Linear description of
ultrasound imaging systems
Notes for the
International Summer School on
Advanced Ultrasound Imaging
Technical University of Denmark
July 5 to July 9, 1999
Release 1.01, June 29, 2001
Jørgen Arendt Jensen
June 10, 1999
Ørsted • DTU, Build. 348,
Technical University of Denmark
DK-2800 Lyngby, Denmark
E-mail: jaj@oersted.dtu.dk
Web: http://es.oersted.dtu.dk/staff/jaj/
CONTENTS
1 Introduction 1
2 Description of ultrasound fields 3
2.1 Fields in linear acoustic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Basic theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Calculation of spatial impulse responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Apodization and soft baffle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Examples of spatial impulse responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Calculation of the scattered signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Ultrasound imaging 31
3.1 Fourier relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Fields from array transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Imaging with arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5 Simulation of ultrasound imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Synthetic phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.7 Anatomic phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Ultrasound systems for flow estimation 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Measurement of flow signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 Calculation and display of the velocity distribution . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 Making images of velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Flow types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Stationary parabolic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.7 Simulation of flow imaging systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
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CHAPTER
ONE
Introduction
These notes have been prepared for the international summer school on advanced ultrasound imaging sponsored
by The Danish Research Academy. The notes should be read in conjunction with the notes prepared by Anderson
and Trahey
1
. The intended audience is Ph.D. students working in medical ultrasound. A knowledge of general
linear acoustics and signal processing is assumed.
The notes give a linear description of general ultrasound imaging through the use of spatial impulse responses.
It is shown in Chapter 2 how both the emitted and scattered fields for the pulsed and continuous wave case can
be calculated using this approach. Chapter 3 gives a brief overview of modern ultrasound imaging and how it is
simulated using spatial impulse responses. Chapter 4 finally, gives a brief description of both spectral and color
flow imaging systems and their modeling and simulation.
Jørgen Arendt Jensen
Technical University of Denmark
June, 1999.
1
M.E. Anderson and G.E. Trahey: A seminar on k-space applied to medical ultrasound, Dept. of Biomedical Engineering, Duke University,
June 21, 1999
1
2
