Biomedical Engineering Reference
In-Depth Information
Figure 6.1
, the sample is illuminated by laser light via a single-mode optical fiber (SM) by
inserting a nonpolarizing beam splitter cube (BS1) into the illumination path of the
microscope's white light source (WS). Behind the microscope lens (MO), the light is
coupled into a Michelson interferometer which is attached to a camera side port of the
microscope. Mirror M2 is tilted by an angle
in such a way that an area of the sample that
contains no object is superposed with the image of the specimen to create a suitable spatial
carrier fringe pattern for off-axis holography (for illustration, see
Figure 6.4
). Note that due
to the Michelson interferometer design in areas without specimen, two wave fronts with
nearly identical curvatures are superimposed. This is even fulfilled for an imaging geometry
with two slightly divergent waves that differ from the collimated arrangement, which is
shown in
Figure 6.2
to simplify the illustration of the measurement principle. The digital
holograms are recorded by a CCD sensor. The numerical calculation of the quantitative
DHM phase contrast images from the resulting self-interference digital holograms can be
performed as described in
Sections 6.3.2 and 6.3.3
.
α
6.3 Recording and Numerical Evaluation of Digital Holograms
In this section, the recording and the numerical evaluation of digital off-axis holograms for
multifocus quantitative phase imaging is described. First, the coding of the object wave in off-
axis holograms is explained. Then, the spatial phase shifting evaluation for the retrieval of the
object wave and the optional numerical propagation of the obtained wave fields to the image
plane by a convolution approach of the Huygens
Fresnel principle are described. Afterward,
the evaluation of off-axis and self-interference digital holograms for multifocus quantitative
phase imaging and the principle of (subsequent) numerical autofocusing is illustrated.
6.3.1 Intensity Distribution in the Hologram Plane
The intensity distribution
I
H
of the interferogram in the hologram plane located at
z
5
z
H
that is created with the experimental setups in
Figures 6.1 and 6.2
by the interference of the
object wave
O
and the reference wave
R
is
[4]
Oðx
;
y
;
z
H
ÞO
ðx
;
y
;
z
H
Þ
1
Rðx
;
y
;
z
H
ÞR
I
H
ðx
;
y
;
z
H
Þ
5
ðx
;
y
;
z
H
Þ
Oðx
;
y
;
z
H
ÞR
ðx
;
y
;
z
H
Þ
1
Rðx
;
y
;
z
H
ÞO
ðx
;
y
;
z
H
Þ
1
p
I
O
ðx
;
y
;
z
H
ÞI
R
ðx
;
y
;
z
H
Þ
I
O
ðx
;
y
;
z
H
Þ
1
I
R
ðx
;
y
;
z
H
Þ
1
2
cos
Δϕ
HP
ðx
;
y
;
z
H
Þ
(6.1)
5
with
I
O
5
OO
and
I
O
5
RR
(
represents the conjugate complex terms). The
parameter
Δϕ
H
(
x
,
y
,
z
H
)
5
ϕ
R
(
x
,
y
,
z
H
)
2
ϕ
O
(
x
,
y
,
z
H
) is the phase difference between
O
and
R
at
z
5
z
H
. In the presence of a sample in the optical path of
O
, the phase distribution
represents the sum
2
2
5
jOj
5
jRj
ϕ
O
ðx
;
y
;
z
H
Þ
5
ϕ
O
H
ðx
;
y
;
z
H
Þ
1
Δϕ
S
ðx
;
y
;
z
H
Þ
with the pure object wave
phase
ϕ
O
H
ðx
;
y
;
z
H
Þ
and the phase change
Δϕ
s
(
x
,
y
,
z
H
) that is effected by the sample. In the
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