handbook of modern sensors

108 3 Physical Principles of Sensing
(A)
(B)
Fig. 3.45. Spatial emissivities for a nonmetal (A) and a polished metal (B).
All nonmetals are very good diffusive emitters of thermal radiation with a remarkably
constant emissivity defined by Eq. (3.139) within a solid angle of about ±70 ◦ . Beyond
that angle, emissivity begins to decrease rapidly to zero with the angle approaching
90 ◦ . Near 90 ◦ , emissivity is very low. A typical calculated graph of the directional
emissivity of nonmetals into air is shown in Fig. 3.45A. It should be emphasized
that the above considerations are applicable only to wavelengths in the far-infrared
spectral range and are not true for the visible light, because emissivity of thermal
radiation is a result of electromagnetic effects which occur at an appreciable depth.
Metals behave quite differently. Their emissivities greatly depend on the surface
finish. Generally, polished metals are poor emitters within the solid angle of ±70 ◦ ,
and their emissivity increases at larger angles (Fig. 3.45B). This implies that even a
very good metal mirror reflects poorly at angles approaching 90 ◦ to normal. Table
A.18 in the Appendix gives typical emissivities of some materials in a temperature
range between 0 ◦ C and 100 ◦ C.
Unlike most solid bodies, gases in many cases are transparent to thermal radiation.
When they absorb and emit radiation, they usually do so only in certain narrow spectral
bands. Some gases, such as N 2 ,O 2 , and others of nonpolar symmetrical molecular
structure, are essentially transparent at low temperatures, whereas CO 2 ,H 2 O, and
various hydrocarbon gases radiate and absorb to an appreciable extent. When infrared
light enters a layer of gas, its absorption has an exponential decay profile, governed
by Beer’s law:
x
= e −αλx , (3.140)
0
where 0 is the incident thermal flux, x is the flux at thickness x, and α λ is the
spectral coefficient of absorption. The above ratio is called a monochromatic transmissivity
γ λ at a specific wavelength λ. If gas is nonreflecting, then its emissivity is
defined as
ε λ = 1 − γ λ = 1 − e −αλx . (3.141)
It should be emphasized that because gases absorb only in narrow bands, emissivity
and transmissivity must be specified separately for any particular wavelength. For
instance, water vapor is highly absorptive at wavelengths of 1.4, 1.8, and 2.7 µm and
is very transparent at 1.6, 2.2, and 4 µm.