Brightness Temperature Tb
Brightness Temperature (Tb)
a parameter that is used for the quantitative characterization of the spectral concentration of the radiance of any body that is heated to a temperature of T and that has a continuous spectrum. The limit of the ratio of the radiance corresponding to a narrow spectral region and the width of the region is called the spectral concentration of radiance, which is denoted b(λ, T).
The brightness temperature Tb of a body in question is equal to the temperature T of a blackbody at which the parameter bbb(λ, T) of the blackbody is equal to the parameter b(λ, T) of the body in question at the same wavelength λ.
The concept of brightness temperature is used in optical pyrometry and in the study of celestial sources of radiation, such as the sun, stars, gaseous nebulas, and the planets. In the general case, brightness temperature is determined on the basis of the Planck radiation formula (seePLANCKS RADIATION LAW). In a spectral region where the Rayleigh-Jeans law is applicable (usually the radio-frequency band), Tb = λ2Fλ/2,760Ω, where Fλ is the radiation flux at a wavelength of λ and Ω is the angular size of the radiation source.
The relationship between brightness temperature Tb and true temperature T is given by the equation
T = TbC2/(C2 + λTb ln αλ,T)
where αλ,T is the spectral absorptivity of a body and C2 = 0.014388 m × °K. For nonblack sources, αλ,T < 1; therefore, Tb is always less than T. For most metals, at T ~ 1000–3000°K, the value of αλ,T lies between 0.3 and 0.7 in the visible region of the spectrum. Therefore, for most metals, Tb is 50–400°K less than T.
For the sun, Tb = 6200°K at a wavelength of λ = 4,500 angstroms (Å) and is about 6000°K at a wavelength of 6,500 Å. For Venus, Tb = 600°K (λ = 3.15 cm). For Jupiter, Tb = 200°K (λ = 8–14 micrometers).