
above. Changing slightly the temperature and/or the pressure may alter the 
harmonic signal shape. 
 
Fig. 3.5 Line shape of the 780 nm transition of Rb during the atomisation stage 
at 1800 °C and 1 atm (upper part), at room temperature and 10
-2
 atm (lower part), 
at low temperature and 10
-3
 atm (box). 
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4. Wavelength Modulation 
The wavelength modulation techniques are characterised by a modula-
tion frequency much smaller than the HWHM (Half Width Half Maximum) 
of the absorption profile. The signal is detected at a given harmonic, usually 
2f or 4f, using a lock-in. 
The optimal conditions for WM techniques suggest to use a modulation 
amplitude few times bigger than the HWHM of the absorption profile. That 
means that the modulation frequency, which often is in the 10 to 100 kHz 
range, is much smaller than the modulation amplitude, which in turn often is 
around a few GHz. 
4.1 General Principles of Modulation Techniques 
The WM technique is based on a modulation of the wavelength λ  of the 
laser light at a frequency f
m 
() ( )
sin 2
ca m
tftλλλ π=+ ,  (4.1)
where λ
c
 is the centre wavelength and λ
a
 is the modulation amplitude. 
Working with diode-lasers this is achieved modulating the feeding current 
of the diode. 
As is more usual to work in frequency space than in wavelength space 
the equation above may be written 
() ( )
sin 2
ca m
tftννν π=+ , (4.2) 
where ν
c
 is the centre frequency and ν
a
 is the modulation amplitude. 
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4.1.1 Time Dependent Absorption Signal 
For monochromatic light the relative absorption A may be defined 
σρ L
e
I
II
A
−
−=
−
= 1
0
0
, (4.3) 
where I
0
 and I are the laser beam intensities before and after the interaction 
with the sample, ρ  is the density of the atomic species to analyse, L the 
interaction zone length and σ  the cross section in the peak of the absorption 
profile. The term σρ L  is often named optical density (OD). 
For low optical densities, we can express the exponential in Taylor se-
ries. Working out the first two terms, we get 
σρ
σρ
Le
L
−=
−
1 . (4.4) 
The absorption can therefore be written as 
σρ L
I
II
A =
−
=
0
0
, (4.5) 
which implies that it is proportional to the density of the atomic species to 
analyse. 
Using modulation techniques, also the shape of the absorption profile is 
of importance for an evaluation of the atomic density. It is convenient to 
assign a profile shape to the cross section as 
()
()
0
0
χ
νχ
σνσ = , (4.6) 
where σ
0
 is the cross section at the profile peak, χ  (ν ) is the area-normalised 
line shape function of the species to analyse and χ
0
 its maximum value. In 
the general case χ (ν ) is a Voigt profile originating from the convolution of 
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an homogeneous Lorentzian broadening, L(ν ), and of a non-homogeneous 
Gaussian broadening, G(ν ). 
The instantaneous absorption is given by 
()
()
(
0
0
sin 2
1exp
ca m
f t
At L
χν ν π
ρσ
χ
 
+
=− −
 
 
 
, (4.7) 
which implies that the instantaneous detector signal can be written  
() ()
()
(
.. 0 0 0
0
sin 2
,1 exp
ca m
ds c
f t
St AtII L
χν ν π
νκ κ ρσ
χ
 
+
=− = −
 

 
 
, (4.8) 
where κ  is an instrumental constant relating the detected signal with the 
light hitting the photo-diode. 
4.1.2 Harmonic Signal 
The instantaneous detector signal is multiplied with a sine function, 
S
ref
(t), whose frequency is n times, being n integer, the modulation fre-
quency, i.e. where φ  is a phase constant. 
() ( )
sin 2
ref m
St nftπ φ=+. (4.9) 
By averaging the product of the detector signal and the reference signal a 
suitable time using a lock-in amplifier we get the signal for the n
th
 Fourier 
component (at frequency nf) 
() () ( ) dttStSS
csdrefc
nf
,
1
..
0
ν
τ
ν
τ
⋅=
∫
. (4.10) 
We have the freedom to choose the phase between the detector and ref-
erence signal. Many modern lock-in amplifiers have also the possibility to 
measure simultaneously the ()
nf c
S ν  signal at two different phases, often 
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separated by π /2. The terms “in phase” and “out of phase” signal, or x and y 
components, are usually used when the phase angle is 0 and π /2 respectively 
() () ()
(
..
0
1
sin 2 sin 2
nf x
cmdscam
S ftSftd
τ
νπνπ
τ
−
=⋅+
∫
 (4.11) 
() () ()
(
2
..
0
1
sin 2 sin 2
nf y
cmdscam
S ftSftd
τ
π
νπ νπ
τ
−
=+⋅+
∫
. (4.12) 
It is also possible to write the signal in complex form, i.e. with an ampli-
tude and a phase angle. The amplitude, named r component, is given by the 
expression 
() ()( ()(
22
c
ynf
c
xnf
c
rnf
SSS ννν
−−−
+= . (4.13) 
If not specified differently, the word “signal” will below be used for this 
r component of the signal, which in many situations is equal to the absolute 
value of the in-phase signal.