Model of a multiple-lens,single-fiber system in a compound eye

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.