Fibre-optic sensors

Why it matters

Fibre-optic sensors measure temperature, strain, pressure, displacement, current and chemical concentration using light inside glass. They carry no electrical energy to the measuring point, so they are intrinsically safe in explosive atmospheres, immune to electromagnetic interference near motors and transformers, light enough to embed in composite structures, and can be multiplexed so that one fibre carries dozens of measurement points over kilometres — as in bridge, pipeline, power-cable and oil-well monitoring.

Key ideas

Basic system. Source (LED, laser or broadband source) → fibre → modulation region where the measurand alters the light → fibre → detector and signal processing. The art lies in making the light change in a known, repeatable way with the measurand and in rejecting everything else.

Intrinsic and extrinsic.

• Extrinsic: the fibre only carries light to and from an external transducer — a moving mirror, a shutter, a diaphragm, a fluorescent tip or a gas cell.
• Intrinsic: the fibre itself is the sensing element — its loss, phase, polarisation or reflected wavelength changes with the measurand.

By the property modulated.

• Intensity: reflective displacement probes (light reflected from a target back into a receiving fibre varies with gap), microbend sensors (corrugated plates bend the fibre and couple light out as pressure rises), evanescent-wave and liquid-level sensors. Simple and cheap, but source drift, connector and bending losses look like signal, so a reference channel or ratio measurement is needed.
• Phase (interferometric): Mach–Zehnder, Michelson, Fabry–Perot and Sagnac arrangements convert tiny changes in optical path length into fringe shifts. Extremely sensitive (hydrophones, fibre-optic gyroscopes), but need coherent sources and careful signal processing.
• Polarisation: the Faraday effect rotates the plane of polarisation in proportion to the magnetic field along the fibre, giving optical current transformers for high-voltage lines.
• Wavelength: fibre Bragg gratings (FBGs) and fluorescence-decay thermometers. The information is in wavelength or time, not in absolute intensity, so it is immune to power fluctuations.

Fibre Bragg grating. A periodic modulation of core index with period Λ is written into a short length of fibre with UV light. It reflects a narrow band centred on the Bragg wavelength λ_B = 2n_eff·Λ and transmits the rest. Strain changes Λ and n_eff (through the photo-elastic effect); temperature changes Λ (thermal expansion α) and n_eff (thermo-optic coefficient ξ). The relative shift is Δλ_B/λ_B = (1 − p_e)·ε + (α + ξ)·ΔT. For silica at 1550 nm, with p_e ≈ 0.22, strain sensitivity is about 1.2 pm per microstrain and temperature sensitivity about 10 pm/K (take exact coefficients from the fibre data sheet). Because one grating responds to both, a strain-free reference grating is used for temperature compensation. Gratings with different λ_B on one fibre are read by wavelength-division multiplexing.

Distributed sensing. Using back-scattered light along an ordinary fibre — Raman (temperature, from the anti-Stokes/Stokes ratio) or Brillouin (strain and temperature, from frequency shift) — with optical time-domain reflectometry gives a continuous profile every metre over tens of kilometres; position follows from round-trip time z = c·t/(2n).

Advantages and limits. Advantages: EMI immunity, electrical isolation and intrinsic safety, small size and weight, high temperature and corrosion tolerance, remote and multiplexed operation. Limits: higher cost of interrogators, cross-sensitivity (strain versus temperature), fragility of bare fibre and sensitivity of intensity types to bend losses.

Formulas

λ_B = 2n_eff·Λ λ_B Bragg wavelength (m), n_eff effective index of the core mode, Λ grating period (m).

Δλ_B/λ_B = (1 − p_e)·ε + (α + ξ)·ΔT p_e effective photo-elastic coefficient (≈ 0.22 for silica), ε strain (dimensionless; 1 µε = 10⁻⁶), α thermal expansion coefficient (1/K), ξ thermo-optic coefficient (1/n)(dn/dT) (1/K), ΔT temperature change (K).

Loss(dB) = 10·log₁₀(P_ref/P) Intensity-sensor attenuation; P_ref and P in the same units.

z = c·t/(2n) z distance of a back-scattering point along the fibre (m), t round-trip time (s), n group index.

Worked examples

Example 1 (standard). An FBG has grating period 535.6 nm in a fibre with n_eff = 1.447. Find the Bragg wavelength, and its shift for 500 µε of strain at constant temperature (p_e = 0.22).

1. λ_B = 2n_eff·Λ = 2 × 1.447 × 535.6 nm = 1550.0 nm.
2. Δλ_B = λ_B(1 − p_e)ε = 1550 × 0.78 × 500 × 10⁻⁶ nm.
3. = 0.605 nm. Answer: λ_B ≈ 1550 nm; shift ≈ 0.60 nm.

Example 2 (GATE level). An FBG strain sensor at 1550 nm (p_e = 0.22, α + ξ = 6.7 × 10⁻⁶ /K) shows a total shift of 0.70 nm while the structure warms by 20 K. A strain-free reference FBG beside it measures the temperature. Find the thermal shift and the true strain.

1. Thermal shift = λ_B(α + ξ)ΔT = 1550 × 6.7 × 10⁻⁶ × 20 = 0.208 nm.
2. Strain shift = 0.70 − 0.208 = 0.492 nm.
3. ε = 0.492/(1550 × 0.78) = 4.07 × 10⁻⁴. Answer: thermal shift ≈ 0.21 nm; strain ≈ 407 µε (ignoring temperature would have reported about 579 µε).

Example 3 (intensity sensor). A reflective displacement probe is calibrated at 0.05 dB per µm of gap change. The received power falls from 100 µW to 80 µW. Find the displacement.

1. Loss = 10·log₁₀(100/80) = 0.969 dB.
2. Displacement = 0.969/0.05 = 19.4 µm. Answer: about 19.4 µm. A 0.97 dB connector or bend change would cause the same reading — the reason for a reference channel.

Common mistakes

• Treating FBG shift as proportional to strain alone; temperature produces a comparable shift.
• Using λ_B = n_eff·Λ (missing the factor 2 from the round-trip Bragg condition).
• Using microstrain values without the 10⁻⁶ factor.
• Writing ξ as dn/dT; in the shift formula it is (1/n)(dn/dT).
• Assuming intensity sensors are self-referenced. Source drift and bend losses must be compensated.
• Forgetting the factor 2 (round trip) when locating a point by time of flight in OTDR or distributed sensing.

For GATE IN

• Classification questions: intrinsic vs extrinsic; intensity, phase, polarisation and wavelength modulation.
• FBG Bragg wavelength and strain/temperature shift numericals.
• Intensity-sensor dB calculations and OTDR distance from time of flight.
• Advantages of fibre sensors for hazardous and high-EMI environments.

Quick check

1. An FBG has n_eff = 1.45 and Λ = 450 nm. What is λ_B?
2. Is a Faraday-effect current sensor intrinsic or extrinsic?
3. Approximate strain sensitivity of a 1550 nm FBG in pm/µε?
4. In OTDR, a reflection returns after 10 µs in fibre of n = 1.5. How far away is it? Answers: 1. 1305 nm. 2. Intrinsic. 3. About 1.2 pm/µε. 4. 1 km.