Ultrasonic tagging of light: Theory

A theory is provided for the detection efficiency of diffuse light whose frequency is modulated by an acoustical wave. We derive expressions for the speckle pattern of the modulated light, as well as an expression for the signal-to-noise ratio for the detector. The aim is to develop a new imaging technology for detection of tumors in humans. The acoustic wave is focused into a small geometrical volume, which provides the spatial resolution for the imaging. The wavelength of the light wave can be selected to provide information regarding the kind of tumor.

Echo-delay resolution in sonar images of the big brown bat, Eptesicus fuscus

Echolocating big brown bats (Eptesicus fuscus) broadcast ultrasonic frequency-modulated (FM) biosonar sounds (20–100 kHz frequencies; 10–50 μs periods) and perceive target range from echo delay. Knowing the acuity for delay resolution is essential to understand how bats process echoes because they perceive target shape and texture from the delay separation of multiple reflections. Bats can separately perceive the delays of two concurrent electronically generated echoes arriving as little as 2 μs apart, thus resolving reflecting points as close together as 0.3 mm in range (two-point threshold). This two-point resolution is roughly five times smaller than the shortest periods in the bat’s sounds. Because the bat’s broadcasts are 2,000–4,500 μs long, the echoes themselves overlap and interfere with each other, to merge together into a single sound whose spectrum is shaped by their mutual interference depending on the size of the time separation. To separately perceive the delays of overlapping echoes, the bat has to recover information about their very small delay separation that was transferred into the spectrum when the two echoes interfered with each other, thus explicitly reconstructing the range profile of targets from the echo spectrum. However, the bat’s 2-μs resolution limit is so short that the available spectral cues are extremely limited. Resolution of delay seems overly sharp just for interception of flying insects, which suggests that the bat’s biosonar images are of higher quality to suit a wider variety of orientation tasks, and that biosonar echo processing is correspondingly more sophisticated than has been suspected.