Instrumentation & Measurement Magazine 24-5 - 18
Fig. 10. Pressure versus normalized output power. Fitted curves are solid and spots show the simulation results: (a) for t=0.25 mm, b=15 mm, r0
NA = 0.18; (b) for t=0.20 mm, b=18 mm, r0 = 50 μm, r1 = 150 μm, NA = 0.22. Its inset shows gain versus pressure. (Silicon-Nitride diaphragm E=300GPa, ν=0.24).
Sensitivity in atm−1
: (c) for the first sensor; (d) for the second sensor.
r0 = 50 μm; r1 = 150 μm; NA = 0.22; h0 = 1.00 mm; the related function
is extrapolated as:
0.771
atm
0.037
pP
1.154 ;
p
p
P
out
in
Also, as it shown in the inset of Fig. 10b, the pressure is a
semi-linear function of optical gain of this sensor as:
1.646 0.051 G G
atm
;
10log out
in
P
P
Fig. 10c and Fig. 10d show both sensors' sensitivities. The
linear sensor has a smooth sensitivity, but the nonlinear one is
more sensitive when the pressure is increased.
Conclusions
Analyzing various parameters affected on a Double-clad Fiber
Optic Pressure Sensor (DFOP), it was realized that:
◗ When the thickness of a diaphragm becomes thinner or its
radius becomes larger, the output power range grows and
its linearity decreases for a definite pressure range.
◗ The thinner diaphragms have a low variation and semilinear
sensitivity for different pressures, and the thicker
ones have smaller slopes and larger ranges of sensitivities
in different pressures.
18
◗ The variation of the central distance of the diaphragm
from the fiber tip versus pressure is linear. If the claddingto-core
radiuses ratio of the fiber optic (r1
/r0
) becomes
larger, it remains linear but its initial distance shifts
further; consequently, only the sensor volume increases.
Also, as the r1
/r0
grows, the sensitivity range decreases,
and its linearity increases.
◗ The maximum central displacement of the diaphragm
is almost the same for an infinite range of pressure by
changing the NAs, but the basic distance will be moved.
Normalized output power versus pressure for various
NAs shows that the greater the NA, the greater the
range, and less linearity is achieved. Also, the larger
the NA, the wider the range but the more nonlinear the
sensitivity.
◗ Based on the above results and due to the availability
of the certain commercial fiber optics, we propose a
DFOP with these characteristics: t = 0.20 mm, b = 18 mm,
r0
= 50 μm, r1 = 150 μm, and NA = 0.22 with a Silicon-Nitride
diaphragm, E=300GPa, ν=0.24. Calibrating it in an initial
distance h0
= 0.606 mm provides a nonlinear model for the
preassuming pressure in terms of the output light power.
So, measuring the pressure is possible using the relevant
function by substituting output power in it.
IEEE Instrumentation & Measurement Magazine
August 2021
= 50 μm, r1
= 200 μm,
Instrumentation & Measurement Magazine 24-5
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