EXFO FTB-5600 Distributed PMD Analyzer - Manual (Page 121)

Distributed Cumulative PMD Measurement Theory
Distributed PMD Analyzer 115
cumulative PMD from 0 to z
n
is determined by multiplying the
roundtrip-PMD by the statistical, averaging roundtrip factor α
rt
2 = 3/8,
where the roundtrip-PMD at point z
n
is deduced from the mean-square
(ms) value of the K random transmission differences divided by a relative
variance of the traces. More precisely, in practice, each of the two traces in
each pair is acquired twice consecutively in time, thus producing a
repeated pair having a difference of
Δ T '
k
(z
n
) , which may differ somewhat
from Δ T
k
(z
n
) . In this way, any change in the local difference between
repeated pairs would be caused only by uncorrected noise. When
averaged over all the different independent pairs, an ms-difference can be
computed as the second-order joint moment of the repeated differences,
thereby eliminating this noise offset.
In order to attain a maximum dynamic range and to minimize the
coherence noise in the backscattered lights, the FTB-5600 generally uses
long pulses (for example, 100 ns or 50 ns). However, depending upon the
local birefringence at any given point zn, the backscattered light
corresponding to this point may be partially depolarized, thereby “washing
out” the transmission differences. The division of the joint moment by the
relative variance
in the equation
above allows this effect to be effectively compensated (here σ
T
2
= 4/45 is a
theoretical variance of the transmission for an infinitesimally short pulse).
Note that the
σ
r
2
(z
n
) is also computed as a joint moment of repeated traces
to avoid noise offset and averaged over the traces obtained for different
wavelengths and uniformly distributed I/O-SOPs.
ΔT
ms
z
n
1
σ
r
2 z
n
( )
---------------- ΔT
k
z
n
( )ΔT′
k
z
n
( ) 〈 〉
K
=
σ
r
2 z
n
( ) T
j
z
n
( )T′
j
z
n
( ) 〈 〉
J
T
j
z
n
( ) 〈 〉
J
2 – ( ) σ
T
2 – ⋅ =