Biomedical Engineering Reference
In-Depth Information
length in wavelengths divided by the refractive index, that is, neglecting
higher-order effects, we obtain
6
−
6
9 35 10
2
.
×
1
.
3
10
1 458
×
in. minimum
(4.17)
L
=
×
(
39 37
.
)
=
52 24
.
π
.
As in the previous case, we have shown that the requisite sensitivity and
resolution should not be a problem. This is in keeping with the Giallorenzi
statement “The phase (or interferometric) sensor, whether for magnetic,
acoustic, rotation, etc., sensing, theoretically offers orders of magnitude
increased sensitivities over existing technologies. In the case of the acoustic
sensor constructed utilizing optical fiber interferometers—these theoreti-
cal predictions have been verified to the limit of state of the art in acoustic
measurements.”
The Mach-Zehnder interferometer output is proportional to the squared
sum of the light amplitudes from the sensing and reference branches and
varies as the phase difference between the electric fields varies. The individ-
ual amplitudes should remain constant. In order that the output variation be
maximum and approach a linear variation with phase angle, a displacement
of π/2 radians or 90° will be created. The operating range of phase variation
is on the order of ±π/4 rad (45°).
This is much less than the anticipated phase variation of the pressure sen-
sor. Large variations are accommodated by means of a phase-locked feed-
back arrangement that maintains near zero phase difference at the output by
stretching the reference fiber to match the phase delay in the sensing fiber.
The control signal to the stretcher in the reference branch is then the system
output. For example, a pressure sensor dropped from the surface to a depth
of 600 ft would have a large phase-locked loop stress built up by the time
it came to rest. Since the absolute depth change during emplacement is of
no particular significance, the sensor could be activated after emplacement.
In the foregoing calculations, we set the phase shift equivalent of 0.01 in.
of water to 20,000 μrad or 20 mrad. If a stable sensor has a more or less lin-
ear range of ±π/4 radians, this corresponds to pressures of ±78 in. of water.
Under ordinary operation, the loop stress would be small, greatly reducing
the probability of breaking phase lock.
The bandwidth of a fiber-optic pressure sensor is determined by the reso-
nances of the transducer and the frequencies of environmentally induced
drifts. The sea should be a relatively benign environment with regard to
thermal effects. It may ultimately be possible to extract pressure, seismic,
and acoustic data from a single sensor by spectral filtering.
There are several noise sources that cannot always be distinguished from
a pressure signal. These effects and the methods of correction are discussed
below. Note that the fiber interferometer discussed in this example could
also be used to sense magnetic field disturbances by mechanically coupling
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