=Paper=
{{Paper
|id=Vol-2654/paper47
|storemode=property
|title=Research by statistical methods of models of the function of transformation of optical circuits of the means of measuring the temperature based on the effect of Raman
|pdfUrl=https://ceur-ws.org/Vol-2654/paper47.pdf
|volume=Vol-2654
|authors=Y. Kryvenchuk,I. Shvorob,Y. Novytskyi,Y. Zasoba,Y. Matviychuk,V. Mykhailyshyn,N. Hrabovs'ka,N. Topylko ,M. Osypov ,H. Yakymyshyn
|dblpUrl=https://dblp.org/rec/conf/cybhyg/KryvenchukSNZMM19
}}
==Research by statistical methods of models of the function of transformation of optical circuits of the means of measuring the temperature based on the effect of Raman==
https://ceur-ws.org/Vol-2654/paper47.pdf
Research by statistical methods of models of the function
of transformation of optical circuits of the means of
measuring the temperature based on the effect of Raman
Yurii Kryvenchuk[0000-0002-2504-5833], Iryna Shvorob[0000-0001-5569-2647],
Yurii Novytskyi[0000-0002-5011-7034], Yevgen Zasoba [0000-0003-4830-8306],
Yaroslav Matviychuk [0000-0002-5570-182X], Vladyslav Mykhailyshyn [0000-0003-1889-9053],
Nataliya Hrabovs'ka [0000-0002-5032-2257], Nataliia Topylko [0000-0002-3200-3391],
Mykhailo Osypov [0000-0002-6611-724X], Hrystyna Yakymyshyn [0000-0002-8772-0101]
Lviv Polytechnic National University, Lviv 79013, Ukraine
yurkokryvenchuk@gmail.com, iryna.b.shvorob@lpnu.ua,
yuranov_lpnu@ukr.net, geka.zasoba@gmail.com, matv@ua.fm,
vladyslavmykhailyshyn@gmail.com, natahagr@gmail.com,
topnatlviv@gmail.com, mykhailo.osypov@gmail.com,
yakymyshyn_hrystyna@ukr.net
Abstract. Industry 4.0 continually flows into the daily technical life of the
world. Germany has created the platform Industry 4.0. Like the Germans,
France launched the initiative, also at the state level. India, China and the Unit-
ed States have strong initiatives. The new concept makes it possible to speed up
the production of various parts and entire products by two, and sometimes by
three times. For such purposes, it is not only necessary to use fast data transfer
protocols, but also to develop new sensors that will perform such fast and accu-
rate work. As a rule, the most controlled parameter in the industry is tempera-
ture, meaning such high-precision thermometric sensors need to be verified to
confirm their metrological characteristics. For this purpose, the most optimal
method is the Raman scattering. In order to confirm the accuracy of metrologi-
cal verification, it is important to know the errors of the conversion function of
optical circuits, since this entails an increase in the relative mean-rms deviation
of the equivalent frequency of the anti-Stokes component of the spectrum,
which in turn directly affects the accuracy of determining the temperature and
metrology.
Keywords: Industry 4.0, Temperature measurement, Raman spectrum, Raman
thermometer, Mathematical model
1 Introduction
In [1], the synthesis of models of functions of transformation of optical elements and
optical circuits of the means of measuring the temperature and spectra of the Raman
was performed. These models allow us to investigate the dependence of the relative
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons Li-
cense Attribution 4.0 International (CC BY 4.0). CybHyg-2019: International Workshop on
Cyber Hygiene, Kyiv, Ukraine, November 30, 2019.
root mean square deviation of the equivalent frequency of the anti-Stokes component
of the Raman spectrum for different spectral models and under the influence of differ-
ent error components at different spectral analyzer resolutions. It is also possible to
determine the best method for determining the equivalent frequency of the anti-Stokes
component of the Raman spectrum. These studies allow us to improve the metrologi-
cal characteristics of temperature measuring instruments that will be used for metro-
logical verification of temperature sensors in the industry. The results can also be
used to determine the lack of parts on the production line.
2 State of arts
Analyzing optical circles and optical elements, it is determined that, as a rule, for each
specific task, they use specific optical circuits, since the objects under study are of
different shapes and sizes, and may also simply be located at different points. Howev-
er, there are five of the most widely used optical circuits worth converting. Each cir-
cuit has its own characteristics due to a different set of optical elements that will dis-
tort the original spectrum, and as a consequence contribute to the error of temperature
measurement by this method. Matlab modeled secondary circuits of optical circuits
and input spectra of Raman scattering. The following parameters were investigated at
the input: the linear, nonlinear components of the error model of the optical element
re-creation function is 2%, the methods of determining the equivalent frequency of
the anti-stokes component of the Raman spectrum: the center of mass method and the
median method. The resolution of the spectrum analyzer at a frequency of 1 ... 10 cm-
1, the forms of simulated spectra for the study: rectangular, triangular, trapezoidal,
sawtooth. The number of bones of random sequences is one thousand. At the output
we obtain the following results: the best method for determining the equivalent fre-
quency of the anti-stokes component of the Raman spectrum, the dependence of the
relative mean-rms deviation of the equivalent frequency of the anti-stokes component
of the Raman spectrum on the frequency resolution of the analyzer. Uncertainty of
determining the equivalent frequency of the anti-stokes component of the Raman
spectrum from the forms of simulated signals, the influence of linear, nonlinear, total
error of the transmitting characteristics of optical elements.
The term "Industry 4.0" was created for the anticipated "fourth industrial revolu-
tion". Accordingly, Industry 4.0 means in-depth digitization in industrial enterprises
in the form of a combination of Internet technologies with future-oriented technolo-
gies in the field of "smart" objects (machines and products). This transforms industrial
production systems so that products control their own production process. The im-
portance of digitalization and the Internet is also reflected in discussions of related
concepts such as the Internet of Things or the Industrial Internet. Industry 4.0 is initi-
ated not by a single technology, but by the interaction of several technological objects
whose quantitative consequences together create new ways of production. The main
advantage over the technological perspective is the ability to facilitate tasks that pre-
viously required heavy manual work, such as high-precision methods of temperature
measurement.
Scientific and technological progress is closely linked to the improvement of
measuring equipment. This is completely true of thermometry, which is constantly
evolving. The measurement range is being expanded, new methods and temperature
measurement tools are being developed to provide their required metro-logical char-
acteristics, since the accuracy of maintaining the temperature regime in most techno-
logical processes is the main parameter on which the quality of the final product de-
pends. Open source obtained quantitative and spatially differentiated temperature data
available for thermal actuator designs using MEMS. The lion's cup of modern MEMS
has become tiny in size. In the process of manufacturing such miniature sensors, a
large number of parameters must be controlled and the most controlled parameter is
the temperature. The results obtained from experimental measurements of the temper-
ature profile for bending type actuators can be used to validate existing models, but do
not allow us to determine the optimal model. Applying artificial intelligence technol-
ogies and Big Data concepts to control temperature and analyze the data obtained will
minimize the output of the defect. Automation facility (Joint Ukrainian-German com-
pany "Spheros-Electron") defects details that have deviations from geometric parame-
ters and / or metallurgical defects. The minimization of metallurgical defects was the
most difficult and interesting task for technologists. The "responsible" for them was
the installation of controlled cooling, since the main causes of such defects - uneven
cooling and violations of temperature. It has become an "optimization point".
3 Materials and Methods
The uncertainty dependence of the determination of the equivalent frequency of the
anti-stokes components of the Raman spectrum of frequency resolution is taken into
account for the linear, nonlinear and random components of the error of the Monte
Carlo optical circuit conversion function for the five most commonly used spectra of
the common optical circuits in the process of obtaining the spectrum.
Finding the dependence of the uncertainty of determining the frequency shift of the
CRC on the frequency resolution for the test signal with a random component of the
error of the transmission characteristic of the elements of the optical circuit, linear and
nonlinear component of the error works according to the following algorithm.
1) Data entry is made, and then, based on the number of frequency resolution val-
ues, minimum and maximum frequency resolutions, the resolution step of the spec-
trometer is formed. This will allow you to select the most optimal frequency analyzer.
2) A spectrum model of a known shape is generated, which alternately falls on the
optical elements of the secondary circuit of the optical circuit, where there is actually
a multiplication of the complex frequency characteristics of the optical elements of
the secondary circuit of the optical circuit with random linear, nonlinear components
of the error of the optical elements and spectrum. Such operation is performed n-
number of times and from each spectrum the equivalent frequency of the anti-Stokes
component of the Raman spectrum is determined by the median and the center of
mass method.
3) The mathematical expectation, variance and root mean square deviation and un-
certainty of the equivalent frequency of the anti-stokes component of the Raman spec-
trum are determined by the two methods mentioned above.
The Matlab code snippet for steps 1-2 is shown below:
x= Vmin:delta_V(j):Vmax;
y1 = trapmf(x,[410 430 430 450]);
y2 = trapmf(x,[400 450 650 800]);
y3 = trapmf(x,[400 450 650 800]);
y_4 = trapmf(x,[523 523 541 541]);
y4=(y_4*(-1)+abs(max(y_4)));
y6 = trapmf(x,[400 424 662 700]);
for k = 1:100;
K_1_poxubka_Linse = double(rand(1)-0.5)*2*K_1_diviation_Linse;
if K_polinom_linse1 == 1
pRange_1 = polyfit([x(1), x(end)], [0,K_1_poxubka_Linse],
K_polinom_linse1); % Random line
elseif K_polinom_linse1 == 2
pRange_1 = polyfit([x(1), x(round(length(x)/2)), x(end)],
[0,K_1_poxubka_Linse, 0], K_polinom_linse1);
end
yRange_1 = polyval(pRange_1,x);
yRandom = K_1_poxubka_Linse_random*(rand(size(yRange_1))-0.5)*2; %
Random
yLinse_1 = y2+yRange_1+yRandom; % summary Random
K_2_poxubka_Linse = double(rand(1)-0.5)*2*K_2_diviation_Linse;
if K_polinom_linse2 == 1
pRange_2 = polyfit([x(1), x(end)], [0,K_2_poxubka_Linse],
K_polinom_linse2);
elseif K_polinom_linse2 == 2
pRange_2 = polyfit([x(1), x(round(length(x)/2)), x(end)],
[0,K_2_poxubka_Linse, 0], K_polinom_linse2);
end
yRange_2 = polyval(pRange_2,x);
yRandom = K_2_poxubka_Linse_random*(rand(size(yRange_2))-0.5)*2;
yLinse_2 = y3+yRange_2 +yRandom; % summary Random
K_1_poxubka_NF = double(rand(1)-0.5)*2*K_1_diviation_NF;
if K_polinom_NF == 1
pRange_3 = polyfit([x(1), x(end)], [0,K_1_poxubka_NF], K_polinom_NF);
elseif K_polinom_NF == 2
pRange_3 = polyfit([x(1), x(round(length(x)/2)), x(end)],
[0,K_1_poxubka_NF, 0], K_polinom_NF); % Random line
end
yRange_3 = polyval(pRange_3,x);
yRandom = K_1_poxubka_NF_random*(rand(size(yRange_3))-0.5)*2; %
Random
yNF = (yRange_1+y4+yRandom); % summary Random
K_poxubka_Lambda = double(rand(1)-0.5)*2*K_2_diviation_Lambda;
if K_polinom_Lambda == 1
pRange_5 = polyfit([x(1), x(end)], [0,K_poxubka_Lambda],
K_polinom_Lambda); % Random line
elseif K_polinom_Lambda == 2
pRange_5 = polyfit([x(1), x(round(length(x)/2)), x(end)],
[0,K_poxubka_Lambda, 0], K_polinom_Lambda);
end
yRange_5 = polyval(pRange_5,x);
yRandom = K_poxubka_Lambda_random*(rand(size(yRange_5))-0.5)*2; %
Random
yLambda = y6 +yRange_5+yRandom; % summary Random
y = (y1.* yLinse_1.* yLinse_2.* yNF.*yLambda);
GC_x(k) = sum(x.*y)/sum(y);
GC_y(k) = sum(x.*y)/sum(x);
[M_y(k),indMax]=max(y);% maximum stocks
SquareY = cumsum(y);
indexSqR_1 = length(y(SquareY <= sum(y)/2));% index of half square ratio
indexSqR_2 = indexSqR_1 +1;
x_1 = x(indexSqR_1);
x_2 = x(indexSqR_2);
y_1 = SquareY(indexSqR_1);
y_2 = SquareY(indexSqR_2);
SqR_y(k) = sum(y)/2;
SqR_x(k) = x_1 + (SqR_y(k)-y_1)/(y_2-y_1)*(x_2-x_1);
M_x(k)=x(indMax);
end
4 Experiment
Figure 1 shows the structure of the secondary circuit of the optical circuit of a temper-
ature measuring instrument with a notch filter.
Iin (v) Iout(v)
HRF (v)
Fig. 1. The structure of the secondary circuit of the optical circuit of the tempera-
ture measuring instrument with a notch filter
The function of converting the secondary circle of the optical circuit is described by
the expression:
I out (v) I in (v) H RF (v)
2
(1)
Figures 2 show the dependences of the relative root mean square deviation of the
equivalent frequency value of the anti-Stokes component of the Raman spectrum for
the corresponding rectangular, trapezoidal, triangular and saw tooth models of the
Raman spectra at linear, nonlinear and total error of the error the ability of the analyz-
er at frequency 1 and 10 cm-1.
uν· 0.03
δσ, Сenter of mass method Median method
%
%
0.025
0.02
0.015
0.01
0.005
0
Fig. 2. Dependences of the relative root mean square deviation of the equivalent
frequency value of the anti-Stokes component of the Raman spectrum for different
spectral models and the linear error component of the conversion function of the opti-
cal circuit elements at 1 cm-1 resolution
The study was performed under the following parameters: frequency band of the
filter filter from 1890 to 1869 cm-1, laser wavelength 532 nm. The linear, nonlinear
components of the error model of the optical element conversion function is 2%.
δσ, 0.025 Сenter of mass method Median method
%
0.02
0.015
0.01
0.005
0
Fig. 3. Dependences of the relative standard deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum for different spectral
models and the linear error component of the conversion function of the elements of
the optical scheme at a resolution of 10 cm-1
δσ,0.025 Сenter of mass method Median method
%
0.02
0.015
0.01
0.005
0
Fig. 4. Dependences of the relative root mean square deviation of the equivalent frequency value of
anti-Stokes component of the Raman spectrum for different spectral models and nonlinear compo-
nent of the error of the conversion function of the elements of optical scheme at resolution of 1 cm-1
δσ,0.03
% Сenter of mass method Median method
0.025
0.02
0.015
0.01
0.005
0
Fig. 5. Dependencies of the relative root mean square deviation of the equivalent frequency val-
ue of the anti-Stokes component of the Raman spectrum for different spectral models and the nonlin-
ear component of the error of the optical circuit conversion function at a resolution of 10 cm-1
δσ,0.05 Сenter of mass method Median method
%
0.04
0.03
0.02
0.01
0
Fig. 6. Dependences of the relative root mean square deviation of the equivalent frequency value of
the anti-Stokes component of the Raman spectrum for different spectral models and the total error of
the conversion function of the elements of the optical scheme at a resolution of 1 cm-1
Studies have shown that for a rectangular model of the Raman spectrum under the
influence of a linear component of the error of the relative standard deviation of the
determination of the equivalent frequency of the anti-stokes component of the spec-
trum of Raman by the center of mass for the resolution of the spectrometer 1 cm-1 the
relative rms of the spectrum % (Figure 2), when exposed to a nonlinear asymmetric
component of error 0.0164% (Figure 4), and the total level of accuracy - 0.0168%
(Figure 6).
δσ, 0.05
Сenter of mass method Median method
%
0.04
0.03
0.02
0.01
0
Fig. 7. Dependences of the relative root mean square deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum for different spectral models and
the total error of the optical circuit conversion function at a resolution of 10 cm-1
For the linear component of error, it is 0.0024% (Figure 2), for the nonlinear compo-
nent of error - 0.0025% (Figure 4), and for the total error - 0.0049% (Figure 6).
Figure 8 shows the structure of the secondary circuit of the optical circuit of the
flame temperature measuring device.
Iin Iout
HMi(v) HL1(v) HL2(v)
Fig. 8. Structure of the secondary circuit of the optical circuit of the flame temperature measur-
ing device
The function of transformation of the secondary circle of the optical circuit (Figure 8)
is described by the expression:
I out (v) I in (v) H L1 (v) H L 2 (v) H Mi (v)
2 2 2
(2)
δσ,
0.09 Сenter of mass method Median method
%
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0
Fig. 9. Dependences of the relative standard deviation of the equivalent frequency value of the
anti-Stokes component of the Raman spectrum for different spectral models and the total error
of the conversion function of the elements of the optical scheme at a resolution of 1 cm-1
δσ, 0.1 Сenter of mass method Median method
%
0.08
0.06
0.04
0.02
0
Fig. 10. Dependences of the relative root mean square deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum for different spectral models and
the total error of the optical circuit conversion function at a resolution of 10 cm-1
Figures 9 - 10 show the dependences of the relative root mean square deviation of the
equivalent frequency of the anti-Stokes component of the Raman spectrum for the
corresponding, rectangular, trapezoidal, triangular and saw tooth models of Raman
spectra at the total error of the transform function of the optical function.
Figure 11 shows the structure of the secondary circuit of the optical circuit of the
temperature measuring tool using a prism and narrow band filter.
Iin Iout
HL2(v) HNF(v) HP(v) HPL(v) HL1(v)
Fig. 11. Structure of the secondary circuit of the optical circuit of the temperature
measuring tool using a prism and narrow band filter
The function of converting the secondary circle of the optical circuit (Figure 11) is
described by the expression:
I out (v) I in (v) H L1 (v) H L 2 (v) H P (v) H NF (v) H PL (v)
2 2 2 2 2
(3)
δσ,
% Сenter of mass method Median method
Fig. 12. Dependences of the relative root mean square deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum for different spectral models and
the total error of the optical circuit conversion function at a resolution of 1 cm-1
Figures 12 -13 show the dependences of the relative root mean square deviation of
the equivalent frequency value of the anti-Stokes component of the spectrum for the
corresponding rectangular, trapezoidal, triangular and saw-like models of Raman
spectra at the total error of the conversion function of the optical circuit elements.
δσ,
% Сenter of mass method Median method
Fig. 13. Dependences of the relative root mean square deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum for different spectral models and
the total error of the optical circuit conversion function at a resolution of 10 cm-1
The study was performed under the following parameters: frequency band of the
harvesting lens from 1428 to 2500 cm-1, frequency band of the filter filter from 1890
to 1869 cm-1, step by frequency 1 and 10 cm-1.
Figure 14 shows the structure of the secondary circle of the optical circuit for tem-
perature measurement using a microscope and aperture.
Іin Іout
H P1(v) H P2(v) HNF(v)
Fig. 14. Structure of the secondary circuit of the optical circuit of the temperature measuring
tool using a microscope and aperture
The function of transformation of the secondary circle of the optical circuit (fig-
ure 14) is described by the expression:
I out (v) I in (v) H P1 (v) H P 2 (v) H NF (v)
2 2 2
(4)
Figures 15-16 show the dependences of the relative root mean square deviation of
the equivalent frequency value of the antistatic component of the spectrum for the
corresponding rectangular, trapezoidal, triangular and saw tooth models of Raman
spectra at the total error of the conversion function of the element of the transfor-
mation function. The pre-survey was performed under the following parameters: fre-
quency band of the filter filter from 1890 1869 cm-1, step at frequency 1 and 10 cm-1.
δσ,
% Сenter of mass method Median method
Fig. 15. Dependences of the relative standard deviation of the equivalent frequency value
of the anti-Stokes component of the Raman spectrum for different spectral models and the total
-1
error of the conversion function of elements of optical scheme at resolution of 1 cm
δσ,
% Сenter of mass method Median method
Fig. 16. Dependences of the relative root mean square deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum for different spectral models and
the total error of the optical circuit conversion function at a resolution of 10 cm-1
A block diagram of a temperature measuring instrument with a notch filter and a
polarizer is shown in figure 17.
Iin Iout
HL2(v) HNF(v) HPL(v) HL1(v)
Fig. 17. Structural optical diagram of a temperature measuring instrument with a notch filter
and a polarizer
The secondary circuit conversion function of the optical circuit is of the form:
I out (v) I in (v) H L1 (v) H LP2 (v) H NF (v) H PL (v)
2 2 2 2
(5)
Figures 18-19 presents the dependences of the relative root mean square deviation
of the value of the equivalent frequency of the anti-Stokes component of the spectrum
for the corresponding rectangular, trapezoidal, triangular and saw tooth models of the
Raman spectra of the combined error of the transform element.
δσ,
% Сenter of mass method Median method
Fig. 18. Dependences of the relative root mean square deviation of the equivalent frequen-
cy value of the anti-Stokes component of the Raman spectrum for different spectral models and
-1
the total error of the conversion function of the optical circuit elements at a resolution of 1 cm
δσ,
Сenter of mass method Median method
%
Fig. 19. Dependences of the relative root mean square deviation of the equivalent frequen-
cy value of the anti-Stokes component of the Raman spectrum for different spectral models and
-1
the total error of the optical circuit conversion function at a resolution of 10 cm
The study was performed under the following parameters: frequency band of the
harvesting lens from 1428 to 2500 cm-1, frequency band of the filter filter from 1890
1869 cm-1, polarizer with coordinates 1428, 1620, 2237, 2500 cm-1, step in frequency
1 and 10 cm -1.
5 Conclusions
Studies have shown that under the influence of the model total error of the function of
conversion of optical elements for all optical circuits, the studied models of the Ra-
man spectra, taking into account the minimum dependence of the relative standard
deviation of the equivalent frequency of the anti-stokes component of the spectrum of
Raman provides the center of mass. Figure 19 presents the results of the study of the
dependence of the relative standard deviation of the equivalent frequency of the anti-
Stokes component of the Raman spectrum on the frequency resolution of the spec-
trum analyzer, taking into account the total error of the elements of the optical circuit,
which is 2%. The limit value of the error of temperature measurement by means based
on the effect of CRC takes the following form:
T m pc sc sa 0,04 0,00008 0,02 0,09 0,15% (6)
δσ,
%
Δv, cm-1
Fig. 20. Dependences of the relative root mean square deviation of the equivalent frequency
value of the anti-Stokes component of the Raman spectrum on the resolution of the frequency
of the analyzer when exposed to a total error
The obtained research results (figure 19) showed that there is a certain value of the
resolution of the spectrum analyzer at a frequency whose decrease practically does
not reduce the dependence of the relative mean-square deviation of the value of the
equivalent frequency of the anti-Stokes component of the Raman spectrum. For ex-
ample, for a resolution of less than 1 cm-1, the dependence of the relative standard
deviation of the equivalent frequency of the anti-Stokes component of the Raman
spectrum is practically unchanged and is approximately 0.00083% for the center of
mass method and 0.00126% for the median method of determination the equivalent
frequency of the anti-Stokes component of the Raman spectrum.
The results obtained (Figure 19) allow for the required relative root-mean-square
deviation of the equivalent frequency of the anti-stokes component of the Raman
spectrum to impose requirements on the metrological and technical characteristics of
the analyzer or to estimate the relative relative error of determining the equivalent
frequency of the anticancer spectrum - nightly characteristics of the analyzer.
The work was implemented during the implementation of an economic agreement
for Spheros-Elektron, Lviv, as an element of the Industrial Internet of Things in In-
dustry 4.0. Consequently, studies have shown that the center of mass method is opti-
mal for determining the equivalent frequency of the anti-Stokes component of the
Raman spectrum. Its use ensures a minimum confidence relative error in the determi-
nation of the equivalent frequency of the anti-Stokes component of the Raman spec-
trum compared to other methods. The dependence of the value of the equivalent fre-
quency of the anti-Stokes component of the Raman spectrum on the laser radiation
intensity is investigated and it is found that the change in the intensity of the laser
beam does not affect the error in determining the equivalent frequency of the anti-
stokes component of the Raman spectrum. The dependence of the relative root mean
square deviation of the value of the equivalent frequency of the anti-Stokes compo-
nent of the Raman spectrum on the frequency resolution of the spectrum analyzer is
investigated. There is a certain value of the resolution of the spectrum analyzer, in
which the value of the relative root mean square deviation of the equivalent frequency
of the anti-Stokes component of the Raman spectrum is practically not reduced. This
allows you to select a spectra analyzer with optimum characteristics for a temperature
measurement tool that is built on the effect of Raman.
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