Operation Manual

Theory of thermography

The spectral emissivity ε

= the ratio of the spectral radiant power from an object to that

from a blackbody at the same temperature and wavelength.

Expressed mathematically, this can be written as the ratio of the spectral emittance of the

object to that of a blackbody as follows:

Generally speaking, there are three types of radiation source, distinguished by the ways in

which the spectral emittance of each varies with wavelength.

• A blackbody, for which ε

= ε = 1

• A graybody, for which ε

= ε = constant less than 1

• A selective radiator, for which ε varies with wavelength

According to Kirchhoff’s law, for any material the spectral emissivity and spectral absorp-

tance of a body are equal at any specified temperature and wavelength. That is:

From this we obtain, for an opaque material (since α

+ ρ

= 1):

For highly polished materials ε

approaches zero, so that for a perfectly reflecting material

(i.e. a perfect mirror) we have:

For a graybody radiator, the Stefan-Boltzmann formula becomes:

This states that the total emissive power of a graybody is the same as a blackbody at the

same temperature reduced in proportion to the value of ε from the graybody.

Figure 37.8 Spectral radiant emittance of three types of radiators. 1: Spectral radiant emittance; 2: Wave-

length; 3: Blackbody; 4: Selective radiator; 5: Graybody.

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