Physics/7. Optics

 

 

V. Poryev, S. Kushnir

 

National Technical University of Ukraine Kyiv Polytechnic Institute

 

The Method to Determine Multispectral Temperature

 

 

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 surfaces 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 bodys 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.