Background information
The Field program system uses the concept of spatial impulse
responses as developed by Tupholme and Stepanishen in a series
of papers [1, 2,
3]. The approach relies
on linear systems theory to find the ultrasound field for both
the pulsed and continuous wave case. This is done through the
spatial impulse response. This response gives the
emitted ultrasound field at a specific point in space
as function of time, when the transducer is
excitated by a Dirac delta function. The field for any kind
of excitation can then be found by just convolving the spatial
impulse response with the excitation function. The impulse
response will vary as a function of position relative to the
transducer, hence the name spatial impulse response.
The received response from a small oscillating sphere can be found
by acoustic reciprocity. The spatial impulse response equals
the received response for a spherical wave emitted by a point.
The total received response in pulseecho can, thus, be found
by convolving the transducer excitation function with the
spatial impulse response of the emitting aperture, with the
spatial impulse response of the receiving aperture, and then
taking into account the electromechanical transfer function
of the transducer to yield the received voltage trace. An explanation
and rigorous proof of this can be found in
[4] and [5].
Any excitation can be used, since linear systems theory is used.
The result for the continuous wave case is found by Fourier
transforming the spatial impulse response for the given frequency.
The approach taken here can, thus, yield all the diffent commenly
found ultrasound fields for linear propagation.
Simulation
A number of different authors have calculated the spatial impulse
response for different transducer geometries. But in general
it is difficult to calculate a solution, and especially if
apodization of the transducer is taken into account. Here the
transducer surface does not vibrate as a piston, e.g. the
edges might vibarte less then the center. The simulation
program circumvents this problem by dividing the transducer
surface into squares and the sum the response of these squares
to yield the response. Thereby any tranducer geometry and any
apodization can be simulated. The approach is described
in [6].
The time for one simulation is also of major concern. As the squares
making up the tranducer apertue
are small, it is appropriate to use a farfield approximation,
making simulation simple. Another issue in keeping the simulation
time down is to use a low sampling frequency. Often spatial
impulse responses are calculated using sampling frequencies in the
GHz range due to the sharp discontinuities of the responses. These
discontinuities are
handled in the Field programs by accurately keeping track of
the time position of the responses and uses the integrated spatial
impulse response as an intermediate step in the calculations. Thereby
no energy is lost in the response, which is far more important
than having an exact shape of the spatial impulse response.
Hereby the Field program ususally does better using 100 MHz
sampling and approximate calculations, than using the exact analytic
expression and GHz sampling.
More information
You can find more information about the background for the program
in the references below. Especially [7] gives
a through introduction to the background.
[1]
G.E. Tupholme:
Generation of acoustic pulses by baffled plane pistons,
Mathematika 16, pp. 209224, 1969.
[2]
P.R. Stepanishen:
The timedependent force and radiation impedance on
a piston in a rigid infinite planar baffle,
J.Acoust.Soc.Am. 49 (3), pp. 841849, 1971A.
[3]
P.R. Stepanishen:
Transient radiation from pistons in a infinite
planar baffle,
J.Acoust.Soc.Am. 49, pp. 16271638, 1971B.
[4]
P.R. Stepanishen:
Pulsed transmit/receive response of ultrasonic
piezoelectric transducers,
J.Acoust.Soc.Am. 69, pp. 18151827, 1981.
[5]
J.A. Jensen:
A Model for the Propagation and Scattering of
Ultrasound in Tissue,
J.Acoust.Soc.Am. 89, pp. 182191, 1991.
[6]
J.A. Jensen and N. B. Svendsen:
Calculation of pressure fields from arbitrarily shaped,
apodized, and excited ultrasound transducers,
IEEE Trans. Ultrason., Ferroelec., Freq. Contr., 39,
pp. 262267, 1992.
[7]
J.A. Jensen:
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, Technical University of
Denmark, June, 1999.
[8]
J.A. Jensen:
Field: A Program for Simulating Ultrasound Systems,
Paper presented at the 10th NordicBaltic Conference on
Biomedical Imaging Published in Medical & Biological Engineering & Computing,
pp. 351353, Volume 34, Supplement 1, Part 1, 1996.
[9]
J. A. Jensen, Darshan Gandhi, and William D. O'Brien:
Ultrasound fields in an attenuating medium,
Proceedings of the IEEE 1993 Ultrasonics Symposium,
pp. 943946, Vol. 2, 1993.
[10]
J. A. Jensen:
Ultrasound fields from triangular apertures,
Journal of the Acoustical Society of America,
Vol. 100(4), pp. 20492056, October, 1996.
[11]
J. A. Jensen:
Simulating arbitrarygeometry ultrasound transducers
using triangles, Proceedings of IEEE International
Ultrasonics Symposium, Vol. 2, pp. 885888, 1996.
[12]
J. A. Jensen and Peter Munk:
Computer phantoms for simulating ultrasound Bmode and cfm images,
23rd Acoustical Imaging Symposium, Boston, Massachusetts,
USA, April 1316, 1997.
[13]
J. A. Jensen:
A new approach to calculating spatial impulse responses, Proceedings of IEEE Ultrasonics
Symposium Proceedings, pp. 17551759, 1997
[14]
J. A. Jensen:
A new Calculation Procedure for Spatial Impulse Responses in Ultrasound,
Journal of the Acoustical Society of America, Vol. 105, pp. 32663274, 1999.
[15]
J. A. Jensen:
Ultrasound Imaging and its modeling,
in "Imaging of Complex Media with Acoustic and Seismic Waves",
Editors: Fink, M.; Kuperman, W.A.; Montagner, JP; Tourin, A., Topics in Applied Physics,
Springer Verlag, pp. 135165, 2002.
[16]
J. A. Jensen:
Speedaccuracy tradeoffs in computing spatial impulse responses for simulation medical
ultrasound imaging, Journal of Computational Acoustics, Vol.9, no..3, pp.731744, 2001
[17]
M. Schlaikjer, S. TorpPedersen and J. A. Jensen:
Simulation of RF data with tissue motion for optimizing stationary echo canceling filters,
Ultrasonics, Vol. 41 (6) , pp. 415419. 2003.
[18]
J. A. Jensen and S. Nikolov:
Fast simulation of ultrasound images,
Proceedings the IEEE Ultrasonics Symposium, vol. 2, pp. 17211724, 2000.
