Biomedical Engineering Reference
InDepth Information
Fig. 4.12
(
a1

a3
) show the reconstructed images of a 2m diameter microsphere in xy, yz, and
xz planes, respectively, using a single LR hologram. (
b1

b3
) show the reconstructed images of a
2m diameter microsphere in xy, yz, and xz planes, respectively, using a SR hologram. (
c1

c3
)
show the computed tomograms in the xy, yz, and xz planes for the same microparticle, obtained
by using the fieldportable lensless tomographic microscope shown in Fig.
4.13
Since we correct for the diffraction between the object and the sensor (i.e.,
hologram plane) by digital holographic reconstruction algorithms as discussed in
earlier sections, the use of a backprojection algorithm, as opposed to a diffraction
tomography approach, only ignores the diffraction within the object. This approx
imation can be justified by the modest NA (0.30.4) and the relatively long DOF
of our lensfree projection images. We can denote the sample's 3D transmission
function as s.x
;y
;
z
/,where.x
;y
;
z
/ defines a coordinate system whose
zaxis is aligned with the illumination angle () at a particular projection. Ignoring
multiple scattering within the sample and by assuming that it weakly scatters the
incident light [
60
], after phase recovery (or twinimage elimination) steps, each
amplitude projection image yields the 2D line integral of our 3D object function,
that is,
R
<DOF>
j
s.x
;y
;
z
/
j
d
z
. That is, a projection image along a given angle
can be approximated to represent a rectilinear summation of the amplitudes of
the transmission coefficients of the 3D object over a length scale of one depth of
focus (DOF) around z
0
,wherez
0
is the depth for which the tomogram is to be