Multipulse Technique Exploiting the Intermodulation of

0885–3010/$25.00 © 2009 IEEE

520 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 56, no. 3, March 2009

Abstract—In recent years, the nonlinear properties of ma-terials have attracted much interest in nondestructive testing and in ultrasound diagnostic applications. Acoustic nonlinear parameters represent an opportunity to improve the informa-tion that can be extracted from a medium such as structural organization and pathologic status of tissue.

In this paper, a method called pulse subtraction intermodu-lation (PSI), based on a multipulse technique, is presented and investigated both theoretically and experimentally. This method allows separation of the intermodulation products, which arise when 2 separate frequencies are transmitted in a nonlinear medium, from fundamental and second harmon-ic components, making them available for improved imaging techniques or signal processing algorithms devoted to tissue characterization.

The theory of intermodulation product generation was devel-oped according the Khokhlov-Zabolotskaya-Kuznetsov (KZK) nonlinear propagation equation, which is consistent with ex-perimental results. The description of the proposed method, characterization of the intermodulation spectral contents, and quantitative results coming from in vitro experimentation are reported and discussed in this paper.

I. Introduction

currently many investigators are involved in the study of acoustic nonlinear properties of materials

to develop new imaging techniques for clinical diagnostic and nondestructive testing (ndT) applications. nonlinear ultrasound parameters represent a significant opportunity to improve the information available about mechanical and structural properties of matter.

In biomedical applications of ultrasound such as echog-raphy, diagnostic methods based on nonlinear imaging achieve a high level of optimization and are in widespread use in many clinical environments. harmonic imaging techniques exploit harmonic generation due to the non-linear propagation of ultrasounds in tissue, which occurs when acoustic pressure is increased to very high levels [1]–[5] rejecting the tissue response in the fundamental band. harmonic images of tissue provide a high level of clarity and reduction of clutter noise and artifacts due to lower lateral side lobes effects of the ultrasound beam; in addition, they show both a better quality grain, if com-

pared with the fundamental image, and an enhancement of lateral and axial resolution [6]. nonlinear imaging is also employed for contrast imaging, thanks to the high-quality images it provided [7]–[9]. The current generation of contrast agents based on microbubble suspension has a strong nonlinear scattering behavior when exposed to an ultrasound field. Portions of biological tissue having a high level of perfusion appear as a bright area in the harmonic B-mode because a strong harmonic content due to the microbubbles is present in the echo signals; in con-trast, tissues with low perfusion exhibit a lack of harmonic generation in the echo signal, and hence, they appear as residual background in the final image.

To achieve a very high contrast to tissue ratio (cTr) value, the tissue response in the fundamental band should be completely rejected. Furthermore, the harmonic bands should be well separated to avoid the superposition of fundamental spectral side lobes (primarily derived from linear tissue response).

removal of the tissue response in the fundamental band, while maintaining the broadband features of the ultrasound signal leading to high axial resolution, was a big challenge in the past, and many different excitation schemes have been developed to detect and extract har-monic contents. Pulse inversion (PI) [10] is a well-known technique in nonlinear imaging because it allows effective separation of the fundamental band from the second har-monic band due to contrast agent or nonlinear tissue re-sponse. In PI technique, a sequence of 2 ultrasonic pulses is transmitted for each line of sight; the second pulse is an inverted replica of the first one. The 2 received rF (radio frequency) echo signals are added together, and the result for a linear medium will be zero, whereas for a nonlinear medium the sum will be different from zero. considering the harmonic response from a nonlinear medium, the PI method is able to suppress the odd bands, such as the fundamental one, and to reinforce the even harmonic com-ponents, such as the second harmonic band, producing a strong signal. PI imaging overcomes the limitation of har-monic imaging (i.e., overlapping of the fundamental and harmonic components and loss of axial resolution due to a narrowing of the transmitted and received bandwidths) by detecting nonlinear echoes with the entire transducer bandwidth.

In the current generation of echographic devices, novel excitation opportunities and strategies have become fea-sible because linear amplifiers are employed for driving the piezoelectric transducers. For example, it is possible

Multipulse Technique Exploiting the Intermodulation of Ultrasound Waves in a

Nonlinear MediumElena Biagi, luca Breschi, Enrico Vannacci, and leonardo Masotti

Manuscript received February 15, 2008; accepted June 18, 2008. This work was supported by Ministero Istruzione, Università e ricerca (MIUr), Ente cassa di risparmio di Firenze and Fondazione Monte dei Paschi di siena.

The authors are with the University of Florence, Electronics and Tele-communications, Firenze, Italy (e-mail: [email protected]).

digital object Identifier 10.1109/TUFFc.2009.1069

to transmit ultrasonic waves with different frequencies to exploit the intermodulation components for contrast im-aging or tissue characterization.

In the past, many investigators approached nonlinear acoustics by studying harmonics and intermodulation gen-eration. In underwater acoustics, intermodulation products were investigated as an improvement over conventional techniques for echo ranging and bottom-deep scattering layer profile [11]–[14]. It was demonstrated that the in-termodulation products generated by parametric arrays, which include the sum and difference of 2 transmitted frequencies, are of great interest for practical underwater acoustics. The major advantages of exploiting intermodu-lation products are high directivity, absence of side lobes, and an inherent broadband capability [15].

although the frequencies employed in underwater acoustics are far from those of diagnostic echography, the advantages mentioned above are still valid. recently, in-termodulation products were investigated to improve the conventional harmonic technique in echography [16]. It was demonstrated that intermodulation products, as well as the second harmonic components, are maintained by a PI scheme and hence they are exploitable for improving nonlinear imaging technique in terms of cTr, signal to clutter ratios, lateral resolution, and artifact reduction. If broadband pulses are employed to achieve high axial-resolution, the second harmonics of the 2 transmitting frequencies overlap the sum frequency component of inter-modulation products, which then become unavailable for further signal processing aimed to image formation.

The present paper reports a novel method based on a multipulse technique allowing separation of the intermod-ulation products from fundamental and second harmonic bands, making them available for an imaging technique. Two composite pulses, each one consisting of 2 tone fre-quencies, are sent into the medium for intermodulation generation. The received echographic signals coming from the medium are appropriately combined, generating a new ultrasonic signal; the spectral contents of transmit-ted bands and their second harmonics are removed from the spectrum, leaving the intermodulation products well separated.

The theory of intermodulation product generation is reported in this work according to a nonlinear model of ultrasound propagation in media described in literature.

In addition, results from an in vitro experimentation of the proposed method, performed in different experimental conditions, are presented and discussed.

II. Method for separating the Intermodulation Products: Theory and simulations

The proposed method, called pulse subtraction inter-modulation (PsI), consists of a multi-pulse technique that is able to reinforce the intermodulation products. PsI can

also remove the second harmonics, one of the 2 transmit-ted bands and its third harmonic.

In particular, 2 composite pulses are generated in the following manner:

1) The first composite pulse, cP1, is constituted by 2 burst signals at different frequencies called, respec-tively, F1 and F2, which are combined by a sum operation (Fig. 1).

2) The second composite pulse, cP2, is constituted by summing F1 and F2* where F2* is an inverted rep-lica of F2 (F2* is in phase opposition respect with F2) (Fig. 1).

For each line of sight, the 2 composite pulses cP1 and cP2 are then subsequently transmitted into a medium and the 2 echo signals (respectively, EcP1 and EcP2) are received from the transducer, digitized, and stored in memory. When an ultrasonic composite pulse passes through a nonlinear medium, the different frequency com-ponents interact with each other, and sum and difference frequency products are generated. These intermodulation components are contained in the received echo signals and must be separated from fundamental and harmonics con-tents. This is achieved by a point-to-point subtraction of the received echo signals. subtraction of the 2 rF signals generates a new signal that contains only intermodulation products and some residual components (such as one of the transmitted bands and its third harmonics) but is de-prived of one transmitted component and of both second harmonics.

The PsI scheme can be theoretically analyzed consider-ing a system described by the following nonlinear equation (for simplicity, a static model with terms up to third order is considered):

S t K S t S t S t

S t S t

o i i i

i i

( ) ( ) ( ) ( )

( ) ( ), .

= + +( )e V

e V

2 3

2 31 1| | | |

(1)

By considering input signal Si(t) as 2 composite puls-es, S1(t) and S2(t), generated according to the proposed method:

S t A t A t1 1 1 2 2( ) cos( ) cos( )= +w w (2)

S t A t A t2 1 1 2 2( ) cos( ) cos( ),= -w w (3)

the outputs S1o(t) and S2o(t) of the model in (1), present (4) and (5) (see next page).

It is worth noting that some of the expression terms in (4) and (5) appear with opposite signs, and hence, the resulting signal D12(t) (difference signal) maintains only a few terms of the basic expressions.

521BIaGI ET al.: multipulse technique exploiting the intermodulation of ultrasound waves

D t S t S t

K A KA K A K A A

o o12 1 2

22

2 23

12

2232

( ) ( ) ( )= -

= + + +æ

èççç

ö

ø÷÷÷÷e V V ccos( )

cos( ) cos(( ) )

cos

w

V w e w we

2

23

2 1 2 1 2

1 2

3 2

2

t

K A t A A K t

A A K

+ + -+ ((( ) )

cos(( ) )

cos(( )

w w

V w w

V w w

2 1

12

2 2 1

12

2 2 1

3 2

3 2

+

+ +

+ -

t

K A A t

K A A t

))

(6)

Frequency components of S1o(t) and S2o(t), as well as D12, can be reported in the frequency domain (Fig. 2) when burst signals are considered instead of pure tone signals.

The signal D12(t) is constituted by:

1) a constant term (independent from the frequency) that is related to a continuous component (black in Fig. 2).

2) a term at frequency f2 that is related to the compo-nents with opposite signs in the transmitted pulses (dark gray in Fig. 2).

3) a term at frequency 3f2 that is the third harmonics of the transmitted component at frequency f2 (white in Fig. 2).

4) Two intermodulation products of second order that are located at the difference |f2 − f1| and sum (f2 + f1) frequencies in the spectrum (dotted shading in Fig. 2).

5) Three intermodulation products of third order that are at the frequencies f2, (f2 + 2f1) and |f2 − 2f1| (di-agonal shading in Fig. 2).

The considered static mathematical model provides useful results explaining the distortion mechanism of in-termodulation focused on PsI scheme. In any case, math-ematical models, which describe the cumulative process of distortion during propagation, lead to a more refined prediction of the behavior of propagating acoustic waves.

For this reason, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) nonlinear propagation equation has been used in the past [17]–[23] to model nonlinear propagation of ul-trasound in a medium when its nonlinear properties are known. The KZK equation was employed by our group for the study of the PsI method and it was numerically solved by FEMlaB (comsol, Inc. Burlington, Ma), a powerful partial differential equation (PdE) solver considering the acoustic parameters of water (ultrasound speed of 1500 m/s, medium density of 998 kg/m3, B/a parameter of 5, and attenuation of 0.0025 dB/cm/Mhz), propagation dis-tance of 25 cm, and plane wave approximation. simulated results of Fig. 3 are obtained for 2 composite pulses (gen-erated according to the PsI scheme of Fig. 2) constituted by 2 sinusoidal bursts F1 and F2 with the same amplitude of 100 kPa and frequencies of, respectively, 4 Mhz and 6 Mhz.

Fig. 3(a) is related to the case of 2 composite pulses cP1 and cP2 resulting from F1 and F2 burst signals, which exhibit the same time duration of 6 μs, i.e., the same bandwidth in the spectral domain for the 2 trans-


S tK A K A

KA K A K A A to11

22

2

1 13

1 22

12 232

( ) cos(= + + + +æ

èççç

ö

ø÷÷÷÷

e eV V w )) cos( )

cos( )

+ + +æ

èççç

ö

ø÷÷÷÷

+

KA K A K A A t

K At

2 23

12

2 2

12

1

32

22

V V w

ew ++ + +

+

K At K A t K A t

A A K

ew V w V w2

2

2 13

1 23

2

1 2

22

12

312

3cos( ) cos( ) cos( )

ee w w e w w

V w w

cos(( ) ) cos(( ) )

cos(( )

1 2 1 2 2 1

12

2 2 132

2

- + +

+ +

t A A K t

K A A tt K A A t

K A A t K A

) cos(( ) )

cos(( ) )

+ -

+ + +

32

2

32

232

12

2 2 1

1 22

2 1

V w w

V w w V 11 22

2 12A tcos(( ) )w w-

(4)

S tK A K A

KA K A K A A to21

22

2

1 13

1 22

12 232

( ) cos(= - + + +æ

èççç

ö

ø÷÷÷÷

e eV V w )) cos( )

cos( )

- + +æ

èççç

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ø÷÷÷÷

+

KA K A K A A t

K At

2 23

12

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12

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32

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V V w

ew ++ + -

-

K At K A t K A t

A A K

ew V w V w2

2

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1 23

2

1 2

22

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312

3cos( ) cos( ) cos( )

ee w w e w w

V w w

cos(( ) ) cos(( ) )

cos(( )

1 2 1 2 2 1

12

2 2 132

2

- - +

- +

t A A K t

K A A tt K A A t

K A A t K A

) cos(( ) )

cos(( ) )

- -

+ + +

32

2

32

232

12

2 2 1

1 22

2 1

V w w

V w w V 11 22

2 12A tcos(( ) )w w-

(5)


Fig. 1. PsI procedure: For each line of sight, the composite pulses cP1 and cP2 are transmitted in the medium and the received echo signals are subtracted. note: The amplitudes of the waveforms are plotted on different vertical scales.

mitted bands; the simulated spectra for the 2 distorted transmitted pulses are reported at the top and center. on the bottom of Fig. 3(a), the spectrum of the subtracted echo signals according to the PsI scheme shows that only one of the 2 transmitted bands (the one at 6 Mhz) is still present, as well as the intermodulation products of second order at 2 Mhz and 10 Mhz and of third order at 14 Mhz. The transmitted band at 4 Mhz and its harmonics (at 8 Mhz and 12 Mhz) are completely removed, creating a free spectral region and significant separation of inter-modulation components. It is worthwhile to note that the intermodulation spectral components have a bandwidth comparable to the transmitted ones. In fact, the intermod-ulation phenomenon occurs during the entire time dura-tion of the composite pulse leading to the generation of an intermodulation pulse that has the same time duration as the original composite pulse, i.e., the same bandwidth.

Fig. 3(b) concerns the simulated result when composite pulse cP1 and cP2 are obtained by F1 and F2 signals with different time durations, i.e., different spectral band-widths. In this example, cP1 is a sum of the F1 signal (Gaussian shape, 4 Mhz central frequency, 1.2 μs time duration, and 200 kPa acoustic pressure) and the F2 sig-nal (Gaussian shape, 6 Mhz central frequency, 16 μs time duration, and 50 kPa acoustic pressure). The second com-posite pulse cP2 is obtained according the PsI method. The simulated spectra of the first and second compos-ite pulses are reported, respectively, on the top and in the center of Fig. 3(b). The presence of narrowband and

broadband harmonics due to nonlinear propagation can be noted. The spectrum of the subtracted signals is reported at the bottom of the figure. It can be observed that one of the 2 transmitted bands (the one at 4 Mhz) is removed, as well as its second harmonics, whereas the intermodula-tion products of second order at 2 Mhz and 10 Mhz and of third order at 14 Mhz are still present.

In this last regard, it can be stated that when compos-ite pulses are composed of 2 frequency components F1 and F2 with different time durations, i.e., different spectral bandwidth, the bandwidth of the intermodulation prod-ucts due to nonlinear propagation is comparable to the bandwidth of the broadband component. In fact, inter-modulation occurs only when the 2 frequency components are simultaneously present in the composite pulse and, hence, the time duration of the intermodulation signals is set by the component signal with the shortest time dura-tion. It can be stated that the bandwidth of the intermod-ulation products is the same as the broadest one between the 2 frequency component signals.

The generation of 2 composite pulses starting from F1 and F2 component signals with different time durations appears to be suitable for developing a broadband imaging technique with great benefits in terms of axial resolution.

The removal of the broadband transmitted component and its harmonics according to the method allows the cre-ation of a free region in the spectral domain where inter-modulation products can be located with a good separa-tion from the remaining frequency contents. Moreover, the


Fig. 2. Top: harmonic and intermodulation components of a burst signal composed of 2 frequency components at f1 and f2, which undergoes a cubic nonlinear distortion. Bottom: Final spectrum after the PsI procedure. The rejection of one fundamental component, its third harmonic, both second harmonics, and a few intermodulation components of the third order can be noted.

bandwidth of the intermodulation products is the same as the broadband component signal, which is removed by the final subtraction. The free spectral region can be addition-ally increased if the unremoved fundamental component is narrowed as much as possible.

To reduce side lobes of the remaining narrowband fundamental (ensuring minimal interference with the intermodulation bands), different kinds of narrowband component signals can be employed instead of uniformly weighted (rectangular windowed) sinusoidal burst signals. a low level for the side lobe amplitude is ensured by a fam-

ily of windowed signals. Windowed signals are signals with an amplitude modulation according to well-known window types such as hanning, hamming, or Gaussian, which al-low smoothing of the initial and final part of the ultrason-ic pulse. This kind of signal is able to reduce the spectral side lobes of the ultrasonic pulse, especially when applied to transducers driven outside their central frequency. In this case, a smoothed excitation signal is able to force the transducer to resonate at the driving frequency and eliminate its free oscillation response located at the initial and final part of the ultrasonic pulse. For windowed ex-


Fig. 3. (a) The spectra of composite pulses cP1 (top) and cP2 (center) obtained by F1 and F2 signals with the same time duration. on the bottom, the spectrum of the subtracted signals according to the PsI scheme is reported; only one of the 2 transmitted bands (6 Mhz) is still present, as well as the intermodulation products of second order (2 Mhz and 10 Mhz) and of third order (14 Mhz). (b) spectra of the second couple of composite pulse cP1 (top) and cP2 (center). Frequency component signals F1 and F2 have different time duration, i.e., different bandwidth in the spectral domain. at the bottom, the spectrum of the final signal resulting from PsI method is reported. note: simulations were performed at a distance of 25 cm from the transducer surface assuming B/a parameter equal to 5.

citation signals, considerations concerning the generation of intermodulation products remain unchanged with the advantage of an effective removal of undesirable frequency contents that could overlap intermodulation contents.

Further considerations can be made regarding the am-plitude of the intermodulation products and hence the signal to noise ratio (snr). It is worth noting in Fig. 3 that amplitudes of the sum and difference intermodula-tion contents are not the same: The sum intermodulation product is 25 dB greater than the difference one. For this reason, the employment of the intermodulation products at sum frequency leads to a higher snr.

The amplitude of final intermodulation signal is a con-sequence of the single amplitude of both frequency compo-nent signals F1 and F2. The amplitude of each frequency component can be set separately when the composite pulse is created with advantageous implications in terms of snr, especially when broadband and narrowband win-dowed components are present in the same composite

pulse. In this case, time durations and amplitudes of the 2 frequency components F1 and F2 need to be optimized separately as a trade-off between snr and acoustic in-tensity limitations in terms of mechanical index (MI) and spatial peak pulse average intensity (IsPPa) [24]) imposed by safety regulations for ultrasound equipment.

III. Method for separating the Intermodulation Products: simulated results

In this section, the procedure to obtain the ultrasonic pulses employed for the experimentation is described and the simulation of the proposed method with the KZK non-linear model is reported.

Fig. 4 reports the composite pulses and their basic components employed in the experimentation. The first composite pulse cP1 (left column), is constituted by the temporal sum of 2 Gaussian-shaped signals with different


Fig. 4. Generation of the composite pulses cP1 and cP2 starting from their basic components F1 and F2.

time durations and center frequencies: the first one (com-ponent F1) is a 5 Mhz Gaussian shaped signal with short time duration (1.2 μs).

component F2 is a 7.5 Mhz center frequency signal with time duration of 16 μs. The second composite pulse cP2 (right column) is the temporal sum of basic compo-nent F1 with F2*, which is the phase inversion signal of the F2 basic component.

simulated signals according to the KZK model whose inputs are cP1 and cP2 are reported, respectively, in Fig. 5(a) and Fig. 5(b). Because the experimentation was car-ried out in a water tank, simulations were performed with the B/a parameter equal to 5 and a propagation distance of 10 cm.

The transmitted components (narrowband and broad-band components) are clearly recognizable in these spec-tra in contrast to nonlinear contents such as harmonics and intermodulation components, which are overlapped and undistinguished.

results of the subtraction between the distorted pulse cP1 and cP2 are reported in Fig. 5(c): suppression of the broadband fundamental and the second harmonics can be noted in the spectrum. The presence of the nar-rowband transmitted frequency (7.5 Mhz), the sum (12.5 Mhz) and difference (2.5 Mhz) intermodulation products according to the theory in section II are worth noting. Moreover, an intermodulation product of third order is present at 17.5 Mhz and a fourth- order intermodulation product is present at 7.5 Mhz.

In Fig. 6(a), the spectrum of the PsI final signal is re-ported as a continuous line. a low pass FIr filter—dashed line in Fig. 6(a)—and a pass band FIr filter—dot-dashed line in Fig. 6(a)—are employed to isolate, respectively, the difference and sum frequency intermodulation prod-ucts from the other spectral contents. Fig. 6(b) and Fig. 6(c) show the 2 intermodulation signals, difference and sum frequencies, respectively, obtained by means of digital FIr filters.


Fig. 5. simulation of propagation of the composite pulse cP1 and cP2 in a nonlinear medium with B/a = 5 at a distance of 10 cm. (a) Propagated signal and spectrum of composite pulse cP1; (b) propagated signal and spectrum of composite pulse cP2; (c) final PsI signal and spectrum obtained according to the proposed method.

considering the filtered signals in Fig. 6(b) and in Fig. 6(c), it can be affirmed that their temporal width is com-parable to the broadband component of cP1 and cP2 reported in Fig. 4, and hence, the final axial resolution of the method is imposed by the broadband component of the transmitted composite signals.

IV. Experimental setup

Three experimental setups were devised to assess the proposed method (Fig. 7).

The first one consists of an experimental transmission system based on 2 single-element transducers aligned ac-


Fig. 6. (a) continuous line: spectrum of the PsI final signal. Basic dash line: low pass (lP) filter (hamming FIr filter with 191 taps). double dash line: band pass (BP) filter (hamming FIr filter with 191 taps). (b) difference frequency intermodulation signal extracted by means of the lP filter. sum frequency intermodulation signal extracted by means of the BP filter.

Fig. 7. left: a block diagram of the acquiring system. as transmitting unit, a single-element ultrasonic transducer is connected to a linear power amplifier (EnI 350l) driven by an arbitrary waveform generator (agilent, 33250a). right: transducer arrangements for the first 2 setups employed for the experimentation.


Fig. 8. PsI method applied to the transmitted signals acquired by the hydrophone described in setup 1. (a) acquired composite pulse cP1 and its spectrum; (b) acquired composite pulse cP2 and its spectrum; (c) subtraction signal between composite pulses cP1 and cP2 and its spectrum with the frequency response of the low pass filter (dashed line) and pass band filter (dot-dashed line) superimposed; (d) sum (right) and difference (left) intermodulation signals extracted from the signal shown in Fig. 8(c) by filtering processing.

cording to the beam axis. The transmitting transducer is a Bdn10 (Gilardoni, Mandello del lario, lecco, Ita-ly) with a diameter of 10 mm, a planar face, a center frequency of 5 Mhz, and a −6dB relative bandwidth of 50%. The receiving transducer is a calibrated hydrophone (PVdF coplanar shielded membrane hydrophone type no. 699/1/00002/200, GEc-Marconi, caswell, Towcester, UK). Because the near field distance n for the Bdn10 transducer is 8.3 cm at 5 Mhz and 12.45 cm at 7.5 Mhz, the distance between the 2 transducers is set at 10 cm. an 80 Mhz arbitrary waveform generator (aWG 33250a; agilent Technologies, Palo alto, ca) generated the com-posite pulses according to the proposed method and was also the trigger for the whole system. The transmit signals were amplified by a broadband 50 dB rF power amplifier (350la; EnI, rochester, ny).

For accurate and low-noise acoustic pressure measure-ments, a 500-Mhz analog bandwidth and 1-Gs/s sam-pling frequency oscilloscope (Tds 520c, Tektronix Inc.,

Portland, or) was employed in connection with the cali-brated membrane hydrophone. a set of 24 different driv-ing voltages (i.e., 24 different acoustic intensities) ranging between 24 and 162 Vpp was employed to evaluate the acoustic levels of the sum and difference intermodulation content generated as a consequence of signal distortion.

The second setup for this experimentation (setup 2) is a system based on a pulse-echo technique with 2 single-element transducers positioned confocally at a 20° angle. The distance from the transducer faces and the acoustic beam intersection is 10 cm. The Bdn10 transducer was employed as transmitter, and the receiving probe, a V382 (Panametrics, Waltham, Ma) with a diameter of 1.3 cm, was a 3.2-Mhz center frequency unfocused transducer with a minus 6 dB relative bandwidth of 100%.

rF received signals were amplified with a low noise, 40-dB rF amplifier (5052 Pr, Panametrics, Waltham, Ma) and sampled at 40 Mhz using one channel of a fast echographic multiparameters multi-image novel appara-


Fig. 9. Experimental assessment of the sum and difference intermodulation amplitude versus the acoustic pressures employing setup 1. (a) definition of negative and positive peak pressure values (PPK-, Ppk+) on an acquired ultrasonic signal; (b) spectrum of the final PsI signals for the case of Fig. 9(a); (c) experimental evaluation of PPK- and Ppk+ values versus the transducer driving voltage; (d) values of sum and difference intermodulation contents evaluated in the spectrum obtained by PsI and normalized by the maximum level of the narrowband fundamental content.


Fig. 10. Experimental assessment of the PsI method: rF echo signals and related spectra acquired with the setup 2. (a) Two rF echo signals re-lated, respectively, to the cP1 and cP2 composite pulses; (b) superposition of the spectra of the echo signal of Fig. 10(a); (c) spectrum of the rF subtracted signal; (d) final intermodulation signal as a result of band pass filtering.

tus (FEMMIna platform) [25], [26], which is echographic equipment able to acquire ultrasonic signals in real-time modality.

The 2 setups were employed with the same kind of com-posite pulses to assess the method both in transmission and in echo modalities. The transmitted sequence consists of 2 composite pulses, cP1 and cP2, with a mutual delay time of 150 μs. The repetition frequency of the sequence is 10 hz. Echo signals were received and processed according to the described method.

a tissue-mimicking phantom was employed in the sec-ond setup as a nonlinear and scattering water-based me-dium. The phantom consisted of a latex tube, 4 cm in diameter and 80 μm thick, filled with a water test fluid (Model 707-G, aTs laboratories, Inc., Bridgeport, cT) and including a calibrated dispersion of 30-μm diameter plastic particles.

a third measurement set-up was employed for ultra-sound beam profile characterization (set-up 3). The trans-mitting transducer (Bdn10) and the coplanar hydro-phone, moved by a micrometric scanning system, were immersed in a water tank filled with degassed water. The beam diagrams of intermodulation components were ob-tained by using the PsI processing method.

V. Experimental results

A. Setup 1: Transmission Setup

Fig. 8 shows the experimental results obtained from setup 1 when the ultrasonic pulses cP1 and cP2 theoreti-cally described in Fig. 4 and simulated in Fig. 5 and in Fig. 6 are transmitted into the water tank. Fig. 8(a) and Fig. 8(b) show the experimental ultrasonic pulses (and their spectra) received by the hydrophone after a 10 cm propagation in water.

The intermodulation components are difficult to recog-nize in the spectra of distorted cP1 and cP2 signals be-cause they are overlapped by the fundamental and second harmonic bands. after the subtraction between cP1 and cP2 signals, second-order intermodulation components appear in the spectrum of Fig. 8(c) and can be separated by low-pass—dashed line of Fig. 8(c)—and pass-band—dot-dashed line of Fig. 8(c)—filters. In Fig. 8(d), the 2 intermodulation pulses extracted from the signal of Fig. 8(c) are shown. It is worth noting how their time duration is comparable to the time duration of the broadband com-ponent of cP1 and cP2 (Fig. 4, basic component signal F1) and their similarity with the simulated signals (Fig. 6, on the bottom).


Fig. 11. radiation diagrams calculated in the frequency domain by means of Fourier Transform. (a) Black line: radiation diagram of the difference intermodulation component (2.5 Mhz); grey line: radiation diagram of the fundamental (5 Mhz). (b) Black line: radiation diagram of the sum inter-modulation component (12.5 Mhz); grey line: radiation diagram of the fundamental (5 Mhz).

Fig. 9 reports the results from experimentation per-formed using setup 1. These results show the behavior of sum and difference intermodulation spectral contents at different increasing acoustic intensities. Fig. 9(a) shows how the measured negative Ppk- and positive Ppk+ peak pressures are defined on a distorted composite pulse. In Fig. 9(b), the spectrum of subtraction signal according to the PsI method is reported: the residual transmitted nar-rowband at 7.5 Mhz, the sum and difference intermodula-tion contents at, respectively, 12.5 Mhz and 2.5 Mhz, the residual third-order intermodulation content at 17.5 Mhz, and the residual fourth-order intermodulation contents at 7.5 Mhz and 22.5 Mhz are all worth noting. Fig. 9(c) reports the positive (Ppk+) and negative (Ppk-) acoustic pressure levels versus the peak-to-peak driving voltage for the cP1 and cP2 composite signals. Fig. 9(d) shows the spectral levels of the sum and difference intermodulation content of the PsI final signal versus the peak-to-peak driving voltage applied to the transducer.

B. Setup 2: Echographic Setup

Fig. 10 reports acquired signals coming from experi-mental setup 2. Two portions of the rF echo signals re-lated to cP1 and cP2 described in Fig. 4 are shown in Fig. 10(a). The 2 rF signals present a maximum value in the central portion due to spatial overlapping of the transmitting and receiving acoustic beams according to the 20-degree alignment of transducers. spectra of the rF echo signals are superimposed in Fig. 10(b). narrowband content at 7.5 Mhz is related to the component F2 of the transmitted cP, and broadband spectral contents in the range 1.5 Mhz to 5.5 Mhz are related to both the trans-mitted component F1 and the intermodulation difference product. It should be noted that the 2 spectral curves are almost superimposable, except in the region between 1.5 and 3 Mhz, where the difference frequency intermodula-tion content is present as shown in the spectrum of the subtracted signal reported in Fig. 10(c). The broadband transmitted components are removed from the spectral domain, and only the difference intermodulation product and the transmitted narrowband component F2 remain according to the theory. The sum intermodulation prod-uct is located outside the receiving transducer bandwidth and hence is overcome by the electronic noise. The differ-ence intermodulation signal of Fig. 10(d) is obtained by the pass-band filtering (91-tap hanning FIr filter) of the subtraction signal resulting from PsI processing.

C. Setup 3: Beam Profile

In Fig. 11, beam radiation diagrams at −18 dB, coming from experimental setup 3, are shown for the sum and dif-ference intermodulation components. Fig. 11(a) represents a comparison between the fundamental broadband beam (dark gray line) and the difference intermodulation beam (black line). Fig. 11(b) represents a comparison of the fun-

damental broadband beam (dark gray line) with the sum intermodulation beam (black line).

VI. discussion

The proposed method allows extraction of the nonlin-ear intermodulation contents from the rF echo signal, making them available for further processing algorithms for tissue characterization or contrast imaging. For these aims, the intermodulation spectral contents must be sepa-rated from the transmitted bands and harmonics to avoid mutual spectral interference.

PI technique operating with multifrequency composite pulses represents the gold standard for nonlinear echo-graphic imaging, allowing fundamental band suppression and reinforcement of intermodulation and harmonic con-tents. Unfortunately, PI technique applied to multifre-quency composite pulses leads to a superposition of the harmonic and intermodulation contents and thus limits the effectiveness of this technique.

The investigation of the PsI technique, both theoreti-cally and experimentally, helps overcome PI drawbacks by removing harmonic contents (especially second harmon-ics) in addition to one of the 2 fundamental transmitted bands. an improved version of this technique consists of transmitting for the composite pulses a narrowband com-ponent with low spectral side lobes to improve the band separation and free up the frequency region for broadband transmitted components, as appears in Fig. 3 and in Fig. 5. This can be achieved by employing as first frequen-cy component a long sinusoidal burst with an amplitude modulation and a broadband pulse as second frequency component (Fig. 5).

In this paper, we have demonstrated, both through nu-merical simulations and experimentally, that the band-width of the intermodulation product is connected to the bandwidth of the broadband frequency component of cP regardless of the time duration of the narrowband com-ponent in the composite pulse. The intermodulation fre-quency bands are the spectral replica of the broadband transmitted ones, as derived from Fig. 5, and hence, the final axial resolution of the method is controlled by the transmitted broadband component in the composite pulse. The narrowband spectral content of the received echo sig-nals can be easily removed by a notch or rejection filter by considering that the smoothness of its shape ensures the lowness of spectral side lobes. another interesting impli-cation of windowed signals is that they avoid free oscilla-tions, which occur around the transducer central frequen-cy when rectangular windowed burst sinusoidal signals are employed. Moreover it is possible to move the frequency of the narrowband signals to appropriately choose the fre-quencies of intermodulation components with respect to the frequency response of the employed transducer.

Further considerations concern the lateral resolution of the method that is imposed by the lateral dimension of the acoustic beam. as reported in [27], [28], the beam


cross section of difference intermodulation component is narrower if compared with that obtained by using the dif-ference frequency as fundamental. Moreover it is possible to assert that beam lateral dimensions of nonlinear con-tents are lower than the fundamental ones. as experimen-tally demonstrated in Fig. 11, the acoustic beam dimen-sion associated with the intermodulation products is lower than the beam associated to the fundamental components leading to an improvement of lateral resolution of the fi-nal echographic image. Furthermore, the intermodulation acoustic beam shows low side lobes with the benefits of artifact reduction in the final echographic image.

The PsI method was tested under different transmit-ted acoustic intensities and frequencies. The method is flexible and adaptable to different insonifying conditions because the intermodulation products are located in the frequency domain in dependence on the mutual position of the 2 fundamental transmitted components F1 and F2. For instance, the difference frequency intermodula-tion content can be positioned at lower frequencies than the fundamental bands and hence exploits the low tissue attenuation or, alternatively, the difference frequency in-termodulation content can be placed in the center of the transducer bandwidth leading to a high snr.

If the basic components of the cP are appropriately chosen, the sum frequency intermodulation content is well separated after PsI and appears, both from simulations and experimentally, with a higher amplitude level with respect to the difference frequency content. Because the sum frequency intermodulation band occurs generally at higher frequencies, its high amplitude is useful for balanc-ing the greater ultrasound attenuation.

Unfortunately, 2 transmissions for each sight line are required; as a consequence, the PsI method suffers from potential motion artifacts as well as any multipulse tech-nique. Moreover, the need for a signal with a long time du-ration leads to a further reduction of the final frame rate.

VII. conclusion

In this work, a method for extracting nonlinear inter-modulation contents from an echographic signal back-propagated from a nonlinear medium is proposed. The method is based on the transmission of 2 composite pulses for each line of sight and then on the subtraction of the 2 acquired echographic signals. The subtraction procedure makes it possible to reject harmonics from the resulting signal (especially second ones) and to achieve good iso-lation of intermodulation sum and difference frequency contents, making them available for further processing al-gorithms.

It has been demonstrated that the intermodulation spectral bandwidth is a replica of the transmitted band-width of the broadband component in the composite pulse if sinusoidal burst signals are employed, and hence, PsI can be suitable for high-resolution imaging techniques. We have also demonstrated the feasibility of the PsI technique

both theoretically and experimentally. The development of optimal waveforms or coded signals exploitable for a pulse compression method will be the focus of further work.

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Elena Biagi was born in Florence, Italy, in 1956. she received the “lau-rea” degree in electronic engineering from the University of Florence, Florence, Italy, in 1982. From 1982 to 1991, her research was mainly de-voted to ultrasonic material characterization and medical imaging. since 1991, she has been an assistant professor in the Electronics and Telecom-munications department of the University of Florence; she became an associate professor for optoelectronics in 2001. her current interests deal with the design of dedicated ultrasonic transducers, signal processing for biological tissue spectral parameters extraction, design arid realization of fast electronics for radiofrequency real-time processing. since 1996, her teaching activity has concerned optoelectronics and sensors.

Luca Breschi was born in Prato, Italy, in 1973. he received the “lau-rea” degree in electronic engineering from the University of Florence, Florence, Italy, in 1999. In 2002, he received the Ph.d. degree in non-destructive testing from the Electronics and Telecommunications de-partment of the University of Florence. his main research activities are nonlinear interaction between ultrasound and tissues and signal process-

ing for tissue characterization. he developed several signal processing algorithms for biological tissue characterization and diagnostic systems for cancer detection by means of contrast agents. he is also holds several patents and is the author of several national and international scientific papers.

Enrico Vannacci was born in Pistoia, Italy, in 1978. he received the “laurea” degree in electronic engineering from the University of Florence, Florence, Italy. In 2008, he received the Ph.d. degree in nondestructive testing from the Electronics and Telecommunications department of the University of Florence.

his research activities include acoustic characterization of ultrasound contrast agents, ultrasound nonlinear imaging, and signal processing for tissue characterization. currently, he is involved in devising new diag-nostics systems for the assessment of the acoustic nonlinear properties of tissues.

Leonardo Masotti was born in Faenza, Italy, in 1939. he received the “laurea” degree in electronic engineering from the University of Engineering in Bologna, Italy, in 1963 and the Italian national libera docenza degree in applied electronics in 1970. his present position is full professor of electronics and research director of the Ultrasound and non destructive Testing laboratory at the department of Electronics and Telecommunications of the University of Florence, Florence, Italy. he has been a member of the scientific committee of the Istituto di Elaborazione dell’lnformazione of the consiglio nazionale delle ricerche (cnr) in Pisa since 1983 and the scientific committee of Istituto di Fisiologia clinica of cnr in Pisa since 1989. he has been president of the consorzio centro di Eccellenza optronica (cEo) since 1992. he also takes part in the Technical direction committee of the high Tech network for the Tuscany region.


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