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.