Synthetic Aperture Techniques with a Virtual Source...

196 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 45, no. 1, january 1998

Synthetic Aperture Techniques with aVirtual Source Element

Catherine H. Frazier, Student Member, IEEE, and William D. O’Brien, Jr., Fellow, IEEE

Abstract—A new imaging technique has been proposedthat combines conventional B-mode and synthetic apertureimaging techniques to overcome the limited depth of fieldfor a highly focused transducer. The new technique im-proves lateral resolution beyond the focus of the transducerby considering the focus a virtual element and applying syn-thetic aperture focusing techniques. In this paper, the useof the focus as a virtual element is examined, consideringthe issues that are of concern when imaging with an arrayof actual elements: the tradeoff between lateral resolutionand sidelobe level, the tradeoff between system complexity(channel count/amount of computation) and the appear-ance of grating lobes, and the issue of signal to noise ratio(SNR) of the processed image. To examine these issues,pulse-echo RF signals were collected for a tungsten wirein degassed water, monofilament nylon wires in a tissue-mimicking phantom, and cyst targets in the phantom. Re-sults show apodization lowers the sidelobes, but only atthe expense of lateral resolution, as is the case for classicalsynthetic aperture imaging. Grating lobes are not signif-icant until spatial sampling is more than one wavelength,when the beam is not steered. Resolution comparable to theresolution at the transducer focus can be achieved beyondthe focal region while obtaining an acceptable SNR. Specifi-cally, for a 15-MHz focused transducer, the 6-dB beamwidthat the focus is 157 �m, and with synthetic aperture pro-cessing the 6-dB beamwidths at 3, 5, and 7 mm beyond thefocus are 189 �m, 184 �m, and 215 �m, respectively. Theimage SNR is 38.6 dB when the wire is at the focus, andit is 32.8 dB, 35.3 dB, and 38.1 dB after synthetic aper-ture processing when the wire is 3, 5, and 7 mm beyondthe focus, respectively. With these experiments, the virtualsource has been shown to exhibit the same behavior as anactual transducer element in response to synthetic apertureprocessing techniques.

I. Introduction

A basic limitation of conventional B-mode imagingis that lateral resolution depends on the depth in theimage. The best resolution is achieved only for the slice ofthe image containing echoes from the focus of the trans-ducer. Passman and Ermert [1] introduced a technique toovercome this resolution limitation. The new technique in-volves treating the focus of the transducer as a virtualsource for synthetic aperture (SA) processing. In their for-mulation, the virtual source is assumed to produce approx-imately spherical waves over a certain aperture angle. Theyconsider the transmit signal in detail, transmitting differ-

Manuscript received February 25, 1997; accepted August 11, 1997.This work was supported by NSF Fellowship (CHF) and U.S. Armycontract (DACA88-94-D0008).

The authors are with the Bioacoustics Research Laboratory, De-partment of Electrical and Computer Engineering, University of Illi-nois, Urbana, IL 61801 (e-mail: [email protected]).

ent signals for each depth and prefiltering with a pseudoin-verse filter to compensate for the attenuation of the tis-sue. These steps are used in an attempt to achieve depth-independent resolution at frequencies up to 250 MHz. Thework reported herein extends previous work with virtualsources by examining more fundamental issues such as lat-eral resolution, sidelobe levels, spatial sampling rate, andSNR for images created at lower frequencies. This workstudies the model for a virtual source and examines im-ages produced with data from virtual sources, processedusing known techniques to improve SA images.

Apodization weights are commonly applied to signalsfrom individual array elements in order to reduce the side-lobe level of the beam pattern. However, these weightsalso have the effect of increasing the main lobe width, de-grading the lateral resolution of the image. This tradeoffbetween sidelobe level and resolution is studied by look-ing at the resolution of wire targets in water and in atissue-mimicking phantom, and by looking at the contrastresolution of cyst targets in images formed using differentapodization weighting functions. It will be shown that, theboxcar weights produce the best lateral resolution and thatthe Hamming weights do not produce the image with thelowest sidelobes, even though the Hamming weights havethe lowest sidelobes of the four weighting functions usedin this study. Cosine or triangle weighting functions pro-duce a compromise between good lateral resolution andlow sidelobe level.

In addition, the formation of grating lobes, which ap-pear if the array is undersampled, is a concern when doingSA imaging. When imaging with an array of elements, thespatial sampling is limited by the physical size of the ele-ments, the required separation of the elements to preventcrosstalk, and the complexity added to the system by hav-ing more channels. With an array of virtual sources, itis preferable to keep the sampling rate low to reduce theamount of computation. When the beam is not steered,grating lobes can appear if the elements are spaced morethan half a wavelength apart; however, it will be shownthat the amplitude of these grating lobes may not be sig-nificant until the spatial sampling is much greater.

SNR is studied to analyze whether or not it can be ac-ceptable for images created with virtual sources. It will beshown that, for targets beyond the focus of the transducer,images created through SA processing have an SNR thatis improved compared to conventional B-mode imaging.And the SNR of these images is comparable to conven-tional B-mode images of targets that are at the focus ofthe transducer.

0885–3010/97$10.00 c© 1998 IEEE

frazier and o’brien: synthetic aperture techniques 197

Fig. 1. Geometry of focusing situation. Elements are numbered suchthat the zeroth element is the center element of the subaperture. Pis the desired focal point and d is the interelement distance.

II. Synthetic Aperture Imaging

Delay-and-sum beamforming uses the appropriate de-lay of received signals to achieve focusing. Because off-lineprocessing is used, the delays are actually implemented asappropriate advances of some received signals.

A portion of the array is shown in Fig. 1. It is desiredto focus at a point P that is located in the far field ofthe individual elements and in the transition region of thesubaperture of the array. The field from the subaperturewill be focused at P if the pulses from all the elementsarrive simultaneously at P, which is achieved by advanc-ing the signals from the elements away from the centerof the subaperture and then summing the received signalsfrom all the elements in the subaperture. Simply using thePythagorean theorem to find the pathlength for an elementi, the amount of the advance should be:

∆ti =2zc

(1−

√1 +

(id)2

z2

)(1)

where ∆ti is the time delay for element i, z is the distanceto the desired focal point from the center of the subaper-ture, c is the speed of sound, and d is the interelementspacing. Then beamforming is accomplished with the fol-lowing sum:

A(t) =∑i

wiSi(t−∆ti) (2)

where A(t) is the computed RF echo return, and wi isa weight assigned to the returned signal, S(t), from ele-ment i.

The number of signals included in the sum of (2) is de-termined by the aperture angle of the transducer beam be-

Fig. 2. Parameters that describe transducer beam. D is the trans-ducer diameter, F is the focal length, d is the diameter of the focalspot, and φ is the aperture angle.

yond the transducer’s focus. The beam spread of a sourceis determined by the geometry of the source and the wave-length of sound in the medium, which will be described inmore detail in the next section.

III. Issues in Synthetic Aperture Imaging

A. Model for Virtual Element

We model the virtual element as a source of sphericalwaves over a certain aperture angle. This model is verifiedby Passman and Ermert [1] through the derivation of thediffraction-impulse-response (equation 8 in [1]). A morecomplete derivation of this impulse response is found in[2], where the transverse field pattern is shown to varywith the type of excitation (transient or sinusoidal) andfor transient excitation, with the type of detection used(positive peak or negative peak). For this study, the beampattern after the focus of the transducer is simulated andmeasured for a 15-MHz transducer with an f-number of 1.5using a technique introduced by Raum and O’Brien [3].

In a simple approximation, the initial beam spread afterthe focus will look like the reverse of the beam narrowingbefore the focus, and the degree of spreading is approxi-mately equal to the degree of focusing before the spot asshown in Fig. 2. The half angle at which the beam spreadscan be approximated by φ2 = tan

−1 D2F , where φ is the an-

gle of spreading measured between nulls, F is the focal dis-tance, and D is the diameter of the focused transducer. Bythis formulation, the virtual source of the 15-MHz trans-ducer used in this experiment has an aperture angle of 36.9degrees. The virtual source for the 20-MHz transducer hasan aperture angle of 28.1 degrees. It is this aperture anglethat determines the number of elements included in thesum in (2).

When imaging with a single focused transducer (con-ventional imaging), lateral resolution is inversely propor-tional to the aperture size; therefore, a large diametertransducer is preferred. In SA imaging, it is desirable tohave a small transducer element to achieve good lateralresolution. SA imaging techniques use a small aperturetransducer element to sample the large aperture, and then


TABLE ITime Domain and Frequency Domain Window

Characteristics for Length-M Windows.

Characteristics for Length-M Windows

Main PeakTime domain lobe sidelobe

Window description width (dB)

boxcar 1 4πM

−13

cosine cos(π2n−M−12M−1

2

)20π3M −23

triangle 1−∣∣∣ 2(n−M−12 )M−1 ∣∣∣ 8πM −27

Hamming 0.54− 0.46 cos 2πnM−1

8πM

−43

the received signals from the elements are summed as in(2) with time delays to synthesize the received signal froma large focused transducer. The image SNR is maximizedby including in the sum all the elements whose beams en-compass the desired focal point, and excluding all otherelements. If each element has a narrow beam, then only afew will have beams that illuminate the desired focal pointand only those few will be included in the sum. The syn-thesized aperture will be small, which means that the syn-thesized aperture cannot achieve good lateral resolution.On the other hand, if each element has a wide beam, thenthe returned signals from more elements can be included inthe sum, and the sampled aperture, which includes moreelements, will be larger. In the case of virtual sources, themore highly focused the transducer, the better resolutionwill be achieved through synthetic aperture processing.

B. Reduction of Sidelobes

The tradeoff between resolution and peak sidelobe levelis examined in this study. In array imaging, weighting theindividual elements is known as apodization. Apodizationmay occur on transmit or receive; however, apodizationon transmit would mean that, in some cases, a lower am-plitude signal is transmitted, reducing the signal to noiseratio. Also, for monostatic data collection, where a singletransducer is used for transmit and receive, the signal fromone position is used several times, with different weightsin different windows. Apodization on transmit would re-quire several transmits from the same transducer positionto get the signals at the appropriate weights for the differ-ent focusing positions. Therefore, in this study, apodiza-tion weights are applied in receive. In signal processing,apodization is called windowing. Signal processing theoryshows that the windowing operation broadens the mainlobe and lowers the sidelobes [4].

Several windows are used for this study. They are theboxcar, triangle, cosine, and Hamming windows. Charac-teristics of these windows are shown in Table I. From thesedescriptions, we expect the boxcar window to produce theimage of the wire with the best lateral resolution and theHamming window to produce the image with the lowestsidelobes. In fact, the Hamming window will not produce

the image with the lowest sidelobes because apodizationweights are applied only on receive; the transmit weightsare always the boxcar weights. The overall beam pattern isthe product of the transmit and receive beam patterns. Forthe cosine, triangle, and Hamming windows, the first side-lobe of the boxcar window (used on transmit) falls withinthe main lobe of the their beam patterns. Taking the prod-uct of the two beam patterns means that the first sidelobeof the overall pattern will be at the location of the firstboxcar sidelobe with slightly reduced amplitude. The re-duction in amplitude depends on how fast the main lobefalls off. As the main lobe width increases, that first box-car sidelobe is closer to the central high part of the mainlobe. Therefore, as the main lobe of the receive beam pat-tern widens, the expected sidelobe level of the overall beampattern increases.

The apodization weights will also have an effect on theimages of cyst targets. Even though both cysts and wiretargets represent large impedance mismatches for the ul-trasound signal, wire targets are more easily distinguishedin an image. When the main lobe is over the cyst, thereare sidelobes over regions that reflect sound. The signalreflected by the sidelobes appears to have been reflectedfrom inside the cyst. The ability to differentiate a cyst fromthe surrounding medium is called contrast resolution. Byreducing the main lobe width or lowering the sidelobes,contrast resolution can be improved.

C. Eliminating Grating Lobes

We also examine the effects of spatial sampling of thearray of virtual sources on the appearance of grating lobes.To eliminate grating lobes, the aperture should be sampledadequately. It has been shown in [5] that, for an array ofsimple sources used in transmission and reception, withone active element and no beam steering, the array musthave elements spaced no greater than λ2 apart to preventthe formation of grating lobes. This fact can be seen fromthe array factor:

HA(θ) =1N

sin(Nkd sin θ)sin(kd sin θ)

(3)

where N is the number of elements in the sum, k is thewave number, d is the interelement spacing, and θ is theazimuth direction. Both the numerator and denominatorgo to zero when kd sin(θ) is an integer multiple of π, asexpressed in (4):

kd sin(θ) = mπ (4)

sin(θ) =λ

2π1dmπ (5)

sin(θ) =mλ2d

for m = 0, 1 · · ·⌊

2dλ

⌋. (6)

Maxima in the beam pattern occur in directions describedby (6). To eliminate grating lobes, the interelement spac-ing, d, should be made slightly smaller than half a wave-length. No effects of steering the array are considered in


this discussion because steering is not used in any process-ing in this paper. It can be shown that, if the beam is to besteered −90 to +90 degrees, the distance between elementsshould not be greater than a quarter of a wavelength [6].

The above analysis shows the directions where gratinglobes occur. With a more detailed approach, the ampli-tude of the grating lobes will be seen to be lower than theamplitude of the main lobe [5]. First, for a real source,the output of the transducer element is limited in direc-tion. Not all the elements will be able to contribute tothe beam pattern at all angles. Therefore, the beam pat-tern of the array will be the product of the array factorin (3) and a modulating factor which is the angular re-sponse from an individual element. This fact is a resultof the Fourier transform property of the far-field pattern.The angular response of a focused transducer is compli-cated. As simulated for the 15-MHz transducer, beyondthe focus and close to the beam axis, the pressure ampli-tude oscillates. Beyond approximately 10 degrees from thebeam axis (where the coordinate origin is at the focus), thepressure amplitude decreases. This modulating factor willreduce the amplitude of grating lobes at all angles beyond10 degrees.

Second, in the above analysis, the transmitted signal isassumed to be a continuous wave. Suppose the transmittedsignal is a gated sinusoid of m cycles. The pulses from allthe elements will sum in phase at the location of the mainlobe because the path lengths are all equal. However, at thefirst grating lobe location, the pulses from onlym elementsadd in phase. The pulse from the m + 1 element will notoverlap with the pulse from the first element because theyhave been separated in time. This reduces the amplitudeof the grating lobe by a factor of 20 log M

m where M is thenumber of signals that contribute to the main lobe and mis the number of cycles in the pulse.

Third, if the transmitted pulse is a burst created byexciting the transducer with a voltage spike rather thana gated sinusoid, the grating lobes are further reduced inamplitude. The lengths of the pulse that overlap at gratinglobe locations will not match exactly as they would for thesinusoidal excitation. The combination of all these effectsmay reduce grating lobes to a level comparable to sidelobesor lower depending on the spatial sampling.

IV. Data Collection

A schematic of the data acquisition system is shown inFig. 3. The system uses of a host PC (ZEOS 66 MHz 486)to control a five-axis (three translational, two rotational)precision positioning system with a positional accuracy of2 µm (Daedal, Inc., Harrison City, PA) and to retrievewaves from a digital oscilloscope. After the transducer hasbeen manually positioned, one translational axis is usedfor the scan. A Panametrics (Waltham, MA) Model 5800pulser-receiver in pulse/echo mode is used to generate the300 V monocycle pulse which excites the transducer. Thereceived signal is amplified (40 dB), bandpass filtered (1–35 MHz), and then displayed on either a Tektronix 11401

Fig. 3. Schematic of data collection system.

(Pittsfield, MA) or a LeCroy 9374L (Chestnut Ridge, NY)digitizing oscilloscope. The PC retrieves the digitized RFwaveforms from the oscilloscope via IEEE-488 communica-tions and stores them. Then the waveforms are transferredvia ftp to a SUN Sparc 20 for processing.

Two Panametrics transducers with different focusingcharacteristics but with focal points of similar size areused to collect the data for this study. The 15-MHz trans-ducer has a 12.7-mm diameter circular aperture and a re-ported 19.1-mm focal distance. The 20-MHz transducerhas a 6.35-mm diameter circular aperture and a 12.7-mmfocal distance. Thus, the quantity λFD for each transduceris 150 µm, where F is the focal distance and D is the di-ameter. The 15-MHz transducer has a measured apertureangle of 42 degrees; the calculated aperture angle is 36.9degrees. The 20-MHz transducer has a measured apertureangle of 33 degrees; the calculated aperture angle is 28.1degrees.

Several data sets are created with a 25-µm tungstenwire target in degassed water. Lateral scans are made usingeach transducer, with the tungsten wire target positionedat the focus and at 3, 5, and 7 mm beyond the focus of thetransducer. The pulse-echo RF data are collected 50 µmand 35 µm apart for the 15-MHz and 20-MHz transduc-ers, respectively. The sampling rate is 500 MHz for thewire positioned at 7 mm and 1 GHz for all other wirepositions. These data are used for measurements of reso-lution, sidelobe level, and SNR. One data set is collectedwith the 15-MHz transducer with the wire at 8 mm be-yond the focus where pulse-echo RF returns are collected20 µm apart and the temporal sampling rate is 500 MHz.This set is used for experiments with spatial sampling.


Two other sets of RF data are acquired using a tissue-mimicking phantom. These data sets are collected with the15-MHz transducer positioned such that the signal of in-terest is not hidden in the reflection from the surface of thephantom. One data set uses embedded wires as the targets.These pulse-echo returns are collected 100 µm apart witha temporal sampling rate of 250 MHz. The second set usesanechoic regions as the targets. Those pulse-echo returnsare collected at positions 50 µm apart with a temporalsampling rate of 200 MHz.

The phantom (Model 539, ATS Laboratories, Inc.,Bridgeport, CT) is made of urethane rubber with a speedof sound of 1450 m/s at room temperature and an attenu-ation of 0.5 dB/cm/MHz. The embedded wire targets aremade of monofilament nylon with a 0.12-mm diameter.The deepest wire in the images is positioned 1 cm belowthe phantom surface. The other three wires are each 1 mmcloser to the surface and 5 mm to the side of the neigh-boring wire. The cyst targets are anechoic regions 2 and3 mm in diameter, both positioned such that their centersare 1 cm beneath the surface of the phantom.

Ideally, to create a high resolution image, SA processingshould proceed in two lateral dimensions. Collecting datausing a lateral scan in one direction perpendicular to theorientation of a wire target effectively converts the problemto two dimensions.

In this study, a C program is used to perform delay-and-sum beamforming with various apodization weights.In this processing, the position of the virtual source isassumed to coincide with the position of the focus asreported by Panametrics. Measurements confirm this towithin 350 µm for the 15-MHz transducer and within260 µm for the 20-MHz transducer [3]. After this process-ing, the data are transferred to Matlab (The MathWorks,Inc., Natick, MA) to produce an image and determine thebeamwidths, sidelobe levels, CNR, and SNR. The imagesare produced by bandpass filtering the RF data, envelopedetection, logarithmic compression, and then displayingthe data over a 50-dB range.

V. Results and Discussion

A. Resolution versus Sidelobe Level

The tradeoff between resolution and sidelobe levelthrough the application of apodization weights is exploredusing tungsten wires in a waterbath, and nylon wires andcyst targets in a tissue-mimicking phantom. Numerical val-ues of 6-dB transmit-receive beamwidth and sidelobe levelfor each transducer, tungsten wire depth, and window aregiven in Table II. The processed images show improvementin both resolution and sidelobe level compared to the un-processed raw data. After processing, the resolution of thewires at 3 mm and 5 mm and only slightly larger than theresolution achieved at the focus of the transducers, whichis 157 µm for the 15-MHz transducer and 159 µm for the20-MHz transducer. Although the resolution should be in-

dependent of depth, the resolution of the wire at 7 mm isworse than for the two more shallow wires.

An improvement in sidelobe levels is observed. The ex-pected sidelobe levels result from the product of the trans-mit beam pattern and the receive beam pattern. When theboxcar window weights are used on receive, the expectedsidelobe level is −26.5 dB, or twice the sidelobe level ofthe weights applied once. The expected sidelobe levels are−30.0 dB, −27.0 dB, and −26.5 dB for the cosine, triangle,and Hamming weights, respectively. The obtained resultsare close to the expected results except for the 3 mm wireposition for the 15-MHz transducer, where the sidelobelevel is lower, and the 7 mm wire position for the 20-MHz transducer, where the sidelobe level is higher thanexpected.

Typical tungsten wire images created by this techniqueare shown in Fig. 4. The boxcar window produces the im-ages with the best lateral resolution for all the depths; how-ever, the sidelobes are also the highest for all the depthscompared to the other windows. The Hamming windowproduces the images with the worst lateral resolution, butthe sidelobe levels are not correspondingly lower than forthe other windows. Images produced with the cosine win-dow have slightly better resolution than those producedwith the triangle window, although the performance ofthese two windows is comparable.

Fig. 5 plots the beamwidth of the main lobe versusdepth with and without SA focusing using the boxcar win-dow. The difference in the plots for no processing and withprocessing shows the improvement in resolution that canbe achieved by applying this technique. Ideally, with SAprocessing, the beamwidth should be independent of thedepth.

In Fig. 6, the beamwidth of the main lobe versus depthis plotted for data processed with the four apodizationweights for the 20-MHz transducer. The plot of the resultsfor the boxcar window for the 20-MHz transducer showsthat SA processing can achieve better focusing than theactual focus of the transducer. This can happen if the ra-tio of the synthetic aperture to the desired focal depth weregreater than the ratio of the transducer’s diameter to itsfocal depth. The difference in beamwidth is actually only27 µm. The wire is 25 µm in diameter. The results forthe 15-MHz transducer are similar with slightly greaterbeamwidths. These beamwidths should be compared tothe beamwidths at the focus of each transducer, whichare found to be 157 and 159 µm for the 15- and 20-MHztransducers, respectively. The 15-MHz transducer has alarger aperture angle, so it can achieve a larger syntheticaperture, but the images produced with the 20-MHz trans-ducer had better resolution due to the smaller wavelengthand the fact that not all of the potential subaperture ofthe 15-MHz transducer was used to reduce computationalcomplexity.

The lateral resolution is degraded by the use of apodiza-tion weights; however, they are still used to lower the side-lobes in the beam pattern. Four beam patterns for the fourdifferent windows studied are shown in Fig. 7 for the wire


Fig. 4. Images produced with synthetic aperture processing displayed over a 50-dB range. All axes are labeled in millimeters. The data arecollected in a degassed waterbath using the 15-MHz transducer with the tungsten wire positioned 5 mm beyond the focus: (a) Raw data,(b) synthetic aperture processing using boxcar apodization weights, (c) cosine apodization weights, and (d) Hamming apodization weights.


TABLE IIBeamwidths and Sidelobe Levels for Tungsten Wire Data.

Resolution and Sidelobe Levels for Tungsten Wires in Degassed Water

15 MHz 20 MHzWire depth (mm) 3 5 7 3 5 7

6-dB Beamwidth (µm)raw data 525 1451 2117 863 1740 2349

boxcar 189 184 215 143 132 161cosine 212 219 263 168 169 202

triangle 222 234 287 182 184 219Hamming 227 242 298 188 191 229

Sidelobe level (dB)raw data −26.0 −15.9 −11.9 −22.3 −12.1 −10.4

boxcar −29.4 −26.6 −25.7 −25.0 −22.1 −15.8cosine −34.0 −27.5 −28.9 −26.9 −28.6 −18.9

triangle −34.3 −30.1 −34.5 −28.7 −29.1 −22.1Hamming −37.1 −28.7 −29.9 −21.4 −23.0 −20.0

Fig. 5. Comparison of 6-dB beamwidth versus depth for the tungstenwire in a degassed waterbath before and after SA processing for the15-MHz (solid lines) and 20-MHz (dashed lines) transducers. Theplot of beamwidth before processing for each transducer has the largeslope. The plot of beamwidth after SA processing for each transduceris almost horizontal.

at depth 3 mm from the focus using the 20-MHz trans-ducer. The use of nonuniform weights lowered the side-lobes as can be seen from the beam patterns and the datain Table II. The improvement is also clear from the im-ages shown in Fig. 4. The cosine and triangle apodizationweights produce images that compromise between the bestlateral resolution and lowest sidelobe level.

The beamwidths calculated from the tissue-mimickingphantom data processed with uniform weights are dis-played in Table III. The 6-dB transmit-receive beamwidthis the smallest for the most shallow wire but remains nearlyconstant over the deeper range in the image. The wiresactually have a width of 120 µm. The modified lateral res-olutions for the tissue-mimicking phantom processed withapodization weights are also listed in Table III. The re-sults are similar to the tungsten wire data results, in that

Fig. 6. Comparison of 6-dB beamwidth versus depth after SA pro-cessing with boxcar (solid line), triangle (dotted line), cosine (dot-dashed line), and Hamming (dashed line) apodization weights forthe 20-MHz transducer with a tungsten wire target in a degassedwaterbath.

TABLE IIIResolution of 120-µm Wire Targets in Tissue-Mimicking

Phantom in Images Produced with Uniform and NonuniformWeights. RF Data are Collected with a 15-MHz

Transducer.

Resolution of Wires in Tissue Phantom

Wire depth in phantom (mm) 7 8 9 10

6-dB Beamwidth (µm)raw data 1632 1866 2244 2385

boxcar 495 536 580 568cosine 588 655 718 721

triangle 632 693 762 784Hamming 694 812 823 825


Fig. 7. Beamplot at wire using (a) boxcar, (b) cosine, (c) triangle, and (d) Hamming apodization weights to produce images from the datacollected with the 20-MHz transducer with the tungsten wire positioned 3 mm beyond the focus.

the wire beam widths increase after processing with thewindows. The Hamming window forces a greater increasein the beamwidth than the other two.

Cyst data are also used to compare the performanceof processing with a boxcar window and processing withother windows. The amount of cyst fill-in gives a qualita-tive measure of the main lobe beamwidths and the side-lobe levels. Images produced using uniform and nonuni-form weights are shown in Fig. 8. In order to quantify thequality of these images, a contrast-to-noise ratio (CNR) iscalculated for each target [7], that is,

CNR =|µc − µb|

σb(7)

where µc is the mean intensity of the cyst in dB, µb isthe mean of the background, and σb is the standard devi-ation of the background. As expected, the CNR is greaterfor the larger cyst than for the smaller one, because it iseasier to isolate a large cyst in the main lobe of a beam

than a small one. Quantitative values of CNR are pre-sented in Table IV for the boxcar window and the otherwindows. The images produced by processing with nonuni-form weights performed better than the boxcar windowdue to the lower sidelobes. Again, the CNR for the cosineand triangle weights are similar; the cosine weights had aslightly better CNR due to the more narrow beam. TheHamming weights do not improve the CNR over the othertwo windows because the beamwidth is too large and thesidelobes are not appreciably lower.

B. Appearance of Grating Lobes Versus Spatial Sampling

In order to test the necessity of collecting signals fromtransducer positions located less than half a wavelengthapart, the tungsten wire data collected 20 µm apart forthe wire located 8 mm beyond the focus are decimatedin the lateral direction. Images are produced with spatialsampling of 2λ5 ,

3λ5 , λ,

7λ5 , and 2λ, corresponding to lateral

decimation factors of 2, 3, 5, 7, and 10.


Fig. 8. Images produced from cyst data with synthetic aperture processing displayed over a 50-dB range. The data are collected usingthe 15-MHz transducer. (a) Raw data, (b) synthetic aperture processing using boxcar apodization weights, (c) cosine apodization weights,(d) Hamming apodization weights.


TABLE IVSNR Characteristics of the RF Data for 25-µm Tungsten Wire Targets in a Waterbath. Meas. RF Signal SNR Refers tothe SNR of a Signal Received by the Transducer at a Given Position. Calc. RF Signal SNR Refers to the SNR of the

Processed RF Signal. Data are Processed with the Boxcar Window.

SNR of RF Data

Wire Ideal SNR Meas. RF Calc. RF Meas. SNRTdr depth improvement signal SNR signal SNR improvement(MHz) (mm) (dB) (dB) (dB) (dB)

15 0 – 64.46 – –3 13.22 44.73 51.52 6.795 15.91 38.93 47.17 8.247 17.56 36.33 60.92 24.59

20 0 – 50.37 – –3 16.13 33.70 46.98 13.285 17.85 25.56 38.49 12.937 19.40 24.84 49.56 24.72

Fig. 9. Grating lobes that appear when RF data are collected two wavelengths apart. Data are collected using the 15-MHz transducer withthe tungsten wire target positioned 8 mm beyond the focus. The image is displayed over a 50-dB range.

No grating lobes are found for data sets sampled at 2λ5 ,3λ5 , or λ. Grating lobes are not expected for the image

sampled at 2λ5 because the spatial sampling is still lessthan half of a wavelength. Even sampling the data at 3λ5gives a sampling rate close to the half wavelength limit.

From (3), grating lobes that exist when the data aresampled one wavelength apart would appear at θ = 30and 90 degrees. Here, no change in the image is expectedfrom the grating lobes at 90 degrees because there is notarget at this location to interfere in the image. However,it would be possible to see a response from a grating lobethat appears at 30 degrees. Because the virtual source hasa limited aperture angle, the grating lobe at 30 degrees isexpected to be down by 22.4 dB. Also, there is a reductionin the size of grating lobes because the image is createdwith a pulse rather than a continuous wave. The minimumnumber of elements used to create a block of the image is17. The pulse has a length of less than two wavelengths.This corresponds to a reduction of 15.0 dB. Finally, thereis an additional reduction in grating lobe strength becausethe pulse is not coherent. Therefore, even though gratinglobes may exist, they do not rise above the noise level inthis image.

Grating lobes are observed for the images created fromthe data decimated by factors of 7 and 10 corresponding to

TABLE VContrast-to-Noise Ratio for Cyst Targets in ImagesProduced with Uniform and Nonuniform Apodization

Weights. RF Data are Collected with a 15-MHzTransducer.

Contrast to Noise Ratios

2 mm cyst 3 mm cystWindow (dB) (dB)

raw data 1.11± 0.32 1.01± 0.33boxcar 1.59± 0.25 1.84± 0.24cosine 1.70± 0.21 1.99± 0.21triangle 1.78± 0.19 2.08± 0.19Hamming 1.71± 0.17 2.01± 0.17

lateral sampling of 7λ5 and 2λ. In the image decimated by 7,the measured grating lobe has a magnitude 18.9 dB belowthat of the main lobe. It is located at 17.9 degrees. There,the reduction due to the directivity of the beam is 7.4 dB,and the reduction due to the pulsed waveform is 12.7 dBfor a total level of −20.1 dB. Further reduction in mag-nitude occurs because the pulse is not a single frequency;so, even when the pulses from neighboring elements dooverlap, they do not overlap exactly. This effect causes thegrating lobe to broaden and be lower in magnitude.


For the image decimated by a factor of 10, the gratinglobes are observed at 14.3 degrees. The image with thegrating lobes is shown in Fig. 9. The grating lobes have anaverage magnitude of 15.7 dB below the main lobe. At thisangle, the reduction due to the limited beam is 3.1 dB, andthe reduction due to the pulse length is 9.5 dB for a totalreduction of 12.6 dB. Again the grating lobes are smeared,because of lack of coherence in the pulse contributing tototal measured reduction.

These results demonstrate that spatial sampling ratecan be less than the λ2 limit without the appearance ofgrating lobes.

C. SNR Results

Electronic SNRs are calculated for individual pulse-echoRF returns and image SNRs are calculated for the imagesformed with boxcar apodization weights. The image SNRis calculated as in [7] using the image data before logarith-mic compression. A value for the signal is measured as therms pixel value in a small rectangle over the wire in theimage. The noise value is taken as the average rms pixelvalue in four rectangles located where there is no signalor sidelobe contribution. The SNR is then the ratio of thesignal to noise expressed in dB.

Assuming uncorrelated, additive electronic noise, theSNR of the processed RF signal would ideally show animprovement over that of a measured pulse-echo RF returnof 10 log10(L) where L is the number of signals includedin the sum to create a single RF signal for the image.The results of these measurements and calculations areshown in Table V. The value in the table given for themeasured pulse-echo RF return is the median value forthe SNR of all the RF returns included in the sum to getthe calculated RF signal whose SNR is listed in the nextcolumn of the table. The SNR showed less than the idealimprovement, which results from quantization errors in thedelays and the range of SNRs for the included pulse-echoRF returns. Received signals show a larger SNR when thewire is near the center of the beam than when the wireis at the edge of the beam. The image SNR is listed inTable VI. With a 40-dB receiver gain, the SNR is 34.1 dBon average. The SNR is higher for the 15-MHz transducerthan for the 20-MHz transducer due to the bandwidth ofthe transmitted pulse. The same experiment is repeatedusing 20-dB gain to amplify the RF signal, which producedan SNR of 19.7 dB on average.

The two transducers show different improvement be-cause more elements are included in the sum for the 20-MHz transducer. This transducer actually has a smallerbeam spread, which would seem to indicate summing fewerRF signals, but the transducer positions were closer to-gether because of the smaller wavelength.

SA processing improves both the SNR of individual RFsignals and the SNR of the image when the wire is locatedbeyond the focus of the transducer. However, the process-ing does not improve either SNR above the level acheived

TABLE VISNR Characteristics of the Processed Images of 25-µm

Tungsten Wire Targets in a Waterbath. Data are Processedwith the Boxcar Window.

SNR of Images

Wire Unprocessed ProcessedTdr depth image SNR image SNR(MHz) (mm) (dB) (dB)

15 0 38.6 –3 33.18± 0.45 32.76± 1.505 23.24± 0.31 35.31± 1.057 21.39± 0.34 38.05± 0.50

20 0 31.9 –3 23.89± 0.36 30.01± 0.785 15.57± 0.39 28.89± 0.957 15.18± 0.19 34.98± 1.14

when the target is located at the focus of the transducer.The SNR of a measured RF signal from a wire at the fo-cus of the transducer is only slightly higher than the SNRof a calculated RF signal when the target is 7 mm awayand a relatively large number of measured RF signals aresummed. Similarly, the SNR of a calculated RF signal froma wire target 3 mm from the focus can be high because itis so close to the focus, even though relatively few mea-sured RF signals are summed. In the intermediate range,the electronic SNR is not as good as that obtained whenthe target is at the focus of the transducer. The imageSNR is also improved greatly through SA processing. Andit shows a similar trend as the electronic SNR, comingclose to the image SNR for a B-mode image when the wireis at the focus when the wire is at 3 mm or 7 mm. Whenthe wire is at 5 mm, the image SNR is not as good as theimage SNR for the conventional B-mode image when thewire is at the focus.

VI. Conclusion

The behavior of a virtual source in response to syntheticaperture processing has been studied. The results showthat it is possible to treat the focus of a transducer as avirtual element for the sake of SA processing. Once theaperture angle of the transducer has been determined, SAprocessing can be performed without regard to whether ornot the element actually exists.

Using SA processing, resolution beyond the focus of thetransducer is improved. The minimum lateral resolutionachievable is limited by the diffraction angle of the trans-ducer. However, we have shown that the achievable reso-lution can be comparable to the resolution at the focus ofthe transducer.

The tradeoff between resolution and sidelobe level isdemonstrated for wire and cyst targets. As with any en-gineering compromise, the best images are produced withthe apodization weights that do not achieve the best res-olution or lowest sidelobe level but rather compromise be-tween the two.


The spatial sampling criterion is investigated by form-ing images with decreasing sampling rates. The acceptedcriterion is shown to be more strict than actually necessary.Therefore, the amount of computation can be reduced byworking beyond the λ2 limit, but not so far that gratinglobes are observed.

The image SNR can be close to the SNR for an imagecreated with conventional B-mode imaging with the targetat the focus. And the image SNR is improved compared toconventional B-mode imaging when the target is beyondthe focus.

One issue in SA imaging that has not been discussed inthis contribution is the problem of phase aberration causedby spatial variations of the speed of sound, which occur inbiological tissue. Tissue inhomogeneity also affects conven-tional B-mode images by increasing the size of the focalspot. With the virtual source technique, the increase insize of the focal spot is not a problem unless the diffrac-tion angle is also reduced. However, tissue inhomogeneitywill cause errors in the calculation of delays. This problemhas limited the use of SA processing in medical imaging,but many groups are currently working on methods to re-duce its effects on SA images. And SA is well-establishedin other applications such as nondestructive evaluation.

References

[1] C. Passman and H. Ermert, “A 100 MHz ultrasound imagingsystem for dermatologic and ophthalmologic diagnostics,” IEEETrans. Ultrason., Ferroelect., Freq. Contr., vol. 43, pp. 545–552,July 1996.

[2] H. Djelouah, J. C. Baboux, and M. Perdrix, “Theoretical andexperimental study of the field radiated by ultrasonic focussedtransducers,” Ultrasonics, vol. 29, pp. 188–200, May 1991.

[3] K. Raum and W. D. O’Brien, Jr., “Pulse-echo field distributionmeasurement technique for high-frequency ultrasound sources,”IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, pp.810–815, July 1997.

[4] J. G. Proakis and D. G. Manolakis, Digital Signal Processing:Principles, Algorithms, and Applications. New York: MacMil-lan, 1992.

[5] O. T. von Ramm and S. W. Smith, “Beam steering with lineararrays,” IEEE Trans. Biomed. Eng., vol. BME-30, pp. 438–452,Aug. 1983.

[6] M. O’Donnell, B. M. Shapo, M. J. Eberle, and D. N. Stephens,“Experimental studies on an efficient catheter array imaging sys-tem,” Ultrason. Imaging, vol. 17, pp. 83–94, 1995.

[7] M. Karaman, P.-C. Li, and M. O’Donnell, “Synthetic apertureimaging for small scale systems,” IEEE Trans. Biomed. Eng.,vol. 42, pp. 429–442, May 1995.

[8] J. T. Ylitalo and H. Ermert, “Ultrasound synthetic apertureimaging: Monostatic approach,” IEEE Trans. Ultrason., Ferro-elect., Freq. Contr., vol. 41, pp. 333–339, May 1994.

Catherine Frazier (S’97) was born on Au-gust 16, 1972, in Bethesda, MD. She receivedthe B.S.E.E. from the University of Mary-land at College Park in 1994, and the M.S.in electrical engineering from the Universityof Illinois at Urbana-Champaign in 1996. Sheis currently working on the Ph.D. in electricalengineering at the University of Illinois.

Ms. Frazier was awarded the NationalScience Foundation Fellowship from 1994 to1997, and the Koehler Fellowship for the1994–1995 academic year. In April 1997 she

was presented the Robert T. Chien Memorial Award for outstandingresearch in electrical engineering.

Her research interests are in acoustical image formation and im-age processing.

William D. O’Brien, Jr. (S’64–M’71–SM’79–F’89) received B.S., M.S., and Ph.D.degrees in 1966, 1968, and 1970, from the Uni-versity of Illinois, Urbana-Champaign.

From 1971 to 1975 he worked with theBureau of Radiological Health (currently theCenter for Devices and Radiological Health)of the U.S. Food and Drug Administration.Since 1975, he has been at the University ofIllinois, where he is a Professor of Electricaland Computer Engineering and of Bioengi-neering, College of Engineering, and Professor

of Bioengineering, College of Medicine, is the Director of the Bioa-coustics Research Laboratory and is the Program Director of theNIH Radiation Biophysics and Bioengineering in Oncology TrainingProgram. His research interests involve the many areas of ultrasound-tissue interaction, including spectroscopy, risk assessment, biologicaleffects, tissue characterization, dosimetry, blood-flow measurements,acoustic microscopy and meat characterization for which he has pub-lished more than 170 papers.

Dr. O’Brien is Editor-in-Chief of the IEEE Transactions on Ul-trasonics, Ferroelectrics, and Frequency Control. He is a Fellow ofthe Institute of Electrical and Electronics Engineers (IEEE), theAcoustical Society of America (ASA), and the American Instituteof Ultrasound in Medicine (AIUM) and a Founding Fellow of theAmerican Institute of Medical and Biological Engineering. He wasrecipient of the IEEE Centennial Medal (1984), the AIUM Presi-dential Recognition Awards (1985 and 1992), the AIUM/WFUMBPioneer Award (1988), the IEEE Outstanding Student Branch Coun-selor Award (1989), and the AIUM Joseph H. Holmes Basic SciencePioneer Award (1993). He has been President (1982–1983) of theIEEE Sonics and Ultrasonics Group (currently the IEEE UFFC-Society), Co-Chairman of the 1981 IEEE Ultrasonic Symposium,and General Chairman of the 1988 IEEE Ultrasonics Symposium.He has also been President of the AIUM (1988–1991) and Treasurerof the World Federation for Ultrasound in Medicine and Biology(1991–1994).

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