Biomedical Engineering Reference
In-Depth Information
object's image without twin-image contamination. This numerical method can be
summarized as follows:
a. In the first iteration, the intensity of the recorded hologram is propagated back to the
object plane by a distance of
2
z
s
, assuming zero as the initial phase value for the
complex field. Object support,
S
, is defined for each object either by thresholding
the field amplitude at the object plane or by finding its local maxima/minima.
b. For the complex field at the object plane,
U
i
the values outside the object
support are substituted with a background value
D
2
z
s
ð
ð
x
;
y
Þ;
2
z
s
x
;
y
Þ;
and the field inside the
object support remains unchanged, i.e.:
m
U
D
2
z
s
ð
x
;
y
Þ;
x
;
y
2
S
U
i
ðx; yÞ
5
U
i
2
1
2
2
z
s
ð
x
;
y
Þ;
x
;
y
A
S
z
s
where
D
2
z
s
ð
is generated by back-propagating the square root of the background image
(obtained in the absence of the objects) and
m
5
mean
x
;
y
Þ
U
i
2
1
ð
ð
x
;
y
ÞÞ=
mean
ð
D
2
z
s
ð
x
;
y
ÞÞ
is a
2
z
s
normalization factor.
c. The modified field at the object plane is then propagated forward to the sensor plane,
on which the updated phase of the sensor plane field remains unchanged but the
amplitude is replaced with the square root of the original recorded hologram intensity.
In other words, the measured amplitude of the sensor plane field will be kept constant
throughout these iterations to ensure convergence of the phase. Accordingly, the
complex diffraction field at the sensor plane after the
i
th iteration,
U
ðiÞ
ðx; yÞ;
can be
0
written as:
U
ðiÞ
U
ð
0
Þ
ð
[
ðiÞ
ð
x
;
y
Þ
5
j
ð
x
;
y
Þj
exp
ð
x
;
y
ÞÞ
0
0
0
where the superscripts refer to the iteration step, and
[
ðiÞ
denotes the phase of the field
at sensor plane after the
i
th iteration. After this modification, the sensor plane complex field
is again propagated backward to the object plane to get the updated object field.
ðx; yÞ
0
By iterating between steps b and c, the phase values of the sensor field typically converge
within 15
20 iterations. Once converged, the complex field is propagated backward to the
object plane as the final output of the microscopic cell images containing both amplitude
and phase profiles.
8.4 On-Chip Imaging of Sperm Using Partially Coherent Lensfree In-Line
Holography
In this section, we are going to explain the implementation of our holographic on-chip
imaging technique that is at the heart of the presented semen analysis platform and clarify
Search WWH ::
Custom Search