OTDR Fibre Trace

What is modelled

An OTDR launches a short pulse and records the power that returns. Rayleigh scattering returns a tiny fraction of the pulse from every metre of fibre, so the trace falls with distance at the fibre loss. A splice drops the level by its loss, a connector or the fibre end reflects a spike, and the pulse length sets how finely two features can be told apart. Noise sets the lowest level that can be read and falls as the square root of the number of averaged sweeps.

Equations

• Pulse length in the fibre Δz = c τ / (2 n); echo delay for distance z: t = 2 n z / c.
• Backscatter level P(z) = b ∫ T² dz over one pulse length, with round-trip transmission T² = 10−2(αz + losses)/10; on the usual 5 log scale the trace slope is −α.
• Fresnel reflectance R = ((n − 1)/(n + 1))² at a flat glass-air end.
• Averaging N sweeps reduces rms noise by 1/√N.

Checks run in the page

• Reflection width against cτ/2n.
• Trace slope against the set attenuation.
• Splice loss recovered by line fits either side of the splice.
• End reflection height against the analytic ratio.
• Noise reduction from averaging 16 sweeps.

Honest simplifications

A single idealised fibre, one splice, one connector and a flat end, a constant backscatter coefficient (1e-10 per metre, about −80 dB at 1 microsecond), Gaussian detector noise of fixed level, no receiver saturation or dead-zone tail, and no splice gain. Real instruments add event tables, dead zones and wavelength-dependent loss.

• Choose Short pulse, fine detail to resolve events close together, and note the lower dynamic range.
• Choose Long span, long pulse and see far fibre that a short pulse cannot reach.
• Choose Noisy, no averaging and then raise the sweeps: every factor 4 lowers the noise by half.