Biomedical Engineering Reference
In-Depth Information
e
jk
s
r
,wherek is the
wave number of illumination,
s
is the direction of incidence, and
r
is the position
vector. Therefore, the back propagation of the hologram needs to be done along
the direction illumination,
s
. For this purpose, digital beam propagation is achieved
by using the angular spectrum approach [
29
], which involves a Fourier domain
implementation of convolution. That is, the Fourier transform of the field to be
propagated is multiplied by the transfer function of free space propagation, and
an inverse Fourier transformation yields the complex field in the plane of interest.
This process, referred to as digital holographic reconstruction, results in a complex
valued microscopic image of the object. However, unlike other holography schemes
such as phase-shifting [
30
] and off-axis holography [
31
], digital in-line holography
suffers from an artifact which compromises the quality of the microscope image,
referred to as the twin image, and can be seen in the interference terms of Eq.
4.1
.
Since the sensor is only sensitive to the intensity of the optical field, the phase of the
field is lost. As a consequence of this, in addition to the desired field s.x; y;
z
0
/,the
term s
.x; y;
z
0
/ is also generated. This last term, also known as twin image, trans-
lates to a defocused image of the object spatially overlapping with the microscopic
image of the object. There are several techniques in the literature that allow the
retrieval of the phase of the field through the knowledge/measurement of its intensity
and certain physical constraints on the field [
32
,
33
]. For this end, one commonly
used phase-retrieval technique in lensfree on-chip holography is an iterative one,
which propagates the optical field back and forth between the sensor and the object
planes. At each iteration, the amplitude of the field that is measured at the sensor
plane is enforced, but the phase is allowed to be updated. In addition to this, at
the object plane, the spatial support of the object is also enforced at each iteration.
Note that this support can still be determined despite the presence of the twin-image
artifact. This algorithm has been successful in retrieving the lost optical phase at the
detector plane, eliminating the twin image for practical considerations [
9
-
15
].
incident beam can be approximated as a plane wave, R
D
4.3
Lensfree Holographic Microscopy of Biochips Using
a Single Partially Coherent Source (LED)
The initial versions of lensfree microscopy prototypes that we developed comprise
a single partially coherent light source (LED) butt-coupled to a large pinhole (with
0:1 mm diameter) and an optoelectronic sensor array (e.g., CMOS or CCD chip) to
record digital in-line holograms of objects within biochips without using any lenses,
as illustrated in Fig.
4.1
. The architectural simplicity of these platforms enabled us
to build lightweight (
5:8 cm), mechanically robust,
and cost-effective telemedicine microscopes as shown in Fig.
4.2
[
10
]. Using a
5-megapixel CMOS sensor with 2:2-m pixel size, these field-portable microscopes
can achieve a sub-pixel lateral spatial resolution of
46 g), compact (4:2
4:2
1:5moveranFOVof
24 mm
2
, which can be particularly useful for high-throughput diagnostic imaging
applications such as blood analysis and rare-cell detection in low-resource settings.
