handbook of modern sensors

110 3 Physical Principles of Sensing
whereas a smaller part is diffusely reflected:
the combined radiated and reflected flux from area a is
ρ = ρ r = (1 − ε b )ε b 0 ; (3.142)
= r + ρ = ε b 0 + (1 − ε b )ε b 0 = (2 − ε b )ε b 0 . (3.143)
As a result, the effective emissivity may be expressed as
ε e = 0
= (2 − ε b )ε b (3.144)
It follows from the above that due to a single reflection, a perceived (effective)
emissivity of a cavity is equal to the surface emissivity magnified by a factor of
(2–ε b ). Of course, there may be more than one reflection of radiation before it exits
the cavity. In other words, the incident on area a flux could already be a result of
a combined effect from the reflectance and emittance at other parts of the cavity’s
surface. The flux intensity will be higher than the originally emanated flux r .
For a cavity effect to work, the effective emissivity must be attributed to the cavity
opening from which radiation escapes. If a sensor is inserted into the cavity too deeply
facing its wall directly, blocking the reflected rays, the cavity effect may disappear
and the emissivity will be equal to that of a wall surface, which is always lower.
A cavity effect will change a perceived emissivity, and if not accounted for, it may
cause error in evaluation of the radiated power. To illustrate this, Fig. 3.47 shows two
photographs: one is taken in visible light and the other in the mid-infrared (thermal
radiation). Note that areas at the nostrils appear a little bit brighter (warmer). Yet, the
temperature of the skin in these spots is the same as nearby. Two wrinkles above the
mustache cause a cavity effect, which increases the skin emissivity from an average
of 0.96 to a higher value. This enhances the intensity of the emanated thermal flux
and gives an illusion of warmer skin.
Fabrication of a laboratory cavity blackbody is not a trivial task. For a cavity effect
to work, a blackbody must have a cavity whose surface area is much larger than the exit
aperture, the shape of the cavity must allow for multiple inner reflections before the
flux can escape from the aperture, and the cavity wall temperature must be uniform all
over its entire surface. Figure 3.46B shows an efficient way to fabricate a blackbody
Fig. 3.47. Photographs in visible light and infrared
thermal radiation which is naturally emanated
from the object. Note the brighter (appearing
warmer) areas at the wrinkles and skin
folds near the nose—a result of the cavity effect.
Eyeglasses appear black (cold) because glass
is opaque in the mid- and far-infrared spectral
ranges and does not pass thermal radiation from
the face. (Photo courtesy of Infrared Training Center,
www.infraredtraining.com.)