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Atmos. Meas. Tech., 12, 4149–4169, 2019
https://doi.org/10.5194/amt-12-4149-2019
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the Creative Commons Attribution 4.0 License.
Recent improvements of long-path DOAS measurements: impact on
accuracy and stability of short-term and automated long-term
observations
Jan-Marcus Nasse1, Philipp G. Eger1,a, Denis Pöhler1, Stefan Schmitt1, Udo Frieß1, and Ulrich Platt1
1Institute of Environmental Physics, University of Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
anow at: Max Planck Institute for Chemistry, Hahn-Meitner-Weg 1, 55128 Mainz, Germany
Correspondence: Jan-Marcus Nasse (jan.nasse@iup.uni-heidelberg.de)
Received: 20 February 2019 – Discussion started: 20 March 2019
Revised: 13 June 2019 – Accepted: 22 June 2019 – Published: 1 August 2019
Abstract. Over the last few decades, differential optical ab-
sorption spectroscopy (DOAS) has been used as a common
technique to simultaneously measure abundances of a variety
of atmospheric trace gases. Exploiting the unique differential
absorption cross section of trace-gas molecules, mixing ra-
tios can be derived by measuring the optical density along a
defined light path and by applying the Beer–Lambert law.
Active long-path (LP-DOAS) instruments can detect trace
gases along a light path of a few hundred metres up to 20km,
with sensitivities for mixing ratios down to ppbv and pptv
levels, depending on the trace-gas species. To achieve high
measurement accuracy and low detection limits, it is crucial
to reduce instrumental artefacts that lead to systematic struc-
tures in the residual spectra of the analysis. Spectral resid-
ual structures can be introduced by most components of a
LP-DOAS measurement system, namely by the light source,
in the transmission of the measurement signal between the
system components or at the level of spectrometer and de-
tector. This article focuses on recent improvements by the
first application of a new type of light source and consequent
changes to the optical setup to improve measurement accu-
racy.
Most state-of-the-art LP-DOAS instruments are based on
fibre optics and use xenon arc lamps or light-emitting diodes
(LEDs) as light sources. Here we present the application of
a laser-driven light source (LDLS), which significantly im-
proves the measurement quality compared to conventional
light sources. In addition, the lifetime of LDLS is about an
order of magnitude higher than of typical Xe arc lamps. The
small and very stable plasma discharge spot of the LDLS al-
lows the application of a modified fibre configuration. This
enables a better light coupling with higher light through-
put, higher transmission homogeneity, and a better suppres-
sion of light from disturbing wavelength regions. Further-
more, the mode-mixing properties of the optical fibre are
enhanced by an improved mechanical treatment. The com-
bined effects lead to spectral residual structures in the range
of 5 −10 ×10−5root mean square (rms; in units of opti-
cal density). This represents a reduction of detection limits
of typical trace-gas species by a factor of 3–4 compared to
previous setups. High temporal stability and reduced oper-
ational complexity of this new setup allow the operation of
low-maintenance, automated LP-DOAS systems, as demon-
strated here by more than 2 years of continuous observations
in Antarctica.
1 Introduction
Active long-path differential optical absorption spectroscopy
(LP-DOAS) is a well-established remote-sensing technique
based on the DOAS principle introduced by Perner et al.
(1976) and Platt and Perner (1980, 1983). It can attain de-
tection limits on the order of ppbv to pptv (nanomole per
mole to picomole per mole) for absorbers in the ultravio-
let to near-infrared spectral range (270–800 nm). Detectable
species include NO2, NO3, HONO, O3, SO2, ClO, OClO,
BrO, IO, OBrO, OIO, I2, OIO, formaldehyde, glyoxal, and
the oxygen dimer O4. LP-DOAS setups have been used in
various applications, such as studying urban pollution (Platt
et al., 1980, 1981; Volkamer et al., 2005; Platt et al., 2009;
Asaf et al., 2010; Chan et al., 2012; Lu et al., 2015) and its
Published by Copernicus Publications on behalf of the European Geosciences Union.
4150 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
vertical distribution (Alicke et al., 2002; Veitel et al., 2002;
Stutz et al., 2004; Wang et al., 2006); in remote sensing of
volcanic emissions (Kern et al., 2009); investigation of at-
mospheric halogen chemistry in coastal (Peters et al., 2005;
Pikelnaya et al., 2007; Keene et al., 2007; Commane et al.,
2011), desert (Hebestreit, 1999; Holla et al., 2015), or polar
regions (Hausmann and Platt, 1994; Hönninger et al., 2004;
Frieß et al., 2011; Liao et al., 2011; Stutz et al., 2011); and
ship-borne in the Arctic sea ice region (Pöhler et al., 2010).
The main advantage of DOAS in atmospheric remote
sensing is that it allows the contact-free and simultaneous
measurement of several trace gases. Exploiting that many
molecules have unique differential absorption cross sections,
mixing ratios can be derived by measuring the optical den-
sity of long light paths in the atmosphere using the DOAS
principle (see, e.g. Platt and Stutz, 2008, for a detailed intro-
duction).
In contrast to passive instruments (e.g. multi-axis DOAS,
MAX-DOAS, or satellite instruments), which use scattered
or reflected light and hence rely on natural light sources
such as solar (or lunar; Wagner et al., 2000) radiation, active
DOAS instruments use artificial light sources such as light-
emitting diodes (LEDs) or arc lamps. The independence from
natural light sources allows continuous observations of trace
gases to study night-time chemistry, for example. It also en-
ables investigations of trace gases absorbing in the deep UV
where no natural light sources exist. Another advantage is
the well-defined light path of up to 20 km. Along this light
path, a mean mixing ratio is determined. In comparison to
passive instruments, this reduces the analytical effort to ob-
tain mixing ratios and usually leads to smaller uncertainties
as no radiative transport models are needed for the interpre-
tation of the data. Furthermore, compared to point measure-
ments, long-path DOAS results are less sensitive to large spa-
tial gradients yielding concentrations with a better represen-
tativeness for comparison with chemistry models or typical
footprints of airborne platforms and satellites.
Most modern LP-DOAS setups use fibre optics for light
transfer between light source, telescope, and spectrometer
(Merten et al., 2011), and a mono-static telescope; i.e. one
telescope is used for both sending and receiving the light re-
flected from a retro-reflector array. In the following, recent
improvements to this setup will be presented which, in com-
bination, can increase accuracy and precision and hence re-
duce detection limits of LP-DOAS measurements by a fac-
tor of 3 to 4 compared to previous setups. To achieve this,
a novel light source type was applied and the light coupling
from the light source to the telescope was optimized to re-
duce stray light. Furthermore, a new configuration of the op-
tical fibres with an improved mode mixing was introduced.
In addition to an enhanced measurement performance, these
improvements have made the previously quite cumbersome
setup of LP-DOAS instruments considerably easier and now
allow the operation of low-maintenance, automated instru-
ments for long-term observations.
In Sect. 2 the state of the art in LP-DOAS instrument de-
sign will be described. Improvements of measurement per-
formance and operation procedure following the introduc-
tion of the novel light source and changes to the fibre con-
figuration are presented in Sect. 3. In Sect. 4 the influence
of residual structures due to fibre modes and a new method
for mode mixing to reduce these structures is presented. In
Sect. 5 the combined contribution to the improved instrument
performance with respect to reduced stray light and reduction
of total noise is quantified based both on lab measurements
and field campaigns, and typical detection limits for setups
that incorporate the improvements are presented.
2 Long-path DOAS
LP-DOAS instruments couple light from an artificial light
source into a telescope, which creates a light beam that is
transmitted through the atmosphere across a distance rang-
ing from a couple of hundred metres to several kilometres.
At the end of this atmospheric path, the light is collected by
a telescope and analysed for spectral absorption structures –
typically with a grating spectrometer. This originally bi-static
setup with separate telescopes for sending and receiving was
replaced by a mono-static setup with a single telescope and a
retro-reflector array introduced by Axelsson et al. (1990). Af-
ter reflection at the retro-reflector, the light is received again
by the same telescope, which reduces the complexity of the
setup with regard to power supply and alignment. It also dou-
bles the length of the light path. State-of-the-art LP-DOAS
instruments mostly rely on fibre optics for light coupling be-
tween light source, telescope, and spectrometer (see Fig. 1).
Compared to traditional systems that use a complex system
of mirrors for the light coupling between light source, tele-
scope, and spectrometer, this approach, first introduced by
Merten et al. (2011), further reduces the complexity of align-
ment of the telescope itself and increases the transmittance
compared to the coaxial Newton-type telescopes used with
the mirror coupling.
2.1 State-of-the-art instrument setup
The crucial components in a modern fibre-based LP-DOAS
setup are the light source and a Y-shaped optical fibre bun-
dle, where one end serves as sending fibre bundle that guides
the light from the light source to the telescope and the other
end serves as a receiving fibre bundle, leading from the tele-
scope to the spectrometer (see Fig. 1). According to Merten
et al. (2011), the fibre bundle in such a “classical” setup (see
upper row in Fig. 2 for a detailed schematic of the sections
of the bundle) on the transmitting end typically consists of a
mono fibre with a large diameter (typically 800 µm) to max-
imize light collection at the light source (at letter A in Fig. 1
and also the upper row of column a in Fig. 2). This fibre is
then coupled to a ring of smaller diameter (200 µm) fibres (at
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4151
Figure 1. Components of a fibre-based LP-DOAS system consist-
ing of a light source, a Y-shaped fibre bundle, a telescope for send-
ing and receiving the light, a retro-reflector array, and a spectrome-
ter. Adapted from Sihler (2007).
letter B in Fig. 1 and column b in Fig. 2) leading to the com-
bined end of the bundle. The monofibre (800 µm) is required
to guarantee an equal illumination of all small diameter fi-
bres of the ring. Then the end of the bundle (letter C in Fig. 1
and column c in Fig. 2) is placed close to the focal point of
the telescope mirror to create a parallelized light beam. For
a fibre at the focal point of a parabolic mirror and omitting
beam widening effects, the light emitted by the sending fi-
bre bundle would be imaged on itself, so that no light would
reach the receiving fibre. However, there are a number of
effects that blur the reflected image of the light source and
lead to a coupling of light into the central receiving fibre:
(a) comatic aberration when the incident beam is parallel but
not paraxial, (b) diffraction at the apertures of telescope and
retro-reflectors, (c) surface irregularities of mirror and retro-
reflectors, (d) defocusing of the fibre bundle, (e) atmospheric
turbulence, and (f) for spherical main mirrors the spherical
aberration in combination with the lateral offset of the beam
at the retro-reflectors (Rityn, 1967; Eckhardt, 1971; Merten
et al., 2011). Merten et al. (2011) have determined (a)–(c)
to have a negligible influence for components typically used
in LP-DOAS systems. Considering (d) and (e) (and (f) if a
spherical main mirror is used), the light throughput of a fibre-
based system is optimized by setting the end of the fibre bun-
dle to a slightly out of focus position in front of the main
mirror.
To homogenize the illumination of the entrance slit of the
spectrometer and hence the grating, different mode-mixing
techniques (see, e.g. Stutz and Platt, 1997) can optionally be
applied between telescope and spectrometer (at letter D in
Fig. 1 and the upper row of column d in Fig. 2) before the
light is coupled into the spectrometer passing an (optional)
optical slit (at letter E in Fig. 1 and column E in Fig. 2) (see
Sect. 4).
For the analysis of the atmospheric absorption, a reference
spectrum without absorption of the gases is required. This
is obtained by temporarily inserting a diffuse reflector, e.g.
a sandblasted white surface, close (i.e. around 1–4 mm dis-
tance) to the end of the fibre at (C), thus creating an opti-
cal “shortcut” (SC) for the light (for a sketch of this mecha-
nism, see Fig. A1 in the Appendix). In the following, spectra
recorded this way will be referred to as reference. The reflec-
tor mechanism will be referred to as shortcut.
To account for scattered sunlight from the atmosphere in
both atmospheric and reference spectra as well as to correct
for the charge-coupled device’s (CCD’s)é dark current and
offset signal, background spectra for both types of measure-
ment spectra are recorded on a regular basis by shutting off
the light source at (A). All four spectrum types are recorded
in an interleaved fashion, typically with a couple of pairs
of reference and atmospheric spectra followed by one atmo-
spheric background and one reference background. Exam-
ples of such measurement routines are discussed in detail in
Appendix C.
2.2 DOAS analysis and measurement accuracy
Obtaining average trace-gas mixing ratios cion the light
path Lbetween telescope and reflector is based on the Beer–
Lambert law. Extended by scattering processes, the attenu-
ation of an initial radiance I0(λ) traversing the atmosphere
yielding the measured spectrum I (λ) can be described by
Eq. (1). The central idea of the DOAS approach is the separa-
tion of narrow band (differential) molecular absorption cross
section σ0
i(λ) of a suited absorber ifrom the broadband por-
tion σB
i(λ):
I (λ) =I0(λ) ·exp −X
ih(σ 0
i(λ) +σB
i(λ)) ·ci·Li
−(R(λ) +M(λ)) ·L).(1)
The optical density τ(Eq. 2) is calculated taking the log-
arithm of the ratio of atmospheric I (λ) and reference spec-
tra I0(λ) after correcting with their respective backgrounds.
Mixing ratios ciare determined by using the differential op-
tical density σ0
i(λ) modelled from differential literature ab-
sorption cross sections σ0
i,Lit. To adapt the high-resolution
literature cross section to the resolution of the spectrome-
ter, prior to the analysis it is convoluted with the instrument
response function, which usually is obtained by recording
the shape of an emission line of a gas discharge lamp (e.g.
mercury). For the detailed mathematical description of the
analysis refer to Platt and Stutz (2008). Broadband absorp-
tion σB
i(λ) in τis combined with (broadband) atmospheric
scattering where R(λ) denotes extinction due to Rayleigh-
scattering and M(λ) accounts for Mie scattering. The broad-
band contributions can either be modelled with a polyno-
mial P (λ) or removed with a high-pass filter. The fitting pro-
cess then minimizes the difference R(λ) between measured
and modelled optical density using a least-squares approach
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4152 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
yielding mixing ratios ci:
τ=ln(I0(λ)/I (λ))
| {z }
Measurement
=X
i
σ0
i,Lit(λ) ·ci·L+P (λ)
| {z }
Model
+R(λ)
|{z}
Residual
.(2)
The measurement accuracy and precision, and hence the de-
tection limit of the retrieved mixing ratios, is determined
from this difference R(λ) called the residual of the DOAS
fit. The magnitude of the residual determines the precision,
while systematic structures limit the accuracy. The magni-
tude of the residual can be affected, e.g. by a low signal-to-
noise ratio or noise generated in the CCD through thermal
excitation or the read-out electronics. Systematic structures
are caused, e.g. by spectral lamp structures, absorbers miss-
ing in the model, inaccurate literature cross sections used
in the model, or inhomogeneous illumination of the spec-
trometer grating, where the angular response of the detector
causes residual structures (Stutz and Platt, 1997). A funda-
mental limit is the photon shot noise, which decreases with
the square root of the count number in spectra. Its relative
contribution to the residual, however, can become very small
(e.g. when several spectra are summed up). Residuals in this
study generally were larger than pure photon shot noise,
indicating that other sources of noise dominate. To reduce
the contribution of systematic structures to the residual, and
hence measurement errors and detection limits, in this study
the influence of different components of the LP-DOAS in-
strumental setup was assessed and optimized.
2.3 LP-DOAS setups used in this study
We tested several improvements to the classic fibre-based
DOAS setup (as described in Sect. 2.1), an overview of the
three different setups is given in Table 1 and will be described
in the following sections. The systematic comparison of im-
provements to the setup was done in the rooftop laboratory
of the Institute of Environmental Physics at the University
of Heidelberg (setup HD) with an Acton 500i spectrometer
and a smaller laboratory telescope that allows quick changes
of components but is not suited for outdoor deployment. For
atmospheric measurements, a 1.55 km light path (one way)
passing over a residential area of Heidelberg to another in-
stitute was used. Tests with atmospheric measurements were
performed during 6 weeks from 11 March until 3 May 2014.
In each configuration, measurements were performed for at
least 24 h to ensure sufficient statistics and the comparability
of different setups.
As for all measurements not performed under fully con-
trolled laboratory conditions, the influence of environmental
parameters has to be considered in such a comparison. An
important factor in LP-DOAS measurements are variations
in the telescope–reflector alignment which can be influenced
by changes to the setup as well as environmental parameters
such as air temperatures. To ensure an optimal alignment, as
part of the measurement routine and in alternation with mea-
surement periods, an optimization of the received signal is
performed on a regular basis by systematically varying the
telescope alignment around the current position and select-
ing the alignment with the highest signal. LP-DOAS tele-
scopes thus adaptively counter sudden changes to the system
transmissivity, e.g. through mechanical interaction with the
telescope structure as well as long-term drifts.
In addition to the alignment, atmospheric visibility be-
tween telescope and reflectors can vary. Potentially very low
visibilities were removed from the comparison data set by
excluding days with rainfall. Other visibility conditions with
a similar influence (e.g. fog or smog) did not occur during
the comparison period.
We estimate the resulting variations in the absolute in-
tensity of the measurement signal from both factors to be
20 %. This value has to be considered when comparing ab-
solute atmospheric intensities achieved with the different se-
tups, which determine the temporal resolution of LP-DOAS
measurements. For accuracy and precision, here this is as-
sessed through the comparison of the root mean square (rms)
of fit residuals (Sect. 2.2); however, due to the use of differen-
tial absorption features in DOAS, variations in the recorded
absolute intensity only influence photon statistics and hence
photon shot noise (i.e. the precision). Therefore, in the com-
parisons of residuals from atmospheric measurements, the
square root of intensity variations has to be considered and
an uncertainty of 10 % has to be assumed. For the majority
of setups tested here, this is much smaller than the system-
atic differences of residual rms values between the different
configurations.
It should be noted that in contrast to passive DOAS in-
struments, changes in the global radiation do not affect LP-
DOAS measurements since the atmospheric background sig-
nal is corrected with regularly recorded background spectra
(see Sect. 2.2). Therefore, measurements under, e.g. over-
cast conditions, can be compared to observations under clear
skies.
The combined changes to the LP-DOAS setup, which were
found to be the best combination, were then tested with a
campaign-grade telescope and a smaller Acton 300i spec-
trometer (setup “NR”) during a 6-week campaign in a rural
area in the “Nördlinger Ries” in southern Germany. Find-
ings from both campaigns were incorporated in a new, low-
maintenance, automated LP-DOAS system (setup “NMIII”).
It was operated on the German Antarctic station Neumayer
III from January 2016 until May 2018 and allows the assess-
ment of the long-term performance of the different compo-
nents. All telescopes investigated here were equipped with
spherical, aluminium-coated mirrors.
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4153
Table 1. Overview of the different LP-DOAS setups used in this study.
Setup HD NR NMIII
Location Heidelberg Campus Nördlinger Ries (Germany) Neumayer III (Antarctica)
Light source various EQ-99 (2014) EQ-99X (2015)
Fibre bundle
Sending bundle length various 6 m +3 m 8.55 m
Receiving bundle length 3 m+7 m 7.55 m +1 m
Sending fibre diameters various 1×200 µm +1×200 µm 1 ×200 µm
Receiving fibre diameters 6 ×200µm +1×800 µm 6 ×200 µm +1×800 µm
Treatment (spectrometer end) various 12 µm coarse polished 5 µm coarse polished
Telescope
Focal length 0.6 m 1.5 m 1.5 m
Mirror diameter 20 cm 30 cm 30 cm
Mirror type spherical spherical spherical
Numerical aperture 0.17 0.1 0.1
Telescope front open open covered with quartz
glass window
Light path total (one way) 1: 3.2 (1.55) km; 2: 5.9 (2.95)km 3.2 (1.55) km/5.9 (2.95)kma
Retroreflector No. of 5.08 cm diameter elements 7 28 1: 24 (heated); 2: 32a
target size (H×W) 21 ×18 cm 45 ×32 cm 1: 60 ×40 cm; 2: 140 ×80cma
Spectrometer
Model Acton 500i Acton 300i Acton 300i
Focal length 500 mm 300 mm 300 mm
F-number 6.5 4 4
Numerical aperture 0.07 0.12 0.12
Optical slit 200µm 150 µm 200 µm
Grating 600 gr. mm−11000 gr. mm−11200 gr. mm−1(600 gr. mm−1b)
300 nm blaze holograph. holograph. (300nm blazeb)
CCD Roper Scientific Roper Scientific Andor DU440 BU
Spectral resolution 0.50 nm 0.49 nm 0.54 nm (0.95 nmb)
Spectral window 85 nm 85nm 65 nm (140 nmb)
aIn this setup two different light paths were available and used in turn. bGrating and spectral properties for VIS I spectral window from 378–521nm (see also Table D1).
3 Light sources and fibre configurations
The light source of a LP-DOAS instrument is a key com-
ponent because it has a major influence on the achievable
signal-to-noise ratio and temporal resolution. The measure-
ment quality depends on both the temporal and (particu-
larly for arc lamps) spatio-temporal stability of the light-
emitting medium (i.e. the plasma) and its spectral character-
istics, namely on its (spectral) radiance (see Platt and Stutz,
2008, for comparison of different light sources).
3.1 Comparison of light sources
In the past, for most LP-DOAS applications xenon arc lamps
have been used that often suffered from poor stability of the
light arc, which affected the optical coupling into the fibre
and hence the effective intensity and shape of the lamp’s
spectral structures. Furthermore, lifetimes of most models
with high radiance were relatively short (200 to 2000h when
in constant use; Kern et al., 2006) and regular replacement
during longer measurements required – in addition to the
considerable expenses – a time-consuming realignment of
the optics after each exchange. Depending on the lamp model
used, power consumption was high (up to 500W plus losses
in the power supply), which limited the applicability of LP-
DOAS instruments. Additionally, the high voltages necessary
for ignition are a shock hazard and cause electromagnetic in-
terference. Although LEDs are useful for compact applica-
tions due to their low power consumption and high spatial
stability of the light-emitting area, up to now light output
is not high enough to achieve sufficient signal-to-noise ra-
tios in the ultraviolet regime below 350nm. Their applica-
tion has been so far limited to very compact “single housing”
systems and to ensure sufficient spectral stability, often con-
siderable efforts for temperature stabilization are necessary
(Kern et al., 2006, 2009; Sihler et al., 2009).
In our new LP-DOAS setups presented here, a novel, com-
mercially available laser-driven light source (Energetiq EQ-
99 and the follow-up model Energetiq EQ-99X, in the fol-
lowing referred to as LDLS) was applied both for laboratory
tests and different field measurements. Supplying energy to
the xenon plasma with an infrared laser (rather than a high
voltage), it combines the advantages of a high-power xenon
lamp with the long lifetime and high spatio-temporal stability
of LEDs at a modest power consumption (140 W). Similar to
conventional xenon lamps, xenon emission lines, whose dif-
ferential nature can limit sensitivity in DOAS applications
(in particular around 450 nm, a spectral window in which,
e.g. IO or glyoxal can be detected), are broadened by a high
Xe pressure in the bulb. Details on the LDLS can be found in
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4154 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
Zhu and Blackborow (2011b),Horne et al. (2010), and Islam
et al. (2013)
We couple the light from the LDLS into a fibre with a lens,
as described in Sect. 3.4 and depicted in Fig. 5. The light
source offers the possibility to purge the lamp housing with
a constant flow of nitrogen gas. This prevents ozone forma-
tion around the light bulb and hence increases output in spec-
tral regions where ozone has absorption bands and reduces
the intrusion of pollutants into the lamp housing (see man-
ufacturers’ technical notes for details; Zhu and Blackborow,
2011a). In a test we performed, the radiance at 255 nm in-
creased by about 30 % compared to no purging when a high
flow of nitrogen (about 1 L min−1) was used. Due to logis-
tical reasons, most of the time the LDLS was purged with
filtered and dried air during the measurements reported in
this study. In the system used for long-term observations in
Antarctica (see Sect. 5.2), the lamp housing was only purged
30 min d−1with filtered and dried air attaining a lifetime of
22 500 h.
3.2 Adaptation of the optical setup to the light source
In addition to a long lifetime and high spatio-temporal sta-
bility, a further advantage of the LDLS is the very small and
stable plasma spot, due to the very precise localization of the
plasma inside the bulb in the focal point of the laser. Its di-
mension on the order of 100 µm (full width at half maximum)
is about 3 times smaller than in conventional arc lamps (see
Table 2). This can be exploited in several ways to further im-
prove the design of LP-DOAS systems – first with respect
to the configuration of the fibre bundle and overall system
optical throughput.
For optical systems in which light propagates unobstructed
in a clear and transparent medium, an invariant, the étendue
Gcan be defined as follows (e.g. Welford and Winston, 1978;
Markvart, 2007):
G=n2A. (3)
It is the product of the square of the refractive index nof
the medium, the area Aof the entrance pupil, and the solid
angle subtended at this pupil by an object. Since the exact
assignment of these quantities depends on the components of
an optical setup that are considered, its definition can vary.
For the étendue of a light source for example, Acould be the
size of the emitting area and the solid angle around the
emitter that is covered by the light collecting optics.
The étendue allows us to link the spectral radiant flux 8(λ)
(in W) through an optical system with transmittance τ (λ) to
the spectral radiance R(λ) (spectral radiant flux per solid an-
gle and surface area in W sr−1m−2) of the light source:
8(λ) =τ (λ)R(λ)G. (4)
For a system that consists of several components with differ-
ent étendues, the overall spectral radiant flux 8(λ) is limited
by the component with the smallest Glim, which makes it a
very useful quantity for optical design considerations. For an
optimal overall throughput, the étendues of all components
should match as closely as possible.
In fibre-based LP-DOAS setups, typically either the spec-
trometer (where Gis the illuminated area of the entrance slit
times the solid angle of acceptance of the spectrometer) or
the telescope (where Gis the entrance area of the fibre core
times the solid angle of the light cone hitting the main mirror)
have the limiting étendue (see Table 3).
For a given light collection solid angle, the LDLS has a
small étendue compared to other light sources owing to its
small plasma spot. The manufacturer indicates, for example,
a maximum attainable numerical aperture of NA =0.447
(determined by the geometry of the lamp housing), corre-
sponding to a solid angle of 0.663. Assuming an emit-
ting surface with 100 µm diameter, this yields an étendue
Gmax =52×10−4sr mm2. This is about 4 times smaller than
for a conventional XBO_75 xenon arc lamp with the same
coupling optics (see Table 2). A small étendue is favourable
for optimal utilization of the light source since, regardless of
the coupling optics, the usable fraction of the emitted radia-
tion cannot be increased beyond the radiant flux through the
element of the system with the limiting étendue.
This is illustrated by an investigation of the coupling be-
tween different light sources and fibres with different diam-
eters. For LP-DOAS systems, a light source that efficiently
can be coupled into a fibre with a smaller diameter is ad-
vantageous because it allows us to use the fibre bundle in a
reversed configuration (see Sect. 3.3 and in the lower row of
Fig. 2).
Using setup HD (see Table 1) with a fixed exposure time
and number of scans in reference mode, the intensity spectra
of several light sources commonly used for LP-DOAS appli-
cations were recorded (shown in Fig. 3). Since angular in-
formation of the light is lost on the sandblasted surface of
the reference plate, the spectrometer only samples the inten-
sity of the scattered light. For the comparison between light
sources and different fibres, therefore, only the coupling be-
tween the light sources and the fibre has to be considered.
First, a classical fibre setup described in Sect. 2.1 was used
(Fig. 3a). The light from the different sources was coupled
into a 1 m fibre with 800 µm diameter that was coupled to
a 6 ×200 µm ring of a 3 m long Y-shaped fibre bundle (see
the upper row of Fig. 2, i.e. “classical setup”). The receiving
fibre was the single 200 µm core fibre of this bundle, which
was coupled to a 10 m long 200 µm fibre that led to the spec-
trometer.
The recorded irradiance of the LDLS in this setup is
about twice as high as the XBO_75, and differential xenon
structures are weaker. The commercially no longer avail-
able Hanovia PLI_500W (in the following referred to as
PLI_500) xenon arc lamp delivers considerably higher irra-
diances. However, due to poor spatial and temporal arc sta-
bility and the resulting introduction of systematic spectral
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4155
Table 2. Specifications of several lamps used for LP-DOAS measurements.
Light source LDLS XBO_75 PLI_500 UV LED
Type Laser-driven LS Xe arc Xe arc Light-emitting diode
Luminous surface [µm] 63×144 250 ×500 300 ×300 1000 ×1000
(Experimental value) 95 ×146 ±6 % (*) (*)
Typical lifetime [h] >10 000 200–2000 <200 >10 000
Power requirements [W] 140 75 500 3
(*) Only valid for new lamps – can increase drastically within days.
Table 3. Étendues for the coupling between the different components in the three setups used in this study (see Table 1). For setup HD, the
spectrometer étendue for two fibre bundle configurations (classical and reversed) are indicated. See Fig. 2 and Sect. 3.3 for a description.
Coupling HD NR NMIII
LDLS →fibre 19.34 ×10−4sr mm221.10 ×10−4sr mm29.80 ×10−4sr mm2
Telescope 28.73 ×10−4sr mm29.89 ×10−4sr mm29.89 ×10−4sr mm2
Fibre →spectrometer 5.74 ×10−4sr mm2(classical config.) 76.66 ×10−4sr mm276.66 ×10−4sr mm2
29.25 ×10−4sr mm2(reversed config.)
structures as well as a very complicated handling and short
lifetime (around 200 h), this light source was excluded from
further investigations. Comparison of the LDLS and high-
power LED light sources (for the UV a 3 W Engin LZ1 and
a 3.5 W Cree XP-E Royal Blue for the blue spectral range)
gives comparable (around 365nm) or superior irradiances
(around 450 nm) for the LEDs, however, only within the
small spectral coverage inherent to the LED principle (Kern
et al., 2006).
In a second measurement, a 1 m long 200µm diameter sin-
gle fibre with the same numerical aperture was added to the
previous setup between the light source and the 800 µm di-
ameter fibre (Fig. 3b). This reduces the étendue of the fibre
setup by a factor of 16 (ratio of fibre cross sections). When
comparing the effect, it has to be kept in mind that the ad-
ditional 200 to 800µm fibre interface introduces a coupling
loss of about 20 %–25 % (empirical value).
In the setup with added 200 µm fibre (Fig. 3b), the smaller
étendue of the fibre bundle favours the LDLS with its
small, high-luminance plasma spot relative to the other light
sources. The decrease in the transmitted radiant flux com-
pared to the previous setup (about a factor of 2–3 when cor-
recting for a coupling loss of 25 %) and relative to all other
light sources, therefore, is the smallest for the LDLS. Both
the XBO_75 xenon lamp (reduction by a factor of 9) and the
LEDs (reduction by a factor of 11–13) clearly have lower ra-
diant fluxes than the LDLS and even that of the PLI_500 (re-
duction of a factor of 10) is now only a factor of 2–3 brighter
than the LDLS.
3.3 Fibre bundle configurations
The favourable properties of the LDLS when coupled into
smaller diameter fibres allow to reverse the Y-shaped fibre
bundle (see lower row of Fig. 2). The ring of fibres previ-
ously used for sending is now used for receiving and the
central fibre that previously received the returning radiation
now sends it out. Reversing the fibre bundle setup has no in-
fluence on the instrument transmissivity since the light path
is reversible (see letter C in Fig. 1 and column c in Fig. 2)
but offers several advantages. The larger 800 µm fibre is now
coupled to the optical slit. If the limiting étendue of the sys-
tem is that of the spectrometer (as in setup HD), a larger il-
luminated area of the slit increases it (e.g. by a factor of 3.8
when comparing a single 200 µm to the 800 µm fibre with a
150 µm optical slit). Furthermore, a larger diameter fibre has
better mode-mixing properties, as will be discussed in detail
in Sect. 4 below.
However, the ring of fibres generally has a larger field of
view. When in the reversed bundle setup the fibre ring is used
for receiving, the atmospheric background light signal (see
Sect. 3.4 below) can be 6 times larger – in particular when
the reflector array size is much smaller than the field of view
of the ring (often the case in field campaigns due to logis-
tical reasons). This trade-off between the favourable aspects
of the reversed fibre bundle configuration like the potential
increase in the measurement signal and an improvement of
signal quality due to mode mixing (see Sect. 4) has to be
weighed against the potentially increased atmospheric back-
ground light. If feasible, the latter should be reduced as much
as possible by, e.g. shielding the area of the ring’s field of
view around the reflectors with a low-reflectance screen.
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4156 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
Figure 2. Schematic diagrams of sections of the fibre setup and corresponding cross sections when a Y-shaped bundle is used in the classical
(top row) or reversed (bottom row) way. Additional fibres or fibre bundles can be coupled to the end of the receiving fibre section to improve
mode mixing or change the cross section (not sketched). The letters A through E correspond to positions marked in Fig. 1.
Figure 3. Intensities of several light sources measured on the short-
cut plate (no atmospheric light path). The position of the lens fo-
cussing the light sources onto the fibre was adapted to the respective
spectral region.(a) Light coupled into a bundle in classical configu-
ration (see Fig. 2) with 800 µm fibre diameter.(b) Light coupled into
the same bundle with an additional 200 µm fibre added in front of
the 800 µm fibre of the bundle (also in classical configuration; see
Fig. 2). For better comparison, the PLI_500 has been downscaled.
Please note that for comparisons between both setups and panels
the loss by the additional coupling of the 200 µm fibre, which we
estimate to be around 20 %–25%, has to be taken into account.
For applications where radiant fluxes are crucial, a cross
section modulating fibre could be used instead of a large di-
ameter single fibre assuming a detector with sufficient ver-
tical extent. However, it would come at the expense of the
favourable mode-mixing properties of larger fibre diameters
and could add a potential complication to the determination
of the spectrometer’s instrument line function, which can
vary along the optical slit for misaligned fibres in the cross
section modulating fibre or when the different fibres due to
atmospheric conditions are not illuminated homogeneously.
In the following sections, the performance of LP-DOAS
systems with both classical and reversed fibre configurations
will be compared and discussed (see the upper and lower
rows of Fig. 2, respectively). For all classical configurations
(upper row of Fig. 2), in the sending section a 800 µm diam-
eter fibre is used to collect the light from the light source,
which is then coupled to a ring of 6 ×200 µm fibres of
Y-shaped bundles. The receiving section consists of a sin-
gle 200 µm that is extended by another 200 µm single fibre
if necessary. These classical configurations will be denoted
“800 →200”. In all reversed configurations (lower row of
Fig. 2), the sending section consists of a single 200 µm fibre
at the light source that is either the core of a Y-shaped bundle
or (if required) an extension fibre then coupled to a core fibre
of a Y-shaped bundle. The receiving section consists of the
ring of 6 ×200 µm fibres then coupled to a 800µm diameter
single fibre. These reversed configurations will be denoted
“200 →800”.
As the influence of lamp performance and fibre configu-
ration in atmospheric measurements cannot be assessed in-
dividually in our setup, the noise of the entire measurement
system was investigated to quantify the improvement of mea-
surement quality of this reversed setup and results are dis-
cussed in Sect. 5.
3.4 Comparison of instrumental stray light
When operating a LP-DOAS, different types of stray light oc-
cur that can cause residual structures and limit the measure-
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4157
ment accuracy. Atmospheric background light is scattered
into the instrument from outside sources (usually the Sun).
It depends on the external light source’s relative position and
orientation, as well as atmospheric properties, e.g. the vis-
ibility. To correct for background light, background spectra
for both atmospheric and reference spectra are recorded on a
regular basis by blocking the light source (see Sect. 2.1 for
details).
Internal or spectrometer stray light is caused by unin-
tended deflections of light inside the spectrometer. In the UV
spectral range in particular, where lamp intensities are low
compared to the visible spectral range of the light source,
this can lead to a systematic underestimation of optical den-
sities since it represents an additive quantity with respect to
the total received radiance.
We investigated the amount and origin of spectrometer
stray light for different spectral regions using setups HD and
NR with the telescope shortcut in place and a set of band-
pass filters that block increasing portions of the UV-VIS
from 280 to 665 nm (see Fig. B1 for the set of filters and
their effect on a spectrum). Considering the UV spectral re-
gion and the spectrometer of setup HD (f=500 mm) with
a 600 grooves mm−1grating (blaze 300 nm), stray-light lev-
els increase from less than 1% around 400 nm to about 15 %
at 240 nm. For smaller wavelengths it quickly reaches 80 %–
90 % due to the diminishing spectral radiance of the LDLS
in this region. About 95 % of the stray light in this config-
uration originates from the visible spectral range between
400 and 650 nm. For a grating with 1200 groovesmm−1in
the same spectrometer, stray-light levels are between 3 and
7 times smaller than in the previous configuration reach-
ing about 2 % at 240 nm. For this grating about 50 % of the
stray light originates from the visible spectral range between
400 and 650 nm, with the other half being from the IR.
The smaller spectrometer of setup NR (f=300 mm) with
1000 grooves mm−1grating has stray-light levels of less than
1 % above 320 nm, which increases to about 10% at 260 nm.
For evaluations in the spectral region around 330 nm and
the 600 grooves mm−1(a typical spectral window for the de-
tection of SO2, BrO, formaldehyde, or ozone), an exemplary
stray-light distribution determined with setup HD with the
shortcut in place is illustrated by the histogram in Fig. 4. The
relative importance of stray light for UV measurements is
further increased when atmospheric spectra are considered.
Since Rayleigh scattering is proportional to λ−4, loss of UV
radiation is higher on the way through the atmosphere com-
pared to the visible parts of the spectrum. This decreases the
ratio between UV and VIS and thus increases the relative im-
portance of stray light from VIS spectral regions on UV mea-
surements. Below 300 nm this is further augmented by strong
ozone absorption bands. For the NR setup stray light in at-
mospheric measurements increases from 1.5 % at 320 nm to
10 % at 290 nm, quickly reaching levels of more than 50 %
for 280 nm and below.
Figure 4. Stray-light reduction in the UV by using a UG-5 filter. The
distribution of the relative contribution of different spectral areas to
the total stray light as determined with a set of bandpass filters is
shown in grey bars. The two curves show the lamp spectrum deter-
mined with setup HD and a classical 800 →200 fibre configuration
by a measurement on the SC plate with (dashed) and without (solid)
a UG-5 bandpass filter between the light source and sending fibre.
There are different ways to suppress spectrometer stray
light to reduce its influence on measurement accuracy. One
is to add bandpass filters (usually coloured glass) between
the light source and fibre to select only the part of the lamp
spectrum needed for measurement. In Fig. 4 the effect of a
UG5 bandpass filter (200–400 nm) on the lamp spectrum is
shown. Over 95% of the light between 400 and 650 nm and
hence of the stray light originating from here can be removed
while keeping light losses around 330 nm at about 40 %–
50 %, yielding stray-light levels of less than 0.1 %.
The LDLS with its small and stable arc spot allows a sec-
ond stray-light reduction before coupling the light into the
fibre. By mounting the entrance of the fibre (A in Fig. 2)
on a stepper motor that can translate around the focal point
along the optical axis of the lens, which projects the plasma
spot onto the fibre end, the chromatic aberration of the lens
can be exploited to selectively optimize the input of differ-
ent spectral ranges (see principle in Fig. 5; see Fig. B2 for
a determination of the relative positions of foci for different
spectral regions).
Due to the steep increase in the refractive index of quartz
glass towards shorter wavelengths (Malitson, 1965), this
chromatic filter is particularly selective for the UV spectral
range. Figure 6 shows the spectral shapes of the radiation
reaching the spectrometer when the position of the fibre is
optimized for (a) measurements around 260 nm (dashed line
in Fig. 6) and (b) for 400 nm (solid black line in Fig. 6). This
can be compared against an artificial intensity distribution
that represents the envelope of spectral distributions when
the fibre position is tuned through several foci between 200
and 800 nm.
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4158 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
Figure 5. Principle of selectively coupling light from a light source
into a fibre for stray-light reduction using the chromatic aberration
of the lens. The foci of different spectral regions can be attained by
a translation of the fibre along the optical axis of the lens.
Figure 6. Comparison of lamp spectra with the position of the fi-
bre entrance optimized for 260 nm (dashed line) and 400nm (drawn
line). For comparison, a modelled spectral distribution of the light
source unaltered by the chromatic aberration of the lens is also
shown (shaded area). The latter was obtained by varying the fibre
position through all foci from 200 to 800 nm and taking the enve-
lope of the resulting spectra.
When this chromatic-aberration filter is optimized for
260 nm, stray light originating around 400, 540, and 680 nm
is reduced by about 60 %, 75 %, and 80 %, respectively (de-
tails are given in Appendix B2).
4 Fibre modes
The modes of an optical fibre represent different distribu-
tions of the light travelling inside the core of the fibre. The
solutions of the Helmholtz wave equation for the fibre core
using Maxwell’s equations and considering core geometry
and boundary conditions yield the possible modes (Kaminow
et al., 2013). For a given wavelength λ0the number nof
modes is proportional to both numeric aperture NAand fi-
bre radius a:
n∝a·NA
λ0.(5)
When the light travels only in a few modes, the resulting light
spot leaving the fibre can be inhomogeneous because of the
intensity patterns of the individual modes. The intensity dis-
tribution between different modes can change along the fi-
bre when energy is transferred from one mode to another,
which is referred to as mode coupling. This can be caused,
e.g. by impurities, temperature changes, or mechanical stress
on the fibre (Stutz and Platt, 1997; Kaminow et al., 2013). In
fibres with a smaller diameter in which fewer modes are pos-
sible, this inherent or “natural” mode coupling has a less ho-
mogenizing effect than for an otherwise identical fibre with
a larger diameter. Therefore, placing a fibre with a larger di-
ameter between telescope and spectrometer, as is the case in
the “reversed fibre configuration” (see lower row of Fig. 2),
improves the mode-mixing capacity of LP-DOAS setups.
4.1 Comparison of mode-mixing techniques
In applications with grating spectrometers, an irregular and
temporally unstable illumination of the grating resulting
from non-uniform illumination of the spectrometer field of
view, e.g. due to fibre modes, can create systematic, tempo-
rally unstable residual structures in the DOAS analysis (see
Stutz and Platt, 1997, for a detailed study) and thus degrade
the measurement accuracy. To reduce these structures, “ar-
tificial”, i.e. intentional, mode coupling can be induced by
different methods. This is referred to as mode mixing (some
publications also use the term mode scrambling).
Suitable fibres containing more impurities inherently lead
to more mode coupling. However, since impurities cause sig-
nal loss when fibres are used in communication applications,
manufacturers have improved fibre purities, leading to a re-
duced inherent mode coupling in modern fibres (Kaminow
et al., 2013). Since larger diameter fibres allow more modes
(Eq. 5), adding such a fibre to the Y-shaped bundle in front of
the spectrometer can have a homogenizing effect. The same
is achieved by adding diffusing discs to the optical setup (at
the expense of transmissivity). Furthermore, mode coupling
by mechanical stress can be induced artificially by squeez-
ing or bending the fibre (micro-bending, e.g. Blake et al.,
1986; Stutz and Platt, 1997). However, this requires bare fi-
bres to ensure the transmission of the pressure, which makes
the handling quite delicate. The mode mixing is also difficult
to reproduce and easily influenced by environmental factors
such as temperature. Stutz and Platt (1997) solved this by
mechanically vibrating a coiled section of the bare fibre in
front of the mode mixer to temporally average over different
mechanical conditions. When the intensity of the fibre vi-
bration is increased, micro-bending and temporal averaging
are effectively combined and can be applied to fibres with
a protective coating. This was done in this investigation by
attaching the fibre to a vibrating filter pump.
A new method we tested for this study is the intentional de-
grading of fibre ends to create a quasi-built-in diffusing disc.
To achieve this, fibre ends were treated with polishing sheets
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4159
Figure 7. 800 µm fibre under the microscope with 30x magnifica-
tion. (a) untreated (factory polished) (b) roughened (12 µm sheet).
– first with 5 µm and then 12 µm granulation. A homogeneous
treatment of the surface was insured by visual inspection us-
ing a fibre microscope. Figure 7 shows microphotographs of
a fibre end surface before and after the treatment.
This new mode-mixing approach was compared to the pre-
viously used techniques in a series of atmospheric measure-
ments over a 1.55km light path (one way) using setup HD
(see Table 1) and the LDLS as light source. All methods were
applied to the fibre bundle between light source (letter A in
Fig. 1) and telescope (C) as well as between the telescope (C)
and spectrometer (E). However, mode mixing between the
light source and telescope had almost no effect which is prob-
ably due to the fact that homogenized light sent out into the
atmosphere still can selectively induce modes in the fibre(s)
leading to the spectrometer. One reason for this can be the
inhomogeneous illumination of the telescope’s field of view
because the retro-reflector elements do not entirely cover the
surface of the array or the light beam partly misses the array.
Therefore, in the following, only mode mixing between tele-
scope and spectrometer is considered. Light losses caused
by the different methods were also quantified and both the
classical and the reversed fibre configurations were tested
(Sect. 3.3). In the former setup, a 200 µm fibre was added be-
tween the single 200 µm core fibre and the spectrometer. For
the latter, a 800µm fibre was used to couple the 6 ×200 µm
fibre ring to the spectrometer. The residual was determined
from a fit of 500 added scans between 313 and 325 nm con-
sidering the cross sections of O3(Bogumil et al., 2003), NO2
(Bogumil et al., 2003), HCHO (Meller and Moortgat, 2000),
and SO2(Bogumil et al., 2003). Results for both setups are
shown in Table 4.
Taking the atmospheric intensity of the uninfluenced fi-
bre as a fixed reference, vibrating the fibre (in the following
indicated by “V”) causes the smallest light losses for both
configurations followed by the novel “Roughened fibre end
mode-mixing method” (in the following indicated by “R”,
12 µm grit). The diffuser (denoted by “D”) leads to light
losses of 90 % (classical setup) and 75 % (reversed setup),
respectively.
The roughened fibre end yields the lowest residual rms
values for both fibre configurations. Vibrating the fibre in
the classical configuration yields comparable residuals at al-
Table 4. Comparison of different mode-mixing methods with LDLS
and classical (upper part) or reversed fibre configuration (lower part)
and their effect on intensity and residual. The number combination
in the legend indicates the fibre diameter on the light source end
(first number) and spectrometer end (second number). The 800 µm
fibre is always coupled to a ring of six 200 µm fibres. Errors in the
atmospheric intensities reflect variations through alignment and at-
mospheric conditions.
Fibre config. Method Atmos. int. Residual rms
(counts ms−1) at 500 scans
– 167 ±33 14 ×10−5
LDLS-800 →200 Vibrated (V) 143 ±28 8 ×10−5
(classical) Diffuser (D) 17 ±3 9 ×10−5
Roughened (R) 83 ±17 8 ×10−5
– 400 ±80 10 ×10−5
LDLS-200 →800 Vibrated (V) 310 ±62 9 ×10−5
(reversed) Diffuser (D) 105 ±21 7 ×10−5
Roughened (R) 250 ±50 6 ×10−5
most twice the intensity of the roughened fibre end. How-
ever, when the fibre is reversed, the roughening yields the
overall smallest residuals and only a modest loss of inten-
sity (38 % compared to the uninfluenced fibre against 23 %
vibrating against the uninfluenced fibre).
4.2 Temporal stability of mode-mixing methods
To reduce measurement errors and to lower detection lim-
its, spectra in the LP-DOAS analysis can be added up be-
fore the DOAS fitting process. At the expense of tempo-
ral resolution, this reduces photon shot noise. It relies on
the high temporal stability of the measurement system. A
good mode-mixing method, therefore, should also be tempo-
rally stable and residuals should decrease when spectra are
summed (with photon shot noise as fundamental limit). The
potential for residual rms reductions by adding spectra for
both the classical and the reversed fibre configuration was in-
vestigated summing spectra over up to 10h (see Fig. 8a and
b). For this, groups of single, consecutively recorded spectra
from the tests with the different configurations were summed
up after the measurements to correspond to periods of 1 to
600 min. Note that in Fig. 8 results for given measurement
times are plotted, thus the effects of the higher photon shot
noise due to signal reduction by the various mode-mixing
techniques are included. Averaging measurement data are not
necessary for typical applications but may be required if very
weak signals need to be identified.
In the classical fibre configuration, the diffusing disc only
attains residual rms values comparable to vibrated and rough-
ened fibres when 10 h of observations are added up. Vibrat-
ing and roughening for all time spans yields lower results
than without additional mode mixing, with lowest residuals
for the roughening (Fig. 8a). In the reversed setup, the dif-
ferences between the methods are generally smaller, which
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4160 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
could be due to the favourable effect on mode mixing of the
800 µm fibre coupling into the spectrometer. Residuals for
measurements with the diffuser after 60 min are even smaller
than for a vibrating fibre. The best overall results for both
fibre configurations and all tested mode-mixing methods are
consistently attained by the reversed (200 →800) configura-
tion with roughened fibre end.
4.3 The optimal mode-mixing setup
Considering light losses (looking at counts per millisecond;
see Table 4), vibrating the fibre leads to smaller losses com-
pared to roughening the fibre end. In the reversed (200 →
800) fibre configuration, this disadvantage of the roughening
is more than compensated for by the smaller residuals and
also yields the best results when considering the summation
of spectra over longer time periods. Compared with vibrating
and especially bending the fibre (Stutz and Platt, 1997), it has
the additional advantage of being very reproducible and lim-
iting mechanical stress on the fibre.
For the laboratory comparison with setup HD and a 3 m
800 µm fibre coupled to a 3 m Y-shaped bundle with 200µm
fibres, a 12 µm grit gave the best results. For a long-term LP-
DOAS instrument for operation in Antarctica with a 8.55m
fibre bundle in reversed configuration that includes a 1m
800 µm fibre (setup NMIII), 5 and 12 µm roughening gave
comparable results with a lower light loss for the 5 µm grit
size. We conclude that the fibre bundle needs to be optimized
for the particular measurement setup it is used with, consid-
ering the trade-off between homogenization of the field of
view illumination and light loss for the intended application.
5 Overall improvement of LP-DOAS measurement
performance
5.1 Intercomparison measurements in Heidelberg
In order to quantify the combined effect of the changes to the
fibre-based LP-DOAS setup discussed above, atmospheric
measurements with different configurations were performed
with setup HD over a residential area of Heidelberg for a pe-
riod of 6 weeks from 11 March until 3 May 2014. During this
time, the different configurations were each tested for at least
1 d. The influence of atmospheric conditions, as well as com-
parability and representativeness of these observations were
discussed in Sect. 2.3.
The measurements were analysed in a UV spectral win-
dow between 300 and 350 nm (where trace gases such as
SO2, BrO, formaldehyde, and ozone absorb). As a bench-
mark, the different improvements were compared against a
setup with a XBO_75 xenon lamp in a classical 800 →200
fibre configuration.
A fibre bundle with a 3 m 800 µm fibre coupled to a 3 m
Y-shaped bundle with 200 µm fibres was used in the classical
(setup XBO_75-800 →200) and reversed (setup XBO_75-
Figure 8. Residual comparison for different mode-mixing methods
and its temporal stability with LDLS and the reversed fibre config-
uration (a) and a classical fibre setup (b; for comparison the plot of
“roughened fibre exit” for the reversed setup is also included). The
mode-mixing methods are abbreviated as follows: V=vibration;
D=diffuser; R=roughened fibre end.
200 →800) fibre configuration before and after the fibre
roughening (R), which is the most efficient mode-mixing
treatment identified above (Sect. 4.3) was applied. The mea-
surement performance achieved with the benchmark setup
during this comparison period agrees with results from previ-
ous measurement campaigns when comparable components
were used. Results are summarized in Table 5.
Comparing the two light sources with a classical fibre con-
figuration (setups LDLS-800 →200 and XBO_75-800 →
200 in Table 5), the higher intensity and better temporal sta-
bility of the LDLS discussed in Sect. 3 are apparent. The av-
erage residual rms for the LDLS is about 30 % smaller, while
the received radiance is about 10% larger. The mode mixing
by roughening of the fibre end (“R”) reduces the residuals
by approximately a factor of 2 for XBO_75 and LDLS (se-
tups LDLS-800 →200-R and XBO_75-800 →200-R). In
the reversed fibre configuration with roughened fibre end
mode mixing (setups LDLS-200 →800-R and XBO_75-
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4161
Table 5. Comparison of atmospheric measurements in Heidelberg
utilizing the LDLS with different fibre configurations with and with-
out roughening (marked with “R”) against the benchmark light
source XBO_75 for the HD setup. The number combination in the
setup indicates the fibre diameter on the light source end (first num-
ber) and spectrometer end (second number). The 800 µm fibre is
always coupled to a ring of six 200 µm fibres. The 500 scans cover
different averaging times due to different intensities for the config-
urations but thus contain a similar amount of recorded photons. Er-
rors of the atmospheric intensities reflect variations through align-
ment and atmospheric conditions.
Fibre config. Atmos. int. Residual rms
(counts ms−1) at 500 scans
LDLS-800 →200 167 ±33 14 ×10−5
XBO_75-800 →200 143 ±28 21 ×10−5
LDLS-800 →200-R 83 ±16 8 ×10−5
XBO_75-800 →200-R 40 ±8 9 ×10−5
LDLS-200 →800-R 250 ±50 6 ×10−5
XBO_75-200 →800-R 26 ±5 7 ×10−5
200 →800-R), average residual rms values are comparable.
However, the received radiance (and hence temporal resolu-
tion for a given signal-to-noise level) of the XBO_75 is 1 or-
der of magnitude smaller than for the LDLS, again illustrat-
ing the advantage of the smaller arc spot of the latter. Con-
sidering the overall improvements from the benchmark setup
XBO_75-800 →200 to setup LDLS-200 →800-R, with re-
versed fibre configuration and roughened fibre end mode
mixing, average residual rms could be reduced by a factor
of 3.5 while detector signals increase by 70 %.
Example residual spectra illustrating the improvement
can be found in Fig. 9. Compared to the benchmark setup
(Fig. 9a), the use of the LDLS and the reversed fibre configu-
ration clearly decreases the residual improving both accuracy
and precision. The additional roughening (compare Fig. 9b
and c) further reduces systematic structures that are still vis-
ible in Fig. 9b, thus further improving the accuracy of the
measurements.
As the systematic comparison of the different configura-
tions with benchmark light source and the LDLS for several
summation periods from 1 min to 10 h in Fig. 10 indicates,
this advantage of the new LP-DOAS configuration even in-
creases to a factor of 5 in residual rms when spectra are
summed for 10 h (Fig. 8 and Sect. 5).
5.2 Performance in field campaigns and stability in
long-term operation in Antarctica
Following the investigations in Heidelberg, the modified
LP-DOAS setup with the overall best performance (LDLS-
200 →800-R, together with stray-light suppression by fil-
ters (see Table D1 for the models used for the different spec-
Figure 9. Examples of residual spectra and corresponding root-
mean-square (rms) values for the benchmark configuration with a
XBO_75W arc lamp and a classical fibre configuration (a), the new
LDLS light source and a reversed fibre bundle (b), and the new
LDLS reversed fibre bundle and roughened fibre ends (c). The lat-
ter was found to give the best results.
tral regions) and using the chromatic-aberration approach for
further stray-light suppression (see Sect. 3.4), was deployed
with a campaign-grade telescope. A description of the mea-
surement procedure for a first campaign in the Nördlinger
Ries in Germany (“NR” in Tables 1 and 6) can be found in
Appendix C.
Given sufficient temporal stability of the instrumental
setup, spectra within sets, across sets, or even across sub-
sequent recordings of a spectral window can be summed to
improve the signal-to-noise ratio and to lower detection lim-
its.
For the comparison of instrument performances in differ-
ent measurement campaigns, no truly regular and univer-
sal temporal resolution exists. We, therefore, indicate typi-
cal residual rms values and detection limits for two temporal
resolution regimes: high (2 to 10 min) and medium (30 min
to 2 h). Typical fit ranges, average residual rms values and
detection limits for selected absorbers are given in Table 6.
A second LP-DOAS setup (NMIII in Table 1) based on
the presented improvements was purpose-built for long-term
operation on the German Antarctic station Neumayer III
(70.67◦S, 8.27◦W) and operated for 31 months from Jan-
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4162 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
Table 6. Attained measurement performance for the detection of different absorbers during the field campaign in the Nördlinger Ries,
Germany (NR; total light path: 5.7 km), and during the long term observations on the German Antarctic Station Neumayer III (NMIII; total
light paths: 3.1 and 5.9 km). Where two values are available, attainable residual rms and detection limits for two different summations, and
hence temporal resolutions corresponding to 10 min (left value) and 30 min to 2h (right value), are indicated.
Absorber ClO O3BrO SO2HCHO NO2IO
Fit range NR 290–305 295–330 290–310 320–380 320–380 420–480 410–450
[nm]NMIII 287–305.5 286.5–329.5 302–346 286.5–329.5 302–346 352.5–386.5 290–310
Temporal res. NR 10∗/120∗30 10∗/120∗30 30 30 10∗/120∗
[min]NMIII 4/40 2/40 2/40 2/40 2/40 2/40 1.7/40
Residual rms NR 20∗/10∗15 15∗/10∗15 15 30 25∗/15∗
[10−5]NMIII 22/19 28/17 21/13 28/17 21/13 22/13 22/17
Detection limit NR 16.5∗/8.2∗1124 3.7∗/2.5∗139 166 61 2.1∗/1.2∗
[ppt]NMIII 7.5/6 420/282 0.81/0.56 21/14 180/138 62/35 1.2/0.5
∗The halogen-containing molecules were not fitted in the measurements from the Nördlinger Ries, as their presence was not expected. Instead, the respective
spectral regions were summed up for 10 min and 2 hand the attained residual rms values were used to estimate upper limits for the detection limits of these trace
gases. See Appendix E for details.
Figure 10. Systematic comparison of LP-DOAS setups with classi-
cal fibre configuration, classical configuration with improved mode
mixing, and the reversed fibre configuration with improved mode
mixing for the benchmark light source XBO_75 and the LDLS. At-
tained residual rms values for different summation periods up to
10 h are plotted.
uary 2016 to August 2018 (Nasse et al., 2019). It was set up
with two light paths, 3.1 km (1.55 km one way) and 5.9 km
(2.95 km one way), with nearly the same geographical ori-
entation between which the instrument could switch au-
tonomously depending on atmospheric conditions. This was
achieved by moving the end of the fibre (letter C in Fig. 1
and column c in 2) via a motorized x–y translation stage in
the focal plane of the telescope main mirror in order to point
the light beam to the respective reflector array. Since visibil-
ity on the ice shelf at Neumayer III station is often reduced
by blowing snow or atmospheric refractions due to strong
vertical temperature inversions (optical scintillation and mi-
rage effects), most of the time measurements were performed
on the shorter light path. The measurement routine was sim-
ilar to the one applied during the Nördlinger Ries campaign
with five different spectral windows (see Table D1). Aver-
age residual rms values and detection limits for selected ab-
sorbers measured with this setup can be found in Table 6.
During this long period of continuous operation, mainte-
nance requirements were mostly limited to a monthly clean-
ing of optical components of the setup, in particular the out-
side of the quartz front window (added to the Neumayer tele-
scope to prevent snow from entering the telescope and al-
low the interior heating of the telescope), and regular wave-
length calibrations. This routine maintenance and the repair
of smaller mechanical malfunctions could be performed by
the station’s wintering crew. Regular major maintenance was
only conducted on a yearly basis.
The long operation time allows us to draw conclusions
about the long-term performance of the light source and po-
tential ageing effects of the entire setup. Due to logistical
reasons and also in view of the low abundances of organ-
ics in the air, the LDLS in this setup was only purged daily
for 30 min with filtered air (rather than nitrogen gas). Am-
bient air was passed through a three-stage filtering system
of silica gel to remove water vapour, active charcoal to re-
move gaseous pollutants and a particle filter. The light source
reached a total operation time of about 22 500h before a per-
manent failure occurred. During this time, no realignment of
the light source-fibre coupling optics was required, which in-
dicates an exceptional spatio-temporal stability of the plasma
spot inside the bulb.
It is not possible in this setup to separate contamina-
tion and ageing phenomena of the optical components from
changes in the radiance of the LDLS. However, an investiga-
tion of reference spectra corrected by their respective back-
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4163
Figure 11. Evolution of the net radiance of reference spectra in the
NMIII setup over time for the five spectral ranges UV I through VIS
II defined in Table D1. The average intensity value (in counts) of the
reference spectra in the different measurement windows was cor-
rected for background light by subtracting corresponding reference
background spectra (light source blocked and shortcut in front of
the fibre end in the telescope). Following this, weekly medians were
calculated. Since the grating was changed in February 2017 in the
VIS I window, the recorded radiances (which due to the lower dis-
persion of the new grating were about 3 times higher) were adjusted
to that of the first grating (dotted line). Maintenance was performed
on a monthly basis (as far as meteorological conditions allowed)
and optical components (filters in the light source) were exchanged
after roughly 1 year of operation. This resulted in temporarily en-
hanced intensities.
grounds for all spectral windows (Table D1) shows similar
decreases in the average intensities for all spectral windows
(see Fig. 11). The largest decreases of 17 % and 12 % un-
til the first general maintenance of the instrument after the
first year of operation are observed for the UV I and UV II
spectral windows. A thorough cleaning of all optical compo-
nents, which was not always possible in Antarctic winter, and
an exchange of the bandpass filters in the light source could
restore intensities to 93 % and 95.5%, respectively. Through-
out the 31-month measurement period, intensities were never
lower than 80 % of the initial values (except for the days di-
rectly before the final lamp failure) even when components
were probably dirty. The seemingly irreversible intensity de-
creases of 4.5 %–7 % for the two UV spectral windows over
2 years might be explained by a permanent reduction of the
transmissivity of optical components, e.g. by solarization of
fibres and lenses or a decreased output of the LDLS.
6 Conclusions
Here we present a series of improvements to fibre-based
long-path differential optical absorption spectroscopy (LP-
DOAS) systems and discuss their respective contributions to
the overall improvement of the measurement accuracy and
precision. The basis for this study was a mono-static LP-
DOAS setup using optical fibre bundles for light coupling
between the different instrumental components.
A laser-driven light source (LDLS) with a high-pressure
xenon bulb was introduced as a new type of light source for
LP-DOAS measurements that combines the broad spectral
coverage of xenon arc lamps with the stability and simple
handling of LEDs (see Sect. 3.2). Compared to a XBO_75W
arc lamp, which was used as the benchmark in our analysis,
employing the LDLS leads to 35 % smaller residuals, while
the received signal and hence the temporal resolution of a
setup is about 70 % higher.
The small plasma spot of the LDLS allows us to reverse
the previously used fibre configuration of the LP-DOAS
which significantly improves performance (see Sect. 3.3).
The mixing of fibre modes that cause spectral structures
and limit accuracy is improved by this reversal through the
favourable properties of larger diameter fibres that now cou-
ple to the spectrometer (see Sect. 4). Furthermore, the overall
light throughput can be increased if the spectrometer has the
limiting étendue of the system (see Tables 1 and 3).
To decrease the influence of stray light on accuracy and
precision, the spectral origins of which were found to mainly
be a region between 450 and 650 nm (see Sect. 3.4), bandpass
filters adapted to the respective measurement spectral win-
dow can be used at the expense of transmissivity (losses of
40 %–50 %), which was already done previously. The appli-
cation of the LDLS allows a further suppression of stray light
by exploiting the chromatic aberration of the quartz lens that
couples the light from the light source into the fibre. Com-
bined, these measures lead to an overall stray-light reduction
of more than 95 % for measurements around 330nm yielding
stray-light levels of less than 0.1%.
To reduce an inhomogeneous illumination of the spec-
trometer grating caused by fibre modes, mode mixing can
be introduced. Here, we compared previously applied tech-
niques like vibrating or micro-bending of the fibre, adding
diffusers to the optical setup and a new fibre roughening
method (see Sect. 4). In this approach, the highly polished
end faces of the fibre bundle are artificially degraded with
polishing sheets (5 to 12 µm grit size). Thus a quasi-built-
in diffuser is added to the fibre. Compared to vibrating the
fibre, in the reversed fibre configuration the attained residu-
als are about 30 % smaller (at slightly higher light losses of
20 % to 40%; see Table 4). Compared to diffuser disks, light
throughput is about 4 to 10 times larger with the roughened
fibres at comparable rms values. It should be noted that this
method is not limited to setups with LDLS but can be ap-
plied, e.g. with conventional xenon arc lamps. The residual
with a “XBO_75W” and classical fibre bundle with a 800 µm
mono- to 200 µm multi-fibre bundle is reduced by a factor of
2, however, at the cost of a 70 % reduction of the total light
throughput (Table 5).
By combining the changes to the LP-DOAS setup, in inter-
comparison field measurements in Heidelberg, the residuals
could be reduced by a factor of 3–4 compared to the bench-
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4164 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
mark setup and residual rms values on the order of 6 ×10−5
in units of optical density could be achieved (see Fig. 10).
When the improvements described above were applied to
two campaign-grade LP-DOAS setups using smaller spec-
trometers (see Table 1), residuals of the order of (0.9−1.0)×
10−4were achieved under optimal conditions and, on aver-
age, 1.1−2.0×10−4in a long-term measurement campaign
in Antarctica. Measurements in the UV spectral region par-
ticularly benefit from these improvements. For instance, dur-
ing the measurements in Antarctica, average detection limits
of ClO were between 6 to 7.5 pptv at temporal resolution be-
tween 4 and 40 min. BrO could be detected at detection limits
of 0.6 to 0.8 pptv at temporal resolutions of 2 to 30 min (see
Table 6).
In conclusion, the application of the LDLS with its greatly
reduced operational complexity and maintenance require-
ments, its high spatial and temporal stability and its long life-
time has enabled a number of technical improvements to the
fibre-based LP-DOAS setup. These increase measurement
accuracy, precision, and reliability of LP-DOAS systems and
make this versatile remote-sensing technique much easier to
deploy even in longer field campaigns or permanently oper-
ated applications.
Data availability. The data in the figures are available upon request
from the corresponding author (Jan-Marcus Nasse).
Atmos. Meas. Tech., 12, 4149–4169, 2019 www.atmos-meas-tech.net/12/4149/2019/
J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4165
Appendix A: Additional information on LP-DOAS
instrumental setup
Figure A1. Working principle of the shortcut system. When the
shortcut is open, light can reach the main mirror, traverse the at-
mospheric light path, and be collected by the fibres (a). To record
a reference spectrum, a diffuse reflector plate (here a sandblasted
aluminium plate) is moved into the light path at a distance of 1 to
4 mm from the fibre end (b). The radiation is scattered from the sur-
face of this plate back into the fibre bundle without traversing the
atmosphere and is thus free of atmospheric absorption.
Appendix B: Details of stray-light investigations
B1 Bandpass filters used in stray-light investigation
Figure B1. Overview of the bandpass and long-pass glass filters
used in the investigation of the spectral origin of spectrometer stray
light and their influence on the spectrum of a LDLS. The spectra
recorded with a filter were scaled to match the spectrum without a
filter in the spectral region between 700 and 800 nm. This explains
the higher intensities of the WG 280 spectrum compared to the one
without a filter. The position of the fibre, with respect to the lens
coupling of the radiation from the LDLS into the fibre, was opti-
mized for filters in the light path. For the spectrum without a filter
this leads to the slightly different spectral shape.
B2 Locations of foci for different spectral ranges
Figure B2. Variation in the relative intensity of selected spectral
regions as a result of the chromatic aberration as a function of the
relative position of the fibre. Panel (a) shows results for a coupling
into a 800 µm fibre, panel (b) is the same as (a) but for a 200 µm
fibre. For both plots, the increasing selectivity towards the UV due
to the non-linear increase in the refractive index is visible. For the
smaller fibre diameter the chromatic-aberration filter becomes even
more selective.
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4166 J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements
Appendix C: Description of campaign in the Nördlinger
Ries (Germany) and technical details of the
measurement routine
A LP-DOAS setup based on the improvements discussed
above (setup “NR” in Table 1) was deployed in a 3.5-month
measurement campaign from 12 August until 8 Decem-
ber 2014 in the Nördlinger Ries, a rural area in southern Ger-
many. The campaign had a focus on investigating the link
between precipitation and emission of NO2and HCHO from
soils. The LP-DOAS was operated in five spectral windows
from the UV to the visible (see Table D1) on a 5.7 km light
path (2.85 km one way). Since these spectral regions are not
covered at the same time by the detector, the grating in the
spectrometer was turned sequentially to attain the different
spectral regions. The measures for stray-light reduction, i.e.
the bandpass filters and the chromatic-aberration filter ap-
proach, and for further stray-light suppression in the light
source (see Sect. 3.4) were changed and adjusted accordingly
between spectral windows.
When set up for a particular spectral window, atmospheric
and reference spectra were recorded alternately in sets (five
reference spectra interleaved with four atmospheric spectra).
At the end of each set, one atmospheric background and
one reference background were recorded after blocking the
light source. Especially when atmospheric conditions change
quickly, short temporal offsets between measurement (atmo-
spheric and reference) and background spectra are important.
In each spectral window, several (3–5) of these sets were
recorded before the grating was turned to the next spectral
position.
To avoid or minimize the influence of detector non-
linearity, exposure times for atmospheric and reference spec-
tra in LP-DOAS measurements were adjusted to yield com-
parable saturations of the CCD. The exposure times of atmo-
spheric spectra and hence the measurement time were, there-
fore, dependent on atmospheric visibility. The revisiting time
of a spectral window (here about 20–30 min) in the whole
measurement routine thus depended on the number and total
recording durations of the other spectral windows and hence
also on atmospheric visibility.
Appendix D: Measurement routine in field campaigns in
the Nördlinger Ries (Germany) and Antarctica
Table D1. Measurement routines for field campaigns in the
Nördlinger Ries (Germany; NR) and long-term observations on the
German Antarctic station Neumayer III (NMIII).
Spectral window UV I UV II VIS I VIS II VIS III
NR
Spectral range [nm] 258–343 308–393 404–489 508–593 603–688
Number of sets 2 5 5 2 2
Bandpass filter UG-5 UG-5 – – OG-550
NMIII
Spectral range [nm] 280–348 327–395 378–521a528–596 614–682
Number of sets 5 5 5 3b3b
Bandpass filter UG-5 UG-5 BG-25 GG-495 RG-610
aDue to instrumental stray-light problems, another grating was used for the VIS I
window in the Neumayer setup (see setup “NMIII” in Table 1). bFor optimization of
the measurement time, these spectral windows were skipped during most of the daytime
(solar zenith angle, SZA <85◦), since trace-gas molecules of interest here are expected
to only be present during the night because of their photochemical instability.
Appendix E: Estimate of detection limits
To estimate the expected detection limit of an absorber that is
not present in the atmosphere and hence not included in the
DOAS fit, the residual rms value in the spectral region where
the absorber would be fitted can be used. A upper limit of a
detectable concentration clim can be inferred by calculating
the concentration of the absorber along the light path Lfor
which the optical depth is as large as the root mean square
(rms) of the residual optical density:
clim =2·Rrms
1σ 0·L.(E1)
This estimate tends to be an upper limit for actually achiev-
able detection limits.
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J.-M. Nasse et al.: Recent improvements of long-path DOAS measurements 4167
Author contributions. JMN composed the manuscript and updated
all figures based on drafts by PGE (except Figs. A1 and 11). To-
gether with DP, SS, UF, and UP, JMN was involved in the planning,
design, and setup of the LP-DOAS instrument in Antarctica and
was responsible for its operation. Supported by DP, SS, UF, and UP,
JMN analysed and interpreted the Neumayer III data set contribut-
ing results in Fig. 11 and Tables D1 and 6. PGE, DP, and SS devised
the fibre-based optical setup including stray-light filtering and fibre
treatment used in the lab studies. PE designed, performed, and eval-
uated all Heidelberg-based measurements supported by DP, SS, and
UP. PGE, DP, and SS performed the measurement campaign in the
Nördlinger Ries. UF coordinates the project activities at the German
research station Neumayer III.
Competing interests. The authors declare that they have no conflict
of interest.
Acknowledgements. For the measurements at the Neumayer III sta-
tion we acknowledge the support from the Alfred Wegener Insti-
tute – Helmholtz Centre for Polar and Marine Research (AWI). We
thank Rolf Weller from AWI for his advice and practical help dur-
ing the entire campaign as well as the 36th, 37th, and 38th wintering
crews of the station and their respective air chemists Thomas Schae-
fer, Zsófia Jurányi, and Helene Hoffmann for taking good care of the
instrument. We thank three anonymous referees for their reviews.
Financial support. The measurement campaign in the Nördlinger
Ries (Germany) has been funded by the Max Planck Institute for
Chemistry in Mainz. Measurements at Neumayer III have been
supported by the Deutsche Forschungsgemeinschaft (DFG) in the
framework of the project HALOPOLE III (grant no. FR 2497/3-
2). Jan-Marcus Nasse was partially supported by the Evangelisches
Studienwerk Villigst (PhD scholarship) and the Studienstiftung des
Deutschen Volkes (PhD scholarship). The publication of this re-
search has been funded by the DFG within the funding programme
Open Access Publishing, the Baden-Württemberg Ministry of Sci-
ence, Research and the Arts, and Ruprecht-Karls-Universität Hei-
delberg.
Review statement. This paper was edited by Cheng Liu and re-
viewed by three anonymous referees.
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