1410 - Illustrate the concept of spectral emissivity and brigthness temperature and compute them in some simple real case

Illustrate the concept of spectral emissivity and brigthness temperature and compute them in some simple real case

Concepts

  • [PP1-1-7] Concepts of Spectral Emissivity and Brightness Temperature.
    All bodies at a temperature T>0 K emit electromagnetic radiation at all wavelengths (thermal emission). Such emission at each wavelength is increasing with T and it is maximum for Black Bodies whose spectral emittance I(λ,T) (at each prefixed T and wavelength λ) is defined by the Planck function B(λ,T). Generic bodies are expected to thermally emit less than a black body (having the same temperature T) at whatever wavelength. Spectral emissivity ε(λ) is defined as the ratio of the spectral radiance I(λ,T) emitted by a generic body and the one emitted by a Black Body at the same temperature, i.e. ε(λ)= I(λ,T) / B(λ,T). By definition its value is less or equal (Black Body) than 1. The spectral emissivity concept allows to describe in a simple way the spectral radiance I(λ,T) thermally emitted by a body at a temperature T by I(λ,T)= ε(λ)*B(λ,T). It is possible to invert the Planck Function to obtain from the emitted radiance at a prefixed wavelength the temperature T=f(B, λ) of the emitting Black Body. If in such expression the spectral radiance I emitted by a generic body is used instead than B, the resulting temperature, Tb=f(I, λ), is named Brigthness Temperature being Tb<=T (with Tb=T in case the emitting body is a Black Body). The concept of Brigthness Temperature is substantially a different way to measure the spectral radiance of a generic body. It is usually preferred (for instance calibrating Thermal InfraRed – TIR – satellite images) because the interpretation of such a digital image is much more intuitive than when spectral radiances are used instead. In fact, as at each prefixed temperature generic bodies are less emitting than Black Bodies, wherever across a digital satellite image we consider the values of reported Tb, we can say that the actual temperature T of the corresponding emitting ground resolution cell is not less than Tb.