# Instrumentation & Measurement Magazine 24-5 - 17

Table 1 - The initial distance of the probe from the
diaphragm for various numerical aperture NA.
(Silicon-Nitride diaphragm E=300 GPa, ν=0.24,
t=0.2 mm, and b=18 mm; r0
NA
0.15
0.18
0.21
0.24
= 50 μm, r1 = 200 μm).
(mm)
1.28
1.19
1.13
1.08
h0
Also, the inset of Fig. 9b shows that if the cladding-to-core
ratio of the fiber optic r1
Table 2 - The initial distance of the probe from
the diaphragm for various cores onto inner clad
radiuses of the fiber optic, r1
/r0 (Silicon-Nitride
diaphragm E=300 GPa, ν=0.24, t=0.2 mm, and
b=18 mm; r0
r1/r0
2
3
4
5
/r0 becomes larger, the variation of the
central distance of the diaphragm from the fiber tip will keep its
linearity versus pressure, but the initial distance shifts further,
as it depicted in Table 2. So, the sensor dimensions run bigger.
Discussion
Regarding above analysis, a suitable set of parameters can
make an optimum linear DFOP sensor as its normalized output
power is shown in Fig. 10a. This set of variables for a
Silicon-Nitride diaphragm (E=300 GPa, ν=0.24) is: t = 0.25 mm;
= 50 μm, NA = 0.2).
h0
(mm)
0.90
1.02
1.15
1.28
b = 15 mm; r0 = 50 μm; r1 = 200 μm; NA = 0.18; h0
vided a linear function as:
 
atm
 2.002 9.633p
;
= 0.606 mm. It proP
p

P
out
in
where  and p are for the inserted pressure difference on the
diaphragm in the atmosphere and the normalized output
power, respectively.
Another wide-range, but nonlinear DFOP sensor depicted
in Fig. 10b. For these set of parameters: t = 0.20 mm; b = 18 mm;
Fig. 8. The spot size radius on the deflected diaphragm versus: (a) pressure; and (b) distance from diaphragm for various central numerical aperture. (SiliconNitride
diaphragm E=300 GPa, ν=0.24, t=0.2 mm, and b=18 mm; r0
= 50 μm, r1 = 200 μm).
Fig. 9. (a) Normalized output power, (b) sensitivity, and the central deflection of the diaphragm, all versus pressure for the various ratios of fiber inner clad onto
its core radius. (Silicon-Nitride diaphragm E=300GPa, ν=0.24, t=0.2mm, and b=18mm; r0
= 50 μm, NA = 0.2).
August 2021
IEEE Instrumentation & Measurement Magazine
17

# Instrumentation & Measurement Magazine 24-5

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