Biomedical Engineering Reference
In-Depth Information
where
k
is a constant,
V
is a normalized frequency (also called
V-number),
λ
is the wavelength of light in the iber core, and
ρ
is the
core radius. After correcting an error in Gloge's original paper,
45
k
is
given by a value of 4/3.
46
However, in evanescent wave spectroscopy
using a iber, the cladding material is often partially removed
and replaced with, in general, a material having a much lower
RI. Thus, only some of the possible bound modes of the sensing
region propagate and the evanescent absorption coeficient can be
described by an expression given by Ruddy:
44
.
αλ
φ
(5.9)
γ=
. .
.
ρ
2
n
(1+sin )
1
c
For a NMNP layer, the absorbance of the NMNP layer changes
when it is immersed in a sample of refractive index
n
S
different from
that of a blank,
n
R
.
19
Previous study indicates that at a long enough
L
, the change in
NA
S
with respect to the change in
n
S
is negligible as
compared to the change of
α
with respect to the change of
n
S
.
24
In
other words, the second term in Eq. 5.5 is negligible when
γ⋅
L
is large
enough. Under this condition, substituting Eq. 5.9 into Eq. 5.5 yields
⎛⎞
. .
I
αλ
L
S
(5.10)
A
=
-log
⎜⎟
=
.
. .
ρ
φ
⎝⎠
I
2
n
(1+sin )
0
1
c
For the PPR sensors, the NMNP acts as a reporter chromophore
and its interaction with an analyte will result in a change in its
bulk absorption coeficient and absorbance. As such, the FO-PPR
measurements actually relect the change in absorbance. 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. 5.10 can be rewritten
as
⎛⎞
. .
I
Δα λ
L
S
Δ =
A
-log
⎜⎟
=
(5.11)
.
. .
ρ
φ
⎝⎠
I
2
n
(1+sin )
R
1
c
where
Δ
A
is the absorbance change from
A
R
(in a blank) to
A
R
+
Δ
A
(in a sample) and 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
.
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