Biomedical Engineering Reference
In-Depth Information
and references therein). Pure phase objects with negligible absorption such as technical
reflective specimens or biological cells are sharply focused at the setting with the least
contrasted contours in the amplitude distributions
[59,60]
. In contrast to the bright-field
case, in digital holography this setting is of particular interest, as the amplitude and phase
distributions are accessible simultaneously, and the focal setting with the least contrasted
amplitude image corresponds to the best resolved structures in the quantitative phase
contrast distribution. In Ref.
[60]
, different numerical methods that calculate a scalar focus
value for the quantification of the image sharpness were compared. Therefore, common
criteria to evaluate the image sharpness in bright-field microscopy
[61,62]
were used. In
agreement with previously reported results for microscopic imaging with white light
illumination
[63,64]
, in Refs.
[60,65]
the evaluation of the weighted and band-pass-filtered
power spectra
X
focus value
5
log
f
1
1
½
F
F
ðjOðx
;
yÞjÞðμ
;
νÞg
(6.5)
μ
;
ν
was identified to be most suitable for a robust determination of the image sharpness in
DHM in combination with the convolution method described in
Section 6.3.2
.In
Eq. (6.5)
,
(
x
,
y
) are the coordinates in spatial domain and (
) denote the corresponding spatial
frequencies. The parameter F
F
ðjOjÞðμ
;
νÞ
denotes the band-pass-filtered Fourier transform
of the amplitude distribution
jO
(
x
,
y
)
j
. Logarithmic weighting is applied in order to consider
also weak parts of the spatial frequency spectrum. The lower boundary of the band-pass
filter is chosen in such a way that the constant background intensity is excluded. To
minimize the computation time as maximum spatial frequency, the value given by the
resolution of the optical imaging system is selected.
μ
,
ν
Figure 6.5
illustrates the principle of digital holographic autofocusing for the example of
time-lapse imaging of the reactions of living human brain microvascular endothelia cells
(HBMECs) co-incubated with a toxin. The experiments were performed with a DHM setup
as shown in
Figure 6.1
using a 40
3
microscope lens (NA
5
0.6,
λ
5
532 nm).
Figure 6.5A
F
shows representative amplitude and phase contrast images. At the beginning
of the experiment (
t
5
0), the investigated HBMECs were imaged sharply in the hologram
plane (
Figure 6.5A and D
). Due to an instability in the experimental setup, after
t
5
31.5 h,
without numerical focus correction the cells appeared unfocused in the reconstructed
amplitude and phase distributions (
Figure 6.5B and E
).
Figure 6.5E
shows further that
defocusing-induced diffraction patterns can lead to phase singularities and thus may cause
phase-unwrapping artifacts which inhibit a further data evaluation. The resulting images
after numerical refocusing are shown in
Figure 6.5C and F
. The cells appear sharply and
subcellular structures are clearly resolved without phase-unwrapping errors. Furthermore,
toxin-induced effects become visible. In
Figure 6.5G
, exemplary focus value curves in
dependence of the propagation distance
Δ
z
are plotted which were calculated by
Eq. (6.5)
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