An approximate model for foliage echoes to study biosonar function in natural environments

Abstract

Natural environments are difficult for current engineered sonars but apparently easy for at least some species of echolocating bats. To better understand the information that foliage echoes provide for biosonar-based sensing, an approximate model of foliage echoes has been developed. The model simplifies the scattering problem through two key assumptions: (i) multi-path scattering was neglected and (ii) all leaves were assumed to be circular disks. Due to the latter, the parameters of the model were reduced to the number of the disks, their positions, sizes, and orientations. The exact far-field scatter from a disk (i.e., simplified leaf) in response to planar incident waves can be obtained by summation over an infinite series of spheroidal wave functions. To reduce the calculation time, the scattered field has been approximated by exponential, polynomial, and cosine fitting functions that also depend on the disk parameters. This allows the simulation of echoes from 100 leaves in 20 s on a standard PC. The model was able to reproduce the echo waveforms from dense and sparse foliages qualitatively. The model should thus be well suited for generation of large echo datasets to explore the existence and utilization of statistical invariants in the echoes from natural environments.