All bodies radiate energy to their surroundings proportional to their absolute temperature. Although the emitted radiation of a body includes all wavelengths, the region in which the amount of radiation is significant to industrial temperature measurement extends from 0.3µm to about 20µm. From 0.4µm to 0.7µm is the visible region. Radiation at wavelengths longer than 0.7µm is in the infrared region, which humans cannot see.
Theoretical Basis for Radiation Measurements
The thermal energy radiated by an object is expressed in relation to the energy radiated at the same temperature by a perfect radiator, traditionally called a black body. A blackbody absorbs all the radiation it receives and radiates more thermal radiation for all wavelength intervals than any other mass of the same area and temperature.
Though the blackbody is an ideal, and no perfect blackbody exists, specially constructed laboratory sources emit radiation with an efficiency compared to a blackbody of 98% or higher. Laboratory sources with 99.98% efficiency compared to a blackbody have been constructed. The most common approach to realizing a blackbody is to use a spherical cavity with a small hole in the surface or a closed-end tube that is longer than its diameter. The opaque walls of the sphere or tube are held at uniform temperature.
As shown below, these constructions provide for multiple reflections of any radiation entering the opening. Thus, though the sphere or tube walls are slightly reflective, after many reflections all the energy is absorbed, i.e., at room temperature the aperture in the sphere or tube appears to be black in the visible part of the spectrum and is also nearly totally absorbing in other regions of the spectrum. At any given temperature the aperture radiates energy at nearly the same rate as a blackbody of the same size and temperature.
As shown in Figure 1, these constructions provide for multiple reflections of any radiation entering the opening. Thus, though the sphere or tube walls are slightly reflective, after many reflections all the energy is absorbed, i.e., at room temperature the aperture in the sphere or tube appears to be black in the visible part of the spectrum and is also nearly totally absorbing in other regions of the spectrum. At any given temperature the aperture radiates energy at nearly the same rate as a blackbody of the same size and temperature.
- Figure 1
This figure illustrates a commercial secondary reference furnace based on a small opening in a uniformly heated spherical cavity.
Another configuration used for a blackbody source is a deep wedge, where the cavity subtends only a small angle. Multiple reflections from the sides of the wedge make it appear black. The real importance of the wedge is conceptual. Surface roughness of an object can be visualized as a multitude of small wedges as in a machined surface or casting. If the surface is very rough, the wedges are deep, and the object will have radiating properties that are closer to those of a blackbody than if the surface were smooth.
The rate at which a blackbody radiates energy is given by the Stefan-Boltzmann Law:
This equation assumes that the body receiving the radiation is at absolute zero. In the practical case, the receiving body is at a temperature T R and radiates to the blackbody
at a rate:
per unit area of the receptor. Thus, the net energy reaching the receptor is:
Where K is a constant, taking into account the areas of the blackbody and receptor and the distance between them.
These equations give the radiation from all wavelengths in the entire spectrum. For more practical use, where the receiving object (the detector in a radiation thermometer, for example) responds significantly only to the short wavelength portion of the spectrum, the Wien-Planck and Wien Laws are more useful.
The Wien-Planck Law expresses the radiation emitted per unit area of a blackbody as a function of wavelength, l, and temperature, T.
This function is plotted for several temperatures in Figure 4.
C1, the first radiation constant = 3.7418 x 10-16 watts/m2
C2 the second radiation constant = 1.43879 x 102 m · K
If C2/ l T is much greater than 1, then the Wien-Planck Law can be approximated by Wien’s Law.
This expression agrees with the Wien-Planck law within 1% if l T is less than 0.003 meter · K (3000m m.K).
At 0.65 m m wavelength, this condition exists for temperatures below 4600K. Therefore, Wien’s Law has been commonly used with high accuracy in the field of optical pyrometry.
Wien’s Displacement Law
In Figure 4. It can be observed that as temperature increases, not only does the amount of radiation per unit area increase, but the wavelength at which the radiation is maximum shifts to shorter wavelengths.
The value of the wavelength of maximum radiation per unit area is given by Wien’s Displacement Law.
Fig. 4 Radiation Intensity as a Function of wavelength and Temperature (Planck’s Law)
All infrared pyrometers, especially those measuring at long wavelengths, have a ”size of source effect" (SSE), meaning that part of their sensitivity lies outside the specified spot diameter. This is caused by unwanted but unavoidable effects like diffraction or multiple reflections inside the lens and between the lens and detector.
If we calibrate to a source with the exact spot diameter, anyone measuring large areas would get tremendously high readings. On the other hand, calibrating to a very large area radiation source would result in a very low reading for those who measure an object at the spot diameter.
The official calibration rules of VDI/VDE 3511 Part 4.4 define the "calibration diameter" as a practical compromise between these two extreme positions.
All LumaSense pyrometers are calibrated according to these rules.
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