Model predicts bat pinna ridges focus high frequencies to form narrow sensitivity beams

The pinnae of bats contain ridges whose function was previously thought to be structural. This paper suggests that ridges form a reflecting Fresnel lens that focuses high-frequency acoustic signals into the ear canal to form a narrow elevation sensitivity beam. E. fuscus ridges are modeled as a series of four paraboloidal strips and the tragus is considered to act as a secondary reflecting element analogous to a Cassegrain system. A diffraction grading having the equivalent spacing suggests frequencies above $150kHz$⁠. Using an example $170kHz$⁠, a random search for ridge dimensions that minimize side-lobes in the frequency magnitude response yields the tapered ridge structure observed in E. fuscus and produces an 18° (full width half energy) beam width. We speculate that the possible high-frequency sources are ecologically (prey) generated and/or the third harmonic of the call. The attenuation at such high frequencies requires that the source be close by. Passive prey localization in the postbuzz stage, when echoes overlap call transmissions and the prey is within $8cm$⁠, could improve prey capture efficiency. An experiment using $40kHz$ ultrasound with human observers verifies that frequencies beyond the audiometric range, when sufficiently intense, can still be perceived.