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Eects of column density on I2 spectroscopy and a
determination of I2 absorption cross section at 500 nm
P. Spietz, J. Gómez Martín, J. P. Burrows
To cite this version:
P. Spietz, J. Gómez Martín, J. P. Burrows. Eects of column density on I2 spectroscopy and a
determination of I2 absorption cross section at 500 nm. Atmospheric Chemistry and Physics, European
Geosciences Union, 2006, 6 (8), pp.2177-2191. �hal-00295944�
Atmos. Chem. Phys., 6, 2177–2191, 2006
www.atmos-chem-phys.net/6/2177/2006/
© Author(s) 2006. This work is licensed
under a Creative Commons License.
Atmospheric
Chemistry
and Physics
Effects of column density on I
2
spectroscopy and a determination of
I
2
absorption cross section at 500 nm
P. Spietz, J. G
´
omez Mart
´
ın, and J. P. Burrows
Institute of Environmental Physics (IUP), University of Bremen
Received: 15 March 2005 – Published in Atmos. Chem. Phys. Discuss.: 22 July 2005
Revised: 16 December 2005 – Accepted: 24 March 2006 – Published: 20 June 2006
Abstract. The use of ro-vibronic spectra of I
2
in the re-
gion of 543 nm to 578 nm as reference spectra for atmo-
spheric Differential Optical Absorption Spectroscopy is stud-
ied. It is shown that the retrieval of atmospheric col-
umn densities with Differential Optical Absorption Spec-
troscopy set-ups at FWHM at and above 1 nm depends crit-
ically on the column density, under which the used refer-
ence spectrum was recorded. Systematic overestimation of
the comparatively low atmospheric column density of I
2
of
the order of 13% is possible. Under low pressure condi-
tions relevant in laboratory studies, the systematic devia-
tions may grow up to 45%. To avoid such effects with
respect to field measurements, new reference spectra of
I
2
were determined under column density of the order of
10
16
cm
−2
close to that expected for an atmospheric mea-
surement. Two typical configurations of Differential Opti-
cal Absorption Spectroscopy, which use grating spectrome-
ters, were chosen for the spectroscopic set-up. One spec-
trum was recorded at similar resolution (0.25 nm FWHM)
but finer binning (0.035 nm/pixel) than previously published
data. For the other (0.59 nm FWHM, 0.154 nm/pixel) no
previously published spectra exist. Wavelength calibration
is accurate to ±0.04 nm and ±0.11 nm respectively. The
absorption cross section for the recordings was determined
under low column density with an accuracy of ±4% and
±3% respectively. The absolute absorption cross section
of I
2
at 500 nm (wavelength: in standard air) in the con-
tinuum absorption region was determined using a method
independent of iodine vapour pressure. Obtained was
σ
I
2
(500 nm)=(2.186±0.021)·10
−18
cm
2
in very good agree-
ment with previously published results, but at 50% smaller
uncertainty. From this and previously published results a
weighted average of σ
I
2
(500 nm)=(2.191±0.02)·10
−18
cm
2
is
determined.
Correspondence to: P. Spietz
(peterspietz@iup.physik.uni-bremen.de)
1 Introduction
Descriptions of resolution related issues in the ro-vibronic
spectrum of I
2
have been reported frequently in the past.
Vogt and Koenigsberger (1923) studied the extinction co-
efficient of iodine vapour in the visible and infrared. They
observed strong variation of extinction with temperature, I
2
concentration
1
and foreign gas pressure and reported a clear
non-linear behaviour of extinction with respect to concen-
tration – i.e. a deviation from Beer-Lambert’s law. Rabi-
nowitch and Wood (1936) determined the transition region
between the continuous part of the spectrum below 500nm
and the structured part above 500 nm by varying foreign
gas pressure. This left the continuous part of the spec-
trum unchanged while the structured part changed its ap-
parent extinction significantly. They distinguished clearly
between changes due to unresolved rotational lines and ef-
fects caused by pressure induced line broadening. Kort
¨
um
and Friedmann (1947) recorded the banded region at mod-
erate resolution, relating the observed structure also to the
unresolved rotational lines. They also distinguished between
pressure induced and concentration induced changes in ob-
served extinction. Ogryzlo and Thomas (1965) proved that
the observed pressure dependence of the I
2
absorption spec-
trum above 500 nm indeed results from pressure broaden-
ing of the rotational lines. Tellinghuisen (1973) thoroughly
studied the extinction coefficient of I
2
in the visible and
NIR under low resolution and resolved the observed spec-
trum into three transitions A(
3
5
1u
)←X(
1
6
0g+
), C(
1
5
1u
)←
X(
1
6
0g+
), and B(
3
5
0u+
)← X(
1
6
0g+
) (see Gray et al., 2001
for labelling of transitions). Today the ro-vibronic spectrum
of I
2
is well documented by high-resolution measurements
1
In some publications the misleading wording “pressure depen-
dence of the I
2
spectrum” was used when relating to I
2
concentra-
tion. In the absence of bath gas, [I
2
] was varied by varying tempera-
ture and thereby vapour pressure. This should not be mixed up with
“pressure dependence” resulting from the presence of a foreign gas.
Published by Copernicus GmbH on behalf of the European Geosciences Union.
2178 P. Spietz et al.: Effects of column density on I
2
spectroscopy
(Gerstenkorn and Luc 1977a, 1977b, 1978, Gerstenkorn et
al., 1982, Kato et al., 2000) and I
2
absorption lines are used
as easily accessible wavelength calibration standards (e.g.
Marcy and Butler 1992).
But quantitative spectroscopy of I
2
in the said region and
under low resolution conditions is still difficult. Because of
unresolved ro-vibronic structure each low-resolution spec-
troscopic measurement is dominated by instrumental arte-
facts. Under such conditions optical density (OD) is not
linear in concentration, when calculated by applying Beer-
Lambert’s law directly to detector outputs, as in that case the
Beer-Lambert’s law is applied to arguments, which are not
monochromatic intensities (to which the Beer-Lambert law
applies), but to convoluted quantities originating from inten-
sities at different wavelengths. Quantitative spectroscopy,
which uses low-resolution laboratory spectra of I
2
as ref-
erence data, is limited if not impeded by this. Interest in
reference spectra of I
2
covering the ro-vibronic region arose
(Saiz-Lopez et al., 2004) after the observation of consider-
able amounts of I
2
in Differential Optical Absorption Spec-
troscopy measurements (DOAS, see e.g. Perner and Platt
(1979), Finlayson-Pitts and Pitts (2000) and Solomon et al.
(1987) on zenith sky absorption measurements) in the marine
boundary layer at Mace Head, Ireland (Saiz-Lopez and Plane
2004).
With respect to the absorption cross section of I
2
at
500 nm, i.e. outside the ro-vibronic region, a number of stud-
ies had been performed in the past. The first determination
of the extinction coefficient of I
2
was published by Vogt and
Koenigsberger (1923). Other studies followed by Rabinow-
itch and Wood (1935), Kort
¨
um and Friedheim (1947), Sulzer
and Wieland (1952), and Tellinghuisen (1973) establishing
the latter’s result of σ
I
2
(500 nm)=(2.20±0.07)10
−18
cm
2
as
the most reliable one. Absorption cross section in this con-
text and throughout this text is defined as a molecular quan-
tity of cm
2
per molecule (SI units: cm
2
). The recent obser-
vation of I
2
in the marine boundary layer by Saiz-Lopez and
Plane initiated further studies on the absorption cross section.
Studies by Saiz-Lopez et al. (2004) as well as previously un-
published results by Bauer et al. (2004) followed yielding
(2.29±0.27) 10
−18
cm
2
and (2.25±0.09) 10
−18
cm
2
respec-
tively. In recent laboratory studies on the determination of
absorption cross sections of iodine oxides as well as related
kinetics studies (e.g. EU Framework 5 Program THALOZ)
the knowledge of the absorption cross section of I
2
is an im-
portant prerequisite to any quantitative analysis adding fur-
ther to the newly increased interest in I
2
.
Both issues, quantitative spectroscopy for DOAS with typ-
ical low resolution and the absolute absorption cross section
of I
2
at 500 nm are being addressed in this work.
2 Reference spectra of I
2
or DOAS
Due to the measurement process performed with a moder-
ately resolving spectrometer and a semi-conductor detector
array, any measurement of unresolved rotational lines will be
dominated by instrumental artefacts. One reason for this is
the unresolved irregular distribution and mixing of strongly
absorbing and absorption free spectral sections within the
low-resolution recording. The instrumental artefacts will be
a non-linear function of column density (the product of ge-
ometric path length and concentration). Likewise such mea-
surements are prone to contain saturated rotational lines, i.e.
lines which are too strong to allow any measurable inten-
sity to pass at their specific wavelength. This is especially
true of laboratory measurements in which it is tempting to
use optical densities of the order of 0.5 to 1.0 to improve the
signal to noise ratio. Already at I
2
vapour pressure (room
temperature) and a path length of 10 cm a large number of
I
2
rotational lines between 510 nm and 560 nm are at optical
densities above 3. If the Beer-Lambert law is directly applied
to the detector output of measured intensities, an apparent
optical density A
app
will be obtained, which is not linear in
concentration. Fig. 1a shows two spectra recorded at signif-
icantly different column densities under otherwise constant
conditions. Resolution was low and rotational lines were far
from being resolved. In the continuum range below 500 nm
the low column density spectrum is scaled to the high col-
umn density one. In the ro-vibrational region the apparent
optical density A
app
clearly grows sub-linearly with column
density. Opposed to that optical density at and below 500 nm
is continuous and therefore perfectly linear in column den-
sity. In the following Sect. 2.1 firstly the effect of resolu-
tion and binning on low-resolution recordings of the I
2
ro-
vibronic spectrum will be studied. As a consequence from
the findings in the simulation section new reference spectra
for I
2
were recorded to be used in atmospheric DOAS re-
trieval. The experiments and the analysis leading to these
new reference spectra are presented in Sect. 2.2.
2.1 Simulations
Spectra were simulated based on a high-resolution spec-
trum of I
2
obtained with a Fourier Transform Spectrometer
(FTS), courtesy of Marcy and Butler (1992). Conditions for
this high-resolution spectrum are specified as signal to noise
S/N=1000, resolution λ/1λ=400 000 (≈0.04cm
−1
), [I
2
] at
vapour pressure (room temperature) without bath gas and
10 cm optical path. A section of this spectrum is shown
in Fig. 1b. Clearly a considerable number of lines already
reaches OD of the order of 2 to 3. In the lack of other high-
resolution data recorded under lower OD and given the large
signal to noise ratio of that measurement, this spectrum was
nevertheless used as the ”true” spectrum in our simulations.
The spectrum was convoluted with a 0.3 cm
−1
Lorentz pro-
file to simulate atmospheric pressure broadening (estimate
Atmos. Chem. Phys., 6, 2177–2191, 2006 www.atmos-chem-phys.net/6/2177/2006/
P. Spietz et al.: Effects of column density on I
2
spectroscopy 2179
480 500 520 540 560 580 600 620 640 660
0,1
0,2
0,3
0,4
0,5
L*[I
2
] ≈
≈≈
≈ 1.1*10
16
molec/cm
2
apparent optical density A
app
(λ)
vac. wavelength (nm)
scaling
region
L*[I
2
] ≈
≈≈
≈ 1.6*10
17
molec/cm
2
(OD scaled)
(a)
545,7 545,8 545,9 546,0 546,1 546,2
0
1
2
3
High-res. FTS
optical density A(λ)
vac. wavelength (nm)
p < 1mbar
p ≈
≈≈
≈ 1000mbar (conv.)
(b)
Fig. 1. (a) Two low resolution absorption spectra of I
2
were recorded at significantly different column densities. The low column density
spectrum was scaled to the other in the continuum region at λ<500 nm. In the ro-vibronic region above 500nm the high column density
measurement shows clear sub-linear growth with column density. (b) A section of the high-resolution absorption spectrum of I
2
obtained
from Fourier Transform Spectrometer measurements is shown (≈ 0.04cm
−1
), courtesy of Marcy and Butler (1992). To simulate atmospheric
pressure broadening, the spectrum was convoluted with a 0.3cm
−1
Lorentz profile (bold line).
www.atmos-chem-phys.net/6/2177/2006/ Atmos. Chem. Phys., 6, 2177–2191, 2006
2180 P. Spietz et al.: Effects of column density on I
2
spectroscopy
Table 1. Spectra were simulated for different spectroscopic configurations. The effect on 1σ
app
is based on an atmospheric column density
≈4.6·10
15
cm
−2
and a reference spectrum recorded at ≈4.6·10
17
cm
−2
. Atmospheric column density would be overestimated by up to 13%.
Configurations A, C, and D are typical atmospheric DOAS configurations. Especially the results for A and B indicate that not binning
(measured as FWHM/1λ) but resolution (FWHM) is the major source of this effect.
config. grating
[grves·mm
−1
]
1λ
[nm/pixel]
FWHM
[nm]
FWHM/1λ
[pixel]
effect on
1σ
app
reference
A 1200 0.035 0.175
(0.25)
5
(7.1)
−2% Saiz-Lopez & Plane (2004)
this work
B 600 0.077 0.35 4.5 −5%
C 600 0.077 1.0 13.0 −12% Aliwell & Jones (1997)
D 300 0.154 1.3 8.4 −13% Richter (1997)
based on comparable air broadened half width in Rothman et
al., 2004). This curve is also shown in Fig. 1b. An FTS
recording of a Xenon lamp obtained at 2cm
−1
resolution
was interpolated onto the grid of the I
2
spectrum to be used
as the reference intensity I
0
(λ). With these three data sets
low resolution and coarsely binned apparent optical densities
A
app
were then simulated under different spectroscopic con-
ditions defined by different FWHM of the (gaussian shaped)
instrument’s function, different linear dispersion and differ-
ent spectral width of the detectors pixels. Spectroscopic
conditions were chosen such that they also cover spectro-
scopic configurations of currently used DOAS instruments
(Roscoe et al., 1999 and references therein), see Table 1.
The high-resolution I
2
absorption spectra (low pressure and
pressure broadened) were scaled to different amplitudes sim-
ulating differently strong true optical densities A
i
(λ). The
change in peak height caused by pressure broadening was
taken into account. Thereby quantitative comparability was
maintained. Applying the Beer-Lambert law, the different
absorption measurements I
i
(λ) were simulated:
I
i
(
λ
)
=I
0
(
λ
)
· exp
[
−A
i
(
λ
)]
(1)
Limited spectral resolution was simulated by convoluting
both I
i
(λ) and I
0
(λ) with a gaussian shaped instrument’s
characteristic function S(λ). The resulting I
c,i
(λ) and I
c,0
(λ)
were then binned (numerically integrated) onto a grid of pix-
els of fixed size (continuous λ → discrete j) and from the
binned signals I
c,i
(j) and I
c,0
(j) an apparent optical density
A
app,i
(j) was calculated:
A
app,i
(
j
)
=ln
I
c,0
(
j
)
I
c,i
(
j
)
=
ln
λ
j+1
R
λ
j
+∞
R
−∞
S(u)·I
0
(
λ − u
)
du · dλ
λ
j+1
R
λ
j
+∞
R
−∞
S(u)·I
0
(
λ − u
)
· exp
(
-A
i
(λ-u)
)
du · dλ
(2)
This use of apparent optical density is the same as in the
study by Tellinghuisen (1973), who tackled the problem in
terms of apparent extinction. The peak amplitude of true op-
tical density A
i
(λ) was varied such that it covered a range
of column densities from ≈1.8·10
15
cm
−2
to 6.4·10
17
cm
−2
relevant for field (low end, compare Saiz-Lopez and Plane
2004) and lab (high end). For comparison, room temperature
saturated vapour pressure of I
2
at 50cm path length produces
a column density of the order of 5·10
17
cm
−2
.
3 Results from simulated data
The comparison of the simulated spectra shows that the pres-
sure broadened spectra grow faster in apparent OD than do
the low pressure spectra, perfectly in line with the obser-
vations of e.g. Rabinowitch and Wood (1935). The faster
increase is caused by redistribution of absorption from the
line centres to the gaps between lines, compare Fig. 1b. The
same as for apparent OD as such is also true for the am-
plitude of differential structures in the apparent OD spec-
trum, see Figs. 2a and b. To detect any non-linear behaviour
of apparent OD with respect to column density (i.e. the
product of concentration and path length), one can either
plot apparent OD at a selected wavelength against column
density as independent variable. Or one normalises appar-
ent OD to column density and checks, whether the result,
i.e. apparent absorption cross section, is constant. Both
types of representation will be used below. As DOAS re-
lies upon differential spectra of apparent OD – designated
by 1A
app
(λ) –, these were extracted by subtracting a suit-
able slowly varying polynomial from A
app
(λ) and then nor-
malising the resulting 1A
app
(λ) to column density to ob-
tain differential cross section 1σ
app
(λ). In the absence
of non-linear effects the differential cross section 1σ (λ)
would be independent of column density. But as non-
linear effects can not be neglected, 1σ
app
(λ) is not inde-
pendent of column density and has therefore to be consid-
ered as an apparent quantity. The results for a selected band
(546 nm) and two different pressures are shown in Fig. 2a
Atmos. Chem. Phys., 6, 2177–2191, 2006 www.atmos-chem-phys.net/6/2177/2006/
