# Incoherent Optical Frequency-Domain Reflectometry Based on Homodyne Electro-Optic Downconversion for Fiber-Optic Sensor Interrogation

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Amplitude-Modulated Incoherent Frequency-Domain Reflectometry

#### 2.2. I-OFDR Using Homodyne Electro-Optic Downconversion

## 3. Experimental System and Signal Processing

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schemes of stepped-frequency I-OFDR systems based on (

**a**) vector network analysis; and (

**b**) electro-optic downconversion. Photonic components are represented in green; RF and electronic components in blue.

**Figure 2.**Backscattering transfer function $10log\phantom{\rule{0.166667em}{0ex}}|{H}_{s}\left(f\right)|$ of SMF at 1.55 $\mathsf{\mu}$m for different fiber lengths: 30 km (blue), 3 km (orange), and 300 m (yellow).

**Figure 3.**System setup. ADC, analog-to-digital converter; AMP, RF amplifier; LF, low-frequency signal generator; FUT, fiber under test; MZM, Mach–Zehnder modulator; PBBS, polarized broadband source; PC, polarization controller; PD, photodiode; RF, stepped RF source. Dashed lines stand for TTL signaling indicating RF steps (Steps) and reference tone (Ref).

**Figure 4.**Interferogram constellations ${A}_{c}\left[k\right]exp(-j\theta )$ after in-phase demodulation and rotation of: (

**a**) a flat fiber end; (

**b**) a 10-km SMF Rayleigh backscattering; and (

**c**) system’s noise level when the RF signal is turned off but the optical source is on (blue), and when both RF and optical sources are off (orange), also for a 10-km SMF spool. The number of points in each constellation, or number of I-OFDR frequency steps ${f}_{k}$, is 5000.

**Figure 5.**(

**a**) Spectral interferogram ${H}_{n}\left[k\right]$ used for normalization and calibration, where the FUT is the reflection in a flat fiber end located 1 m after the circulator. Inset: Zoom over the 9-GHz region. Points are ${H}_{n}\left[k\right]$ samples; (

**b**) Normalized and calibrated interferogram $H\left[k\right]$, where the flat fiber end is situated 3 m after the calibration plane. Notice the constant level in a 10-GHz bandwidth and the trimming of $H\left[k\right]$.

**Figure 6.**(

**a**) System measurements limited by dynamic range (attenuated PC-air reflection, red) and sensitivity, (APC-air reflection, blue); and (

**b**) peak (orange) and rms noise floor (blue) levels for progressively attenuated PC-air reflections.

**Figure 7.**(

**a**) FBG array measurement with orthogonally polarized light; (

**b**) addition of traces on (

**a**)) with (orange) and without (blue) CFBG right before down-converting MZM; and (

**c**) FBG array reflectivity spectrum with resolution bandwidth 0.5 nm (blue) and 0.06 nm (orange).

**Figure 8.**Zoom view of the two rightmost reflective peaks of Figure 7c, corresponding to the FBG at ∼1554 nm, with (blue) and without (orange) dispersive element. The window used here is rectangular.

**Figure 9.**(

**a**) Reflectometric traces, in $10log$ scale, of a 10-km spool of SMF using I-OFDR (blue) and a commercial OTDR (orange); (

**b**) I-OFDR traces for 10-km SMF with $B=20\mathrm{MHz}$ (blue) and $B=5\mathrm{MHz}$ (orange); (

**c**) I-OFDR (blue) and commercial OTDR (orange) measurements for the 10-km SMF coil followed by a 3-dB attenuator and 1.6 km of SMF; and (

**d**) I-OFDR traces for 1.6-km SMF ended in PC (blue) and APC (orange) connectors. The acquisition time was 30 s at a pulse width of 1 $\mathsf{\mu}$s for the OTDR and ≲2 min for the I-OFDR.

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**MDPI and ACS Style**

Clement, J.; Maestre, H.; Torregrosa, G.; Fernández-Pousa, C.R.
Incoherent Optical Frequency-Domain Reflectometry Based on Homodyne Electro-Optic Downconversion for Fiber-Optic Sensor Interrogation. *Sensors* **2019**, *19*, 2075.
https://doi.org/10.3390/s19092075

**AMA Style**

Clement J, Maestre H, Torregrosa G, Fernández-Pousa CR.
Incoherent Optical Frequency-Domain Reflectometry Based on Homodyne Electro-Optic Downconversion for Fiber-Optic Sensor Interrogation. *Sensors*. 2019; 19(9):2075.
https://doi.org/10.3390/s19092075

**Chicago/Turabian Style**

Clement, Juan, Haroldo Maestre, Germán Torregrosa, and Carlos R. Fernández-Pousa.
2019. "Incoherent Optical Frequency-Domain Reflectometry Based on Homodyne Electro-Optic Downconversion for Fiber-Optic Sensor Interrogation" *Sensors* 19, no. 9: 2075.
https://doi.org/10.3390/s19092075