Abstract: In earlier work, we showed that a simple apposition compound eye can
form the hardware basis for a new type of inertial navigation system, that can
be used on micro air vehicles. One of the key properties of a simple apposition
eye is that it is a low pass, spatial filter. This property had been shown in
mathematical models based on Fourier optics for a single lens and single fiber
system. However, a simple apposition compound eye usually consists of thousands
of lenses called ommatidia. An important question that has not been studied is
the effect the presence of multiple lenses have on the angular sensitivity, or
in some other words, the bandwidth of the low pass, spatial filter. In this
paper, we develop a Fourier optics model for a multiple lens, single-fiber
system. We obtain expressions for the intensity distribution near the focus of
a single lens due to the presence of neighboring lenses and for the angular
sensitivity of the system. Numerical simulations show a less than 10 percent
increase in the angular sensitivity, even when five or more lenses are
considered to focus light on a single rhabdom in a worker bee and an artificial
eye.
