Black body hemispherical spectral

Where n is the refractive index, a is the absorption coefficient from the Lambert-Beer law and JE is the Planck function specifying the spectral hemispherical em/ssivity of a black body ... 

The wavelength and temperature dependency given by (5.37) correspond to a relationship found by W. Wien [5.3] in 1896 to be approximately valid for the hemispherical spectral emissive power M S(X,T ) of an ideal radiator, a black body, with a temperature T. We will come back to the properties of black bodies in section 5.1.6 and more extensively in 5.2.2. In our example a spectral irradiance E M s has been assumed, so that its indirect dependence on T appears explicitly in (5.37). 

Hollow enclosure radiation and radiation of a black body (a x = 1) have identical properties. The black body radiates diffusely from (5.18) it holds for its hemispherical spectral emissive power that... 

A black body is defined as a body where all the incident radiation penetrates it and is completely absorbed within it. No radiation is reflected or allowed to pass through it. This holds for radiation of all wavelengths falling onto the body from all angles. In addition to this the black body is a diffuse radiator. Its spectral intensity LXs does not depend on direction, but is a universal function iAs(A,T) of the wavelength and the thermodynamic temperature. The hemispherical spectral emissive power MXs(X,T) is linked to Kirchhoff s function LXs(X,T) by the simple relationship... 

We refrain from deriving the equations for the spectral intensity and the hemispherical spectral emissive power of a black body, found by M. Planck [5.6], for... 

Fig. 5.23 Hemispherical spectral emissive power MXs(X,T) of a black body according to Planck s radiation law (5.50)...

Table 5.3 Hemispherical spectral emissive power of a black body divided by the fifth power of the temperature, according to (5.54) and fraction function F(0, AT) according to (5.60) as a function of the product AT...

Fig. 5.30 Hemispherical spectral emissive power M (A, T) of a real body compared to the hemispherical spectral emissive power M g(A, T) of a black body at the same temperature. The hatched area represents the emissive power M(T) of the real body 0...

A radiator emits its maximum hemispherical spectral emissive power at Amax = 2.07 /im. Estimate its temperature T and its emissive power M(T), under the assumption that it radiates like a black body. 

The oven wall is exposed to radiation from glowing coal the spectral irradiance E can be assumed to be proportional to the hemispherical spectral emissive power M s(Tk) of a black body at Tk = 2000 K. 

Because the performance of infrared detectors is limited by noise, it is important to be able to specify a signal-to-noise ratio in response to incident radiant power. An area-independent figure of merit is D ( dee-star ) defined as the rms signal-to-noise ratio in a 1 Hz bandwidth per unit rms incident radiant power per square root of detector area. D can be defined in response to a monochromatic radiation source or in response to a black body source. In the former case it is known as the spectral D, symbolized by Df X, f, 1) where A is the source wavelength,/is the modulation frequency, and 1 represents the 1 Hz bandwidth. Similarly, the black body D is symbolized by Z> (T,/1), where T is the temperature of the reference black body, usually 500 K. Unless otherwise stated, it is assumed that the detector Held of view is hemispherical 2n ster). The units of D are cm Hz Vwatt. The relationship between )J measured at the wavelength of peak response and D" (500 K) for an ideal photon detector is illustrated in Fig. 2.14. For an ideal thermal detector, Df = D (T) at all wavelengths and temperatures. 

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