Temperature spectral radiance

Figure 4.24. The Planck distribution law spectral radiance of blackbody radiation as a function of temperature and wavelength. (After Touloukian and DeWitt (1972). Plenum Press.)...

Black-and-white photography, fixation in, 19 213 Blackbody color of, 7 327 emittance from, 19 131-132 spectral radiance of, 24 453 Blackbody radiation law, 24 452 Blackbody responsivity, 19 132 Blackbody temperature sensor, 11 149-150 Black-box approach, to reliability modeling, 26 987-988, 990 Black copper, 16 144 Black crappie, common and scientific names, 3 187t... 

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.

For maximum sensitivity, the wavelength of the infrared pyrometer should also be selected based on where the spectral radiancy changes most rapidly. For example, in the temperature range depicted in Figure 8.3, a frequency of 1.5 x 10u Hz (2 /im) will permit more precise temperature measurement than a frequency of 0.4 x 1014 Hz (7.5 /im). 

Any object at a temperature above absolute zero emits thennal radiation, it is a thermal radiator. Ideally, its atoms or molecules are in a thennal equilibrium, the entire ensemble has a definite temperature. In contrast to lasers, thermal radiation sources produce non-coherent radiation. Its quanta have a random phase distribution, both spatially and temporarily. Planck s law defines the. spectral radiance of a black body the radiant power per solid angle, per area, and per wavelength L j (Eq. 3.3-2) or per wavenumber L j (Eq. 3.3-3) ... 

The Planck-Kirchhoff law allows a good approximation of the spectral radiance of any thermal radiator, the sources as well as the samples and detectors. Thermal radiators are characterized by a definite temperature as well as by their absorption coefficients f(i>) or a(i>), which describe the characteristic spectrum of the radiator ... 

Fig. 3.4-3 shows the infrared emission spectrum (the spectral radiance) of a sample of butadiene gas alp = 107 mbar in a cuvette v, th a thickness of 10 cm at 800 K, compared to the emi.ssion spectrum of a black body at the same temperature. It is interesting to note that - as theory predicts - the percentage emission of butadiene compared to that of a black body almost equals the percentage absorption of the same gas at room temperature as recorded with an ordinary spectrometer. 

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 major problem in using a single wavelength radiation thermometer to measure the surface temperature is the unknown emissivity of the measured surface. The emissivity is the major parameter in the spectral radiance temperature equation (Eq. 16.28) for the temperature evaluation. Objects encountered for temperature measurements are often oxidized metal surfaces, molten metal, or even semitransparent materials. On these surfaces, the emissivity is usually affected by the surface temperature and the manufacturing process for these materials. 

To reduce the error in the temperature evaluation caused by the uncertainty of the emissivity, radiation measurements for two or multiple distinct wavelengths may resolve the problem. For each wavelength, both spectral radiance temperature equations can be respectively written as... 

In ratio pyrometers [5], a device is designed to measure the spectral radiance temperatures and 7, at two wavelengths and X. Then, the true temperature Tm is determined from the ratio temperature Tra and is given by... 

To overcome the problems faced by the single-wavelength radiation thermometer and the ratio pyrometer, a double-wavelength radiation thermometer (DWRT) measures the spectral radiance itself at two distinct wavelengths for surface temperature evaluation. For this method to be used, the emissivity compensation function e i = fl v) must be defined. A detailed description of the principle for DWRT can be found in Ref. 53. When the emissivity relation x.i = Ae ) at two distinct wavelengths e i = fl v) is established, the true temperature on the measured surface can be determined from the inferred temperature, which is defined as... 

Figure 10.39. The spectral radiance of a blackbody at various temperatures from top to bottom 2000, 1500, and 1000 K,...

FIGURE 7 Spectral radiance distributions of a blackbody radiator at three temperatures. [From Wyszecki, G., and Stiles, W. S. (1982). Color Science Concepts and Methods, Quantitative Data and Formulae, 2nd ed. Copyright 1982 John Wiley Sons, Inc. Reprinted by permission of John Wiley Sons, Inc.]... 

Fig. 33. Spectral radiance for 50 bandwidths. The temperature is kept constant at 1000 K (727 °C). Inset Growth coefficient of emitted energy at the beginning and end of each of the bands selected.

This approach can be generalized to include multiple atmospheric parameters, providing there is adequate information content in the spectral radiance measurements. For example, it has been used to simultaneously infer both temperature profiles and molecular para-hydrogen profiles from Voyager IRIS measurements of Jupiter, Saturn, Uranus, and Neptune (Conrath et al., 1998). 

A temperature of 0 K is called absolute zero . It coincides with the minimum molecular activity, i.e., thermal energy of matter. The thermodynamic temperature was formerly called absolute temperature . In practice, the International Temperature Scale of 1990 (ITS-90) [i] serves as the basis for high-accuracy temperature measurements. Up to 700 K, the most accurate measurements of thermodynamic temperature are the NBS/NIST results for Constant Volume Gas Thermometry (CVGT). Above 700 K, spectral radiometry is used to measure the ratio of radiances from a reference... 

The continuous irradiation source, IL in Figure 30, is a 250-W short-arc xenon lamp fed by a power supply, ILS. The lamp has a daylight spectral type output, a high radiance, and an almost constant color temperature. The pulsed irradiation... 

By measuring the spectral distribution of the upwelling infrared radiation emitted by the Earth and its atmosphere, spaceborne sensors can provide information on the vertical temperature profile and on the atmospheric abundance of radiatively active trace gases. When local thermodynamic equilibrium conditions apply, the radiance received by a detector with spectral response function y> over frequency interval Av and viewing vertically downwards is given by (see Eq. 4.69a)... 

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