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Экспериментальные средние спектральные характеристики рефлектограмм.
Experimental average spectral characteristics of the OTDR intensity traces
Consider the average spectral characteristics of OTDR intensity traces with singular probe pulses which close to rectangular and close to Gaussian shapes. The experimental setup is depicted on figure 4, however to measure spatial spectral characteristics of the intensity traces I/Q demodulation scheme and PZT transducer should be excluded from the setup.
The
measurement of the average PSDs was performed by recording a large
number of intensity traces (100 traces), corresponding to different
spatial distribution of scattering centers
,
calculation of the PSD for each trace and subsequent averaging over
100 realizations. The experiment results are shown on figure 5.
Continuous lines on figure 5 show the PSDs averaged over 100
realizations when the probe pulse close to rectangular shape is used:
curve 1, with the FWHM of the intensity (not amplitude) pulse shape
equal to 90 ns and the risetime equal to 10 ns and when probe pulse
close to Gaussian is used: curve 2, with FWHM of the intensity (not
amplitude) pulse shape equal to 100 ns, the experimental curves are
shown by circles. The theoretical curves were calculated numerically
with the use of 9 and 20 the probe pulses
were approximated by Super Gaussian shapes of corresponding width
:
4646\* MERGEFORMAT (),
where
were chosen to fit the initial probe pulse in the best way. As it
can be seen,
the theoretical curves coincide well with the experimental, that
proves the validity of the proposed consideration. We should note
that when moving along the fiber, the spectrum of the probe pulse
broadens due to the frequency chirp phenomenon. Moreover, a probe
pulse with Gaussian shape experienced more significant spectral
broadening comparing with a probe pulse with rectangular shape. The
spectral broadening of the moving probe pulse consequently led to the
spatial spectral broadening of resulting OTDR intensity trace power
spectrum in such a way,
that the spatial spectrum, measured in the beginning of the fiber
line, was much narrower than the spatial spectrum, measured in the
segments close to the end of the fiber line. In this
work
the arising nonlinear effects are not considering,
so the average PSDs, shown on figure 5 correspond to the OTDR
intensity traces, measured in the beginning of fiber line.
When
calculating the spectral characteristics, the additional broadening
of spatial PSD due to the fact that recorded intensity traces have
finite temporal extent, i.e. spectral leakage, is not considering.
The experimental PSD were calculated for the intensity trace segment
of temporal extent equal to 2
,
which led to additional spatial spectral broadening at 440 kHz that
is 20 times as less as FWHM of averaged PSD and can thereby be
neglected.
From figure 5
it follows that the FWHM of the average
OTDR intensity trace spatial power spectrum
,
when the probe pulse with the shape close to rectangular is used,
equal to
12.5 MHz, at the same time the width of the initial probe pulse power
spectrum
is
equal to
9.8 MHz, which means that the average PSD of the OTDR trace broadens
in comparison with the PSD of the initial probe pulse as much as 1.27
times. When the probe pulse with the shape close to Gaussian is used,
the FWHM of the average
OTDR intensity trace spatial power spectrum
equals to
6.9
MHz, the width of the initial probe pulse power spectrum
is
equal to
6.6 MHz, which means that the average PSD of the OTDR trace broadens
in comparison with the PSD of the initial probe pulse as much as 1.04
times. These results are fully consistent with those calculated in
the second part of this
article.
So one should expect that when a dual-pulse with carrier frequencies difference of 100MHz is used as a probe signal in OTDR, the mean relative error of a phase measurement will be less than 12.5% for the pulse of rectangular shape. This phase error could be reduced by increasing the difference of the carrier frequencies or by reduction the width of the average OTDR intensity trace spatial power spectrum