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                                                            I. Shardakov et alii, Frattura ed Integrità Strutturale, 62 (2022) 561-572; DOI: 10.3221/IGF-ESIS.62.38 
 

561 
 

 

 
 
 
  
Estimation of nonlinear dependence of fiber Bragg grating readings 
on temperature and strain using experimental data 
 
 
I. Shardakov, A. Shestakov, I. Glot, V. Epin, G. Gusev, R. Tsvetkov  
Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Science, 1, Korolev street, Perm, Russia  
shardakov@icmm.ru, https://orcid.org/0000-0001-8673-642X 
shap@icmm.ru, https://orcid.org/0000-0003-3387-7442 
glot@icmm.ru, https://orcid.org/0000-0002-2842-7511 
epin.v@icmm.ru, https://orcid.org/0000-0001-5625-2678 
gusev.g@icmm.ru, https://orcid.org/0000-0002-9072-0030 
flower@icmm.ru, https://orcid.org/0000-0001-9617-407X 
 
 
ABSTRACT. The readings of the Bragg grating are determined based on the 
optical radiation reflected from it. A quantitative characteristic of this 
radiation is the wavelength at which the maximum power of the optical signal 
is achieved. This characteristic is called the central wavelength of the grating. 
The central wavelength shift depends on temperature and strain. As a rule, a 
linear approximation of this dependence is used. However, from the available 
literature it is known that, the grating wavelength shift demonstrates a strong 
nonlinear dependence on temperature at 5<T<200K and a weak quadratic 
dependence close to room temperature. Thus far, the authors have not found 
studies that consider all terms in the quadratic expansion of the central 
wavelength of the Bragg grating as a function of temperature and strain at 
near-room temperatures. Our work is intended to fill this gap. The article 
describes an experiment in which an optical fiber with Bragg grating was 
subjected to loading using three different weights. A step-wise temperature 
change from 5 to 100 0С was realized for each weight. Based on these data, all 
terms of the quadratic expansion of the desired function are determined. The 
contribution of each term is estimated. 
  
KEYWORDS. Fiber Bragg grating; Sensor calibration; Temperature 
compensation; Quadratic approximation. 
 

 

 
 

Citation: Shardakov, I., Shestakov, A., Glot, 
I., Epin, V., Gusev, G., Tsvetkov, R.., 
Estimation of the nonlinear dependence of 
the indications of a fiber Bragg grating on 
temperature and strain from experimental 
data, Frattura ed Integrità Strutturale, 62 
(2022) 561-572. 
 
Received: 02.07.2022 
Accepted: 09.09.2022 
Online first: 13.09.2022 
Published: 01.10.2022 
 
Copyright: © 2022 This is an open access 
article under the terms of the CC-BY 4.0, 
which permits unrestricted use, distribution, 
and reproduction in any medium, provided 
the original author and source are credited. 

 

 
INTRODUCTION 
 

he fiber Bragg gratings are used as optical temperature and strain sensors. Optical sensors have a number of 
advantages over traditional measuring facility: optical sensors are not sensitive to electromagnetic interference, can 
be easily create long measuring lines, allow switching of many sensors on one measuring line, have very small size 

and weight, have low heat capacity, the optical line has a low thermal conductivity, line and sensor demonstrate high 
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I. Shardakov et alii, Frattura ed Integrità Strutturale, 62 (2022) 561-572; DOI: 10.3221/IGF-ESIS.62.38                                                                             
 

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explosion resistance. Due to these advantages, optical sensors have found wide application in the monitoring of buildings, 
bridges, pipelines, mines and tunnels due to their great length. Fiber optic sensors are widely used for monitoring 
composite materials, as they can be embedded in the material without weakening its strength characteristics due to small 
sizes of sensors and measuring line. A variety of sensing devices such as the displacement, strain, pressure, acceleration 
and temperature sensors are created based on the fiber Bragg gratings. The fields of application of fiber Bragg sensors are 
described in [1, 2]. 
The readings of the Bragg grating sensor are calculated based on the shift of the central wavelength of the grating. This 
index depends on temperature and strain. Generally, it is not known, which of these factors causes the wavelength shift so 
there is a measurement uncertainty. As a rule, temperature measurements are conducted at a free state of the fiber within 
the grating area, when it is not subjected to external loads. In this case, the strain is known and is expressed in terms of 
temperature. For strain measurements different methods are used [3]. The simplest and most reliable method is to use two 
gratings: one grating is attached to the test object and the second grating is freely located near the first one [4]. In this case, 
temperature sensing is provided by the second grating. Knowing the temperature and wavelength shift of the first grating 
it is possible to evaluate its strain. One further implementation of this approach is based on the method, in which a Bragg 
grating designed to determine temperature is attached to a metal plate with a known coefficient of thermal expansion. 
Another method that implements the use of two gratings is that the gratings are fixed in the stretched and compressed 
zones of the sensor, in this case the difference in wave shifts does not depend on temperature [5,6]. There are also many 
techniques that do not require maintaining a special mechanical state of one of the gratings [7-13]. These methods use not 
only a shift of the grating spectrum, but also a change in the shape of this spectrum or changes in the amplitudes of parts 
of the spectrum. 
The individual calibration of grating can be reasonably done in the following cases: temperature compensation is 
performed based on the temperature measured by any means; sensor design is supposed to maintain a free state of the 
fiber in the Bragg grating area; sensor design does not allow individual calibration of the sensor assembly. This is 
especially true for high-precision strain gauges, the design of which involves fiber attachment by soldering or welding the 
metal-coated fiber [3]. In this case, long-term stability of measurements is achieved. 
As a rule, the calibration of Bragg grating sensors is carried out in the framework of a linear approximation [3, 5-15]. 
Although there has been experimental evidence that the temperature dependence of a shift of the central wavelength of 
the grating has a strongly nonlinear character at 5<T<200 K [1,16,17]. There are also studies, which have established a 
reliably measured quadratic dependence of the grating wavelength shift on temperature at -30<T<80 0C [18,19]. In [18], 
an explanation of the temperature dependent non-linear behavior of the fiber Bragg grating is given based on the Ghosh 
model, which relates the non-linear behavior of the refractive index of quartz glass to temperature. Note that in addition 
to nonlinearity associated with temperature, there is nonlinearity due to deformation. This is shown in [18]. The authors of 
this work conducted an experiment, in which the fiber was subjected to loading at constant temperature and plotted 
graphs of the error of a linear approximation of the dependence of the wavelength shift on strain. As is evident from this 
graph, there is a weak negative quadratic dependence. However, they did not quantify this relationship. Thus, for near-
room temperatures the present-day literature provides comprehensive information on the linear terms of the expansion of 
the grating wavelength shift ∆λ as the function of strain С1·ε and temperature С2·∆T, there are estimates for the quadratic 
expansion term С4·∆T2. However, we have not found any information on the consideration of quadratic С3·ε2 and cross 
С1·ε·∆T terms of the expansion. Our paper is intended to fill this gap. 
The paper is structured as follows. Section 1 describes the principle of operation of the fiber Bragg grating and provides 
substantiation of parameters used to make calibration. Section 2 describes the experimental setup. The experimental 
results and the data processing algorithm are discussed in Section 3. The parameters of the full quadratic approximation 
are determined in Section 4. The last Section summarizes the results obtained.  
 
 
THE WORKING PRINCIPLE OF THE FIBER BRAGG GRATING 
 

he Bragg grating is a region of an optical fiber, in which the refractive index periodically changes. The period of 
this structure is called the period of the Bragg grating. A structural diagram of the grating is shown in Fig. 1. The 
fiber area with applied grating reflects a narrow part of the optical radiation spectrum, which is determined by the 

grating period, the stress-strain state of the fiber in the grating area, and temperature. The measurement process involves 
the generation of a broadband optical signal and the registration of the reflected spectrum. 
 

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Figure 1: Structural diagram of the Bragg grating in an optical fiber. 
 
The sensor indications are determined by the shift of the spectrum of the reflected optical signal. Two spectra of the 
optical signal are shown in Fig. 2. Spectrum 1 corresponds to the grating in the initial state, spectrum 2 - to the deformed 
state. The spectra are characterized by their central wavelengths λ1 and λ2. The shift of the spectrum is quantified by the 
change in the central wavelength ∆λ= λ2- λ1. 
 

 
 

Figure 2: Spectra of optical signals (spectrum 1 - grating in the initial state, spectrum 2 - grating in the deformed state) 
 
The central wavelength of the grating is determined by the expression 
 

      2 , ln T Lε           (1) 
 
where: n(T, ε) is the refractive index of quartz in the grating area; T is temperature; ε is the strain tensor of the fiber in the 
grating area; L is the grating period; εl is the total strain along the fiber. Let us define the reference state of the grating, 
which is characterized by zero strains, the reference state temperature T0, and the grating period in the reference state L0. 
The wavelength in the reference state is defined by 
 

       0 0 0 0 02 , 2n T L n L0          (2) 
 
where: n0 is the refractive index in the reference state. The current value of the refractive index represented in increments 
relative to the reference state is written as 
 

           0 0 0, , ,n T n T n T T n nε 0 ε        (3) 
 
where: ∆n – is the increment of the refractive index. The grating period in the actual (deformed) state is determined by the 
expression 
 

      0 1l lL L           (4) 
 
The wave length in the actual state (1), according to expressions (3) and (4) takes the following form  
 



 

I. Shardakov et alii, Frattura ed Integrità Strutturale, 62 (2022) 561-572; DOI: 10.3221/IGF-ESIS.62.38                                                                             
 

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          0 02 1 ln n L          (5) 
 
After opening the brackets we get 
 

              0 0 0 0 02 2 2 1l ln L n L n L        (6) 
 
The multiplication of the numerator and denominator of the summand at ∆n by n0 yields 
 

                0 0 0 0 0 0
0

2 2 2 1l l
n

n L n L n L
n

      (7) 

 
The underlined expressions according to (2) are the central wavelengths of the grating in the reference state 
 

             0 0 0
0

1l l
n

n
        (8) 

 
Using simple arithmetic operations, expression (8) is transformed to  
 

    

 

   0
0 0

1l l
n

n
         (9) 

 
The resulting expression determines the relative change in the wavelength. From this expression we can draw an 
important conclusion that the relative change in the wavelength is independent of the grating period in the reference 
configuration L0. The refractive index increment depends on the strain and temperature ∆n=∆n(T-T0,ε), so that 
 

 
 

    


 
     00 0 0

0 0

,
1 , ,l l

n T T
f T T n

n

ε
ε       (10) 

 
The expression f(T-T0,ε,n0) depends on the temperature, strain and refractive index of the optical fiber in the reference 
configuration n0=n(T0,0). Under the same conditions of determining the reference configuration ε=0 and T=T0, for the 
same type of optical fiber and the same technology of applying the grating on the fiber, the quantity n0 will be a constant. 
It follows from the above that 
 

  



 0 0
0

,f T T ε           (11) 

 
Under the described conditions, dependence (11) will be valid for gratings with different periods. In the case when the 
side surface of the fiber in the region of the Bragg grating is free (not stressed), the radial and circumferential 
deformations of the fiber depend only on temperature and deformation along the fiber. Under these conditions, the 
remaining components of the strain tensor ε are equal to zero. Therefore, (11) takes the form 
 

   



 0 0
0

, lf T T           (12) 

 
In the quadratic approximation function f(T-T0,εl) is written as 
 

                      220 1 2 0 3 4 0 5 0( , )l l l lf T T C C T T C C T T C T T    (13) 
 
In what follows, we will describe the experiments that allow us to determine the parameters of this expansion. 



 

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DESCRIPTION OF EXPERIMENTAL SETUP 
 

he photograph of the experimental setup is shown in Fig.3 It consists of a glass cylindrical vessel 1, on which a 
nichrome wire 6 is evenly wound to provide its heating and maintain the prescribed temperature. Air inside the 
vessel is stirred to ensure the uniform temperature distribution. In the process of stirring, the air is drawn in by the 

turbine 3 in the lower part of the vessel, and then it moves through the aluminum tube 7 into the chamber in the upper 
part of the vessel 8. After that, the air returns to the working area of the vessel through the perforated plate. From above 
the vessel is plugged with seal 9, which does not allow the air from the environment to get into the vessel. From below it 
is protected by insulating pad 2 to reduce a heat flux through the bottom. Inside the vessel there is an optical fiber with a 
Bragg grating 11. Fiber is loaded with a set of weights 4. Attachment to the fiber is by means of grip 5. Through the 
distributing plate 13 the fiber is clamped between rubber pads 14. Compressive force is produced by elastic clamp 12. To 
reduce the compressive force in the clamp 12 to a level that ensures no damage to the fiber, a ring element is provided in 
the grip 5. This reduction in clamping force is achieved due to the frictional forces generated by winding the fiber around 
the annular part. Changing the amount of winding makes it easy to adjust the axial force in the fiber with a constant 
compressive force in the clamp12. The temperature sensor 10 is brought to the fiber in the region of the Bragg grating 11 
at a distance of 1-2 mm. To minimize the influence of the environment, during the experiment the vessel is placed inside a 
cube made of 50 mm thick foam plastic. 
 

 
 

Figure 3: Experimental setup. 
 
Power supply to the heating wire is regulated with a microcontroller and an external circuit on a field-effect transistor. The 
microcontroller is controlled by a computer, which measures temperature. A special computer program was developed to 
implement the PID regulation algorithm, which maintains the prescribed temperature inside the vessel and operates the 
step-wise temperature loading. 
The generation of a broadband optical signal and recording of the spectra reflected from the Bragg grating were 
accomplished using the ASTRO A322 interrogator manufactured by FiberSensing. The Bragg grating is fabricated in a 
single-mode fiber of the SM1500(9-125)P series. The initial grating wavelength is 1525 nm Temperature registration is 
performed using the B57861-S 103-F40 thermistor manufactured by EPCOS. The thermistor resistance is measured with 
a 24-bit Leonardo 2 ADC and a GSPF-052 generator manufactured by Rudnev-Shilyaev producer. Synchronization of 

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temperature measurements and spectra of the Bragg grating is provided automatically using a specially developed program 
in the Delphi language. The temperature sensor is calibrated with TL-4 mercury thermometers, which have two 
temperature scales of 0-50 and 50-100 0С. The division value of thermometers and, as a result, the calibration accuracy is 
0.1 degrees. 
 
 
EXPERIMENT PROCEDURE AND DATA PROCESSING 
 

he experiment includes two operations: hanging of weights an optical fiber and setting temperature from 5 to 100 
0С with an increment of 5 0С. The temperature in the thermal chamber is set in steps with an exposure time of 15 
minutes per step. In the area of the Bragg grating, the insulation was removed from the fiber to eliminate the 

influence of the polymer shell. The weight sets the elastic deformation ε0 in the grating region, which does not change 
with temperature. We performed a set of experiments with three different weights (m1=29.040g, m2=109.975g, 
m3=216.431g), which allowed us to determine all parameters of the quadratic approximation. The strains ε0, corresponding 
to these weights were 321με, 1216με, 2395με, respectively. 
Evolution of the temperature and the corresponding change in the central wavelength of the grating at several stages of 
temperature loading are shown in Fig. 4. 
 

 
 

Figure 4: Evolution of temperature (a) and Bragg grating wavelength (b) as a function of time. 
 
At each step, the readings were averaged over two minutes. The averaged values were used to plot the grating wavelength 
versus temperature (Fig. 5) at different initial strains ε0. 
 

 
 

Figure 5: Dependence of the grating wavelength on temperature at different initial strains ε0. 
 
Quite often, the central wavelength of the Bragg grating is determined from the maximum of the spectrum. However, this 
approach does not provide stable results. This is illustrated by the spectrum graphs (Fig. 6a) obtained from 4 consecutive 
measurements at constant temperature and strain. It can be seen from these plots that the wavelength at which the 
maximum value is reached may differ from one measurement to the next. To overcome this difficulty, an algorithm is 
proposed that determines the value of the central wavelength as the wavelength corresponding to the centre of mass of a 
figure bounded by points A, B, C (fig.6b). Point B corresponds to the maximum of the spectrum, and points A and C are 
closest to B, where  value 20 dB below the maximum is achieved. 

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Figure 6: The shapes of the spectral maxima for four consecutive measurements at constant temperature and deformation (a), the 
search algorithm for the central wavelength of the Bragg grating (b). 
 
The developed algorithm can significantly reduce the processed data scattering and increase the sensitivity of the 
measuring system. This is clearly seen in Fig. 7, which shows the evolution of the central wavelengths determined by 
means of direct registration of the spectrum maximum (Fig. 7a) and calculation of the centre of mass (Fig. 7b). According 
to these graphs, the developed algorithm reduces the scatter of the processed data by a factor of 10. It should be noted 
that the developed algorithm and time averaging over an interval of 1 minute (60 measurements) allowed us to obtain the 
wavelength sensitivity of ≈0.1pm. 
 

 
 

Figure 7: Wavelengths calculated with the use of the algorithms based on spectrum maximum (a) and centre of mass (b). 
 
 
DETERMINATION OF PARAMETERS OF QUADRATIC APPROXIMATION 
 

he approximation of the function describing the relative wavelength change is expressed as follows 
 

              2 21 2 3 4 5( , )f T C C T C C T C T      (14) 
 
where ∆T=T-T0. Here, unlike Eqn. (13), the lower index of ε is omitted. The longitudinal strain ε of a fiber stretched by 
applying a weight of mass m under conditions of variable temperature is given as  
 

    0 T            (15) 
 
where: ε0 is the strain of the fiber due to the applied weight; α – is the coefficient of linear expansion of quartz equal to 
0.54·10-6 1/0С. The deformation ε0 is determined using the expressions  
 

 
 

 
  

2

0 , ,
4

l
l

m g D
S

E S
         (16) 

 

T 



 

I. Shardakov et alii, Frattura ed Integrità Strutturale, 62 (2022) 561-572; DOI: 10.3221/IGF-ESIS.62.38                                                                             
 

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where: σl is the stress along the fiber; E is Young's module of quartz equal to 72.3·109 Pa; m is the mass of the weight; g is 
the acceleration of gravity equal to 9.81 m/s2; D is the diameter of the fiber equaling to 125 μm; S is the fiber cross-
sectional area.  
Based on the results of experiments, three tabular dependencies were obtained  
 

  ,j ji iT            (17) 
 
where: j determines the belonging to the corresponding weight and varies from 1 to 3; i indicates the belonging to a given 
temperature and varies from 1 to 20. Using expression (15), we can calculate the strains corresponding to weights j and 
temperatures i. 
 

    0
j j j

i iT           (18) 
 
Using the least squares method, we perform series expansion of the dependence of the central wavelength on deformation 
and temperature. 
 

                2 20 1 2 3 4 5( , )T q q q T q q T q T      (19) 
 
To this end we introduce the following row vectors 
 

     

     



   
        

   

1 1 2 2 3 3
1 1 1

1 1 2 2 3 3
1 1 1

1 1 2 2 3 3
1 1 1

[1 ... 1]

... ... ...

... ... ...

... ... ...

N N N

N N N

N N N

T T T T T T

1

ε

ΔT

λ

     (20) 

 
where 1 is the unit row vector of size 3·N; N is the number of points of temperature loading, which is equal to 20. The 
introduced vectors are used to generate a matrix of the following form 
 

 
 
 
 

  
 
 
 
  





1

ε

ΔT
M

ε ε

ΔT ΔT

ε ΔT

          (21) 

 
where: ° is the component product. According to least squares method, the system of linear algebraic equations with 
respect to the approximation parameters of expression (19) is represented as 
 

      T TM M q M λ           (22) 
 
where: · is the scalar product; T is the transposition operator; q is the column vector of the approximation parameters. The 
approximation parameter q1 is equal to the central wavelength of the grating in the reference configuration (∆T=0,ε=0) 
 

 0 0q             (23) 
 
To calculate the relative change in the wavelength using expression (19), we must subtract λ0 from it and divide it by λ0.  
 



 

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  
  


  

           2 20 0 0 3 4 51 2
0 0 0 0 0 0 0

( , )T q q q q qq q
T T T

q q q q q q
    (24) 

 
Comparing expressions (14) and (24) we obtain the coefficients of required expansion (14) 
 

    3 4 51 21 2 3 4 5
0 0 0 0 0

, , , ,
q q qq q

C C C C C
q q q q q

       (25) 

 
They have the following values: 

           6 9 51 2 3 4 50.782, 5.66 10 , 2.49, 7.03 10 , 6.31 10C C C C C     (26) 
 
Let us consider the expansion error (14) with respect to the initial experimental data (17), (18). It is determined by 
expression (27).  
 

 
 




  0
0

( , )
j

j j ji
i i if T          (27) 

 
Graphs of the approximation error (27) are shown in Fig. 8. These graphs correspond to three weights j=1,2,3, which set 
the initial deformation ε0= 321με, 1216με, 2395με. 
 

 
 

Figure 8:Approximation error for three levels of initial strain and temperature variations from 5 to 100 0С 
 
The graph shows that for strains changing from 0 to 2400με and temperature changing from 5 to 100 0С the maximum 
error of approximation of the relative wavelength is δmax= ±2·10-6. This value corresponds to the error of strain of 
≈±2.5με. Four fragments in Fig. 9 show how the approximation error changes depending on temperature and 
deformation when various terms are excluded from the expression (14). These graphs clearly demonstrate the 
contribution of each non-linear term. Fig. 9a shows the error, which occurs when the term С3·ε2 (С3=0) is excluded from 
the expansion. In this case, the maximum error value was δmax= -18·10-6. Figs. 9b and 9c show the graphs of 
approximation error due to removal of terms С4·∆T2 and С5·∆T·ε, and Fig. 9d corresponds to the situation when all non-
linear terms С3·ε2, С4·∆T2, С5·∆T·ε are excluded. Based on these graphs, the following conclusions can be drawn. The 
largest approximation error occurs due to removal of the non-linear term С4·∆T2 (Fig. 9b). The maximum error value in 
this case is equal to δmax= 46·10-6. Nonlinear terms enter the expansion with different signs and partially compensate each 
other. Compared to the approximation error (Fig. 8), the contribution of the non-linear terms shown in Fig. 9 is 
substantial. 
The contribution of each term of expansion (14) at temperature ∆T=100 0C and strain ε=2500με is evaluated as 
 

       61955 566 15 70 15 10          (28) 
 



 

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The contributions of the summands with respect to the first term of the expansion are expressed in percentages as (29). 
The parentheses indicate the belonging to the corresponding term of the expansion. 
 

     2 2( ) ( ) ( ) ( ) ( )100% ,  29% ,  0.8% ,  3.6% ,  0.8%T T T      (29) 

 
 

Figure 9: Graphs of approximation errors for three strain levels at different numbers of expansion terms 
 
 
CONCLUSIONS 
 

everal important conclusions follow from the analysis of the obtained ratio 14. 
When using sensors based on the Bragg grating to measure strain, it is necessary to take into account not only the 
accuracy of estimating the shift of the grating wavelength, but also the accuracy of temperature measurement. If the 

temperature is measured roughly, and the shift of the grating wavelength is estimated very accurately, then the accuracy of 
determining the deformation will be determined by the accuracy of the temperature measurement. To ensure the strain 
measurement accuracy of ±1με, the temperature measurement accuracy should be no worse than ±0.10С. 
Comparison of the contributions of individual terms given in relation (28) makes it possible to estimate which terms of 
expansion (14) must be taken into account to ensure the required accuracy of the measuring system. So, if the allowable 
error in strain measurement is 5% or more, only linear terms can be taken into account in expansion (14). To ensure the 
accuracy of the measuring system of 1% or better, it is necessary to take into account the quadratic terms of the 
expansion. 
The reliability of the obtained results can be demonstrated by comparing them with the data presented in [16]: 
С1=0.782(0.806), С2=5.66·10-6(5.77·10-6), С4=7.03·10-9(8.02·10-9). Here the values of the coefficients (26) are given, and in 
parentheses are the corresponding values taken from [16]. 
The obtained individual calibration dependence of the Bragg grating in the form of relation (14) makes it possible to 
evaluate how the sensor readings depend on the features of its design. In the process of creating and debugging a Bragg 
grating sensor, it is quite difficult to determine how the sensor readings depend on the method of fiber attachment. 
Having an individual calibration dependence for a particular grating, it is possible to reliably identify the contribution to 
the sensor readings due to fiber attachment, and take appropriate measures to reduce this value. This is especially true 
when creating high-precision measuring systems that provide an accuracy of 0.1% or better. 
The construction of a quadratic approximation for the calibration dependence of the grating requires careful control of 
the parameters of the reference configuration (temperature T0 and external mechanical stresses of the fiber, which must be 

S 



 

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571 
 

zero). To do this, it is proposed to carry out a series of successive loadings of the fiber placed in a thermostat. Loading is 
performed by successive suspension of weights on the fiber, which ensures the straightness of the fiber. Then the 
dependence of the grating wavelength on the load value is constructed. Approximation of this dependence to the zero 
value of the load makes it possible to obtain the value λ0. The calibration dependence obtained in this way is universal 
when using the same reference configuration, the same type of optical fiber, and the same technology for applying the 
grating to the fiber. 
The accuracy of determining the central wavelength with the aid of modern interrogators is 1 pm. This corresponds to a 
strain of ≈0.8με. Therefore, to ensure the full-scale realization of capabilities of modern interrogators, one should use a 
quadratic approximation taking into account all terms of the expansion. 
 
 
ACKNOWLEDGMENTS 
 

he paper was prepared in the framework of the program for the creation and development of the world-class 
scientific center «Supersonic»; for 2020-2025 with the financial support of the Ministry of Education and Science 
of the Russian Federation (Agreement No. 075-15-2020-925 of November 16, 2020 ). 

 
 
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