Abstract
A systematic study is presented of the sensitivity of acoustic time-reversal mirrors (TRMs) to errors. One result is a novel acoustic method for determining the root-mean-square, rms, height and the surface-height autocorrelation function of rough surfaces. In particular, the effects of misregistering a TRM are studied with respect to a rough surface—the reflected wavefield is recorded in one place, time reversed, and then rebroadcast in a second place. This displacement causes the signal to depend importantly on the surface’s rms height and autocorrelation function. Simple closed-form formulas are presented for determining the rms height and the normalized surface-height autocorrelation function for both deterministic and randomly rough surfaces. Also presented is a numerical study that illustrates the statistical uncertainty in and the spatial resolution of the proposed method. An accompanying experimental article tests the proposed method with measurements made on a number of different rough surfaces.
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