5 Near-Field Scanning Optical Microscope Combined with Digital …
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ˆ
E
SF
H
k x , k y , 0
= SF
ˆ
E H
k x , k y , 0
3. Propagation in k-space from z = 0 to any plane z. This is done by multiplying the
resulting complex field by a z-propagation function G
k x , k y , z
= exp(ik z z):
ˆ
E
SF
H
k x , k y , z
= ˆ
E
SF
H
k x , k y , 0
· G
k x , k y , z
4. Second Fourier Transform to move back to the spatial domain:
E O (x, y, z) = FT
−1
ˆ
E
SF
H
k x , k y , z
An example of the above reconstruction procedure is presented in Fig. 5.4. Here,
we use an aperture NSOM tip in contact with a sample made up of a 40 nm gold
film on a glass substrate. A typical hologram recorded in the plane of the camera
is shown in Fig. 5.4a. This hologram is the result of interference between the light
scattered through the aperture probe and the reference beam. Because of our offaxis configuration, interference fringes can be clearly seen (Fig. 5.4a inset). The first
step of the reconstruction (Fourier transform of the recorded real space hologram) is
shown in Fig. 5.4b, where we can clearly see the three diffraction orders separated in
k-space. The zeroth order is seen at the center, and the +1 and −1 diffraction orders
are separated symmetrically on both sides, also because of the off-axis configuration.
The +1 interference term needed to reconstruct the 3D image (highlighted by a
red circle) is chosen and the two other terms are filtered out. We then propagate
the filtered Fourier transform of the hologram in k-space by multiplying by the
propagator G. Finally, an inverse Fourier transform is performed which allows us
to calculate the complex electromagnetic field in any z plane from the plane of the
camera up to the plane of the NSOM tip. Piling up all the images together gives us
the 3D reconstructed EM field scattered from the probe, where both the amplitude
and phase can be calculated from a single hologram. Examples of the reconstructed
images of intensity scattered through the substrate are shown in Fig. 5.4c for z =
10 μm below the tip up to the contact position (z = 0 μm).
5.3 Near-Field Scanning Optical Microscopy Combined
with Digital Holography
In this section, we describe the results that we obtained with our integrated
holography-NSOM technique, where we study the light scattered by nanosized
probes in various environments. We observe that the aperture tip in free space scatters light mainly in the forward direction with a broad angular distribution. When
it is placed in contact with a glass substrate, light is scattered exactly at an angle
matching the critical angle of an air/glass interface. Finally, when the tip is placed
119
ˆ
E
SF
H
k x , k y , 0
= SF
ˆ
E H
k x , k y , 0
3. Propagation in k-space from z = 0 to any plane z. This is done by multiplying the
resulting complex field by a z-propagation function G
k x , k y , z
= exp(ik z z):
ˆ
E
SF
H
k x , k y , z
= ˆ
E
SF
H
k x , k y , 0
· G
k x , k y , z
4. Second Fourier Transform to move back to the spatial domain:
E O (x, y, z) = FT
−1
ˆ
E
SF
H
k x , k y , z
An example of the above reconstruction procedure is presented in Fig. 5.4. Here,
we use an aperture NSOM tip in contact with a sample made up of a 40 nm gold
film on a glass substrate. A typical hologram recorded in the plane of the camera
is shown in Fig. 5.4a. This hologram is the result of interference between the light
scattered through the aperture probe and the reference beam. Because of our offaxis configuration, interference fringes can be clearly seen (Fig. 5.4a inset). The first
step of the reconstruction (Fourier transform of the recorded real space hologram) is
shown in Fig. 5.4b, where we can clearly see the three diffraction orders separated in
k-space. The zeroth order is seen at the center, and the +1 and −1 diffraction orders
are separated symmetrically on both sides, also because of the off-axis configuration.
The +1 interference term needed to reconstruct the 3D image (highlighted by a
red circle) is chosen and the two other terms are filtered out. We then propagate
the filtered Fourier transform of the hologram in k-space by multiplying by the
propagator G. Finally, an inverse Fourier transform is performed which allows us
to calculate the complex electromagnetic field in any z plane from the plane of the
camera up to the plane of the NSOM tip. Piling up all the images together gives us
the 3D reconstructed EM field scattered from the probe, where both the amplitude
and phase can be calculated from a single hologram. Examples of the reconstructed
images of intensity scattered through the substrate are shown in Fig. 5.4c for z =
10 μm below the tip up to the contact position (z = 0 μm).
5.3 Near-Field Scanning Optical Microscopy Combined
with Digital Holography
In this section, we describe the results that we obtained with our integrated
holography-NSOM technique, where we study the light scattered by nanosized
probes in various environments. We observe that the aperture tip in free space scatters light mainly in the forward direction with a broad angular distribution. When
it is placed in contact with a glass substrate, light is scattered exactly at an angle
matching the critical angle of an air/glass interface. Finally, when the tip is placed