Optical Backscatter Reflectometer 4600 191
User Guide
where U
j
is the reference spectrum for a given segment of data, U
j
( ν – ∆ν
j
) is the
measurement spectrum under a strain or temperature change, and the symbol is
used to denote the cross-correlation operator. In other words, the Spectral Shift
Quality is the maximum value of the cross correlation of the Reference and
measurement
spectra normalized by the maximum expected value, i.e. the maximum
of the reference spectra autocorrelation.
In practical use, the Spectral Shift Quality will be a value between 0 and 1, where
1 is a perfect correlation, and zero is uncorrelated. In general, the data sets should
be considered well correlated if the Spectral Shift Quality is above about 0.15. Note
that as Strain or Temperature Change increases, Spectral Shift Quality will
decrease. This is expected since exposing a fiber to a change in strain or temperature
induces a temporal shift as well as a temporal stretch or compression.
Temporal Shift
The temporal shift ∆t results from the integrated effect of local time shifts along the
FUT between the origin at the front panel of the OBR and the delay time at which
the shift is being evaluated. This temporal shift is calculated from the spectral shift
using the following relationship:
j
λ
1
λ
2
SensorSpacing
∆τ
(
τ
)j ≈
–a
0
----------
---------------------------------------
∑∆vi
,
c
λ
c
GaugeLength
i = 0
8
where the summation is over the Gauge Length (as set by the user in the Data
Processing area); a
0
denotes a scaling constant; λ
1
, λ
2
and λ
c
are the Start, End
and Center Wavelengths of the scan, respectively; and c is the speed of light. It is
assumed that the Temporal Shift value is equally distributed over the Gauge
Length. When this is not a valid assumption, the Temporal Shift data will become
noisy; a smaller Gauge Length is required for the calculations to succeed. Note that
when the Sensor Spacing is equal to the Gauge Length, this expression is exact.
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