Nano-Holographic Interferometry for In-Vivo Observations - Biomedical Optical Phase Microscopy and Nanoscopy - page 353

scale and with properties that are unlike classical FT holograms must be discussed.
However, the power of the original idea of Gabor is still present under a different form.
The first step is to analyze the optical path of the wavefronts that lead to the recording of
FTH images. The basic process will be illustrated in this section with a simple example of a
prismatic object that later on will be one of the nano-objects actually observed in the
measurements. In Section 17.1 , the idea of the observed objects as optical resonators was
introduced and a simple one-dimensional model was developed. The optical resonator is a
nano-object smaller in size than the wavelength of light that arrives to it. The object itself
becomes a light source emitting different frequencies that are determined by the geometry
and by the properties of the material of the object.
What is received by the sensor of the optical setup shown in Figure 17.2 is an inline FT
lens hologram where the source of illumination is the observed object. This is a
fundamental aspect to understand the process of information recording in the CCD sensor.
The source of illumination and the observed object coincides. This is a variant of the
original idea but still preserves the basic feature: information of an object is retrieved in the
FT field providing an increase in the spatial resolution.
Figure 17.8 shows the optical circuit bringing the images to the CCD detector. The object,
in this example a prismatic dielectric material resting on the upper surface of the
microscopic slide, is excited by the electromagnetic field of the evanescent waves and at
the interface with the microscope slide emits wavefronts. These wavefronts are diffraction
orders of the object. Assuming that the prism ( Figure 17.8 , Part 1) is approximately parallel
to the image plane of the CCD, the successive diffraction orders emerge at different angles
with respect to the normal of the slide surface that is assumed to be approximately parallel
to the normal of the sensor. The largest fraction of energy is concentrated in the zero order
and the first order [10] . Part 2 of Figure 17.8 shows the trajectories of the zero and first
diffraction orders entering and emerging the relay lens. Part 3 of Figure 17.8 shows the
image formation at the focal plane of the relay lens. As stated in [18] (section 5.2, page
103), the formed image is the FT of the object placed against the lens, with the presence of
an additional quadratic phase factor.
Part 4 of Figure 17.8 shows the image that the microscope projects into the CCD
sensor. Since the size of the object is small compared to the size of the relay lens, it is
possible to make the assumption of plane wavefronts. Consequently, the quadratic phase
factor becomes negligible in the current analysis of the image formation. The sensor
hence displays the FT of the observed object. Since the hologram is an inline hologram,
the zero order and the first order overlap—this is a characteristic of the inline holograms.
However, in the present case, the zero-order diffraction pattern is simultaneously the
source and the object itself, and hence the zero order contains information relevant to the
object.