Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal
(2004) In SIAM Journal on Applied Mathematics 64(6). p.19541986 Abstract
 In the present paper an iterative timereversal 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 leastsquares sense. Thus the iterative timereversal 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 boundarycontrol 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... (More)
 In the present paper an iterative timereversal 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 leastsquares sense. Thus the iterative timereversal 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 boundarycontrol 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 timereversal cavity and timereversal 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 timereversal 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/144364
 author
 Jonsson, B. Lars G.; Gustafsson, Mats ^{LU} ; Weston, Vaughan H. and de Hoop, Maarten V.
 organization
 publishing date
 2004
 type
 Contribution to journal
 publication status
 published
 subject
 in
 SIAM Journal on Applied Mathematics
 volume
 64
 issue
 6
 pages
 1954  1986
 publisher
 SIAM Publications
 external identifiers

 wos:000224122400006
 scopus:11044226943
 ISSN
 00361399
 DOI
 10.1137/S0036139903426964
 language
 English
 LU publication?
 yes
 id
 212c62d23f8643cba275babbedb5773b (old id 144364)
 alternative location
 http://www.jstor.org/stable/4096105
 date added to LUP
 20070705 13:35:49
 date last changed
 20190220 07:59:46
@article{212c62d23f8643cba275babbedb5773b, abstract = {In the present paper an iterative timereversal 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 leastsquares sense. Thus the iterative timereversal 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 boundarycontrol 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 timereversal cavity and timereversal 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 timereversal 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.}, author = {Jonsson, B. Lars G. and Gustafsson, Mats and Weston, Vaughan H. and de Hoop, Maarten V.}, issn = {00361399}, language = {eng}, number = {6}, pages = {19541986}, publisher = {SIAM Publications}, series = {SIAM Journal on Applied Mathematics}, title = {Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal}, url = {http://dx.doi.org/10.1137/S0036139903426964}, volume = {64}, year = {2004}, }