FBG Optical Fiber Temperature Estimator

Developed by Dr. Farhan Mumtaz | Optical Fiber Bragg Wavelength Shift & Thermal Regression Engine

Select your optical fiber type, specify your reference baseline room-temperature Bragg wavelength (λ₀), and input the measured peak wavelength under thermal load. The model computes temperature strictly within calibrated domain boundaries.

Select Optical Fiber Type:

Polynomial Fitting Order:

Reference Baseline (λ₀, nm):

Measured Peak Wavelength (λ, nm):

Calibration Curve: Wavelength (nm) vs. Temperature (°C)

Fitted Calibration Equation

—

R² = —

λ in nm, T in °C, fit against — using this fiber's calibration dataset, rescaled to your chosen λ₀

Fiber Cross-Sections

Real cross-section micrographs of all six optical fibers used in the calibration models above — each image shows the full fiber cross-section.

Cross-section micrograph of Silica SMF-28e single-mode optical fiber showing the ~8.2 µm core centered in a 125 µm cladding — **Silica (SMF-28e)** — 125 µm clad, ~8.2 µm core

Cross-section micrograph of coreless silica optical fiber, a solid uniform-index rod with no discrete core — **Coreless Silica**

Cross-section micrograph of single-crystal sapphire optical fiber, showing its faceted multimode geometry — **Single-Crystal Sapphire**

Cross-section micrograph of Lu2O3 crystalline optical fiber measuring approximately 104.7 by 80.9 microns — **Lu₂O₃** — 104.7 × 80.9 µm

Cross-section micrograph of spinel (MgAl2O4) crystalline optical fiber — **Spinel (MgAl₂O₄)**

Cross-section micrograph of copper-coated single-mode optical fiber, showing the metallic Cu jacket around the silica cladding — **Copper-Coated SMF**

All six optical fibers used in the calibration models above are shown here.

FBG Inscription Techniques

Two femtosecond-laser writing methods used to inscribe the gratings behind these calibration curves.

Side-by-side microscope comparison of point-by-point FBG inscription in single-mode fiber, showing a ~125 µm clad and ~8.2 µm core with discrete index points, versus line-by-line FBG inscription in sapphire fiber, showing continuous transverse grating lines across a 125 µm span with a 90 µm period window — Microscope comparison: point-by-point inscription (single-mode silica fiber, left) vs. line-by-line inscription (sapphire multimode fiber, right).

Point-by-Point FBG (Single-Mode Fiber)

A tightly focused femtosecond pulse modifies the refractive index at a single point inside the ~8.2 µm core; the fiber steps forward and the next point is written, building the grating one discrete index modification at a time along the core axis. Because silica SMF is intrinsically photosensitive and single-moded, a sub-micron focal spot reliably couples into the fundamental mode, giving precise control over grating period and apodization — the standard approach for silica-based FBG sensors.

Line-by-Line FBG (Sapphire, Multimode)

Each grating plane is inscribed as a full transverse line across the fiber's cross-section in one femtosecond-laser pass, then the fiber advances and the next line is written. Single-crystal sapphire is extremely hard, chemically inert, and not intrinsically photosensitive at typical writing fluences, so a single tightly-focused point cannot build a usable index contrast — a scanned line integrates enough modified volume across the multimode core to produce a strong, high-temperature-stable reflection, at the cost of coarser period control than point-by-point writing.

Both techniques modify the local refractive index with a femtosecond laser to form a periodic Bragg structure; the difference is whether that structure is built one focal point or one full line at a time.

Associated Calibration & Research Publications

The calibration models integrated into this tool are backed by peer-reviewed research publications and technical reports:

Silica SMF-28e & EAF Bottom Anode Applications: "Advancing Temperature Monitoring of the Bottom Anode in Direct Current Electric Arc Furnace Operations with Distributed Optical Fiber Sensors," IEEE Transactions on Instrumentation and Measurement, 2025.
Continuous Metal Temperature Monitoring in CPI and Refinery Applications: "Fiber Optics for High Temperature Applications (408) Final Report," Materials Technology Institute (MTI).
Coreless Silica Fiber Annealing & Stability: "Ultrafast annealing improves SNR and long-term stability of a highly multiplexed line-by-line FBG array inscribed by femtosecond laser in a coreless fiber for extreme applications," IEEE Transactions on Instrumentation and Measurement, vol. 73, pp. 1-10, 2024.
Single-Crystal Sapphire Fiber (Coincident FBGs): "Discrimination of Temperature and Strain by Characterizing Two Femtosecond Laser-Written Coincident Sapphire Fiber Bragg Gratings for Harsh Environment Applications," IEEE Transactions on Instrumentation and Measurement, vol. 73, pp. 1-8, 2025.
Lu₂O₃ Crystalline Optical Fiber: "Femtosecond laser inscription of fiber Bragg gratings in lutetium oxide (Lu₂O₃) single-crystal optical fiber for ultra-high-temperature sensing," Optics Letters, 2026.
Spinel (MgAl₂O₄) Optical Fiber: "High-temperature performance of femtosecond laser inscribed MgAl2O4 spinel fiber Bragg gratings," Optics Letters, vol. 51, pp. 2644–2647, 2026.
Copper-Coated SMF Optical Fiber: "Multilayer metal-coated fiber Bragg grating for high-temperature sensing," X. Wang, X. Sun, Y. Hu, J. Duan, Measurement, vol. 226, 114132, 2024.

Frequently Asked Questions (FAQ)

1. Which optical fibers does this FBG calibration tool support?

This tool includes calibration models for six optical fibers: Silica (SMF-28e), Coreless Silica, Single-Crystal Sapphire, Lu₂O₃ (lutetium oxide), Spinel (MgAl₂O₄), and Copper-Coated SMF. Each has its own polynomial fit derived from that fiber's measured Bragg wavelength shift versus temperature, valid up to that fiber's tested domain limits (as high as roughly 1600°C for the crystalline fibers). Cross-section micrographs of all six appear further down this page.

2. What is the Reference Baseline (λ₀) in an FBG calibration?

The reference baseline is the initial Bragg grating wavelength measured at standard room temperature (typically 24°C to 25°C) before the optical fiber experiences any thermal load. Changing this scales the normalization formula relative to your specific sensor's baseline.

3. Why do different optical fibers require distinct FBG calibration datasets?

Silica, single-crystal sapphire, lutetium oxide (Lu₂O₃), and spinel (MgAl₂O₄) possess entirely different coefficient of thermal expansion (CTE) and thermo-optic properties. Their thermal response curves behave non-linearly at high temperatures, requiring material-specific polynomial models.

4. What is the difference between 1st, 2nd, and 3rd order polynomial fitting for FBG temperature calibration?

A 1st order fit assumes a linear thermal response (constant sensitivity). However, high-temperature optical materials experience thermal expansion non-linearities. 2nd (Quadratic) and 3rd (Cubic) order fits capture these curve variations more accurately across extreme ranges up to 1600°C, generally at the cost of extrapolation stability outside the calibrated range.

5. What happens if a measured FBG wavelength falls outside the calibration domain?

To prevent inaccurate extrapolations or false data reporting, the engine features built-in domain bounds. If a wavelength falls outside verified empirical limits, a warning alert triggers to block uncalibrated estimation.

6. What is the difference between point-by-point and line-by-line FBG inscription?

Point-by-point inscription focuses a femtosecond laser pulse to modify the refractive index at a single point inside the core, stepping forward one index modification at a time — used here on single-mode silica fiber (SMF). Line-by-line inscription writes each grating plane as a full transverse line across the fiber in one pass — used here on single-crystal sapphire multimode fiber, whose hardness and lack of intrinsic photosensitivity make point-by-point writing impractical. See the micrograph comparison below.

Dr. Farhan Mumtaz

Assistant Research Professor, Electrical & Computer Engineering | Missouri S&T

Dr. Farhan Mumtaz specializes in photonics, high-temperature instrumentation, fiber-optic distributed sensing, and advanced materials for extreme environments. Bridging fundamental scientific innovation with industrial-scale engineering systems, his research portfolio advances optical measurement resilience for aerospace, energy systems, and extreme materials.

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