Fiber Optic Gyroscope (FOG)
Sagnac scale factor, shot-noise angle random walk, Earth-rate phase, transit time and proper frequency of an interferometric fiber optic gyroscope.
Scale Factor S
0.67608 s
Δφ per rad/s
ARW (shot noise)
5.756e-5 °/√h
Allan N; one-sided rate ASD 4.884e-3 (°/h)/√Hz
Earth-Rate Phase
4.930e-5 rad
Ω_E = 15.04 °/h, axis at the pole
Phase Noise σ_φ
16.01 nrad/√Hz
P_d = 1.000 mW at ±π/2 bias
Transit Time
2.449 µs
n_g·L/c
Proper Frequency
204.2 kHz
1/(2τ): bias modulation
Max unambiguous rate
133.1 °/s
Sagnac phase reaches π/2: π/(2S)
Turns
1592
L/(πD)
Formulas
Sagnac phase: Δφ = S·Ω, S = 2πLD/(λc) (no dependence on the fibre index)
Shot noise at ±π/2 bias: σ_φ = √(2hν/(η·P_d)) rad/√Hz, P_d = P_source·10^(−loss/10)
Rate noise (one-sided ASD): σ_Ω = σ_φ/S
ARW (Allan, σ²(τ) = N²/τ): N [°/√h] = σ_Ω [(°/h)/√Hz] / (60·√2) (IEEE Std 952)
Transit time τ = n_g·L/c; proper frequency f_p = 1/(2τ)
The loss includes the 3 dB of the ±π/2 bias point, the coupler passes, the polarizer and splices. Datasheets that divide the one-sided ASD by 60 alone quote an ARW √2 higher. Ideal shot-noise limit. Broadband sources add excess intensity noise, often the larger term, and the length trade-off with fibre attenuation is left to the loss input.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Ideal reciprocal I-FOG at the ±π/2 bias point, shot-noise limit only (no source excess noise, backscatter or Kerr bias). ARW is the Allan N: one-sided rate ASD/√2.
- Arditty H. J., Lefèvre H. C. (1981). Sagnac effect in fiber gyroscopes. Opt. Lett. 6, 401. Δφ = 2πLDΩ/(λc), independent of the index. doi:10.1364/OL.6.000401
- Lefèvre H. C. (2014). The Fiber-Optic Gyroscope, 2nd ed., §2.1, §3.1–3.2 (Sagnac phase, photon-noise limit, proper frequency). Artech House.
- IEEE Std 952-1997. Specification format guide and test procedure for single-axis interferometric fiber optic gyros. Annex C: angle random walk from the Allan variance. doi:10.1109/IEEESTD.1998.86153