Biomedical Engineering Reference
In-Depth Information
a specific pose. The intriguing feature is that the same laser source is used for two
functions, termed “drive and analyze”
[53]
. The intriguing feature here is that the same
laser source is used for making two functions: drive and analyze
[53]
. To do this, two laser
beams are used from a single laser source. The two beams are slightly noncollinear,
differing from each other by a small angle. The interference between the two laser beams
generates a sequence of digital holograms while one of the beams creates the driving force.
Methods and experimental results using latex spheres and living cells in vitro are reported
in later sections.
10.2.1 Trapping Theory
Here, an experiment is shown to prove trapping and driving operations. Latex particles
(diameter
D
p
5
9.7
, a ray
approach can be applied, neglecting diffraction effects. Since the net momentum must be
conserved in the process, the change in the momentum generates forces that can be
divided into two types: the scattering and the gradient force. The gradient force,
F
grad
,is
proportional to the gradient of the laser beam's intensity. As the gradient force points
toward the high-intensity region, it acts as a force that attracts the particle. On the
contrary, the scattering force,
F
scat
, acts like a repulsive force and points in the
direction of propagation of the ray. The two forces can be expressed by the following
equations
[42]
,
μ
m) dispersed in a liquid medium are employed. If
D
p
.
10
λ
ð
2
π
ð
π=
2
n
0
2
c
1
1
R
cos 2
θ
2
T
2
cos 2
ðθ
2
ϑÞ
1
R
cos 2
θ
F
scat
5
Iðr; zÞ
1
1
R
2
1
2
R
cos 2
ϑ
0
0
(10.1)
2
D
p
2
sin 2
θ
d
θ
d
Θ
3
ð
2
π
ð
π=
2
n
0
2
c
θ
2
T
2
sin 2
ðθ
2
ϑÞ
1
R
sin 2
θ
F
grad
52
Iðr; zÞ R
sin 2
1
1
R
2
1
2
R
cos 2
ϑ
0
0
(10.2)
2
D
p
2
sin 2
θ
cos
Θ
d
θ
d
Θ
3
where
n
0
is the refractive index of the medium,
c
is the speed of light, and
r
is the radial
offset of the sphere from the Gaussian beam center axis. Moreover,
z
is the axial distance
from the minimum beam waist while
R
and
T
are the Fresnel's coefficients of reflectance
and transmittance, respectively, and
θ
is the incident angle of the photon stream with
respect to the normal direction of the sphere surface.
ϑ
5
sin
2
1
(
n
0
/
n
1
)sin
θ
is the refraction
angle obtained by Snell's law,
n
1
being the refractive index of the particle, and
Θ
is the
polar angle. Beam intensity profile,
I
(
r
,
z
), is given by:
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