An approach for reducing adjacent element by Pieter van Rooyen

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CONTROL, VOL. 50, NO.

12, DECEMBER 2003

An Approach for Reducing Adjacent Element Crosstalk in Ultrasound Arrays Shiwei Zhou, Gregory L. Wojcik, Member, IEEE, a n d J o h n A. Hossack, Senior Member, IEEE Abstract-A method is presented for active cancellation of crosstalk effects in ultrasonic arrays. T h e approach makes use of t h e programmable t r a n s m i t t e r waveform generators t h a t a r e now being used with growing prevalence in diagnostic ultrasound systems. T h e array's transmit mode transfer function is represented by a transfer function matrix. Eiements of t h i s matrix a r e determined by exciting a single, central element with a wideband waveform a n d determining t h e resulting pressure o u t p u t from t h e central element and adjacent elements. T h e desired o u t p u t t h e n is defined (e.g., finite o u t p u t from a single, central element) and zero o u t p u t from all o t h e r elements. T h e transfer function matrix equation can be solved t o determine t h e required excitation functions o n b o t h t h e central a r r a y element a n d its neighbors. These excitation functions will result in reduced evidence of crosstalk o n t h e o u t p u t signals. Therefore, t h e singleelement, angular-response function is improved. Using superposition, t h e approach can h e extended t o beamformed array excitation. A variety of theoretical and experimental results a r e shown. T h e method also can he used in t h e receive mode h u t with a less satisfactory soiution. A transmitting mode experiment based o n a prototype fiveelement transducer has provided results indicating t h a t sidelohes in t h e angular response can h e reduced using this technique.

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Wrnl acoustic ouq,ut fmm Central

FJoment

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uuuuu Adjacent C c n h d A d j n m t Element#l Element Element #2 "bray elements sitling on a mrehanifd support (hncker) - not shown Fig. 1. Schematic of interelement crosstalk.

I. INTRODUCTION phased arrays displaced mechanically scanned diagnostic ultrasound systems many years ago. In these systems, ultrasonic beams are synthesized in both transmit and receive mode to produce highquality, diagnostically useful images. However, interelement crosstalk (or cross coupling) causes degradation of singleelement, angular response. The main lobe of the singleelement response is narrowed and peaks/nulls may be observed at angles corresponding to constructive/destructive interference of waves emanating from the array surface due to wave energy propagating outward from the element under consideration. Crosstalk may be separated into acoustic and electrical cross-coupling functions. Electrical crosstalk is controlled by carefully shielding individual array element cables and the array interconnect structure. Electrical crosstalk usually can be limited to approximately -35 dB in a well designed array [l].Notice that electrical crosstalk and acoustic crosstalk result in different array beamforming artifacts. Electrical crosstalk is practically instantaneous and, hence, is associated with in-phase effective widening of in-

LTRASONIC

Manuscript received March 24, 2003; accepted June 23, 2003. The authors are with the Biomedical Engineering Department. University of Virginia, Charlottesviile, VA 22908-0759 (+mal: hossack0virginmedu).

dividual array elements. This results in a more directional array element and, therefore, may result in a stronger than expected zero steer (broadside) acoustic beam intensity. Acoustic crosstalk is associated with relatively slow acoustic wave propagation between successive array elements. Fig. l illustrates schematically the desired output energy from a central array element and the delayed and attenuated outputs from immediately neighboring elements resulting from acoustic crosstalk. This phenomenon has heen investigated by many researchers over the years for conventional PZT-based transducers [2]-[6], PZT-epoxy 1:3 composite transducer arrays [7]-[9], and silicon micromachined transducers [10]-(13]. Cross coupling in 1:3 piezc-composites and silicon micromachined transducers are generally higher due to lack of isolation cut between the elements and the continuous solid acoustic path between elements. This is particularly true in siliconbased transducers in which the silicon substrate provides a very low-loss acoustic path. A common theme in work on minimizing crosstalk is that physical separation, usually via a gas- or vacuum-filled slot, is preferred. In some applications the fabrication of a slot is not unduly burdensome and is accepted practice. Most commonly, these slots are made with semiconductor dicing saws that are capable of kerfs of 25 pm or less and high-aspect ratiosover 10 times deeper than wide. However, even with these kerfs, there is still some residual crosstalk in many cases. Additionally, in 1:3 composite transducers and silicon micromachined transducers, an added dicing step defeats the underlying motivation for using the transducer technol-

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ZHOU et al.: REDUCING ELEMENT CROSSTALK IN ULTRASOUND ARRAYS

ogy. The 1:3 composite transducers already are diced as

part of their fabrication process, and a primary motivation for using MEMS silicon-based transducers is to specifically avoid time-consuming, intricate processes such as sequential element-by-element dicing. Additionally, dicing to form kerf spaces between elements invariably reduces the robustness of the transducer, resulting in potential for low manufacturing yield and reduced reliability in practical use. Thus, there is interest in new approaches that may supplant the dicing process or may augment the crosstalk reduction obtained by dicing. The impact of relatively slowly propagating crosstalk related acoustic waves on the diffraction pattern of array elements also bas been investigated widely [4], [14]-[16]. The earliest of these papers likened cross coupling to an effective widening of the array element that resulted in an expected narrowing of the single-element beam pattern. However, more recent work [I61 takes account of the relative phasing of the crosstalkelements and results in a more accurate and complex estimate of the impact of crosstalk on the single element diffraction pattern. The negative impact of crosstalk on the diffraction pattern is clear; consequently, the need to minimize acoustic crosstalk also is readily evident. In addition to acoustic crosstalk through a filled kerf or through the backing medium, another significant source of crosstalk is through the matching layer and lens material. Clearly, crosstalk through the matching layers may be minimized by dicing the matching layer-though this is not always done for a variety of practical reasons. It is not practical to use physical separation in the lens as this forms the fluid impermeable outer surface of the transducer. Taking account of all these design issues, a reasonable upper limit on crosstalk suppression in conventional diced PZT arrays is approximately -35 dB [I].

11. THEORY This paper describes an electrical stimulation-based approach for canceling out the effects of acoustic crosstalk. In summary, an electrical stimulation function for adjacent elements is developed to cancel out the acoustic output from adjacent elements that would otherwise occur. Modern diagnostic transducer arrays are operated as phased systems. Each array element in a phased-array system is stimulated by an electrical waveform with specific shape, amplitude, and delay. Historically, these driving waveforms were simple in form-impulses, steps, or square wave bursts. However, the current state of the art in diagnostic ultrasound involves the use of waveforms with programmed shape in which the harmonic components are minimized. The major motivation behind the widespread use of reduced transmitted harmonic signals is for harmonic imaging modes of operation. In the context of this paper, the significance of these developments is that, if the capability for providing programmed, shaped wav.4forms exists on an ultrasound machine, the machine has the capability-at least in p r i n c i p l e t o take advantage

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= H4i

H51 H52 H53 H54 H55 H56 H57 H61 H6z H63 H64 H65 H66 H67 - H ~H I 72 H73 H74 H75 H16 H77-

V, V, , V5

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(1)

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P4 P3 p

’”ad= P7

Fig. 2. Seven-element array with seven field points right above array surface.

where H [abbreviated from H ( f ) ] is the transfer function matrix relating input voltages, V,, to the output pressures,

P, . The example shown here is for a seven-element array, but this can b e expanded as required. Fig. 2 illustrates this configuration. We will consider the ideal case in which an impulse is applied to the center element. (In this paper the term center element will be used to denote the desired, driven element. The term adjacent element will be applied to the nearest neighboring element on one side. Generally, we assume that there is symmetry around the center element and, therefore, the adjacent element could equally be on one side or the other.) V, is an impulse (i.e., uniform amplitude for all frequencies in the frequency domain). V, to V3 and V5 to V7 are zero. P4 is the direct output from the fourth element. However, because some of the nondiagonal terms in the H matrix are nonzero, there will be finite output from the other elements (i.e., some of PI,Pz, P3, 5 , PG,and P7 will be nonzero). Once the matrix His defined, we can solve the matrix problem to find values for VI to V7 such that we do actually get the desired output (i.e., PI to P3 = 0, P4 = ideal impulse response of the fourth element and P5 to P7 = 0). In fact, crosstalk is only significant on a few neighboring elements. In the c s e below we assume that crosstalk is limited to two elements on each side of the element being excited. However, this is not a limitation here; we can consider the full matrix encompassing all crosstalk terms if required. The matrix becomes a banded matrix with bandwidth 5. All other values of H are 0. This simplifies the characterization of the H matrix and allows for more efficient matrix solution. Notice that there is significant symmetry in the matrix. We typically assume that crosstalk from array element three to array element four is the same as from array element four to array element five, and so on. There might be some irregular behavior at the ends of the array due to different boundary conditions. However, even in this case the change in crosstalk is probably modest as it is common practice to have one or two “test” elements that are used during manufacture to ensure alignment of the saw blade with the designed kerf location before dicing the “real” elements. For the matrix shown in (Z), we only need to measure the crosstalk function of the two adjacent elements resulting from impulse excitation of a cen-

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0 H75 f f x

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% -v7.

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(2)

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- - -

TABLE I

ACOUSTIC PROPERTIES FOR THE FEA MODEL.

P24 P3 P4

PZT Matching material Backing material Lens

-’

P6 P7 -’

Material

points. In this case we have more defined “output” conditions than defined “inputs”. Thus, the problem is overconstrained and requires a pseudwinverse solution. This will find a best-fitting solution in a least-squares sense. The Matlab “pinv” command implements this operation in an efficient and easy-to-use manner. This command uses singular value decomposition to find the pseudo-inverse:

Impedance

(MRayl)

34.2 3.92 2.15 1.5

possible approach would be to assume that the crosstalk is equivalent to “interference”, or ‘gamming”, in the language of adaptive beamforming and calculate filters that place a null at the direction of the “jamming”. Because the array’s sidelobe response is fixed internally, it should be possible to use a relatively simple adaptive beamforming approach because a significant amount of apriori and time-independent information about the origin of the sidelobe should be accessible. A discussion of basic, a i d nioie advanced, forms of adaptive beamforming can be found in 1181. In this paper we concern ourselves with crosstalk cancellation in the transmit path as a more complete and satisfying solution to the problem is available. Additionally, since the two-way heam pattern can be approximated by the product of the transmit and receive beam pattern, an elimination of the sidelobes caused by crosstalk in the transmit heam pattern alone probably will provide sufficient suppression to enable satisfactory two-way beam response.

111. SIMULATION RESULTS

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(4)

Finite element analysis software has evolved to the point that there is considerable confidence in the results obtained using it. The limitations in accuracy when compared to experimental results primarily result from inexact knowledge of actual component geometry and component material parameters. Material parameters are very challenging to characterize fully in terms of all the cross terms in the elasticity matrix and all the attenuation terms. Additionally, bond lines can be difficult to model with high accuracy. All of these factors increase the difficulty in obtaining good experimental data if one is relying on an FEA model to determine the required compensation signals. Therefore, in this paper we present the bulk of our results using FEA simulation data. In addition, we present some limited experimental data obtained using a prototype array.

A . Tkansmitting Mode A 2-D ultrasound transducer array model was modeled using PZFlex. The model is illustrated in Fig. 4. The actual FEA model takes advantage of the symmetry plane and, hence, only the FEA models one half of the device illustrated. Important acoustic properties and geometry design parameters are described in the Tables I and 11. Seven elements are indexed from one to seven simulated in this model, in which four is the center element (Fig. 4).

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'i" 1

Fig. 5.Illustration of the electrical terminations when central element is being subject to transmitter waveform. The resistor value is 50 R.

Fig. 4. Geometry of the 2-D FEA array transducer model

TABLE I1 GEOMETRYDESIGNPARAMETERS FOR

THE

FEA MODEL.

Parameter

Size

Composite layer thickness Backing layer thicknas Matching layer thicknm Lens layer thickness Element pitch Elevation length Kerf width Kerf cut depth into backing

0.70 mm 1.00 mm 0.35 m& 0.30 mm 0.30 mm 10.0 mm 0.10 mm 0.08 mm

-an

-5

-10

-15

4 . 6 8 Time (Microseconds)

Fig. 6. Input electrical stimulation pulse applied to the center element (element four).

The pressure output signals are measured at seven field points immediately above the center of elements. In these simulations we assume a 50 R source impedance. When we transmit on the central element, we set the voltage to zero at the source for the adjacent elements so the adjacent elements are properly terminated with 50 R to ground. The adjacent elements are not directly shorted to ground. This approach is necessary in order to apply the current superposition theorem correctly. The circuit is illustrated in Fig. 5. We use a wideband Gaussian pulse (2.5 MHz, 80% -6 dB fractional bandwidth) as the central element excitation. Time domain records of pressure outputs were transferred t o a computer running Matlab. Using a fast Fourier transform in Matlab, we converted the time domain records to their equivalent frequency d e main responses and formed the frequency domain transfer functions and crosstalk functions. These responses then were used to populate the matrix equation (1). Our initial calculations use as many pressure measuring locations as transducer source points. Therefore, we are using a square matrix amenable to standard Gaussian elimination. Fig. 6 illustrates the applied input pulse to (center) element four in the time domain. Fig. 7 illustrates the pressure outputs from elements four and five, respectively, in both time and frequency domain. It is evident from these

figures that the crosstalk level in the transmit mode is approximately -18 dB. Notice that, to first order, the crosstalk signal is a delayed and attenuated version of the desired signal output from element four. Fig. 8 illustrates the selected desired output waveform from the central element. In the interests of transmission efficiency, this waveform is chosen to be somewhat similar to the observed output for a wideband Gaussian excitation. Fig. 9 illustrates the excitation functions to be applied to each of elements one, two, three, and four, in which the fourth is the central element. The functions applied to five, six, and seven correspond to those applied to three, two, and one, respectively, due to the symmetry of the structure. These functions were derived from the solution to (1). The actual matrix solution, as stated before, is performed in the frequency domain, and the waveforms illustrated in Fig. 10 are obtained via an inverse Fourier transform. Fig. 10 illustrates the pressure output obtained from the central and adjacent elements when the excitation functions illustrated in Fig. 9 were applied to the transducer terminals. A significant reduction in crosstalk has been achieved. Crosstalk has been reduced from -18 dB to -27 dB.

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Fig. 7. Pressure outputs (obtained via FEA) from center element (four) and adjacent element (five),in time (left) and frequency (right) domain.

-2b

6 8 Time (Microseconds)

Fig. 8. Deired output pressure waveform from the central element.

The crosstalk reduction process then was repeated using approximately twice as many pressure field sample points-ne in front of the center of each element and one in additional point midway between these sample points (i.e., above the intermediate kerf region). In this case there are 13 field points for the seven transducer elements. In fact, due to symmetry, only seven field points and four transducer elements were analyzed. Again, a broadband Gaussian pulse, identical to that used above, was used as the desired central element output. Following the process described in the above theory section, the required excitation functions were obtained after finding a pseudo-inverse solution to the matrix equation (3). The actual waveforms calculated using this second approach, and the consequent reduction in crosstalk, are so similar to those reported above for the square matrix case (1) that they are not plotted. This suggests that, at least for this example, the simple square matrix approach is sufficient.

B. Single-Element Angular Response

-1 2-

4 . 6 8 Time (Microseconds)

Fig. 9.Excitation functions to be applied on each of element, one to seven, where four is the center element (arbitrary amplitude units).

Ultimately, the major impact of crosstalk is the degradation of the single-element, angular response. Generally, beamforming starts from the assumption that individual elements behave as point or line sources with an approximately uniform response as a function of angle. Typically, for example, a half wavelength element has an angular response that is reduced by no more than -6 dB out to the limits of expected use (Le., 45 degrees). However, crosstalk may cause main lobe narrowing (due to wider effective aperture) and sidelobes due to constructive/destructive interference due to waves propagating along the array surface and leaking into the fluid medium. Therefore, a singleelement heamplot is a valuable indicator of crosstalk performance. Fig. 11illustrates the theoretical single-element, angular transmit response using Selfridgeâ&#x20AC;&#x2122;s equation [19]. Fig. 11 also illustrates the single-element response obtained (using FEA) for both the case without crosstalk cancellation and with crosstalk cancellation. The improvement in single element angular response is readily evident.

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VOL. 50,

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2x 10

.......

e -

E -1-

-2

Frequency (MHz)

Time (Microseconds)

Fig. 10. The pressure outputs from center and adjacent element (obtained via FEA) after applying the compensation signals, in time and frequency domain. Time domain, left; frequency domain;right.

Water Region

Ground Layer,

- Void kerf filler - ideal

....... No compensation I ----- With compensation

-4 j ~

-5‘

’

-40

-20

Degrees

;’

PCB Board

;’

I 1,

Fig. 12. Experimental trsnsducer configuration.

Fig. 11. Theoretical angular response (&t2.5 MHz) and FEA simulb tion of the angular response for both the no compensation and with compensation case.

IV. EXPERIMENTAL RESULTS A prototype transducer array was fabricated for testing the crosstalk cancellation method (Fig. 12). The transducer active element was made of PZT-SH type piezoelectric ceramic (HD3203, CTS Ceramics, Albuquerque, NM). The elements are 16 mm long (elevation) and 1.64 mm thick. Five elements were diced to form elements with a 0.6 mm center-to-center pitch. The kerf was 90 pm wide and filled with an unfilled, nonconductive epoxy. A 1-mm thick glass reinforced plastic printed circuit board (PCB) was used as the substrate and conductive silver-epoxy used to bond the transducer elements to the substrate. The electrical contact from the lower surface of the PZT to the PCB was used as the electrical signal path. The kerfs were cut 0.2 mm into the PCB board to assure the electrical isolation between neighbor elements. On the top of the transducer, a thin, gold-plated polyester layer was used as the “ground” return. Critical acoustic properties and geometry parameters are described in Tables 111 and N.

ACOUSTICPROPERTIES

TABLE 111 FOR THE EXPERIMENTAL MODEL

Material

Impedance (MRayl)

PZT Epoxy PCB board

34.20

3.05 6.65

The acoustic properties for all component materials were obtained from manufacturers’ datasheets, or measured experimentally. All critical transducer dimensions were measured. We then simulated the device using PZFlex and used a 1-MHz, 50% -6 dB fractional bandwidth Gaussian pulse as the excitation applied to the center element. We obtained the direct output from the central element and from the nearest two neighbors and p o p ulated the transfer function matrix (1). We then solved the equation and obtained the required excitation functions for the array. We attempted to measure the outputs from the individual elements by placing a GL-0085 hydrophone (Onda Corp./Specialty Engineering Associates, Sunnyvale, CA) adjacent to the elements. However, this measurement did not provide useful results. We believe that we cannot get close enough t o the transducer element

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d.:REDUOIN(: ELEMENT CROSSTALK IN ULTRASOUND ARFAYS

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Amplifler

Preamplifier

Watertank

Fig. 13. Schematic of experimental apparatus used to make measurements of angular response. TABLE IV GEOMETRY DESIGN PARAMETERS FOR THE EXPERIMENTAL MODEL. Parameters

Size ~

PZT layer thickness PCB board thickness Elevation length Element pitch Kerf width Kerf cut depth into backing

1.64 mm 1.04 mm 16.0 mm 0.60 mm 0.09 mm 0.20 mm

to obtain responses that are not confounded by diffracting contributions from the center element. Therefore, we decided to concentrate on measuring the beamplots of the array in order to determine if the cancellation technique was suppressing any sidelobes. Because we could not measure the transfer function of the elements directly using the hydrophone, we had to rely on a FEA model of the transducer. This approximation impacted the quality of our experimental results and is discussed later. Fig. 13 illustrates the configuration of the experiment. We generated the required signals on the computer USing the PZFlex simulation result, then transferred them to the dual channel Waveform Generator (AWG2021, Tektronix, Beaverton, OR). These signals (central and adjacent) were amplified by EN1 325LA FW amplifiers and connected to the central and adjacent elements, respectively. After carefully aligning the central element with the hydrophone by searching for the peak signal, the transducer was rotated using a motion-control stage (PFSOCC, Newport Inc., Irvine, CA). A range of 30 mm was used between the array element and the hydrophone. Acoustic signals detected up by the hydrophone were amplified and sampled using a digital oscilloscope (9310A, LeCroy, Chestnut Ridge, NY).A pulser (SP-801, Ritec Inc., Warwick, RI) was used to synchronize the arbitrary waveform generator and the oscilloscope. Finally, the waveforms recorded in the oscilloscope were saved on a computer and processed in Matlab.

Angle (degrees) Fig. 14. Experimentally measured original beam pattern and beam pattern with the compensation technique. Each curve is normalized to its own p d .

Fig. 14 illustrates the original beam pattern before and after application of the cancellation signal. The cancellation technique clearly has reduced the sidelobes occurring at approximately 40' and 50". However, the main lobe has been narrowed. This would suggest that we are, in fact, somewhat widening the main (in-phase) aperture. This is probably because the cancellation functions we applied are not perfectly matched to the actual physical device. The approximation implied by using a simulation-based compensation waveform, rather than a waveform derived from accurate, experimental measurements of transducer element output, probably is significant, and we continue to investigate approaches for obtaining a reliable experimental measurement. Specifically, when a laser interferometry system becomes available to us, we plan to measure transducer element surface displacements directly. This approach has the spatial resolution and bandwidth to obtain exact information about the output of both the central element and the adjacent element.

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V. DISCUSSION

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adjacent element. There are few effective approaches for reducing crosstalk in silicon-based transducers (or continuous 1:3 composite array structures) other than forming deep trenches by etching or dicing [ll].In these situations, even a modest improvement offered by the cancellation technique discussed here may be very worthwhile. In this paper we have not directly addressed the issue of stability of the crosstalk cancellation method. However, based on the somewhat disappointing experimental results, it is clear that the method is dependent on accurate characterization of the transducer materials and geometry. However, with increasing quality control and better materials characterization, the impact of this limitation is expected to lessen over time. The study presented here has focused on crosstalk in 1D arrays, and our modeling used a 2-D FEA mesh. Clearly, the approach can be extended to use for 2-D arrays and use 3-D FEA. In fact, since 2-D arrays are inherently more intricate than 1-D arrays, the crosstalk problems may be more serious; therefore, they probably have a greater requirement for some form of crosstalk reduction technique. However, the requirement for programmable waveform generators for each of N 2elements rather than simply N (as in a 1-D array), may be prohibitively expensive.

In ultrasound systems in which the capability to program arbitrary-shaped transmitter voltage waveforms on an element-by-element basis, the approach described above can, in principle, yield a useful improvement with no added hardware complexity. The method and results in themselves may not justify the added expense of the programmable waveforms; but, if they are being justified for other purposes (such as harmonic imaging), then a useful improvement may be obtained at an economic cost (i.e., the added engineering investment required to enable the waveforms proposed here). It is recognized that the software development required to implement these modified waveforms on a channel-by-channel hasis may be nontrivial. The approach may b e applied in a relatively straightforward manner for the transmit mode. Once the element transfer function and interelement crosstalk functions are known, a matrix equation solution method may he a p plied to determine the correct crosstalk reduction functions. However, in the receive mode, it is very much more problematic to try to remove the effects of cancellation due to the compounded nature of the received data resulting from the desired element response and the crosstalk component added from adjacent elements. A signal subtraction approach could be used, but this inevitably would reduce VI. CONCLUSIONS SNR. When the approach was investigated using a FEA In this paper, we analyzed the crosstalk in ultrasound model, very satisfactory results were obtained. Crosstalk transducer arrays using a transfer function matrix apwas reduced from -18 dB to -27 dB. We then attempted proach. By defining the direct and cross-coupling terms to perform an experimental verification of the technique. in the matrix, it is possible to solve the matrix equaUnfortunately, this experiment was very difficult to per- tion to obtain required excitation functions for central form with the resolution that is required. We did demon- and adjacent elements so that, within practical limitastrate a significant reduction in sidelobe activity. But it tions, there is finite output from the central element alone. is clear from the main lobe width reduction that we did The method has been shown to be effective in FEA simnot obtain a response corresponding to a single, well iso- ulations. However, our initial experimental data suggest lated, element. We are investigating possible improvements that either very careful experimental characterization or, to our experiment by, for example, wing a better charac- alternatively, very meticulous modeling is required in orterized array. We believe that, with sufficient investment der to obtain the desired effects experimentally. The prcin transducer characterization, results similar to those grammable waveform generators found in some modern uldemonstrated using FEA can be obtained. It is widely ac- trasound machines may enable the implementation of the cepted that FEA provides very realistic results when the techniques discussed here a t minimal cost. materials and geometry are exceptionally well characterized. It follows from this that, eventually, reductions such as we demonstrate here using FEA (a 9 dB reduction) are ACKNOWLEDGMENTS practically attainable. Further work is required to test the ability of the This work was partially funded by the Whitaker Founmethod to improve the performance of very high crosstalk dation. Thanks also are due to Paul Reynolds, Ph.D., at arrays such as silicon MEMS-based transducers. In these Weidlinger Associates Inc. for advice on the use of the devices, and many others with highly acoustic crosstalk, PZFlex FEA code. We also thank the anonymous reviewthere is a significant transverse wave component to the ers for their advice. crosstalk. Because the method here is based around a 1-D consideration of each element's behavior and crosstalk, it may be expected that the method cannot as fully oomREFERENCES pensate for transverse wave related crosstalk as, for example, a 1-D acoustic wave propagating into the backing, [l] C. Desilets, "Medical ultrmonic transducer array design and a p across the kerf base, and up the backing support into an plications," presented at Proc. IEEE Ultmson. Symp.. 1997.

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ZHOU et Of.: REDUCING ELEMENT CROSSTALK IN ULTRASOUND ARRAYS

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Shiwei Zhou was born in Beijing, China in 1974. He received the B.S.and M.S. degrees in optical-electrical engineering from Beijing Institute of Technology, Beijing, China, in 1996 and 1999, respectively. He is currently working towards the Ph.D. degree in medical ultrasound imaging at the Department of Biomedical Engineering of the University of Virginia, Charlottesville, VA. His research interests are ultrasound transducer modeling and design using finite element analysis. applications of digital signal processing techniqies in ultra sound, and the use of ultrasound with microbubbles for diagnosic and therapeutic applicat.ions.

J o h n A. Hossack (S’9D-M’92-SM’02) was born in Glasgow, Scotland. in 1964. He earned his B.Eng. Hons(1) degree in electrical electronic engineering from Strathclyde University, Glasgow, in 1986 and his Ph.D. de. gree in the same department in 1990. From 1990 to 1992, Dr. Hossaek was a post doctoral researcher in the E. L. Ginzton Laboratory of Stanford University working under B. A. Auld’s guidance. His research was on modeling of 0 3 and 1:3 Diemelectric comuw ite transducers. In 1992, he joined Acukn, Mountain View, CA, initially working on transducer design. During his time a t Acuson his interests diversified into beamfarming and 3-D imaging. Dr. Hossack was made a Fellow of Acuson for ‘excellence in technical contribution’ in 1999. In 2000 he joined the Biomedical Engineering Department at the University of Virginia, Charlottesville, VA . His current interests are in improved 1 D ultrasound imaging and high bandwidth transducers/signal procesing. Dr. Hossack is amember of the IEEE and serves on both the Administrative Committee and the Technical Program Committee of the Ultrasonics Section. He also is an Associate Editor of the IEEE 7bnsaetions on Ultmsonics, Femeleetrics, and Fkquency Control.

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