Instrumentation & Measurement Magazine 24-5 - 15
yr y w
;
;
00
00
f
f
M M hR
,
y
where in a
f
f
M hR ,
y
R
11
01 2
hh
1 0 1
10
(5.b)
y,α set, y shows the lateral distance of ray from the
optic-axis, and α is its angle relative to the optical axis. Finally,
we can approximately choose the w as yf
on the RF surface:
wyf
For the DFOP sensor calibration, one should choose h0
h hY 0
0 b max
(6)
, the
initial distance of the probe from the diaphragm, as a way that:
(7)
where Ymax
in pressure range and hb
0 is the maximum deflection of the diaphragm
stands for the place that the emitting
light almost fully covers the receiving area that includes both
the core and inner clad, and Rb
Hence, hb
is its corresponding curvature.
f
r1
Mh R
r0
bb,
tan0
gets from this equation:
(8.a)
2 tan
2 tan
RRbb
h h 0
002
r
bb
rr
10
S
where according to para-axial approximation α0
sin α0
≈ tan α0
≈
, and for simplicity we considered the basic-curvature
at the one-tenth of diaphragm radius for the maximum pressure
as:
RR b
0.1
b
(8.b)
max
sin NA n n
22
01
(8.c)
dp
dP
Δ
or S
Δ
p
;
p
P
out
in
(10)
where shows the pressure and p is the normalized output light
power, and Δ denotes a difference of two values. Fig. 6a and
Fig. 6c show the normalized output light power quantity versus
the pressure difference for various diaphragm thicknesses
with a fixed radius and various diaphragm radiuses with a fixed
thickness, respectively. When the thickness of diaphragm becomes
thinner or its radius becomes larger, the relevant output
light power range grows while its linearity misses for a definite
pressure range. Fig. 6b shows that the sensitivity of a thinner
diaphragm has a low variation and is semi-linear for different
pressures, and Fig. 6d shows that a thicker diaphragm has a
smaller sensitivity slope in different pressures but its sensitivity
range increases. Referring to these facts, and what was mentioned
about Fig. 2 and Fig. 3, we decided to select a diaphragm
with t= 0.2 mm and b=18 mm as a suitable selection for further investigation.
To some extent, this set provides a reliable range, has
semi-linear variation, and is more sensitive to pressure sensing.
Normalized output power versus pressure for various NAs
Fig. 5. Different possible overlap patterns between the emitted light with
double-clad fiber on receiving area after reflection when: (a) w > r1
August 2021
; (b) w < r1
.
shows that the greater NA, the greater range and less linearity
will be achieved, as in Fig. 7a. Furthermore, Fig. 7b shows that
the larger NA, the more but nonlinear the sensitivity range is.
Also, drawing minimum /central distance of diaphragm from
the fiber probe versus the pressure for various NAs, as in the
IEEE Instrumentation & Measurement Magazine
15
(5.a)
where NA is the central numerical aperture of fiber, and α0
corresponding acceptance angle. n0 and n1 are the refractive inis
its
dexes of core and inner clad, respectively. So, one can solve the
(8.a) and get hb
0
b
for defined values of fiber and diaphragm parameters.
Also, the central point of the diaphragm will place at
, or w < r1, respectively.
min
Therefore, the output power will be:
P K I 2
out
where
min rw,
min
1
(9.b)
Also, K is a coefficient due to the receiving power loss
related to central numerical aperture, NA and transmission coefficient,
but we consider it due to the existence of the coupler/
splitter [19]. We assumed it to be about 0.5 in our calculations.
Results: Optical Characteristics
In an experimental setup, the optical power meter measures
the input and output powers. In fact, the overlapping between
the returned light to the fiber with a cross-section included the
core and the inner clad (on an area with a radius ≤ r1
2
d KP
in 22
ww
2
exp
hh Y far from the optical fiber end-tip, and the receiving
light on the fiber in these states will be as Fig. 5a or Fig. 5b
shows, dependent on w ≥ r1
d (9.a)
) can measure
as the output power. Since the input and output powers
are available, the sensitivity of the DFOP sensor is meaningful
as the ratio of the output power differences (or normalized of
it) relative to the related pressure differences or:
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