Biomedical Engineering Reference
In-Depth Information
a
c
b
Z
Z
Z
X
X
X
Fig. 4.8
170 nm fluorescent bead as imaged by a Zeiss LSM 510 confocal microscope fit with a
63X
/
1
.
2 water immersion lens. Axial MIP of the (
a
) observed bead images, (
b
) distilled PSF and
(
c
) the theoretically calculated PSF using the estimated experimental parameters [
53
]. The radial
pixel size is
37
nm and the width of each slice is
151
nm. The backprojected pinhole size is about
0
.
5 AU
obtained by distilling microsphere images are affected by its size (as can be seen by
comparing Fig.
4.8
b with the theoretical PSF in Fig.
4.8
c).
4.2.1.4
Image Formation Model
Mathematical Blurring Model.
In incoherent imaging, the distribution of inten-
sity in the image volume is found by integrating the intensity distributions in
the diffraction images of the PSF associated with each point in the specimen.
Mathematically, the process of blurring is modeled as a convolution between the
object intensity function,
o
:
Ω
s
→
R
x
=(
x
,y
,z
)
∈ Ω
s
at the 3-D coordinate
in the specimen volume, and the system PSF,
h
:
Ω
s
→
R
. By the scalar diffraction
theory, the observed image
i
:
Ω
s
→
R
(in the absence of any other degradation)
can be written using a discrete framework as
)=
x
∈Ω
s
x
−
x
)
o
(
x
)
,
i
(
x
h
(
(4.6)
where
is the 3-D coordinates in the image space. Here, the specimen coordinates
were normalized by the magnification to make the model Linear shift invariant
(LSI) [
32
]. Making it “shift invariant” implies that the PSF is constant over the field
of view. However, this assumption holds true only large NA objective and when
imaging the central part of the field. Equation (
4.6
) can be simply written as
x
i
(
x
)=(
h ∗ o
)(
x
)
, ∀
x
∈ Ω
s
,
(4.7)
where the interaction between the functions
h
and
o
is a '3-D convolution'. As
i
is the known entity and
o
the unknown, from the computational viewpoint, this
Search WWH ::
Custom Search