FBG sensor

An FBG sensor is a fiber Bragg grating whose reflected wavelength is used as the measurement. The grating reflects a narrow band, typically 0.1–0.3 nm wide, centered on the Bragg wavelength $\lambda_B = 2 n_{eff} \Lambda$. Stretching the fiber lengthens the period $\Lambda$ and changes the index; heating it does the same through thermal expansion and the thermo-optic effect. At 1550 nm the reflected peak moves by about 1.2 pm per microstrain (µε) and by about 10 pm per kelvin, so an interrogator that locates the peak to 1 pm resolves about 0.8 µε or 0.1 K. The device physics of the grating itself is covered under fiber Bragg grating; this entry covers its use as a fiber-optic sensor.

Strain and temperature response

The fractional wavelength shift is the sum of a strain term and a temperature term:

$$\frac{\Delta\lambda_B}{\lambda_B} = (1 - p_e)\,\varepsilon + (\alpha + \xi)\,\Delta T$$

Here $p_e \approx 0.22$ is the effective strain-optic coefficient of silica, $\alpha \approx 0.55 \times 10^{-6}$ K⁻¹ its thermal expansion coefficient and $\xi$ its normalized thermo-optic coefficient, $(1/n)\,dn/dT$, about $6$–$9 \times 10^{-6}$ K⁻¹ depending on the fiber. At $\lambda_B$ = 1550 nm:

• strain: $0.78 \times 1550$ nm $\times 10^{-6}$ = 1.21 pm/µε, so 100 µε shifts the peak by 121 pm;
• temperature: 10–13 pm/K from the range of $\xi$; the thermo-optic term dominates.

Both coefficients scale with $\lambda_B$, so a grating at 830 nm is about half as sensitive in picometers. They should be calibrated for the fiber type in use, particularly the temperature coefficient.

Cross-sensitivity and packaging

A temperature change of 1 K produces the same shift as about 8 µε, so an uncompensated strain sensor in an environment that swings by 10 K carries an error near 80 µε. The standard remedy is a second, strain-free reference grating at the same temperature, whose shift is subtracted. Other schemes use two gratings with different sensitivities (different wavelengths, fiber types or claddings) and solve the two equations for both unknowns.

Mounting changes the temperature coefficient. A grating bonded to a steel structure ($\alpha \approx 12 \times 10^{-6}$ K⁻¹) is strained by the steel's expansion, which adds about $0.78 \times (12 - 0.55) \times 10^{-6} \times 1550$ nm ≈ 14 pm/K to the free-grating value. Whether that thermal strain should be removed depends on whether the user wants total strain or only load-induced strain. Temperature sensors, conversely, are packaged loose in a tube so that no strain reaches the grating. Strain transfer through polyimide or acrylate coatings and adhesive is incomplete over short bond lengths, so gauge factors are calibrated in the final installation.

Interrogation

The interrogator measures the reflected spectrum and finds each peak. Three architectures are common:

• Broadband source and spectrometer. A superluminescent diode or ASE source illuminates the array through an optical circulator, and a grating spectrometer with an InGaAs line camera records the reflection. There are no moving parts, and rates of kHz are possible.
• Swept laser. A tunable laser sweeps across the band while a photodiode records the reflection against a wavelength reference, such as a gas cell or an etalon. This gives higher power per grating, longer reach and picometer-level accuracy, usually at lower sweep rates.
• Edge filter or ratiometric detection. The peak is placed on the slope of a filter and the ratio of transmitted to reference power is read. It is fast and simple, but covers a small range and suits dynamic measurements.

Peak location uses centroid, Gaussian or polynomial fits over several spectral samples, which is why the wavelength resolution can be much finer than the spectrometer pixel.

Multiplexing

Many gratings on one fiber are distinguished by wavelength, in the manner of wavelength-division multiplexing. Each sensor needs a window wide enough for its full measurement range. A strain range of ±2000 µε takes 4.8 nm, a 100 K temperature range adds 1.0 nm, and with a guard band the sensor occupies about 7 nm; an 80 nm source then supports about 11 sensors. Time-division multiplexing with weak gratings of identical wavelength, read like reflectometer events, extends a single fiber to hundreds or thousands of points at lower sampling rates.

Pitfalls

• Transverse load makes the fiber birefringent, splitting the peak in two and corrupting the fit.
• Standard UV-written gratings decay above about 300 °C; high-temperature sensing uses regenerated or femtosecond-written gratings.
• Strong reflections from connectors or unrelated gratings in the band produce false peaks.

Common questions

What is the strain sensitivity of an FBG?

About 1.2 pm/µε at 1550 nm, from $(1 - p_e)\lambda_B$ with $p_e \approx 0.22$. At 1310 nm it is about 1.0 pm/µε.

How is strain separated from temperature in an FBG sensor?

With a strain-isolated reference grating that sees only temperature, subtracted from the strained grating, or with two gratings of different known sensitivities solved simultaneously. A separate electrical temperature sensor is also used where available.

How many FBG sensors can be placed on one fiber?

With wavelength multiplexing, typically 10–40, depending on each sensor's range and the source bandwidth. Time- or frequency-domain multiplexing of weak identical gratings reaches hundreds to thousands.

References: A. D. Kersey et al., J. Lightwave Technol. 15, 1442 (1997); A. Othonos, K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999); R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic Press, 2010).