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Distributed Cumulative PMD Measurement Theory
116
FTB-5600
For very small values of PMD
·
δν
,
the ms-difference
Δ
T
ms
( z
n
)
is proportional
to
(PMD
·
δν
)
2
.
Hence, there the measured transmission differences may be
very small, leading to a very poor dynamic range, since the differences
may be of the same magnitude as the coherence noise. In order to use the
largest possible optical-frequency difference δν , the large-step formula
below is used to compute the cumulative PMD:
where
Δ
T
o
2
= 8/45 is a “saturated” value of the ms-difference when
PMD
·
δν → ∞ and
α
dT
= 15 is a proportional constant when δν → 0.
When the PMD is obtained from a single measurement at a given time, the
cumulative PMD curve,
PMD (z
n
)
, will exhibit fluctuations as a function of
distance
z
, even if the cumulative PMD is constant. Therefore, it can be
advantageous to average over some length Δ
z
, for example 0.5 km to 4 km,
to obtain a clear picture of the cumulative PMD curve. Moreover, the use of
a larger number of random and independent combinations of frequency
and I/O-SOP, for example K = 200 to 500, permits a corresponding
reduction in the measurement uncertainty.
Δ
T
ms
z
n
( ) Δ
T
o
2
1
2
π
PMD z
n
( )δν
α
rt
α
dT
Δ
T
o
-------------------------------------
⎝ ⎠
⎛ ⎞
–
2
⎝ ⎠
⎛ ⎞
exp – =