rus
Issue #3/2021
O. V. Burdysheva, E. S. Sholgin, A. Yu. Maksimov
Optimization of the Design of an Experimental Reflective Element for an Amplitude Fiber-Optic Vibration Sensor of a Reflective Type
Optimization of the Design of an Experimental Reflective Element for an Amplitude Fiber-Optic Vibration Sensor of a Reflective Type
DOI: 10.22184/1993-7296.FRos.2021.15.3.246.260
This work is devoted to the development of a design of a reflective element for an amplitude fiber-optic vibration sensor, as well as testing the performance of such a design. In the presented work, a mathematical model of transverse vibrations is described, which helps to determine the resonance frequencies depending on the length of the free fiber. A reflective surface is implemented, which is a periodic structure of lithium niobate and areas covered with gold. The layout and design of a vibration sensor with the ability to tune the resonance frequency is presented, and an experimental circuit is demonstrated. The signal obtained using the described circuit lends itself to Fourier transform processing, the calculated frequencies coincide with the vibration frequencies of the vibration source. The amplitude-frequency characteristic is obtained, the resonance frequency correlates with the frequencies obtained by the mathematical model (Pearson’s correlation coefficient is 0.977). The results of the implementation of this development are important for a new interdisciplinary direction – agrobiophotonics, provide a key to a more subtle and accurate study of animal vibration sensitivity and plant vibrotropism.
This work is devoted to the development of a design of a reflective element for an amplitude fiber-optic vibration sensor, as well as testing the performance of such a design. In the presented work, a mathematical model of transverse vibrations is described, which helps to determine the resonance frequencies depending on the length of the free fiber. A reflective surface is implemented, which is a periodic structure of lithium niobate and areas covered with gold. The layout and design of a vibration sensor with the ability to tune the resonance frequency is presented, and an experimental circuit is demonstrated. The signal obtained using the described circuit lends itself to Fourier transform processing, the calculated frequencies coincide with the vibration frequencies of the vibration source. The amplitude-frequency characteristic is obtained, the resonance frequency correlates with the frequencies obtained by the mathematical model (Pearson’s correlation coefficient is 0.977). The results of the implementation of this development are important for a new interdisciplinary direction – agrobiophotonics, provide a key to a more subtle and accurate study of animal vibration sensitivity and plant vibrotropism.
Теги: amplitude reflective type sensor fiber-optic sensor sensor vibration vibration monitoring vibration sensor амплитудный датчик отражательного типа вибрация вибромониторинг волоконно-оптический датчик датчик датчик вибрации
Optimization of the Design of an Experimental Reflective Element for an Amplitude Fiber-Optic Vibration Sensor of a Reflective Type
O. V. Burdysheva , E. S. Sholgin , A. Yu. Maksimov
Laboratory of Agrobiophotonics, Perm Federal Research Center, Ural Branch of the Russian Academy of Sciences, Perm, Russia
Institute of Ecology and Genetics of Microorganisms, Perm Federal Research Center, Ural Branch of the Russian Academy of Sciences, Perm, Russia
This work is devoted to the development of a design of a reflective element for an amplitude fiber-optic vibration sensor, as well as testing the performance of such a design. In the presented work, a mathematical model of transverse vibrations is described, which helps to determine the resonance frequencies depending on the length of the free fiber. A reflective surface is implemented, which is a periodic structure of lithium niobate and areas covered with gold. The layout and design of a vibration sensor with the ability to tune the resonance frequency is presented, and an experimental circuit is demonstrated. The signal obtained using the described circuit lends itself to Fourier transform processing, the calculated frequencies coincide with the vibration frequencies of the vibration source. The amplitude-frequency characteristic is obtained, the resonance frequency correlates with the frequencies obtained by the mathematical model (Pearson’s correlation coefficient is 0.977). The results of the implementation of this development are important for a new interdisciplinary direction – agrobiophotonics, provide a key to a more subtle and accurate study of animal vibration sensitivity and plant vibrotropism.
Key words: sensor, fiber-optic sensor, amplitude reflective type sensor, vibration sensor, vibration, vibration monitoring
Received on: 17.04.2021
Accepted on: 10.05.2021
Introduction
The demand for sensors is growing rapidly due to the development of information and measurement systems, automated control systems and production management. In addition to high metrological characteristics, the sensors should have such properties as low weight, small dimensions, low power consumption, and compatibility with microelectronic information processing devices. These requirements are met to the maximum extent by fiber-optic sensors (FOS) [1, 2].
FOSs are often made of materials that are dielectrics, which eliminates the risk of sparks and, as a result of fire, the fiber itself is resistant to corrosion and radiation. Also FOSs have good performance and low cost, can be located at a great distance from the controlled object, it is possible to serially connect many sensitive elements in one line, there are also distributed fiber-optic sensors [1, 3, 4, 5]. Their use is especially interesting in new, interdisciplinary areas: for example, in monitoring the acoustic fields of flora and fauna of various natural locations (in the field of physiology and regulation of plant growth, zoology, agrobiophotonics, aquaculture, productivity of dairy farming, etc.) distributed sensors operating on ultra-weak backscattered signals and requiring complex signal processing are almost not applicable. In such cases, the best practical solutions would be either quasi-distributed sensors or point sensor arrays. Quasi-distributed sensors require a rather serious and expensive hardware base, while simple point FOSs can be the optimal solution.
Thus, it is known that plants are sensitive to vibration of water, soil, insects-pollinators, insects that eat plants and react to these effects by movement, tropisms and the synthesis of protective metabolites [6, 7]. In particular, among root tropisms, the movement of plants in the direction of vibrations generated by flowing water was found, but the sound recording of flowing water did not cause such a reaction, therefore, the plant reacts to low-frequency mechanical vibrations [6, 8]. However, the absence of highly sensitive sensors, the operation of which does not depend on external electric fields and electromagnetic oscillations, sound interference, high humidity and the threat of biodeterioration, limits the development of such studies. The sensitivity of animals to vibrations and irregular mechanical vibrations caused by other living systems, as well as natural and anthropogenic phenomena, such as tectonic phenomena, natural, biogenic and technogenic vibrations of the earth and the aquatic environment is also known. They are especially important for aquatic organisms [9, 10]. These phenomena are also insufficiently studied, and their understanding, in addition to new fundamental knowledge, makes it possible to use them to increase the productivity of agricultural production.
In measuring technology, the most simple to process the output signal are FOSs based on amplitude modulation of the signal. Amplitude modulation schemes impose practically no special requirements on the source or receiver of radiation [3,12]. Also, FOSs need an additional circuit that processes the output signal of the sensor, since the amplitude-modulated signal is directly recorded using a conventional photodetector [1,13]. In [3], the physical foundations of amplitude modulation methods are considered in detail, the issues of constructing amplitude sensors and their classification are also considered.
In open-type fiber optic sensors [1], the reflective surface is the most complex and expensive part. The reflective surface is susceptible to shape distortion and degradation of reflective characteristics against a background of temperature fluctuations, which can severely degrade sensor performance. In this regard, the problem of creating a reflective element for FOSs, which have a simpler design and low production cost, remains urgent.
A number of works are known aimed at optimizing the circuits of fiber optic sensors with a lens [14–24]. The authors of these works carried out mathematical modeling, which makes it possible to determine the design parameters of fiber-optic converters, at which these designs are the most sensitive.
There are works [25–27] to improve the known from the literature designs of fiber-optic converters of the reflective type, in which modulation is carried out by changing the position of the (mirror) reflecting surface, such designs are mainly used in pressure sensors. In these works, computer modeling and experimental studies were carried out in order to improve the metrological characteristics, reduce optical losses, increase the sensitivity of the presented structures with varying geometric and optical parameters.
Also of great interest are works devoted to modeling the parameters of fiber-optic converters with a reflective attenuator [24], this design is a periodic structure. Analyzing the simulation results, the authors of [24] have chosen the optimal parameters of the fiber-optic converter, which provides the maximum sensitivity.
The cited works [14–24] are of interest in terms of the theoretical foundations for modeling amplitude fiber-optic converters (FOCs), which can be used to simulate new FOCs. In addition to works aimed at optimizing the structures that have become standard by varying design parameters in order to increase efficiency, there are known works that are aimed at improving the efficiency of the FOCs by changing the structure of the reflective element [25–27].
The authors of the patent for a fiber-optic microdisplacement sensor [28] proposed the design of a reflective element in the form of a flat relief element (Fig. 1), aimed at increasing the sensitivity by reducing optical losses by matching the mode structure of the reflected radiation with the receiving fiber. The radiation beam formed by the light guide 1 is converted by the reflective element 4 and excites the radiation in the light guide 2. External influences leading to the movement of the reflector 4 cause the intensity modulation of the directional modes of the light guide 2.
The work presents formulas for calculating the height of the relief of the reflecting plate and the total size of the reflecting element. However, this reflective element is difficult to manufacture due to its specific shape. The authors of this patent did not present a solution to the design of the sensor in which this reflective element can be used. It is not clear from the description of the patent what the transformation mechanism looks like; therefore, the limits of applicability and sensitivity of such a FOC are not so obvious.
The authors of the patent “Reflective element for fiber-optic sensor” [29] solved the problem of low sensitivity by manufacturing a reflective surface in the form of a multistage reflective element Fig. 2, however, such a design can hardly be called easy to manufacture, although it is performed by etching, the creation of attenuator zones is strictly regulated by an angle of 70 degrees.
The invention is based on the back reflection of a beam from a glass surface with areas of different reflection coefficients and the passage of this beam into the fiber. When vibration occurs, the end of the fiber begins to vibrate, as a result of which it deviates from its original position. When crossing the boundary of the section, the intensity of the reflected beam changes and, falling back into the FOS waveguide, is detected by a photodetector.
In [30], a fiber-optic sensor is presented that uses a transmissive grating of a periodic structure, a mirror, and a composite metal element that is sensitive to temperature changes. To register vibration, a structure is used in which the grating is attached to a spring, and when exposed to vibration, the grating deviates from the equilibrium position, thereby modulating the signal. This design is similar to the considered sensor models, however, the periodic structure is used not as a reflective element, but as a barrier between the fiber and the reflective surface.
Based on the works discussed above, it can be concluded that the problem of developing reflective elements of amplitude fiber-optic sensors that are sensitive to certain physical influences, have a simpler design and low production cost, according to the authors, is still unsolved.
The aim of this work is to create a reflective element for amplitude FOSs of vibration of the reflective type. Implementation of an experimental model of a vibration sensor to test the performance of the proposed reflective structure, a series of experiments.
Basic principle
The reflective element can be represented by various structures. The experiment is aimed at selecting the structure of the reflecting surface in order to find the best option for measuring vibrations in one axis of action. The proposed reflective element is a periodic structure in the form of bands of lithium niobate (LiNbO3) with a reflection coefficient of k1 = 0.04 and gold with a reflection coefficient of k2 = 0.96.
The analysis of the distribution of the radiation intensity at the output of the optical fiber is carried out. The distribution of the intensity of the light beam in the fiber corresponds to the Gaussian distribution, the light will be emitted from the fiber within the numerical aperture.
Depending on the distance from the end of the fiber to the reflective surface (L) and the numerical aperture (NA) you can calculate the radius of the “light” spot R, thereby determining how wide the strip of gold and lithium niobate should be. The bands of gold and niobate must be 2R wide in order for the entire Gaussian beam to fit into one band.
For sensitivity to small amplitudes (on the order of microns) of vibrations, it is necessary that the centre of the fiber be directed to the gold / lithium niobate media section, since the intensity distribution in the light beam corresponds to a Gaussian distribution, that is, the maximum intensity is concentrated in the centre of the beam. Due to the proposed structure, the measurement is performed only in the specified direction, perpendicular to the direction of the strokes.
Experiment
An experimental model of an amplitude fiber-optic vibration sensor of a reflective type has been implemented. The principle of operation of the sensitive element is as follows. Optical radiation from the source through the light guide is transmitted to the reflecting plate with stripes with different reflectances, the reflected light partially returns to the light guide and is transmitted to the photodetector module. When exposed to vibration, the free end of the fiber vibrates, as a result of which the signal received by the photodetector module is modulated.
In the manufactured experimental sample of the sensor (Fig. 5) there is a possibility of tuning the parameters of the sensitive element, namely, the length of the free optical fiber, the distance to the reflecting surface, the possibility of displacing the reflecting surface along two axes, the possibility of replacing the reflecting plate.
FOS experimental setup for testing a reflective surface is shown in Fig. 6. It contains a radiation source (IR) that generates radiation at a wavelength of 1550 nm; sensitive element (SE); mounted on a vibration source TIRA Power Amplifier type BAA 120 (VS); frequency generator GW Instek GFG‑3015 (FG) setting signal for the vibration source; oscilloscope LeCroy WA 232 (O), which picks up a signal from the photodetector module HCA-S‑200M–IN-FC (PDM).
The result of the experiment is shown in Fig. 7. It can be seen from the figure that the generated signal (a) at 100 Hz (pre-resonant frequency) correlates (Pearson’s correlation coefficient is 0.78) with the recorded signal of the photodetector (b).
Modeling the parameters of the sensitive element
To determine the parameters of the sensitive element of the fiber-optic sensor and develop a mathematical model, the transverse vibrations of the fiber light guide, fixed on one side in the sensitive part of the developed vibration sensor, are considered, taking into account its shape, size, and material, using the theory of mechanical vibrations of a beam of constant cross-section [31, 32]. To simulate the vibrations of the fiber, we used the differential equation of transverse vibrations for a uniform beam of constant cross-section:
(1)
the disturbing load is taken into account in the boundary conditions, steady forced oscillations will be performed with the frequency of the disturbing force. Therefore, the equation of motion of the fiber will be described as the product of the amplitude part of the displacement u(x) and the harmonic function
. (2)
To verify the mathematical model, the amplitude-frequency characteristic was experimentally determined, shown in Fig. 8, from which it can be seen that the amplitude slowly increases with increasing frequency up to the resonance boundary, where the amplitude sharply increases after passing through the resonance zone, the amplitude returns to the level before resonance and practically does not change, the resonance frequency is f ≈ 800 Hz.
The calculation of the natural vibration frequency is carried out according to the formulas (7). The inertial mass in the sensor is the fiber itself. When the SE is subjected to vibration acceleration, the free end of the fiber will deflect, representing a harmonic oscillator.
Optical fiber parameters and quartz characteristics: r = 2 203 kg / m3 is silica fiber density; E = 58 GPa is technical Young’s modulus for quartz glass; d = 125 μm; l = 10 mm is the length of the cantilever part of the prototype;
The natural frequencies of the oscillatory system are determined by the expression:
Hz.
Fig. 9 presents the theoretical dependence of the natural frequency on the length of the free fiber, from which it can be seen that the short length of the free fiber is more attractive due to long-range resonance, but such lengths will have a low seismic mass and high rigidity, which, as a consequence, reduces the sensitivity. It can be seen that the theoretical natural frequency of oscillations correlates with the obtained data of resonance frequencies (Pearson’s correlation coefficient is 0.977).
Taking into account the results of the mathematical model and the results obtained experimentally, the length of the free fiber was selected equal to 10 mm, since at this length the seismic mass and stiffness allows measurements at low amplitudes over a wide range of frequencies. When the length of the free fiber is less than 10 mm, the combined effect of this seismic mass and this stiffness makes it impossible to perceive the vibration impact, which requires the introduction of a load (additional seismic mass) into the structure. When the length of the free fiber is more than 10 mm, the resonance frequency is shifted to the frequencies of interest.
Conclusion
As a result of this work, a reflecting element in the form of a periodic structure was proposed. This reflective element is simple in design, due to its periodic structure and the arrangement of the grooves, only one vibration axis is recorded, and the adjustment to the media section ensures sensitivity to small displacements of the order of a micrometer. From the data presented in the work, it is obvious that the operational characteristics of the model satisfactorily meet the requirements for the FOSs of the similar types, while in work [30] is used as an elastic element is not a fiber (which is a fairly reliable material – homogeneous, elastic with a glassy structure), which complicates and increases the cost of such a structure. In addition, in most of the works known to the authors, high requirements are imposed on the manufacture of a reflective element, in [29] the sensor measures vibration in the range of 5–1000 Hz, but the attenuation zone is regulated by an angle of 70 degrees and has a multi-stage profile.
In this work, we used a reflective element, the periodic structure of which was created by sawing at right angles. Also, often in the design of the sensitive element there are emitting fibers and receiving ones, the design proposed in this work combines the role of a receiver and a transmitter in one fiber. The reflecting surface, as well as the sensing element based on its use, are easy to manufacture, while the sensing element, using the proposed reflective plate in its design, retained its low weight and dimensions.
The experimental sensing element created by the authors has a resonance of 800 Hz, which is metrologically the upper limit of measurements, however, in this work, an experimental model was used, which is not a monolithic structure, but a composite platform with the possibility of adjusting parameters; such a design negatively affects the measuring range.
One of the technical areas of application of this development is the study of plant responses to mechanical vibrations.
The results of the implementation of this development are important for a new interdisciplinary direction – agrobiophotonics, provide the key to a more subtle and accurate study of the vibration sensitivity of animals and vibrotropism of plants, to the use of this phenomenon to control the growth and productivity of cultivated plants, both in photoculture conditions and in open field conditions., breeding and increasing the productivity of farm animals and aquaculture.
A further area of work is the implementation of a structure with the ability to register two vibration axes. Also in [33], the possibility of multiplexing was demonstrated, which can be adapted to the presented sensitive element, which opens up the possibility of further modernization.
Research is also planned to develop a technology for increasing grain productivity under vibration. Research carried out [34] in 2007–2009, seeds of spring and winter wheat were subjected to vibration with a frequency of 70 Hz and an amplitude of 0.5 mm for 12 and 14 hours. It is shown that the effect of vibration treatment of wheat seeds can manifest itself: in accelerating the transition of plants to the generative phase of development; in enhancing the growth of shoots; in stimulating tillering and in increasing the grain productivity of plants. The data obtained indicate that such a dynamic factor as vibration affects the epigenetic level.
Vibration treatment of wheat seeds did not cause an increase in the number of chromosomal rearrangements, which confirmed the previously known facts about the absence of the effect of vibration on chromosome rearrangements.
Funding
The work was carried out within the framework of a state assignment with the topic state registration number AAAA-A19-119051390040-5.
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AUTHORS
Burdysheva Olga Vasilievna, junior researcher, Laboratory of Agrobiophotonics, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Perm, Russia. Research interests: fiber optics, fiber optic sensors; Corresponding author, e-mail: Burdyshevaolga@gmail.com.
ORCID: 0000-0002-7395-4361
Sholgin Evgeniy Sergeevich, junior researcher, Laboratory of Agrobiophotonics, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Perm, Russia. Research interests: fiber optics, fiber optic sensors; e-mail: Faler01@yandex.ru.
ORCID: 0000-0002-8068-8815
Maksimov Alexander Yurievich, Cand.of Science(Biolog.), Head of Laboratory of Agrobiophotonics, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Senior Researcher, Institute of Ecology and Genetics of Microorganisms, Ural Branch of the Russian Academy of Sciences, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Perm, Russia.
ORCID: 0000-0003-2591-3351
WOS Research ID T-8070-2017
O. V. Burdysheva , E. S. Sholgin , A. Yu. Maksimov
Laboratory of Agrobiophotonics, Perm Federal Research Center, Ural Branch of the Russian Academy of Sciences, Perm, Russia
Institute of Ecology and Genetics of Microorganisms, Perm Federal Research Center, Ural Branch of the Russian Academy of Sciences, Perm, Russia
This work is devoted to the development of a design of a reflective element for an amplitude fiber-optic vibration sensor, as well as testing the performance of such a design. In the presented work, a mathematical model of transverse vibrations is described, which helps to determine the resonance frequencies depending on the length of the free fiber. A reflective surface is implemented, which is a periodic structure of lithium niobate and areas covered with gold. The layout and design of a vibration sensor with the ability to tune the resonance frequency is presented, and an experimental circuit is demonstrated. The signal obtained using the described circuit lends itself to Fourier transform processing, the calculated frequencies coincide with the vibration frequencies of the vibration source. The amplitude-frequency characteristic is obtained, the resonance frequency correlates with the frequencies obtained by the mathematical model (Pearson’s correlation coefficient is 0.977). The results of the implementation of this development are important for a new interdisciplinary direction – agrobiophotonics, provide a key to a more subtle and accurate study of animal vibration sensitivity and plant vibrotropism.
Key words: sensor, fiber-optic sensor, amplitude reflective type sensor, vibration sensor, vibration, vibration monitoring
Received on: 17.04.2021
Accepted on: 10.05.2021
Introduction
The demand for sensors is growing rapidly due to the development of information and measurement systems, automated control systems and production management. In addition to high metrological characteristics, the sensors should have such properties as low weight, small dimensions, low power consumption, and compatibility with microelectronic information processing devices. These requirements are met to the maximum extent by fiber-optic sensors (FOS) [1, 2].
FOSs are often made of materials that are dielectrics, which eliminates the risk of sparks and, as a result of fire, the fiber itself is resistant to corrosion and radiation. Also FOSs have good performance and low cost, can be located at a great distance from the controlled object, it is possible to serially connect many sensitive elements in one line, there are also distributed fiber-optic sensors [1, 3, 4, 5]. Their use is especially interesting in new, interdisciplinary areas: for example, in monitoring the acoustic fields of flora and fauna of various natural locations (in the field of physiology and regulation of plant growth, zoology, agrobiophotonics, aquaculture, productivity of dairy farming, etc.) distributed sensors operating on ultra-weak backscattered signals and requiring complex signal processing are almost not applicable. In such cases, the best practical solutions would be either quasi-distributed sensors or point sensor arrays. Quasi-distributed sensors require a rather serious and expensive hardware base, while simple point FOSs can be the optimal solution.
Thus, it is known that plants are sensitive to vibration of water, soil, insects-pollinators, insects that eat plants and react to these effects by movement, tropisms and the synthesis of protective metabolites [6, 7]. In particular, among root tropisms, the movement of plants in the direction of vibrations generated by flowing water was found, but the sound recording of flowing water did not cause such a reaction, therefore, the plant reacts to low-frequency mechanical vibrations [6, 8]. However, the absence of highly sensitive sensors, the operation of which does not depend on external electric fields and electromagnetic oscillations, sound interference, high humidity and the threat of biodeterioration, limits the development of such studies. The sensitivity of animals to vibrations and irregular mechanical vibrations caused by other living systems, as well as natural and anthropogenic phenomena, such as tectonic phenomena, natural, biogenic and technogenic vibrations of the earth and the aquatic environment is also known. They are especially important for aquatic organisms [9, 10]. These phenomena are also insufficiently studied, and their understanding, in addition to new fundamental knowledge, makes it possible to use them to increase the productivity of agricultural production.
In measuring technology, the most simple to process the output signal are FOSs based on amplitude modulation of the signal. Amplitude modulation schemes impose practically no special requirements on the source or receiver of radiation [3,12]. Also, FOSs need an additional circuit that processes the output signal of the sensor, since the amplitude-modulated signal is directly recorded using a conventional photodetector [1,13]. In [3], the physical foundations of amplitude modulation methods are considered in detail, the issues of constructing amplitude sensors and their classification are also considered.
In open-type fiber optic sensors [1], the reflective surface is the most complex and expensive part. The reflective surface is susceptible to shape distortion and degradation of reflective characteristics against a background of temperature fluctuations, which can severely degrade sensor performance. In this regard, the problem of creating a reflective element for FOSs, which have a simpler design and low production cost, remains urgent.
A number of works are known aimed at optimizing the circuits of fiber optic sensors with a lens [14–24]. The authors of these works carried out mathematical modeling, which makes it possible to determine the design parameters of fiber-optic converters, at which these designs are the most sensitive.
There are works [25–27] to improve the known from the literature designs of fiber-optic converters of the reflective type, in which modulation is carried out by changing the position of the (mirror) reflecting surface, such designs are mainly used in pressure sensors. In these works, computer modeling and experimental studies were carried out in order to improve the metrological characteristics, reduce optical losses, increase the sensitivity of the presented structures with varying geometric and optical parameters.
Also of great interest are works devoted to modeling the parameters of fiber-optic converters with a reflective attenuator [24], this design is a periodic structure. Analyzing the simulation results, the authors of [24] have chosen the optimal parameters of the fiber-optic converter, which provides the maximum sensitivity.
The cited works [14–24] are of interest in terms of the theoretical foundations for modeling amplitude fiber-optic converters (FOCs), which can be used to simulate new FOCs. In addition to works aimed at optimizing the structures that have become standard by varying design parameters in order to increase efficiency, there are known works that are aimed at improving the efficiency of the FOCs by changing the structure of the reflective element [25–27].
The authors of the patent for a fiber-optic microdisplacement sensor [28] proposed the design of a reflective element in the form of a flat relief element (Fig. 1), aimed at increasing the sensitivity by reducing optical losses by matching the mode structure of the reflected radiation with the receiving fiber. The radiation beam formed by the light guide 1 is converted by the reflective element 4 and excites the radiation in the light guide 2. External influences leading to the movement of the reflector 4 cause the intensity modulation of the directional modes of the light guide 2.
The work presents formulas for calculating the height of the relief of the reflecting plate and the total size of the reflecting element. However, this reflective element is difficult to manufacture due to its specific shape. The authors of this patent did not present a solution to the design of the sensor in which this reflective element can be used. It is not clear from the description of the patent what the transformation mechanism looks like; therefore, the limits of applicability and sensitivity of such a FOC are not so obvious.
The authors of the patent “Reflective element for fiber-optic sensor” [29] solved the problem of low sensitivity by manufacturing a reflective surface in the form of a multistage reflective element Fig. 2, however, such a design can hardly be called easy to manufacture, although it is performed by etching, the creation of attenuator zones is strictly regulated by an angle of 70 degrees.
The invention is based on the back reflection of a beam from a glass surface with areas of different reflection coefficients and the passage of this beam into the fiber. When vibration occurs, the end of the fiber begins to vibrate, as a result of which it deviates from its original position. When crossing the boundary of the section, the intensity of the reflected beam changes and, falling back into the FOS waveguide, is detected by a photodetector.
In [30], a fiber-optic sensor is presented that uses a transmissive grating of a periodic structure, a mirror, and a composite metal element that is sensitive to temperature changes. To register vibration, a structure is used in which the grating is attached to a spring, and when exposed to vibration, the grating deviates from the equilibrium position, thereby modulating the signal. This design is similar to the considered sensor models, however, the periodic structure is used not as a reflective element, but as a barrier between the fiber and the reflective surface.
Based on the works discussed above, it can be concluded that the problem of developing reflective elements of amplitude fiber-optic sensors that are sensitive to certain physical influences, have a simpler design and low production cost, according to the authors, is still unsolved.
The aim of this work is to create a reflective element for amplitude FOSs of vibration of the reflective type. Implementation of an experimental model of a vibration sensor to test the performance of the proposed reflective structure, a series of experiments.
Basic principle
The reflective element can be represented by various structures. The experiment is aimed at selecting the structure of the reflecting surface in order to find the best option for measuring vibrations in one axis of action. The proposed reflective element is a periodic structure in the form of bands of lithium niobate (LiNbO3) with a reflection coefficient of k1 = 0.04 and gold with a reflection coefficient of k2 = 0.96.
The analysis of the distribution of the radiation intensity at the output of the optical fiber is carried out. The distribution of the intensity of the light beam in the fiber corresponds to the Gaussian distribution, the light will be emitted from the fiber within the numerical aperture.
Depending on the distance from the end of the fiber to the reflective surface (L) and the numerical aperture (NA) you can calculate the radius of the “light” spot R, thereby determining how wide the strip of gold and lithium niobate should be. The bands of gold and niobate must be 2R wide in order for the entire Gaussian beam to fit into one band.
For sensitivity to small amplitudes (on the order of microns) of vibrations, it is necessary that the centre of the fiber be directed to the gold / lithium niobate media section, since the intensity distribution in the light beam corresponds to a Gaussian distribution, that is, the maximum intensity is concentrated in the centre of the beam. Due to the proposed structure, the measurement is performed only in the specified direction, perpendicular to the direction of the strokes.
Experiment
An experimental model of an amplitude fiber-optic vibration sensor of a reflective type has been implemented. The principle of operation of the sensitive element is as follows. Optical radiation from the source through the light guide is transmitted to the reflecting plate with stripes with different reflectances, the reflected light partially returns to the light guide and is transmitted to the photodetector module. When exposed to vibration, the free end of the fiber vibrates, as a result of which the signal received by the photodetector module is modulated.
In the manufactured experimental sample of the sensor (Fig. 5) there is a possibility of tuning the parameters of the sensitive element, namely, the length of the free optical fiber, the distance to the reflecting surface, the possibility of displacing the reflecting surface along two axes, the possibility of replacing the reflecting plate.
FOS experimental setup for testing a reflective surface is shown in Fig. 6. It contains a radiation source (IR) that generates radiation at a wavelength of 1550 nm; sensitive element (SE); mounted on a vibration source TIRA Power Amplifier type BAA 120 (VS); frequency generator GW Instek GFG‑3015 (FG) setting signal for the vibration source; oscilloscope LeCroy WA 232 (O), which picks up a signal from the photodetector module HCA-S‑200M–IN-FC (PDM).
The result of the experiment is shown in Fig. 7. It can be seen from the figure that the generated signal (a) at 100 Hz (pre-resonant frequency) correlates (Pearson’s correlation coefficient is 0.78) with the recorded signal of the photodetector (b).
Modeling the parameters of the sensitive element
To determine the parameters of the sensitive element of the fiber-optic sensor and develop a mathematical model, the transverse vibrations of the fiber light guide, fixed on one side in the sensitive part of the developed vibration sensor, are considered, taking into account its shape, size, and material, using the theory of mechanical vibrations of a beam of constant cross-section [31, 32]. To simulate the vibrations of the fiber, we used the differential equation of transverse vibrations for a uniform beam of constant cross-section:
(1)
the disturbing load is taken into account in the boundary conditions, steady forced oscillations will be performed with the frequency of the disturbing force. Therefore, the equation of motion of the fiber will be described as the product of the amplitude part of the displacement u(x) and the harmonic function
. (2)
To verify the mathematical model, the amplitude-frequency characteristic was experimentally determined, shown in Fig. 8, from which it can be seen that the amplitude slowly increases with increasing frequency up to the resonance boundary, where the amplitude sharply increases after passing through the resonance zone, the amplitude returns to the level before resonance and practically does not change, the resonance frequency is f ≈ 800 Hz.
The calculation of the natural vibration frequency is carried out according to the formulas (7). The inertial mass in the sensor is the fiber itself. When the SE is subjected to vibration acceleration, the free end of the fiber will deflect, representing a harmonic oscillator.
Optical fiber parameters and quartz characteristics: r = 2 203 kg / m3 is silica fiber density; E = 58 GPa is technical Young’s modulus for quartz glass; d = 125 μm; l = 10 mm is the length of the cantilever part of the prototype;
The natural frequencies of the oscillatory system are determined by the expression:
Hz.
Fig. 9 presents the theoretical dependence of the natural frequency on the length of the free fiber, from which it can be seen that the short length of the free fiber is more attractive due to long-range resonance, but such lengths will have a low seismic mass and high rigidity, which, as a consequence, reduces the sensitivity. It can be seen that the theoretical natural frequency of oscillations correlates with the obtained data of resonance frequencies (Pearson’s correlation coefficient is 0.977).
Taking into account the results of the mathematical model and the results obtained experimentally, the length of the free fiber was selected equal to 10 mm, since at this length the seismic mass and stiffness allows measurements at low amplitudes over a wide range of frequencies. When the length of the free fiber is less than 10 mm, the combined effect of this seismic mass and this stiffness makes it impossible to perceive the vibration impact, which requires the introduction of a load (additional seismic mass) into the structure. When the length of the free fiber is more than 10 mm, the resonance frequency is shifted to the frequencies of interest.
Conclusion
As a result of this work, a reflecting element in the form of a periodic structure was proposed. This reflective element is simple in design, due to its periodic structure and the arrangement of the grooves, only one vibration axis is recorded, and the adjustment to the media section ensures sensitivity to small displacements of the order of a micrometer. From the data presented in the work, it is obvious that the operational characteristics of the model satisfactorily meet the requirements for the FOSs of the similar types, while in work [30] is used as an elastic element is not a fiber (which is a fairly reliable material – homogeneous, elastic with a glassy structure), which complicates and increases the cost of such a structure. In addition, in most of the works known to the authors, high requirements are imposed on the manufacture of a reflective element, in [29] the sensor measures vibration in the range of 5–1000 Hz, but the attenuation zone is regulated by an angle of 70 degrees and has a multi-stage profile.
In this work, we used a reflective element, the periodic structure of which was created by sawing at right angles. Also, often in the design of the sensitive element there are emitting fibers and receiving ones, the design proposed in this work combines the role of a receiver and a transmitter in one fiber. The reflecting surface, as well as the sensing element based on its use, are easy to manufacture, while the sensing element, using the proposed reflective plate in its design, retained its low weight and dimensions.
The experimental sensing element created by the authors has a resonance of 800 Hz, which is metrologically the upper limit of measurements, however, in this work, an experimental model was used, which is not a monolithic structure, but a composite platform with the possibility of adjusting parameters; such a design negatively affects the measuring range.
One of the technical areas of application of this development is the study of plant responses to mechanical vibrations.
The results of the implementation of this development are important for a new interdisciplinary direction – agrobiophotonics, provide the key to a more subtle and accurate study of the vibration sensitivity of animals and vibrotropism of plants, to the use of this phenomenon to control the growth and productivity of cultivated plants, both in photoculture conditions and in open field conditions., breeding and increasing the productivity of farm animals and aquaculture.
A further area of work is the implementation of a structure with the ability to register two vibration axes. Also in [33], the possibility of multiplexing was demonstrated, which can be adapted to the presented sensitive element, which opens up the possibility of further modernization.
Research is also planned to develop a technology for increasing grain productivity under vibration. Research carried out [34] in 2007–2009, seeds of spring and winter wheat were subjected to vibration with a frequency of 70 Hz and an amplitude of 0.5 mm for 12 and 14 hours. It is shown that the effect of vibration treatment of wheat seeds can manifest itself: in accelerating the transition of plants to the generative phase of development; in enhancing the growth of shoots; in stimulating tillering and in increasing the grain productivity of plants. The data obtained indicate that such a dynamic factor as vibration affects the epigenetic level.
Vibration treatment of wheat seeds did not cause an increase in the number of chromosomal rearrangements, which confirmed the previously known facts about the absence of the effect of vibration on chromosome rearrangements.
Funding
The work was carried out within the framework of a state assignment with the topic state registration number AAAA-A19-119051390040-5.
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AUTHORS
Burdysheva Olga Vasilievna, junior researcher, Laboratory of Agrobiophotonics, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Perm, Russia. Research interests: fiber optics, fiber optic sensors; Corresponding author, e-mail: Burdyshevaolga@gmail.com.
ORCID: 0000-0002-7395-4361
Sholgin Evgeniy Sergeevich, junior researcher, Laboratory of Agrobiophotonics, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Perm, Russia. Research interests: fiber optics, fiber optic sensors; e-mail: Faler01@yandex.ru.
ORCID: 0000-0002-8068-8815
Maksimov Alexander Yurievich, Cand.of Science(Biolog.), Head of Laboratory of Agrobiophotonics, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Senior Researcher, Institute of Ecology and Genetics of Microorganisms, Ural Branch of the Russian Academy of Sciences, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Perm, Russia.
ORCID: 0000-0003-2591-3351
WOS Research ID T-8070-2017
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