Fiber Bragg Grating Sensor

How a fiber Bragg grating works

Shine broadband light down an ordinary optical fiber and almost all of it travels through unchanged. Now imagine that somewhere in the glass core, over a centimetre-long stretch, the refractive index rises and falls in a regular ripple — a few hundred thousand thin, parallel "fences" of slightly higher index, each spaced about half a micron apart. At each fence a tiny fraction of the light reflects backward. For most colors those tiny reflections arrive out of step and cancel. But for one special wavelength they all add up in phase, and that color is reflected almost completely while everything else passes through. That mirror-for-one-color is a fiber Bragg grating.

The condition for the reflections to add coherently is the Bragg condition. It fixes the reflected wavelength precisely in terms of two physical quantities — how tightly the index ripple is spaced and how fast light travels through the core:

Bragg condition:    λ_B = 2 · n_eff · Λ

  λ_B    reflected (Bragg) wavelength
  n_eff  effective refractive index of the guided mode (~1.447 in SMF-28)
  Λ      grating period — spacing of the index ripple

Example:  n_eff = 1.447,  Λ = 535.6 nm
          λ_B = 2 × 1.447 × 535.6 nm = 1550 nm   (telecom C-band)

The key insight for sensing: anything that changes either Λ or n_eff changes the reflected wavelength. Stretch the fiber and you pull the ripple apart, increasing Λ; the photoelastic effect simultaneously nudges n_eff. Heat the fiber and the glass expands (changing Λ) while the thermo-optic effect changes n_eff far more strongly. In both cases the single reflected peak slides up or down the spectrum. Read where that peak sits and you have read the strain and temperature at that exact spot in the fiber — no electronics at the sensing point, just glass.

The governing physics: strain and temperature shift

Differentiate the Bragg condition and you get the master sensing equation. The fractional wavelength shift is the sum of a strain term and a temperature term:

Δλ_B / λ_B  =  (1 − p_e)·ε   +   (α + ξ)·ΔT

  p_e   effective photoelastic constant  ≈ 0.22   →  (1 − p_e) ≈ 0.78
  ε     axial strain (microstrain, µε = 1e-6)
  α     thermal expansion of silica      ≈ 0.55e-6 /°C
  ξ     thermo-optic coefficient         ≈ 6.7e-6 /°C   (dominant)
  ΔT    temperature change (°C)

Put numbers in at λ_B = 1550 nm and the two sensitivities pop out as practical pm-per-unit figures engineers actually quote:

Strain:       Δλ_B = λ_B·(1 − p_e)·ε
              = 1550 nm × 0.78 × 1e-6  per µε
              ≈ 1.2 pm / µε

Temperature:  Δλ_B = λ_B·(α + ξ)·ΔT
              = 1550 nm × 7.25e-6  per °C
              ≈ 11 pm / °C  (often quoted 10–13 pm/°C)

So a high-quality interrogator that resolves wavelength to 1 pm resolves about 0.8 µε of strain or 0.08 °C of temperature. A 1000 µε strain event — roughly the working strain of a loaded steel beam — moves the peak by 1.2 nm, an enormous, easily measured shift. And here is the unavoidable consequence written right in the equation: both terms move the same peak. A bare grating cannot, by itself, tell whether the wavelength moved because the structure stretched or because the sun came out. Resolving that ambiguity — temperature compensation — is the central design problem of every real FBG strain installation.

Reading the peak: the interrogator

An FBG by itself is passive — the cleverness lives in the box that reads it, the interrogator. It launches light into the fiber, captures the reflected spectrum, and computes the centroid of each Bragg peak to a fraction of a picometer. Two architectures dominate:

• Swept-laser interrogators. A tunable laser sweeps across the band (say 1510–1590 nm) at kilohertz rates; a photodiode records reflected power versus instantaneous wavelength. High optical power, excellent signal-to-noise, picometer resolution, and dynamic sampling into the kHz range for vibration. Most expensive.
• Broadband-source + spectrometer interrogators. A wideband source (SLED/ASE) illuminates all gratings at once; a fixed grating spectrometer with a detector array images the whole reflected spectrum in one shot. Cheaper, rugged, no moving parts, but lower resolution and slower update.

Either way, the measured quantity is purely a wavelength — a color — which is why FBGs are called intrinsically self-referencing: source power can fade, connectors can attenuate, the fiber can bend, and the peak still sits at the same wavelength. That stability against intensity drift is a decisive advantage over intensity-based optical sensors.

Many sensors, one fiber: wavelength-division multiplexing

The feature that made FBGs win the structural-sensing market is that each grating answers on its own color. Write grating 1 at Λ giving a 1530 nm peak, grating 2 at 1535 nm, grating 3 at 1540 nm, and so on. The interrogator sees a comb of peaks and tracks each independently. This is wavelength-division multiplexing (WDM), and it lets one thin fiber and one connector replace a thick loom of wires.

Sensor budget on one fiber (WDM):

  Source / interrogator window:        ~40 nm  (e.g. 1525–1565 nm)
  Wavelength slot per sensor:          ~1.0 nm
     measurement range (±2500 µε):     ±3 nm worst case → trim to expected range
     plus guard band so peaks never overlap
  Typical practical count:             15 – 40 sensors / fiber

  Add time-division (pulsed) or frequency-domain schemes
  → hundreds to thousands of weak gratings on a single line.

The constraint is the spectral budget: if you allow large strain ranges, each peak needs a wider slot and fewer sensors fit. Designers size the per-sensor wavelength window to the expected strain at each location so peaks never collide as they move.

Comparison: FBG vs other strain & temperature sensors

	Fiber Bragg grating	Foil strain gauge	Vibrating wire	Thermocouple (temp)	Distributed fiber (DTS/DAS)
Sense point	Discrete (each grating)	Discrete	Discrete	Discrete (junction)	Continuous along fiber
Points per cable	15–40 (1000s w/ TDM)	1 per pair of wires	1 per cable	1 per pair of wires	1000s (per metre)
EMI immunity	Total (optical)	Poor	Good	Moderate	Total
Strain sensitivity	~1.2 pm/µε; ~1 µε res.	~1 µε	~1 µε	n/a	~1–10 µε
Temp range	−40 to 300 °C (regen. to 800+)	−75 to 200 °C	−20 to 80 °C	−200 to 1700 °C	−40 to 700 °C
Update rate	Up to kHz (swept laser)	kHz+	~1 Hz (pluck/read)	Hz	Hz to minutes
Intrinsically safe	Yes (no current)	No	No	No	Yes
Readout cost	$3k–$40k interrogator	~$5 gauge + bridge	~$200 + readout	~$10 + meter	$30k+ analyser

Real numbers and where FBGs are used

FBGs moved out of the lab in the 1990s and are now standard instrumentation wherever many measurement points, electromagnetic noise, long distances, or harsh chemistry rule out copper. Representative figures and systems:

Application	What is measured	Why FBG
Bridge & dam structural health monitoring	Strain, deflection, temperature over decades	Dozens of points on one fiber, lightning-immune, no drift; e.g. cable-stayed bridges instrument main cables and deck girders
Wind-turbine blade load sensing	Root bending strain (live, per blade)	Lightning strikes the blade routinely; an all-glass sensor carries no current and feeds active pitch control to shed gust loads
Aircraft & spacecraft composites	In-layup strain, cure monitoring, impact	Fiber thinner than a human hair (≈125 µm cladding) embeds between plies; lightweight, distributed; flown on demonstrators and launch tanks
Oil & gas downhole sensing	Pressure, temperature to 150–300 °C, km depth	One fiber runs the whole well; survives heat and pressure where electronics fail; permanent reservoir monitoring
High-voltage power equipment	Transformer winding & busbar temperature	Sits inside live HV insulation with zero electrical connection — impossible for a thermocouple
Rail & pipeline monitoring	Track strain, wheel loads, pipe ovality / leaks	Tens of kilometres of route on a few fibers; immune to traction-current EMI
Telecom / lasers (non-sensor use)	Wavelength filtering, DFB stabilization, DWDM	The same device is a precision wavelength reference and add/drop filter — sensing was a spin-off of the telecom grating

Typical hardware envelope: a single grating is 5–10 mm long; reflectivity is engineered from a few percent (weak, for dense multiplexing) up to >99% (strong, for a single high-quality sensor); spectral width 0.1–0.3 nm. Standard gratings drift and erase if held above ~300 °C, so high-temperature work uses regenerated or femtosecond-written gratings stable to 800–1000 °C. Interrogators range from roughly $3,000 for a slow broadband unit to $40,000+ for a multi-channel kHz swept-laser system.

Design tradeoffs and failure modes

• Strain–temperature cross-talk. The single biggest field error. One grating sees Δλ from both effects; uncompensated, a 10 °C ambient swing masquerades as roughly 100 µε. The standard fix is a co-located reference grating in a strain-isolating loose tube (temperature only) that is subtracted, or a dual-grating matrix that solves for both unknowns.
• Strain transfer and bonding. The grating only reads what reaches the core. A poorly bonded patch, a thick soft adhesive, or a recoat that creeps under load means the fiber strains less than the structure, reading low. Surface-mount patches and embedment in composite plies are engineered for high strain transfer; calibration accounts for the rest.
• Fiber fragility and handling. Bare 125 µm fiber is glass and snaps if kinked, nicked, or over-bent below its minimum bend radius. Practical sensors are packaged in metal tubes, polymer patches, or composite tapes. A single break kills every downstream grating on a TDM line.
• Chirp and peak distortion under non-uniform strain. If strain varies along the 5–10 mm grating (a strain gradient, or transverse load), the period is no longer uniform and the once-sharp peak broadens, splits, or chirps — degrading the centroid the interrogator relies on. Keep gratings short relative to the strain field, or use the broadening as extra information.
• Anneal-out at high temperature. The UV-induced index change relaxes with heat and time; standard Type-I gratings fade above ~300 °C and erase by ~450 °C. Use regenerated or fs-written gratings for furnaces, turbines, and downhole.
• Polarization and birefringence. Transverse load makes the fiber birefringent, splitting the peak into two polarization states — a problem for high-precision work, exploited deliberately in transverse-load and shape sensors.

How gratings are written

• Phase-mask UV writing. The workhorse. UV light (244 nm doubled argon-ion or 248 nm KrF excimer) passes through a fused-silica phase mask whose surface corrugations diffract it into ±1 orders; their interference pattern photo-imprints the index ripple into germanium-doped, often hydrogen-loaded, photosensitive core. The period is set by the mask geometry — not the laser wavelength — giving superb repeatability and easy mass production.
• Interferometric (Talbot) writing. A UV beam is split and recombined at an adjustable angle; tuning the angle tunes the period continuously, so any Bragg wavelength can be written from one setup. Flexible but alignment-sensitive.
• Femtosecond point-by-point. A focused IR femtosecond laser writes index changes plane by plane in any fiber — including pure-silica, sapphire, and uncoated fibers — for gratings stable to 1000 °C. No photosensitivity or hydrogen loading needed.
• Draw-tower gratings. Written in-line during fiber drawing, in the millisecond window after the glass solidifies but before the protective coating is applied. The pristine, never-stripped fiber gives the highest mechanical strength and most uniform sensors — ideal for embedment and long-life monitoring.

Common misconceptions and pitfalls

• "The grating measures light intensity." No — it measures wavelength. That is the whole point: intensity drifts with source aging, bends, and connector loss, but the peak's position does not. An FBG system that tries to infer strain from reflected power is throwing away its main advantage.
• "One grating gives you strain." One grating gives you a wavelength that mixes strain and temperature. Without a temperature reference you do not have a calibrated strain measurement, full stop.
• "More reflectivity is always better." A near-100% grating is great as a single sensor but spectrally greedy and can spawn side lobes; for dense multiplexing you deliberately write weak (few-percent) gratings so many fit in the band and downstream ones still see light.
• "It's just like a fiber laser mirror." Physically yes — the same Bragg structure stabilizes DFB lasers and builds fiber lasers. As a sensor, though, the goal is the opposite: you want the wavelength to move with the environment, not stay locked.
• "FBG and distributed sensing (DAS/DTS) are the same thing." They are different. FBGs are discrete sensors at written points; DAS/DTS use Rayleigh/Raman/Brillouin scattering in plain fiber to sense continuously everywhere. They are often deployed together — discrete high-accuracy FBGs plus continuous distributed coverage.
• "Bend the fiber and you lose the reading." Macro-bending attenuates power but, because the measurand is wavelength, the peak position is unaffected until loss is severe enough to bury the peak in noise — the self-referencing property in action.