OTDR Analysis
Model an OTDR on single-mode fiber: two-point resolution, Rayleigh backscatter coefficient, one-way dynamic range versus pulse width and averaging, cumulative splice steps and Fresnel peaks.
Fibre
Enter the MFD at the chosen wavelength (SMF-28: ≈ 9.2 µm at 1310 nm, 10.4 µm at 1550 nm).
OTDR
Two-Point Resolution
10.21 m
cτ/(2n_g); the ideal event dead zone
Dynamic Range (one-way)
20.5 dB
Backscatter -42.5 dBm over noise -83.6 dBm
Far-End Margin
10.5 dB
DR − span loss 10.00 dB; clean-fibre reach 108 km
Backscatter Coefficient
-82.5 dB
at 1 ns; -62.5 dB at 100 ns (S -27.9 dB)
Far-End Fresnel Peak
23.9 dB
above backscatter; cleaved end R = -14.8 dB
Launch Connector Peak
8.8 dB
R = -45 dB
Rayleigh Scattering Loss
0.147 dB/km
A/λ⁴ at 1550 nm
Minimum Acquisition Time
32.1 s
65536 round trips of 490 µs
Model OTDR Trace
Green: model trace with the launch-connector and far-end Fresnel peaks and 5 splice steps of 0.1 dB. Dashed yellow: the fibre slope of 0.19 dB/km. Dotted red: the noise level, 20.5 dB below the near-end backscatter.
Dynamic Range vs Pulse Width
One-way dynamic range against pulse width; the dot marks 100 ns. Each tenfold longer pulse gains 7.5 dB but worsens the two-point resolution tenfold (0.102 m per ns at n_g 1.4682).
Model
Δz = cτ/(2n_g) P_bs(z) = P₀ · S α_s (v_g τ/2) · e^(−2αz) S = (3/2)·(λ/(2πn w))²
P_n = NEP·√(1/(2τ))/√N DR = 5 log₁₀(P_bs(0)/P_n) peak = 5 log₁₀(1 + R/η)
Rayleigh scattering (α_s = A/λ⁴) sends a fraction S back into the fundamental mode (Brinkmeyer, for a Gaussian mode of radius w = MFD/2); the pulse lights a length v_gτ/2 at a time (Barnoski & Jensen). The backscatter coefficient η = S α_s v_gτ/2 rises 10 dB per decade of pulse width (for long pulses v_gτ/2 becomes sinh(αΔz)/α); data sheets quote it for 1 ns (SMF-28: −82 dB at 1550 nm).
Noise is the receiver's noise-equivalent power over the matched bandwidth 1/(2τ), reduced by √N for N averages. For this ideal matched receiver the one-way dynamic range grows 7.5 dB per decade of pulse width (less on real instruments) and 1.5 dB per 4× averages. OTDRs display one-way dB (5 log₁₀), so a splice of 0.1 dB steps the trace down by 0.1 dB and the fibre slope equals its loss in dB/km.
Not included: receiver recovery after strong reflections (attenuation dead zones several times Δz), the 98 %-noise dynamic range some vendors quote (≈ 1.5–2 dB lower), coherent fading noise and the non-Gaussian mode tail. The near-end connector loss is hidden in the launch dead zone.
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
Barnoski–Jensen backscatter with Brinkmeyer's Gaussian-mode capture fraction; ideal matched receiver, SNR = 1 noise. Receiver recovery, fading noise and the 98 % DR convention not included.
- Barnoski M. K., Jensen S. M. (1976). Fiber waveguides: a novel technique for investigating attenuation characteristics. Appl. Opt. 15, 2112. Backscattered power P₀ S α_s (v_g τ/2) e^(−2αz). doi:10.1364/AO.15.002112
- Brinkmeyer E. (1980). Analysis of the backscattering method for single-mode optical fibers. J. Opt. Soc. Am. 70, 1010. Capture fraction S = (3/2)(λ/(2πnw))² for a Gaussian mode. doi:10.1364/JOSA.70.001010
- Corning (2024). SMF-28 Ultra Optical Fiber, product information PI 1424. Rayleigh backscatter coefficient −82 dB (1 ns) at 1550 nm, MFD 10.4 µm, used as the check value. csmedia.corning.com