IEEE Geoscience and Remote Sensing Magazine - June 2019 - 77

At-Sensor Measured Radiance
950
900

Upwelling Radiance

Radiance

850

500

800

T = 285 K
T = 310 K

750
700

Radiance

400

650
600

300

8

9

10
11
Wavelength (µm)

0.9
200

13

0.8
0.7
8

9

10
11
Wavelength (µm)

12

13

Radiance

100

12

Atmospheric
Transmission

0.6
0.5
0.4
0.3
0.2

Downwelling Radiance

8

9

10
11
Wavelength (µm)

12

13

700

1,100

500

1,000

400

900
Radiance

Radiance

600

300
200
8

9

10
11
Wavelength (µm)

12

13

Ground-Leaving
Radiance

T = 285 K
T = 310 K

800
700
600
500

8

9

Emissivity

10
11
Wavelength (µm)

12

13

Blackbody Radiance

0.95

1,200

Emissivity

Ground-Reflected
Radiance

0.8
0.75
0.7
0.65
0.6

Ground-Emitted
Radiance

1,100
1,000
Radiance

0.9
0.85

Hard (Solid) Targets
8

9

10
11
Wavelength (µm)

12

13

T = 285 K
T = 310 K

900
800
700
600

8

9

10
11
Wavelength (µm)

12

13

FIGURE 4. A pictorial illustration of the spectral quantities that are part of the at-sensor measured radiance signal model. Because

the blackbody radiation varies with temperature, the ground-leaving radiance and at-sensor measured radiance change with the
ground temperature.

instead focus more on the spectral discrimination properties of imaging spectrometers.
The challenges faced in the design and manufacture
of high-performing imaging spectrometers in the LWIR
are manifold. The starting point is an optical design form
where the point and field aberrations are well controlled
for use with an FPA. This design form should be compact
so that the imaging spectrometer can be cooled to reduce
the self-emission from the optics that would, at a minimum, limit the dynamic range. The design should include
a cold stop, particularly if it has warm elements, such as
an uncooled telescope, to ensure that the FPA is exposed
only to cold or low-emissivity surfaces. Cold filters are often used to eliminate the out-of-band spectral radiance.
Precision parts, such as a diffraction grating and a slit for
a dispersive system, must be of high quality to minimize
stray light and optimize spectral performance. The instrument builder must also be skilled at assembling the sensor
so that the alignment tolerances, which are on the order of
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

TABLE 1. THE CONTRIBUTIONS OF ATMOSPHERIC
TRANSMISSION, UPWELLING RADIANCE, AND
DOWNWELLING RADIANCE TO THE AT-SENSOR MEASURED
RADIANCE FOR DIFFERENT SENSING GEOMETRIES.
AIRBORNE/SATELLITE
GEOMETRY

NADIR

LONGSLANT PATH

STANDOFF

Atmospheric Transmission

Strong

Extreme

Minor

Upwelling Radiance

Minor

Strong

Minor

Downwelling Radiance

Small

Small

Strong

microns, are met when the sensor is cooled. The imaging
spectrometer must be radiometrically stable over a reasonable time period, and the FPA should have high spatial uniformity, adequate quantum efficiency or detector responsivity as a function of wavelength, linear response, and low
noise. Fortunately, imaging spectrometer development has
77
IEEE Geoscience and Remote Sensing Magazine - June 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2019
