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technospheramag
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ТЕХНОСФЕРА_РИЦ
Issue #2/2024
I. A. Kazakov, K. M. Malakhov, E. E. Kovalev, A. A. Mkrtchyan, M. S. Mishevskiy, V. V. Svetikov, A. V. Shipulin
Study of Operational Algorithm for Interrogator with Arrayed Waveguide Grating on a Photonic Integrated Circuit
Study of Operational Algorithm for Interrogator with Arrayed Waveguide Grating on a Photonic Integrated Circuit
DOI: 10.22184/1993-7296.FRos.2024.18.2.122.135
This paper presents analytical and experimental investigations of a fiber Bragg grating interrogator based on the arrayed waveguide grating made with a photonic integrated circuit technology. The key specifications of the interrogator are determined analytically based on the parameters of the arrayed waveguide grating used as a spectral demultiplexer and the photodetector’s operating error. In addition, the detection methods and algorithms for obtaining the reflectance spectrum maximum of fiber Bragg gratings are proposed and evaluated. Experimental measurements of the fiber Bragg grating central wavelength using the proposed algorithm are carried out, including calibration and measurement procedures using the data obtained under the influence of temperature and mechanical stress on the fiber Bragg grating. The system performance is experimentally confirmed with the accuracy of determination of a central wavelength of fiber Bragg grating reflection peak not less than 61 pm.
This paper presents analytical and experimental investigations of a fiber Bragg grating interrogator based on the arrayed waveguide grating made with a photonic integrated circuit technology. The key specifications of the interrogator are determined analytically based on the parameters of the arrayed waveguide grating used as a spectral demultiplexer and the photodetector’s operating error. In addition, the detection methods and algorithms for obtaining the reflectance spectrum maximum of fiber Bragg gratings are proposed and evaluated. Experimental measurements of the fiber Bragg grating central wavelength using the proposed algorithm are carried out, including calibration and measurement procedures using the data obtained under the influence of temperature and mechanical stress on the fiber Bragg grating. The system performance is experimentally confirmed with the accuracy of determination of a central wavelength of fiber Bragg grating reflection peak not less than 61 pm.
Теги: arrayed waveguide grating fiber bragg grating interrogator photonic integrated circuit волоконная брэгговская решетка дифракционная волноводная решетка интеррогатор фотонная интегральная схема
Study of Operational Algorithm for Interrogator With Arrayed Waveguide Grating on a Photonic Integrated Circuit
I. A. Kazakov 1, 2, 3, K. M. Malakhov 1, 2, 3, E. E. Kovalev 1, A. A. Mkrtchyan 1, M. S. Mishevskiy 1, V. V. Svetikov 4, 5, A. V. Shipulin 1, 2
Skolkovo Institute of Science and Technology, Moscow, Russia
PICsTech LLC, Moscow, Russia
Fiber Flight LLC, Moscow, Russia
Zelenograd Nanotechnical Center JSC, Zelenograd, Moscow, Russia
Prokhorov Institute of General Physics of the Russian Academy of Sciences, Moscow, Russia
This paper presents analytical and experimental investigations of a fiber Bragg grating interrogator based on the arrayed waveguide grating made with a photonic integrated circuit technology. The key specifications of the interrogator are determined analytically based on the parameters of the arrayed waveguide grating used as a spectral demultiplexer and the photodetector’s operating error. In addition, the detection methods and algorithms for obtaining the reflectance spectrum maximum of fiber Bragg gratings are proposed and evaluated. Experimental measurements of the fiber Bragg grating central wavelength using the proposed algorithm are carried out, including calibration and measurement procedures using the data obtained under the influence of temperature and mechanical stress on the fiber Bragg grating. The system performance is experimentally confirmed with the accuracy of determination of a central wavelength of fiber Bragg grating reflection peak not less than 61 pm.
Keywords: interrogator, arrayed waveguide grating, fiber Bragg grating, photonic integrated circuit
Article received: February 20, 2024
Article accepted: March 05, 2024
Introduction
The optical interrogator is a device for collecting and analyzing data received from the fiber-optic sensors. This device is used to control various physical quantities, including temperature [1], mechanical stress, pressure, and displacement [2]. The interrogators have become widely applied in the structural monitoring systems for building and bridge structures [3], pipelines [4] and distillation columns [5], unmanned aerial vehicles [6], aircrafts [7] and satellites [8], chemical sensing systems [9] and other applications. The interrogator’s architecture is mainly determined by the type of sensors used. The configurations of devices for interrogating sensors based on a fiber Bragg grating (FBG) will be further considered.
The interrogator’s layouts for interrogating FBGs can be divided into two main groups: based on a mini-spectrometer and based on a tunable laser. Moreover, there are more over-the-top approaches based on radio-photonic methods [10], tunable filters [11], and their combinations [12]. The mini-spectrometer-based interrogators, including an interrogator based on an arrayed waveguide grating (AWG) on a photonic integrated circuit (PIC), provide a position detection accuracy of the FBG peak wavelength up to 0.32 pm [13], while the tunable laser-based interrogators provide less than 0.1 pm [14], and both layouts use the PIC technology to produce key elements of the device. One of the disadvantages of the AWG-based interrogator circuit is the low power arriving at the photodetectors, which is due to the low spectral power density of the broadband source and the narrow reflection spectrum of the FBG. However, this circuit is the simplest to implement, easily reconfigurable, and scalable. Moreover, it has a high interrogating rate, limited only by the operating frequency of photodetectors and electronics. The interrogators based on a tunable laser are more popular due to their versatility but have a significantly more comprehensive structure and operating algorithms. Due to the limited scanning rate, they have a lower sensor interrogating frequency. It is worth noting that the detection algorithm for a physical quantity is determined by the interrogator’s design and the type of interrogated sensors.
This article aims to develop and test an algorithm for use in the AWG-based FBG sensors interrogator with AWG on PIC. The developed algorithm can detect all types of FBG sensors (temperature, mechanical stress, etc.) as part of structural health monitoring systems.
Theory and calculation
Figure 1 shows a scheme of the AWG-based interrogator, including a superluminescent diode (SLD), a circulator, an FBG, an AWG, photodiodes (PD), and a signal processing system.
The operating principle of the AWG-based interrogator for interrogating sensors on the FBG is as follows. The light from a broadband SLD source is passed through a circulator to the sensors, the sensitive element of which is an FBG. Each FBG reflects radiation at a certain wavelength (λ1, λ2... λn) that is guided to the AWG input through the circulator. Depending on any changes in the external parameters, for example, temperature and/or mechanical stresses, the FBG period is changed, and consequently, the reflection spectrum maximum position is also changed. The AWG is used as a spectral-selective device since its output channels are spectrally equidistant from each other and transmit a narrow band of wavelengths in the vicinity of their maximum. The data processing system receives information related to any changes in the powers detected by PD1, PD2…PDm and converts it into the wavelength of the reflected radiation peak from each FBG sensor further rescaled into a measurable physical quantity.
Fig. 2 illustrates the operation methodology for the AWG-based interrogator. During operation, the maximum of the FBG reflection spectrum is predominantly located between two AWG channels. At each moment, the position of the FBG reflection spectrum maximum is determined based on the power values on adjacent channels.
In this paper, we will consider an approximation within which the FBG reflection spectrum represents the delta function (RFBG(λ) = δ(λ – λFBG)), and the FBG channel transmission spectrum represents the Gaussian function (1, 2). This approximation allows us to analytically review the system and obtain qualitative conclusions about its operation.
In the approximation used, the transmission spectra of AWG channels can be indicated as follows (1, 2):
; (1)
, (2)
where σch = σchn = σchn+1 – half-width of the channels that are equal to each other for one AWG;
λchn, λchn+1 – central wavelengths of the AWG channels.
The detected powers in the AWG channels will be as follows with due regard to the sifting property of the delta function:
; (3)
. (4)
In general, to determine the wavelength, it is necessary to obtain a calibration function in the space of Pn, Pn+1 that provides the most probable position of the FBG peak wavelength for the given values of Pn and Pn+1 or returns an error in the input data. In the general case, the number of AWG channels is m, and the number of detected FBG peaks is n. This problem is overdetermined and can be solved by many methods, including machine learning, in which case it is possible to use more channels per FBG for calculation, and the best results are expected.
In this paper, we propose to proceed from the fact that the main characteristic for the FBG wavelength determination is the ratio of powers on adjacent channels that, among other things, avoids disturbances introduced by variations in the radiation source power. It is also easier to be processed by the microcontrollers and requires less computing power. It is proposed at each moment of time to determine two channels with the highest optical power, then measure the power on each channel, to determine the ratio of the powers measured, and then, by using a two-dimensional calibration curve, to reconstruct the wavelength value of the FBG reflection spectrum maximum. An analytical description of this method is given below.
To solve the inverse problem of the wavelength determination, let us introduce the following calibration function:
. (5)
While substituting the expressions (3) and (4) into (5), we will get the following:
, (6)
where Δλ = λchn+1 – λchn – a distance between the AWG channels;
λC = (λchn+1 + λchn)/2 – a wavelength of the center between the AWG channels.
Next, we will calculate the FBG wavelength calculation error (λFBG):
, (7)
where δP = δP1 = δP2 – the power measurement error in the AWG channels.
We will assume that δP1 = δP2 = const. While substituting the values of partial derivatives into (7), we will determine the wavelength determination error (8):
. (8)
Thus, based on the calculations, it is found that the position determination error of the reflected spectrum maximum of the FBG sensor depends on the following parameters: the half-width of the AWG channels (σch), the distance between the AWG channels (Δλ), power measurement errors in the AWG channels (δP). The smallest error in the wavelength determination is made when the maximum is located at the point in the middle between the AWG channels (λc) and increases exponentially as it moves away from it.
Methods and materials
During the research, a test bench has been assembled, simulating the operation process of an interrogator. A calibration process has been performed, and the accuracy of the device’s operation has been assessed. Figure 3 shows the interrogator layout used in the experimental measurements, including the SLD, fiber amplifier (FA), circulator, FBG, AWG, power meter (PM).
An EXS210066-01 SLD produced by Exalos was used as a broadband source as a part of the experimental setup, and an SF8075-NM driver manufactured by Maiman Electronics was applied to control and supply power. The PEFA-SP-C-PM‑27-B130-FA-FA produced by Keopsys was used to amplify the SLD radiation. Two series-connected FBGs produced by Inversia-Sensor were applied as the sensors, the reflection spectra of which were measured at room temperature and in the absence of applied mechanical stress. The positions of the reflection spectrum maximums of the FBGs No. 1 and No. 2 at room temperature were 1545.90 and 1557.78 nm, and their widths at half maximum were 212 and 195 pm. This paper presents an analysis of experimental data related to the FBG No. 2 with a central wavelength of about 1557.78 nm.
A packaged 16‑channel PIC-based AWG module with a TEC controller, developed by FOTIS LLC and produced in the integrated photonics department of Zelenograd Nanotechnology Center JSC, was used as a demultiplexer [15]. During the measurements, the TEC controller maintained a constant temperature of the AWG module equal to the room temperature. To measure the transmission spectrum of the AWG channels and the FBG reflection spectrum, a Deviser AE8600 optical spectral analyzer was used, and the spectra were obtained with a wavelength resolution of 50 pm. The Thorlabs S132Cb optical power meters were used as the PDs. The experimentally obtained transmission spectra of the PIC-based AWG channels at room temperature, together with the FBG reflection spectra at room temperature and a temperature of 166 °C in the absence of mechanical stress, are shown in Fig. 4.
Results and discussion
Three experiments were performed as parts of the research: changes in the FBG temperature, changes in the FBG mechanical stresses, and simultaneous changes in both temperature and mechanical stresses. During the experiments, the following data were recorded: powers at all photodetectors, the wavelength of the FBG reflection peak (with a resolution of 50 pm), and, accordingly, the FBG temperature and mechanical stresses. As a part of this paper, only information related to the FBG No. 2 with a central wavelength of 1557.78 nm at room temperature and, accordingly, readings on the PDs connected to the AWG channels which filter the reflected light from the FBG (channel No. 1 and channel No. 2) are considered.
Data from the photodetectors on the AWG channels No. 1 and No. 2 is given in Fig. 5. This data is used to further plot the calibration curve and assess the FBG central wavelength determination error using this proposed interrogator scheme and method.
The data was divided into two sampling groups: calibration and verification. The calibration sampling group included information from experiments No.1 and No.2, and the verification sampling group included information from experiment No.3. According to the method proposed above, to evaluate the algorithm functioning were used only points whose wavelength lies in the range between the peaks of the AWG channels No. 1 and No. 2, as well as one point to the right and left around this range. The expression (5) was used as a calibration function, from which the decimal logarithm was taken for better visualization:
. (9)
The calibration function values for the test sampling group are presented in Fig. 6.
The logistic function (sigmoid) (Fig. 7) was used for approximation of the given points, indicated by the expression (10):
. (10)
The root-mean-square deviations of the measured wavelength from the true value for the calibration and validation data turned out to be 61 pm and 35 pm, respectively. These values have the same order of magnitude as the resolution of the optical spectrometer (50 pm), suggesting that the accuracy of this scheme may be less than or equal to the resolution of the spectrometer used, namely 50 pm. Therefore, the operating error of the given circuit is estimated to be less than or equal to 61 pm.
Conclusions
During this work, the analytical and experimental research of the FBG interrogator based on the PIC-based AWG was performed. The theoretical analysis leads to the dependence of the wavelength measurement error by the interrogator on the system key parameters, such as the measurement error of the photodetector and the width and distance between the AWG channels. It was shown that the FBG wavelength determination error, in general, depends on the FBG wavelength position relative to the AWG channels: the closer the FBG reflection spectrum peak is to the position between the AWG channels, the smaller the error, and the higher the accuracy of the interrogation. However, in the case when the channel width and the distance between the channels of AWG are equal, this dependence could be minimized. Also, during the work, it was concluded that the greater the distance between the AWG channels, the lower the interrogator’s accuracy.
As a part of experimental studies, an algorithm for calibration and subsequent detection of the FBG wavelength using an AWG on a photonic chip was tested. The calibration function was selected, namely the logistic function (sigmoid) (10), which most accurately described the behavior of the calibration function as a FBG peak wavelength function. The wavelength determination error was also estimated to be no more than 61 pm, which could not be limited from below due to the fact that the used resolution of the spectrometer was 50 pm.
In the future, we plan to conduct research using measuring equipment with a smaller instrumental error and collect a larger amount of information in order to determine the real accuracy of the interrogator. It is also scheduled to conduct an experiment using a larger number of AWG channels and several FBGs to demonstrate the algorithm and study its behavior under boundary conditions. In addition, experiments with a larger set of data are scheduled to be conducted to obtain a representative sampling group for a better statistical assessment of the interrogator’s operation and the interrogation algorithm for the FBG-based sensors. In addition, the research will be conducted in relation to other algorithms, both using machine learning procedures and other calibration functions.
In conclusion, the analytical description of the interrogator’s operation using the AWG as a demultiplexer was provided, and the interrogator algorithm accuracy with an error of no more than 61 pm was demonstrated that corresponded to the determination error of the temperature value of 6 oC on the used FBGs.
AUTHORS
Kazakov Ivan A., Master of Sc., PhD student, Research engineer, Skolkovo Institute of Science and Technology; Senior researcher, Picstech LLC, Moscow, Russia; CTO, Fiber Flight LLC, Moscow, Russia.
ORCID: 0000-0001-7509-1064
Web of Science ResearcherID: ADK-4828-2022
ID Scopus: 57203957427
ID RSCI: 4506-1355
Malakhov Kirill M., Master of Sc., PhD student, Research engineer, Skolkovo Institute of Science and Technology; Developer, Picstech LLC, Moscow, Russia; CEO, Fiber Flight LLC, Moscow, Russia.
ORCID: 0009-0004-1624-5018
Kovalev Egor Evgenievich, Bachelor of Sc., Master student, Laboratory assistant, Skolkovo Institute of Science and Technology, Moscow, Russia.
Mkrtchyan Aram A., Cand of Sc.(Phys.&Math.), Senior research scientist, Skolkovo Institute of Science and Technology, Moscow, Russia.
ORCID: https://orcid.org/0000-0002-6610-6006
Web of Science ResearcherID: AAP‑8995-2020
ID Scopus: 57200541614
ID RSCI 2718–5434
Mishevsky Mikhail Sergeevich, Master of Sc., PhD student, Skolkovo Institute of Science and Technology; Moscow, Russia.
ORCID: https://orcid.org/0009-0005-5019-299X
Web of Science Researcher ID: HOF‑4239-2023
Scopus ID: 57444853400
Svetikov Vladimir Vasilyevich, Cand. of Sc. (Phys.&Math.) General Physics Institute of the Russian Academy of Sciences; Head of the Integrated Photonics Department, JSC Zelenograd nanotechnology center
Scopus ID: 6508026938
ID RSCI: 23451716
Shipulin Arkady Vladimirovich, Dr.of Sc.(Phys.&Math.), Habilitation in Physics, Associate Professor, Skolkovo Institute of Science and Technology; CEO, Picstech LLC, Moscow, Russia.
Contributions
of the team of authors
I. A. Kazakov: development and implementation of the experiment, provision of the calculation formulas, experimental data processing, preparation and editing of the manuscript, coordination of the manuscript preparation work; K. M. Malakhov: implementation of the experiment, provision of drawings, preparation, and editing of the manuscript, coordination of works to submit the manuscript; E. E. Kovalev: implementation of the experiment, processing of the experimental results, preparation and editing of the manuscript; A. A. Mkrtchyan: development and implementation of the experiment, editing of the manuscript; M. S. Mishevskiy: implementation of the experiment, editing of the text of the manuscript; V. V. Svetikov: provision of the PIC-based AWGs and data related to the measurements of its specifications, editing of the manuscript text; A. V. Shipulin: guidance and support during the research, editing of the manuscript.
Conflict of interest
The authors declare no conflict of interest and agree with the distribution of contributions to the work.
I. A. Kazakov 1, 2, 3, K. M. Malakhov 1, 2, 3, E. E. Kovalev 1, A. A. Mkrtchyan 1, M. S. Mishevskiy 1, V. V. Svetikov 4, 5, A. V. Shipulin 1, 2
Skolkovo Institute of Science and Technology, Moscow, Russia
PICsTech LLC, Moscow, Russia
Fiber Flight LLC, Moscow, Russia
Zelenograd Nanotechnical Center JSC, Zelenograd, Moscow, Russia
Prokhorov Institute of General Physics of the Russian Academy of Sciences, Moscow, Russia
This paper presents analytical and experimental investigations of a fiber Bragg grating interrogator based on the arrayed waveguide grating made with a photonic integrated circuit technology. The key specifications of the interrogator are determined analytically based on the parameters of the arrayed waveguide grating used as a spectral demultiplexer and the photodetector’s operating error. In addition, the detection methods and algorithms for obtaining the reflectance spectrum maximum of fiber Bragg gratings are proposed and evaluated. Experimental measurements of the fiber Bragg grating central wavelength using the proposed algorithm are carried out, including calibration and measurement procedures using the data obtained under the influence of temperature and mechanical stress on the fiber Bragg grating. The system performance is experimentally confirmed with the accuracy of determination of a central wavelength of fiber Bragg grating reflection peak not less than 61 pm.
Keywords: interrogator, arrayed waveguide grating, fiber Bragg grating, photonic integrated circuit
Article received: February 20, 2024
Article accepted: March 05, 2024
Introduction
The optical interrogator is a device for collecting and analyzing data received from the fiber-optic sensors. This device is used to control various physical quantities, including temperature [1], mechanical stress, pressure, and displacement [2]. The interrogators have become widely applied in the structural monitoring systems for building and bridge structures [3], pipelines [4] and distillation columns [5], unmanned aerial vehicles [6], aircrafts [7] and satellites [8], chemical sensing systems [9] and other applications. The interrogator’s architecture is mainly determined by the type of sensors used. The configurations of devices for interrogating sensors based on a fiber Bragg grating (FBG) will be further considered.
The interrogator’s layouts for interrogating FBGs can be divided into two main groups: based on a mini-spectrometer and based on a tunable laser. Moreover, there are more over-the-top approaches based on radio-photonic methods [10], tunable filters [11], and their combinations [12]. The mini-spectrometer-based interrogators, including an interrogator based on an arrayed waveguide grating (AWG) on a photonic integrated circuit (PIC), provide a position detection accuracy of the FBG peak wavelength up to 0.32 pm [13], while the tunable laser-based interrogators provide less than 0.1 pm [14], and both layouts use the PIC technology to produce key elements of the device. One of the disadvantages of the AWG-based interrogator circuit is the low power arriving at the photodetectors, which is due to the low spectral power density of the broadband source and the narrow reflection spectrum of the FBG. However, this circuit is the simplest to implement, easily reconfigurable, and scalable. Moreover, it has a high interrogating rate, limited only by the operating frequency of photodetectors and electronics. The interrogators based on a tunable laser are more popular due to their versatility but have a significantly more comprehensive structure and operating algorithms. Due to the limited scanning rate, they have a lower sensor interrogating frequency. It is worth noting that the detection algorithm for a physical quantity is determined by the interrogator’s design and the type of interrogated sensors.
This article aims to develop and test an algorithm for use in the AWG-based FBG sensors interrogator with AWG on PIC. The developed algorithm can detect all types of FBG sensors (temperature, mechanical stress, etc.) as part of structural health monitoring systems.
Theory and calculation
Figure 1 shows a scheme of the AWG-based interrogator, including a superluminescent diode (SLD), a circulator, an FBG, an AWG, photodiodes (PD), and a signal processing system.
The operating principle of the AWG-based interrogator for interrogating sensors on the FBG is as follows. The light from a broadband SLD source is passed through a circulator to the sensors, the sensitive element of which is an FBG. Each FBG reflects radiation at a certain wavelength (λ1, λ2... λn) that is guided to the AWG input through the circulator. Depending on any changes in the external parameters, for example, temperature and/or mechanical stresses, the FBG period is changed, and consequently, the reflection spectrum maximum position is also changed. The AWG is used as a spectral-selective device since its output channels are spectrally equidistant from each other and transmit a narrow band of wavelengths in the vicinity of their maximum. The data processing system receives information related to any changes in the powers detected by PD1, PD2…PDm and converts it into the wavelength of the reflected radiation peak from each FBG sensor further rescaled into a measurable physical quantity.
Fig. 2 illustrates the operation methodology for the AWG-based interrogator. During operation, the maximum of the FBG reflection spectrum is predominantly located between two AWG channels. At each moment, the position of the FBG reflection spectrum maximum is determined based on the power values on adjacent channels.
In this paper, we will consider an approximation within which the FBG reflection spectrum represents the delta function (RFBG(λ) = δ(λ – λFBG)), and the FBG channel transmission spectrum represents the Gaussian function (1, 2). This approximation allows us to analytically review the system and obtain qualitative conclusions about its operation.
In the approximation used, the transmission spectra of AWG channels can be indicated as follows (1, 2):
; (1)
, (2)
where σch = σchn = σchn+1 – half-width of the channels that are equal to each other for one AWG;
λchn, λchn+1 – central wavelengths of the AWG channels.
The detected powers in the AWG channels will be as follows with due regard to the sifting property of the delta function:
; (3)
. (4)
In general, to determine the wavelength, it is necessary to obtain a calibration function in the space of Pn, Pn+1 that provides the most probable position of the FBG peak wavelength for the given values of Pn and Pn+1 or returns an error in the input data. In the general case, the number of AWG channels is m, and the number of detected FBG peaks is n. This problem is overdetermined and can be solved by many methods, including machine learning, in which case it is possible to use more channels per FBG for calculation, and the best results are expected.
In this paper, we propose to proceed from the fact that the main characteristic for the FBG wavelength determination is the ratio of powers on adjacent channels that, among other things, avoids disturbances introduced by variations in the radiation source power. It is also easier to be processed by the microcontrollers and requires less computing power. It is proposed at each moment of time to determine two channels with the highest optical power, then measure the power on each channel, to determine the ratio of the powers measured, and then, by using a two-dimensional calibration curve, to reconstruct the wavelength value of the FBG reflection spectrum maximum. An analytical description of this method is given below.
To solve the inverse problem of the wavelength determination, let us introduce the following calibration function:
. (5)
While substituting the expressions (3) and (4) into (5), we will get the following:
, (6)
where Δλ = λchn+1 – λchn – a distance between the AWG channels;
λC = (λchn+1 + λchn)/2 – a wavelength of the center between the AWG channels.
Next, we will calculate the FBG wavelength calculation error (λFBG):
, (7)
where δP = δP1 = δP2 – the power measurement error in the AWG channels.
We will assume that δP1 = δP2 = const. While substituting the values of partial derivatives into (7), we will determine the wavelength determination error (8):
. (8)
Thus, based on the calculations, it is found that the position determination error of the reflected spectrum maximum of the FBG sensor depends on the following parameters: the half-width of the AWG channels (σch), the distance between the AWG channels (Δλ), power measurement errors in the AWG channels (δP). The smallest error in the wavelength determination is made when the maximum is located at the point in the middle between the AWG channels (λc) and increases exponentially as it moves away from it.
Methods and materials
During the research, a test bench has been assembled, simulating the operation process of an interrogator. A calibration process has been performed, and the accuracy of the device’s operation has been assessed. Figure 3 shows the interrogator layout used in the experimental measurements, including the SLD, fiber amplifier (FA), circulator, FBG, AWG, power meter (PM).
An EXS210066-01 SLD produced by Exalos was used as a broadband source as a part of the experimental setup, and an SF8075-NM driver manufactured by Maiman Electronics was applied to control and supply power. The PEFA-SP-C-PM‑27-B130-FA-FA produced by Keopsys was used to amplify the SLD radiation. Two series-connected FBGs produced by Inversia-Sensor were applied as the sensors, the reflection spectra of which were measured at room temperature and in the absence of applied mechanical stress. The positions of the reflection spectrum maximums of the FBGs No. 1 and No. 2 at room temperature were 1545.90 and 1557.78 nm, and their widths at half maximum were 212 and 195 pm. This paper presents an analysis of experimental data related to the FBG No. 2 with a central wavelength of about 1557.78 nm.
A packaged 16‑channel PIC-based AWG module with a TEC controller, developed by FOTIS LLC and produced in the integrated photonics department of Zelenograd Nanotechnology Center JSC, was used as a demultiplexer [15]. During the measurements, the TEC controller maintained a constant temperature of the AWG module equal to the room temperature. To measure the transmission spectrum of the AWG channels and the FBG reflection spectrum, a Deviser AE8600 optical spectral analyzer was used, and the spectra were obtained with a wavelength resolution of 50 pm. The Thorlabs S132Cb optical power meters were used as the PDs. The experimentally obtained transmission spectra of the PIC-based AWG channels at room temperature, together with the FBG reflection spectra at room temperature and a temperature of 166 °C in the absence of mechanical stress, are shown in Fig. 4.
Results and discussion
Three experiments were performed as parts of the research: changes in the FBG temperature, changes in the FBG mechanical stresses, and simultaneous changes in both temperature and mechanical stresses. During the experiments, the following data were recorded: powers at all photodetectors, the wavelength of the FBG reflection peak (with a resolution of 50 pm), and, accordingly, the FBG temperature and mechanical stresses. As a part of this paper, only information related to the FBG No. 2 with a central wavelength of 1557.78 nm at room temperature and, accordingly, readings on the PDs connected to the AWG channels which filter the reflected light from the FBG (channel No. 1 and channel No. 2) are considered.
Data from the photodetectors on the AWG channels No. 1 and No. 2 is given in Fig. 5. This data is used to further plot the calibration curve and assess the FBG central wavelength determination error using this proposed interrogator scheme and method.
The data was divided into two sampling groups: calibration and verification. The calibration sampling group included information from experiments No.1 and No.2, and the verification sampling group included information from experiment No.3. According to the method proposed above, to evaluate the algorithm functioning were used only points whose wavelength lies in the range between the peaks of the AWG channels No. 1 and No. 2, as well as one point to the right and left around this range. The expression (5) was used as a calibration function, from which the decimal logarithm was taken for better visualization:
. (9)
The calibration function values for the test sampling group are presented in Fig. 6.
The logistic function (sigmoid) (Fig. 7) was used for approximation of the given points, indicated by the expression (10):
. (10)
The root-mean-square deviations of the measured wavelength from the true value for the calibration and validation data turned out to be 61 pm and 35 pm, respectively. These values have the same order of magnitude as the resolution of the optical spectrometer (50 pm), suggesting that the accuracy of this scheme may be less than or equal to the resolution of the spectrometer used, namely 50 pm. Therefore, the operating error of the given circuit is estimated to be less than or equal to 61 pm.
Conclusions
During this work, the analytical and experimental research of the FBG interrogator based on the PIC-based AWG was performed. The theoretical analysis leads to the dependence of the wavelength measurement error by the interrogator on the system key parameters, such as the measurement error of the photodetector and the width and distance between the AWG channels. It was shown that the FBG wavelength determination error, in general, depends on the FBG wavelength position relative to the AWG channels: the closer the FBG reflection spectrum peak is to the position between the AWG channels, the smaller the error, and the higher the accuracy of the interrogation. However, in the case when the channel width and the distance between the channels of AWG are equal, this dependence could be minimized. Also, during the work, it was concluded that the greater the distance between the AWG channels, the lower the interrogator’s accuracy.
As a part of experimental studies, an algorithm for calibration and subsequent detection of the FBG wavelength using an AWG on a photonic chip was tested. The calibration function was selected, namely the logistic function (sigmoid) (10), which most accurately described the behavior of the calibration function as a FBG peak wavelength function. The wavelength determination error was also estimated to be no more than 61 pm, which could not be limited from below due to the fact that the used resolution of the spectrometer was 50 pm.
In the future, we plan to conduct research using measuring equipment with a smaller instrumental error and collect a larger amount of information in order to determine the real accuracy of the interrogator. It is also scheduled to conduct an experiment using a larger number of AWG channels and several FBGs to demonstrate the algorithm and study its behavior under boundary conditions. In addition, experiments with a larger set of data are scheduled to be conducted to obtain a representative sampling group for a better statistical assessment of the interrogator’s operation and the interrogation algorithm for the FBG-based sensors. In addition, the research will be conducted in relation to other algorithms, both using machine learning procedures and other calibration functions.
In conclusion, the analytical description of the interrogator’s operation using the AWG as a demultiplexer was provided, and the interrogator algorithm accuracy with an error of no more than 61 pm was demonstrated that corresponded to the determination error of the temperature value of 6 oC on the used FBGs.
AUTHORS
Kazakov Ivan A., Master of Sc., PhD student, Research engineer, Skolkovo Institute of Science and Technology; Senior researcher, Picstech LLC, Moscow, Russia; CTO, Fiber Flight LLC, Moscow, Russia.
ORCID: 0000-0001-7509-1064
Web of Science ResearcherID: ADK-4828-2022
ID Scopus: 57203957427
ID RSCI: 4506-1355
Malakhov Kirill M., Master of Sc., PhD student, Research engineer, Skolkovo Institute of Science and Technology; Developer, Picstech LLC, Moscow, Russia; CEO, Fiber Flight LLC, Moscow, Russia.
ORCID: 0009-0004-1624-5018
Kovalev Egor Evgenievich, Bachelor of Sc., Master student, Laboratory assistant, Skolkovo Institute of Science and Technology, Moscow, Russia.
Mkrtchyan Aram A., Cand of Sc.(Phys.&Math.), Senior research scientist, Skolkovo Institute of Science and Technology, Moscow, Russia.
ORCID: https://orcid.org/0000-0002-6610-6006
Web of Science ResearcherID: AAP‑8995-2020
ID Scopus: 57200541614
ID RSCI 2718–5434
Mishevsky Mikhail Sergeevich, Master of Sc., PhD student, Skolkovo Institute of Science and Technology; Moscow, Russia.
ORCID: https://orcid.org/0009-0005-5019-299X
Web of Science Researcher ID: HOF‑4239-2023
Scopus ID: 57444853400
Svetikov Vladimir Vasilyevich, Cand. of Sc. (Phys.&Math.) General Physics Institute of the Russian Academy of Sciences; Head of the Integrated Photonics Department, JSC Zelenograd nanotechnology center
Scopus ID: 6508026938
ID RSCI: 23451716
Shipulin Arkady Vladimirovich, Dr.of Sc.(Phys.&Math.), Habilitation in Physics, Associate Professor, Skolkovo Institute of Science and Technology; CEO, Picstech LLC, Moscow, Russia.
Contributions
of the team of authors
I. A. Kazakov: development and implementation of the experiment, provision of the calculation formulas, experimental data processing, preparation and editing of the manuscript, coordination of the manuscript preparation work; K. M. Malakhov: implementation of the experiment, provision of drawings, preparation, and editing of the manuscript, coordination of works to submit the manuscript; E. E. Kovalev: implementation of the experiment, processing of the experimental results, preparation and editing of the manuscript; A. A. Mkrtchyan: development and implementation of the experiment, editing of the manuscript; M. S. Mishevskiy: implementation of the experiment, editing of the text of the manuscript; V. V. Svetikov: provision of the PIC-based AWGs and data related to the measurements of its specifications, editing of the manuscript text; A. V. Shipulin: guidance and support during the research, editing of the manuscript.
Conflict of interest
The authors declare no conflict of interest and agree with the distribution of contributions to the work.
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