2 Physical Principles and Technical Aspects of Remote Sensing
17
Radiation Laws. Any material emits radiation in dependence of its temperature and physical properties. As a convenient concept the ideal thermal
emitter, called blackbody, describes the maximum rate of emitted energy at
a given temperature and wavelength. According to Planck's law the blackbody spectral exitance ME,).. (Wm- 2 JLm- 1 ) is a function of thermodynamic
temperature (T) in degrees Kelvin and can be written in dependence of wavelength:
(2.1)
where h is Planck's constant, c is the speed of light in vacuum, and k is
Boltzmann's constant. ME,).. represents the spectral emission from a unit
area into the hemisphere. Figure 2.3 shows the spectral radiant exitance for
blackbodies at 330 K, 270 K, and 210 K, temperatures observable on the
earth's surface. The wavelength, Amax, for which the blackbody spectral exitance reaches its maximum, depends on the temperature, and is described
by the Wien displacement law: AmaxT = canst. The exitance of a blackbody
integrated over all wavelengths is described by the Stefan-Boltzmann law:
(2.2)
where (j = 5.6698 . 1O- 8 W m -2 K- 4 • In remote sensing the radiance, L, is
frequently used, specifying the flux of radiant energy per unit time across a
unit area into a cone defined by the unit solid angle (steradian, sr). For an
ideal diffuse radiator (a Lambertian radiator) the relation between spectral
radiance, L).. (W m- 2 sc1JLm- 1 ), and spectral exitance is given by
(2.3)
In the microwave region the spectral exitance emitted by the earth's surface is several orders of magnitude smaller than at the spectral maximum.
330 K
270 K
210 K
Fig. 2.3. Spectral radiant exitance of blackbodies at 3 different temperatures
17
Radiation Laws. Any material emits radiation in dependence of its temperature and physical properties. As a convenient concept the ideal thermal
emitter, called blackbody, describes the maximum rate of emitted energy at
a given temperature and wavelength. According to Planck's law the blackbody spectral exitance ME,).. (Wm- 2 JLm- 1 ) is a function of thermodynamic
temperature (T) in degrees Kelvin and can be written in dependence of wavelength:
(2.1)
where h is Planck's constant, c is the speed of light in vacuum, and k is
Boltzmann's constant. ME,).. represents the spectral emission from a unit
area into the hemisphere. Figure 2.3 shows the spectral radiant exitance for
blackbodies at 330 K, 270 K, and 210 K, temperatures observable on the
earth's surface. The wavelength, Amax, for which the blackbody spectral exitance reaches its maximum, depends on the temperature, and is described
by the Wien displacement law: AmaxT = canst. The exitance of a blackbody
integrated over all wavelengths is described by the Stefan-Boltzmann law:
(2.2)
where (j = 5.6698 . 1O- 8 W m -2 K- 4 • In remote sensing the radiance, L, is
frequently used, specifying the flux of radiant energy per unit time across a
unit area into a cone defined by the unit solid angle (steradian, sr). For an
ideal diffuse radiator (a Lambertian radiator) the relation between spectral
radiance, L).. (W m- 2 sc1JLm- 1 ), and spectral exitance is given by
(2.3)
In the microwave region the spectral exitance emitted by the earth's surface is several orders of magnitude smaller than at the spectral maximum.
330 K
270 K
210 K
Fig. 2.3. Spectral radiant exitance of blackbodies at 3 different temperatures