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A sonographic technique to reduce beam distortion by curved interfaces
Uhrasoundin Med & Biol Vol. 15, No. 4, pp. 375 382. 1989 Printed in the U.S.A.
0301-5629/89 $3.00 + .00 co, 1989 Pergamon Press plc
OOriginal Contribution A SONOGRAPHIC TECHNIQUE TO REDUCE BEAM DISTORTION BY CURVED INTERFACES G . KOSSOFF, D . A. C A R P E N T E R , D . E. ROBINSON, D . O S T R Y af a n d P. L. H O Ultrasonics Institute, Sydney, Australia t Division of Radiophysics, CS1RO, Sydney, Australia ( Receiw,d 25 February 1988; in final fi?rm 10 November 1988)
Abstract--Ultrasonic beams are distorted during propagation between two media with different velocities if the traversed interface is curved within the ultrasonic beamwidth. The distorting effects of various interfaces on a beam generated by a multi-element transducer are analyzed and a technique to reduce these by controlling the time delays to the individual elements is presented. Key Words: Beam computation, Beam correction, Ultrasonic imaging.
All sonographic imaging equipment is designed on the assumption that the velocity of propagation of ultrasound in soft tissue is constant. In fact the velocity varies from 1450 m / s in fat to over 1600 m / s in tissues rich in collagen. Although the propagation through a flat interface does not distort the shape of the ultrasonic beam, it does give rise to effects such as range shift and beam deflection. Distortion of the ultrasonic beam also takes place if the interface is curved within the ultrasonic beam width. This distorts the geometry of the displayed structure, smears the resolution and in the extreme case can give rise to duplicate image artifacts ( Buttery and Davison 1984; Muller et al. 1984; Yagisawa et al. 1986). The effects on the beam include a s y m m e t r i c widening o f the beam and increase in side lobes level leading to further image degradation ( Robinson et al. 1981 ). When a flat linear array transducer is applied to the anterior abdominal wall, the effect is to compress the subcutaneous layers and flatten the superficial side o f the abdominal muscle, as shown in the CT scan of Fig. 1. These parallel flat layers have no detrimental effect on the transmitted beam shape. However the curved posterior wall of the muscle will have a defocusing and distorting effect on the beam shape. Several techniques have been described to compensate for distortion due to propagation through curved interfaces. These include interactive correlation techniques and estimate of least mean square error to determine the properties o f the interface and to correct for the aberrations that are introduced
(Hirama et al. 1982; Hirama and Sato 1984). Although some success was achieved, the methods involved extensive calculations or apply to limited regions of the image (Gamboa-Aldesco et al.). Phase correction techniques following measurement of the waveform of the transmitted signal and on-line phase correction for propagation through a flat layer have also been described (Smith et al. 1979; Smith et al. 1986). These have concentrated on correction for propagation through bony layers where gross impedance and velocity mismatches are present and have shown to give partial compensation by the use of relatively simple techniques. Most m o d e r n sonographic e q u i p m e n t uses a multi-element transducer to generate the ultrasonic beam. This multi-element configuration allows the implementation of a sonographically based compensating technique to refocus the beam by adjusting the time delay to the individual elements and potentially reduce many of the current image degrading effects. P R I N C I P L E OF C O M P E N S A T I N G TECHNIQUE
Figure 2(a) illustrates how beam distortion is i n c u r r e d d u r i n g p r o p a g a t i o n t h r o u g h an angled curved interface. As shown, the beam is generated by eight elements which, for simplicity, are shown to be energized simultaneously to generate a plane wave in the first, slow velocity, medium. The distortion of the beam occurs during the propagation through the 375
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Ultrasound in Medicine and Biology
Volume15, Number 4, 1989 As illustrated, the transmission sequence of the compensating technique is determined by the geometry of the interface and the velocity in the two media. The former may be obtained sonographically with the equipment functioning in the original mode with its aperture adjusted to provide the o p t i m u m beam at the position of the interface, the latter from a priori information about the acoustic properties of the two media. The principle may be extended to apply to focused beams by adding the compensating timing sequence to the one being used for focusing. It may also be used in situations in which attenuation by the first
Fig. 1. Anatomy of the subcutaneous tissues at the level of the pelvic brim with compression of the subcutaneous fat by a simulated linear array transducer.
SLOW
. . . . . . . . . ~ ~
PLANE WaVE l
NIERFACE ~ / / / / ' 7 / ' / / / " / ~
~
Wh/EFRON]'S ~1
~ T T R A N S ' n O N
transition zone. This zone is defined as the region in which the wavefront closest to the interface, in the figure element 8, traverses the interface and begins to propagate in the second, fast velocity, m e d i u m while the energy from the furthest element, in the figure element l, still propagates in the first medium. Because of the velocity difference, the wave front from element 8 traverses a longer distance thereby angling the wavefront away from the original direction o f propagation. Also because the interface is curved the center elements (4 and 5 ) travel a greater distance at the higher velocity in the transition zone than would have been the case for a flat interface thereby distorting the plane wave into a divergent one. Figure 2 ( b ) illustrates the principle o f the compensating technique which allows the transmission of a plane wave in the second medium. As shown, the energizing sequence is altered so that an angled convergent wave is generated in the first medium. The timing of the sequence is such that the longer distance in the second medium traversed by the wavefront from elements 5 to 8 is equal to the advance distance due to earlier energizing plus the shorter distance in the transition zone traveled by the wavefront from elements 1 to 4. This effectively converts the angled convergent b e a m into a plane wave in a m a n n e r which is analogous to the plane correction technique proposed for correction due to propagation through bony layers (Phillips et al. 1975). By applying an additional focusing delay pattern, a focused, convergent beam can be obtained.
~
ZONE
FAST
DIVERGINGWaVE (a)
DI2113114-1D[] [] CONVERGING SLOW ~
WaVE ~-.,.n'ntflTt~.,>/////~
RroRFACC~ ~ / / / / / / / / / / / ~ y
wAErRO, n-s ./TRA~nON ZONE
FAST PLANE WavE (b)
Fig. 2 (a) Beam divergence generated by propagation through a curved interface. (b) Compensation technique by which a convergent beam in the first medium is reformed into a plane wave in the second medium.
Reduced beam distortion • G. KOSSOFFet al. medium may change the amplitude apodization distribution used to shape the beam by including an appropriate amplitude sequence. The compensation may also be applied in a sequential m a n n e r to compensate for beam distortion in propagation through two or more interfaces. Finally, reciprocity considerations dictate that a similar timing sequence in reception will bring into focus echoes originating in the second medium. In some cases o f complex geometry, multiple equal paths may exist between the transducer, the interface and the field in the second medium. In those cases the beam cannot be reformed by this technique. Such instances are however seldom encountered in sonographic examinations with the size of aperture of beams c o m m o n l y utilized and the geometry o f the interfaces between tissues. T H E O R E T I C A L AND E X P E R I M E N T A L RESULTS The beam reforming property of the compensating technique was evaluated by theoretical analysis and experimental measurement o f the beamwidth following propagation through curved interfaces. The experiments were performed on a medium cost commercially available linear array scanner. In this equipment the ultrasonic beam is formed by energizing, with uniform amplitude, eight elements of the array. The beam is focused in the plane o f the scan by a spherical time delay sequence corresponding to a geometric focus o f 100 m m while a lens is used to provide a weakly focused beam in the other plane. The center frequency of the array is specified as 3.5 M H z while the width and the height of the elements are given as 1.8 and 12 mm, respectively. The nature o f the beam transmitted into normal saline at 37°C (v = 1540 m / s ) was investigated using a 1 m m nominal diameter polymer hydrophone. The waveform of the transmitted pulse at the geometric focus o f 100 m m is shown in Fig. 3. Spectral analysis o f the pulse indicates that the center frequency, defined as the mean o f the two frequencies at which the amplitude is 3 dB down on m a x i m u m , is 3.2 MHz. Due to mechanical coupling an energized element gives rise to a mechanical aperture which is greater than the width o f the element. Measurement of the beampattern of a single element showed that it could be approximated by one generated by a uniformly vibrating element 2.2 m m in width and 12 m m in height. The effective radius of curvature of the cylindrical lens providing weak focusing in the height plane was estimated to be 200 mm. The shape o f the beam was calculated using a
377
i i t
\
Fig. 3. Waveform of transmitted pulse at position of acoustic focus. combination of ray tracing and Rayleigh diffraction theory. Analysis of the shape of the beam is carried out in the scan plane of the array. Each element is treated as an independent rectangular transducer. Starting with the basic equation for the initial response of the field Cs( R , t )
= ~ 6(t-R/c_____~)d S . 27rR
,b,(R,f) =
~s ~e -jkR d S
pi = - p . j
• 2rrc g cb,(R,f).
The calculations are based on the assumptions that the field point is being evaluated in the Fresnel field for the element height and in the far field for the element width. Using coordinates defined in Fig. 4, the relative field contribution Pi due to a single ele-
i Fig. 4. Coordinates of the field used for the calculation of the beampattern: a is the effective element width, b is the element height in the out-of-scan plane, z is the perpendicular distance to the field plane, x the offset of the field point from the centre line of the element, and R is the slant range from element to field point.
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Ultrasound in Medicine and Biology
ment in a homogeneous medium is determined by the product of five factors. These are an amplitude factor which is inversely proportional to the square root of R for the range spreading, cos O due to the baffle, an amplitude factor proportional to a(sin x)/x from the polar pattern due to the element width, an amplitude factor calculated from the Fresnel integral due to the element height, and a phase factor due to the distance from the element to the point (Ostry, personal communication 1988 ). The equation governing these relationships is given by: Pi
O~
~-~-~
[ax].F[Trb2]e-JkR
COSO" a sin c ~-~
[ 4R~ J
where ksin
271"
sin 7rX
cX - - -
F(X)
7rX
= [C(X)-jS(X)]
r2~7~
S(X)=
0sin
u ~ du
The total field strength is the sum of contributions from all transducer elements. Because the calculations are carried out in the frequency domain, the response at each field point is multiplied by the spectrum of the transmitted pulse shown in Fig. 3 before being transformed to the time domain to obtain the pressure waveform at the field point. Finally the pressure waveform is peak detected and the maximum value is taken to represent the beampattern at that point. In calculating the field following propagation through an interface, account is taken of the refraction at the interface in finding the ray path taken by the beam. The azimuth angle of the ray and the path length from the element to the field point is computed and used to evaluate the field contributions as in the case for the homogeneous medium. The calculated and experimentally measured beampattern at the geometric focus of 100 mm for the eight transducer elements of 2.2 mm width radiating into a medium with velocity of 1540 m / s is shown in Fig. 5 (a). The aperture formed by the total width of the transducer determines the shape of the main beam and the position of the side lobes. The
Volume 15, Number 4, 1989
first side lobe, at the - 3 2 dB level, lying at a lateral offset of 5 mm is clearly identified. The second side lobe at twice the lateral offset, however, is barely visible in the general skirt of the beam. More laterally, at the - 4 6 dB level, lie the first grating lobes associated with the interelement spacing of the transducer. There is good agreement between theory and experiment. Figure 5 (b) illustrates the calculated beampattern following propagation through a flat interface at normal incidence into a second medium with velocity of 1600 m/s. No significant change in beampattern is noted. Figure 5 (c) shows the beampattern following propagation through a flat interface inclined at 30 °. The axis of the beam is displaced by 1.5 mm due to refraction, but apart from some small loss of symmetry in the skirt and the grating lobes, it is essentially unchanged. Figure 5(d) shows the calculated and experimentally measured beampattern after propagation through an interface that is cylindrically curved, with its center of curvature at one edge of the beam. The main lobe is displaced 1.5 mm by refraction, it is widened, the side lobe levels have been increased while the skirt and the grating lobes have been elevated and have lost their previous symmetry. Figure 5 (e) shows the beampattern following propagation through two symmetrically positioned cylindrically curved interfaces, the velocities in the media being 1450, 1600, and 1540 m/s, respectively. Because of the symmetry of the interface the beam direction remains unchanged. The interfaces however cause degradation in the beampattern which include widening of the main beam and a greatly increased beamwidth at the - 4 6 dB level of performance. Figure 5 (f) shows the beampattern following the sequential application of the compensating technique. The beampattern, which is illustrative for other cases of compensation, has been recentralized and reformed and is nearly identical to the one shown in Fig. 5 (a). The value of beamwidth at various dB levels below maximum is given in Table 1 and shows that the beam is widened by 100% at the - 3 0 to - 4 0 dB level of performance following propagation through the curved interfaces. Techniques for improving the beampattern include use of narrower elements to reduce the grating lobes and of amplitude apodization of excitation to reduce the side lobes. Figure 6 illustrates only the calculated improvements obtained by the use of these techniques. Figure 6(a) shows the initial beampattern, that is, of the transducer consisting of eight, four wavelength wide elements. Figure 6 (b) illustrates the beampattern of a transducer consisting of 32 elements, one wavelength in width. Because the total aperture remains unchanged, the main lobe and the
I
....
Fig. 5. (a) Beampattern at the geometric focus in a homogeneous medium with velocity of 1540 m / s . The dots indicate experimentally measured values. The first side lobe and grating lobe lie at a lateral offset of 5 and 26 ram. (b) Beampattern after propagation through a flat interface at normal incidence at a distance of 45 mm from the transducer into a medium with velocity of 1600 m/s. No change in beampattern is noted. (c) Beampattern after propagation through a flat interface inclined at 30 °. Apart from a small displacement no change in beampattern is noted. (d) Beampattern following propagation through a convex cylindrically curved interface radius 20 mm. The interface is offset such that its centre of curvature is located at the right hand edge of the transducer. The beam is displaced and has undergone significant distortion. (e) Beampattern following propagation through two cylindrically curved interfaces, radius of each interface being 25 mm. The closer interface is concave and is 25 m m distant from the centre of the transducer, the further is convex and is 50 m m from the transducer. Because the interfaces are symmetric relative to the beam axis no displacement of the beam is noted. The shape however has been distorted. (f) Beampattern after propagation through two curved interfaces using sequential application of the compensating techniques. The beam has been essentially reformed. 379
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Ultrasound in Medicine and Biology
Volume 15, Number 4, 1989
Table 1. Beamwidth at various dB levels derived from curves shown in Fig. 4(a), (d), (e), and (f). Beam width in mm Transducer consisting of 8, 4~. wide elements Into 1540 m/s After propagation through one interface After propagation through two interfaces Following compensation
- 6 dB
- 1 0 dB
- 2 0 dB
- 3 0 dB
- 4 0 dB
- 5 0 dB
6
13.5
58.5
3
4
5
3.5
4.5
6.5
12
18
60
3.5 3
4.5 4
6 5
12 6
17 12
60 56
side lobes are unaltered but there is a major improvement in the skirt due to removal of the grating lobes. Figure 6(c) illustrates the beampattern using one wavelength wide elements energized with a Hamming apodization function which consists of a 92% cosine wave and a 8% step function. This apodization function is well known for its side lobe removal property, which is illustrated by the figure. The main lobe however has been significantly widened and there is a 12 dB axial loss in field strength. The balance between the triad of side lobe level, width of main beam and field strength is well known in antenna theory, the selection of level of performance between these parameters being determined by the nature of the application. Figure 6(d) shows the beampattern using an apodization function consisting of a 75% amplitude cosine wave and a 25% step function. Although some side lobes are present at the - 6 0 dB level, the main lobe has been widened only by a small amount and there is less axial loss in field strength compared to the Hamming apodization. Figure 6(e) shows the distortion in beampattern by a cylindrically curved interface on the previous beam. The beam is deflected by 1.5 mm, and widened, and there is loss in beam symmetry with an increase in side lobe level. Figure 6 (f) shows the beam essentially restored following application of the compensating technique. The value of beamwidth at various dB levels below maximum is given in Table 2. The marked improvement at - 4 0 to - 6 0 dB level of performance obtained by going to more narrow elements and use of amplitude apodization is illustrated. The apodization used in Fig. 6(d) gives a beampattern which is about 25% more narrow than that obtained with the Hamming apodisation. Propagation through a single cylindrical interface widens the beam uniformly by approximately 20%. DISCUSSION The performance of most imaging techniques may be improved if a priori information is incorporated. In the described technique this applies to the
- 6 0 dB
utilization of the a priori known value of velocity in the two media. Although this limits the general utilization of the method, a potentially important application of the technique is the reduction of distortion incurred during propagation through the subcutaneous tissues. In this case advantage may be taken of the constancy of anatomical and acoustical relationships, that is, the abdominal subcutaneous tissues of every individual consist of the skin, the subcutaneous fat, the abdominal muscles and possibly the interspersed and retro abdominal muscle fatty layers. The acoustic properties of these tissues are known. The only variables are their thickness and curvature and this may be derived from an initial conventional sonographic technique optimized for subcutaneous tissues examination. The results described in the previous section show that the compensating technique may be used to recentralize and refocus the beam over the range of velocities and geometries encountered in sonographic examinations and following propagation through at least two interfaces. The reforming properties extend to at least the - 5 0 dB level of performance, the range of beampattern shape utilized by high performance equipment (Maslak 1985). This result is obtained with the relatively coarse as well as the fine transducer element construction and with simple as well as complex excitations. The compensating technique has certain functional advantages. The timing sequence which is utilized is identical to the one used by high performance equipment to generate transmitted beams which may be focused at different depths and to dynamically focus the echoes in reception. Thus it may be implemented on such equipment without major change to their basic architectural design. Incorporation of automatic edge detection techniques to determine the geometry of interfaces and to calculate the required timing compensation would allow automatic focusing of the beam for its line of sight. Stepping these lines of sight in the conventional image focusing mode would provide automatic compensation for the whole image.
Reduced beam distortion Q G. KOSSOFFet al.
Fig. 6. (a) Beampattern of original transducer shown is Fig. 4 (a). (b) Beampattern from a transducer of same total width but using thirty two one wavelength elements. The grating lobes have been removed and the second side lobe is evident. (c) Beampattern using Hamming amplitude apodisation sequence. The side lobes have been reduced to - 8 0 dB level, but the main lobe has been widened and there is - 12 dB loss in axial field strength. (d) Beampattern using 25% step function and 75% cosine apodisation. The side lobes are at the - 6 4 dB level. The main lobe has suffered less degradation. (e) Distortion of beam shown in Fig. 5(d) by propagation through a cylindrically curved interface described in Fig. 4(d). (f) Beampattern following application of compensating technique. The beam has been recentralized and its shape has been essentially reformed.
381
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Volume 15, Number 4, 1989
Ultrasound in Medicine and Biology
Table 2. Beamwidth at various dB levels derived from curves shown in Fig. 5(b), (c), (d), (e) and (f). Beamwidth in mm Transducer
- 6 dB
32, 1~, wide elements 92% cosine, 8% step amplitude apodisation 75% cosine, 25% step amplitude apodisation After propagation through one interface Following compensation
- 1 0 dB
20 dB
- 3 0 dB
- 4 0 dB
- 5 0 dB
- 6 0 dB
3
4
5
6
12
19
38
4.5
6
8
9
l0
12
13.5
4
5.5
7
8
4.5 4
6 5.5
7.5 7
8.5 8
CONCLUSION U l t r a s o n i c b e a m s are d i s t o r t e d d u r i n g p r o p a g a t i o n t h r o u g h c u r v e d i n t e r f a c e s . T h e effects i n c l u d e beam displacement, asymmetric beam widening and i n c r e a s e in side l o b e a n d g r a t i n g l o b e level. T h e c o m p e n s a t i n g t i m i n g s e q u e n c e a l l o w s full r e c e n t r a l i z i n g a n d r e f o c u s i n g o f t h e b e a m t o its i n i t i a l s h a p e . S h o u l d t h e s e results h o l d in c l i n i c a l p r a c t i c e , t h e t e c h n i q u e holds promise to reduce the distortion effects inc u r r e d d u r i n g p r o p a g a t i o n t h r o u g h s u b c u t a n e o u s tissues.
REFERENCES Buttery, B.; Davison, G. The ghost artifact. J. Ultrasound in Med. 3:49-53; 1984. Gamboa-Aldesco, D.; Macovski, A.; Somewhere, G. Imaging through inhomogeneous media with a linear phased array; results and implementation. Ultrasonic Imaging 6:209-210; 1984. Hirama, M.; Ikeda A.; Sato, T. Adaptive ultrasonic array imaging system through an inhomogeneous layer. J. Acoust. Soc. Am. 71:100-109; 1982. Hirama, M.; Sato, T. Imaging through an inhomogeneous layer by
8.5 10 8
9.5 12 9.5
10.5 14 I1
least mean square error fitting. J. Acoust. Soc. Am. 75:11421147; 1984. Kossoff, G.; Carpenter, D. A.; Robinson, D. E. The subcutaneous tissues--A veil over good sonographic images. In: Bondestan, S.; Alanen, A.; Jouppila, P., eds. Proc. Euroson 87. Helsinki: The Finnish Society for Ultrasound in Medicine and Biology; 1987:364-365. Maslak, S. H. Computed sonography ultrasound annual 1985. In: Saunders, R. C.; Hill, M. C., ed. NY: Raven Press; 1985:1-16. Muller, N.; Cooperberg, P. L.; Rowley, V. A.; Mayo, J. Ultrasonic refraction by the rectus abdominus muscle: the double image artifact. J. Ultrasound Med. 3:515-519; 1984. Phillips, D. J.; Smith, S. W.; von Ramm, O. T.; Thurstone, F. L. Acoustical holography Vol. 6. In: Booth, N., ed. New York: Plenum Press; 1975:103-120. Robinson, D. E.; Wilson, L. S.; Kossoff, G. Shadowing and enhancement in ultrasonic echograms by reflection and refraction. J. Clin. Ultrasound 9:181-188; 1981. Smith, S. W.; Phillips, D. J.; von Ramm, O. T.; Thurstone, F. L. Some advances in acoustic imaging through the skull. Ultrasonic tissue characterization II. In: Linzer, M., ed. National Bureau of Standards Pub. 525; Washington DC: U.S. Government Printing Office; 1979:209-218. Smith, S. W.; Trahey, G. E.; von Ramm, O. T. Phased array ultrasound imaging through planar tissue layers. Ultrasound Med. Biol. 12:229-243; 1986. Yagisawa, H.; lshida, H.; Arakawa, H.; Masamune, O. Double image of the left portal vein. Jap. J. Med. Ultrasonics. 13, Suppl. II: 1077-1078; 1986.
0301-5629/89 $3.00 + .00 co, 1989 Pergamon Press plc
OOriginal Contribution A SONOGRAPHIC TECHNIQUE TO REDUCE BEAM DISTORTION BY CURVED INTERFACES G . KOSSOFF, D . A. C A R P E N T E R , D . E. ROBINSON, D . O S T R Y af a n d P. L. H O Ultrasonics Institute, Sydney, Australia t Division of Radiophysics, CS1RO, Sydney, Australia ( Receiw,d 25 February 1988; in final fi?rm 10 November 1988)
Abstract--Ultrasonic beams are distorted during propagation between two media with different velocities if the traversed interface is curved within the ultrasonic beamwidth. The distorting effects of various interfaces on a beam generated by a multi-element transducer are analyzed and a technique to reduce these by controlling the time delays to the individual elements is presented. Key Words: Beam computation, Beam correction, Ultrasonic imaging.
All sonographic imaging equipment is designed on the assumption that the velocity of propagation of ultrasound in soft tissue is constant. In fact the velocity varies from 1450 m / s in fat to over 1600 m / s in tissues rich in collagen. Although the propagation through a flat interface does not distort the shape of the ultrasonic beam, it does give rise to effects such as range shift and beam deflection. Distortion of the ultrasonic beam also takes place if the interface is curved within the ultrasonic beam width. This distorts the geometry of the displayed structure, smears the resolution and in the extreme case can give rise to duplicate image artifacts ( Buttery and Davison 1984; Muller et al. 1984; Yagisawa et al. 1986). The effects on the beam include a s y m m e t r i c widening o f the beam and increase in side lobes level leading to further image degradation ( Robinson et al. 1981 ). When a flat linear array transducer is applied to the anterior abdominal wall, the effect is to compress the subcutaneous layers and flatten the superficial side o f the abdominal muscle, as shown in the CT scan of Fig. 1. These parallel flat layers have no detrimental effect on the transmitted beam shape. However the curved posterior wall of the muscle will have a defocusing and distorting effect on the beam shape. Several techniques have been described to compensate for distortion due to propagation through curved interfaces. These include interactive correlation techniques and estimate of least mean square error to determine the properties o f the interface and to correct for the aberrations that are introduced
(Hirama et al. 1982; Hirama and Sato 1984). Although some success was achieved, the methods involved extensive calculations or apply to limited regions of the image (Gamboa-Aldesco et al.). Phase correction techniques following measurement of the waveform of the transmitted signal and on-line phase correction for propagation through a flat layer have also been described (Smith et al. 1979; Smith et al. 1986). These have concentrated on correction for propagation through bony layers where gross impedance and velocity mismatches are present and have shown to give partial compensation by the use of relatively simple techniques. Most m o d e r n sonographic e q u i p m e n t uses a multi-element transducer to generate the ultrasonic beam. This multi-element configuration allows the implementation of a sonographically based compensating technique to refocus the beam by adjusting the time delay to the individual elements and potentially reduce many of the current image degrading effects. P R I N C I P L E OF C O M P E N S A T I N G TECHNIQUE
Figure 2(a) illustrates how beam distortion is i n c u r r e d d u r i n g p r o p a g a t i o n t h r o u g h an angled curved interface. As shown, the beam is generated by eight elements which, for simplicity, are shown to be energized simultaneously to generate a plane wave in the first, slow velocity, medium. The distortion of the beam occurs during the propagation through the 375
376
Ultrasound in Medicine and Biology
Volume15, Number 4, 1989 As illustrated, the transmission sequence of the compensating technique is determined by the geometry of the interface and the velocity in the two media. The former may be obtained sonographically with the equipment functioning in the original mode with its aperture adjusted to provide the o p t i m u m beam at the position of the interface, the latter from a priori information about the acoustic properties of the two media. The principle may be extended to apply to focused beams by adding the compensating timing sequence to the one being used for focusing. It may also be used in situations in which attenuation by the first
Fig. 1. Anatomy of the subcutaneous tissues at the level of the pelvic brim with compression of the subcutaneous fat by a simulated linear array transducer.
SLOW
. . . . . . . . . ~ ~
PLANE WaVE l
NIERFACE ~ / / / / ' 7 / ' / / / " / ~
~
Wh/EFRON]'S ~1
~ T T R A N S ' n O N
transition zone. This zone is defined as the region in which the wavefront closest to the interface, in the figure element 8, traverses the interface and begins to propagate in the second, fast velocity, m e d i u m while the energy from the furthest element, in the figure element l, still propagates in the first medium. Because of the velocity difference, the wave front from element 8 traverses a longer distance thereby angling the wavefront away from the original direction o f propagation. Also because the interface is curved the center elements (4 and 5 ) travel a greater distance at the higher velocity in the transition zone than would have been the case for a flat interface thereby distorting the plane wave into a divergent one. Figure 2 ( b ) illustrates the principle o f the compensating technique which allows the transmission of a plane wave in the second medium. As shown, the energizing sequence is altered so that an angled convergent wave is generated in the first medium. The timing of the sequence is such that the longer distance in the second medium traversed by the wavefront from elements 5 to 8 is equal to the advance distance due to earlier energizing plus the shorter distance in the transition zone traveled by the wavefront from elements 1 to 4. This effectively converts the angled convergent b e a m into a plane wave in a m a n n e r which is analogous to the plane correction technique proposed for correction due to propagation through bony layers (Phillips et al. 1975). By applying an additional focusing delay pattern, a focused, convergent beam can be obtained.
~
ZONE
FAST
DIVERGINGWaVE (a)
DI2113114-1D[] [] CONVERGING SLOW ~
WaVE ~-.,.n'ntflTt~.,>/////~
RroRFACC~ ~ / / / / / / / / / / / ~ y
wAErRO, n-s ./TRA~nON ZONE
FAST PLANE WavE (b)
Fig. 2 (a) Beam divergence generated by propagation through a curved interface. (b) Compensation technique by which a convergent beam in the first medium is reformed into a plane wave in the second medium.
Reduced beam distortion • G. KOSSOFFet al. medium may change the amplitude apodization distribution used to shape the beam by including an appropriate amplitude sequence. The compensation may also be applied in a sequential m a n n e r to compensate for beam distortion in propagation through two or more interfaces. Finally, reciprocity considerations dictate that a similar timing sequence in reception will bring into focus echoes originating in the second medium. In some cases o f complex geometry, multiple equal paths may exist between the transducer, the interface and the field in the second medium. In those cases the beam cannot be reformed by this technique. Such instances are however seldom encountered in sonographic examinations with the size of aperture of beams c o m m o n l y utilized and the geometry o f the interfaces between tissues. T H E O R E T I C A L AND E X P E R I M E N T A L RESULTS The beam reforming property of the compensating technique was evaluated by theoretical analysis and experimental measurement o f the beamwidth following propagation through curved interfaces. The experiments were performed on a medium cost commercially available linear array scanner. In this equipment the ultrasonic beam is formed by energizing, with uniform amplitude, eight elements of the array. The beam is focused in the plane o f the scan by a spherical time delay sequence corresponding to a geometric focus o f 100 m m while a lens is used to provide a weakly focused beam in the other plane. The center frequency of the array is specified as 3.5 M H z while the width and the height of the elements are given as 1.8 and 12 mm, respectively. The nature o f the beam transmitted into normal saline at 37°C (v = 1540 m / s ) was investigated using a 1 m m nominal diameter polymer hydrophone. The waveform of the transmitted pulse at the geometric focus o f 100 m m is shown in Fig. 3. Spectral analysis o f the pulse indicates that the center frequency, defined as the mean o f the two frequencies at which the amplitude is 3 dB down on m a x i m u m , is 3.2 MHz. Due to mechanical coupling an energized element gives rise to a mechanical aperture which is greater than the width o f the element. Measurement of the beampattern of a single element showed that it could be approximated by one generated by a uniformly vibrating element 2.2 m m in width and 12 m m in height. The effective radius of curvature of the cylindrical lens providing weak focusing in the height plane was estimated to be 200 mm. The shape o f the beam was calculated using a
377
i i t
\
Fig. 3. Waveform of transmitted pulse at position of acoustic focus. combination of ray tracing and Rayleigh diffraction theory. Analysis of the shape of the beam is carried out in the scan plane of the array. Each element is treated as an independent rectangular transducer. Starting with the basic equation for the initial response of the field Cs( R , t )
= ~ 6(t-R/c_____~)d S . 27rR
,b,(R,f) =
~s ~e -jkR d S
pi = - p . j
• 2rrc g cb,(R,f).
The calculations are based on the assumptions that the field point is being evaluated in the Fresnel field for the element height and in the far field for the element width. Using coordinates defined in Fig. 4, the relative field contribution Pi due to a single ele-
i Fig. 4. Coordinates of the field used for the calculation of the beampattern: a is the effective element width, b is the element height in the out-of-scan plane, z is the perpendicular distance to the field plane, x the offset of the field point from the centre line of the element, and R is the slant range from element to field point.
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Ultrasound in Medicine and Biology
ment in a homogeneous medium is determined by the product of five factors. These are an amplitude factor which is inversely proportional to the square root of R for the range spreading, cos O due to the baffle, an amplitude factor proportional to a(sin x)/x from the polar pattern due to the element width, an amplitude factor calculated from the Fresnel integral due to the element height, and a phase factor due to the distance from the element to the point (Ostry, personal communication 1988 ). The equation governing these relationships is given by: Pi
O~
~-~-~
[ax].F[Trb2]e-JkR
COSO" a sin c ~-~
[ 4R~ J
where ksin
271"
sin 7rX
cX - - -
F(X)
7rX
= [C(X)-jS(X)]
r2~7~
S(X)=
0sin
u ~ du
The total field strength is the sum of contributions from all transducer elements. Because the calculations are carried out in the frequency domain, the response at each field point is multiplied by the spectrum of the transmitted pulse shown in Fig. 3 before being transformed to the time domain to obtain the pressure waveform at the field point. Finally the pressure waveform is peak detected and the maximum value is taken to represent the beampattern at that point. In calculating the field following propagation through an interface, account is taken of the refraction at the interface in finding the ray path taken by the beam. The azimuth angle of the ray and the path length from the element to the field point is computed and used to evaluate the field contributions as in the case for the homogeneous medium. The calculated and experimentally measured beampattern at the geometric focus of 100 mm for the eight transducer elements of 2.2 mm width radiating into a medium with velocity of 1540 m / s is shown in Fig. 5 (a). The aperture formed by the total width of the transducer determines the shape of the main beam and the position of the side lobes. The
Volume 15, Number 4, 1989
first side lobe, at the - 3 2 dB level, lying at a lateral offset of 5 mm is clearly identified. The second side lobe at twice the lateral offset, however, is barely visible in the general skirt of the beam. More laterally, at the - 4 6 dB level, lie the first grating lobes associated with the interelement spacing of the transducer. There is good agreement between theory and experiment. Figure 5 (b) illustrates the calculated beampattern following propagation through a flat interface at normal incidence into a second medium with velocity of 1600 m/s. No significant change in beampattern is noted. Figure 5 (c) shows the beampattern following propagation through a flat interface inclined at 30 °. The axis of the beam is displaced by 1.5 mm due to refraction, but apart from some small loss of symmetry in the skirt and the grating lobes, it is essentially unchanged. Figure 5(d) shows the calculated and experimentally measured beampattern after propagation through an interface that is cylindrically curved, with its center of curvature at one edge of the beam. The main lobe is displaced 1.5 mm by refraction, it is widened, the side lobe levels have been increased while the skirt and the grating lobes have been elevated and have lost their previous symmetry. Figure 5 (e) shows the beampattern following propagation through two symmetrically positioned cylindrically curved interfaces, the velocities in the media being 1450, 1600, and 1540 m/s, respectively. Because of the symmetry of the interface the beam direction remains unchanged. The interfaces however cause degradation in the beampattern which include widening of the main beam and a greatly increased beamwidth at the - 4 6 dB level of performance. Figure 5 (f) shows the beampattern following the sequential application of the compensating technique. The beampattern, which is illustrative for other cases of compensation, has been recentralized and reformed and is nearly identical to the one shown in Fig. 5 (a). The value of beamwidth at various dB levels below maximum is given in Table 1 and shows that the beam is widened by 100% at the - 3 0 to - 4 0 dB level of performance following propagation through the curved interfaces. Techniques for improving the beampattern include use of narrower elements to reduce the grating lobes and of amplitude apodization of excitation to reduce the side lobes. Figure 6 illustrates only the calculated improvements obtained by the use of these techniques. Figure 6(a) shows the initial beampattern, that is, of the transducer consisting of eight, four wavelength wide elements. Figure 6 (b) illustrates the beampattern of a transducer consisting of 32 elements, one wavelength in width. Because the total aperture remains unchanged, the main lobe and the
I
....
Fig. 5. (a) Beampattern at the geometric focus in a homogeneous medium with velocity of 1540 m / s . The dots indicate experimentally measured values. The first side lobe and grating lobe lie at a lateral offset of 5 and 26 ram. (b) Beampattern after propagation through a flat interface at normal incidence at a distance of 45 mm from the transducer into a medium with velocity of 1600 m/s. No change in beampattern is noted. (c) Beampattern after propagation through a flat interface inclined at 30 °. Apart from a small displacement no change in beampattern is noted. (d) Beampattern following propagation through a convex cylindrically curved interface radius 20 mm. The interface is offset such that its centre of curvature is located at the right hand edge of the transducer. The beam is displaced and has undergone significant distortion. (e) Beampattern following propagation through two cylindrically curved interfaces, radius of each interface being 25 mm. The closer interface is concave and is 25 m m distant from the centre of the transducer, the further is convex and is 50 m m from the transducer. Because the interfaces are symmetric relative to the beam axis no displacement of the beam is noted. The shape however has been distorted. (f) Beampattern after propagation through two curved interfaces using sequential application of the compensating techniques. The beam has been essentially reformed. 379
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Ultrasound in Medicine and Biology
Volume 15, Number 4, 1989
Table 1. Beamwidth at various dB levels derived from curves shown in Fig. 4(a), (d), (e), and (f). Beam width in mm Transducer consisting of 8, 4~. wide elements Into 1540 m/s After propagation through one interface After propagation through two interfaces Following compensation
- 6 dB
- 1 0 dB
- 2 0 dB
- 3 0 dB
- 4 0 dB
- 5 0 dB
6
13.5
58.5
3
4
5
3.5
4.5
6.5
12
18
60
3.5 3
4.5 4
6 5
12 6
17 12
60 56
side lobes are unaltered but there is a major improvement in the skirt due to removal of the grating lobes. Figure 6(c) illustrates the beampattern using one wavelength wide elements energized with a Hamming apodization function which consists of a 92% cosine wave and a 8% step function. This apodization function is well known for its side lobe removal property, which is illustrated by the figure. The main lobe however has been significantly widened and there is a 12 dB axial loss in field strength. The balance between the triad of side lobe level, width of main beam and field strength is well known in antenna theory, the selection of level of performance between these parameters being determined by the nature of the application. Figure 6(d) shows the beampattern using an apodization function consisting of a 75% amplitude cosine wave and a 25% step function. Although some side lobes are present at the - 6 0 dB level, the main lobe has been widened only by a small amount and there is less axial loss in field strength compared to the Hamming apodization. Figure 6(e) shows the distortion in beampattern by a cylindrically curved interface on the previous beam. The beam is deflected by 1.5 mm, and widened, and there is loss in beam symmetry with an increase in side lobe level. Figure 6 (f) shows the beam essentially restored following application of the compensating technique. The value of beamwidth at various dB levels below maximum is given in Table 2. The marked improvement at - 4 0 to - 6 0 dB level of performance obtained by going to more narrow elements and use of amplitude apodization is illustrated. The apodization used in Fig. 6(d) gives a beampattern which is about 25% more narrow than that obtained with the Hamming apodisation. Propagation through a single cylindrical interface widens the beam uniformly by approximately 20%. DISCUSSION The performance of most imaging techniques may be improved if a priori information is incorporated. In the described technique this applies to the
- 6 0 dB
utilization of the a priori known value of velocity in the two media. Although this limits the general utilization of the method, a potentially important application of the technique is the reduction of distortion incurred during propagation through the subcutaneous tissues. In this case advantage may be taken of the constancy of anatomical and acoustical relationships, that is, the abdominal subcutaneous tissues of every individual consist of the skin, the subcutaneous fat, the abdominal muscles and possibly the interspersed and retro abdominal muscle fatty layers. The acoustic properties of these tissues are known. The only variables are their thickness and curvature and this may be derived from an initial conventional sonographic technique optimized for subcutaneous tissues examination. The results described in the previous section show that the compensating technique may be used to recentralize and refocus the beam over the range of velocities and geometries encountered in sonographic examinations and following propagation through at least two interfaces. The reforming properties extend to at least the - 5 0 dB level of performance, the range of beampattern shape utilized by high performance equipment (Maslak 1985). This result is obtained with the relatively coarse as well as the fine transducer element construction and with simple as well as complex excitations. The compensating technique has certain functional advantages. The timing sequence which is utilized is identical to the one used by high performance equipment to generate transmitted beams which may be focused at different depths and to dynamically focus the echoes in reception. Thus it may be implemented on such equipment without major change to their basic architectural design. Incorporation of automatic edge detection techniques to determine the geometry of interfaces and to calculate the required timing compensation would allow automatic focusing of the beam for its line of sight. Stepping these lines of sight in the conventional image focusing mode would provide automatic compensation for the whole image.
Reduced beam distortion Q G. KOSSOFFet al.
Fig. 6. (a) Beampattern of original transducer shown is Fig. 4 (a). (b) Beampattern from a transducer of same total width but using thirty two one wavelength elements. The grating lobes have been removed and the second side lobe is evident. (c) Beampattern using Hamming amplitude apodisation sequence. The side lobes have been reduced to - 8 0 dB level, but the main lobe has been widened and there is - 12 dB loss in axial field strength. (d) Beampattern using 25% step function and 75% cosine apodisation. The side lobes are at the - 6 4 dB level. The main lobe has suffered less degradation. (e) Distortion of beam shown in Fig. 5(d) by propagation through a cylindrically curved interface described in Fig. 4(d). (f) Beampattern following application of compensating technique. The beam has been recentralized and its shape has been essentially reformed.
381
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Ultrasound in Medicine and Biology
Table 2. Beamwidth at various dB levels derived from curves shown in Fig. 5(b), (c), (d), (e) and (f). Beamwidth in mm Transducer
- 6 dB
32, 1~, wide elements 92% cosine, 8% step amplitude apodisation 75% cosine, 25% step amplitude apodisation After propagation through one interface Following compensation
- 1 0 dB
20 dB
- 3 0 dB
- 4 0 dB
- 5 0 dB
- 6 0 dB
3
4
5
6
12
19
38
4.5
6
8
9
l0
12
13.5
4
5.5
7
8
4.5 4
6 5.5
7.5 7
8.5 8
CONCLUSION U l t r a s o n i c b e a m s are d i s t o r t e d d u r i n g p r o p a g a t i o n t h r o u g h c u r v e d i n t e r f a c e s . T h e effects i n c l u d e beam displacement, asymmetric beam widening and i n c r e a s e in side l o b e a n d g r a t i n g l o b e level. T h e c o m p e n s a t i n g t i m i n g s e q u e n c e a l l o w s full r e c e n t r a l i z i n g a n d r e f o c u s i n g o f t h e b e a m t o its i n i t i a l s h a p e . S h o u l d t h e s e results h o l d in c l i n i c a l p r a c t i c e , t h e t e c h n i q u e holds promise to reduce the distortion effects inc u r r e d d u r i n g p r o p a g a t i o n t h r o u g h s u b c u t a n e o u s tissues.
REFERENCES Buttery, B.; Davison, G. The ghost artifact. J. Ultrasound in Med. 3:49-53; 1984. Gamboa-Aldesco, D.; Macovski, A.; Somewhere, G. Imaging through inhomogeneous media with a linear phased array; results and implementation. Ultrasonic Imaging 6:209-210; 1984. Hirama, M.; Ikeda A.; Sato, T. Adaptive ultrasonic array imaging system through an inhomogeneous layer. J. Acoust. Soc. Am. 71:100-109; 1982. Hirama, M.; Sato, T. Imaging through an inhomogeneous layer by
8.5 10 8
9.5 12 9.5
10.5 14 I1
least mean square error fitting. J. Acoust. Soc. Am. 75:11421147; 1984. Kossoff, G.; Carpenter, D. A.; Robinson, D. E. The subcutaneous tissues--A veil over good sonographic images. In: Bondestan, S.; Alanen, A.; Jouppila, P., eds. Proc. Euroson 87. Helsinki: The Finnish Society for Ultrasound in Medicine and Biology; 1987:364-365. Maslak, S. H. Computed sonography ultrasound annual 1985. In: Saunders, R. C.; Hill, M. C., ed. NY: Raven Press; 1985:1-16. Muller, N.; Cooperberg, P. L.; Rowley, V. A.; Mayo, J. Ultrasonic refraction by the rectus abdominus muscle: the double image artifact. J. Ultrasound Med. 3:515-519; 1984. Phillips, D. J.; Smith, S. W.; von Ramm, O. T.; Thurstone, F. L. Acoustical holography Vol. 6. In: Booth, N., ed. New York: Plenum Press; 1975:103-120. Robinson, D. E.; Wilson, L. S.; Kossoff, G. Shadowing and enhancement in ultrasonic echograms by reflection and refraction. J. Clin. Ultrasound 9:181-188; 1981. Smith, S. W.; Phillips, D. J.; von Ramm, O. T.; Thurstone, F. L. Some advances in acoustic imaging through the skull. Ultrasonic tissue characterization II. In: Linzer, M., ed. National Bureau of Standards Pub. 525; Washington DC: U.S. Government Printing Office; 1979:209-218. Smith, S. W.; Trahey, G. E.; von Ramm, O. T. Phased array ultrasound imaging through planar tissue layers. Ultrasound Med. Biol. 12:229-243; 1986. Yagisawa, H.; lshida, H.; Arakawa, H.; Masamune, O. Double image of the left portal vein. Jap. J. Med. Ultrasonics. 13, Suppl. II: 1077-1078; 1986.