Biomedical Engineering Reference
In-Depth Information
For multimode EW optical iber sensors, Payne and Hale
46
showed that the simple Beer's law model overestimated the iber
absorbance and an expression for such sensors at the condition of
very strong absorption was derived:
πρ
. .
I
V
NA
S
0
≈ =
α
(5.12)
.
. .
I
L
λ α
L
0
Again, the FO-PPR measurements actually relect the change of
light attenuation through the iber. When
I
R
is deined as the sensor
response of a NMNPs-modiied optical iber in a blank,
I
S
is the
sensor response of a NMNPs-modiied optical iber in a sample, and
I
0
is the sensor response of the same optical iber without NMNPs
and is in the blank, then Eq. 5.12 can be rewritten as
I
I
α
≈
αΔα
S
(5.13)
R
R
+
R
where the bulk absorption coeficient changes from
α
R
(in a blank)
to
α
R
+
Δα
(in a sample) when the RI of the medium surrounding the
NMNP layer changes from
n
R
to
n
S
.
Further theoretical work is needed to relate the sensor response
with respect to the parameters to construct the iber optic sensor.
Nevertheless, both Eqs. 5.10 and 5.12 indicate that the use of a
smaller core radius may be beneicial to improve the sensitivity
of the sensor. However, a smaller core radius also lead to a lower
intensity signal received by the detector and is very fragile. Thus, a
trade-off core radius is often employed.
The bulk absorption coeficient of a NMNP is related to the
extinction cross-section of a particle. According to Mie's theory, the
extinction cross-section of a single spherical particle much smaller
than the wavelength of light can be approximately expressed by the
following relationship:
12
233/2
S
24
πε
εω
()
.
σ =
2
(5.14)
ext
λ
εω ε εω
2
2
(()+2)+()
1
S
2
where
σ
ext
is the extinction cross-section of the particle,
r
is the
radius of the particle,
λ
is the wavelength of light, and
ε
S
and
ε
(
ω
) =
ε
1
(
ω
) +
i
ε
2
(
ω
) are the dielectric functions of the surrounding
medium and the metal itself, respectively. While the dielectric
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