Biomedical Engineering Reference
In-Depth Information
Fig. 4.9
A photograph and schematic diagram of a field-portable pixel super-resolution micro-
scope. It is comprised of 23 LEDs, each butt-coupled to 23 multimode optical fibers. These LEDs
are turned on sequentially, each generating a slightly shifted lensfree hologram compared to the
others. These shifted holograms are then processed to generate a single hologram with a much
smaller effective pixel size [
19
]
algorithms [
39
,
40
]. First, the shifts between the different holograms need to be
calculated, which can be done
without
the prior knowledge of any of the physical
parameters of our imaging systems, adding to the robustness of the approach. Integer
pixel shifts between holograms are redundant and add no useful information regard-
ing high-frequency content. Therefore, as a first step, the integer part of the shifts
between holograms is calculated through a simple correlation, and the images are
approximately aligned to each other. The more useful sub-pixel shifts between the
holograms can be computed, for example, using an iterative gradient method [
40
].
If the hologram I
2
is a slightly shifted version of the hologram I
1
,thatis,I
2
.x;y/
D
I
1
.x
C
a;y
C
b/,thenI
2
can be approximated using I
1
and its derivatives:
@I
1
@x
@I
1
@y
I
2
.x; y/
I
1
.x; y/
C
a
C
b
(4.2)
The parameters a and b can be estimated by minimizing the squared distance
between the measured I
2
and its approximation I
2
. If desired, I
1
can be shifted by
the calculated parameters, and then, the same linear approximation can be repeated
for a better estimate of the shifts.
