Understanding and mimicking the dual optimality of the fly ear

Abstract

The fly Ormia ochracea has the remarkable ability, given an eardrum separation of only 520 μm, to pinpoint the 5 kHz chirp of its cricket host. Previous research showed that the two eardrums are mechanically coupled, which amplifies the directional cues. We have now performed a mechanics and optimization analysis which reveals that the right coupling strength is key: it results in simultaneously optimized directional sensitivity and directional cue linearity at 5 kHz. We next demonstrated that this dual optimality is replicable in a synthetic device and can be tailored for a desired frequency. Finally, we demonstrated a miniature sensor endowed with this dual-optimality at 8 kHz with unparalleled sound localization. This work provides a quantitative and mechanistic explanation for the fly's sound-localization ability from a new perspective, and it provides a framework for the development of fly-ear inspired sensors to overcoming a previously-insurmountable size constraint in engineered sound-localization systems.

Figure 1. Dual-optimality of the fly ear and a fly-ear inspired sensor.

(a), Schematics of the fly ear structure and the lumped parameter model of the fly ear (redrawn from ref. 11). (b), The two vibration modes of the fly ear (redrawn from ref. 11). (c), Dual optimality of the fly ear achieved at the frequency of the cricket's calling song; that is, maximum average directional sensitivity (ADS) and minimum nonlinearity (NL) simultaneously achieved at 5 kHz. The inset shows the directional sensitivity (DS) at three different frequencies. (d), Natural frequencies (normalized by the optimal working frequency) determined through optimization analysis to ensure the dual-optimality characteristic as a function of the wavelength-to-separation ratio χ for two damping scenarios: i) ξ₁ = 0.89, ξ₂ = 1.23 and ii) ξ₁ = 0.18, ξ₂ = 0.05. The two cases marked by the red dots correspond to working frequencies of 5 kHz in i) (the fly ear) and 8 kHz in ii) (a low damping device). (e), Phase difference mIPD at 5 kHz as a function of azimuth for different coupling strength scenarios: stiff (natural frequency ratio η = 20), medium (η = 4.36; i.e., the fly ear case), soft (η = 2), and uncoupled (η = 1). The results were obtained by using the fly ear's structural parameters with varying bridge stiffness k₃. (f), Frequency spectra of ADS and NL for i) soft coupling and ii) stiff coupling. (g), Dual optimality of a fly-ear inspired sensor designed to work at 8 kHz.

Figure 2. Fly-ear inspired sensor.

(a), Cross-sectional view of the sensor, which has four layers: (1) device layer, (2) perforated holes layer, (3) back chamber layer, and (4) back plate layer. (b), Low-coherence fiber optic interferometer for detecting membrane vibration. (c), Photo of the assembled prototype shown next to a kitchen match. The length of the scale bar is 2 mm.

Figure 3. Characterization of the fly-ear inspired sensor.

(a), Phase difference as a function of frequency and incident azimuth: (i) experiments and (ii) simulations. (b), Two vibration modes obtained with a laser scanning vibrometer. (c), Average directional sensitivity (ADS) and nonlinearity (NL) as a function of frequency (circles and squares for experimental results and solid lines for simulation results). (d), Phase difference mIPD as a function of azimuth at the optimal working frequency 8 kHz (red circles for experimental results, green solid lines for simulation results). (e), An example of the bio-inspired localization-lateralization scheme. With an initial azimuth of 80° for the sound source (in the lateralization range), the fly-ear inspired sensor is rotated until the source falls in the linear (localization) range of the sensor, at which a final turn is made to pinpoint the source.