Biologically Inspired Optical Systems - Biomimetics: Biologically Inspired Technologies - page 293

Variable fluid
chamber

Thickened sclera

Figure 11.2 Biological fluidic adaptive lens schematic. The thickened sclera allows the eye to withstand pressures
at increased diving depths.

By using similar principles, Zhang et al. (2003) at the University of California at San Diego have
created an adaptive fluidic lens. The lens itself is made of an inexpensive polymer, polydimethyl-
siloxane (PDMS), processed using soft lithography to include a fluid chamber and injection port.
The 60-mm thick PDMS membrane is then bonded to a glass substrate using oxygen plasma
bonding technology. By filling the chamber, Zhang et al. were able to demonstrate a focal length
range from 41 to 172 mm, with corresponding numerical aperture values of 0.24 to 0.058. The
highest recorded resolution was 25.39 lp/mm in both horizontal and perpendicular directions. These
results are shown in Figure 11.3.
This unique design allows for a variable focal length system in a rather compact and robust
arrangement. It should be noted, however, that it may be possible to improve upon their design by
studying nature further. It is well known that a homogenous spherical lens will suffer from spherical
aberration, when the peripheral light rays are refracted more than the axial ones. In the biological
world, this problem has been managed in two ways. The first, and most appropriate to this design, is
to have a nonspherical profile such that the periphery of the lens is flatter than the center. By
following nature's example again, Zhang et al. may achieve even better results.

11.2.2 An Artificial Cephalopod Eye

As alluded to in the previous section, there is a second method nature has used to deal with spherical
aberration (Land, 1988). This involves the use of a ball lens with a spherically-symmetric refractive
index gradient that decreases from the center outwards (Figure 11.4). This is a particularly
appropriate adaptation to the watery habitat of cephalopods, such as octopi and squid. Such an
environment necessitates that the entire focusing power of the eye lie within the lens itself, as both
sides of the cornea consist of essentially the same medium. In this arrangement, a spherical lens
provides the shortest possible focal length. The result is a wide field of view from a relatively
compact apparatus.
The theory that cephalopods use a spherical lens with a refractive index gradient was initially
postulated in the latter half of the 1800s, first by Maxwell and later by Matthiessen (Land, 1988).
Indeed, it was Matthiessen who determined that the ratio of the focal length to the lens radius is
approximately 2.5 (''Matthiessen's ratio'') in animals with lenses of this design. A precise math-
ematical description of the gradient was not established until 1944 (Luneberg, 1944), followed by a
numerical solution in 1953 (Fletcher, 1953). Still, it was not until 33 years later that Koike et al.
created an artificial ball lens with the required index of refraction gradient (Koike et al., 1986).
Besides the lens, construction of an artificial cephalopod eye involves a critical design issue.
The retinas of many animals including cephalopods are curved structures, whereas man-made
photodetector arrays are flat. This has much to do with the way electronics are manufactured in
general, on flat semiconductor surfaces. Hung et al. (2004) have overcome this limitation by