Introduction
Within the last decades, progress in optical remote sensing of
atmospheric trace gases has led to a better understanding of many important
processes including air pollution, ozone, and halogen chemistry and the
evolution of volcanic plumes. Narrow-band structures in the trace gas
molecule's absorption spectrum are used to identify and quantify the amount
of a trace gas integrated along a line of sight, i.e. its column density (CD,
typically in units of molecules per cubic centimetre), and to separate its absorption
signal from interfering gas absorptions and scattering processes.
Differential optical absorption spectroscopy DOAS; seefor
details has become a well established technique for atmospheric
trace gas remote sensing in the UV–Vis with high sensitivity (detection
limits within the parts per billion to parts per trillion range for atmospheric light paths of a few
kilometres). A spectrometer and a telescope with narrow field of view (FOV)
are used to record spectra I(λ) of scattered sunlight, which are
compared to a reference spectrum I0(λ). The Beer–Lambert law describes
the corresponding spectral optical density τ(λ) with
σi(λ) and ci(l) being the absorption cross section and the
concentration of trace gas species i along a line of sight L,
respectively:
τ(λ)=-logI(λ)I0(λ)=∫0L∑iσi(λ)ci(l)dl+scatteringatmoleculesandaerosols.
Atmospheric UV–Vis optical densities are dominated by trace gas absorption
and scattering processes at air molecules or aerosols. The known absorption
cross sections of the trace gases together with a polynomial, which accounts
for the broad-band absorption and scattering effects, are fitted to the
measured spectral optical density. The fit coefficients represent the CDs
Si=∫0Lci(l)dl, i.e. the integrated trace gas
concentration along the light path difference of I(λ) and the
reference I0(λ). In principle, spatial distributions of trace gases
(images or height profiles) can be recorded by scanning of viewing angles
with a narrow FOV telescope e.g. multi-axis DOAS;.
More complicated optical set-ups allow us to record spectra of an entire image
column at once by using a two-dimensional detector array e.g. imaging
DOAS;. Images can then be recorded by column (push broom)
scanning. The acquisition times of these techniques used to be rather
large (often several minutes per image or profile for typical trace gas CDs),
limiting their application to processes that are spatially homogeneous on
that timescale or processes with very high trace gas CDs. Recently,
reported NO2 measurements with a hyperspectral
camera based on the imaging DOAS technique with considerably higher temporal
resolution (∼0.08Hz).
Determination of two-dimensional atmospheric trace gas distributions with
high time resolution at timescales of the order of seconds, i.e. fast
imaging, of atmospheric trace gases is possible with techniques recording all
spatial pixels of an image at once for a low number of spectral channels
see e.g.. This allows the study of phenomena which are not
accessible to conventional scanning methods. With fast trace gas imaging
techniques, sources and sinks of trace gases can be identified and quantified
on much smaller spatial and temporal scales than with conventional remote-sensing techniques. This allows us to, for instance, gain insight into small-scale
mixing processes and to distinguish chemical conversions from transport.
Most of the presently used atmospheric trace gas imaging schemes use either a
set of two band pass filters (BPFs) e.g. SO2 camera,
∼1Hz for volcanic emissions; see
e.g. or a tuneable BPF as a wavelength selective element e.g. NO2 camera,
∼3min per image for stack emissions of power
plants;. These techniques either involve intricate optical
set-ups with low light throughput or yield a rather coarse spectral
resolution, which might result in strong cross interferences see
e.g..
Here we study the application of Fabry–Pérot interferometers (FPIs) as
wavelength selective elements for trace gas imaging in the UV–Vis range. The
periodic FPI transmission spectrum is matched to the spectral absorption
structures of trace gases that often show a similar periodicity. Thanks to
the high correlation of the transmission spectrum of the wavelength selective
element and the trace gas absorption spectrum, a high sensitivity can be
reached and cross interferences with other absorbers are minimised, even if
only a small number of spectral channels (FPI tuning settings) is used
see and the discussion in Sect.
below. Air spaced FPI etalons are very robust devices and allow
for simple optical designs that can easily be implemented in imaging sensors.
We present a model study on the sensitivity and selectivity of FPI
correlation spectroscopy applied to SO2, BrO and NO2
(Sect. ). For exemplary measurement scenarios, we infer the
possible spatio-temporal resolution of these measurements for a specific
instrument implementation. We find that, for the three gases, imaging with
spatio-temporal resolutions about 2 orders of magnitude higher than state-of-the-art methods should be possible. In addition, we present a proof-of-concept study of the technique for volcanic sulfur dioxide (SO2),
validating the expected high accuracy and sensitivity of the technique with a
1-pixel prototype instrument. Further, we show that SO2 CDs can be
accurately retrieved from the recorded data without calibration (Sect. ).
(a) FPI schematics indicating the splitting of incident
radiation into partial beams that interfere to cause the FPI transmittance
spectrum (b), which is characterised by periodic transmission maxima
with a FWHM of δλ and a FSR of Δλ. The BrO
absorption cross section (upper panel) shows approximately periodic structures allowing for a high correlation with
spectral FPI transmittance. This leads to a modulation of the BrO optical
density as seen through the FPI with changing surface displacement d
(c). The apparent absorbance is the difference of the optical
densities of FPI settings A and B, representing maximum and minimum
correlation of FPI transmission and absorption cross section σ.
Fabry–Pérot interferometer correlation spectroscopy
Fabry–Pérot interferometer
The FPI is a fundamentally very simple optical device, known for more than a
century e.g. . In principle, it consists of two plane
parallel surfaces each with reflectance R, separated by a distance d (see
Fig. ). The medium between the plates has the index of
refraction n. Incident light (angle of incidence α) is split up in
partial beams with different optical path lengths between the two surfaces.
Due to interference of the transmitted partial beams, the spectral
transmission of the FPI is characterised by periodic transmission peaks,
referring to constructive interference. For high enough orders of
interference, the free spectral range (FSR) Δλ between two
transmission peaks in units of wavelength λ is approximately given
by
Δλ(λ)≈λ22ndcosα.
The finesse F of a FPI represents the ratio of FSR to the full width half maximum (FWHM) δλ of a transmission peak:
F=Δλδλ.
The finesse is a measure for the number of effectively interfering partial
beams and therefore increasing with the surface reflectance. However, it
also depends on the alignment and quality of the surfaces.
The spectral transmission as a function of λ and the FPI's instrument
parameters is given by
TFPI(λ)=1+4R(1-R)2sin22πdncosαλ-1.
Despite its simple design, the challenge in manufacturing FPI devices lies in
creating set-ups keeping d stable to a fraction of a wavelength across the
effective aperture.
Differential CDs assumed for the
different measurement scenarios. The values represent high values for CD
variations within a typical imaging FOV. The targeted detection limits are
indicated in italic.
Differential CD across imaging FOV (molec cm-2)
SO2: volcanic emission (low)
BrO: volcanic emission (high)
NO2: stack emission
300–315 nm
330–355 nm
424–445 nm
SO2
1×1017 (volcanic)
3×1018 (volcanic)
–
BrO
1×1014 (volcanic)
1×1014 (volcanic)
–
NO2
1×1017 (bgr. pollution)
1×1016 (bgr. pollution)
1×1016 (stack plume)
O3
3×1017 (SZA change strat.)
3×1017 (SZA change strat.)
3×1017 (SZA change strat.)
HCHO
5×1015 (background)
5×1015 (background)
–
H2O
–
–
1×1023 (background)
OClO
5×1013 (volcanic)
5×1013 (volcanic)
–
O4
–
1×1043 (O2 dimer, molec2cm-5)
1×1043 (O2 dimer, molec2cm-5)
Typical values based on
, , and . Absorption cross
sections are based on
, , , , , ,
and .
Detection principle
The concept of using FPI correlation to detect atmospheric
trace gases is described in . The correlation of periodic
absorption structures of atmospheric trace gases and the FPI transmission is
exploited. An apparent absorbance τ̃i of a trace gas i is
calculated from the optical densities of an on-band τA and off-band
τB channel:
τ̃i=τA-τB=logIA,0IA-logIB,0IB=(σ‾A,i-σ‾B,i)Si=Δσ‾iSi.
Si denotes the CD of a trace gas i. For the on-band channel, the
spectral pattern of the FPI transmittance is chosen to correlate with the
absorption band structure of the target trace gas, while for the off-band
channel the FPI is tuned to show minimum correlation with the target trace
gas absorption (see Fig. ). The apparent absorbance is – for
low trace gas optical densities – proportional to the CD of the trace gas.
The proportionality is Δσ‾, representing the difference
of the effective absorption cross section seen by channel A and channel B.
The optical densities τk are calculated from measured radiances Ik
transmitted by the FPI in a setting k=A,B:
Ik=∫ΔλI(λ)⋅TFPI,k(λ)dλ.
Ik,0 denotes the reference radiance without the target trace gas in the
light path. In practice, a wavelength range Δλ of high
correlation of spectral trace gas absorption and FPI transmission is
preselected with a BPF. Within this spectral range the FPI
physical parameters are optimised. Figure c shows the optical
density of BrO seen through an FPI with varying surface displacement
d. The maximum difference between maximum and minimum optical density
determines the FPI settings A and B. In addition, the finesse is chosen to
maximise the signal-to-noise ratio.
Here we apply FPI correlation spectroscopy for passive imaging of a trace gas
in the atmosphere. This means that the light source is scattered sky
radiation that is measured within an imaging FOV (e.g. 20∘ aperture
angle). We assume in the following that a reference I0 (i.e. a part
without trace gas) is always present within the image, so that S denotes
the differential trace gas CD compared to that reference.
The proportionality Δσ‾ of apparent absorbance
τ̃ and trace gas CD S (see Eq. ) can be calculated from
literature absorption cross sections of the target trace gas, a background
spectrum I0(λ) and a modelled instrument transfer function (see Sects. and ). Alternatively,
Δσ‾ can be determined through calibration see
e.g..
Model study for SO2, NO2 and BrO
FPI correlation spectroscopy can be applied to every trace gas species that
yields sufficiently strong spectral absorption structures in the regarded
wavelength range. In this section we present exemplary model studies for
imaging of SO2, NO2 and BrO. For each target trace gas
we regard a typical exemplary measurement scenario (Table ).
For the target species BrO and SO2 we use typical measurement
scenarios of volcanic emissions in the UV spectral range. For SO2 we
assume CDs that are typically measured in volcanic plumes of a comparably
weak volcanic emitter or an already highly diluted plume (required detection
limit of 1×1017 moleccm-2; see Table ). We
additionally chose a high and probably disturbing NO2 CD (1×1017 moleccm-2) in order to make the scenario also applicable to
SO2 measurements at ship or industrial stack emissions. Existing
filter-based SO2 cameras are subject to strong cross interferences in
this CD range see e.g.. In the scenario for
BrO we assume a relatively strong but not uncommon volcanic emitter,
with BrO mixing ratios of tens to hundreds of parts per trillion within the plume
(required detection limit of 1×1014 moleccm-2; see Table ) and high SO2 CDs
(3×1018 moleccm-2).
Gradients in the BrO distributions can give insight into in-plume
halogen chemistry see
e.g.. The NO2 scenario
(blue spectral range) is applicable to measurements of stack emissions at, for example, a coal power plant see e.g. but also to local
gradients induced by traffic (required detection limit of 1×1016 moleccm-2; see Table ).
We calculate the sensitivities and study the cross interference of the
apparent absorbance with other atmospheric absorbers for typical differential
CDs for the respective measurement scenario. Table lists the
assumed differential CDs of the trace gases absorbing in the same spectral
range as the trace gases under investigation. For these potentially
interfering trace gases we chose relatively high values, so that the
indicated cross interferences correspond to upper limits. The listed CDs
represent differential CDs across a typical image FOV (∼20∘),
assuming that within the image a reference region I0 without the
target trace gas is always present.
In a second step, we calculate the corresponding photon budgets in order to
infer the approximate achievable spatial and temporal resolution of the
respective imaging measurement.
Description of the model
The apparent absorbance is calculated from radiances
Ik (in photonss-1mm-2sr-1) of scattered solar
radiation transmitted by the respective spectral channel k=A,B (on-band and
off-band FPI setting):
Ik=∫dλI0(λ)e-∑iσi(λ)SiTFPI,k(λ)TBPF(λ).
A spectrum recorded on a clear day in Heidelberg with a solar zenith angle of
73∘ (160∘ relative solar azimuth, 89∘ viewing zenith
angle) was used to approximate the spectral radiance I0(λ).
I0(λ) was scaled with scattered sky radiance measurements from
. The radiance measurements were performed in
Innsbruck in February 1995 with a solar zenith angle of 68∘. For our
calculations we used the values for a 180∘ relative solar azimuth and
70∘ viewing zenith angle. Si is the CD of an absorbing gas species
i with spectral absorption cross section σi(λ). TFPI,k
is the FPI transmittance in configuration k (see Eq. ) and
TBPF the transmittance of the BPF isolating the measurement wavelength
range for the respective target trace gas. TBPF was modelled with a
higher-order Gaussian function:
TBPF(λ)=Pe-(λBPF-λ)22c2p,
with a FWHM of
δλ,BPF=2c2(log2)1p.
P describes the peak transmission at a central wavelength λBPF.
An order p=6 was used to approximate interference filter transmission
profiles.
With Eq. () and the intensities Ik from Eq. (), the
apparent absorbance τ̃i can be calculated, allowing us to study the
sensitivity and selectivity of the detection of a trace gas i for given FPI
instrument settings.
Instrument parameters of FPI, BPF and optical set-up used for the
simulations. The radiance for the on-band setting IA at the detector was
approximated based on the instrument parameters and sky radiance values from
.
Instrument parameters
SO2
BrO
NO2
dA (µm)
21.60
11.52
23.72
FPI surface displacement setting A
dB (µm)
21.44
11.62
23.63
FPI surface displacement setting B
R
0.7
0.7
0.7
FPI surface reflectivity
PBPF
0.7
0.7
0.7
BPF peak transmission
λBPF (nm)
308
342
434
BPF central wavelength
δλ,BPF (nm)
10
20
18
BPF FWHM
f (mm)
50
focal length of imaging optics
Θ (∘)
1
required parallelisation
a (mm)
0.44
aperture radius of imaging optics
aFPI (mm)
7.5
aperture radius of FPI
η
0.25
0.5
loss factor
γFOV (∘)
17
imaging FOV of camera
IA (photonss-1mm-2sr-1)
4.51×109
1.48×11
5.17×1011
In addition, we approximate the respective detection limits based on photon
shot noise. In order to calculate the number of photons that reach the
detector of the imaging device, we need to know the etendue (product of
entrance area A and aperture solid angle Ω) of the employed optics.
suggest several optical set-ups for FPI correlation
spectroscopy imaging implementations. Here, we chose the set-up in which, with
help of image space telecentric optics (see Fig. ), the
incident radiation from the imaging FOV is parallelised before traversing the
FPI and BPF. In order to avoid strong blurring of the FPI transmission
spectrum due to different incidence angles, the divergence Θ of the
light beams traversing the FPI should not be much larger than Θ=1∘. With a lens of focal length f this condition limits the maximum
aperture radius a to
a=ftanΘ2.
The FPI clear aperture radius aFPI determines the imaging FOV aperture
angle:
γFOV=2arctanaFPIf.
The etendue per pixel Epix is determined by the spatial resolution of
the recorded image, which can be varied by binning individual pixels. For
npix being the number of pixels along a column of a square detector
array, the approximate etendue per pixel of the instrument is
Epix=ApixΩpix≈a2sin2γFOV2npixπ2.
The detectors' quantum efficiency and losses within the optics are considered
to be not wavelength dependent in the regarded spectral ranges and combined
in a loss factor η. We chose a somewhat lower loss factor for the UV
range
(0.25 for SO2 and BrO) compared to the visible range (0.5 for
NO2) due to the higher quantum efficiency of commonly used detectors.
Each FPI channel (on-band and off-band setting) requires one image
acquisition. We assume a measurement limited by photoelectron shot noise,
where for an exposure time Δt the number of counted photoelectrons
per pixel and image is
Nphe,pix=IEpixηΔt,
with an uncertainty of ΔNphe,pix=Nphe,pix. The uncertainty in the apparent absorbance τ̃ is then
Δτ̃≈2Nphe,pix,
assuming the intensities Ik for the two FPI settings k=A,B are similar
and that the reference intensities I0,k have to be recorded only once.
Note that the used sky radiances, loss factors and dimensions of the optics
(see Table ) represent conservative assumptions. For instance the
light throughput could be enhanced by more than an order of magnitude by
choosing a different optical set-up see. There, the FPI
is placed in front of the lens using the full clear aperture and the full
aperture angle of the FPI and the optics. Each viewing direction of the FOV,
however, will have a different incidence angle onto the FPI and therefore a
different FPI transmission spectrum, which has to be accounted for in the
data analysis. Alternatively, simply a larger FPI could be used. The results
of the following calculations for the image space telecentric optics,
therefore, represent lower limits of the performance.
Model results for SO2: (a) the differential optical
densities of the assumed differential trace gas CDs are plotted in the upper
panel. The lower panel shows the spectral radiance of the sky (dashed line)
and the transmitted spectral radiances of the FPI and BPF (drawn lines,
on-band in black, off-band in grey). Panel (b) shows the calculated calibration
curve for SO2 only (drawn line) and with different interfering
species included (dashed lines, CDs in molecules per square centimetre; see legend
and Table ).
Model results for BrO: (a) the differential optical densities
of the assumed differential trace gas CDs are plotted in the upper panel. The
lower panel shows the spectral radiance of the sky (dashed line) and the
transmitted spectral radiances of the FPI and BPF (drawn lines, on-band in
black, off-band in grey). Panel (b) shows the calculated calibration curve for
BrO only (drawn line) and with different interfering species included
(dashed lines, CDs in molecules per square centimetre; see legend and Table ).
Model results for NO2: (a) the differential optical
densities of the assumed differential trace gas CDs are plotted in the upper
panel. The lower panel shows the spectral radiance of the sky (dashed line)
and the transmitted spectral radiances of the FPI and BPF (drawn lines,
on-band in black, off-band in grey). Panel (b) shows the calculated calibration
curve for NO2 only (drawn line) and with different interfering
species included (dashed lines, CDs in molecules per square centimetre; see legend
and Table ).
Results of the simulations
The FPI correlation spectroscopy technique allows for
numerous different realisations regarding the used spectral window and FPI
instrument parameters that can be chosen according to, for example, measurement
conditions or availability of optical components (FPI, BPF). Here, we
identified spectral windows in which the target trace gas absorption cross
sections exhibit approximately periodic structures and appropriate FPI
parameters were determined in order to maximise the correlation of FPI
transmission and trace gas absorption according to the procedures described
in . Table lists the parameters for the
exemplary set-ups we use in this work.
The results for SO2, BrO and NO2 are summarised in
Figs. , and , which show the
differential optical densities of the target trace gas and the potentially
interfering trace gases for the respective measurement wavelength ranges
(Figs. 2a, 3a, 4a). In the lower panels, the transmitted spectral radiances of the
respective FPI spectral channels (on-band, off-band) are plotted. The
SO2 and NO2 trace gas optical densities clearly dominate the
total differential optical density for the targeted detection limits. For
BrO the other trace gases exhibit differential optical depths on the
same order of magnitude as BrO. In Figs. 2b, 3b and 4b,
the respective simulated calibration curves are plotted, where the dashed
lines indicate the impact of the individual interfering gases for the
assumed amounts. For all three gases these impacts are well below the
targeted detection limit. Especially for the case of BrO this
illustrates how FPI correlation spectroscopy can effectively separate the
absorption structure of a single trace gas from a multitude of trace gas
optical densities of the same order of magnitude. By using more than two FPI
settings, the selectivity can be enhanced even further.
Image space telecentric optical set-up for parallelising light from
the imaging FOV before traversing the FPI and BPF.
Simulation results: the spatial resolution of a FPI correlation
spectroscopy measurement was calculated for an exposure time of 10s
and the target detection limits, shown in Table .
Simulation results
SO2
BrO
NO2
Δσ‾ (cm-2)
1.5×10-19
6×10-18
1.1×10-19
Target det. lim. (moleccm-2)
1×1017
1×1014
1×1016
Target det. lim τ̃
0.015
0.0006
0.0011
Required Nphe,pix
8.9×103
5.6×106
1.7×106
Required Epix (mm2sr)
7.9×10-7
1.5×10-5
6.6×10-7
Max. spatial resolution (npix×npix)
226×226
51×51
252×252
The absorption bands of NO2 are not ideally periodic in the chosen
wavelength window. Therefore, at first glance they appear to be non-ideal for
FPI correlation. The apparent absorbance, however, is still reasonably high
with extremely low cross interferences to water vapour and O4. This
demonstrates that periodical absorption structures are ideal but not
necessary for FPI correlation spectroscopy. For a different measurement
scenario (here we optimised for stack and ship emissions; see above) there
might also be a better choice for instrument parameters. For instance for a
high-radiance and low-NO2 scenario one might use a single FPI
transmission peak on the NO2 absorption band at ∼435nm
(as setting A) and at ∼438nm (as setting B) in order to
increase the sensitivity (see Fig. ).
Table summarises the results of the photon budget calculations.
We calculated the maximum possible spatial resolution of the imaging
measurement for a 10s exposure time and the instrument parameters
listed in Table . For this, spatial pixels are co-added until the
targeted detection limit was reached. We find that for the targeted detection
limits the spatial resolutions of the imaging measurements for the chosen
parameters are 226 by 226 pixels for SO2,
51 by 51 pixels for BrO and 252 by 252 pixels for NO2
for a temporal resolution of 10 s. The temporal resolution could be
enhanced at the expense of the spatial resolution or vice versa. For
instance, cutting the linear spatial resolution in half (e.g. from 226 by 226
to 113 by 113 pixels for SO2), would reduce the temporal resolution
to 5 s for the same detection limit.
When comparing to corresponding DOAS measurements the increase in
spatio-temporal resolution becomes evident. A state-of-the-art DOAS
measurement takes around 1s to reach a detection limit of
1×1014moleccm-2 BrO for one spatial pixel. To
scan the ca. 2600 pixels of the assumed BrO image would take 2600 s. This is,
however, a comparison with an instrument that is not optimised for these kinds
of imaging measurements. recently recorded NO2
images with a hyperspectral camera, based on imaging DOAS. A detection limit
of
around 1×1016moleccm-2 NO2 is reached with a
spatial resolution of 480 by 640 pixels and 3 by 3 pixel binning with
12 sframe-1. This is only a factor of 2.2 slower than our
calculation for the telecentric set-up. By applying the standard optics
introduced in , the light throughput is increased by another
factor of 32. Therefore, theoretically, the FPI technique can be a factor
of ∼70 times faster. Of course these values always depend on the size of
the assumed instrument optics. Our results show that FPI correlation
spectroscopy can be about 2 orders of magnitude faster than conventional
DOAS measurements while maintaining a similar degree of selectivity and
interference suppression.
The presented results of the exemplary calculations for SO2,
BrO and NO2 suggest that FPI correlation spectroscopy can also
be implemented for other trace gases with similarly strong and structured
absorption, such as, for example, O3, HCHO, IO or OClO.
Proof of concept: field measurements of volcanic SO2
Sensitivity and ozone interference
The above model study on trace gas detection with FPI correlation
spectroscopy was validated in a proof-of-concept field study for volcanic
SO2. In a 1-pixel prototype a single photodiode was used as a
detector. A BPF (λBPF≈310nm,δλ,BPF≈10nm) was used for the preselection of
a wavelength range, for which the SO2 differential absorption is strong
and approximately periodic (see Fig. ). A FPI (air-spaced
etalon from SLS Optics Ltd.) with a FSR of 2.1nm and a
finesse of 7 across a clear aperture of 20mm was tilted by a servomotor in order to tune it to the on-band and off-band transmission settings.
The individual plates of the FPI have a finite thickness and two surfaces;
the outer surfaces have an anti-reflective coating and are slightly wedged
from the inner surfaces of the plates, so their influence can be neglected
here. The optical set-up behind FPI and BPF consists of a fused silica lens
(f≈50mm), which projects light from a narrow FOV (∼0.8∘ aperture angle) onto the photodiode.
Radiances for the on-band and off-band channels were recorded, delivering an
apparent absorbance measurement with 0.42Hz. A telescope (∼0.5∘ aperture angle) was co-aligned with the 1-pixel FPI set-up and
connected to a temperature-stabilised spectrometer (spectral resolution ∼0.8nm). The recorded spectra (∼0.13Hz) were evaluated
with the DOAS algorithm.
The measurement was performed at the Osservatorio Vulcanologico Pizzi
Deneri (lat 37.766, long 15.017,
2800 ma.s.l.) at
Mt Etna on Sicily on 30 July 2017. The device was pointed towards the
volcanic plume of Mt Etna with a constant viewing angle (8∘ viewing
elevation, azimuth 280∘ N). A plume-free part of the sky (zenith
viewing direction) was used for reference measurements and recorded prior to
the plume measurement. Figure shows the time series of the
apparent absorbance of the FPI correlation spectroscopy prototype together
with the SO2 CD retrieved from the co-recorded spectra. The apparent
absorbance shows high correlation with the retrieved SO2 CD. In
Fig. the correlation plot is shown. For high SO2 CDs
the sensitivity of τ̃SO2 decreases slightly due to
saturation effects. The scatter of the values mainly originates from slight
misalignment and the difference of the two narrow FOVs.
Time series of the apparent absorbance of the 1-pixel FPI
correlation spectroscopy prototype for SO2 detection (top trace, left
scale) recorded at Etna, Sicily, on 30 July 2017. A co-aligned telescope was
used to simultaneously record spectra for DOAS evaluation of SO2 and
O3 (centre and bottom traces and right and bottom left scales,
respectively). The apparent absorbance nicely correlates with the SO2
CD (see Fig. ), while no O3 impact is observable. The
growth of the retrieved O3 differential CD is expected due to the
increasing stratospheric O3 column for increasing solar zenith angle
(see text).
Correlation plot of the recorded FPI correlation spectroscopy
apparent absorbance and the SO2 CD retrieved by DOAS. A sensitivity
of about Δσ‾SO2 of 10-19cm2
is reached for lower SO2 CDs. For higher CDs a flattening of the
curve is observed that is induced by saturation effects due to the high
SO2 optical densities at the absorption peaks.
The recorded UV spectra also allow for evaluation of the O3 absorption.
The lower panel of Fig. c shows the change of the differential
O3 CD during the measurement with respect to the reference. The
observed increase in the O3 CD by more than
4×1018moleccm-2 during the plume measurement is due to
the increasing stratospheric light path with increasing solar zenith angle
(63.58 to 79.31∘ during the measurement sequence).
Within an imaging FOV (of 17∘, for example) much lower differential
O3 CDs are expected (see Table ), since all pixels are
similarly affected by the change in O3 background. Even with this
extreme change in O3 CD no impact on the recorded SO2
apparent absorbances is observed.
The presented data also indicate the potential of using an additional DOAS
measurement for the calibration of the apparent absorbance of an FPI imaging
device. The position of the narrow FOV of a DOAS telescope pointing into the
wide imaging FOV can be retrieved from time series and used for an
in-operation calibration see e.g..
Calculation of SO2 CDs by modelling effective absorption cross sections
As stated in Sect we can also directly
calculate the SO2 CDs from the apparent absorbance τ̃ by
modelling the effective absorption cross sections and thereby
Δσ‾SO2. This requires knowledge about the
instrument spectral transmission, the background scattered light spectrum and
the SO2 absorption cross section.
We modelled the instrument transfer function with the transmission spectrum of
the used BPF, the calculated FPI transmission spectrum (see
Sect. ) and the quantum efficiency of the photodiode. The
background scattered sunlight spectrum was modelled using a high-resolution
solar atlas spectrum according to , scaled by the
wavelength to the fourth power (assuming Rayleigh scattering) and multiplied
with the transmission of the total slant atmospheric ozone column. The ozone
column was estimated to 2.5×1019moleccm-2 using the
vertical ozone column for the measurement day according to satellite
measurements, TEMIS database; multiplied with a geometric
air mass factor for the average solar zenith angle during the measurement.
The SO2 absorption cross section of was used.
Correlation plot of the SO2 CDs retrieved by modelling and
the SO2 CDs retrieved by DOAS. The error bars indicate the
uncertainty of the FPI finesse (±3 %) and the background spectral
radiance in the model (±10 %) and the DOAS retrieval error. A high correlation is observed and the saturation effect is
accounted for by the model as well.
The largest uncertainties are the finesse of the FPI and the modelled
background spectrum, in which Rayleigh scattering approximation and the assumed
ozone column introduce uncertainties. A finesse of about 7 is reported by
the manufacturer for perpendicularly incident radiation. For the instrument
model we have to calculate the effective finesse for a divergent light ray
(∼0.8∘ aperture angle) for the two FPI tilt positions (around
0∘ for setting B and 5∘ for setting A, corresponding to a
finesse of around 7 and 5, respectively). Since the divergent light ray
reaching the detector is dependent on focal length, detector area and the
alignment of the optical components and due to the uncertainty in the
reflectance of the FPI, we can determine the finesse only with an uncertainty
of ±3 %. Further, we estimate an uncertainty in the background spectrum
by ±10 % in our calculation, accounting for uncertainties in atmospheric
radiative transfer and ozone column.
Figure shows the SO2 CDs calculated with the
described FPI model as a function of the SO2 CDs retrieved from the
DOAS spectra. We observe an excellent agreement with a slope of 0.99, an
intercept of 7.5×1015moleccm-2 and R2=0.96. The
uncertainties in background spectral radiance and finesse result in a
uncertainty in the SO2 sensitivity
Δσ‾SO2 of around ±10 % and therefore a
relative uncertainty of ±10 % in the retrieved SO2 CD. Here, it
is important to highlight the difference between ozone interference with the
apparent absorbance and the influence of an uncertainty in the total ozone
column assumed in the model. The former seems to be negligible as shown by
the measurements (Fig. ) and in the model
study (Sect. ). The latter influences the modelled sensitivity of the
measurement. This means it introduces a small relative uncertainty to the
retrieved CDs, which has almost no influence on the detection limit. The
saturation effects observed for high CDs in the apparent absorbances (see
Fig. ), meaning the CD dependency of
Δσ‾SO2, are accounted for by the model as
well. This is a very promising result, pointing towards the possibility of
calibration-free measurements, which would be another major advantage of the
FPI correlation spectroscopy compared to, for example, filter-based SO2
cameras.
Imaging
The 1-pixel FPI correlation spectroscopy prototype, introduced in this
study, can be implemented in a full-frame imaging instrument. This is the
major advantage of the technique compared with the DOAS technique. The
imaging implementation can be achieved with, for example, the image space telecentric
optical set-up, used for the above calculations and shown in Fig. . In principle, the single-pixel detector (photodiode) is
replaced by a two-dimensional detector array (UV sensitive for SO2
and BrO) and an aperture stop is added in the focal plane in front of
the lens. This would, however, reduce the light throughput per pixel of the
imaging set-up compared to the 1-pixel prototype. Alternatively, the FPI
could be placed in front of the lens using the full clear aperture and the
full aperture angle of the FPI and the optics, increasing the light
throughput by a factor of 32 see. This leads to a much
higher light throughput; however, the incidence angle of the incident light
onto the FPI and thereby the FPI transmission spectrum becomes dependent on
the pixel (i.e. the viewing direction within the imaging FOV) and has to be
accounted for in the data evaluation.
Conclusions
Many locally variable atmospheric processes are difficult to
quantify with state-of-the-art UV–Vis remote-sensing methods (e.g. DOAS) due
to the limited spatio-temporal resolution. This makes it difficult to, for
example,
study the emission of point sources or to separate the effects of transport
and chemical conversion on local scales. proposed the FPI
correlation spectroscopy for SO2 in the UV wavelength range after
similar approaches have been studied in infrared wavelength ranges
e.g. . The major motivation is
to reduce the number of spectral channels used for the trace gas detection in
order to increase the spatio-temporal resolution of the measurement while
maintaining its selectivity.
In a model study we investigated the sensitivity and determined the photon
budget of FPI correlation spectroscopy for three measurement scenarios for
SO2, BrO and NO2. For SO2 we assumed a
scenario with rather low volcanic emissions, which is also representative for
industrial stack or ship emissions. For BrO a scenario with stronger
volcanic emissions was assumed, with BrO mixing ratios of 10 to
100ppt within the volcanic plume and high SO2 CDs. The
NO2 measurement scenario represents typical stack emissions of power
plants and gradients of local air pollution induced by traffic, for example.
For all three investigated gases, cross interferences with other trace gases
absorbing in the preselected spectral ranges were found to be very low,
meaning that the selectivity of FPI correlation spectroscopy can be similar
to the selectivity of conventional techniques (e.g. DOAS). In this study, we
only used two FPI settings. A larger number of FPI settings could be used to
further reduce possible cross interferences.
Using rather conservative assumptions regarding the intensity of the incoming
radiation and the size of the instrument optics, we calculated the highest
possible spatio-temporal resolution of the FPI correlation spectroscopy
measurements for the different scenarios and found that they can be more than
2 orders of magnitude higher compared to state-of-the-art DOAS measurements
for the same trace gas CD. This means that in the same time period a
conventional dispersive technique records a single viewing direction (i.e. a
single spatial pixel), almost an entire image can be recorded with the FPI
correlation spectroscopy. This strongly indicates that future instruments
based on FPI correlation spectroscopy can provide unprecedented insight into
short time or small-scale processes in the atmosphere.
In the second part, we presented a proof-of-concept field study for FPI
correlation spectroscopy applied to volcanic SO2, which confirms the
model simulations by comparing the measured apparent absorbance to
SO2 CDs retrieved by a co-aligned DOAS measurement. One particularly
important finding is that, as expected from the model study, no O3
cross interference can be observed over a large O3 CD range. Further,
SO2 CDs could be directly calculated from the instrument model and a
very simple radiative transfer model very accurately and with a ∼10 %
uncertainty of the sensitivity. This indicates that CDs can be retrieved
directly from the FPI radiance data without calibration.
The extension of the 1-pixel prototype to a camera can be accomplished
comparably easily by minor modifications of the optics and by using a UV-sensitive detector array and should be the aim of future studies. By
replacing the FPI and the BPF, the instrument is adjusted to measure
different trace gases, e.g. BrO and NO2, according to the model
calculations performed in Sect. .
The applications of UV–Vis FPI correlation spectroscopy mentioned in this
work represent only some examples for trace gases and phenomena that could be
studied. Beyond the volcanological application, FPI imaging can for instance
be used to study SO2 in air pollution or BrO in salt pans
see e.g.. The technique can also be applied to other
trace gases with similarly strong and structured absorption, such as, for
example,
O3, HCHO, IO or OClO.