IEEE Geoscience and Remote Sensing Magazine - June 2019 - 75

some gets radiated to the surface (irradiance) and reflected
back to the sensor, commonly known as the reflected downwelling sky irradiance. One effect of the sky irradiance is the
reduction of the spectral contrast of the emitted radiance,
due to Kirchhoff's law. Assuming the directional variation
in emissivity is small (Lambertian assumption) and using
Kirchhoff's law to express the hemispherical-directional reflectance as directional emissivity, the clear sky at-sensor
measured radiance can be written as
L m (m) = x a (m) L g (m) + L u (m),

(3)

L g (m) = e (m) B (m; Tg) + [1 - e (m)] L d (m),

(4)

where L g (m) is the total ground-leaving radiance, e (m) is
the surface emissivity, B (m; Tg) is the Planck function at the
surface temperature, Tg, L d (m) is the downwelling or downemitted radiance, L m (m) is the at-aperture radiance measured by the sensor, x a (m) is the atmospheric transmission
function, and L u (m) is the upwelling or path radiance. This
model provides the basis for the ground radiance, emissivity, and temperature-retrieval algorithms.
Although the model specified by (3) and (4) was derived
for an airborne downlooking nadir geometry, it also holds

VNIR-SWIR

MWIR

LWIR

AT-SENSOR MEASURED
RADIANCE SIGNAL MODEL
The at-sensor measured radiance in
the LWIR spectral region is a combination of different terms from surface emission and the atmosphere
(see Figure 4). The Earth-emitted
radiance is a function of temperature
and emissivity and gets attenuated
by the atmosphere on its path to the
sensor. The atmosphere also emits
radiation, of which some reaches the
sensor directly as path radiance while
JUNE 2019

Irradiance (W/m2/µm)

Transmission

values and low spectral contrast. Combined with canopy
scattering (which further reduces spectral contrast), vegetation, in general, behaves like a blackbody emitter with extremely high emissivities and minuscule features [3]. Emissivities for background materials are shown in the "Scene
Modeling And Classification" section. Surface roughness,
caused by pits between particles (e.g., in sand, cobbles, and
boulders), pits in a solid surface, or roughness at the grain
scale, reduces the spectral contrast [4].
The properties of LWIR spectral signatures of solidphase materials have a number of significant implications
in LWIR HSI, the most significant of which are as follows.
1) Spectral signatures typically have low contrast, and a
weaker signature is more difficult to detect and characterize. Weak surface signatures are also more difficult to
separate from atmospheric effects. The diminished spectral contrast is important because it places higher signalto-noise ratio requirements for spectroscopic detection
and identification.
2) Spectral signatures lack rotational structure; as a result, their bands are usually relatively broad and indistinct (i.e., less characteristic).
3) The spectral shape varies nonlinearly with particle size
and mixing effects, and there is no general theory of
band shape that can be used in a
manner similar to that of modeling gas-phase spectra. This makes
it exceedingly difficult to develop
a complete solid-phase spectral
1
library as well as to interpret the
0.8
measured field spectra [5].
It is important to note that the
0.6
MWIR spectral region, between 3 and
0.4
5 nm, has been underutilized. The
main reason is the hybrid nature of
0.2
this spectral region-it comprises a
0
combination of reflected and emitted
0.3
radiation during daytime operation
[6]. This is illustrated in Figure 2 and
shows that Planck's emission spectra
104
for the Sun and Earth overlap at the
MWIR region.
103

2.5
4
Wavelength (µm)

8

14

(a)
Sun Blackbody
Earth Blackbody
At-Sensor Sun Irradiance
At-Sensor Earth Irradiance

102
101
100

0.3

2.5
4
Wavelength (µm)

8

14

(b)
FIGURE 2. (a) The atmospheric windows as determined by the transmission spectra of the
total atmosphere. (b) The plots of two blackbodies at T = 5, 500 K (Sun) and T = 300 K (Earth)
and plots of the radiance reaching a surface-looking sensor at the top of the atmosphere. Note
that, during daytime operation, the MWIR window receives reflected radiation (Sun) and emitted radiation (Earth).

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IEEE Geoscience and Remote Sensing Magazine - June 2019

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