Biomedical Engineering Reference
In-Depth Information
Fig. 14.9.
An example of a calibration curve for the conversion of the QPD output
voltage into the axial position of a particle in a fiber-optical dual-beam trap
beads of different sizes as well as Chinese hamster ovary cells trapped in a
fiber-optical dual-beam trap, and analyzed their position distribution to ob-
tain the optical force field approximated by a three-dimensional parabolic
potential well [14, 15]. Under the parabolic potential approximation and the
classical Boltzmann statistics, the associated optical force constant along each
axis can be calculated from the following two equations [41]:
ρ
(
z
)=
C
exp [
−E
(
z
)/
K
B
T
]
,
(14.6)
−K
B
T
ln
ρ
(
z
)+
K
B
T
ln
C
=
k
z
Z
2
2
,
E
(
z
)=
(14.7)
where
ρ
(
z
) is the probability function of the trapped particle position along the
z
-axis,
C
is the normalization constant,
E
(
z
) is the potential energy function
along the
z
-axis,
K
B
is the Boltzmann constant, and
k
z
is the optical force
constant along the
z
-axis. Identical set of equations also apply for the
x
-axis
and the
y
-axis. As a specific example, a set of experimental data representing
the parabolic potential
E
(
x
)and
E
(
z
) of the optical force field on a 2.58
m
diameter silica particle in a fiber-optical dual-beam trap (total trapping power
= 22 mW, distance between the fiber end-faces = 125
µ
m,) is depicted in
Fig. 14.10. The solid lines represent the theoretical curves based on (14.7)
given above; the corresponding optical force constants, defined by (14.7), were
k
x
µ
m
−
1
. The force constant along the
optical axis is weaker than those along the transverse axes, which is consistent
with the theoretical results reported earlier [45]. This is also true in the case of
optical tweezers [46]. For clarity sake, the experimental data for
y
-axis along
m
−
1
=0
.
16 pN
and
k
z
=0
.
04 pN
µ
µ
