Page 289 - Modern Optical Engineering The Design of Optical Systems

268 Chapter Twelve

As an aside, note that this (300 K) is a reasonable value for the
ambient temperature and that our result indicates that the earth and
most things on it are strongly emitting at a wavelength of 10 m. This
is the basis of the “see in the dark” FLIR systems which are sensitive
to this spectral region; most such systems use germanium optics,
which transmit well in the 8- to 14- m region (which also happens to
be a good transmission window of the atmosphere). Thus there is no
such thing as darkness if you can detect 10- m radiation.
Suppose we wish to know the characteristics of this blackbody in the
wavelength region between 4 and 5 m. We express these wavelengths
in terms of max as 4/9.66 0.414 and 5/9.66 0.518. From Fig. 12.6,
the corresponding values of W /W , max are 0.07 and 0.25; these values,
multiplied by W , max 3.13 10 3 W cm 2 m 1 give us the spectral
radiant emittances for these wavelengths
At 4 m:
W 0.22 10 3 W cm 2 m 1

At 5 m:
W 0.78 10 3 W cm 2 m 1

Using the fraction scale across the top of the chart, we find that
about 0.011 of the radiation is emitted below 5 m (rel. 0.518) and
about 0.0015 below 4 m. Thus, approximately 1 percent of the total
radiation (W TOT ), amounting to about 4 10 4 W/cm , is emitted in this
2
spectral band. The radiance of the surface will be 4 10 / W ster 1
4
cm 2 in this spectral band. If the blackbody is a foot square, with an
2
area of about 1000 cm , it will radiate about 0.4 W between 4 and 5 m
into a hemisphere of 2 ster.
Most thermal radiators are not perfect blackbodies. Many are what are
called gray-bodies. A gray-body is one which emits radiation in exactly
the same spectral distribution as a blackbody at the same temperature,
but with reduced intensity. The total emissivity ( ) of a body is the ratio
of its total radiant emittance to that of a perfect blackbody at the same
temperature. Emissivity is thus a measure of the radiation and
absorption efficiency of a body. For a perfect blackbody 1.0, and
most laboratory standard blackbodies are within a percent or two of
this value. The table of Fig. 12.7 lists the total emissivity for a number
of common materials. Note that emissivity varies with both wave-
length and with temperature.
Radiation incident on a substance can be transmitted, reflected (or
scattered), or absorbed. The transmitted, reflected, and absorbed frac-
tions obviously must add up to 1.0. The absorbed fraction is the emis-
sivity. Thus a material with either a high transmission or a high
reflection must have a low emissivity.