Time-reversal mirrors and rough surfaces: Experiment

Abstract

A novel acoustic time-reversal technique has been tested for determining the surface-height autocorrelation function and rms height of rough surfaces. A time-reversal mirror (TRM) was used to insonify periodically and “randomly” rough surfaces of otherwise flat samples immersed in water. The standard use of the TRM is as follows: transmit an initial planar pulse, record the signals at each array element, digitally time reverse each signal, and then retransmit the time-reversed signal. As expected from time-reversal symmetry, one approximately recovers the incident planar pulse after the reflection of the retransmitted wave. The new technique is a simple modification of this procedure. Namely, as before, we record and time reverse the initial reflection. However, we next translate the transducer a fixed distance parallel to the surface before retransmitting. For very small displacements, little change is observed in the TRM’s signal. For larger and larger translations, the TRM’s signal decorrelates, i.e., it less and less resembles the incident pulse. The signal’s decorrelation as a function of displacement is directly related to the autocorrelation function of the rough surface—within the limits set by the system’s point response function. The TRM was used both in reflection mode and in transmission mode. Samples consisted of “randomly” rough surfaces of metal and plastic plates, as well as metal plates machined to have periodically rough surfaces. Evidence is provided that the time-reversal mirror is sensitive to the surface-height autocorrelation and, in favorable cases, determines the autocorrelation function and rms height.