Sparse 2-D Array Design for Real Time Rectilinear Volumetric Imagingtransducers.bme.duke.edu/pubs/uffc_2000_93-110.pdf · Sparse 2-D Array Design for Real Time Rectilinear Volumetric

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 47, NO. 1, JANUARY 2000 93

Sparse 2-D Array Design for Real Time Rectilinear Volumetric Imaging

Jesse T. Yen, Jordan P. Steinberg, and Stephen W. Smith, Member, IEEE

Abstract-Several sparse 2-D arrays for real time rectilinear volumetric imaging were investigated. All arrays consisted of 128 x 128 = 16 384 elements with X spacing operating at 5 MHz. Because of system limitations, not all of the elements could be used. From each array, 256 elements were used as transmitters, and 256 elements were used as receivers. These arrays were compared by computer simulation using Field 11. For each array, beamplots for the on-axis case and an illustrative off-axis case were obtained. For the off-axis case, the effects of receive mode dynamic focusing were studied to maintain the beam perpendicular to the transducer face. Main lobe widths, side lobe heights, clutter floor levels, and pulse-echo sensitivities were quan- tified for each array. The sparse arrays, including a vernier periodic array, a random array, and a Mills cross array, were compared with a fully sampled array that served as the “gold standard.” The Mills cross design showed the best overall performance under the current system constraints.

I. INTRODUCTION

OR REAL TIME B-scan ultrasound imaging, several F types of transducer arrays have been developed to scan various regions of the human body. Such arrays include sectored phased arrays and linear sequential arrays. Sec- tored phased arrays produce a pie-shaped scan by steering and focusing the acoustic beam to a desired location. They are ideal for cardiac imaging because they allow a wider field of view far away from the transducer and avoid inter- ference from the ribs [Fig. l(a)]. Linear sequential arrays scan a rectangular area for which the width of the scan is equal to the transducer length [Fig. l(b)]. These are more useful for obstetric, breast, or vascular imaging for which overlying bone is absent from the field of view. Because linear scans have a wider field of view closer to the transducer than sector scans, anatomical structures close to the skin surface such as the thyroid, carotid artery, and lesions in the breast can more easily be examined.

In the field of real time volumetric ultrasound imaging, the Duke University system uses a 2-D phased array to in- sonify a pyramidal volume equivalent to 64 sector scans of 64 lines each stacked in the elevation direction [Fig. l(c)] [1]-[4]. This scanner includes 256 transmitters and 256 receivers and scans a 65”pyramid using 256 transmit pulses and 16:l parallel processing to acquire 64 x 64 = 4096 image lines at a rate of 30 vol/s. Multiple image planes at any

Manuscript received February 1, 1999; accepted October 29, 1999. This work supported in part by HHS Grant CA-56475 and NSF ERC-8622201. ~

The authors are with the Department of Biomedical Engineering, Duke University, Durham, NC 27708 (e-mail: [email protected]).

desired angle, depth, and origin within the pyramid can be viewed in real time. The system currently uses transducers with frequencies ranging from 2 to 5 MHz [5]. This system has been used clinically for cardiac scanning for 3 yr and is now commercially available.

Notwithstanding the success of the pyramidal volumetric scanner for cardiac applications, no high speed volumetric analog of the linear sequential array currently exists. Instead, as recently reviewed by Fenster and Downey [6], numerous experimental and commercial systems are in use, employing off-line 3-D reconstruction of serial B-scans. In 1986, Smith and von Ramm proposed a high speed volumetric scanner to obtain a rectilinear volumetric scan using a 2-D array analog of the linear sequential array [7]. Such an array would scan a rectilinear volume by performing many rectangular scans stacked in the elevation direction [Fig. l(d)]. A system for rectilinear volumetric imaging has not yet been developed, and its design is the topic of this paper.

In linear sequential arrays, a group of elements, or subaperture, is selected to direct an acoustic beam perpendicular to the transducer face. Through the use of multiplexing circuits, this subaperture is stepped across the entire aperture, and one line is drawn for each step, giving a rectangular field of view. Similarly, in rectilinear volumetric imaging a 2-D subaperture of elements will be selected to move an acoustic beam over the transducer face in both azimuth and elevation dimensions. The Duke volumetric system does not now include multiplexing capability so that a subset of the 256 transmit and receive channels will be switched in and out using amplitude apodization to produce the stepped subaperture. In Fig. 2 for example, a subaperture with cosine apodization located at the center of the transducer is used to obtain the on-axis image line indicated by line A. To produce the off-axis line that is shown by line B, the subaperture is moved to the corner so that an acoustic beam may be focused approximately perpendicular to the transducer face.

In designing a 2-D array for rectilinear volumetric imaging, several challenges must be considered. Typically, a linear sequential array may contain about 256 elements and use 128 elements per line, but, for a 2-D array, this would require 256 x 256 = 65 536 elements, an unrealistic goal. Therefore, very sparse array design must be considered. The first important goal in sparse array design is to min- imize the main lobe width, which implies that elements must be spread over most of the transducer aperture. How- ever, as elements are spread throughout the aperture, the density of elements becomes smaller. This sparseness of

0885-3010/$10.00 @ 2000 IEEE

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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 47, NO. 1, JANUARY 2000

4

Elevation t

Azimuth 'I Fig. 1. Several different types of transducers and their field of view rectilinear scan.

elements results in grating lobes off-axis, the second con- sideration. In addition, receive mode parallel processing should be included so that many receive beams can fit in one wide transmit beam, thus leading to a higher data acquisition rate needed for real time volumetric imaging [3]. The last issue is beam steering. For 1-D linear sequential arrays, an element or group of elements transmits an acoustic beam perpendicular to the transducer face; this must also be the case for 2-D arrays. If the acoustic beam is significantly steered, this could lead to image distortion. Transmitting an acoustic beam perpendicular to the transducer face can become very difficult when generating lines off-axis.

As illustrated in Fig. 3, we have investigated several different sparse 2-D array designs and compared them with a fully sampled array [Fig. 3(a)]. Periodic or vernier arrays have been proposed by Lockwood et al. [9], [lo]. In this design, receive elements are spread evenly through-

. , a) sector scan, b) linear sequential scan, c) pyramidal scan, and d)

out the aperture spaced by a distance p d , where p is an integer indicating a sparseness factor and d is the interelement spacing. Transmit elements are spaced by a distance ( p - 1)d. Usually, the interelement spacing d is N X/2. Because transmit and receive elements have different peri- odicities, secondary lobes will occur at different locations, thereby suppressing secondary lobe level caused by the multiplicative process of transmit and receive. Variations of periodic arrays have been developed by Light et al. [5] for pyramidal volumetric scanning. A schematic of an illustrative vernier array for rectilinear volumetric scanning is shown in Fig. 3(b).

The third array, the random array as described by Stein- berg [ll] and Turnbull et al. [12], reduces any possibility of grating lobes by selecting the locations of transmit and receive elements using a pseudorandom number generator. Davidsen et al. [13] proposed using a Gaussian distribution of transmit elements across the entire aperture to give a

YEN et al.: REAL TIME RECTILINEAR VOLUMETRIC IMAGING

/I

95

..................................

Apodization Level

1 .o

0.75

0.5

0.25

0.0

Fig. 2. Moving subapertures for 2-D arrays. Subapertures employ cosine apodization as shown by the gray scale color bar. Line A represents the on-axis line focused at 0 , 0 , 30 mm, and line B represents the off-axis line focused at 16, 16, and 30 mm.

wider transmit beam for parallel processing and a uniform distribution of receive elements. Although no grating lobes are present because of the lack of spatial periodicity, such a random distribution of elements gives a sidelobe pedestal at a level (in decibels) approximately equal to

1 P ( 0 , a) M 2010g ___ VmK

where Nt and N, are the number of transmit and receive elements, respectively. A schematic of an example of the random array is shown in Fig. 3(c).

Smith et al. [a] and Song et al. [8] have investigated Mills cross designs for pyramidal volumetric scanning. Fig. 3(d) shows an example Mills cross that consists of center rows of transmitters in azimuth and center columns of receivers in elevation. The transmit beam will be very narrow in the azimuth dimension but very wide in elevation. However, the receive beam works in an opposite manner, having a very narrow beam in elevation and a very wide beam in azimuth. The result is a narrow pulse-echo beam in both dimensions because of the multiplicative process of transmit and receive.

In this paper, we compare several different array designs by computer simulation using Field I1 software from Jensen and Svendsen [14]. A fully sampled array, a vernier array, a random array, and a Mills cross array are compared. It is our hypothesis that the Mills cross pattern is comparable with or outperforms the other very sparse array geometries in terms of beamwidths, side lobe heights, peak pressures, and off-axis distortion.

11. METHODS

All simulations were performed using the Field I1 (v. 1.32) program written by Jensen. Field I1 uses the spatial

impulse response method in which the pulse-echo field is calculated by

where * indicates convolution [14]. In this equation, CO is the speed of sound and vpe is the pulse-echo electromechan- ical impulse response, including the excitation function. The variables ht and h, are the spatial impulse responses of the transmit and receive apertures, respectively. In this paper, we use the program's abilities to generate pulse- echo fields. For the excitation pulse, a Gaussian-weighted sine wave with a 50% -6-dB fractional bandwidth and center frequency of 5 MHz was used. Each array, with dimensions of 38.4 x 38.4 mm, consisted of 128 x 128 = 16 384 elements with 256 transmit channels and 256 receive channels with an interelement spacing of X = 0.308 mm and 25 pm kerf. An angular response of the form sin(z)/z was assumed for each element. The number of transmitters and receivers was limited by the electronics of the Duke University phased array volumetric scanner. In the case of linear sequential imaging, X spacing is not a significant problem because the grating lobes are located at f90" at 5 MHz.

Except for the random array, each array used cosine amplitude apodization in both elevation and azimuth dimensions, giving a dome-like apodization function over the subaperture. We used an F/2 subaperture in transmit and an F/1 aperture in receive. For each array, we calculated beamplots to simulate the application of breast scanning or vascular scanning for foci at (0, 0, 30) mm and (16, 16, 30) mm, the on-axis and illustrative off-axis cases, respectively. For the on-axis case, the center of the apodization function is directly over the center of the focus. How- ever, in the off-axis case, the apodization function has been

L

96 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 47, NO. 1, JANUARY 2000

off-axis

D)

on-axis

= Transmit

0.0 0.25 0.5 0.75 1.0 c] = Receive

Apodization Level =Shared

i - on-axis

5 - - - - off-axis

1 .o 0.75

0.5

0.25

Apodization Level

' 0.0 1

Fig. 3. Schematic of the four different arrays and moving subapertures of on-axis and off-axis cases: a) Fully sampled array, b) vernier periodic array, c) random array, and d) Mills cross array.

YEN et al.: REAL TIME RECTILINEAR VOLUMETRIC IMAGING

TABLE I ACTUAL NUMBER OF ELEMENTS USED IN ON-AXIS AND OFF-AXIS

CASES FOR THE FOUR ARRAYS.

97

On-axis Off-axis Array type Nt . NT Nt NT

Fully sampled 2305 9409 2401 9410 Vernier 49 169 49 169 Random 33 152 37 156

Mills cross 98 194 97 196

shifted so that the center is as close to the focus as possible. It is not possible to center the apodization function directly over the focus in every off-axis case without truncating the function because of the physical dimension of the aperture (Fig. 2). Truncating the apodization function should be avoided because this will lead to a decrease in pulse-echo sensitivity and will also give rise to higher sidelobe levels. Avoiding truncation should also help maintain a more uniform pulse-echo sensitivity, independent of the focus. In the off-axis case, the apodization function does not lie directly on top of the focus, so the steering errors will worsen. However, steering errors can be alleviated by employing multiple receive foci. XZ contour plots were obtained to analyze the steering errors in each of the four arrays. Twenty receive foci were placed every 3 mm from 0 mm where the transducer face is located to a depth of 60 mm.

It is important to note that because of the necessity of uniformly distributing the elements over the transducer for rectilinear volumetric scanning, elements are not iden- tically distributed for each type of array. The number of elements used per image line varied for each array. The number of elements also varied for the on-axis and off-axis cases. Table I shows the number of elements used in transmit and receive for the four arrays in both on-axis and off-axis cases. Among the sparse arrays, the Mills cross array has the greatest number of transmitters and receivers. This is because its elements are more densely packed in the azimuth direction for transmit and the elevation direction for receive mode than the other sparse arrays. The vernier and random have transmit and receive elements sparsely distributed in both dimensions. Because the number of elements used varied in each array, the pulse-echo sensitivity also varied.

Each beamplot was generated in a square area of 28 x 28 mm at a depth of 30 mm away from the transducer. Once the apodization function has been determined, each element is assigned its appropriate apodization value and normalized to a maximum value of one. Apodization helps suppress sidelobes at the sacrifice of a larger beamwidth. To determine the strength of the signal from each point in the field, an RMS energy value was calculated from the received voltage trace. All RMS energy values were converted to decibels after normalizing to the maximum energy level for the on-axis image line of the fully sampled array.

The fully sampled array serves as our “gold standard” with which all sparse arrays will be compared. The fully sampled array simply uses all 16 384 elements in both transmit and receive using X spacing = 0.3 mm. Although a fully sampled array will not be built in the near future, it serves as a useful comparison because sparse arrays are designed to approach the performance of a fully sampled array. Fig. 3(a) shows a schematic of the fully sampled array and how the subaperture is moved from the on-axis case to the off-axis case.

The vernier array, as proposed by Brunke and Lock- wood [lo], suggests placing a receive element every p elements apart and placing a transmit element every ( p - 1) elements apart, where p is an integer indicating the sparseness. For our purposes, a sparseness factor of p = 8 was necessary so that elements would be placed across the entire aperture to get the best possible beamwidth and cover the entire rectilinear field of view. Brunke and Lock- wood suggest using an interelement spacing of X/2, but this would require a sparseness factor of 16, resulting in very high sidelobe levels [lo]. In this paper, we tested the vernier array under much harsher constraints than in the previous analysis of Brunke and Lockwood [lo].

In the random array, we approximated a uniform distribution of transmit and receive elements. The location of these elements was first determined by dividing the array into four identical quadrants to ensure a more uniform distribution of elements. In each quadrant, the location of 64 transmit and 64 receive elements was determined using a uniform random number generator. Based on our previous experience, cosine apodization was not used in the random arrays but the aperture was still limited to F /2 transmit and F/1 receive [13].

The Mills cross array consists of two rows of transmit arms; each row consists of 128 elements. Both rows are located in the center of the array. Two columns of 128 receive elements are placed in the elevation direction. The layout for our version of the Mills Cross is shown in Fig. 3(d). By the geometry of the Mills cross, there are no elements directly over the off-axis focus. Instead, the subapertures have been moved to the right and to the top because using these elements would give the least amount of steering error. The subaperture becomes the union of these two apodization functions, and the focus is located at the in- tersection of the two subapertures.

111. RESULTS

Fig. 4(a through d) contains beamplots for the fully sampled array focused at (0, 0, 30) mm. Fig. 4(a) is a 3-D view of the acoustic beam. Fig. 4(b and c) are elevation and azimuth profiles, respectively, and Fig. 4(d) is a contour map with contours at -10, -20, -40, and -60 dB. These beamplots have several attractive features. The main beam remains very narrow all the way down to -70 dB. No grating lobes are present, and the clutter floor drops to near -80 dB. Focusing off-axis at (16, 16, 30) mm, the beam becomes broader, but still remains


0 0

-20 -20

I

-40 -40

- 60 B) C) - 60

-80 -80

-100 -100

Elevation (mm) Azimuth (mm)

Elevation (mm)

YEN et al.: REAL TIME RECTILINEAR VOLUMETRIC IMAGING 99

I 0 I

-20

G) -40 F) - 60

-80

-100

Azimuth (mm) Elevation (mm)

25

l: I , , , , , , ; . , , , , , , , , , , , , , , , , , , , , j 5 10 15 20 25 M

Elevation (mm)

Fig. 4. On-axis beamplots for the fully sampled array including a) 3-D view, b) elevation projection, c) azimuth projection, and d) contour map, as well as off-axis beamplots for the fully sampled array including e) 3-D view, f ) elevation projection, g) azimuth projection, and h) contour map.



10

I 5 W

N 4 -5

-10

-10 -5 0 5 10

Elevation (mm)


h m 10 I

-20 -20

-40 -40 G) - 60 - 60

-80 - 80

-100 -100


Elevation (mm)

Fig. 5. On-axis beamplots for the vernier array including a) 3-D view, b) elevation projection, c) azimuth projection, and d) contour map, as well as off-axis beamplots for the vernier array including e) 3-D view, f ) elevation projection, g) azimuth projection, and h) contour map.


3 b) > b) 3

Azimuth (mm)

-5 0 5 10

Elevation (mm) . .,.,

5 0 -5 -10

Azimuth (mm)

Elevation (mm)

YEN et al.: REAL TIME RECTILINEAR VOLUMETRIC IMAG!NG 103

I I

F)


10 “i “4 1 1 5 . 20 25

Elevation (mm)

Fig. 6. On-axis beamplots for the random array including a) 3-D view, b) elevation projection, c) azimuth projection, and d) contour map, as well as off-axis beamplots for the random array including e) 3-D view, f) elevation projection, g) azimuth projection, and h) contour map.


I 0 I

-20

-40

- 60

-EO

-inn _ _ I . -10 -5 0 5 10

Elevation (mm) 10 5 0 -5 -10

Azimuth (mm)

- I O 1 -10 -5 10

Elevation (mm)


Elevation (mm) Elevation (mm) 2 1"

Elevation (mm)

0 I

-20

. -- I 25 20 15 l o

Azimuth (mm)

i 10. 20 25

Elevation (mm)

Fig. 7. On-axis beamplots for the Mills cross array including a) 3-D view, b) elevation projection, c) azimuth projection, and d) contour map, as well as off-axis beamplots for the Mills cross array including e) 3-D view, f ) elevation projection, g) azimuth projection, and h) contour map.


fairly narrow down to -40 dB [Fig. 4(e through h)]. In the on-axis case, beamwidths were 0.52, 0.96, and 1.73 mm for -6, -20, and -40 dB, respectively (Table 11). For off-axis, beamwidths were measured to be 0.50, 1.10, and 2.0 mm at the same decibel levels (Table 11). All peak pressures were normalized to the fully sampled array focused on- axis because this is the case in which the highest pulse- echo sensitivity will occur. A -3.30-dB loss was found in the fully sampled array when comparing on-axis and off- axis pulse-echo sensitivity because of element angular response when the apodization function is not centered over the line (Table 111). This drop in pulse-echo sensitivity should be minimized because a uniform pulse-echo sensitivity throughout the whole volume is desired. Also, the width of the main beam is wider for the off-axis case because the effective transducer aperture is smaller. Fig. 8(a) is an XZ contour map of the acoustic beam focused at (0, 0, 30) mm. Fig. 8(b) is an XZ contour map of the off-axis beam with a transmit focus at (16, 16, 30) mm and a dynamically focused receive beam. In all of the XZ contour maps, the contour levels shown are 0, -6, -12, -18, -24, and -42 dB. As expected, there is no steering angle for the focus at (0, 0, 30) mm. In the off-axis case, the beam does not exhibit much of a steering angle; however, there is noticeable asymmetry in the beam. This is because of the asymmetric distribution of transmit and receive elements about the focus. The effect of the dynamic receive is especially visible at depths greater than the depth of the transmit focus.

Fig. 5(a through d) shows the beamplots of the pulse- echo field of the sparse vernier array focused at (0, 0, 30) mm. Because the elements are spread throughout the entire aperture, the main beam is very narrow and has a width of 0.54 mm at -6 dB. However, grating lobes rise up to -10 dB at f 5 . 0 mm away from the center of the array in both the elevation and azimuth dimensions. These high lobes are due to the sparseness of the array and the square shape of the aperture. At (16, 16, 30) mm the main beam has become slightly wider in both elevation and azimuth [Fig. 5(e through h)]. Because the beam is now slightly steered to avoid truncating the apodization function, some asymmetry in the beam is observed. On'one side, the grating lobe is at a peak level of -5 dB, and, on the other side, the grating lobe level is at -15 dB. The main beam width has increased to 0.80 mm in both elevation and azimuth dimensions at the -6-dB level. One important feature to note is that only 3.5 dB is lost in pulse-echo sensitivity in going from on-axis to off-axis because the apodization function has not been truncated. Fig. 8(d) show the XZ contour plots for a transmit focus at (16, 16, 30) mm and dynamic receive focusing. At depths less than 30 mm, the beam pattern indicates that the vernier array is not well focused. This would cause image degradation close to the transducer face. The beam pattern becomes more focused at depths greater than 30 mm as indicated by the contour circles located along the axis of the focus.

Beamplots of the random pattern can be found in Fig. 6(a through h). For this random array, the F/2 trans-

mit aperture included 33 transmit elements, and the F/1 receive aperture included 152 elements. For the on-axis case, it can be seen that the beam pattern has no side lobes but has a uniform pedestal of about -36 dB, which is in close agreement with -37 dB as predicted by (1) where the system contains 33 transmitters and 152 receivers. The -6 dB beamwidths of 0.55 and 0.46 mm are narrower than the fully sampled because cosine apodization was not used, so the effective aperture is larger than the other three arrays. At -20 dB, the beamwidth is still narrower than the fully sampled, but the -40 dB beamwidth is effec- tively very large because of the high pedestal level. This is also true in the off-axis case. In the off-axis case, the -6 dB beamwidths in azimuth and elevation are 0.55 and 0.46 mm, respectively. These beamwidths are comparable with the on-axis beamwidths. However, because of the changing random distribution of the elements at each image line, it is difficult to predict what the beam width will be in the overall volumetric scan. In terms of pulse-echo sensitivity, the random array has an on-axis pulse-echo sensitivity of -61.9 dB and an off-axis pulse-echo sensitivity at -65.0 dB, relative to the fully sampled array. The XZ contour plots for the random array are shown in Fig. 8(d and h). The on-axis XZ contour plot exhibits mild asymmetry because of the random distribution of transmitters and receivers. In the off-axis case, the dynamically focused random array does not appear well focused at depths less than 30 mm, much like the vernier array.

Fig. 7(a through d) shows the beamplots for the Mills cross array focused at (0, 0, 30) mm. The beamwidth in elevation is not equal to the beamwidth in azimuth because the beamwidth in the azimuth dimension is primar- ily dependent on the f-number of the transmit aperture and the beamwidth in the elevation dimension is controlled mainly by the f-number of the receive aperture. Because the f-numbers of the transmit and receive apertures are unequal, the beamwidths will be unequal. Unlike the vernier array, the Mills cross array does not exhibit grating lobes until f90" because of the X spacing. Instead, the beam pattern gradually drops to a level of -70 dB at a distance of 14 mm from the center of the transducer in elevation and to a level of -65 dB in azimuth. The beamplot for a focus at (16,16,30) mm shows again a very slight degradation in beamwidth in both azimuth and elevation [Fig. 7(e through h)]. The -6 dB and -20 dB beamwidths are 2.20 and 1.48 mm in azimuth and elevation, respectively. Peak energy levels range from -43.6 dB for a focus at (0, 0, 30) mm to -52.2 dB at (16, 16, 30) mm. The XZ contour plots of the Mills cross array can be seen in Fig. 9(c and d). The off-axis contour plot shows asymmetry in the beam about the line of focus because the apodization function cannot be centered over the image line.

IV. DISCUSSION AND FUTURE WORK

In these preliminary studies, we have attempted to char- acterize several 2-D array designs for real time rectilinear volumetric imaging including vernier, random, and Mills Cross designs. It can be concluded that the vernier array


A B

-10 -6 -6 -4 -2 0 2 4 6 6 10

Azimuth (mm)

C

E !3 n

Azimuth (mm)

D

5

10

15

20

25

30

n

v

5 8 35 Q 4 0

45

50

55

6 6 10 12 14 16 16 20 22 24 26

Azimuth (mm) Azimuth (mm)

Fig. 8. On-axis and off-axis XZ contour plots of the fully sampled and vernier arrays. Numbers next to contours indicate decibel level. a) Fully sampled array on-axis, b) Fully sampled array off-axis, c) Vernier array on-axis, and d) Vernier array off-axis.

TABLE I1 BEAMWIDTHS AT -6, -20, AND -40 DB FOR THE FOUR ARRAYS FOCUSED AT ON-AXIS AT (0, 0 , 30) MM AND OFF-AXIS AT (16, 16, 30) MM.

BEAMWIDTHS ARE EQUAL IN BOTH AZIMUTH AND ELEVATION DIMENSIONS BECAUSE OF SYMMETRY.

Fully sampled Vernier Random Mills cross

dB level Azimuth Elevation Azimuth Elevation Azimuth Elevation Azimuth Elevation

On-axis beamwidths -6 0.52 . -20 0.96 -40 1.73

Off-axis beamwidths -6 0.50

-20 1.1 - 40 2.0

0.52 0.54 0.96 12 1.73 Clutter

floor

0.50 0.80 1.1 19.5 2.0 Clutter

floor

0.54 0.42 12 0.80

Clutter Clutter floor floor

0.80 0.55 19.5 0.88

Clutter Clutter floor floor

0.49 1.1 0.58 0.84 2.0 1.0

Clutter 5.8 3.5 floor

0.46 1.24 0.71 1.06 2.40 1.48

Clutter 7.0 4.7 floor


TABLE I11 NORMALIZED PULSE-ECHO SENSITIVITY VALUES AT T W O DIFFERENT FOCI (IN DECIBELS).

Arrav tvDe ~

Focus &lly sampled Vernier array Random Mills cross (0, 0, 30) mm 0 -69.8 -61.9 -43.6

(16, 16, 30) mm -3.30 -73.3 -65.0 -52.2

A 5

10

15

20

w 1 25 30

.fl 8 35 40

45

50

55

-10 -8 -6 -4 -2 0 2 4 6 6 10

Azimuth (mm) C

Azimuth (mm)

B

I 6 8 10 12 14 16 18 20 22 24 26

Azimuth (mm) D

6 8 10 12 14 16 18 20 22 24 26

Azimuth (mm)

Fig. 9. On -axis and off-axis XZ contour plots of random and Mills cross arrays. Numbers next to contours indicate decibel level. a) Random array on-axis, b) random array off-axis, c) Mills cross array on-axis, d) mills cross array off-axis.

would not be a suitable array design because of the degree of sparseness necessary for such a large aperture. In this study, we have put the vernier array under harsher constraints than previously studied [lo]. The full wavelength element spacing definitely degraded the performance of the vernier array compared with half wavelength element spacing. However, full wavelength spacing is necessary to create the large aperture needed for rectilinear volumetric imaging. The extreme degree of sparseness, sparseness factor

of p = 8, degrades the performance of the vernier array. The Brunke and Lockwood study [lo] gives design curves for sparse arrays. The design curves given are only for the fully sampled array and sparse vernier arrays with p = 3, 4, and 5. However, no design curve for p = 8 is given; so, an extrapolation must be done, which would be consistent with our results.

In our experience, the vernier array is best suited for moderately sparse arrays. Moderately sparse arrays are de-


fined as arrays in which approximately 7 to 20% of the elements are used. In this paper an extremely sparse vernier array, in which 1 to 2% of the elements are used, does not perform as well. Such spreading of elements gives rise to high sidelobe levels.

Although the random array has very narrow beam widths at -6 and -20 dB, it would be less suitable because of the high pedestal level. This pedestal would appear as clutter throughout the entire image degrading image con- trast. It also has a fairly low pulse-echo sensitivity because of the sparse distribution of elements. The reason why the Mills cross has the highest pulse-echo sensitivity among the sparse arrays is because of the greater number of elements used (Table I). By the geometry of the Mills cross, elements are densely packed in either azimuth or elevation directions. From these results, the Mills cross array outperforms the vernier and the random array. It is the superior design in terms of the three criteria of beamwidth, pulse- echo sensitivity, and off-axis distortion given our current system limitation.

Using the transducer beamplot results, we can determine the specifications of the rectilinear volumetric scan. The -6-dB beamwidth for the Mills cross is 1.1 mm in the azimuth direction and 0.58 mm in the elevation dimension. According to the Nyquist criterion, this means that image lines must be created at least every 0.55 mm in azimuth and 0.3 mm in elevation to sample the volume properly. If 8:l receive mode parallel processing is used, a transmit beam that is wide in the elevation dimension will allow eight narrow receive beams to be placed within this transmit beam. The eight receive beams are separated by 0.3 mm, which means that the transmit beam must be at least 8 x 0.3 mm = 2.4 mm wide in elevation. Thus, if 8:l parallel processing is used, transmit beams should be at least 2.4 mm wide in the elevation dimension and 0.3 mm wide in the azimuth dimension. To sample the entire volume (38.4 x 38.4 x 60 mm), then 38.4 mm + 2.4 mm = 16 transmit beams in elevation and 38.4 mm t 0.3 mm = 128 transmit beams in azimuth must be used. This translates to a total of 16 x 128 = 2048 transmit lines. With the 8:l parallel processing, a total of 2048 x 8 = 16 384 image lines are required to represent the volume. For a maximum depth of 60 mm with a sound speed of 1500 m/s, a com- plete volumetric scan can be generated in 164 ms or at a rate of 6 vol/s. Such a scan rate is adequate for breast imaging and most abdominal imaging. Increased parallel processing would increase the volumetric scan rate.

Another possible alternative for the transducer design is to use electronic multiplexers within the transducer han- dle. Denser subapertures can then be created and stepped across the entire aperture to generate the volume. With the use of multiplexers, the Mills cross may not be the optimal design, but the vernier pattern may prove to be the best choice. However, employing multiplexing increases the complexity in the design. A whole new multiplexing system must be designed, built, and interfaced with the current volumetric scanner. More elements will be used, so a higher density of connections is required thus making

transducer fabrication more difficult. In addition, typical multiplexers such as the Supertex HV202 (Supertex, Inc., Sunnydale, CA) add capacitance typically around 12 pF per channel, which can reduce the signal-to-noise ratio of the elements [15]. Heating of the multiplexers will also be a concern [15], [16].

REFERENCES

0. T. von Ramm and S. W. Smith, “Real time volumetric ultrasound imaging system,” in Proc. SPIE Symp. Med. Imag. IV, Newport Beach, CA, pp. 15-22, 1990. S. W. Smith, H. E. Pavy, and 0. T. von Ramm, “High-speed ultrasound volumetric imaging system part I: Transducer design and beam steering,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 38, pp. 100-108, Mar. 1991. 0. T. von Ramm, S. W. Smith, and H. E. Pavy, “High-speed ultrasound volumetric imaging system - part 11: Parallel processing and image display,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 38, pp. 109-115, Mar. 1991. G. D. Stetten, T. Ota, C. J. Ohazama, C. Fleishman, J. Castel- lucci, J . Oxaal, T. Ryan, J. Kisslo, and 0. T. von Ramm, “Real- Time 3D ultrasound: A new look at the heart,” J . Cardzovasc. Dzagn. Proc., vol. 15, no. 2, pp. 73-84, 1998. E. D. Light, R. E. Davidsen, T. A. Hruschka, and S. W. Smith, “Two dimensional arrays for real time volumetric imaging,” Ul- trason. Imag., vol. 20, pp. 1-16, Jan. 1998. A. Fenster and D. B. Downey, “3-D ultrasound imaging: A re- view,” IEEE Eng. Med. Bzol., vol. 15, pp. 41-51, Nov. 1996. S. W. Smith and 0. T. von Ramm, “Acoustic orthoscopic imaging system,” U.S. Patent 4 596 145, 1986. P. Alais, P. Challande, and L. Eljaafari, “Development of an underwater frontal imaging system, concept of 3-D imaging system,” Acoust. Imag., vol. 18, 1991. G. R. Lockwood and F. S. Foster, “Optimizing the radiation pattern of sparse periodic two-dimensional arrays,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 43, pp. 15-19, Jan. 1996.

[lo] S. S. Brunke and G. R. Lockwood, “Broad-bandwidth radiation patterns of sparse two-dimensional vernier arrays,” IEEE Trans. Ultrason., Femoelect., Freq. Contr., vol. 44, pp. 1101-1109, 1997.

[ll] B. D. Steinberg, Prznczples of Aperture and Array System De- szgn. New York, NY: Wiley and Sons, 1976, pp. 138-169.

[12] D. H. Turnbull and F. S. Foster, “Beam steering with pulsed two- dimensional transducer arrays,” IEEE Trans. Ultrason., Ferro- elect., Freq. Contr., vol. 38, no. 4, pp. 320-333, 1991.

[13] R. E. Davidsen, J. A. Jensen, and S. W. Smith, “Two- dimensional random arrays for real time volumetric imaging,”

1141 J. A. Jensen and N. B. Svendsen, “Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers,” IEEE Trans. UZtrason., Ferroelect., Freq. Contr., vol. 39, pp. 262-267, Mar. 1992.

[15] R. E. Davidsen and S. W. Smith, “A two-dimensional array for B-mode and volumetric imaging with mulitplexed electrostric- tive elements,” Ultrason. Imag., vol. 19, pp. 235-250, Oct. 1998.

[16] L. J. Busse, C. G. Oakley, M. J. Fife, J . V. Ranalletta, R. D. Morgan, and D. R. Dietz, “The acoustic and thermal effects of using mulitplexers in small invasive probes,’’ in 1997 IEEE UZtrason. Symp. Proc., Toronto, Ontario, Canada, vol. 2, pp.

Ultrason. Imag., vol. 16, pp. 143-163, Jul. 1994.

1721-1724.

Jesse T. Yen was born in Houston, TX, on September 23, 1975. He received a B.S.E. degree in biomedical and electrical engineering from Duke University in Durham, NC, in 1997. He is currently working on the Ph.D. degree in biomedical engineering at Duke Uni- versity. His current research is on 2-D arrays for volumetric ultrasound imaging.


Jordan P. Steinberg was born in Marl- Stephen W. Smith (M’91) was born in boro, NJ, on October 3, 1977. He is cur- Covington, KY, on July 27, 1947. He re- rently an undergraduate student at Duke Uni- ceived the BA degree in physics in 1967 from versity (Durham, NC) and will obtain the Thomas More College, F t Mitchell, KY; the Bachelor of Science in Engineering degree in MS degree in physics in 1969 from Iowa State May 1999 with a major in biomedical en- University, Ames; and the P h D. degree in gineering. His research experiences have in- biomedical engineering in 1975 from Duke cluded work in medical ultrasound transducer University, Durham, NC. design and fabrication at Duke University In 1969, he became a Commissioned Of- and in peripheral blood stem cell transplanta- ficer in the U.S. Public Health Service, as- tion for advanced-stage cancer patients at the signed to the Food and Drug Administration, Bone Marrow Stem Cell Transplant Institute Center for Devices and Radiological Health,

(Boynton Beach, FL). His ultrasound transducer research has incor- Rockville, MD, where he worked until 1990 in the study of medical porated the modeling and simulation of various 2-D array patterns imaging, particularly diagnostic ultrasound and in the development for rectilinear volumetric imaging and 2-D catheter-mounted arrays of performance standards for such equipment. In 1978, he became an for cardiac scanning. He will embark on studies for the M.D./Ph.D adjunct Associate Professor of Radiology at Duke University Medical degree in the fall of 1999 Center In 1990, he became Associate Professor of Biomedical En-

gineering and Radiology and Director of Undergraduate Studies in Biomedical Engineering at Duke University. He holds seven patents in medical ultrasound and has authored 100+ publications in the field.

Dr. Smith has served on the education committee of the American Institute of Ultrasound in Medicine, the executive board of the Amer- ican Registry of Diagnostic Medical Sonographers, and the editorial board of Ultrusonzc Imagzng. He was co-recipient of the American Institute of Ultrasound in Medicine Matzuk Award in 1988 and 1990 and co-recipient of the IEEE-UFFC Outstanding Paper Award in 1983 and 1994

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Sparse 2-D Array Design for Real Time Rectilinear Volumetric Imagingtransducers.bme.duke.edu/pubs/uffc_2000_93-110.pdf · Sparse 2-D Array Design for Real Time Rectilinear Volumetric