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From Blackbodies to Real Surfaces
At first it would seem that a radiation thermometer would utilize the entire spectrum, capturing most of the radiant emission of a target in its particular temperature range. There are several reasons why this is not practical.
  In the equations for infrared radiation derived above, it was found that at very low wavelengths, the radiance increases rapidly with temperature, in comparison to the increase at higher wavelengths, as shown in Figure 2-4. Therefore, the rate of radiance change is always greater at shorter wavelengths. This could mean more precise temperature measurement and tighter temperature control. However, at a given short wavelength there is a lower limit to the temperature that can be measured. As the process temperature decreases, the spectral range for an infrared thermometer shifts to longer wavelengths and becomes less accurate.
  The properties of the material at various temperatures must also be considered. Because no material emits as efficiently as a blackbody at a given temperature, when measuring the temperature of a real target, other considerations must be made. Changes in process material emissivity, radiation from other sources, and losses in radiation due to dirt, dust, smoke, or atmospheric absorption can introduce errors.
  The absorptivity of a material is the fraction of the irradiation absorbed by a surface. Like emission, it can be characterized by both a directional and spectral distribution. It is implicit that surfaces may exhibit selective absorption with respect to wavelength and direction of the incident radiation. However, for most engineering applications, it is desirable to work with surface properties that represent directional averages. The spectral, hemispherical absorptivity for a real surface is defined as:

where is the portion of irradiation absorbed by the surface. Hence, depends on the directional distribution of the incident radiation, as well as on the wavelength of the radiation and the nature of the absorbing surface. The total, hemispherical absorptivity, represents an integrated average over both directional and wavelength. It is defined as the fraction of the total irradiation absorbed by a surface, or:

  The value of depends on the spectral distribution of the incident radiation, as well as on its directional distribution and the nature of the absorbing surface. Although is independent on the temperature of the surface, the same may not be said for the total, hemispherical emissivity. Emissivity is strongly temperature dependent.   The reflectivity of a surface defines the fraction of incident radiation reflected by a surface. Its specific definition may take several different forms. We will assume a reflectivity that represents an integrated average over the hemisphere associated with the reflected radiation to avoid the problems from the directional distribution of this radiation. The spectral, hemispherical reflectivity then, is defined as the spectral irradiation that is reflected by the surface. Therefore:

where is the portion of irradiation reflected by the surface. The total, hemispherical reflectivity r is then defined as:

If the intensity of the reflected radiation is independent of the direction of the incident radiation and the direction of the reflected radiation, the surface is said to be diffuse emitter. In contrast, if the incident angle is equivalent to the reflected angle, the surface is a specular reflector. Although no surface is perfectly diffuse or specular, specular behavior can be approximated by polished or mirror-like surfaces. Diffuse behavior is closely approximated by rough surfaces and is likely to be encountered in industrial applications.
  Transmissivity is the amount of radiation transmitted through a surface. Again, assume a transmissivity that represents an integrated average. Although difficult to obtain a result for transparent media, hemispherical transmissivity is defined as:

where is the portion of irradiation reflected by the surface. The total hemispherical transmissivity is:

The sum of the total fractions of energy absorbed reflected and transmitted must equal the total amount of radiation incident on the surface. Therefore, for any wavelength:

This equation applies to a semitransparent medium. For properties that are averaged over the entire spectrum, it follows that:

For a medium that is opaque, the value of transmission is equal to zero. Absorption and reflection are surface properties for which:


For a blackbody, the transmitted and reflected fractions are zero and the emissivity is unity.

Figure 2-5: Soda-Lyme Glass Spectral Transmittance

  An example of a material whose emissivity characteristics change radically with wavelength is glass. Soda-lime glass is an example of a material which drastically changes its emissivity characteristics with wavelength (Figure 2-5). At wavelengths below about 2.6 microns, the glass is highly transparent and the emissivity is nearly zero. Beyond 2.6 microns, the glass becomes increasingly more opaque. Beyond 4 microns, the glass is completely opaque and the emissivity is above 0.97.

  References and Further Reading
  Temperature Measurement in Engineering, H. Dean Baker, E.A. Ryder, and N.H. Baker, Omega Press, 1975.
  Heat and Thermodynamics, 6th ed., Mark W. Zemansky, and Richard H. Dittman, McGraw-Hill, 1981.
  Industrial Temperature Measurement, Thomas W. Kerlin and Robert L. Shepard, Publishers Creative Series, Inc., ISA.
  Introduction to Heat Transfer, 2nd ed., Frank P. Incropera, and David P. DeWitt, John Wiley & Sons, 1990.
  The Invisible World of the Infrared, Dodd, Jack R. White, Mead & Company, 1984.
  Process/Industrial Instruments and Controls Handbook, 4th ed., Douglas M. Considine, McGraw-Hill, 1993.
  Theory and Practice of Radiation Thermometry, David P. DeWitt and Gene D. Nutter, John Wiley & Sons, 1988.
  Thermodynamics, 5th ed., Virgil M. Faires, The Macmillan Company, 1971.

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