1.7 Black Body Radiation

1.7 Black Body Radiation

An object radiates unique spectral radiant flux depending on the temperature and emissivity of the object. This radiation is called thermal radiation because it mainly depends on temperature. Thermal radiation can be expressed in terms of black body theory.

A black body is matter which absorbs all electro-magnetic energy incident upon it and does not reflect nor transmit any energy. According to Kirchhoff's law the ratio of the radiated energy from an object in thermal static equilibrium, to the absorbed energy is constant and only dependent on the wavelength and the temperature T. A black body shows the maximum radiation as compared with other matter. Therefore a black body is called a perfect radiator.

Black body radiation is defined as thermal radiation of a black body, and can be given by Plank's law as a function of temperature T and wavelength as shown in Figure 1.7.1 and Table 1.7.1.

In remote sensing, a correction for emissivity should be made because normal observed objects are not black bodies. Emissivity can be defined by the following formula-

Emissivity ranges between 0 and 1 depending on the dielectric constant of the object, surface roughness, temperature, wavelength, look angle etc. Figure 1.7.2 shows the spectral emissivity and spectral radiant flux for three objects that are a black body, a gray body and a selective radiator.

The temperature of the black body which radiates the same radiant energy as an observed object is called the brightness temperature of the object.

Stefan-Boltzmann's law is obtained by integrating the spectral radiance given by Plank's law, and shows in that the radiant emittance is proportional to the fourth power of absolute temperature (T). This makes it very sensitive to temperature measurement and change.

Wien's displacement law is obtained by differentiating the spectral radiance, which shows that the product of wavelength (corresponding to the maximum peak of spectral radiance) and temperature, is approximately 3,000 (mK). This law is useful for determining the optimum wavelength for temperature measurement of objects with a temperature of T. For example, about 10 m is the best for measurement of objects with a temperature of 300K.