Biomedical Engineering Reference
In-Depth Information
hologram plane
[26]
. However, numerical refocusing also may be performed with other
common numerical propagation methods, including in particular more general approaches
of the convolution method
[38]
and the angular spectrum method
[41,50]
. During the
propagation process, the parameter
zin
Eq. (6.2)
is chosen so that the holographic
amplitude image
jOj
appears sharply, like, for example, a microscopic image under white
light illumination. In the special case that the image of the sample is sharply focused in the
hologram plane with
Δ
z
5
0 and thus
z
IP
5
z
H
, the reconstruction process can be accelerated
because no propagation of
O
by
Eq. (6.2)
is required.
Δ
6.3.3 Quantitative Phase Imaging
In addition to the amplitude
jO
(
x
,
y
,
z
IP
)
j
that represents the image of the sample, from the
numerically reconstructed and optionally propagated complex object wave
O
(
x
,
y
,
z
IP
)(see
Eq. (6.2)
) also the sample induced phase change
Δϕ
S
(
x
,
y
,
z
IP
) is obtained
[10,29]
:
Δϕ
S
ðx
;
y
;
z
IP
Þ
5
arctan
Im
f
O
ð
x
;
y
;
z
IP
Þg
Re
fOðx
;
y
;
z
IP
Þg
ð
mod 2
πÞ
(6.3)
After removal of the 2
ambiguity by phase unwrapping
[4]
, the data obtained by
Eq. (6.3)
can be used for quantitative phase imaging.
π
In
transmission mode
(see
Figures 6.1 and 6.2
), the induced phase change
S
(
x
,
y
,
z
IP
)ofa
semitransparent sample is influenced by the sample thickness, the refractive index of the
sample, and the refractive index of the medium that surrounds the investigated specimen.
Thus, for quantitative cell imaging, information about the cellular refractive index is
required. Different interferometric and holographic methods for the determination of the
refractive index have been developed (see Refs.
[12,51,52]
and
Section 6.4
). For cells in
cell culture medium with the refractive index
n
medium
, and the assumption of a known
homogeneously distributed integral cellular refractive index
n
cell
, the cell thickness
d
cell
(
x
,
y
,
z
IP
) can be determined by measuring the OPL change
Δϕ
Δϕ
cell
of the cells to the
surrounding medium
[10,29]
:
d
cell
ðx
;
y
;
z
IP
Þ
5
λΔϕ
cell
ð
x
;
y
;
z
IP
Þ
2
1
n
cell
2
n
medium
(6.4)
U
π
λ
The parameter
in
Eq. (6.4)
represents the wavelength of the applied laser light. For
adherently grown cells, the parameter
d
cell
can be interpreted as the cell shape.
Nevertheless, the results from
Eq. (6.4)
have to be handled critically, e.g., if toxically and
osmotically induced reactions of cells
[29,53]
are analyzed that may cause dynamic changes
in the cellular refractive index.
Figure 6.3
shows the numerical processing of a digital off-axis hologram by spatial phase
shifting-based reconstruction.
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