# Compact Interrogation System of Fiber Bragg Grating Sensors Based on Multiheterodyne Dispersion Interferometry for Dynamic Strain Measurements

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## Abstract

**:**

## 1. Introduction

## 2. Principle of Measurement

#### 2.1. Electro-Optic Dual Optical Frequency Comb

_{0}splits into two arms, each one corresponding to an optical frequency comb generated by an electro-optic phase modulator (EOM). The frequency applied to EOM

_{1}is slightly different to the frequency applied to EOM

_{2}. The optical frequency of one arm is shifted by an acousto-optic modulator (AOM). Both arms are combined to beat the two optical frequency combs and, as a result, a multi-heterodyne interferometer is obtained. The signal revealed on a photo-detector is a replica of the optical frequency comb around ${f}_{0}$ (frequency spacing: ${f}_{pm1}$ − ${f}_{pm2}$) that is downshifted to a frequency comb around ${f}_{shift}$ (frequency spacing: ${f}_{pm1}$ − ${f}_{pm2}$). Note that ${f}_{0}$ >> ${f}_{pm1}$, ${f}_{pm2}$, ${f}_{shift}$ and that the two combs are coherent because they come from the same highly coherent seed.

#### 2.2. Compact Dual-Drive Electro-Optic Dual Optical Frequency Comb

#### 2.3. Multiheterodyne Dispersion Interferometer

## 3. Methods

#### 3.1. Experimental Set-Up

#### 3.2. Demodulation

#### 3.3. Calibration

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Basic scheme of an electro-optic dual optical frequency comb connected to a photodetector. EOM, electro-optic phase modulator; signal generators of EOM at frequencies f

_{pm}

_{1}and f

_{pm}

_{2}; AOM, acousto-optic modulator; signal generator of AOM at frequency f

_{shift}; PD, photodetector.

**Figure 2.**Electro-optic dual optical frequency comb spectra: (

**a**) two optical frequency combs of slightly different frequencies applied to the phase modulator; (

**b**) two optical frequency combs with additional frequency shifts; and (

**c**) photo-detected comb as the beat response of the dual comb of (

**b**).

**Figure 3.**Basic scheme of a dual optical frequency comb (DOFC) generated by a dual-drive Mach–Zehnder modulator (DD-MZM) and phase-generated carrier (PGC). PM, phase modulator.

**Figure 4.**Basic scheme of the multiheterodyne dispersion interferometer for interrogating a fiber Bragg grating (FBG). DOFC, dual optical frequency comb; DD-MZM, dual-drive Mach–Zehnder modulator; FOC, fiber optic coupler/splitter; PD, photo-detector. The arrows indicate the direction of propagation of the light.

**Figure 5.**Principle of measurement based on a multiheterodyne dispersion interferometer to interrogate an FBG: (

**a**) example of photo-detected output of a dispersion interferometer with an FBG obtained with a SLED and an optical spectrum analyzer (OSA); (

**b**) sampling of specific wavelengths with a DOFC for an optical phase read-out.

**Figure 7.**DOFC read-out on the photo-detector. Detected signal with multiple read-out combs, each one centered on one carrier of the multiple carriers generated by the PGC.

**Figure 8.**Demodulation algorithm implementation with analog mixers, differential stage and low-pass filtering. PD, photodetector at the output of Figure 4.

**Figure 9.**Vibration assembly for the calibration system and FBG sensor. LD2, laser diode of the calibration interferometer; PD2, photodetector; AOM, acousto-optic modulator.

**Figure 10.**Reference of the calibration obtained with the heterodyne interferometer for an excitation of the PZT transducer of 20 V and 20 kHz. Signal on the photodetector PD2.

**Figure 11.**Amplitude stability of the proposed system with the EOM-AOM DOFC architecture and the DD-MZM in-chip DOFC architecture.

**Figure 13.**Detected vibration signals after the lock-in amplification stage: (

**a**) calibrated measurement of the FBG dynamic strain at 30 kHz equivalent to 0.1 rad over a 10 cm length of fiber; (

**b**) frequency sweep of the mechanical vibration.

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**MDPI and ACS Style**

Poiana, D.A.; Posada-Roman, J.E.; Garcia-Souto, J.A.
Compact Interrogation System of Fiber Bragg Grating Sensors Based on Multiheterodyne Dispersion Interferometry for Dynamic Strain Measurements. *Sensors* **2022**, *22*, 3561.
https://doi.org/10.3390/s22093561

**AMA Style**

Poiana DA, Posada-Roman JE, Garcia-Souto JA.
Compact Interrogation System of Fiber Bragg Grating Sensors Based on Multiheterodyne Dispersion Interferometry for Dynamic Strain Measurements. *Sensors*. 2022; 22(9):3561.
https://doi.org/10.3390/s22093561

**Chicago/Turabian Style**

Poiana, Dragos A., Julio E. Posada-Roman, and Jose A. Garcia-Souto.
2022. "Compact Interrogation System of Fiber Bragg Grating Sensors Based on Multiheterodyne Dispersion Interferometry for Dynamic Strain Measurements" *Sensors* 22, no. 9: 3561.
https://doi.org/10.3390/s22093561