Heated solid bodies emit radiation that is particularly concentrated in the infrared region of the spectrum, roughly from 1 to 10 Î¼m in wavelength. Such heated solid bodies emit their radiation in a continuum of wavelengths, rather than at a collection of discrete spectral lines characteristic of gaseous emission. To describe the radiation characteristic of a source which emits a finite total power over a range of wavelengths, we must introduce spectral quantities. Spectral quantities have units of Î¼m in the denominator, and are denoted with a subscript Î» to distinguish them from the corresponding integrated quantities. For example, spectral radiance L Î» has units of W/(cm2 sr Î¼m), and is the radiance per Î¼m of wavelength interval. For a measurement over a 1-Î¼m spectral bandpass, the integrated radiance (also called the in-band radiance) numerically equals the spectral radiance. For spectral bandpasses larger or smaller than 1 Î¼m, the integrated radiance scales with ÎÎ»â¡Î» 1 âÎ» 2 , as seen in Eqs. (4.1) and (4.2): L[Watt cm 2 sr ]=â« Î» 2 Î» 1 L Î» [Watt cm 2 srÎ¼m ]dÎ»[Î¼m] M[Watt cm 2 ]=â« Î» 2 Î» 1 M Î» [Watt cm 2 Î¼m ]dÎ»[Î¼m] The integration is usually carried out numerically, using the trapezoidal approximation seen in Fig. 4.1. This process can be made as accurate as desired, by choice of the interval size ÎÎ». As seen in Fig. 4.2, to maintain accuracy for a wider passband, individual intervals are summed together. It is necessary to choose interval locations properly if the desired passband includes a peak of the radiation curve.
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