Biomedical Engineering Reference
In-Depth Information
P
FOV since the extent of
will be suppressed by a large aperture. Therefore,
incoherent illumination through a large aperture will provide better image quality for
characterizing dense cell suspensions such as undiluted semen samples.
ðð
2
a
=λ
0
z
a
Þ;
0
Þ
The final two terms (
Eqs. (8.3) and (8.4)
) represent the holographic diffraction patterns
in the recorded intensity and are the foci of all digital holographic imaging systems,
including the on-chip implementation discussed in this chapter. Ideally, these terms should
dominate the information content of the recorded intensity, which is typically true for
weakly scattering objects. More specifically,
H
1
(
x
D
,
y
D
) is the holographic diffraction of the
first scatterer
c
1
δ
(
x
2
a
,
y
); and
H
2
(
x
D
,
y
D
) is the holographic diffraction of the second
(
x
1
a
,
y
). Since
h
C
(
x
D
,
y
D
) creates twin-image artifacts at the reconstruction
plane when propagated in the reverse direction, the complex conjugate (c.c.) terms in
Eqs. (8.3) and (8.4)
represent the source of the twin images. Numerical elimination of these
twin-image artifacts will be discussed in
Section 8.3
.
scatterer c
2
δ
As indicated by the terms inside the curly brackets in
Eqs. (8.3) and (8.4)
, a scaled and
shifted version of the aperture function
P
(
x
,
y
) coherently diffracts around the position of
each scatterer. In other words, each point scatterer projects a scaled version of the aperture
function (i.e.,
p
(
2
x
D
M
,
2
y
D
M
)) to a location shifted by
F
folds from origin, and the
distance between the object and the sensor planes is now also scaled by
F
folds (i.e.,
Δ
z
s
). It is also important to emphasize that the aperture size is effectively narrowed
down by an
M
fold at the object plane. For
M
z
5
F
200), a spatially incoherent
light source through a large aperture can still provide coherent illumination to each cell
individually for generating each cell's holographic signature on the sensor plane. This is
true as long as the cell's diffraction pattern is smaller than the coherence diameter at the
sensor plane. In our geometry, coherence diameter is typically 500
c
1 (typically 50
0
and it is
much larger than the practical width of cell holograms on the sensor plane, which is easy to
satisfy especially for small
z
s
values. Consequently, for a completely incoherent source
emanating through an aperture width of
D
a
and illuminating a sensor area of
A
, the
effective width of each point scatterer diffracting toward the sensor plane would be
D
a
/
M
and the effective imaging FOV would be
A
/
F
2
. Considering typical values for
z
a
(e.g.,
B
3
λ
1000
λ
0
10 cm) and
z
s
(0.5
2 mm), the scaling factor (
M
) becomes
.
100 and
F
1, as a
μ
result of which even a 50
m wide pinhole would be scaled down to
,
500 nm and the
entire active area of the sensor array now can be used as the imaging FOV (i.e.,
FOV A
).
Although the entire derivation above is based on the formalism of wave theory, the final
result is also matched to a scaling factor of (
M
5
z
a
/z
s
) (see
Figure 8.1B
) predicted by
simple geometrical optics. In the case of
Mc
1 with partially coherent illumination, each
cell hologram only occupies a tiny fraction of the entire FOV and has little cross-talk with
other cell holograms. As a result, unlike conventional lensless in-line holography, there is
no longer an overall Fourier transform relationship between the sensor and the object
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