IFMBE Proceedings 34 - Non-linear Imaging sing an Experimental ...

IFMBE Proceedings 34 - Non-linear Imaging sing an Experimental ...

IFMBE Proceedings 34 - Non-linear Imaging sing an Experimental ...


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<strong>Non</strong>-<strong>linear</strong> <strong>Imaging</strong> U<strong>sing</strong><br />

<strong>an</strong> <strong>Experimental</strong> Synthetic Aperture Real Time<br />

Ultrasound Sc<strong>an</strong>ner<br />

1 Center for Fast Ultrasound <strong>Imaging</strong>, Department of Electrical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark<br />

Abstract— This paper presents the first non-<strong>linear</strong> B-mode<br />

image of a wire ph<strong>an</strong>tom u<strong>sing</strong> pulse inversion attained via <strong>an</strong><br />

experimental synthetic aperture real-time ultrasound sc<strong>an</strong>ner<br />

(SARUS). The purpose of this study is to implement <strong>an</strong>d<br />

validate non-<strong>linear</strong> imaging on SARUS for the further<br />

development of new non-<strong>linear</strong> techniques. This study presents<br />

non-<strong>linear</strong> <strong>an</strong>d <strong>linear</strong> B-mode images attained via SARUS <strong>an</strong>d<br />

<strong>an</strong> existing ultrasound system as well as a Field II simulation.<br />

The non-<strong>linear</strong> image shows <strong>an</strong> improved spatial resolution<br />

<strong>an</strong>d lower full width half max <strong>an</strong>d -20 dB resolution values<br />

compared to <strong>linear</strong> B-mode imaging on the other systems. For<br />

the second scatterer at 47 mm depth the -20 dB resolution<br />

value for the non-<strong>linear</strong> SARUS image is 0.9907 mm <strong>an</strong>d<br />

1.1970 mm for the <strong>linear</strong> image from SARUS.<br />

Keywords— non-<strong>linear</strong> imaging, pulse inversion, synthetic<br />

aperture real time ultrasound sc<strong>an</strong>ner.<br />


One way to improve the spatial resolution of a B-mode<br />

ultrasound image is to perform non-<strong>linear</strong> imaging. The<br />

pulse inversion (PI) technique [1] has for m<strong>an</strong>y years been<br />

<strong>an</strong> easy method to perform non-<strong>linear</strong> imaging. This technique<br />

acquires data in the same direction twice, where the<br />

second emitted pulse is phase shifted 180 o compared to the<br />

first pulse. Adding the two received signals will c<strong>an</strong>cel the<br />

1 st harmonic component of the received summed pulse due<br />

to the 180 o phase shift. The 2 nd harmonic component is<br />

phase shifted 2 · 180 o <strong>an</strong>d will therefore add constructively<br />

<strong>an</strong>d be amplified. The technique c<strong>an</strong> thus isolate the 2 nd<br />

harmonic component even for broad b<strong>an</strong>d signals.<br />

While non-<strong>linear</strong> imaging benefits from a good spatial<br />

resolution <strong>an</strong>d low side lobes, PI suffers from lower penetration<br />

depth <strong>an</strong>d a loss in frame rate. At the Center for Fast<br />

Ultrasound <strong>Imaging</strong> (CFU) a new fast non-<strong>linear</strong> imaging<br />

technique aimed at solving these issues is being developed<br />

u<strong>sing</strong> the experimental synthetic aperture real-time ultrasound<br />

sc<strong>an</strong>ner (SARUS) [2]. The purpose of this paper is to<br />

document the first non-<strong>linear</strong> imaging attempts u<strong>sing</strong> PI on<br />

SARUS <strong>an</strong>d compare the results to existing ultrasound imaging<br />

systems <strong>an</strong>d simulations.<br />

Joachim Rasmussen 1 , Yig<strong>an</strong>g Du 1,2 , <strong>an</strong>d Jørgen Arendt Jensen 1<br />

2 BK Medical Aps, Mileparken <strong>34</strong>, Herlev, Denmark<br />


In PI two consecutive waveforms, x1 <strong>an</strong>d x2, that are<br />

identical except for a 180 o phase shift are emitted [1],[3].<br />

That is, x1=-x2 (see Fig. 1). The received signals, y1 <strong>an</strong>d y2,<br />

contain higher order harmonics due to the non-<strong>linear</strong> propagation<br />

of sound waves in tissue. That is,<br />

y1 = a1x1+a2x1 2 +… (1)<br />

y2= a1x2+a2x2 2 +…= a1(-x1)+a2(-x1) 2 +…, (2)<br />

where ai are non-<strong>linear</strong> const<strong>an</strong>ts.<br />

When the received waveforms, y1 <strong>an</strong>d y2, are summed the<br />

out of phase odd number harmonics (1 st , 3 rd , …) c<strong>an</strong>cel out<br />

while the even in phase harmonics (2 nd , 4 th , …) add. The<br />

amplitude of the even harmonics in the summed signal is<br />

twice that of the amplitude seen in either of the two received<br />

signals (see bottom of Fig. 2).<br />

Normalized amplitude<br />

Normalized amplitude<br />

1<br />

0.5<br />

0<br />

−0.5<br />

1<br />

0.5<br />

0<br />

−0.5<br />

Raw ch<strong>an</strong>nel data from SARUS − regular <strong>an</strong>d inverted pulse<br />

Regular pulse<br />

Inverted pulse<br />

56.5 57 57.5 58<br />

Time [μs]<br />

58.5 59<br />

Summed ch<strong>an</strong>nel data from SARUS − summed pulse<br />

Summed pulse<br />

56.5 57 57.5 58<br />

Time [μs]<br />

58.5 59<br />

Fig. 1 Raw ch<strong>an</strong>nel data from SARUS showing the normalized amplitude<br />

of the received regular pulse, the received inverted pulse, <strong>an</strong>d the summed<br />

pulse used for PI imaging.<br />

K. Dremstrup, S. Rees, M.Ø. Jensen (Eds.): 15th NBC on Biomedical Engineering & Medical Physics, <strong>IFMBE</strong> <strong>Proceedings</strong> <strong>34</strong>, pp. 101–104, 2011.<br />


102 J. Rasmussen, Y. Du, <strong>an</strong>d J.A. Jensen<br />

Amplitude [dB]<br />

Amplitude [dB]<br />

0<br />

−10<br />

−20<br />

−30<br />

−40<br />

−50<br />

−60<br />

B<strong>an</strong>dwidth of the BK 8804 tr<strong>an</strong>sducer<br />

BK 8804<br />

−70<br />

0 2 4 6 8 10 12 14 16 18 20<br />

Frequency [MHz]<br />

0<br />

−10<br />

−20<br />

−30<br />

−40<br />

−50<br />

−60<br />

Received spectrum for regular <strong>an</strong>d summed pulse<br />

Regular pulse<br />

Summed pulse<br />

−70<br />

0 2 4 6 8 10 12 14 16 18 20<br />

Frequency [MHz]<br />

Fig. 2 B<strong>an</strong>dwidth of the BK 8804 tr<strong>an</strong>sducer (top) <strong>an</strong>d the spectrum of the<br />

received regular pulse <strong>an</strong>d summed pulse (bottom). The fundamental<br />

frequency of 5 MHz is easily detected for the regular pulse as well as the<br />

2 nd harmonic component at 10 MHz. Both are well within the b<strong>an</strong>dwidth of<br />

the tr<strong>an</strong>sducer. For the summed pulse the fundamental frequency is<br />

suppressed by 17 dB while the 2 nd harmonic component is enh<strong>an</strong>ced by 4<br />

dB compared to the 2 nd harmonic component of the regular pulse.<br />

III. SETUP<br />

A B-mode sc<strong>an</strong> of a wire ph<strong>an</strong>tom u<strong>sing</strong> PI is performed<br />

u<strong>sing</strong> SARUS. Similar <strong>linear</strong> sc<strong>an</strong>s are performed on the<br />

ProFocus sc<strong>an</strong>ner from BK Medical <strong>an</strong>d a Field II [4],[5]<br />

simulation of the sc<strong>an</strong> is performed. The Full Width Half<br />

Max (FWHM) <strong>an</strong>d -20 dB resolution values for each scatterer<br />

is measured in all images for comparison.<br />

Tr<strong>an</strong>sducer: A 192 element BK 8804 <strong>linear</strong> array tr<strong>an</strong>sducer<br />

from BK Medical is used. The center frequency of<br />

this tr<strong>an</strong>sducer is 7 MHz. Sixty-four active ch<strong>an</strong>nels are<br />

used for both tr<strong>an</strong>smit <strong>an</strong>d receive. Apodization for tr<strong>an</strong>smit<br />

is done u<strong>sing</strong> a Hamming function, whereas receive apodization<br />

is set to one for all 64 elements.<br />

Ph<strong>an</strong>tom: A water-filled wire ph<strong>an</strong>tom containing 6<br />

equidist<strong>an</strong>t wires is used. The dist<strong>an</strong>ce between each wire is<br />

2.5 cm. The tr<strong>an</strong>sducer is held in a fixed setup centered over<br />

the wires in the ph<strong>an</strong>tom with the surface of the tr<strong>an</strong>sducer<br />

slightly submerged in water.<br />

SARUS setup: For the SARUS sc<strong>an</strong> 129 dual emissions<br />

are obtained to derive the non-<strong>linear</strong> image. The total collection<br />

of received data c<strong>an</strong> be used for <strong>linear</strong> B-mode images<br />

(one for the regular pulse; one also for the inverted<br />

pulse) <strong>an</strong>d one PI non-<strong>linear</strong> B-mode image (from the<br />

summed pulse).<br />

Since the tr<strong>an</strong>sducer of the system has a limited b<strong>an</strong>d<br />

width, the tr<strong>an</strong>smitted center frequency must be chosen such<br />

that it allows for the detection of the 2 nd harmonic component<br />

in the received signal. From the b<strong>an</strong>dwidth plot of the<br />

tr<strong>an</strong>sducer in Fig. 2, a 5 MHz center frequency for the excitation<br />

pulse with a 10 MHz 2 nd harmonic component is chosen.<br />

Both frequencies are well within the b<strong>an</strong>dwidth of the<br />

BK 8804 tr<strong>an</strong>sducer.<br />

A fixed focal depth of 40 mm is used <strong>an</strong>d the 64 ch<strong>an</strong>nel<br />

received data are beam formed u<strong>sing</strong> the BFT3 toolbox [6].<br />

ProFocus sc<strong>an</strong>ner setup: Twenty consecutive B-mode<br />

sc<strong>an</strong>s u<strong>sing</strong> 129 emissions with a 7 MHz center frequency<br />

are obtained u<strong>sing</strong> the ProFocus system from BK Medical.<br />

A fixed focal depth of 40 mm is set for all sc<strong>an</strong>s.<br />

Field II setup: A simulation of a B-mode sc<strong>an</strong> of the<br />

ph<strong>an</strong>tom is obtained u<strong>sing</strong> Field II with a 70 MHz sampling<br />

frequency, 5 MHz center frequency, 129 emissions, <strong>an</strong>d a<br />

40 mm fixed focal depth.<br />

Axial dist<strong>an</strong>ce [mm]<br />

25<br />

50<br />

75<br />

100<br />

125<br />

150<br />

PI (SARUS)<br />

−10 0 10<br />

Lateral dist<strong>an</strong>ce [mm]<br />

<strong>IFMBE</strong> <strong>Proceedings</strong> Vol. <strong>34</strong><br />

Axial dist<strong>an</strong>ce [mm]<br />

Linear (SARUS)<br />

25<br />

50<br />

75<br />

100<br />

125<br />

150<br />

−10 0 10<br />

Lateral dist<strong>an</strong>ce [mm]<br />

Axial dist<strong>an</strong>ce [mm]<br />

25<br />

50<br />

75<br />

100<br />

125<br />

150<br />

ProFocus<br />

−10<br />

−20<br />

−30<br />

−40<br />

−50<br />

−60<br />

−10 0 10 dB<br />

Lateral dist<strong>an</strong>ce [mm]<br />

−70<br />

Fig. 3 B-mode images obtained from SARUS. Left shows the non-<strong>linear</strong><br />

B-mode image of the wire ph<strong>an</strong>tom created via PI. Middle shows the same<br />

image obtained via <strong>linear</strong> B-mode imaging. Right shows the B-mode image<br />

obtained u<strong>sing</strong> the ProFocus sc<strong>an</strong>ner. Note that the ProFocus image depth<br />

is only 125 mm.<br />


<strong>Non</strong>-<strong>linear</strong> <strong>Imaging</strong> U<strong>sing</strong><br />

<strong>an</strong> <strong>Experimental</strong> Synthetic Aperture Real Time Ultrasound Sc<strong>an</strong>ner 103<br />

Time [μs]<br />

Time [μs]<br />

28.5<br />

29<br />

29.5<br />

28.5<br />

29<br />

29.5<br />

6dB contour plot of PSF of 2nd wire − PI image<br />

−4 −2 0 2 4 6 8<br />

Lateral dist<strong>an</strong>ce [mm]<br />

6dB contour plot of PSF of 2nd wire − <strong>linear</strong> image<br />

−4 −2 0 2 4 6 8<br />

Lateral dist<strong>an</strong>ce [mm]<br />

−12 dB<br />

−24 dB<br />

−36 dB<br />

−48 dB<br />

−60 dB<br />

−12 dB<br />

−24 dB<br />

−36 dB<br />

−48 dB<br />

−60 dB<br />

Fig. 4 Six dB contour plot of the PSF around the 2 nd wire. Top shows the<br />

PSF for the non-<strong>linear</strong> PI B-mode image, bottom shows the PSF for the<br />

<strong>linear</strong> B-mode image.<br />


B-mode images are obtained from all sc<strong>an</strong>s <strong>an</strong>d from the<br />

Field II simulation. Fig. 3 shows the non-<strong>linear</strong> B-mode<br />

image from the PI sc<strong>an</strong>, the <strong>linear</strong> B-mode image from a<br />

<strong>linear</strong> sc<strong>an</strong> on the SARUS system, <strong>an</strong>d a <strong>linear</strong> B-mode image<br />

from the ProFocus system. All 6 wires in the ph<strong>an</strong>tom<br />

are detectable in both the SARUS images as well as the<br />

structure of the bottom of the ph<strong>an</strong>tom at 150 mm depth.<br />

The ProFocus image depth is only 125 mm due to the settings<br />

on the system. Consequently, only the first 5 wires are<br />

seen <strong>an</strong>d the bottom of the ph<strong>an</strong>tom c<strong>an</strong> only just be perceived.<br />

The point spread functions (PSF) for both the PI signal<br />

<strong>an</strong>d the regular <strong>linear</strong> signal from the SARUS images<br />

around the 2 nd wire in the ph<strong>an</strong>tom are shown in Fig. 4. In<br />

this figure it is clearly seen that the spatial resolution in the<br />

PI B-mode image is improved compared to the <strong>linear</strong><br />

B-mode image. The PSF for the 2 nd harmonic pulse has<br />

more narrow side lobes th<strong>an</strong> the <strong>linear</strong> fundamental pulse.<br />

Another qu<strong>an</strong>titative measure for the spatial resolution of<br />

the B-mode image is the FWHM <strong>an</strong>d -20 dB resolution values<br />

for each of the wires as shown in Fig. 5. From the top<br />

view of Fig. 5 it is seen that both SARUS imaging modalities<br />

have almost same FWHM values for all depths. The<br />

ProFocus system, however, has a lower FWHM resolution<br />

value th<strong>an</strong> <strong>an</strong>y of the other imaging system for the 4 th wire<br />

indicating a better spatial resolution at this point.<br />

In the bottom view of Fig. 5 it is seen that both imaging<br />

modalities on the SARUS system <strong>an</strong>d the Field II simulation<br />

have generally lower -20 dB resolution values th<strong>an</strong> the<br />

ProFocus system indicating <strong>an</strong> overall better spatial resolution.<br />

Especially at the 1 st <strong>an</strong>d 5 th wire the ProFocus system<br />

is outperformed by all of the other imaging modalities. Furthermore,<br />

it is seen that SARUS PI <strong>an</strong>d SARUS <strong>linear</strong> imaging<br />

have almost same resolution values except at the 4 th<br />

<strong>an</strong>d 6 th wire where PI has lower -20 dB resolutions. At the<br />

3 rd wire the -20dB resolution of both SARUS modalities is<br />

lower th<strong>an</strong> both Field II <strong>an</strong>d ProFocus <strong>an</strong>d at the 6 th wire<br />

SARUS PI outperforms all other modalities.<br />

On close inspection of the second wire at 47 mm depth,<br />

close to the focal point, the FWHM value of the non-<strong>linear</strong><br />

SARUS image is found to be 0.7017 mm <strong>an</strong>d the -20 dB<br />

resolution value to be 0.9907 mm. In comparison the<br />

FWHM of the <strong>linear</strong> SARUS image is 0.6604 mm <strong>an</strong>d<br />

1.1970 mm. These values indicate that although <strong>linear</strong> SA-<br />

RUS has lower FWHM value th<strong>an</strong> non-<strong>linear</strong> SARUS, the<br />

shape of the PSF of the non-<strong>linear</strong> SARUS scatterer has<br />

more narrow side lobes due to the lower -20 dB resolution<br />

value. This is further verified by the PSF plot in Fig. 4<br />

which also shows <strong>an</strong> improved spatial resolution of the non<strong>linear</strong><br />

image.<br />

FWHM resolution [mm]<br />

−20dB resolution [mm]<br />

4<br />

3.5<br />

3<br />

2.5<br />

2<br />

1.5<br />

1<br />

0.5<br />

<strong>IFMBE</strong> <strong>Proceedings</strong> Vol. <strong>34</strong><br />

FWHM resolution values for scatteres in B−mode image.<br />

SARUS B−mode sc<strong>an</strong><br />

SARUS PI B−mode sc<strong>an</strong><br />

Me<strong>an</strong> of ProFocus B−mode sc<strong>an</strong>s<br />

Field II simulation<br />

Focal depth<br />

0<br />

20 40 60 80 100 120 140 160<br />

Axial dist<strong>an</strong>ce [mm]<br />

9<br />

8<br />

7<br />

6<br />

5<br />

4<br />

3<br />

2<br />

1<br />

−20dB resolution values for scatteres in B−mode image.<br />

SARUS B−mode sc<strong>an</strong><br />

SARUS PI B−mode sc<strong>an</strong><br />

Me<strong>an</strong> of ProFocus B−mode sc<strong>an</strong>s<br />

Field II simulation<br />

Focal depth<br />

0<br />

20 40 60 80 100 120 140 160<br />

Axial dist<strong>an</strong>ce [mm]<br />

Fig. 5 FWHM (top) <strong>an</strong>d -20 dB (bottom) resolution values for each wire in<br />

the ph<strong>an</strong>tom obtained u<strong>sing</strong> different imaging systems. Values for <strong>linear</strong><br />

SARUS B-mode, PI SARUS B-mode, <strong>linear</strong> ProFocus, <strong>an</strong>d Field II<br />

imaging are shown. Notice that only the first 5 wires of the ph<strong>an</strong>tom were<br />

imaged u<strong>sing</strong> the ProFocus system.

104 J. Rasmussen, Y. Du, <strong>an</strong>d J.A. Jensen<br />


From the results in Fig. 5 it is seen that the imaging modalities<br />

on SARUS generally has lower -20 dB resolution<br />

values th<strong>an</strong> the ProFocus system. The very high -20 dB<br />

resolution values for the 1 st <strong>an</strong>d 5 th wire in the ProFocus<br />

image could indicate a poor spatial resolution of the wire.<br />

While this is the case for the 5 th wire the spatial resolution<br />

of the 1 st wire in the image is in fact not as bad as indicated.<br />

This is due to the shape of the PSF around the 1 st wire. Here<br />

the PSF takes a very pointy appear<strong>an</strong>ce with a very high<br />

maximum value <strong>an</strong>d steep slopes, but with very wide lowlevel<br />

side lobes. This leads to a high -20 dB resolution value<br />

while the spatial resolution remains good. Accordingly, had<br />

the PSF taken the appear<strong>an</strong>ce of a hump with low maximum<br />

value, but with narrow side lobes, the -20 dB resolution<br />

value would be lower but the spatial resolution poor. When<br />

determining the spatial resolution of <strong>an</strong> imaging modality<br />

the FWHM <strong>an</strong>d -20dB resolution values c<strong>an</strong>not be used<br />

alone, but must be compared to the actual image of the<br />

sc<strong>an</strong>ning before conclusions c<strong>an</strong> be made.<br />

Both SARUS imaging modalities have low FWHM <strong>an</strong>d<br />

-20 dB resolution values compared to both Field II <strong>an</strong>d<br />

ProFocus. In addition, in close comparison of the two<br />

SARUS B-mode images in Fig. 3, it is seen that the spatial<br />

resolution of the wires in the non-<strong>linear</strong> B-mode image is<br />

better th<strong>an</strong> in the <strong>linear</strong> B-mode image. The low attenuation<br />

in the images is a result of the water filled ph<strong>an</strong>tom that is<br />

used. Had the ph<strong>an</strong>tom been filled with a subst<strong>an</strong>ce that<br />

mimics hum<strong>an</strong> tissue, the attenuation would have made detection<br />

of deep wires harder.<br />


While non-<strong>linear</strong> imaging u<strong>sing</strong> PI has the benefits of<br />

improved spatial resolution <strong>an</strong>d low side lobes, it also has<br />

some drawbacks. First of all, two emissions need to be received<br />

in order to derive the summed pulse used in PI. This<br />

reduces the frame rate of the imaging system by a factor 2<br />

compared to <strong>linear</strong> B-mode imaging. The dual emissions<br />

also increase the amount of data the processor of the imaging<br />

system must be able to h<strong>an</strong>dle without further loo<strong>sing</strong><br />

frame rate. The loss of frame rate could prove very disadv<strong>an</strong>tageous,<br />

if the sc<strong>an</strong> is made on non-stationary tissues.<br />

Here <strong>an</strong>y tissue motion may lead to a phase ch<strong>an</strong>ge in the<br />

paired received signals severely reducing the 2 nd harmonic<br />

component of the summed pulse.<br />

Secondly, the tr<strong>an</strong>sducer must function optimally over a<br />

broad spectrum to be able to tr<strong>an</strong>smit <strong>an</strong>d receive a maximum<br />

energy at the fundamental <strong>an</strong>d 2 nd harmonic center<br />

frequency. If there is <strong>an</strong> energy loss at either frequencies the<br />

signal to noise ratio (SNR) in the image will decrease.<br />

<strong>IFMBE</strong> <strong>Proceedings</strong> Vol. <strong>34</strong><br />

Thirdly, the attenuation of the 2 nd harmonic signal is<br />

much higher th<strong>an</strong> the attenuation of the fundamental signal.<br />

This is because only a fraction of the tr<strong>an</strong>smitted signal is<br />

converted to the 2 nd harmonic component. Further, the<br />

attenuation is proportional in dB to the frequency of the<br />

signal leading to a higher attenuation of the 2 nd harmonic<br />

component compared to the fundamental wave. In all this<br />

leads to a much lower SNR of the 2 nd harmonic component.<br />


<strong>Non</strong>-<strong>linear</strong> B-mode imaging has successfully been accomplished<br />

u<strong>sing</strong> SARUS. The spatial resolution of the<br />

image is determined to be better th<strong>an</strong> both the <strong>linear</strong> Bmode<br />

image from SARUS, the B-mode images from the<br />

ProFocus system, <strong>an</strong>d from the Field II simulation.<br />


This work was supported by gr<strong>an</strong>t 024-2008-3 from the<br />

D<strong>an</strong>ish Adv<strong>an</strong>ced Technology Foundation <strong>an</strong>d BK Medical<br />

Aps, Denmark.<br />


1. Chapm<strong>an</strong> C S <strong>an</strong>d Lazenby J C (1997) Ultrasound imaging system<br />

employing phase inversion subtraction to enh<strong>an</strong>ce the image. Official<br />

Gazette of the United States Patent <strong>an</strong>d Trademark Office Patents,<br />

Vol. 1198, Issue 4, pp. 2249.<br />

2. Jensen J A, Tomov B G, Nikolov S I, H<strong>an</strong>sen M <strong>an</strong>d Holten-Lund H<br />

(2007) System architecture of <strong>an</strong> experimental synthetic aperture realtime<br />

ultrasound system. <strong>Proceedings</strong> IEEE Ultrasonics Symposium,<br />

2007, pp. 636-640.<br />

3. Ji<strong>an</strong>g P, Mao Z <strong>an</strong>d Lazenby J C (1998) A new tissue harmonic imaging<br />

scheme with better fundamental frequency c<strong>an</strong>cellation <strong>an</strong>d higher<br />

signal-to-noise ratio. <strong>Proceedings</strong> IEEE Ultrasonics Symposium,<br />

1998, Vol. 2, pp. 1589-1594.<br />

4. Jensen J A (1996) Field: A program for simulating ultrasound sys-<br />

th<br />

tems. 10 Nordic-Baltic Conference on Biomedical <strong>Imaging</strong> vol. 4<br />

supplement 1, part 1:351-353.<br />

5. Jensen J A <strong>an</strong>d Svendsen N B (1992) Calculation of pressure fields<br />

from arbitrarily shaped, apodized, <strong>an</strong>d excited ultrasound tr<strong>an</strong>sducers.<br />

IEEE Tr<strong>an</strong>s. Ultrason., Ferroelec., Freq. Contr., 39:262-267.<br />

6. H<strong>an</strong>sen J M, Hemmsen M C <strong>an</strong>d Jensen J A (2011) An objectoriented<br />

multi-threaded software beam formation toolbox. SPIE,<br />

Medical <strong>Imaging</strong>, Ultrasonic <strong>Imaging</strong> <strong>an</strong>d Signal Proces<strong>sing</strong>, 2011.<br />

Corresponding author: Joachim Rasmussen<br />

Institute: Technical University of Denmark<br />

Street: Oersteds Plads <strong>34</strong>9<br />

City: Kgs. Lyngby<br />

Country: Denmark<br />

Email: jr@elektro.dtu.dk

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