Radiance value

The instrument observes the radiance emitted by the atmosphere at different values of the spectral frequency and the limb-viewing angle. The dependence of the spectra on the unknown profiles is not linear. A theoretical model, called forward model, simulates the observations through a set of parameters, i.e. the atmospheric profiles that have to be retrieved. The inversion method consists in the search for the set of values of the parameters that produce the best simulation of the observations. 

Figure 8.5 Spectral radiancy of a blackbody, real bodies stainless steel (1400°C) and alumina (1200°C), and greybody approximations. Real body spectra were calculated based on emittance values from reference [5]. Greybody approximations (dot-dot-dashed lines) were based on emittances of 0.33 for alumina and 0.75 for stainless steel. The high emittance of stainless steel is a result of oxidation to form a rough iron oxide surface. The greybody approximation appears good for stainless steel and poor for alumina. This may not be the case for different temperatures where the most intense portion of the blackbody spectra shifts in wavelength the constancy of emittance differs in different regions of the spectrum.

If the vibrational temperature is determined by using the intensities of different bands, a distinct value is obtained for each band. These values do not represent the arithmetic mean of all temperatures. Due to the nonlinear increase of the spectral radiance by the black body radiator, the hot zones appear more pronounced than the cold ones. On the other hand, the influence of the more distant zones with respect to the observer is reduced by stronger self-absorption. The vibrational temperatures deduced from bands with high absorption coefficient are therefore lower than those derived from bands with smaller absorption coefficient. Nevertheless, all thus obtained temperature values are between the lowest and the highest temperature of the sample. The method of fitting calculated spectral profiles to the observed ones has been successfully applied in these cases, too. 

The SNR is a figure of merit that is frequently cited in product literature. Values are often reported as peak-to-peak absorbance measured for a given spectrometer configuration over a specified time period and spectral range and at a specified spectral resolution. The SNR varies in direct proportion to the instrument throughput, source spectral radiance, detector D, and spectral resolution [35]. SNR also increases with the square root of measurement time which... 

We now introduce a fifth assumption critical to determining an analytic solution to Eq. (5) We assume that the radiance is slowly varying with the variable n, so that we can replace the entire angular distribution (at a given level) with two values, and I. This is the gist of the famous two-stream approximation. It allows us to make the following simplifications ... 

Digital image consists of discrete picture elements called pixels. Associated with each pixel is a number represented as Dn (Digital number), that depicts the average radiance of a relatively small area within a scene (pixel). The size of this area determines the reproduction of details within the scene. As the pixel size is reduced, more scene details are preserved in a digital representation. The pixel has a gray scale value where 0 corresponds to black and 255 for white in between there are shades of gray [1-5]. 

The mono-window algorithm proposed by Qin et al. [25] is based on the thermal radiance transfer equation to calculate LST. It utilizes transmittance and mean attnospheric temperature to estimate LST. The LST estimation is done considering the fact that brightness temperature at satellite can be computed by estimation of radiance from Dn value and conversion of radiance into brightness temperature. The radiance calculation from Dn of TM data utilizes an equation developed by Markham and Barker [31], shown below. 

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