When a beam emitted from an active monostatic sensor system sweeps across a volume, the echoes from scatterers present will fluctuate from ping to ping due to various interference phenomena and statistical processes. Observations of these fluctuations can be used, in combination with models, to infer properties of the scatterers such as numerical density. Modeling the fluctuations can also help predict system performance and associated uncertainties in expected echoes. This tutorial focuses on "physics-based statistics," which is a predictive form of modeling the fluctuations. The modeling is based principally on the physics of the scattering by individual scatterers, addition of echoes from randomized multiple scatterers, system effects involving the beampattern and signal type, and signal theory including matched filter processing. Some consideration is also given to environment-specific effects such as the presence of boundaries and heterogeneities in the medium. Although the modeling was inspired by applications of sonar in the field of underwater acoustics, the material is presented in a general form, and involving only scalar fields. Therefore, it is broadly applicable to other areas such as medical ultrasound, non-destructive acoustic testing, in-air acoustics, as well as radar and lasers.

The twilight feeding migration of fish around a shallow water artificial reef (a shipwreck) was observed by a horizontal-looking, mid-frequency sonar. The sonar operated at frequencies between 1.8 and 3.6 kHz and consisted of a co-located source and horizontal line array deployed at 4 km from the reef. The experiment was conducted in a well-mixed shallow water waveguide which is conducive to characterizing fish aggregations at these distances. Large aggregations of fish were repeatedly seen to emerge rapidly from the shipwreck at dusk, disperse into the surrounding area during the night, and quickly converge back to the shipwreck at dawn. This is a rare, macroscopic observation of an ecologically-important reef fish behavior, delivered at the level of aggregations, instead of individual fish tracks that have been documented previously. The significance of this observation on sonar performance associated with target detection in the presence of fish clutter is discussed based on analyses of echo intensity and statistics. Building on previous studies of long-range fish echoes, this study further substantiates the unique utility of such sonar systems as an ecosystem monitoring tool, and illustrates the importance of considering the impact of the presence of fish on sonar applications.

Animals enhance sensory acquisition from a specific direction by movements of head, ears or eyes. As active sensing animals, echolocating bats also aim their directional sonar beam to selectively "illuminate" a confined volume of space, facilitating efficient information processing by reducing echo interference and clutter. Such sonar beam control is generally achieved by head movements or shape changes of the sound-emitting mouth or nose. However, lingual-echolocating Egyptian fruit bats, Rousettus aegyptiacus, which produce sound by clicking their tongue, can dramatically change beam direction at very short temporal intervals without visible morphological changes. The mechanism supporting this capability has remained a mystery.

Here we measured signals from free-flying Egyptian fruit bats and discovered a systematic angular sweep of beam focus across increasing frequency. This unusual signal structure has not been observed in other animals, and cannot be explained by the conventional and widely used "piston model" that describes the emission pattern of other bat species. Through modeling we show that the observed beam features can be captured by an array of tongue-driven sound sources located along the side of the mouth, and that the sonar beam direction can be steered parsimoniously by inducing changes to the pattern of phase differences through moving tongue location. The effects are broadly similar to those found in a phased array–an engineering design widely found in human-made sonar systems that enables beam direction changes without changes in the physical transducer assembly. Our study reveals an intriguing parallel between biology and human engineering in solving problems in fundamentally similar ways.

It has long been postulated that the elongated hindwing tails of many saturniid moths have evolved to create false sonar targets to divert the attack of echolocation-guided bat predators. However, rigorous echo-acoustic evidence to support this hypothesis has been lacking. In this study, fluttering luna moths (Actias luna), a species with elongated hindwing tails, were ensonified with frequency modulated chirp signals from all angles of orientation and across the wingbeat cycle. High-speed stereo videography was combined with pulse compressionsonar processing to characterize the echo information available to foraging bats. Contrary to previous suggestions, the results show that the tail echoes are weak and do not dominate the sonar returns, compared to the large, planar wings and the moth body. However, the distinctive twisted morphology of the tails create persistent echoes across all angles of orientation, which may induce erroneous sonar target localization and disrupt accurate tracking by echolocating bats. These findings thus suggest a refinement of the false target hypothesis to emphasize sonar localization errors induced by the twisted tails, and highlight the importance of physics-based approaches to study the sensory information involved in the evolutionary arms race between moths and their bat predators.

Animals rely on sensory feedback from their environment to guide locomotion. For instance, visually guided animals use patterns of optic flow to control their velocity and to estimate their distance to objects. In this study, we investigated how acoustic information guides locomotion of animals that use hearing as a primary sensory modality to orient and navigate in the dark, where visual information is unavailable. We studied flight and echolocation behaviors of big brown bats as they flew under infrared illumination through a corridor with walls constructed from a series of individual vertical wooden poles. The spacing between poles on opposite walls of the corridor was experimentally manipulated to create dense/sparse and balanced/imbalanced spatial structure. The bats’ flight trajectories and echolocation signals were recorded with high-speed infrared motion-capture cameras and ultrasound microphones, respectively. As bats flew through the corridor, successive biosonar emissions returned cascades of echoes from the walls of the corridor. The bats flew through the center of the corridor when the pole spacing on opposite walls was balanced and closer to the side with wider pole spacing when opposite walls had an imbalanced density. Moreover, bats produced shorter duration echolocation calls when they flew through corridors with smaller spacing between poles, suggesting that clutter density influences features of the bat’s sonar signals. Flight speed and echolocation call rate did not, however, vary with dense and sparse spacing between the poles forming the corridor walls. Overall, these data demonstrate that bats adapt their flight and echolocation behavior dynamically when flying through acoustically complex environments.