Biomedical Engineering Reference
In-Depth Information
Fig. 8.8 Gradient index lens
with minimized spherical
aberrations
M1
GRIN
polishing line
M2
This concept has been exploited in the design of a lens with a graded refracted index
distribution fabricated, as illustrated in Fig. 8.8 , by pressing an planar graded index
polymer film between two molds, M1 and M2, with different radii of curvature, R 1
and R 2 , respectively ( Jin et al. 2007 ). The graded index distribution is preserved
in the process and a plano-convex lens with a graded index can be obtained after
subsequent polishing the shaped film along a horizontal plane. The planar 4-mm-
thick polymer film consists of 20,000 layers that induce a total index of refraction
gradient across the structure of n D 0:08. Refractive index differences between
nanolayers as small as 0.0009 can be obtained by varying the ratios of polycarbonate
(with an index of 1.58) and poly(methyl methacrylate) with a refractive index of 1.49
in the material. These ultrathin layers do not scatter light since they are thinner than
a quarter wavelength, their effect on the incident radiation being to modulate the
effective index of refraction. The focal lengths of the lenses fabricated in this way
are of tens of millimeters.
Nature is a source of inspiration not only for efficient gathering of ambient
light but also for configurations of solar cells. For example, the so-called Gratzel
or dye-sensitized solar cell is a photoelectrochemical system that mimics the
photosynthesis process of chlorophyll in green leaves ( O'Regan and Gratzel 1991 ).
It consists of a porous layer of TiO 2 nanoparticles surrounded by an absorbing
dye, which replaces the organic dye porphyrin, found in plants as chlorophyll
and in animals as hemoglobin. The nanoparticles, in contact with a transparent
anode, are immersed in an electrolyte solution containing a platinum cathode. The
photogenerated electrons are injected in the conduction band of wide-bandgap TiO 2
nanoparticles and subsequently collected by the anode, the electrolyte having the
role of regenerating the electrons in dye, and thus closing the electrical circuit,
through redox reactions.
Irrespective of the type of solar cell, the conversion efficiency can be greatly
improved if the number of incident photons is maximized. A wide field of view
certainly improves light collection. The common housefly Musca domestica ,for
example, has a field of view of 270 ı , its compound eyes consisting of cylindrical
ommatidia with a diameter of 20m, positioned on a curved surface. Prismatic
compound lenses, inspired from the housefly and made from silicon and silicon
dioxide, were studied in Chiadini et al. ( 2010 ). A detailed fractal model was
considered for their design, the original zeroth-stage cross section of the lens, in
the form of a segment of a circle being decorated in the first stage by a number of
circular segments with decreasing radii, which are decorated in the second stage
with circular segments with still smaller radii, and so on. The zeroth and first
stages of the cross section of the prismatic lens, which is constant along the y
direction, are shown in Fig. 8.9 . Extended ray-tracing simulations have confirmed
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