In the previous chapter it was stated that if a part
of the universe completely "intercepted" the reception pattern of the
horn antenna then the measured antenna temperature would equal the
temperature of that part of the universe. This assumes that the part of
the universe viewed by the horn antenna is at a uniform
temperature. We also assumed that the part of the universe being viewed
is a blackbody, meaning
that no photons incident upon it are reflected (from either direction,
i.e., all photons coming from within the material are able to
penetrate the material surface without being reflected). When these
conceptually simple conditions are met then it can be said that the
measured antenna temperature equals the "physical temperature" of the
emitting material. When these assumptions cannot be made we use the
concept "brightness temperature," TB. A surface emitting 95% of the
photons incident upon it (from either direction) appewars the same to a
radiomter as a surface with 100% emissivity at a temperature that is
0.95 times its actual physical temperature. Therefore, it is useful to
define brightness temperature as physical temperature times emissivity.
It follows that a material's brightness temperature equals its physical
temperature when it is 100% emissive. The atmosphere is ~100% emissive
at microwaves, so this greatly simplifies analysis of MTP observers. It
is typical for dry ground to have an emissivity of ~90%, which means
that an MTP that views only the ground will be viewing a target that
has a brightness temperature that is ~90% of the ground's physical
(Kelvin) temperature plus 10% of whatever emission is incident upon the
ground (and being partially reflected). The reason for this lower
emissivity for the
ground is that there's an abrupt change in the real part of dielectric
constant experienced by a photon incident upon the ground-to-air
boundary.
Let's consider another of the assumptions in the first paragraph. It
was stated that we assumed that the entirety of the antenna's reception
pattern was "intercepted" by a part of the universe whose brightness
temperature was under discussion. The word "intercepted" deserves
comment, and that's what this paragraph is about. It is very useful to
sometimes think of a passive radiometer, attached to a horn antenna, to
be "radiating" photons instead of receiving them (which was alluded to
in the previous chapter). With this direction
reversal we can then ask "what percentage of the radiated photons are
intercepted by an extended target of interest?" If 99% of the radiated
photons are intercepted by the target of interest, then it can also be
stated that this target fills only 99% of the antenna pattern of the
radiometer. The radiation pattern of a horn antenna consists of a main
beam, Gaussian in shape, and surrounding sidelobes. It is typical for
the main beam to contain ~98% of the radiated photons. Hence, a target
that has a solid angle that exactly matches the main beam will fill
only ~98% of a horn antenna's reception pattern. The rest of the 4-pi
solid angle fills the remaining ~2% of the reception pattern.
In order to reduce the influence of sidelobes it is common to arrange
for the horn antenna to "under-illuminate" the reflector, or to employ
an over-sized reflector (either
flat or curved). The
over-sized reflector can serve to intercept some of the sidelobe
pattern and "direct it" onto the same part of the sky viewed by the
main beam.
As a practical matter only ~99% of a horn antenna's antenna pattern can
be directed to a small patch of sky, with ~1% directed at locations
that are difficult to determine. This means that measured antenna
temperature is a weighted-average of the intended patch of sky and an
unknown part of the rest of the 4-pi sphere. For example, consider that
the MTP main beam and nearby sidelobes are directed at the atmosphere
having a brightness temperature of TB_atmos, and a stray 1% of
the
antenna pattern is directed at the fairing that shields the MTP from
the airstream and that the fairing has a brightness temperature
TB_fairing. The measured antenna temperature will be 0.99 * TB_atmos
+
0.01 * TB_fairing. The closer together the brightness
temperatures
of the fairing and atmosphere are to each other the smaller will be the
unwanted effect.
Returning to the meaning of brightness temperature, note that the
fairing's brightness temperature will be slightly different from its
physical temperature: TB_fairing = T_physical_fairing *
Emissivity_fairing, where Emissivity_fairing ~90%. In
other words, the
fairing will emit only ~90% of the radio photons that would be emitted
by a blackbody at the same temperature as the fairing. This also means
that the fairing reflects ~10% of the radio photons incident upon it,
and these will be received by the horn antenna. Let's not get involved
with a complete equation for brightness temperature here; rather, the
goal of this chapter is to state that:
Brightness Temperature = Physical Temperature
times Emissivity (plus smaller terms related to
reflected photons)
which states that when emissivity = 100%, as it does for the
atmosphere,
Brightness Temperature =
Physical Temperature (when viewing the atmosphere)
For the MTP case, where most of the antenna pattern intercepts the
atmosphere and a small fraction (such as 1%) intercepts nearby
material,
Antenna Temperature = Atmosphere Physical
Temperature (plus small corrections related to sidelobes)
This discussion of "brightness temperature" and its relationship to the
thing that can be measured, antenna temperature, prepares the way for
understanding how to interpret observations of a real atmosphere with a
temperature that changes with depth along the line-of-sight. This will
be discussed in the next chapter.
Go to Chapter #4
(next chapter)
This is Chapter 3
Return to Chapter #2
(previous chapter)
Return to Introduction
____________________________________________________________________