signal at the TRM is the impulse response of the channel. The TRM sends the reversed version of the impulse response back through the same channel, effectively autocorrelating it. This autocorrelation function has a peak at the origin, where the original source was. It is important to realize that the signal is concentrated in both space and time (in many applications, autocorrelation functions are functions of time only). Another way to think of a time reversal experiment is that the TRM is a "channel sampler". The TRM measures the channel during the recording phase, and uses that information in the transmission phase to optimally focus the wave back to the source. Experiments A notable researcher is Mathias Fink of École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris. His team has done numerous experiments with ultrasonic TRMs. An interesting experiment involved a single source transducer, a 96-element TRM, and 2000 thin steel rods located between the source and the array. The source sent a 1 μs pulse both with and without the steel scatterers. The source point was measured for both time width and spatial width in the retransmission step. The spatial width was about 6 times narrower with the scatterers than without. Moreover, the spatial width was less than the diffraction limit as determined by the size of the TRM with the scatterers. This is possible because the scatterers increased the effective aperture of the array. Even when the scatterers were moved slightly (on the order of a wavelength) in between the receive and transmit steps, the focusing was still quite good, showing that time reversal techniques can be robust in the face of a changing medium. In addition, José M. F. Moura of Carnegie Mellon University has led a research team working to extend the principles of Time Reversal to electromagnetic waves, and they have achieved resolution in excess of the Rayleigh resolution limit, proving the efficacy of Time Reversal techniques. Their efforts are focused on radar systems, and trying to improve detection and imaging schemes in highly cluttered environments, where Time Reversal techniques seem to provide the greatest benefit. Applications The beauty of time reversal signal processing is that one need not know any details of the channel. The step of sending a wave through the channel effectively measures it, and the retransmission step uses this data to focus the wave. Thus one