Importance and limitation of spectral measurements

To measure the emissivity there are many approaches that we can classify in two categories: the direct methods measure the energetic radiation of the studied surface and the indirect methods deduce emissivity from other optical properties of the surface.

Among the direct methods, one can quote the calorimetric method which consists in measuring the electric power to be supplied to a sample (placed in a cryostat under vacuum) to maintain its surface temperature equal to the temperature at which one wishes to know the emissivity. The National Metrology and Testing Laboratory (LNE) has a measuring bench of this type [3].

Another method, called radiometric, consists in measuring the thermal radiation coming from the surface of the material. This measurement can be done as a function of the angle to obtain the directional emissivity and as a function of the wavelength (with an FTIR spectrometer for example) to obtain the directional spectral emissivity. The CEMHTI device (Extreme Conditions and High Temperature Materials and Irradiation) allows this type of measurement at very high temperature [4].

For the measurement of emissivity at ambient temperature, the level of the flux is too low to be measured with good precision: this is the privileged domain of indirect methods. These use Kirchhoff’s law relating the emissivity ε to the reflectance ρ and to the transmittance τ for a wavelength λ given:

the emissivity being equal to the absorptivity. For an opaque material, the emissivity is therefore equal to:

To obtain the total emissivity we must therefore add the spectral reflection factor (first time I see this word) weighted by the spectral energy distribution of the black body at the temperature at which one wishes to know the emissivity:

The other solution is to measure the global reflection factor by illuminating the surface with a light source having this energy distribution.

Several commercial devices measuring emissivity use this method. Their main quality is to measure the reflectance in a spectral band ranging from 1 to 50 µm which represents 95% of the energy radiated by a black body at ambient temperature (around 300K). However, they integrate the reflection factor for a spectral distribution different from the ambient temperature.

In fact, they use black or gray bodies as infrared sources at a temperature above ambient temperature. These sources have spectral distributions different from that of a black body at 300 K. This difference in spectral distribution leads to emissivity measurement errors for non-gray bodies of up to 5%. This defect is nothing new.

Indeed the standard ASTM E408-71 (Standard Test Method for Total Normal Emittance of Surface Using Inspection-Meter Techniques) states it. We can also refer to [5] where this type of error is briefly mentioned.

The emissometers developed at CERTES [1,2] use infrared sources modulated in temperature at temperatures very close to ambient temperature. The problem remains unresolved because modulation significantly affects the spectral distribution of the source (see box 1).

This is frequently the case for this type of ceramic. Furthermore, bibliographic data cannot be used. Indeed, depending on the allotropic variety, the degree of crystallization, the different heat treatments, etc., the values ​​of the directional spectral emissivity of alumina are very variable [6].

When the temperature of the surface studied varies from room temperature to higher temperatures, the maximum luminance of the Planck function L ( λ, T) shifts by 10 µm to shorter wavelengths.The maximum luminance is reached for a wavelength λmax(in µm) = 3000 /T, with T in K.

For alumina, this has the effect of increasing stress on a much more emissive spectral region. The emissivity therefore increases with temperature. We can calculate the emissivity by taking into account only the spectral band from 1 to 20 µm. These data are presented in Table 1. This calculation neglects an important part of the useful spectrum. The calculated emissivity value is therefore incorrect.

However, given the monotonicity of the Planck function for wavelengths greater than 20 µm for this temperature, the variations in emissivity as a function of temperature therefore only depend on the spectral band from 1 to 20 µm. In the absence of knowing the value of the emissivity, we can therefore deduce the coefficient of variation of the emissivity according to the temperature fairly precisely. If we are able by another means to measure the emissivity for a temperature higher than the ambient temperature, we can therefore deduce the emissivity at all temperatures around 300 K.

This can be seen on the graphs of figure 4. From the spectral measurements (top graph of figure 4) we can obtain the variations in emissivity as a function of temperature (bottom graph of figure 4, blue line). The EM2 emissometer of CERTES [2] (figure 5) makes it possible to obtain an unbiased value of the emissivity but only at 360K. From these two pieces of information, we go back to the unbiased emissivity as a function of the temperature (bottom graph of figure 4, red line).