Physics**/**7. Optics

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**V. Poryev, S. Kushnir**

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*National Technical University of Ukraine “Kyiv Polytechnic Institute”*

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**The
Method to Determine Multispectral Temperature**

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In
the modern pyrometry a multiple conventional temperatures, such as the
radiation temperature, brightness temperature and the temperature of spectral
ratio. At the same time the true temperature at the surface’s body is the
thermodynamic temperature specific to the state of the surface. We propose the
new method to determine the thermodynamic temperature based on using the
multispectral television evaluation tool (ET).

In
generalized form the spectral signal of the ET could be written as

_{
} (1),

where
_{
}is the spectral signal, _{
} is some constant
irrelevant in this discourse since it is not decisive in temperature
measurement, _{
} is the body’s surface
brightness, _{
}is the emission ratio, _{
}is the spectral characteristics (SC) of the ET,_{
}is the wavelength used in the signal measurement, T is the
surface temperature.

Given
the assumption that the emission ratio is linear in the range of _{
}, we can define the intermediate emission ratios on the near
wavelengths _{
}as such:

_{
} (2),

Where
_{
} and _{
} are some parameters
for this relation.

Writing ET signal
for the three different wavelengths in accordance with (2) we get:

_{
} (3)

Introducing the
substitution

_{
} (4)

Then the (3)
system could be rewritten as

_{
} (5)

We shall find _{
} and _{
} parameters from the
first two equations of the (5) system to use in the third equation, which will
yield the following:

_{
} (6)

For convenience
let us choose _{
} values such that _{
}.

Then (6) could be
rewritten as

_{
} (7)

And after the
substitution of _{
}

_{
} (8)

_{
} (9)

In the (10) system we shall use
Planck formula for brightness function, then we get the following:

** _{
} **(10)

The specific of
this formula is that it contains the relation between spectral signals and SC
values for the chosen wavelengths. Therefore, one could choose any triplet of
the wavelengths and get the values for the temperature independent of the
chosen wavelengths.

Evaluation of the
temperature according to this method opens new possibilities for metrology and
simplifies the calibration of the existing pyrometers in the lab.