Optical Engineering 57(11), 114102 (November 2018)

Sensitivity limits on optical gas imaging due to
air turbulence
Nathan Hagen*Utsunomiya University, Center for Optical Research and Engineering (CORE), Department of Optical Engineering, Utsunomiya, Japan

Abstract. Infrared cameras are widely used for the detection of fugitive gas leaks and for quantifying gas emissions. While the gas detection sensitivity in the presence of noise is now well understood, we show that windturbulence-induced thermal fluctuations place a fundamental lower limit on gas detection sensitivity. While formany gases the lower limit is too low to be important, we show that for some gases it places a real limitation on
measurements when the background is a near-ground surface. © The Authors. Published by SPIE under a Creative Commons
Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its
DOI. [DOI: 10.1117/1.OE.57.11.114102]

Keywords: infrared gas imaging; gas leak detection; turbulence.
Paper 180851 received Jun. 13, 2018; accepted for publication Oct. 23, 2018; published online Nov. 10, 2018.

1 Introduction
With tightening controls on emissions at industrial chemical
processing facilities, there is an increasing need for improved
gas leak detection equipment and methods. In particular, thehigh cost of leak detection presents a challenge that many aretrying to meet with automated monitoring to replace the current labor-intensive methods.1 Spectrally filtered infrared
cameras have become an indispensable tool for this effort,2,3
with researchers trying to develop tools to automate the process of detecting and quantifying gas leaks from infrared
video data.4,5
To detect and measure gas leaks with spectrally filteredinfrared cameras, the user looks for changes in the detected
thermal radiance while viewing a background scene, searching for patterns that indicate a gas cloud moving across thefield of view. Gases that have the strongest absorption crosssections, and whose absorption regions are narrowest, are theeasiest to detect, and thus have the lowest detection threshold. In the MWIR (3 to 5 μm), the alkane hydrocarbon gases
have strong absorption features and so allow sensitive detection, while in the LWIR (8 to 13 μm), the alkenes allow
sensitive detection. Under ideal circumstances, these sensitivities are determined by the signal-to-noise ratio (SNR) of
the gas absorption signal to the measurement noise (detector
noise plus photon shot noise).6,7 In practice, however, naturalchanges in the thermal signature of the scene background is
an important nuisance that also interferes with detection.
This can result, for example, from the cooling of a sun-illuminated surface after clouds block the sunlight, or simply
due to sudden changes in wind speed or direction.
There is another previously unacknowledged effect thatinterferes with detection—an effect that is particularly problematic because its spatiotemporal behavior is fluid-like.
Turbulent wind flow across surfaces induces thermal fluctuations that move with the wind and that can appear similar toflowing gas. These turbulence-induced thermal fluctuations
are a phenomenon that has only recently come to attention8,9
as a method for imaging wind and which create patterns that

*Address all correspondence to: Nathan Hagen, E-mail: nh@hagenlab.org

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are visible in trace gas imaging data. Infrared gas imaging
and infrared wind imaging both use passive detection in primarily outdoor environments, relying on the same thermal
contrast ΔT between the fluid and the background to produce signals. Existing algorithms used for analyzing infrared
camera video sequences for gas detection use the fluid-likespatiotemporal behavior to filter out anomalies and reduce
false detections. Thus, these turbulence-induced thermal
fluctuations will cause false detections if the detection
threshold is placed below a lower limit that we estimate
quantitatively below. At the sensitivity limit, the small surface thermal fluctuations induced by air turbulence appear as
small thermal changes induced by trace gases. This limit is“fundamental” in the sense that it is unrelated to detector or
shot noise, has gas-like spatiotemporal behavior, and does
not vary with the scene thermal contrast.
In the discussion below, we review the measurement models for infrared gas imaging and wind imaging. Equating thetwo enables us to calculate the corresponding gas detection
sensitivity limits, and we provide example values for various
gases in the MWIR and LWIR bands, respectively.
2 Thermal Effects of Wind Turbulence Overa Surface
Figure 1 shows an example scene showing wind-induced
thermal fluctuations on a sun-illuminated concrete surface
on a warm afternoon. The air temperature for the scene is
35°C, the concrete surface temperature 50°C, and the ambient air at 75% relative humidity. We define the “thermal
contrast” of a pixel in the scene as the effective temperature
difference between the surface and the ambient air: ΔT ¼
T bkg − T air . The camera used for this measurement is an
InSb detector array (IRCameras LLC, QuazIR SD) with a
640 × 512 image size, 20-μm pixels, and 14-bit output at
60 frames∕s. The detector is cryocooled to 77 K and operates across the MWIR spectral range with a cold filter transmitting from 3.00 to 3.90 μm. The camera uses an f∕2.3 lens(Janos Technology Inc., ASIO 50 mm) with a 50-mm focal
length. With this configuration, the camera noise-equivalenttemperature difference (NETD) is 15 mK, and the integration
time is 2 ms.

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November 2018 • Vol. 57(11)Hagen: Sensitivity limits on optical gas imaging due to air turbulence
Table 1 Estimated NETD values for the QuazIR SD MWIR camera
imaging different surface temperatures, assuming a surface emissivity of 0.95, with 1, 4, or 80 frames averaged.

Surfacetemperature (°C)

Fig. 1 One frame from a temporally filtered video of a scene composed primarily of solar-illuminated concrete, with some equipment
at the center right side of the image. Red arrows indicate the local
direction of wind flow along the concrete. The filtered image grayscale
display has been linearly scaled to black/white at brightness temperature differences of 75 mK.

When turbulent cool air passes across a warm surface,some surface regions are briefly cooled by the rapid
exchange of (warm) low-velocity air lifted away from thesurface with (cool) high-velocity air pushed in toward thesurface.10–12 These small temperature differences δT generally relax over a period of a couple of seconds as the heat
conducts into the material beneath the surface.9
To visualize the temperature changes δT of objects ina scene down to the several millikelvin level, we can use
a simple second-order derivative filter given by the difference
between two temporal moving averages:
EQ-TARGET;temp:intralink-;sec2;63;390

δTðx; yÞ ¼ hTi4 − hTi80 ;where hTii is the time average over i frames. Figures 1 and 2
show the result, where 4 frames and 80 frames correspond totimes of 0.067 and 1.33 s, respectively. The short-baseline
moving average hTi4 is used to reduce noise, while stillretaining enough temporal resolution to visualize the thermal
fluctuations. Subtracting the long-baseline moving average
hTi80 removes slow thermal drifts, which is important as
these drifts tend to dominate over time spans of several seconds or more. Applying these processing steps to an infrared
video sequence allows us to visualize the thermal fluctuations in a scene as in Fig. 1. This 20 mK thermal change

NETD (mK)

4-frame avg
NETD (mK)

80-frame avg
NETD (mK)

23

15.0

7.5

1.7

30

14.3

7.2

1.6

50

12.5

6.3

1.4

60

11.7

5.9

1.3

flowing across the field of view can appear as the flow ofa trace amount of gas.
A larger air-surface thermal contrast ΔT generates larger
thermal fluctuations δT. For outdoor measurements, thermal
contrast during the day is usually produced by the absorptionof sunlight on a surface, heating it above the temperature of
the ambient air. For Fig. 1, a contrast of ΔT ∼ 15°C produces
thermal fluctuations on the order of δT ∼ 20 mK (Fig. 2).
Such a small temperature change is visible to a thermal camera having a rated NETD of 15 mK, because the NETD
decreases with higher surface temperatures and also withincreasing number of frames averaged as shown in Table 1.
On a hot summer day, sunlit concrete often exceeds 50°C,
and asphalt pavement can exceed 60°C.13 These elevatedtemperatures improve the NETD significantly. If we model
the blackbody radiance spectrum of a surface at each temperature, integrated across the detector passband and weighted
by the detector responsivity, we obtain the estimated NETD
values for various object temperatures shown in Table 1.
Another factor to take into account is the reduction ofnoise due to summing of multiple frames. Algorithms used
for gas imaging typically employ spatiotemporal processing
similar to that used for wind visualization—the backgroundscene is assumed to be slowly varying while the gas itself
varies over a much shorter timescale. The actual timescales
vary with algorithm and with the scale of the leak—imaging
small leaks typically requires faster frame rates, and larger
leaks lower frame rates. Using a four-frame average asa baseline for the gas layer motion, the NETD will decreaseby 2. As a result, for imaging 50°C surfaces with four-frame
averaging, the camera NETD decreases to 6 mK, so that the
20 mK turbulence-induced thermal fluctuations become
easily visible above the noise (see Table 1).
3 Infrared Gas Imaging
Infrared gas imaging analyzes the radiance changes ina scene to look for absorption or emission signatures generated by gases passing between the camera and thebackground.14–17 Gases that are cooler than the backgroundare seen in absorption, while gases warmer than the background (e.g., when passing in front of a cold blue sky)
are seen in emission.
We can model the effect of a gas cloud in the scene witha three-layer radiative transfer system (Fig. 3), in which

Fig. 2 The temperature history of an example pixel over time, showing hT i4 (black line), hT i80 (thick-gray line), and δT (red line). The
dashed lines indicate 20 mK from the mean.
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1. Spectral radiance Lb ðλÞ is generated within a source
region that can be either an opaque object such as
November 2018 • Vol. 57(11)Hagen: Sensitivity limits on optical gas imaging due to air turbulenceFig. 3 The measurement geometry for a single pixel in a gas cloud
imager: the camera line of sight views the background infrared radiation (1) through a gas cloud layer (2) and a foreground atmosphericlayer (3). Each layer has a spectral radiance L, transmission τ, andtemperature T .

the ground, or the atmosphere itself, such as whenviewing a cloudless sky, or a combination of the two.
2. The source spectral radiance traverses the gas cloudlayer, and is attenuated/increased by absorption/emission of gases located there.
3. The radiation passes through an atmospheric layer toreach the camera.
This three-layer model is quite general in that it does not
require any assumptions on the spectrum Lb ðλÞ of lightbehind the gas cloud.18
For a pixel in the scene observed by the camera, we canwrite the radiative transfer equation of a ray along the line ofsight to give an at-pupil radiative flux M of
EQ-TARGET;temp:intralink-;e001;63;435

M¼

Z λ
λ1

2

ϵf ðλÞBðT f ; λÞ þ τf ðλÞϵg ðλÞBðT g ; λÞþ τf ðλÞτg ðλÞLb ðλÞdλ≈ Δλ½ϵf BðT f ; λÞ þ τf ϵg BðT g Þ þ τf τg Lb ;(1)where the subscripts f, g, and b indicate the foreground,gas, and background layers; λ1 and λ2 give the passbandof the infrared filter; BðTÞ is the Planck blackbody
spectral radiance function for temperature T; τ is the spectral transmission of a layer; and ϵ the spectral emissivity ofa layer. An overbar indicates an average across the spectral
passband. Using Kirchhoff’s law and an assumption of
local thermodynamic equilibrium, we can make the substitution ϵ ¼ 1 − τ. The overbars on parameters become tedious, and so we will drop them in the equations below,
leaving the average over the passband implied, except
for parameters in which an explicit wavelength dependence
is shown.
For gas cloud imaging, we look for radiance changes inthe scene that may indicate absorption or emission by a gas
cloud by comparing the current frame against a reference
gas-free frame. We can use spatiotemporal statistics of thespectrum to determine the presence of gas and to estimate
the reference radiance value. Writing the radiance of the current frame of a video sequence as M1 and that of the reference frame as M 0 , we have
EQ-TARGET;temp:intralink-;sec3;63;117

M0 ¼ ð1 − τf ÞBðT f Þ þ τf Lb
M1 ¼ ð1 − τf ÞBðT f Þ þ τf τg BðT g Þ þ τf τg Lb :Optical Engineering

Fig. 4 Example spectra for propylene gas at column density
ζ ¼ 22000 ppm:m, showing the radiance spectrum MðλÞ when the
background source is a blackbody at T b ¼ 30°C.

Taking the difference between the two spectra gives
ΔM ¼ M1 − M 0 ¼ −τf αg ½BðT g Þ − Lb :

EQ-TARGET;temp:intralink-;e002;326;557

Figure 4 shows αg ðλÞ for propylene gas, together with an
example ΔMðλÞ for a background blackbody at 30°C anda 0°C gas passing between it and the camera. Rearranging
Eq. (2) to solve for the gas absorption, we obtain
αg ¼

EQ-TARGET;temp:intralink-;e003;326;481

M1 − M0:τf ½BðT g Þ − Lb 

(3)

The denominator of this equation has the gas-to-background radiance contrast ΔL ¼ ½BðT g Þ − Lb , a quantitythat is closely related to the thermal contrast ΔT. From
Eq. (2), we can use the gas-free frame to solve for Lb :Lb ¼

EQ-TARGET;temp:intralink-;sec3;326;392

1½M − ½1 − τf BðT f Þ;τf 0

and substitute the result into Eq. (3) to give
αg ¼

EQ-TARGET;temp:intralink-;e004;326;338

M1 − M0:
BðT g Þ − M0

(4)

Note that τf has disappeared from the equation: the foreground layer plays no role in the absorption estimate, except
insofar as it reduces the measurement SNR. All of the variables on the right-hand side of this equation are quantities
that we can measure or estimate.
To convert the measured absorption to gas column density, we use the Beer–Lambert–Bouguer law:Z lτg ðλÞ ¼ exp −σðλÞρðzÞdz ≈ expð−σρlÞ;(5)
EQ-TARGET;temp:intralink-;e005;326;2170where σðλÞ is the absorption cross-section spectra, l is theline-of-sight path length through the gas, and τ ¼ 1 − α. We
use ρðzÞ for the gas concentration (number density) along theline of sight and ρ (with no explicit z-dependence) as theaverage concentration along the line of sight. Because theaverage concentration ρ and gas cloud path length l cannot
be separated from one another, they are grouped together intoa single quantity—the column density ζ ¼ ρl.
When the gas concentration is low (thin gas approximation), Eq. (5) can be written as αg ≈ σζ—the gas column

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November 2018 • Vol. 57(11)Hagen: Sensitivity limits on optical gas imaging due to air turbulenceFig. 5 Example gas detection image. (Adapted with permission ofRebellion Photonics, Inc.21)

density ζ becomes a linear function of the absorption. Goingfrom the estimated absorption to estimated gas column density, therefore, requires only scaling by the cross section:
ζ ¼ αg ∕σ:

EQ-TARGET;temp:intralink-;e006;63;506(6)

The column density has units of m−2 , but it is common toconvert this to units of ppm.m by multiplying by the densityof molecules in air (ρair ¼ 2.687 × 1025 m−3 at standard temperature and pressure), and scaling the result by 106.19,20
Figure 5 shows an example of applying this estimation toeach pixel of gas in an image, for a controlled methanegas leak.

4 Calculating the Bandpass-Averaged Absorption
Cross Section
For spectrally filtered gas imaging cameras, the filter design
directly impacts measurement performance, and there aretrade-offs to consider when selecting the filter passband.
One generally wants to have an absorption cross section
as large as possible, so that for many spectra a naive choice
would be to design a narrowband (≲10 nm) filter centered ona strong absorption line feature, such as the narrow peak at
10.97 μm in Fig. 4. While this works for laser-illuminatedsystems, it gives poor performance for passive imagers
because the background signal SNR becomes too low. By
widening the filter passband, we increase the background
SNR, but we sacrifice the highest absorption cross section
as the measured absorption will be an average across theentire passband. In practice, one can achieve good SNR
for passbands wider than about 0.1 μm.
In addition to trading-off the absorption cross section forincreased background SNR, the filter design must also consider that absorption features with cross sections below 1.0 ×
10−25 m2 are of limited utility in typical measurement environments. Here, the trade-off is that when we include spectral
regions with low absorption cross section, we are increasing
the measurement shot noise while doing little to increase theabsorption signal. For σ ≲ 1.0 × 10−25 m2, this balance typically tips in the favor of rejecting light in that range.
The final consideration for filter design is that wewill only investigate the case of single-passband filters.
Multiband filters can be used for optimizing the averagecross section when the absorption spectrum has multiple
peaks, such as propane and butane have in the LWIR (Fig. 6).
However, these are specialized items that are not in common
use in the infrared.

Fig. 6 Absorption spectra for methane and propane in the MWIR, and ethane and propane in the LWIR.
The horizontal red line indicates the width of the suggested bandpass filter to use for detecting the gas,
while the vertical position of the line indicates the average cross section within that passband.

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November 2018 • Vol. 57(11)Hagen: Sensitivity limits on optical gas imaging due to air turbulence
Table 2 Turbulence-induced lower limits for gas sensitivity.

MWIR

LWIR

Gas

Filterbandpass (μm)σ (m2 )

Sensitivity lower
limit (ppm.m)

Filterbandpass (μm)σ (m2 )

Sensitivity lower
limit (ppm.m)

Ammonia2.90 to 3.42

2.62 × 10−25

185

10.31 to 10.86

4.73 × 10−24

10.2

Benzene3.20 to 3.31

4.90 × 10−24

9.88

9.41 to 9.89

1.07 × 10−24

45.1

n-butane

3.33 to 3.51

2.76 × 10−23

1.75

9.91 to 10.75

8.16 × 10−25

59.3

Isobutylene

3.21 to 3.52

1.31 × 10−23

3.70

10.67 to 11.77

9.93 × 10−24

4.87

Ethane3.26 to 3.51

−24

4.74 × 10

10.2

11.28 to 12.98−25

3.59 × 10

135Ethylene

3.12 to 3.40

1.08 × 10−24

45.0

10.12 to 10.66

5.39 × 10−24

8.98

Methane3.17 to 3.48

6.28 × 10−25

77.0

7.90 to 8.22

4.17 × 10−25

116

Propane3.32 to 3.50

2.11 × 10−23

2.29

8.38 to 13.10

1.54 × 10−25

313

Propylene

3.19 to 3.52

2.48 × 10−24

19.5

9.78 to 11.61

2.33 × 10−24

20.8

SO2

2.90 to 5.10

4.36 × 10−25

111

7.90 to 10.02

1.08 × 10−24

44.8

Implementing a simple filter design that considers these
trade-offs gives the resulting passbands shown in Fig. 6 andTable 2. The thick red horizontal line in each figure indicatesthe suggested filter passband appropriate to optimizing
the measurement performance of the imaging system forthat gas.
5 Detection Limits
In Sec. 2, we showed that in conditions of thermal contrast
ΔT ∼ 15°C, we observe air-turbulence-induced surface thermal fluctuations of about 20 mK, which traverse the scene at
the same speed as the airflow. A gas detection camera will
see these thermal fluctuations as apparent changes in gas
layer absorption, so that if we place a gas detection thresholdthat is too low, these thermal fluctuations will appear as tendrils of gases flowing across the scene. To estimate thethreshold at which this occurs, we can convert the thermal
fluctuations into absorption units αlimit , from which we
can use [Eq. (6)] to calculate the equivalent column density
ζ limit for any given gas type.22 This gives us the lower sensitivity limit for the gas.
For these measurement conditions, we find the apparent
absorption:
αlimit ¼

EQ-TARGET;temp:intralink-;e007;63;229

δM δT
0.020 K≈¼
¼ 0.0013:
ΔM ΔT
15 K

(7)

Although this apparent absorption is calculated for areference scene thermal contrast of ΔT ¼ 15°C, both the turbulence and gas signals vary linearly with thermal contrast
for typical values of ΔT, so that the ratio used to calculate
αlimit is approximately invariant to scene conditions. Thus, ascene contrast of only 5°C will produce thermal fluctuationsof about 7 mK, resulting in the same αlimit value of 0.0013.
The following gives an example calculation for the case of
methane gas in the MWIR. The average absorption cross section of methane gas in the 3.17- to 3.48-μm range is
σ ¼ 6.28 × 10−25 m2 (see Table 2 for gas absorption crossOptical Engineering

sections). By scaling the apparent change in absorption toa corresponding change in apparent gas column density,
we obtain the detection sensitivity limit for methane as
αlimit1 × 106 ppm
ζ limit ¼
ρair
σ



0.0013
1 × 106 ppm¼
6.28 × 10−25 m2
2.69 × 1025 m−3
EQ-TARGET;temp:intralink-;e008;326;450¼ 77 ppm:m.

Performing the same calculation for propane in the LWIR,
we obtain the sensitivity limit of
0.0013
1 × 106 ppm
ζ limit ¼
1.54 × 10−25 m2
2.69 × 1025 m−3

EQ-TARGET;temp:intralink-;e009;326;336¼ 313 ppm:m:(9)

The results for the same calculations, performed in the
MWIR and LWIR for several common hydrocarbon gases,
are shown in Table 2. As gas imaging cameras have difficulty
in detecting column densities <10 ppm:m, we can see from
Table 2 that only ammonia, methane, and ethylene experience a sensitivity limit in the MWIR band that could potentially restrict performance. In the LWIR band, the gases tend
to have lower absorption cross sections, so that propane,ethane, and methane have detection limits that impose a significant limit on detection. In practice, this can be seen as ananomalous increase in false-detections across the field ofview when trying to image propane at the bottom limit ofdetectability. This limit does not change with larger thermal
contrast because the turbulence effects also increase linearlywith ΔT. In practice, we also find that wind speed has little
effect on the detection limits because the primary effect of anincrease in wind speed is to reduce the thermal contrast.
Although these detection limits are prevalent in gas imaging, they are not present everywhere. The turbulence-

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November 2018 • Vol. 57(11)Hagen: Sensitivity limits on optical gas imaging due to air turbulence

induced thermal fluctuations are only apparent on nearby
surfaces, so that any gas imaging that uses a distant background, such as sky, clouds, or mountains, is not subject
to these limits. In addition, the calculations of Table 2 ignore
the effects of water vapor on the absorption spectra. This particularly affects the cross section of methane in the LWIR as
the absorption spectrum partially overlaps with the water
absorption spectrum. As a result, the sensitivity limit will
depend on the local temperature and relative humidity.
6 Conclusions
Wind passing over the ground produces dynamic thermal
fluctuations that follow wind speed and direction. Tracequantities of infrared gases passing across the field ofview create subtle spatiotemporal patterns that can be used
to detect gas leaks. Analyzing these two effects together, wehave shown that the thermal signatures induced by air turbulence create a fundamental lower limit on the ability to detect
trace gases with infrared imaging, independent of measurement noise. Although researchers have shown that LWIR
detection limits for uncooled infrared imaging cameras
under good measuring conditions are generally in the regionof 50 to 1000 ppm.m for many of the common hydrocarbon
gases, and 1000 to 5000 for propane,4,7,23 temporal averaging
while staring at a scene containing gas can bring down theselimits by a factor of 10 or more. At these lower limits,
however, any gas having a small absorption cross section(≲2 × 10−25 m2 ) will start to encounter limitations due tothe turbulence effects. Thus, imaging propane gas with
LWIR cameras will experience difficulties for propane column densities below about 300 ppm.m. Practical experience
with trying to measure propane in the LWIR reinforces
this—researchers have not yet succeeded in consistently imaging propane at levels near this value when the camera uses
a nearby surface for background. These sensitivities havebeen reached when imaging propane in the LWIR against
a blue sky background because the turbulence effects do
not apply there, and because blue sky also provides a strong
thermal contrast for measurement. This gives two good reasons to choose an upward-viewing geometry for imaging
propane leaks in the LWIR: better contrast and lack of turbulence fluctuations.
While the calculations of Table 2 focus on a filtered camera model for measurement, spectral imaging cameras havealso become increasingly common for gas sensing. The advantage of a spectral imager is that it can analyze the signal
change in multiple bands simultaneously, allowing it to see
the difference between a broadband spectral change (such asthat generated by the turbulence-induced fluctuations) anda spectral change that has a shape specific to a given gas.
Thus, a spectral imager can make use not only of the spatiotemporal distribution of intensity changes to detect gas
clouds, but can also use the correlation between the measured absorption spectrum with the known gas spectrum.
As a result, spectral instruments will be less susceptible to

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the turbulence-induced fluctuations affecting their detection
limits.
References
1. D. W. Furry et al., “Evaluation of instrument leak detection capabilities
for smart LDAR application: chemical plant testing,” Environ. Progr.
26, 197–205 (2007).
2. Eastern Research Group, “Spectral testing of gas imaging cameras andspectral library,” Summary Report prepared for U.S. EPA, Office ofEnforcement and Compliance Assistance, Air Enforcement Division,
EPA Contract No. EP-W-09–033, Work Assignment ETS-2–1(ERG), Rev. No. 2 (2014).
3. D. R. Lyon et al., “Aerial surveys of elevated hydrocarbon emissions
from oil and gas production sites,” Environ. Sci. Technol. 50(9),4877–4886 (2016).
4. N. Hagen et al., “Video-rate spectral imaging of gas leaks in the longwave infrared,” Proc. SPIE 8710, 871005 (2013).
5. H. Abdel-Moati et al., “New optical gas-imaging technology for quantifying fugitive-emission rates,” in Int. Petroleum Technology Conf.,
IPTC-18471-MS (2015).
6. D. F. Flanigan, “Vapor-detection sensitivity as a function of spectral resolution for a single Lorentzian band,” Appl. Opt. 34(15), 2636–2639(1995).
7. E. Naranjo, S. Baliga, and P. Bernascolle, “IR gas imaging in an industrial setting,” Proc. SPIE 7661, 76610K (2010).
8. A. Inagaki et al., “Thermal image velocimetry,” Boundary Layer
Meteorol. 149(1), 1–18 (2013).
9. N. Hagen, “Passive imaging of wind surface flow using an infrared
camera,” Infrared Phys. Technol. 87, 47–54 (2017).
10. B. J. Cantwell, “Organized motion in turbulent flow,” Ann. Rev. Fluid
Mech. 13, 457–515 (1981).
11. J. Jiménez, “Turbulent flows over rough walls,” Ann. Rev. Fluid Mech.
36, 173–196 (2004).
12. G. Kawahara, “Theoretical interpretation of coherent structures in nearwall turbulence,” Fluid Dyn. Res. 41(6), 064001 (2009).
13. T. Asaeda, V. T. Ca, and A. Wake, “Heat storage of pavement and its
effect on the lower atmosphere,” Atmos. Environ. 30, 413–427 (1996).
14. D. F. Flanigan, “Prediction of the limits of detection of hazardous vapors
by passive infrared with the use of MODTRAN,” Appl. Opt. 35(30),6090–6098 (1996).
15. J. Sandsten, H. Edner, and S. Svanberg, “Gas visualization of industrialhydrocarbon emissions,” Opt. Express 12(7), 1443–1451 (2004).
16. A. Ben-David and C. E. Davidson, “Probability theory for 3-layer
remote sensing radiative transfer model: univariate case,” Opt.
Express 20(9), 10004–10033 (2012).
17. S. Sabbah et al., “Remote sensing of gases by hyperspectral imaging:system performance and measurements,” Opt. Eng. 51(11), 111717(2012).
18. M. A. Rodríguez-Conejo and J. Meléndez, “Hyperspectral quantitative
imaging of gas sources in the mid-infrared,” Appl. Opt. 54(2), 141–149(2015).
19. N. B. Gallagher, B. M. Wise, and D. M. Sheen, “Estimation of trace
vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images,” Anal. Chim. Acta 490(1–2), 139–152(2003).
20. S. Niu et al., “New approach to remote gas-phase chemical quantification: selected-band algorithm,” Opt. Eng. 53(2), 021111 (2014).
21. https://rebellionphotonics.com/.
22. N. Hagen, “Millikelvin thermal dynamics of infrared scenes: sensitivity
limits on optical detection of gas leaks,” Proc. SPIE 10403, 104030G(2017).
23. S. E. Golowich and D. G. Manolakis, “Cramer-Rao bounds for longwave infrared gaseous plume quantification,” Opt. Eng. 53, 021109(2014).
Nathan Hagen is an assistant professor at Utsunomiya University.
He received his BS degree in physics and astrophysics from the
University of California at Berkeley in 1993 and his PhD in optical sciences from the University of Arizona in 2007. From 2011 to 2016,he led the research and algorithms group at Rebellion Photonics,
developing spectral imaging cameras for gas detection and quantification. He has authored 30 journal articles and is a member of SPIE.

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November 2018 • Vol. 57(11)