Fundamentals of Thermal Radiation
- Blackbody Planck Function
Microwave photons, like all photons, interact with
matter. Whether solid, gaseous or plasma, matter causes photons to be
absorbed, emitted or refracted. Emitted photons are either "thermal" in
origin, or non-thermal (synchrotron, Cerenkov, laser, etc). Thermal
emitted with all energies (wavelengths), but their number varies with
wavelength according to the Planck blackbody radiation equation.
Consider a thick slab of material (a semi-infinitie "half-space"),
having a uniform temperature throughout, that does not reflect photons
incident upon it. Imagine further that there are no photons incident
upon it because it shares a universe consisting of vacuum for the other
semi-infinite half-space. How many photons will be radiated by this
surface per second, per square micron?
Figure 1. Blackbody photon count (per second, per square
micron, per unit of wavelength) for various temperatures.
This figure shows the blackbody photon emission for a range of
temperatures corresponding to a very hot star surface (30,000 K), a
cool star surface (3000K), a typical Earth surface ambient temperature
(300 K), a cooled radiomter detector (30 K), and the coldest anything
in the universe can reach (in a natural setting), the cosmic background
level of 3 K. It may
be difficult to see in this figure, but longward of a certain
wavelength, for each temperature, the number of photons radiated is
proportional to the temperature. For all wavelengths longer than 1000
microns (1 mm) the number of photons is proportional to temperature,
regardless of the material's temperature (given that temperature
will never be colder than 3 K). It is also interesting to note that the
bottom level corrresponds to there being only a 50% chance that in one
second a photon will be emitted. It is therefore slightly misleading to
state that every material emits photons at all wavelengths, since for
every temperature there is a wavelength shotward of which it can be
that at no time duing the age of the universe is it likely that a
photon will have been radiated.
For present purposes it is only necessary to note that for the
wavelengths of a microwave radiometer, and for temperatures typical of
the earth's atmosphere (e.g., 300 K), the number of photons emitted is
proportional to temperature.
As an aside, not necessary for an understanding of the MTP, the above
graph is usually presented as a plot of energy radiated (per unit
wavelength, per unit area, per second). If a spectrum of energy
radiated is integrated throughout all wavelengths, the area enclosed
(the total energy radiated) is propotional to T4. This is
called the Stefan-Boltzmann law: E = constant * T4.
I'll refer to this in the next chapter.
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This is Chapter 1
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