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92 Analytical Techniques for Atmospheric Measurement
function of the parameter y, while the inset shows the relationship as a function of the
pressure in torr. The three molecules shown – which have vastly different Doppler widths
at the frequencies selected: OH (
D
= 00053 cm
−1
CH
2
O
D
= 00032 cm
−1
and HBr
D
=00018 cm
−1
– were chosen to represent the range of Doppler halfwidths that one
would typically encounter in atmospheric studies. As can be seen in the main plot, all
three molecules yield the same behavior as a function of the parameter y, as expected from
Equation 2.19a; for each fixed value of x in this equation the y parameter governs the
value of the fractional term in the brackets. Hence, in addition to the example calculation
above, one may use the main plot of Figure 2.7(a) as a convenient means to quickly
determine the value for the normalized line centre Voigt function. In this procedure, one
(1) determines the y value for the specific molecule of interest at the sampling pressure
employed, and (2) the normalized line centre Voigt function is determined utilizing the
curve.
The inset in Figure 2.7(a) shows the normalized line centre Voigt function versus
sampling pressure, and this indicates that equivalent y values occur at different sampling
Γ(ν
0
)
V
Γ(ν
0
)
D
1.0
0.8
0.6
OH
CH
2
O
HBr
0.4
0.2
0.0
05
0.03044
+ 0.3603 exp – [0.2969y] + 0.6032 exp – [1.560y]
y
1510
0
0.0
0.2
y = 1
0.4
0.6
0.8
1.0
50
Pressure (torr)
100 150 200 250
20
(a)
Figure 2.7 (a) Calculated (at 296 K) line center Voigt function
0
V
normalized to the line center
Doppler function
0
D
versus the parameter y for three different molecules with vastly different Doppler
widths and comparable pressure broadening coefficients ∼01cm
−1
atm
−1
OH
0
=35684169 cm
−1
,
D
= 00053 cm
−1
,CH
2
O
0
= 28316417 cm
−1
,
D
= 00032 cm
−1
, and HBr
0
= 26061991 cm
−1
,
D
=00018 cm
−1
. The curve is a double exponential fit of the data and the resulting fit equation is given
above the curve for facility in calculating the normalized function. The inset shows this same normalized
Voigt function versus sampling pressure in Torr. The horizontal line intersects the three curves at y =1
at different sampling pressures, and this yields approximately the same normalized ratio value of 0.44
for the three molecules. (b) Plots of the Voigt line center spectral intensities in units of cm
2
molecule
−1
versus sampling pressure for the three molecules in Figure 2.7a.
Infrared Absorption Spectroscopy 93
9
8
7
6
5
4
3
2
1
250200150100500
Pressure (torr)
S(ν
0
)
V
×10
–18
OH
CH
2
O
HBr
(b)
Figure 2.7 (Continued).
pressures for the three molecules. As can be seen, pressure broadening has a smaller effect
on the normalized ratio for larger Doppler halfwidths, and this effect is most pronounced
at intermediate pressures in the 10–50 torr range. The value for the normalized Voigt
function from either plot or the spreadsheet calculations can be used to determine the
Voigt function at line centre from a simple multiplication of this normalized value with
the peak of the Doppler function at line centre. Equation 2.20b is then used to calculate
the Voigt spectral line intensity at line centre, S
0
V
, and Figure 2.7(b) plots these
values as a function of pressure for the three molecules. The values in this plot, which
show similar behavior as the inset of Figure 2.7(a), are the final values needed in the
Beer–Lambert Law absorbance calculations of the next section.
The Voigt profile just presented assumes that the Doppler distribution is unaltered by
collisions between molecules. However, at low pressures approximately in the 1–10 torr
range, the Maxwell–Boltzmann velocity distribution can be affected by collisions, and
this results in the phenomenon known as collisional-narrowing or Dicke-narrowing (see
Pine and Fried, 1985, and references therein). This effect is most pronounced in light
molecules (larger Doppler widths), cases where the pressure-broadening coefficients are
small, and where the mismatch in rotational energy levels between collisional partners is
small (i.e. where the collisional partner is the gas of interest such as in self-broadening
measurements). In such cases the Voigt profile underestimates the peak absorbance and
compensates with too much absorbance in the wings of the profile. Various collision
models and profiles have been developed to better describe the resulting lineshape, but
these will not be presented here. At typical sampling conditions, where the pressures are
of several 10s of torr and the broadening gas is air, the errors in the Voigt profile are
generally less than a few percent.
94 Analytical Techniques for Atmospheric Measurement
The IR absorption lineshapes just presented play an important role not only on
measurement sensitivity but also on selectivity. In addition, these lineshapes dictate
whether or not one can employ frequency modulation techniques, which rely on
modulating on and off absorption features. The relatively narrow absorption features
of Figure 2.7 all have Voigt linewidths less than 001 cm
−1
for sampling pressures of
50 torr. This is a major advantage of working in the IR spectral region compared to
the visible and ultraviolet regious, particularly when in situ measurements are carried
out employing a narrow spectral bandwidth laser light source and an absorption cell
operated at reduced sampling pressures of typically several torr to ∼100 torr. Under these
conditions, the IR Voigt absorption lineshapes for individual or small groups of lines are
generally well resolved from other absorption features, including features from the same
molecule and/or interference molecules. Even in cases where spectral overlapping occurs,
high selectivity can still be achieved in many cases since the interfering lines are generally
well characterized and small in number, and the absorption lineshapes are well known.
As a result, spectral deconvolution methods are frequently successful in minimizing such
problems. By contrast, in the visible and UV spectral regions the absorption features
often appear as dense clumps of unresolvable features, even under reduced sampling
pressures. The significantly increased Doppler halfwidths in the UV compared to the IR
are partially responsible for this congestion. Equation 2.14 indicates that
D
is directly
proportional to the line centre frequency (
0
, which in the UV is approximately one
order of magnitude larger than the IR.
2.3.2 Beer–Lambert absorption law and absorbance
The discussion in the previous section relating line centre Voigt spectral line intensities
to pressure does not give the complete picture for the instrument sensitivity one might
expect from an IR spectrometer. As we will now discuss, one must also fold in the number
density of the absorbing species and the sample pathlength, l. The absorber number
density is expressed by the product of three terms, P (the sample pressure in atm units),
the sample-volume mixing ratio (typically in ppmv, 10
−6
; in ppbv, 10
−9
; or in pptv,
10
−12
), and the total number density for the bath gas in the probed sampling volume,
N (molecules cm
−3
atm
−1
). These terms are used in the well-established Beer–Lambert
Law, which relates the above molecular parameters to measured light intensities:
I = I
0
exp−SPNl =I
0
exp−A (2.21)
This expression provides the basis upon which many IR absorption instruments rely,
directly or indirectly, for converting measured light intensities to quantitative mixing
ratio results. In this expression, I and I
0
are the frequency-dependent transmitted
and incident intensities, respectively, S is the spectral line intensity discussed in the
previous section, and the term A is the absorbance. The ratio I/I
0
is referred to as the
transmittance or sometimes simply as the transmission. Strictly speaking, according to the
International Union of Pure and Applied Chemistry, the term ‘absorbance’ is reserved for
Equation 2.21 written in base 10 logarithmic units, and the term A in Equation 2.21 is
properly called the optical depth, optical density,oroptical mass. However, it is common
Infrared Absorption Spectroscopy 95
practice in atmospheric studies to designate Av in base e units as the absorbance, and
we shall adopt this common usage here. In remote measurements (to be discussed) the
exponent is oftentimes referred to as the extinction, , which has contributions from
molecular absorption and scattering, as well as aerosol scattering and absorption.
Equation 2.21 is written for a single absorbing species; multiple absorbers are written
as a summation of terms in the exponent. Equation 2.21 applies equally well to intensities
integrated over the absorption feature or at line centre. In the case of the former, one
employs the integrated spectral line intensity, S, while in the latter one employs the line
centre spectral intensity, S
0
, and the line centre absorbance A
0
. In either case, it
is important to emphasize that the Beer–Lambert law relationship provides quantitative
results based on fundamental parameters and fundamental measured quantities, which
are independent of instrumental factors. Hence, direct absorption measurements using
this approach are considered absolute and, as will be discussed, do not require calibration
standards. This is in contrast to other measurement techniques such as fluorescence. The
lower panel of Figure 2.8 depicts the resulting relationship between the incident and the
transmitted intensities for a hypothetical absorption.
We now examine in more detail the unitless exponential term of Equation 2.21 at line
centre. In most cases in atmospheric studies, the unitless absorbance is considerably less
than 0.2, and the exponential term e
−A
can be replaced by its linear form 1−A. This is
referred to as the ‘optically thin’ absorption region. Using this approximation, one can
easily derive the following expression between the absorbance and the fractional change
in light intensity, I/I
0
:
A
0
=
I
0
I
0
0
(2.22)
Infrared
laser
source
Detector
&
data
reduction
Intensity
Time/wavelength Time/wavelength Time/wavelength
In
Out
Absorption cell
Temperature
pressure
gauge
I
O
I
O
I
I
Δν
Laser
<< Δν
Absorption
Figure 2.8 The top panel depicts the fundamental components of an IR absorption setup. The lower
panel shows the resulting recorded direct absorption profile along with the incident I
0
and transmitted
I intensities employed in Beer–Lambert Law calculations. Since the wavelength of the laser source is
scanned in time, the x-axis can be represented by either variable.
96 Analytical Techniques for Atmospheric Measurement
The smallest resolvable fractional change in light intensity at line centre, and hence the
minimum detectable line centre absorbance, is frequently employed in many atmospheric
studies as one means of characterizing instrument performance. This term is designated
A
0
min
or A
min
for short, and will be used throughout the rest of this chapter. Rewriting
Equation 2.21 for line centre conditions we arrive at the following expression with
associated units:
A
0
= S
0
cm
2
molecule
−1
P atmN molecules cm
−3
atm
−1
l cm (2.23)
This expression, which is the culmination of many of the previous expressions, is
highlighted to indicate its importance and the fact that it will be employed throughout
the remainder of this chapter when discussing instrument performance. Mostly, the
instrument performance figure of merit is given by A
min
normalized to absorption
pathlength and an effective detection bandwidth, typically in units of Hz
−1/2
:
A
min
lcm
√
effective bandwidth (Hz)
(2.24)
The following example illustrates how Equation 2.23 is used to calculate line centre
absorbance. We employ in this example the molecule CH
2
O, the conditions discussed in
the Example 1, and realistic sampling conditions we employ with our airborne tunable
diode laser system.
Example 2
Conditions of example
Gas is CH
2
O
M =30026 g mole
−1
T =296 K
0
= 28316417 cm
−1
(from HITRAN)
S = 504×10
−20
cm
2
cm
−1
molecule
−1
at 296 K (from HITRAN)
P = 500torr = 00658atm
S
0
V
= 202 ×10
−18
cm
2
molecule
−1
(from Example 1, at P = 50torr, or from
Figure 2.7b)
Pathlength l =100 m =10 000 cm
= CH
2
O = 1 ppbv = 1 ×10
−9
N = LT
0
/T =268678 ×10
19
27315/296 = 2479 ×10
19
molecules cm
−3
atm
−1
P atmN molecules cm
−3
atm
−1
= 00658 atm1 ×10
−9
2479 ×10
19
molecules cm
−3
atm
−1
= 16 ×10
9
molecules cm
−3
A
0
= 202 × 10
−18
cm
2
molecule
−1
16 × 10
9
molecules cm
−3
10 000 cm =
33 ×10
−5
Infrared Absorption Spectroscopy 97
Figure 2.9 shows the resulting A
0
calculations for CH
2
O as well as for OH and HBr
at other sampling pressures, using the data of Figure 2.7 and Equation 2.23. The three
profiles of Figure 2.9 reveal the results of two opposing terms with pressure: the decreasing
spectral line centre intensities with increasing pressure (Figure 2.7b) and the increasing
absorber number density N with increasing pressure. At low pressures, A
0
linearly
increases with pressure (Doppler regime), while at high pressures A
0
asymptotically
approaches its pressure-independent Lorentz value. In the case of the latter, the increase
in pressure in Equation 2.23 is cancelled by the P
−1
dependence; the Lorentz line centre
spectral intensity of Equation 2.23 is proportional to the Lorentz line centre shape factor
of Equation 2.18, which from Equation 2.17 indicates a P
−1
dependence. At intermediate
sampling pressures both pressure dependencies are operable. The profiles of Figure 2.9,
which essentially reflect the inverse behavior of Figure 2.7b, indicate a different asymptotic
roll-off region for the three molecules shown. The shaded points represent the A
0
value
equal to ∼90% of the asymptotic value at high pressure for each profile, and these occur at
different pressures. The larger the Doppler influence, the higher the roll-off pressure (e.g.
compare the largest Doppler profile of OH versus the smallest Doppler profile for HBr).
Figure 2.9 reveals the optimum pressure regime for the three example molecules shown
using mid-IR detection. The highest pressure yields the largest line centre absorbance, and
10
9
8
7
6
5
4
3
2
1
0
250200150100500
Pressure (torr)
A(ν
0
)
V
×10
–5
OH
CH
2
O
HBr
Figure 2.9 Plot of Voigt line center absorbance, A
0
V
, calculation for OH, CH
2
O, and HBr for
the conditions of Figure 2.7a as a function of sampling pressure for conditions of: T = 296 K, mixing
ration = 1 ppbv, pathlength = 100 m. The curves are double exponential fits of the data, and the three points
highlighted by shading on the three profiles represent ∼90% of the maximum line center absorbance
value for each profile. The relative magnitudes of the three profiles largely reflect the differences in the
integrated spectral line intensities for the three molecules. At 50 torr, the Voigt halfwidths are 94×10
−3
,
83 ×10
−3
, and 65 ×10
−3
cm
−1
respectively for the three molecules.
98 Analytical Techniques for Atmospheric Measurement
hence the highest sensitivity at the expense of measurement selectivity. Conversely, sampling
in the linear low-pressure regime yields the best selectivity at the expense of sensitivity and
the precision with which the sampling pressure must be controlled (i.e. a fluctuation in the
sampling pressure here results in a larger sensitivity change compared to the roll-off regime).
Given these two extremes, one should operate at sampling pressures somewhere around the
shaded points for the three profiles. One can use Figure 2.9 to estimate the optimum pressure
regime for other molecules. However, Equation 2.23 and the calculations of Example 1
for the particular conditions at hand should be utilized for precise determinations.
2.4 Trace gases in the atmosphere
With the exception of nitrogen, which exhibits the weak IR quadrupole transitions discussed
earlier, the mixing ratios for IR-active atmospheric constituents vary from the percent range
in the case of H
2
O near the surface to the pptv range in the case of various trace species.
Table 2.2 Typical mixing ratios of various trace atmospheric species
a
Constituent Chemical formula Volume mixing ratio Data source
Carbon dioxide CO
2
375 ppmv b
Ozone (troposphere) O
3
10–500 ppbv f
Ozone (stratosphere) O
3
0.5–10 ppmv f
Nitrous oxide N
2
O 318 ppbv b
Carbon monoxide (background) CO 50–160 ppbv c
Carbon monoxide (Airborne Bkg
levels to pollution plumes)
CO 17–1113 ppbv d
Methane CH
4
1755 ppbv b
Sum of Non-methane hydrocarbons NMHCs 1–25 ppbv e
Nitric oxide NO 0–1450 pptv d
Nitrogen dioxide NO
2
0–3349 pptv d
Nitric acid HNO
3
3–7412 pptv d
Ammonia NH
3
10 pptv–1 ppbv f
Hydroxyl radical OH 0–0.6 pptv d
Hydroperoxy radical HO
2
0.2–34 pptv d
Hydrogen peroxide H
2
O
2
50 pptv–10 ppbv d
Formaldehyde CH
2
O 25 pptv–11 ppbv d
Sulfur dioxide SO
2
3 pptv–31 ppbv d
Sum of halocarbons HCs 1.4–5 ppbv d
Carbonyl sulfide OCS 438–1219 pptv d
a
Mixing ratios vary considerably depending upon season, altitude, latitude, year, air mass type, proximity to local sources
and sinks as well as many other variables. The last column indicates the source of the data for the mixing ratio range.
b
2003 global average background levels from the NOAA Climate Monitoring & Diagnostic Laboratory (CMDL),
www.cmdl.noaa.gov
c
2003 range of background levels found in the southern and northern hemispheres from NOAA CMDL.
d
Range of airborne measurements during TRACE-P airborne campaign ( Jacob et al., 2003, data available from:
www-gte.larc.nasa.gov) spanning the 0–12 km altitude range.
e
Airborne measurements of the sum of alkanes and alkenes during the TOPSE 2000 airborne campaign (Atlas et al.,
2003) spanning the 0–8 km altitude range.
f
Brasseur and Schimel (1999).
Infrared Absorption Spectroscopy 99
12
11
10
9
8
7
6
5
4
3
2
1
0
Palt (km)
8007006005004003002001000
Mixing ratio (pptv)
[NO]
[NO
2
]
[CH
2
O]
[H
2
O
2
]
Figure 2.10 Pressure altitude median mixing ratios for eight different altitude bins for four different
trace constituents measured (1 minute measurements) in the Western Pacific region (110–150
longitude)
during the TRACE-P study. In the case of NO and NO
2
these measurements were obtained from the
Georgia Institute of Technology Laser-Induced Fluorescence Instrument as described in Sandholm et al.
(1997); the CH
2
O measurements were obtained from our tunable diode laser absorption spectrometer
as described in Fried et al. (2003b); and the H
2
O
2
measurements were obtained from the University of
Rhode Island Instrument as described in Snow et al. (2003).
During the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) airborne
campaign (Jacob et al., 2003, data available from: www-gte.larc.nasa.gov), for example, H
2
O
vapor mixing ratios spanned the range from 1 to 3% (10 000–31 000 ppmv) near the ocean
surface to 3–50 ppmv at altitudes around 12 km. Other atmospheric constituents measured
during this campaign and/or measured by global monitoring networks are tabulated in
Table 2.2. As can be seen, with the exception of the abundant atmospheric gases H
2
O,
CO
2
,O
3
,N
2
O, CO, and CH
4
, all other trace species typically exhibit atmospheric mixing
ratios below 50 ppbv and more frequently below 1 ppbv. In fact, in many instances during
this and many other campaigns, the mixing ratios of most trace atmospheric constituents
are frequently below 100 pptv, particularly when sampling remote background air at
high altitudes. This behavior is shown in Figure 2.10 for four different gases measured
during the TRACE-P campaign. Such ultra-low mixing ratios require not only long
absorption pathlengths but also very low A
min
values of less than 10
−5
.
2.5 Measurement approaches employing IR absorption
spectroscopy
In all the IR absorption methods that will be discussed, an absorption spectrum of
one form or another is ultimately generated, and quantitative results are obtained by
100 Analytical Techniques for Atmospheric Measurement
measuring the change in light intensity as a function of wavelength or frequency (in
wavenumbers). The methods that will be discussed differ with respect to the means
employed in acquiring absorption spectra as well as the methods used in converting
the acquired spectra into absorber mixing ratios. However, all methods are linked by
the fundamental requirement to wavelength disperse either the source or the received
radiation. In this section, we will present an overview of the various approaches that have
been employed, with specific emphasis on the broad distinctions between approaches.
Further details on each technique will then be presented in subsequent sections. The
various applications that will be discussed are only meant to provide a broad overview
of the field and not an exhaustive review of all applications.
One can characterize IR absorption methods in two broad categories: in situ and
remote. Figures 2.8 and 2.11 further depict two different variants of in situ measurements.
In both cases, the probed sample, which is in close proximity to the IR source and
detector, captures an in situ, spatially localized snapshot of the mixing ratio for the target
gas of interest. In most cases, the probed sample is continuously drawn through an
absorption cell at reduced pressure, and this is shown by the fundamental components
depicted in Figure 2.8. This approach is designated as extractive in situ sampling and has
the advantage that one may control the sampling conditions of pressure and temperature
to optimize the measurement performance. In practice, the absorption cell is typically a
multipass cell and a number of transfer optics are required to image the IR beam into
and out of the multipass cell and onto an IR detector.
The same basic components shown in Figure 2.8 are also applicable to the second
type of in situ system: open path in situ airborne measurements. Only in this case,
the sampling cell is replaced by the open atmospheric path, one example of which is
depicted in Figure 2.11. This example is described in detail by Diskin et al. (2002) for
ambient water vapor measurements on NASA’s DC-8 aircraft. In this approach, in situ
water vapor is probed in the 28.5 m round trip open path between the laser transceiver
mounted in the aircraft cabin and a panel of retroreflecting road-sign material mounted
on the outboard engine of the DC-8 aircraft. Unlike extractive in situ measurements,
one can neither control the sampling conditions in this open path arrangement nor add
calibration standards and/or zero air (air scrubbed of the gas of interest) to the sampling
stream while in flight. Instead one must employ a calibration-calculation matrix, which
is derived in the laboratory, to calibrate the instrument for various sampling conditions
of pressure and temperature. Despite these issues, open path in situ measurements are
ideally suited for reactive and ‘sticky’ gases, where the sample does not contact inlet and
cell sampling surfaces.
The IR light source schematically depicted in Figure 2.8 is an extremely important
component of all in situ measurement systems, and one can further define two broad
categories of IR light sources. The first category includes tunable solid-state laser sources,
as well as semi-continuously tunable gas laser sources, where accidental coincidences with
the molecular absorption features of interest are exploited. The study by Nelson et al.
(2002) is one of many examples of the former. The second category utilizes broadband IR
emission from hot filaments sources, which are ultimately wavelength dispersed before or
after the sampling cell using various types of monochromators, FTIR spectrometers, or
gas correlation cells and filter wheels. Both types of IR light sources yield high temporal
resolution and have produced very important flux measurements of various trace gases.
Infrared Absorption Spectroscopy 101
Laser
Transceiver
Retro-Reflecting
Panel (on Engine)
28
m Optical Path
NASA Dryden Flight Research Center DC-8
Figure 2.11 An example of an in situ open path system for airborne measurements of ambient water
vapor on NASA’s DC-8 aircraft (Diskin et al., 2002). Ambient water is probed in the 28.5 m round trip
open path between the laser transceiver mounted in the aircraft cabin and a panel of retroreflecting road-
sign material mounted on the outboard engine of the DC-8 aircraft. This figure was graciously supplied
by Diskin, Sachse, and colleagues at NASA.
For example, Ham and Heilman (2003) employed a commercial LI-COR instrument
using a broadband IR emission source and a chopper filter wheel assembly to measure
the eddy covariance flux of CO
2
and H
2
O from a tallgrass prairie and a cedar forest.
The study by Griffith et al. (2002) represents an example of FTIR flux measurements
of CO
2
,CH
4
,N
2
O, and H
2
O over agricultural fields using the flux-gradient technique.
Section 2.6 will highlight a third example where IR absorption measurements employing
a tunable solid-state laser source have been utilized to measure trace gas fluxes. The
studies of Grutter (2003) and Yokelson et al. (2003) represent examples of extractive
in situ FTIR measurements to investigate pollution and smoke emissions on ground-
based and airborne platforms, respectively. Although one can cite many other examples
and approaches, the discussions in the rest of this chapter will focus exclusively on