Biomedical Engineering Reference
In-Depth Information
frequencies. By this we are saying that the smallest detectable phase differ-
ence is 2000 μrad. We can define our goal to measure with good precision a
pressure change of 0.01 in. of water. For reasonable accuracy this should be
equivalent to 10 times the smallest resolvable phase increment. This means
that a phase change of 20,000 μrad will represent a pressure change of 0.01 in.
of water. Since phase change relates directly to fiber elongation and optical
wavelength, we can pick an appropriate light source and calculate the neces-
sary elongation as a function of pressure without initially defining the pres-
sure transduction process.
Selection of the light wavelength is influenced by the availability and cost
of suitable single-mode laser diodes and single-mode fibers. Reduction of
wavelength translates to smaller fiber diameters and lower losses for a given
bending radius. However, intrinsic fiber losses are higher for the shorter
wavelengths. Low loss transmission windows at 1.3 and 1.55 μm provide a
strong incentive for operation at those wavelengths. Suitable laser diodes
are available at 830-850 nm as well as at 1.3 and 1.55 μm. We will use the
1300 nm wavelength for feasibility calculations. The actual fiber elongation
is nearly
−
e
20 000 10
2
,
×
1 3 10
6
−
Δ
l
=
(
wavelengths
)
×
( .
×
)
m
π
(4.10)
×
−
9
=
4 14 1 m
.
0
This is the elongation to be produced by a pressure increase of 0.01 in. of
water. Particular applications may require a dynamic range of say ±20 in. of
water. For this case, the total elongation will be
−
3
2 20 4 14 10
0 01
(
) .
.
×
Δ
l
=
−
6
=
16 56 1
.
×
0
m
(4.11)
We need to find the total length of fiber in each branch. The minimum over-
all length is related to the total elongation and the allowable stress in the
fiber as well as to the transducer area exposed to the hydrostatic pressure.
Polarization-preserving single-mode doped silica fibers are the appropriate
choice. The tensile stress at which a fiber will fail depends on the composi-
tion, residual internal stresses, and surface defects. Polarization-preserving
birefringence is induced by the inclusion of stress rods in the fiber when it
is fabricated. For these reasons, the ultimate allowable stress is considerably
less than could be expected from the properties of pure silica alone. We used
ITT fiber #T1605 in previous related experiments [54]. The manufacturer's
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