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Planck Function

The \(\textit{Planck function}\) is used to compute the radiance emitted from objects that radiate like a perfect "Black Body". The inverse of the \(\textit{Planck Function}\) is used to find the \(\textit{Brightness Temperature}\) of an object. The precise formula for the Planck Function depends on whether the radiance is determined on a \(\textit{per unit wavelength}\) or a \(\textit{per unit frequency}\). In the ISO System of Quantities, \(\textit{Planck Function}\) is defined by the formula: \(Y = -G/T\), where \(G\) is Gibbs Energy and \(T\) is thermodynamic temperature.

\(B_{\nu}(T)\)

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19680008986_1968008986.pdf

http://pds-atmospheres.nmsu.edu/education_and_outreach/encyclopedia/planck_function.htm

http://www.star.nesdis.noaa.gov/smcd/spb/calibration/planck.html

http://www.iso.org/iso/catalogue_detail?csnumber=31890

The Planck function, \(B_{\tilde{\nu}}(T)\), is given by: \(B_{\nu}(T) = \frac{2h c^2\tilde{\nu}^3}{e^{hc / k \tilde{\nu} T}-1}\) where, \(\tilde{\nu}\) is wavelength, \(h\) is Planck's Constant, \(k\) is Boltzman's Constant, \(c\) is the speed of light in a vacuum, \(T\) is thermodynamic temperature.