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Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal

Publiceringsår: 2003
Språk: Engelska
Sidor: 36
Publikation/Tidskrift/Serie: Technical Report LUTEDX/(TEAT-7115)/1-36/(2003)
Dokumenttyp: Rapport
Ytterligare information: Published version: SIAM J. Appl. Math., Vol. 64, No. 6, pp. 1954-86, 2004.


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.



  • Electrical Engineering, Electronic Engineering, Information Engineering


  • Electromagnetic theory

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