- Email: [email protected]
A new digital phased array system for dynamic focusing and steering with reduced sampling rate
ULTRASONIC
IMAGING
12,
1-16,
(1990)
A NEW DIGITAL PHASED ARRAY SYSTEM FOCUSING AND STEERING WITH REDUCED
FOR DYNAMIC SAMPLING RATE
Tai K. Song and Song B. Park
Department of Electrical Engineering Korea Advanced Institute of Science & Technology P.O. Box 150, Chongyangni, Seoul, Korea
In order to enhance the resolution of the ultrasonic B-mode image, digital techniques for dynamic focusing and steering have been receiving a great deal of attention for a long time. In this paper, we present the theory and preliminary experimental results for a new architecture of a fully digital B-mode imaging system with this desired feature. The system employs the Pipelined-Sampled-Delay-Focusing (PSDF) scheme to eliminate the bulky memory addressing and interpolation circuits which are needed in conventional digital imaging systems. To reduce hardware requirements and the bandwidth required for digital processings, we describe an efficient method to generate the sampling clocks for dynamic focusing and steering and some modified bandwidth sampling techniques to reduce the sampling rate for signal digitization. Using these methods, it is possible to achieve dynamic focusing and steering in realtime sector imaging using a linear phased array. 01990 AcademicPress, Inc. Key words
: Digital beamforming; dynamic ling; sampling rate reduction.
focusing
and steering; bandwidth
samp-
I. INTRODUCTION Electronic dynamic focusing and steering using a phased array is perhaps the most powerful1 approach to improve the image quality of real-time ultrasonic medical imaging systems. In a real-time ultrasonic scanner, near-optimal resolution can be obtained by employing dynamic focusing in receive, which is accomplished by summing the ultrasound pulse echoes received at all array elements with proper delay compensations corresponding to the propagation time delays from all imaging points of view. In a conventional analog imaging system, the lumped L-C delay lines as delay elements are extremely bulky for the dynamic focusing and steering, since the delay patterns for focal points through the depth along the radial direction are different for each element and for each steering direction, requiring very complex switching circuitry. Moreover, the analog delay elements which satisfy the required dynamic range and the bandwidth of the echoes are expensive and subject to inherent artifacts such as insertion loss, impedance mismatching, and switching transients. In recent years, digital techniques to achieve dynamic focusing and steering have received a great deal of attention [l-5]. This is because digital techniques enable more precise and rapid changing of the receiver delay times, so that the focal point may
1
0161-7346/90 $3.00 Copyright 0 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.
SONG AND
PARK
track the returning echoes along any steering direction. In digital imaging systems, in general, a pulse echo received at each array element is sampled and stored prior to delay compensation. The stored samples for all array elements are then addressed dynamically according to the receiving time delays for each observation point and summed to obtain the constructive interference. The amplitude of the envelope of the focused signal is displayed with corresponding brightness. Hence, digital beamforming can be defined as a Sampling-DeIay-Sum-Detection process [5] and the analog imaging as a Delay-Sum-Detection-Sampling process. The sampling technique in a digital imaging system involves substantial technical problems, since it relies on a sampling rate of at least twice the highest frequency component, which is normally lo-20 MHz for current ultrasound diagnostic systems. In general, the delay quantization error should not exceed 1/8f, [6] to achieve acceptable focused field patterns, and hence the sampling rate must be higher than SfO, which is much higher than 20 MHz in most ultrasonic imaging systems. Hence, for the Nyquist sampling rate of the received signals, interpolation hardware must be added to generate the sample for each focal point with a delay quantization error less than 1/8f,. This high sampling rate requires wide bandwidth digital circuitry and a large amount of digital memory with bulky memory addressing and interpolation logic. In this paper, we propose several techniques to reduce the sampling rate and eliminate the memory addressing and the interpolation hardware for real-time cardiac sector imaging using a linear phased array, which enables dynamic focusing and steering. To reduce the sampling rate to the bandwidth of the signals or the Nyquist rate of their envelopes, some bandwidth sampling techniques can be used [7,8]. The limitations of these techniques are analyzed in this paper and some modified methods are proposed as alternatives. The resultant sampling techniques are then applied to a new digital imaging system with the Pipelined-Sampled-Delay-Focusing (PSDF) scheme [S], in which the received echoes are steered and focused without the above-mentioned memory addressing and interpolation hardware. In section II, we briefly review the digital imaging techniques and discuss the problems of conventional uniform sampling techniques as applied to them. In section III, we suggest some quadrature sampling techniques to reduce the sampling rate. From the results of sections II and III, a new architecture of a digital phased array system is presented and some preliminary experimental results of the new digital imaging system are illustrated in section IV.
II. DIGITAL
IMAGING
TECHNIQUES
Figure l(a) shows the Sample-Delay-Sum-Detection architecture commonly employed in a digital imaging system using an array transducer, in which the delay processing is realized by the memory addressing logic corresponding to the propagation time delay for each array element [l-3]. The samples of each element are stored in digital memories and read by addressing logic according to the propagation time delays. Since it is unrealistic to store all of the actual samples at the exact delay times for each focal point, they are interpolated by interpolation logic. As shown in this figure, for each channel one ADC, memory addressing logic and an interpolator are necessary and their hardware requirements are wholely dependent on the sampling rate of the ADC’s. To eliminate the memory addressing and the interpolation circuits for each channel, the Pipelined-Sampled-Day-Focusing (PSDF) architecture as shown in figure l(b) was proposed by the authors [5]. In the PSDF scheme, focusing is carried out not by the addressing logic but by the sampling clock for the ADC’s; in other words, the sampling clock for each channel from the Sampling-Clock-Generator (SCG) is delayed individually and dynamically corresponding to the propagation time delay of that channel for successive imaging points. As a result, all the samples for actual imaging points can be obtained and the interpolator and addressing logic are com-
2
DIGITAL
PHASED
ARRAY
Data memories
TRD
Uniform sampling rate f s
~ss,‘,’
SYSTEM
Interpolators
‘y-=,
(4 FIFO’s as buffer memory
delay patterns
Fig. 1
Digital beamforming tirate sampling.
techniques
using (a) uniform
pletely replaced by the SCG, which can be implemented When the pulse echo for the i-th element is expressed as fi(t)
= Ai(t-Ti(t))cos[q,(t-q(t))++]
sampling
and (b) mul-
with much less hardware.
0)
where am is the receiving delay time of the i-th element and wa denotes the center frequency of the received signal, then the focused signal f (kT,) can be. expressed as
= 2 fi(t).8[t i=l
- (/CT, + T~(~T,))]
(3)
SONG AND PARK
where T, is the uniform sampling period at the center element and N is the total number of independently phased: array elements. We recognize that S[.] in Eq. (3) can be regarded as the sampling clock. Since the samples for any imaging point are sampled at different times by all elements and the maximum time delay of Eq. (4) is normally greater than the sampling interval, it is necessary to store the samples temporarily in the PSDF scheme. The First-In-First-Out (FIFO) memory acts as the buffer memory because the samples for each focal point can be automatically arranged at the FIFO output by the fall-through operation of the FIFO. The minimum length of the buffer memories for each channel is T,,,/T, I, when ‘max = mux (Ti (k )) > T,
(4)
In any structure, the most stringent limitation is imposed by the sampling rate, on which the hardware complexity and the bandwidth of the digital circuitry are mainly dependent. We want to reduce the sampling rate as much as possible without causing much error in the detected envelope of the focused signal, and hence it is very important to analyze the resulting detection error. For this purpose, we will concentrate on the Sampling-Sum-Detection process instead of Sampling-Delay-Sum-Detection process. Let us first investigate the reduction methods using the conventional uniform sampling technique. Figure 2 shows the Sampling-Sum-Detection process for this case. In this figure, all the N channels are represented, by a single line with a crossed slash and the delay processing is not shown. The sampling rate fs must be greater than the Nyquist rate to reconstruct the original signal, or f, > fN the center frequency and B is the bandwidth of the recetv’ eJ’ultr=asZG.B ‘X-CIZZe~“tlZ sampling rate can be reduced below fNyq,, since only the envelope of the focused’signal is needed in the ultrasound B-scan imaging system. When the frequency-translated signal fM (t) is sampled with a frequency fs, we have a periodic repetition (with a period of f,) of the spectrum of fM (t) as shown in figure 3(c). To reconstruct the envelope, there must not be frequency aliasing on the baseband which is bounded from -B/2 to B/2. There are two possible cases satisfying this requirement, as shown in figures 3(c) and 3(d), from which the allowable range of f, is given by fo+B/2
< 2fo-B
(Q > 1.5)
(Fig. 3(c))
(5)
0%. W-0)
(6)
or
f, ’ WI3 + B
The case of Eq. (6) is not useful. For the case of Eq. (5), the sampling rate can be reduced to fNyq,/2, if the quality factor Q of the transducer is greater than 1.5. (For actual signals, the bandwidth B is not ideally bandlimited and must be defined as the frequency range outdside which the energy is negligible.) For a narrowband application, as in a Doppler imaging system, the sampling rate can further be reduced according to the quality factor of the employed pulse. The detected envelope A(kT,) expressed as A (kT,) = +A
(kT,) cos[(wo-oc)kTs
+$I]
(7)
involves some error due to the frequency-dependent attenuation. In the real situation, the phase component + in Eq. (1) is not constant and the center frequency f o varies due to multiscattering, frequency-dependent attenuation, and other phenomena. That is,
‘This applies for dual-port memory type FIFO’s; for standard FIFO’s, the length may increase substantially because of the fall through time.
4
however,
DIGITAL
PHASED
SYSTEM
Focusing with uniform
Fig. 2
the modulating carrier the received echoes.
ARRAY
frequency f,
sampling.
can not be identical
to the center frequency fa of
In another method, the signals are mixed to a lower frequency md to reduce the sampling rate by multiplying the signals with a sinusoidal carrier COSW,~ followed by filtering out the high frequency component to obtain fi(t)
= Ai(t--7i(t))~~.~(~dt
- co,?;(t)
+ +)
(8)
where od = wo-oC. Hence, the modulated echoes must be delayed by (o~/w~)T~ instead of TV. However, this may cause the focusing error, since the center frequency varies along depth due to attenuation. Moreover, it is very difficult to implement the balanced modulators with identical characteristics for all channels, which are required to satisfy the dynamic range and the bandwidth of the ultrasound echoes.
FIf(t) I ALLrLf 0
f0
(a)
fo+Bnc
f, <2
FIfM(t)l &iLL 0
fg -B
fa
F{fMfkTs)l
f, - 2 fo : 812 (4
Fig. 3
>2 fo+B
F{fM(kTs)l
f, -
I
fs-2
2 fo
W
2 f.
- B/2
f. - B/2
(a) Fourier transform of a focused signal. (b) Fourier transform of the frequency translated signal. (c) Spectrum of fM(kT,) for the case in which Eq. (5) is satisfied. (d) Spectrum of fM(kT,) for the case in which Eq. (6) is satisfied.
SONG AND PARK
For these reasons, uniform sampling methods are difficult to reduce the sampling rate in the ultrasonic medical imaging. Some bandwidth sampling methods can be used to reduce the sampling rate [7,8], among which the second order sampling method has widely been used [2,9]. In the next section, we analyze the limitations of this method and suggest a modified second order sampling technique. We also suggest a new quadrature sampling method for digital imaging systems.
III. SAMPLING
BATE
REDUCTION
BY BANDWIDTH
SAMPLING
To reconstruct the envelope of a bandlimited signal, the sampling rate must be greater than twice the maximum frequency component according to the conventional uniform sampling theorem. However, since the bandwidth of the envelope is much less than that of the original signal, it is plausible to reduce the sampling rate to the bandwidth. This can be achieved by using some bandwidth sampling methods such as the second order, quadrature, and analytic sampling techniques. Among these, the analytic sampling method is not suitable to ultrasound imaging because of the requirement of a Hilbert transformer for each channel, while the others are. The conventional quadrature sampling is illustrated in figure 4(a), in which the two modulated signals
(4
I sin wet
‘TS
(W
(4 Fig. 4
Sin’w,
kTs
Digital beamforming using the quadrature sampling technique. (b) A conventional method. (c) A modified method - sampling and LPF are exchanged. (c) Hardware-reduced scheme of (b).
6
DIGITAL
PHASED
ARRAY
SYSTEM
are low-pass filtered, yielding in-phase and quadrature phase components and then can be sampled with the minimum rate of twice the envelope bandwidth. However, this
method involves following practical problems: (1) Baseband focusing results in poor resolution (2) Two analog balanced modulators are needed for each channel (3) Two LPF’s are needed for each channel (4) Two ADC’s for each channel and two adder blocks are needed. In baseband focusing, we can avoid the degradation of lateral resolution by mixing the reflected signals with quadrature carriers that have an additive phase term, tiara in Eq. (S), which is different for each channel and varies with time. This requires a complicated phase control circuitry for the quadrature carrier signals; otherwise, problems (1) degrades the resolution. Also, the other problems increase the system complexity. The conventional quadrature sampling method shown in figure 4(a) can be modified to the structure of figure 4(b) to solve problem (1) by exchanging the sampling and LPF. This can further be modified to figure 4(c), in which one ADC for each channel and only two LPF’s for the whole imaging system are required and thus problems (3) and (4) are solved. Also, only one balanced modulator is necessary, which can be implemented simply using the digital memory as a lookup table. As a result, all the problems are eliminated. The only limitation in the final scheme is the increased sampling rate. Since the sampling and the LPF must be exchanged to effect the envelope reconstruction, the resultant sampling rates are subject to Eqs. (5) and (6); that is, the minimum sampling rate is increased from the signal bandwidth B to
f
o+B/2.
As an alternative approach, the second order sampling technique can be used to reduce the sampling rate, in which, as shown in figure 5, a pair of two samples are obtained by a uniform sampling on the first channel and a delayed sampling on the second channel. As a special case, when we use a uniform sampling rate and a delay defined by [7,8] r,
= .-!.-
< B-’
,
1=+1,+2,...
2fo
then the two samples can be expressed
(104
kT;
kT,-a
Fig. 5
A general scheme of the second order sampling method.
SONG AND PARK
Noting that these are samples of the quadrature components of the signal and that for the high Q signal, the quadrature components vary only slowly, we get
and hence a good approximation
of the envelope is obtained by
&kT,)= vf (kT,)+ f;(kT,-a)]“* ,
WI
which can be readily computed. This technique has been applied to the digital imaging system as shown in figure 6(a) [2,9], in which, problems (l), (2), and (3) are solved and problem (4) can also be eliminated in the modified scheme as shown in figure 6(b), in which one ADC is used for two samples and thus the digital processing rate is increased now twice on average as compared to the case of figure 6(a). However, since the center frequency of the reflected ultrasound changes, the requirements of Eq. (9) can not be satisfied strictly. In order to solve this problem, we change T, and a in accordance with the center frequency so that the two samples are now expressed as follows:
f2(kTS -a)
= A (kT, -a)cos(y,kT,
-~,a++)
= A (kT, -a)sin(wukT,
+&)
(14)
kTs, I kTs-a (b)
Fig. 6
(a) A simplifeid envelope detection scheme using the second order sampling. (b) A second order sampling scheme using one ADC.
8
DIGITAL
PHASED
ARRAY
SYSTEM
where C$ = ~F/~-w,,cx+~ = A+++. Substitution of Eqs. (13) and (14) into Eq. (12) yields the following approximation for the squared envelope:
.P(kT,) = ff(kT,) + &kTs-a) l+cos2(o&T,+~) = A2(kTs)
=
l-cos2(wOkTs + A2(kT, -a)
2
A2(kT,)+A2(kT,
+$ )
2
-a)
2
A*W,)
+ ---cos2(w&T, 2
++)-
A*(kT, -a) cos2(w&T, 2
which can be reexpressed as follows, when A$ is negligible i’(kT,)
= A:(kTs -a/2)
Af(kT,)
=
+ Ae2(kTs -d2)cos2(wOkTs
+& )
(1%
or $ = $ : +$ )
(16)
where A’(kT,)
+ A2(kTs-a) >
2 A’(kT,)
- A2(kTs-a)
Ae2(kTs) =
(174
(17b)
2
Note that the error term, A,‘(.), in Eq. (16) is negligible for high Q signals. But high frequency components in Eq. (15) are not negligible because of the difference of C$ and $. In both cases, we can extract the term Af(kT,) as a good approximation to the envelope by filtering out the high frequency components, which, to be successful, requires the sampling rate to satisfy Eq. (18) (th e only change in figures 3(c) and 3(d) is the increase of bandwidth from B to 2B due to the square operation), f,+B
< f, < 2fO-2B
(Q > 3) ,
W)
So far, we have discussed the limitations of the quadrature sampling techniques and suggested some modified methods. For the application to sector scanning using a phased array, the second order sampling techniques may be inadequate in view of hardware complexity, since two ADC’s for each channel as can be seen figure 6(a) and two N channel digital adders are required. In the next section, we propose a new architecture of the digital phased array system, which employs the modified quadrature sampling technique (Fig. 4(c)). The resultant performance measures for the various sampling techniques discussed above are compared in table I.
9
SONG AND PARK
Table I. Comparisons of various sampling techniques Detection error
g
large Quadrature sampling
f,>B
very high
2nd order sampling
f,>lfo>B 1=1,2,...
high
no FJdependent
no
IV. PROPOSED
DlGITAL
PHASED
SYSTEM
AND EXPERIMENTS
Though the sampling rate reduction techniques given in table 1 can reduce the amount of digital memory, the bandwidth of the ADC, digital adders, and other digital circuitry, the memory addressing and the interpolation circuits are still required in the structure of figure l(a). These can be completely eliminated, however, by the use of SCG in the PSDF structure of figure l(b), which can be implemented with much less hardware requirements than the addressing logic and interpolators. The resultant architecture of a new phased array system is shown in figure 7, where the transmit-trigger pulses for the high voltage pulser for the respective array elements are generated by the SCG with proper delays so that transmit focusing is achieved at a specific depth along a given steering direction. Except for this SCG, all other parts in this architecture are very straightforward. Thus, it is most important to realize the SCG as simple as possible. In the following, we describe a simple realization of the SCG.
Transmit-trigger
Fig. 7
pulse
The proposed digital beamforming sampling method (Fig. 4(c)).
10
scheme using the modified
quadrature
DIGITAL
PHASED
ARRAY
SYSTEM
The most effective way to generate focused sampling clocks seems to be simply reading digital memories, into which the delay patterns for focusing are written. In the digital memory matrix as shown in figure 8, the l’s in the i-th column define the sampling times for the i-th channel (i=1,2, ....N). and the set of the j-th l’s in the successive columns defines the correct sampling times for the j-th focal point. In this case,
1 st channel --
.
Samplil
Master
0
i
Digital memory
Exact sampling time of some channel for focusing
Bit pattern in a column of memory
; ! i4-g
1;
0
1
0
1
: Maximum delay error
03 Fig. 8
Generation of multirate sampling clocks. (a) Delay patterns are stored in memories. (b) From the top figure, exact sampling time for some channel, actual sampling clock, and the bit pattern in a column of memory. (Maximum delay quantization error is determined by the period of the master clock.)
11
SONG AND PARK
the length and amount of memory are given by LSCG
= 2 . (max.
MSCG
= N XL,,,
imaging
where c is the ultrasound velocity addressing counter in the SCG.
depth ) .fM
and f,,,
/c
:
length
(194
:
amount
Wb)
is the master clock
frequency
for the
The delay quantization error of this sampling clock is dependent on fnr , and the maximum delay error (peak-to-peak error) is l/f, as can be seen in figure 8(b). To reduce the delay quantization error, the master clock frequency must be increased, in which case two blocks of memories may be necessary, and by switching them, the master clock frequency can be increased to 2.fM. (In this case, for example, if fM is 25 MHz, the maximum delay error is 20 ns, which is less than l/Sf o for a 6.25 MHz transducer.) For a maximum imaging depth of 20 cm and a master clock of 50 MHz, the length (Eq. (19)) is 12987 (< 16K), and hence the total memory size is 16K X N/2, since focusing delays are symmetric to the center element of the N-element array. In the imaging scheme of figure l(a), the amount of data memory is MSCG X (bit number of data) and complex memory addressing logic and interpolation hardware are needed. For example, with a 64-element phased array, eight 8K X 8 SRAM’s with maximum access time of 40 ns are required for the SCG. The most severe drawback of using the SCG for steering is that the memory size increases linearly with the number of steering angles, since the delay patterns are different for different steering angles. To obviate this problem, we will separate the steering and the focusing delays [4]. Strictly speaking, the focusing delay changes with the steering angle. However, the focusing delay error can be kept within an acceptable value (say, less than 1/16f u), if we divide the total steering angle into a few groups and for each group a slightly different focusing delay is employed. The focusing delays are first achieved by the SCG of figure 8 and then the steering delays are added on the focused clocks. Two realizations are conceivable; reading each column of the memories in SCG after steering delays of the channel, or reading all columns simultaneously followed by delaying them. The former method requires individual memory and address counters for all N channels. The latter can be implemented by attaching a number of N FIFO’s to the SCG as described above and delaying their
Channel SCG for focusing .
:
DIGITAL
PHASED
ARRAY
outputs linearly, as shown in figure 9. The maximum MLFIFO
SYSTEM
FIFO length is given by
= fan(e,,,/2).(0/2).f~/c
(20)
where 0,,, is the maximum steering angle and D denotes the aperture size. For a 3.5 MHz 64-element phased array, the maximum length of Eq. (20) is leas than 256 when can easily be 8 max = 45“ and fM = 50 MHz. Hence, the Read-Start-Controller implemented using presettable 8 bit counters. As a result, the new SCG enables fully digital beam steering and dynamic focusing for the sector scan imaging. In order to verify the the proposed digital imaging system, we have performed some preliminary experiments by implementing an experimental system as shown in figure 10, in which an &element linear transducer with a center frequency of 2.25 MHz and an element spacing of 1 mm was excited with transmit steering and focusing delays. A line target of diameter 8 mm was placed at a depth d=5.7 cm along a direction 0 = 0, and then 8 = -5’. The reflected signals were sampled by S-bit ADC’s with receive steering and dynamic focusing delays obtained from the SCG and fed to the FIFO’s The SCG was implemented for 8 channels with a maximum master And the FIFO outputs were addeded by a digital clock frequency up to 30 MHz. adder and stored in memories which were interfaced to VAX-11/750 computer. In the experiments, we used several different sampling rates. At first, a sampling rate of 12.6 MHz was used to obtain the correct signals and their envelopes. (Actually, we constructed the system with a maximum sample rate of 15 MHz, so that a transducer of a center frequency up to 5 MHz can be used without requiring any sampling rate reduction technique.) Figures 11(a) and 11(b) show the waveforms and envelopes, respectively, of the pulse echo from the target located at d-5.4 cm along 0 = -5’ (dynamic focusing was applied, of course). The -6 dB bandwidth of the signal was 1.2 MHz. The detected envelopes for other sampling rates are also depicted in figure 11(c) through 11(e), where we see that the envelope for f,=2.965 MHz* shows a close agreement to the correct envelope (Fig. 11(b)), because this sampling rate satisfies the requirement of Eq. (5) or 2.85 MHz
< f, < 3.3 MHz.
(22)
Linear TRD (8 elements)
Transmit-trigger
pulse
Fig. 10
and scan
An experimental
system.
*This frequency was used, although f,=3.075 MHz is desirable, limitation of available frequency from the master clock.
13
conversion
because of the
SONG
AND PARR
(C)
fs = 2.52
MHz
f .q = 2.965
MHz
67.5 (a) fs = 12.6 MHZ
(d)
I 73.4
67.5
W
w
fs=12.6MHz
f
I ;
I
67.5 (e)
Fig. 11
73.4 fs =3.269
ps
MHz
Received signals and their envelopes for various sampling
rates.
On the other hand, the envelope for f,=2.52 MHz significantly deviates from the correct one and the envelope for f,=3.289 MHz shows slightly enhanced high frequency components due to the frequency aliasing effect. Figure 12 shows the measured steering beam patterns in a sector coordinate for f,=12.6 MHz when a wire target is placed at d=5.7 cm along t3 = O” and the beam is steered from 0= -7O to +7” with an increment of lo. Figure 13 shows the interpo-
14
DIGITAL
PHASED
ARRAY
SYSTEM
+ 7"
Fig. 12
Sector scanned beam pattern for a wire target placed at d=5.7 O=o”.
cm along
lated beam patterns for f,=2.96 MHz in a Cartesian coordinate of the sector scanned image when the wire target is placed at d=5.4 cm along u=-5’ and the beam is steered from 0= -12” to + 12” . Both figures show the expected results, while figure 13 shows grating lobes for 8 > 0, which is attributable to the fact that for a certain range of positive scan angles the wire target reflects a strong ultrasound pulse due to the first grating lobe in the negative angle of the Point-Spread-Function (PSF) [lo].
Fig. 13
Beam pattern of a sector scanned image for a wire target placed at d=5.4 cm along 6=-5’.
15
SONG AND PARK
From the above experiments, it is seen that the proposed digital phased array system can achieve dynamic focusing and steering simultaneously with a reduced sampling frequency and an enhanced resolution of the sector-scanned image.
V. CONCLUSIONS We have presented a new digital phased array system using the PSDF scheme which performs real-time dynamic focusing and steering. The proposed method for generating the sampling clocks can replace the bulky memory and interpolation circuits required in conventional systems, with much less hardware requirements. It was shown that the commonly-used second order sampling technique for sampling rate reduction cause detection error of high frequency components, which can be negligible for low Q signals. This detection error can be eliminated in the proposed quadrature sampling technique with a slightly increased sampling rate (but the sampling rate is still half the Nyquist sampling rate of the received signal). In the view of its hardware complexity, the second-order sampling technique is unsuitable for a phased array system using a linear array transducer, since it needs two ADC’s for each channel and beamforming blocks. From the preliminary experiments for the proposed system, it was verified that the sampling rate and hardware requirements can be much reduced. A practical instrument with 64 array elements is under construction at our laboratory.
REFERENCES
[l]
Gehlbach, S. M. and Alvarez, R. E., Digital ultrasound imaging techniques using vector sampling and raster line reconstruction systems, Ultrasonic Imaging 3, 83107 (1981). [2] Mucci, R. A., A comparison of efficient beamforming algorithms, IEEE Trans. Acoust. Speech Signal Processing. ASSP-32, 548-558 (1984). [3] Peterson, D. K. and Kino G. S., Real-time digital image reconstruction: A description of imaging hardware and an analysis of quantization errors, IEEE Trans. Sonics Ultrasonics W-31, 337-351 (1984). [41 am, Y. G and Park, S. B., New dynamic focusing scheme for ultrasound scanners, Electronic letters 23, 181-182 (1987). [5] Kim, J. H., Song, T. K., and Park, S. B., A pipelined sampled delay focusing in ultrasound imaging systems, Ultrasonic Imaging 9, 75-91 (1987). [6] Manes, G. F., Atzeni, C., and Susini, C., Design of a simplified delay system for ultrasound phased array imaging, IEEE Trans. Sonics Ultrasonics W-30, 350-354 (1983). [7] Linden, D. A., A discussion of the sampling theorem, Proc. IRE 47, 1219-1226 (1959). [8] Grace, 0. D. and Pitt, S. P., Sampling and Interpolation of bandlimited signals by quadrature methods, J. Acoust. Sot. Am. 48, 1311-1318 (1970). [9] Powers, J. E., Phillips, D. J., Brandestini, D. J., and Sigelmann, R. A., Ultrasound phased array delay lines based on quadrature sampling techniques, IEEE Trans. Sonics Ultrasonics SU-29, 287-295 (1980). [lo] Macovski, A., Ultrasonic imaging using arrays, Proc. IEEE 67, 484-495 (1979).
16
IMAGING
12,
1-16,
(1990)
A NEW DIGITAL PHASED ARRAY SYSTEM FOCUSING AND STEERING WITH REDUCED
FOR DYNAMIC SAMPLING RATE
Tai K. Song and Song B. Park
Department of Electrical Engineering Korea Advanced Institute of Science & Technology P.O. Box 150, Chongyangni, Seoul, Korea
In order to enhance the resolution of the ultrasonic B-mode image, digital techniques for dynamic focusing and steering have been receiving a great deal of attention for a long time. In this paper, we present the theory and preliminary experimental results for a new architecture of a fully digital B-mode imaging system with this desired feature. The system employs the Pipelined-Sampled-Delay-Focusing (PSDF) scheme to eliminate the bulky memory addressing and interpolation circuits which are needed in conventional digital imaging systems. To reduce hardware requirements and the bandwidth required for digital processings, we describe an efficient method to generate the sampling clocks for dynamic focusing and steering and some modified bandwidth sampling techniques to reduce the sampling rate for signal digitization. Using these methods, it is possible to achieve dynamic focusing and steering in realtime sector imaging using a linear phased array. 01990 AcademicPress, Inc. Key words
: Digital beamforming; dynamic ling; sampling rate reduction.
focusing
and steering; bandwidth
samp-
I. INTRODUCTION Electronic dynamic focusing and steering using a phased array is perhaps the most powerful1 approach to improve the image quality of real-time ultrasonic medical imaging systems. In a real-time ultrasonic scanner, near-optimal resolution can be obtained by employing dynamic focusing in receive, which is accomplished by summing the ultrasound pulse echoes received at all array elements with proper delay compensations corresponding to the propagation time delays from all imaging points of view. In a conventional analog imaging system, the lumped L-C delay lines as delay elements are extremely bulky for the dynamic focusing and steering, since the delay patterns for focal points through the depth along the radial direction are different for each element and for each steering direction, requiring very complex switching circuitry. Moreover, the analog delay elements which satisfy the required dynamic range and the bandwidth of the echoes are expensive and subject to inherent artifacts such as insertion loss, impedance mismatching, and switching transients. In recent years, digital techniques to achieve dynamic focusing and steering have received a great deal of attention [l-5]. This is because digital techniques enable more precise and rapid changing of the receiver delay times, so that the focal point may
1
0161-7346/90 $3.00 Copyright 0 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.
SONG AND
PARK
track the returning echoes along any steering direction. In digital imaging systems, in general, a pulse echo received at each array element is sampled and stored prior to delay compensation. The stored samples for all array elements are then addressed dynamically according to the receiving time delays for each observation point and summed to obtain the constructive interference. The amplitude of the envelope of the focused signal is displayed with corresponding brightness. Hence, digital beamforming can be defined as a Sampling-DeIay-Sum-Detection process [5] and the analog imaging as a Delay-Sum-Detection-Sampling process. The sampling technique in a digital imaging system involves substantial technical problems, since it relies on a sampling rate of at least twice the highest frequency component, which is normally lo-20 MHz for current ultrasound diagnostic systems. In general, the delay quantization error should not exceed 1/8f, [6] to achieve acceptable focused field patterns, and hence the sampling rate must be higher than SfO, which is much higher than 20 MHz in most ultrasonic imaging systems. Hence, for the Nyquist sampling rate of the received signals, interpolation hardware must be added to generate the sample for each focal point with a delay quantization error less than 1/8f,. This high sampling rate requires wide bandwidth digital circuitry and a large amount of digital memory with bulky memory addressing and interpolation logic. In this paper, we propose several techniques to reduce the sampling rate and eliminate the memory addressing and the interpolation hardware for real-time cardiac sector imaging using a linear phased array, which enables dynamic focusing and steering. To reduce the sampling rate to the bandwidth of the signals or the Nyquist rate of their envelopes, some bandwidth sampling techniques can be used [7,8]. The limitations of these techniques are analyzed in this paper and some modified methods are proposed as alternatives. The resultant sampling techniques are then applied to a new digital imaging system with the Pipelined-Sampled-Delay-Focusing (PSDF) scheme [S], in which the received echoes are steered and focused without the above-mentioned memory addressing and interpolation hardware. In section II, we briefly review the digital imaging techniques and discuss the problems of conventional uniform sampling techniques as applied to them. In section III, we suggest some quadrature sampling techniques to reduce the sampling rate. From the results of sections II and III, a new architecture of a digital phased array system is presented and some preliminary experimental results of the new digital imaging system are illustrated in section IV.
II. DIGITAL
IMAGING
TECHNIQUES
Figure l(a) shows the Sample-Delay-Sum-Detection architecture commonly employed in a digital imaging system using an array transducer, in which the delay processing is realized by the memory addressing logic corresponding to the propagation time delay for each array element [l-3]. The samples of each element are stored in digital memories and read by addressing logic according to the propagation time delays. Since it is unrealistic to store all of the actual samples at the exact delay times for each focal point, they are interpolated by interpolation logic. As shown in this figure, for each channel one ADC, memory addressing logic and an interpolator are necessary and their hardware requirements are wholely dependent on the sampling rate of the ADC’s. To eliminate the memory addressing and the interpolation circuits for each channel, the Pipelined-Sampled-Day-Focusing (PSDF) architecture as shown in figure l(b) was proposed by the authors [5]. In the PSDF scheme, focusing is carried out not by the addressing logic but by the sampling clock for the ADC’s; in other words, the sampling clock for each channel from the Sampling-Clock-Generator (SCG) is delayed individually and dynamically corresponding to the propagation time delay of that channel for successive imaging points. As a result, all the samples for actual imaging points can be obtained and the interpolator and addressing logic are com-
2
DIGITAL
PHASED
ARRAY
Data memories
TRD
Uniform sampling rate f s
~ss,‘,’
SYSTEM
Interpolators
‘y-=,
(4 FIFO’s as buffer memory
delay patterns
Fig. 1
Digital beamforming tirate sampling.
techniques
using (a) uniform
pletely replaced by the SCG, which can be implemented When the pulse echo for the i-th element is expressed as fi(t)
= Ai(t-Ti(t))cos[q,(t-q(t))++]
sampling
and (b) mul-
with much less hardware.
0)
where am is the receiving delay time of the i-th element and wa denotes the center frequency of the received signal, then the focused signal f (kT,) can be. expressed as
= 2 fi(t).8[t i=l
- (/CT, + T~(~T,))]
(3)
SONG AND PARK
where T, is the uniform sampling period at the center element and N is the total number of independently phased: array elements. We recognize that S[.] in Eq. (3) can be regarded as the sampling clock. Since the samples for any imaging point are sampled at different times by all elements and the maximum time delay of Eq. (4) is normally greater than the sampling interval, it is necessary to store the samples temporarily in the PSDF scheme. The First-In-First-Out (FIFO) memory acts as the buffer memory because the samples for each focal point can be automatically arranged at the FIFO output by the fall-through operation of the FIFO. The minimum length of the buffer memories for each channel is T,,,/T, I, when ‘max = mux (Ti (k )) > T,
(4)
In any structure, the most stringent limitation is imposed by the sampling rate, on which the hardware complexity and the bandwidth of the digital circuitry are mainly dependent. We want to reduce the sampling rate as much as possible without causing much error in the detected envelope of the focused signal, and hence it is very important to analyze the resulting detection error. For this purpose, we will concentrate on the Sampling-Sum-Detection process instead of Sampling-Delay-Sum-Detection process. Let us first investigate the reduction methods using the conventional uniform sampling technique. Figure 2 shows the Sampling-Sum-Detection process for this case. In this figure, all the N channels are represented, by a single line with a crossed slash and the delay processing is not shown. The sampling rate fs must be greater than the Nyquist rate to reconstruct the original signal, or f, > fN the center frequency and B is the bandwidth of the recetv’ eJ’ultr=asZG.B ‘X-CIZZe~“tlZ sampling rate can be reduced below fNyq,, since only the envelope of the focused’signal is needed in the ultrasound B-scan imaging system. When the frequency-translated signal fM (t) is sampled with a frequency fs, we have a periodic repetition (with a period of f,) of the spectrum of fM (t) as shown in figure 3(c). To reconstruct the envelope, there must not be frequency aliasing on the baseband which is bounded from -B/2 to B/2. There are two possible cases satisfying this requirement, as shown in figures 3(c) and 3(d), from which the allowable range of f, is given by fo+B/2
< 2fo-B
(Q > 1.5)
(Fig. 3(c))
(5)
0%. W-0)
(6)
or
f, ’ WI3 + B
The case of Eq. (6) is not useful. For the case of Eq. (5), the sampling rate can be reduced to fNyq,/2, if the quality factor Q of the transducer is greater than 1.5. (For actual signals, the bandwidth B is not ideally bandlimited and must be defined as the frequency range outdside which the energy is negligible.) For a narrowband application, as in a Doppler imaging system, the sampling rate can further be reduced according to the quality factor of the employed pulse. The detected envelope A(kT,) expressed as A (kT,) = +A
(kT,) cos[(wo-oc)kTs
+$I]
(7)
involves some error due to the frequency-dependent attenuation. In the real situation, the phase component + in Eq. (1) is not constant and the center frequency f o varies due to multiscattering, frequency-dependent attenuation, and other phenomena. That is,
‘This applies for dual-port memory type FIFO’s; for standard FIFO’s, the length may increase substantially because of the fall through time.
4
however,
DIGITAL
PHASED
SYSTEM
Focusing with uniform
Fig. 2
the modulating carrier the received echoes.
ARRAY
frequency f,
sampling.
can not be identical
to the center frequency fa of
In another method, the signals are mixed to a lower frequency md to reduce the sampling rate by multiplying the signals with a sinusoidal carrier COSW,~ followed by filtering out the high frequency component to obtain fi(t)
= Ai(t--7i(t))~~.~(~dt
- co,?;(t)
+ +)
(8)
where od = wo-oC. Hence, the modulated echoes must be delayed by (o~/w~)T~ instead of TV. However, this may cause the focusing error, since the center frequency varies along depth due to attenuation. Moreover, it is very difficult to implement the balanced modulators with identical characteristics for all channels, which are required to satisfy the dynamic range and the bandwidth of the ultrasound echoes.
FIf(t) I ALLrLf 0
f0
(a)
fo+Bnc
f, <2
FIfM(t)l &iLL 0
fg -B
fa
F{fMfkTs)l
f, - 2 fo : 812 (4
Fig. 3
>2 fo+B
F{fM(kTs)l
f, -
I
fs-2
2 fo
W
2 f.
- B/2
f. - B/2
(a) Fourier transform of a focused signal. (b) Fourier transform of the frequency translated signal. (c) Spectrum of fM(kT,) for the case in which Eq. (5) is satisfied. (d) Spectrum of fM(kT,) for the case in which Eq. (6) is satisfied.
SONG AND PARK
For these reasons, uniform sampling methods are difficult to reduce the sampling rate in the ultrasonic medical imaging. Some bandwidth sampling methods can be used to reduce the sampling rate [7,8], among which the second order sampling method has widely been used [2,9]. In the next section, we analyze the limitations of this method and suggest a modified second order sampling technique. We also suggest a new quadrature sampling method for digital imaging systems.
III. SAMPLING
BATE
REDUCTION
BY BANDWIDTH
SAMPLING
To reconstruct the envelope of a bandlimited signal, the sampling rate must be greater than twice the maximum frequency component according to the conventional uniform sampling theorem. However, since the bandwidth of the envelope is much less than that of the original signal, it is plausible to reduce the sampling rate to the bandwidth. This can be achieved by using some bandwidth sampling methods such as the second order, quadrature, and analytic sampling techniques. Among these, the analytic sampling method is not suitable to ultrasound imaging because of the requirement of a Hilbert transformer for each channel, while the others are. The conventional quadrature sampling is illustrated in figure 4(a), in which the two modulated signals
(4
I sin wet
‘TS
(W
(4 Fig. 4
Sin’w,
kTs
Digital beamforming using the quadrature sampling technique. (b) A conventional method. (c) A modified method - sampling and LPF are exchanged. (c) Hardware-reduced scheme of (b).
6
DIGITAL
PHASED
ARRAY
SYSTEM
are low-pass filtered, yielding in-phase and quadrature phase components and then can be sampled with the minimum rate of twice the envelope bandwidth. However, this
method involves following practical problems: (1) Baseband focusing results in poor resolution (2) Two analog balanced modulators are needed for each channel (3) Two LPF’s are needed for each channel (4) Two ADC’s for each channel and two adder blocks are needed. In baseband focusing, we can avoid the degradation of lateral resolution by mixing the reflected signals with quadrature carriers that have an additive phase term, tiara in Eq. (S), which is different for each channel and varies with time. This requires a complicated phase control circuitry for the quadrature carrier signals; otherwise, problems (1) degrades the resolution. Also, the other problems increase the system complexity. The conventional quadrature sampling method shown in figure 4(a) can be modified to the structure of figure 4(b) to solve problem (1) by exchanging the sampling and LPF. This can further be modified to figure 4(c), in which one ADC for each channel and only two LPF’s for the whole imaging system are required and thus problems (3) and (4) are solved. Also, only one balanced modulator is necessary, which can be implemented simply using the digital memory as a lookup table. As a result, all the problems are eliminated. The only limitation in the final scheme is the increased sampling rate. Since the sampling and the LPF must be exchanged to effect the envelope reconstruction, the resultant sampling rates are subject to Eqs. (5) and (6); that is, the minimum sampling rate is increased from the signal bandwidth B to
f
o+B/2.
As an alternative approach, the second order sampling technique can be used to reduce the sampling rate, in which, as shown in figure 5, a pair of two samples are obtained by a uniform sampling on the first channel and a delayed sampling on the second channel. As a special case, when we use a uniform sampling rate and a delay defined by [7,8] r,
= .-!.-
< B-’
,
1=+1,+2,...
2fo
then the two samples can be expressed
(104
kT;
kT,-a
Fig. 5
A general scheme of the second order sampling method.
SONG AND PARK
Noting that these are samples of the quadrature components of the signal and that for the high Q signal, the quadrature components vary only slowly, we get
and hence a good approximation
of the envelope is obtained by
&kT,)= vf (kT,)+ f;(kT,-a)]“* ,
WI
which can be readily computed. This technique has been applied to the digital imaging system as shown in figure 6(a) [2,9], in which, problems (l), (2), and (3) are solved and problem (4) can also be eliminated in the modified scheme as shown in figure 6(b), in which one ADC is used for two samples and thus the digital processing rate is increased now twice on average as compared to the case of figure 6(a). However, since the center frequency of the reflected ultrasound changes, the requirements of Eq. (9) can not be satisfied strictly. In order to solve this problem, we change T, and a in accordance with the center frequency so that the two samples are now expressed as follows:
f2(kTS -a)
= A (kT, -a)cos(y,kT,
-~,a++)
= A (kT, -a)sin(wukT,
+&)
(14)
kTs, I kTs-a (b)
Fig. 6
(a) A simplifeid envelope detection scheme using the second order sampling. (b) A second order sampling scheme using one ADC.
8
DIGITAL
PHASED
ARRAY
SYSTEM
where C$ = ~F/~-w,,cx+~ = A+++. Substitution of Eqs. (13) and (14) into Eq. (12) yields the following approximation for the squared envelope:
.P(kT,) = ff(kT,) + &kTs-a) l+cos2(o&T,+~) = A2(kTs)
=
l-cos2(wOkTs + A2(kT, -a)
2
A2(kT,)+A2(kT,
+$ )
2
-a)
2
A*W,)
+ ---cos2(w&T, 2
++)-
A*(kT, -a) cos2(w&T, 2
which can be reexpressed as follows, when A$ is negligible i’(kT,)
= A:(kTs -a/2)
Af(kT,)
=
+ Ae2(kTs -d2)cos2(wOkTs
+& )
(1%
or $ = $ : +$ )
(16)
where A’(kT,)
+ A2(kTs-a) >
2 A’(kT,)
- A2(kTs-a)
Ae2(kTs) =
(174
(17b)
2
Note that the error term, A,‘(.), in Eq. (16) is negligible for high Q signals. But high frequency components in Eq. (15) are not negligible because of the difference of C$ and $. In both cases, we can extract the term Af(kT,) as a good approximation to the envelope by filtering out the high frequency components, which, to be successful, requires the sampling rate to satisfy Eq. (18) (th e only change in figures 3(c) and 3(d) is the increase of bandwidth from B to 2B due to the square operation), f,+B
< f, < 2fO-2B
(Q > 3) ,
W)
So far, we have discussed the limitations of the quadrature sampling techniques and suggested some modified methods. For the application to sector scanning using a phased array, the second order sampling techniques may be inadequate in view of hardware complexity, since two ADC’s for each channel as can be seen figure 6(a) and two N channel digital adders are required. In the next section, we propose a new architecture of the digital phased array system, which employs the modified quadrature sampling technique (Fig. 4(c)). The resultant performance measures for the various sampling techniques discussed above are compared in table I.
9
SONG AND PARK
Table I. Comparisons of various sampling techniques Detection error
g
large Quadrature sampling
f,>B
very high
2nd order sampling
f,>lfo>B 1=1,2,...
high
no FJdependent
no
IV. PROPOSED
DlGITAL
PHASED
SYSTEM
AND EXPERIMENTS
Though the sampling rate reduction techniques given in table 1 can reduce the amount of digital memory, the bandwidth of the ADC, digital adders, and other digital circuitry, the memory addressing and the interpolation circuits are still required in the structure of figure l(a). These can be completely eliminated, however, by the use of SCG in the PSDF structure of figure l(b), which can be implemented with much less hardware requirements than the addressing logic and interpolators. The resultant architecture of a new phased array system is shown in figure 7, where the transmit-trigger pulses for the high voltage pulser for the respective array elements are generated by the SCG with proper delays so that transmit focusing is achieved at a specific depth along a given steering direction. Except for this SCG, all other parts in this architecture are very straightforward. Thus, it is most important to realize the SCG as simple as possible. In the following, we describe a simple realization of the SCG.
Transmit-trigger
Fig. 7
pulse
The proposed digital beamforming sampling method (Fig. 4(c)).
10
scheme using the modified
quadrature
DIGITAL
PHASED
ARRAY
SYSTEM
The most effective way to generate focused sampling clocks seems to be simply reading digital memories, into which the delay patterns for focusing are written. In the digital memory matrix as shown in figure 8, the l’s in the i-th column define the sampling times for the i-th channel (i=1,2, ....N). and the set of the j-th l’s in the successive columns defines the correct sampling times for the j-th focal point. In this case,
1 st channel --
.
Samplil
Master
0
i
Digital memory
Exact sampling time of some channel for focusing
Bit pattern in a column of memory
; ! i4-g
1;
0
1
0
1
: Maximum delay error
03 Fig. 8
Generation of multirate sampling clocks. (a) Delay patterns are stored in memories. (b) From the top figure, exact sampling time for some channel, actual sampling clock, and the bit pattern in a column of memory. (Maximum delay quantization error is determined by the period of the master clock.)
11
SONG AND PARK
the length and amount of memory are given by LSCG
= 2 . (max.
MSCG
= N XL,,,
imaging
where c is the ultrasound velocity addressing counter in the SCG.
depth ) .fM
and f,,,
/c
:
length
(194
:
amount
Wb)
is the master clock
frequency
for the
The delay quantization error of this sampling clock is dependent on fnr , and the maximum delay error (peak-to-peak error) is l/f, as can be seen in figure 8(b). To reduce the delay quantization error, the master clock frequency must be increased, in which case two blocks of memories may be necessary, and by switching them, the master clock frequency can be increased to 2.fM. (In this case, for example, if fM is 25 MHz, the maximum delay error is 20 ns, which is less than l/Sf o for a 6.25 MHz transducer.) For a maximum imaging depth of 20 cm and a master clock of 50 MHz, the length (Eq. (19)) is 12987 (< 16K), and hence the total memory size is 16K X N/2, since focusing delays are symmetric to the center element of the N-element array. In the imaging scheme of figure l(a), the amount of data memory is MSCG X (bit number of data) and complex memory addressing logic and interpolation hardware are needed. For example, with a 64-element phased array, eight 8K X 8 SRAM’s with maximum access time of 40 ns are required for the SCG. The most severe drawback of using the SCG for steering is that the memory size increases linearly with the number of steering angles, since the delay patterns are different for different steering angles. To obviate this problem, we will separate the steering and the focusing delays [4]. Strictly speaking, the focusing delay changes with the steering angle. However, the focusing delay error can be kept within an acceptable value (say, less than 1/16f u), if we divide the total steering angle into a few groups and for each group a slightly different focusing delay is employed. The focusing delays are first achieved by the SCG of figure 8 and then the steering delays are added on the focused clocks. Two realizations are conceivable; reading each column of the memories in SCG after steering delays of the channel, or reading all columns simultaneously followed by delaying them. The former method requires individual memory and address counters for all N channels. The latter can be implemented by attaching a number of N FIFO’s to the SCG as described above and delaying their
Channel SCG for focusing .
:
DIGITAL
PHASED
ARRAY
outputs linearly, as shown in figure 9. The maximum MLFIFO
SYSTEM
FIFO length is given by
= fan(e,,,/2).(0/2).f~/c
(20)
where 0,,, is the maximum steering angle and D denotes the aperture size. For a 3.5 MHz 64-element phased array, the maximum length of Eq. (20) is leas than 256 when can easily be 8 max = 45“ and fM = 50 MHz. Hence, the Read-Start-Controller implemented using presettable 8 bit counters. As a result, the new SCG enables fully digital beam steering and dynamic focusing for the sector scan imaging. In order to verify the the proposed digital imaging system, we have performed some preliminary experiments by implementing an experimental system as shown in figure 10, in which an &element linear transducer with a center frequency of 2.25 MHz and an element spacing of 1 mm was excited with transmit steering and focusing delays. A line target of diameter 8 mm was placed at a depth d=5.7 cm along a direction 0 = 0, and then 8 = -5’. The reflected signals were sampled by S-bit ADC’s with receive steering and dynamic focusing delays obtained from the SCG and fed to the FIFO’s The SCG was implemented for 8 channels with a maximum master And the FIFO outputs were addeded by a digital clock frequency up to 30 MHz. adder and stored in memories which were interfaced to VAX-11/750 computer. In the experiments, we used several different sampling rates. At first, a sampling rate of 12.6 MHz was used to obtain the correct signals and their envelopes. (Actually, we constructed the system with a maximum sample rate of 15 MHz, so that a transducer of a center frequency up to 5 MHz can be used without requiring any sampling rate reduction technique.) Figures 11(a) and 11(b) show the waveforms and envelopes, respectively, of the pulse echo from the target located at d-5.4 cm along 0 = -5’ (dynamic focusing was applied, of course). The -6 dB bandwidth of the signal was 1.2 MHz. The detected envelopes for other sampling rates are also depicted in figure 11(c) through 11(e), where we see that the envelope for f,=2.965 MHz* shows a close agreement to the correct envelope (Fig. 11(b)), because this sampling rate satisfies the requirement of Eq. (5) or 2.85 MHz
< f, < 3.3 MHz.
(22)
Linear TRD (8 elements)
Transmit-trigger
pulse
Fig. 10
and scan
An experimental
system.
*This frequency was used, although f,=3.075 MHz is desirable, limitation of available frequency from the master clock.
13
conversion
because of the
SONG
AND PARR
(C)
fs = 2.52
MHz
f .q = 2.965
MHz
67.5 (a) fs = 12.6 MHZ
(d)
I 73.4
67.5
W
w
fs=12.6MHz
f
I ;
I
67.5 (e)
Fig. 11
73.4 fs =3.269
ps
MHz
Received signals and their envelopes for various sampling
rates.
On the other hand, the envelope for f,=2.52 MHz significantly deviates from the correct one and the envelope for f,=3.289 MHz shows slightly enhanced high frequency components due to the frequency aliasing effect. Figure 12 shows the measured steering beam patterns in a sector coordinate for f,=12.6 MHz when a wire target is placed at d=5.7 cm along t3 = O” and the beam is steered from 0= -7O to +7” with an increment of lo. Figure 13 shows the interpo-
14
DIGITAL
PHASED
ARRAY
SYSTEM
+ 7"
Fig. 12
Sector scanned beam pattern for a wire target placed at d=5.7 O=o”.
cm along
lated beam patterns for f,=2.96 MHz in a Cartesian coordinate of the sector scanned image when the wire target is placed at d=5.4 cm along u=-5’ and the beam is steered from 0= -12” to + 12” . Both figures show the expected results, while figure 13 shows grating lobes for 8 > 0, which is attributable to the fact that for a certain range of positive scan angles the wire target reflects a strong ultrasound pulse due to the first grating lobe in the negative angle of the Point-Spread-Function (PSF) [lo].
Fig. 13
Beam pattern of a sector scanned image for a wire target placed at d=5.4 cm along 6=-5’.
15
SONG AND PARK
From the above experiments, it is seen that the proposed digital phased array system can achieve dynamic focusing and steering simultaneously with a reduced sampling frequency and an enhanced resolution of the sector-scanned image.
V. CONCLUSIONS We have presented a new digital phased array system using the PSDF scheme which performs real-time dynamic focusing and steering. The proposed method for generating the sampling clocks can replace the bulky memory and interpolation circuits required in conventional systems, with much less hardware requirements. It was shown that the commonly-used second order sampling technique for sampling rate reduction cause detection error of high frequency components, which can be negligible for low Q signals. This detection error can be eliminated in the proposed quadrature sampling technique with a slightly increased sampling rate (but the sampling rate is still half the Nyquist sampling rate of the received signal). In the view of its hardware complexity, the second-order sampling technique is unsuitable for a phased array system using a linear array transducer, since it needs two ADC’s for each channel and beamforming blocks. From the preliminary experiments for the proposed system, it was verified that the sampling rate and hardware requirements can be much reduced. A practical instrument with 64 array elements is under construction at our laboratory.
REFERENCES
[l]
Gehlbach, S. M. and Alvarez, R. E., Digital ultrasound imaging techniques using vector sampling and raster line reconstruction systems, Ultrasonic Imaging 3, 83107 (1981). [2] Mucci, R. A., A comparison of efficient beamforming algorithms, IEEE Trans. Acoust. Speech Signal Processing. ASSP-32, 548-558 (1984). [3] Peterson, D. K. and Kino G. S., Real-time digital image reconstruction: A description of imaging hardware and an analysis of quantization errors, IEEE Trans. Sonics Ultrasonics W-31, 337-351 (1984). [41 am, Y. G and Park, S. B., New dynamic focusing scheme for ultrasound scanners, Electronic letters 23, 181-182 (1987). [5] Kim, J. H., Song, T. K., and Park, S. B., A pipelined sampled delay focusing in ultrasound imaging systems, Ultrasonic Imaging 9, 75-91 (1987). [6] Manes, G. F., Atzeni, C., and Susini, C., Design of a simplified delay system for ultrasound phased array imaging, IEEE Trans. Sonics Ultrasonics W-30, 350-354 (1983). [7] Linden, D. A., A discussion of the sampling theorem, Proc. IRE 47, 1219-1226 (1959). [8] Grace, 0. D. and Pitt, S. P., Sampling and Interpolation of bandlimited signals by quadrature methods, J. Acoust. Sot. Am. 48, 1311-1318 (1970). [9] Powers, J. E., Phillips, D. J., Brandestini, D. J., and Sigelmann, R. A., Ultrasound phased array delay lines based on quadrature sampling techniques, IEEE Trans. Sonics Ultrasonics SU-29, 287-295 (1980). [lo] Macovski, A., Ultrasonic imaging using arrays, Proc. IEEE 67, 484-495 (1979).
16