Pattern — and Amplitude — Optimization Of Random Sparse 2-D Transducer Arrays for 3-D Electronic Beam Steering and Focusing

  • P. K. Weber
  • R. M. Schmitt
Part of the Acoustical Imaging book series (ACIM, volume 22)


Two dimensional (2D) ultrasonic arrays provide the possibility of three dimensional (3D) electronic focussing and beam-steering and thus 3D imaging. To prevent grating lobes in the array response, it is necessary to fulfill the.λ/2-condition in element spacing.1 The focusing depth of a transducer is determined by the relation (D/λ) of aperture size D and the wavelength λ. The axial and lateral resolution is determined by the inverse of this factor and the beamwidth of the ultrasonic signal.2 For focusing and beam steering in medical imaging in the lower frequency range a (D/λ)-factor of 30 up to 50 is necessary. For a fully sampled 2D-array this will result in a number of 3,600 up to 10,000 elements and electronical channels. Using existing technologies, the fabrication and implementation of such arrays and the beamforming electronics is not possible.


Main Lobe Beam Pattern Transducer Array Ultrasonic Signal Dense Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    B.D. Steinberg, Principles of Aperture and Array System Design, John Wiley and Sons, New York (1976)Google Scholar
  2. 2.
    M. Arditti, W.B. Taylor, F.S. Foster, J.W. Hunt, An Annular Array System for High Resoluiton Breast Echography, Ultrasonic Imaging 4, 1–31 (1982)Google Scholar
  3. 3.
    S.W. Smith, G.E. Trahey, O.T. von Ramm, Two Dimensional Arrays for Medical Ultrasound, Ultrasonic Imaging 14, 213–233 (1992)Google Scholar
  4. 4.
    D.H. Turnbull, F.S. Foster, Beam Steering with Pulsed Two Dimensional Transducer Arrays, UFFC, 38 4, 320–333 (1991)CrossRefGoogle Scholar
  5. 5.
    T. Blümecke, Optimierungsverfahren in der Gegenüberstellung, c’t, 12, 230 (1991)Google Scholar
  6. 6.
    I. Rechenberg, Evolutionsstrategie — Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution, frommann-holzboog-Verlag, Stuttgart (1973).Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • P. K. Weber
    • 1
  • R. M. Schmitt
    • 1
  1. 1.Fraunhofer Insitute Biomedical EngineeringDept. of Ultrasound EnsheimerSt.IngbertGermany

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