Biomedical Engineering Reference
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that the angle defined between the optical axis and the shorter CCD direction (typically the
vertical one) will be half the oblique illumination angle (
ILUM
to be
twice the angle defined by the NA in the shorter CCD direction while satisfying the
Nyquist condition imposed by the
s
distance. In any case, a contiguous frequency band will
be diffracted on-axis when vertical tilted illumination impinges on the input object. Thus,
the new vertical cutoff frequency becomes expanded three times or, equivalently, the
resolution is improved by a factor of 3 in the vertical Fourier direction. However, when
applying the proposed method in other directions, the resolution gain will be slightly lower
than 3 because the CCD is normally wider in the horizontal than in the vertical axis.
θ
ILUM
), or by selecting
θ
After angular multiplexing the object's spectrum with different sequential tilted beam
illuminations, each recorded hologram is numerically processed to synthesize the expanded
SA. The digital manipulation implies, first, a coordinate transformation to remove the
nonlinear geometrical distortion incoming from the violation of the Fresnel approximation
[15,20]
. Second, an input plane numerical back propagation can be achieved by
implementing the convolution approach in the Rayleigh
Sommerfeld equation
[20,54
56]
.
Third, a correct reallocation of the spectral content of each bandpass image while
generating the SA
[57]
. Finally, the SR image is obtained by FT of the information
contained in the SA.
In order to validate the proposed method experimentally, we present two experiments. In the
first one, we propose the use of a Blu-ray source as illumination light (
m) and a
positive high-resolution 1951 USAF test target as input object to calibrate the setup. Note that
the test target must be positive (clear background) instead of negative (opaque background) to
fulfill the Gabor's regime. A CCD camera (Basler A312f, 582
3
782 pixels, 8.3 pixel size,
12 bits/pixel) is used to record the in-line holograms. A commercial grade standard
microscope lens (DIN 40
3
, 0.65NA) is used to provide point source divergent high NA
illumination in the setup. The illuminator (Blu-ray source with the microscope lens) is placed
onto a motorized linear translation stage to allow off-axis displacement. The point-source-test
and point-source-CCD distances are
z
S
5
400 and
z
D
5
11 mm, respectively, so the
magnification of the setup is
M
5
28.5. With this
M
value, a sample's detail of 1
λ
5
0.405
μ
μ
m occupies
28.5
μ
m at the CCD plane and becomes properly sampled by the 8.3
μ
m size CCD pixel.
m(
s
distance) from the optical axis to allow two off-axis
recordings for the vertical (V) and horizontal (H) orthogonal directions, respectively. Note
that this distance is lower than the one defined by the Nyquist criterion (
s
m
5
0.268
μ
m) and
it is the proper distance to transmit quasi-contiguous spectral content in the shorter (V)
CCD direction. As a result, the NA of the tilted illumination is NA
ILUM
5
0.4. Since the
USAF test target mainly has diffracted components in the horizontal (H) and vertical (V)
directions, we have only considered off-axis illuminations into the H and V planes.
Figure 9.2
images the central part of both the four recovered bandpass images when tilted
μ
The point source is shifted 175
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