Echolocating bats use sonar to guide interception of insects, recognize objects by shape, and even track prey in clutter. Broadcasts of the big brown bat are 0.5 to 20 ms FM signals in the 20-100 kHz ultrasonic band. Insects consist of several reflecting glints, each equivalent in cross- section to a small sphere of 2 mm to 2 cm radius, while clutter is typically composed of numerous glints distributed over a large volume. The bats' signals extend in space for many target lengths, while ka values for each glint are 0.5 to 30 across the broadcast band. Bats perceive acoustic images having echo delay as their primary dimension, and space is perceived in terms of the distribution of target glints in range. Range disparities between the ears provide two 'looks' at each target from slightly different locations as well as information about azimuth. The bats auditory system encodes the FM sweeps of broadcasts and echoes as linear-period spectrograms with integration-times of 300-400 micrometers . Bats nevertheless perceive individual glints in targets for echo-delay separations well inside the integration-time window. Deconvolution is achieved by spectrogram correlation in the time domain and spectral shape transformation in the frequency-domain, with all output evidently being displayed in the time domina. Neural responses in the bat's auditory system seem limited in time precision to 20-50 micrometers at best and 300 microsecond(s) to 3 ms in a broader sample, and stimulus phase is thought to be lost for frequencies above 1-3 kHz. Yet bats perceive echo delay with an accuracy of 10-15 ns and have two-echo resolution of about 2 microsecond(s) . Moreover, bats perceive echo phase-shifts as the correctly corresponding shifts in echo delay. Successive images are subtracted to enhance perception of shape from multiple 'looks', and echo phase is an integral part of this critical process. Utterly novel time-scale magnification appears in the bat's neural responses to ultrasonic broadcasts and echoes, with time-stretch factors of roughly 10 to 100 that account for the bat's mysteriously high temporal acuity. Bats reconstruct time-domain features of FM broadcasts and echoes in a compact, distributed format that incorporates delay, phase, glint separation, and inter-ear delay differences along the same image dimension.