Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal

Författare

B Lars G Jonsson
Mats Gustafsson
Vaughan H. Weston
Maarten V. de Hoop

Summary, in English

In the present paper an iterative time-reversal algorithm, that retrofocuses an

acoustic wave ﬁeld to its controllable part is established. For a ﬁxed temporal

support, i.e., transducer excitation time, the algorithm generates an optimal

retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm

reduces the temporal support of the excitation from the requirement of

negligible remaining energy to the requirement of controllability. The timereversal

retrofocusing is analyzed from a boundary control perspective where

time reversal is used to steer the acoustic wave ﬁeld towards a desired state.

The wave ﬁeld is controlled by transducers located at subsets of the boundary,

i.e., the controllable part of the boundary.

The time-reversal cavity and time-reversal mirror cases are analyzed. In the

cavity case, the transducers generate a locally plane wave in the fundamental

mode through a set of ducts. Numerical examples are given to illustrate the

convergence of the iterative time-reversal algorithm. In the mirror case, a

homogeneous half space is considered. For this case the analytic expression

for the retrofocused wave ﬁeld is given for ﬁnite temporal support. It is shown

that the mirror case does not have the same degree of steering as the cavity

case. It is also shown that the pressure can be perfectly retrofocused for

inﬁnite temporal support. Two examples are given that indicate that the

inﬂuence of the evanescent part of the wave ﬁeld is small.

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