Nano-Holographic Interferometry for In-Vivo Observations - Biomedical Optical Phase Microscopy and Nanoscopy - page 359

If one is dealing with objects that have central symmetry with respect to the center of
coordinates, the C factor must be utilized to reduce coordinates in the FT space to
coordinates in the object space. In this way, it is possible to convert frequency space
information into metrological data. If the object does not have central symmetry, the
inverse relationship between the object space and the frequency space must be applied.
17.9 Observation of Nano-Sized Objects
The next step is the verification of the proposed model by carrying out observation of
prismatic nano-sized objects and spherical particles. The prismatic objects present in the
field of view are different isomers of sodium chloride (NaCl) that precipitate on the surface
of the microscopic slide. Isomer dimensions were theoretically computed and
experimentally verified in literature [22] . The other observed nano-objects are small
polystyrene spheres that were injected into the NaCl solution. Among the large amount of
objects present in the region under observation, only a number of them are analyzed.
17.9.1 Prismatic NaCl Nanocrystals
The NaCl nanocrystals are located in the recorded images by observing the image of the
lens hologram with increasing numerical zooming. A square region around a selected
particle is cropped and the image is digitally re-pixelated to either 512 3 512 pixels or
1024 3 1024 pixels to increase the numerical accuracy of the FT of the crystals' images.
Image intensities are also normalized from 0 to 255. Figure 17.10 illustrates the case of a
square cross-section crystal of size 86 nm. Figure 17.10A is the recorded image;
Figure 17.10B and C shows the FT of the image and components that are filtered.
Figure 17.10D shows the filtered zero order while Figure 17.10E shows the result of the
filter shown in Figure 17.10C . Finally, Figure 17.10F is the addition of Figure 17.10D
and E .
In order to further understand the structure of the image, the pattern shown in
Figure 17.10F was numerically generated. As mentioned above, this pattern results from the
sum of different filtered components ( Figure 17.10D and E ). Utilizing edge-detection digital
techniques, the outlines of the zero order and the first order of diffraction are indicated in
Figure 17.10A . In that figure, the scale transformation between the actual image and the FT
was introduced, thus directly providing the space information measures. Since the pattern
presents asymmetry in the right side, only the shift in the left side was evaluated. Later
study of the geometry of the nanocrystal shows that there is a step on the right side of the
particle.
A numerical simulation of the image pattern is shown in Figure 17.11B . This pattern was
created by summing over the following: (i) a square area of uniform intensity corresponding