Biomedical Engineering Reference
In-Depth Information
the vertical resolution of the proposed holographic configuration is common to all other
Fourier DH setups.
As final example, we report, in
Figure 10.7
, the well-recognizable phase map signature of a
sperm cell obtained with the same configuration to show that holographic configuration
works in the proper way also for more complex objects.
10.3 Particle Tracking in 3D
3D tracking is performed using the similar experimental setup described in the previous
section by evaluating the double out-of-focus projections of the particles due to the twin
beams onto the array detector plane. As shown in
Figure 10.1
, each particle forms two
shadows on the CCD array. The separation between the two shadows is a function of the
longitudinal position of the particle
[58]
.
10.3.1 Modeling for 3D Tracking
In our model, beams on two distinct planes are sent through a microscope objective in a
configuration depicted in
Figure 10.8.
From a mathematical point of view, we can sketch
the imaged volume as composed by two cones, transmitted into the microfluidic sample.
The two cones are partially superimposed in the image space. On the CCD digital sensor,
the intersection between the beam and the sensor plane of each cone is a circle ellipse with
radius
r{d
c
, where
d
c
is the distance between the digital sensor and the vertex of the cone.
We consider a reference system of coordinates
Oxyz
, where the plane
xy
is on the digital
sensor with
O
in the center and we define the vertex of both cones
C
1
(
x
1
,
y
1
,
z
1
) and
C
2
(
x
2
,
y
2
,
z
2
), where (
x
1
,
y
1
) and (
x
2
,
y
2
) are given by the center of two circles in the sensor plane and
z
1
5
z
2
52
d
c
. We suppose that the principal axes of cones are parallel and a microscopic
object, which can be considered a point with coordinates
P
(
x
p
,
y
p
,
z
p
), is in the volume
defined by the union of the two cones, that is
P
A
(
C
1
,
Ω
,
(
C
2
,
Ω
Ω
Ω
1
)
2
), where
1
,
2
are the
cones' the solid angles. In this scenario, we have three possible situations:
C
1
P
P
1
P
2
C
2
Figure 10.8
Geometrical sketch of two interfering laser beams for 3D tracking.
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