Biomedical Engineering Reference
In-Depth Information
Fig. 14.7.
A schematic illustration of the measurement of transverse optical force
by balancing the optical force against a viscous fluid drag
leads to random errors in the experimental results. Interestingly, the three-
dimensional Brownian motion of a particle in an optical trap, when tracked
and measured with high precision, can be used to probe the three-dimensional
optical force field on the particle with relative ease and with fairly high preci-
sion. This method, also known as photonics force microscopy [41,42], is briefly
described below in this section.
Tracking and the measurement of three-dimensional Brownian motion of
a particle in an optical trap are often accomplished with the aid of one or
more position sensing devices such as a quadrant photo-diode (QPD). From
the projection of the particle position fluctuation as a function of time [
x
(
t
),
y
(
t
), and
z
(
t
)] along each orthogonal axis, the corresponding optical force
constant (
k
x
,
k
y
,and
k
z
) along each axis can be deduced by any one of the
three methods: (1) root-mean-square (rms) fluctuation of the particle position
[36], (2) the Boltzmann distribution of the particle in a parabolic potential
well [41,42], (3) the temporal frequency analysis of particle position fluctuation
[43,44]. To limit the length of this chapter, only the second approach based on
Boltzmann distribution of the particle in a parabolic potential well is discussed
below in this section.
An experimental setup used by the authors to probe the three-dimensional
optical force field on a particle trapped in a fiber-optical counter-propagating
dual-beam trap is shown in Fig. 14.8 [14]. A laser beam (cw,
λ
= 532 nm from
a Nd:YVO
4
laser) was expanded and collimated via a 3X beam-expander (3X
BE) through a half-wave plate (
λ
/2) and a polarizing beam splitter (PBS)
cube to split into two beams with equal optical power, and each coupled into
a single-mode fiber (NA = 0
.
11) via a single-mode fiber coupler (SMFC). The
output ends of the two fibers were aligned so that the two laser beams exiting
from the fibers formed a pair of counter-propagating beams along a common
optical axis inside a sample chamber where microparticles or living cells were
trapped in PBS solution. The distance between the two fiber end-faces was
kept at 125
m. Portions of the trapping beams scattered by the trapped par-
ticle were collected by a pair of orthogonally oriented long-working distant
objectives (LOB
µ
I
and LOB
II
,
×
50, NA = 0
.
42) and projected onto a pair of
quadrant photodiodes (QPD
II
collected the scattered lights and tracked the position of the trapped particle
I
and QPD
II
). LOB
I
/QPDI and LOB
II
/QPD
