Biomedical Engineering Reference
In-Depth Information
Figure 12.5A
shows the phase image
m polystyrene bead (Polysciences
Inc.) taken at zero incidence angle.
Figure 12.5B
shows the typical amplitude image of
U
φ
(
x
,
y
;
θ
5
0) of a 6
μ
ð
k
x
;
k
y
; θÞ
on a logarithmic scale.
To apply the Fourier diffraction theorem (
Eq. (12.6)
), (
k
x
,
k
y
) on the right-hand side is
converted into (
K
x
,
K
y
) as follows:
i
ð
K
z
1
k
z
0
Þ
U
ð
S
Þ
F
z
1
5
0
ð
K
x
;
K
y
;
K
z
Þ
5
ð
K
x
1
k
x
0
;
K
y
1
k
y
0
;
Þ
(12.9)
π
U
ð
S
Þ
(
Eq. (12.2)
)or
U
ð
S
Þ
Then, either
(
Eq. (12.8)
) is calculated from
measured complex fields. Shifting the spectrum by (
2
k
x
0
,
2
k
y
0
) in spatial frequency space
ð
k
x
;
k
y
; θÞ
ð
k
x
;
k
y
; θÞ
Rytov
4
1.5
3
1
2
1
0.5
0
0
-1
(A)
(B)
-8
-10
-12
-14
-16
-18
K
x
(
μ
m
-1
)
K
x
(
μ
m
-1
)
(C)
(D)
Figure 12.5
Mapping of the complex E-field onto the 3D Fourier space of the object function.
(A) Quantitative phase image of a 6
m polystyrene bead at zero-degree illumination. The color
bar indicates phase in radians. Scale bar, 5
μ
m. (B) Amplitude of the Fourier transform of
the complex E-field image at zero-degree illumination on a logarithmic scale. (C) Amplitude
distribution in K
x
K
y
plane after mapping all the angular E-field images. (D) Amplitude
distribution in the K
x
K
z
plane. The color bar indicates base-10 logarithm of the amplitude of
E-field. The scale bars in (B
μ
m
2
1
[24]
.
D) indicate 2
μ
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