Biomedical Engineering Reference
In-Depth Information
y
z
CCD
x
BS
QPD
Nd : YVO
4
λ
=532nm
LOB
SMFC
LOB
SMFC
3X BE
PBS
λ
/2
QPD
Lamp
Fig. 14.8.
A schematic illustration of the experimental setup for the mapping of
three-dimensional optical force field on a particle in a fiber-optical dual-beam trap
projected on the
xz
-plane and the
yz
-plane, respectively (the
xyz
co-ordinate
system is depicted in the upper left corner in Fig. 14.8). Besides, the LOBI was
also used for imaging the trapped particle on a CCD camera (752
×
582 pixels)
via incoherent illumination from a lamp. To obtain the conversion factor that
converts the output voltage of the QPD into the particle displacement, we
trapped the microparticle of interest on the optical axis in the middle of the
end-faces of two optical fibers via equal laser power from the two fibers, and
momentarily turned off one of the laser beams to drive the particle (by the
remaining single beam) along the optical axis towards the opposite end-face
of the optical fiber. The second beam was subsequently turned on to drive
the particle back along the optical axis towards the original equilibrium po-
sition at the middle of the fiber end-faces. As the microparticle was driven
back along the optical axis under the illumination of both beams, the corre-
sponding output voltage of the quadrant photodiode and the position of the
microparticle on the CCD camera were recorded simultaneously. An illustra-
tive example of such a calibration curve (i.e., QPD output voltage vs. particle
position recorded on the CCD) is depicted in Fig. 14.9, which shows a linear
dependence with a slope of approximately 0.986
mV
−
1
µ
within the region
of approximately 3.4
m. Besides the Brownian fluctuation, the accuracy of
this approach is mainly limited by the determination of the particle position
from the incoherent image of the illuminated particle on the pixelated dig-
ital CCD camera. The calibration method described above was carried out
during the return trip of the particle (from a point offset from the center
to the center equilibrium position) when both laser beams were on to ensure
that the particle was evenly illuminated from both sides. Recently the authors
have tracked the three-dimensional Brownian motion of polystyrene and silica
µ
