Fig 1.
(A) Experimental space and arrangement of instruments, including a three-dimensional array of 34 ultrasonic microphones, 10 high-speed motion-capture cameras, and 4 high-speed imaging cameras. (B) The head stage (indicated by red arrows) used to track the bat’s head movements.
Fig 2.
Measured beam pattern features of R. aegyptiacus.
(A) Normalized beam pattern at 35 kHz for a pair of consecutive clicks (top) and the average clicks obtained by merging all measured clicks (bottom). Crosses (“x”) indicate projected microphone locations, and plus signs (“+”) indicate the locations of sonar beam center. (B) Multi-frequency beam pattern structure of the same pair of clicks shown in (A) (top) and of the average clicks (bottom). The −3 dB contours (main lobe locations) of normalized beam pattern across multiple frequencies are color-coded. The average clicks appear more centered in both (A) and (B) because the 35-kHz beam axis of each individual click was aligned to the origin before averaging. (C) Model predictions of beam pattern and multi-frequency structure of a circular piston, plotted in the same color scales as in (A) and (B). The conventional piston model does not capture the beam pattern features of R. aegyptiacus. Note that all beam patterns in this study are plotted using the Eckert IV map projection from the bat’s perspective (see middle inset for orientation). The “stretch” in elevation of this map projection was compensated for in all the analyses.
Fig 3.
The transmission array beam pattern model.
(A) A close-up view of the bat’s mouth during click emission extracted from a high-speed video (S2 Video). (B) Illustration of model formulation. The beam pattern is formed by coherent summation of the contributions of array elements along the narrow mouth opening. The phase of each element is shifted by , determined by its distance to the clicking tongue (rn) and frequency (through the wavenumber k). (C) Operation of an engineered phased array. The sound beam is directed perpendicularly from the array when all elements transmit in phase (left). The beam is steered in other directions when the elements transmit with systematically varying phase shifts (right). Our model differs from the engineered phased array in that the phase shifts at array elements are not individually controlled. Instead, it is the overall phase shift pattern that is varied by the tongue position change. (D) Shape representations of the bat head used in the BEM model implementation. The red and blue dots show the locations of the tongue and array element, respectively. (E and F) Model beam patterns of individual clicks (E) and average clicks (F) at 35 kHz, predicted using the bat head shapes shown in (D). The model average clicks were reconstructed based on Monte Carlo simulated data generated using bat and microphone locations recorded during the experiment (S1 Text). (G) Multi-frequency structure of the individual model clicks shown in (E). The plotting conventions in (E-F) are identical to those in Fig 2. BEM, boundary element method; μCT, micro computed tomography.
Fig 4.
Beam steering using the transmission array model.
(A) A series of tongue clicking positions and corresponding −3 dB contours of the normalized model beam patterns (color-coded). Blue dots on the outline of the bat head represent locations of array elements. (B) Model beam patterns at 35 kHz predicted using tongue positions shown in (A). The models were calculated using the bat head mesh derived from μCT scans. The range of azimuth shown is from −90° to 90°. The solid dots inside the contours in (A) and the plus signs (“+”) in (B) indicate the locations of sonar beam center. μCT, micro computed tomography.