Millimeter-Wave Measurements of High Level and Low Level Activity Glass Melts Page: 4 of 12
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B. Analytic Modeling
1. Temperature and Emissivity
Thermal emission signals are proportional to the product of the emissivity and temperature (s7)
of the material that is viewed. Methods that can resolve the emissivity and temperature are of
general interest to materials analysis. An important accomplishment has been to derive the
analytical basis for determining these parameters using the thermal return reflection method.
The basic concept was to use the thermal radiation from the viewed source as a probe of its
emissivity. There is a significant advantage to using incoherent thermal radiation for probing
versus coherent probe beam as demonstrated in an earlier work [7], and use of the viewed objects
own emission as a probe greatly simplifies the instrumentation hardware requirements.
The reader is referred to the TRR M
publication [8] for details of N
the derivation. Here we just rs , s , Ts
state the results with the aid rbs , bs
of Figure 4. The receiver z, ,W, Tg
views a sample (S) through a WG Receiver
beamsplitter (BS) and
waveguide system (WG). S r
The analysis requires taking
into account all of the sources
and losses of signal in the Figure 4. Illustration for defining the terms in the analytical results for
field of view of the receiver. the TRR method.
Each component has
associated with it an
emissivity (E), temperature (T), transmission factor (r), and reflectivity (r). If a component is at
room temperature, then its emissivity and temperature will cancel out as in the case of the
beamsplitter.
The analytical results for the measured temperature at the receiver for the two TRR cases are
given by:
Tf = EwgTg + T,9ET + rr,, sg Twg (1)
S 1- rr 2 (2)
1--.9rr
where Teff and Te> are the MMW temperatures measured at the receiver without and with the
thermal return reflection, respectively, TWg and TS are the waveguide and melt surface
temperatures, E8g and zWg are the waveguide emissivity and transmission related by
Ewg = (I - zWg) , Es and rs are the emissivity and reflectivity of the viewed surface related by
, = (i - r) , rbs is the beamsplitter reflectivity, and TK is the viewed surface coupling factor.
These two equations can be solved to obtain the emissivity and temperature of the viewed4
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Woskov, Paul. Millimeter-Wave Measurements of High Level and Low Level Activity Glass Melts, report, March 2, 2005; Cambridge, Massachusetts. (https://digital.library.unt.edu/ark:/67531/metadc777109/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.