Ultrasound in Med & Biol.. Vol. 5. p p 187-193 Pergamon Press Ltd.. 1979. Printed tn Great Britain

TRANSDUCER DESIGN CONSIDERATIONS DYNAMIC FOCUSING

IN

J. VOGEL, N. BOM, J. RIDDERand C. LANCEE Faculteit der Geneeskunde, Erasmus Universiteit, Rotterdam, Postbus 1738, Rotterdam, The Netherlands

(First received 20 December 1978; and in .final yorm 3 April 1979) Abstract--The design of a dynamic focusing transducer is an important factor in improvement of the quality of diagnostic images. Dynamic focusing allows narrowing of the acoustic beam and therefore diminishes the error caused by the limited lateral resolution of ultrasound systems. Beamwidth, sidelobe effects and complexity of the system are discussed for both sectorscanning and linear scanning. For a given set of practically selected parameters a comparison is made and in both methods a beamwidth between 3 and 4 mm can be obtained. Image formation requires about the same number of elements. The methods are different in complexity, probe mobility, display format, "around the corner" sensitivity and side lobe aspects.

Key Words: Ultrasound, Focusing, Array techniques, Sectorscanning.

INTRODUCTION

Real time ultrasound two-dimensional imaging devices have been introduced over the last few years. Two "direct contact" electronically activated multi-element systems are presently in use. As early as 1968 Somer published an electronically phased sectorscan method designed to be used in neurological patients. Linear array technique was first applied in 1971 in the Thoraxcenter in Rotterdam (Born et al., 1971). Both systems differ in beamsteering technique, probe size, complexity and image format. Newer developments include dynamic focusing in reception as an adjunct to the linear array as well as the phased sectorscan method. In 1973 Thurstone and von Ramm described a dynamically focused phased sectorscan with optimal parameters for cardiological work. In 1977 the Thoraxcenter in Rotterdam developed the Fociscan, an apparatus with a dynamically focused linear array scanning method. With dynamic focusing the errors resulting from poor lateral resolution are diminished since it allows narrowing of the acoustic beam width. The ultrasound beam width is an important parameter for the quality of the diagnostic image. The width depends on acoustic aperture, frequency and depth. The dependance of the number and size of the individual subelements of any element array will be discussed in this article. Besides the main lobe acoustic beam and the well known smaller adjacent side lobes, in 187

array configurations sometimes a second or third off axis high sensitivity exists. This so called grating lobe is a result of the regular pattern of, and the distance between the centers of the individual elements. A grating lobe arises only if this spacing is larger than ½ wave length. Adequate design of phased array systems for medical diagnosis prescribes design of an array with as few elements as necessary which still yields an acceptable resolution and low side lobe level. Minimizing the complexity and thus the costs of a system requires insight in the effect of the total number and the width of the individual elements of an array. Both effects will be discussed for dynamically focused sectorial and linear arrays with regular element distance. The first parameter that will be studied is the selected active acoustic width of each individual element within the acoustic aperture. INDIVIDUAL ELEMENT WIDTH

It is apparent that the active aperture for the electronically steered linear array must contain a number of small individual acoustic elements. For the sectorscan these elements will have to be designed such that a good acoustic beam will result at various angles. For the linear array the subset has to be optimal for one main axis beam direction only, since all other beams will be parallel and are formed with a similar adjacent subset of small elements.

J. VOGEL et

188

In dynamically focused sectorial or linear scanners where all elements or a subgroup of elements are used to form "a focused acoustic beam", the individual element width parameter is very important. In the far field and at field locations near a focal point (Skolnik, 1962; O'Neill, 1949) the relative directivity sensitivity of a beam steered array is given by the expression:

I(o, ,It) = L ( o ) x 1o(o, ~ ) .

(1)

This expression is valid for continuous wave calculations. I ( O , ~ ) is the intensity distribution of the radiation pattern at any constant distance to the centre of the array as a function of O and gr. The angle • indicates the selected beam steering direction at any moment. The radiation pattern can be expressed as a function of angle O. Both angles are measured from the normal to the array (Fig. I). I,(O) is the intensity distribution pattern of the individual elements. Ia(0, ~ ) , the so called array factor, is the intensity distribution pattern of the array c o m p o s e d of isotropic elements positioned at the individual element centers. In this array factor N d is associated with total transducer aperture.

\ p

[a ( O, ~I¢) : ( 1

/

sin N q ] ~

"~lff"q "/

(2) (3)

where p = (~ra/A) sin 0; a = width of an element; A = wavelength; q = (n-d/X)(sin 0 - sin qt); d = distance between element centers; N = number of elements. 0o

.~0 LIIIII Fig. I. Radiation patterns of an array with beem steering angle q~.

al.

In order to obtain an effective focusing of ultrasound, the aperture of the array has been selected so that the largest scandepth is still in the near field of the array. In the near field, the above given expression for directivity sensitivity I(0, qt) of the array may not be applied at larger distance from the focal point where no longer a phase equality condition for the array elements exists. H o w e v e r , for a study of sensitivity on the main axis (0 = ~ ) this expression for I(0, ~ ) may be used as an approximation. For 0 = ~ , I(',It, ~ ) describes the intensity on the main axis as a function of the steering angle ~ . If0--*qt

then

q~0

and .. [ 1 sin Nq'~ 2 limo_,/~(O, ~ ) = nmq-.o ~ sin q J = 1 (4) Thus:

I ( ~ , ~t') is I,(q').

Therefore, the contribution term of the individual elements may be used as an approximate description of the sensitivity of an array on the main axis as function of the steering angle. The beam characteristics of the individual elements are illustrated by Fig. 2. This figure shows the peak intensity I for 0", 15°, 30* and 45 ° respectively as function of the width of a single element. As expected the resulting intensity I for larger steering angles decreases rapidly as function of element width. It appears that the sensitivity at 45 ° of'-an individual element of approximately 1½A element width is almost zero. Another aspect is the change in intensity distribution along the array aperture. For a reflector at a given steering angle, each of the array elements " s e e s " this reflector at a different angle. For instance for a reflector at a distance of one aperture length and at a steering angle of 30* the change in angle between individual elements will be more than 45 °. In order to avoid a significant decrease in sensitivity by larger scan angles and an important change in sensitivity along the aperture for distances close to the transducer the element width has to be for sectorial beam smaller than 1 wavelength. An element width of about 1 wavelength limits the decrease in sensitivity to - 1 0 d B for a 45 ° steering direction. For 30 ° this would

Transducer design considerations in dynamic focusing

189

Peak intensity

(normo]i~d 0o

1.0 0.9 0.8 0,7 0& 0..5 0.4 0.3 0.2 0.1 1

2

3

4 element width (;n wove length)

Fig. 2. C o n t r i b u t i o n o f i n d i v i d u a l e l e m e n t s o n t h e m a i n a x i s f o r v a r i o u s s t e e r i n g a n g l e s a s f u n c t i o n o f element width,

result in a decrease to approximately half the maximum sensitivity. It may be stated that for sectorial beam steering the elements must be small. For the linear array no such condition follows. Thus: • In a sectorial beam steering the individual elements must be small in order to achieve enough sensitivity "around the corner". • No restriction yet follows for the individual element width in linear arrays. These calculations have been derived from calculations on sensitivity of individual elements. From calculations on array processing further additional restrictions on element width may result.

PARAMETERSANn CALCULATIONS In order to obtain an insight in the behaviour of the beamwidth and the grating lobe with equally positioned individual elements in an array a fixed set of practical parameters has been selected and introduced and will be kept constant in the following examples. These parameters are an aperture of 2.5 cm; a selected frequency of 2 MHz; the beam width is calculated at a fixed distance of 10 cm from the aperture center and has been defined at the - 1 0 d B intensity level. Changes in the fixed parameters will influence the beam width and grating lobe effects in a strict predictable way. Thus using above selected parameters, an insight may be obtained in array design considerations. A well-known phasing technique in transmission is the so called axicon focus (McLeod 1954; Ligtvoet et al., 1977). This UMB Vol. 5, No. 2--D

axicon produces a focal line, resulting in moderated focusing over the entire scandepth. Dynamic focusing may be applied in reception, either as a dynamic point focus or a stepwise approximation. In the presented example point focusing has been assumed in transmission as well as reception in order to illustrate some parameters. Point focusing in transmission is introduced in order to avoid unnecessarily discussion about different transmission techniques. The calculations as illustrated in the Figs. 2, 4 and 5 have been based on the continuous wave approximation. In pulsed echo the broadband character of the signal results in a decreased level of the grating lobes. However, dispersion and transducer characteristics limit the extent to which a pulse may be shortened. Therefore the calculations approximate closely the, practical situation where the pulse will extend over at least a few wavelengths. The calculations are performed by means of a program, whereby each element is composed of N isotropic line sources over the element width, with a density of 4 line sources per wavelength. The soundpressure of the array is calculated in a series of discrete points at an axial distance x from the transducer. For a given point A at an axial distance x and a lateral distance y continuous wave soundpressure of a line source n in the far field may be written as l

PA, = C ~ - ~ exp ( - j ( k r n + (b,))

190

J. VOGEL et al.

aperture. Beamwidth depends on this aperture; by an increase of the scan angle the effective aperture decreases. Figure 4 shows that optimal beam width is obtained in the 0° direction while the resolution decreases as N 1 function of scan angle. It also appears that p,~. = NCt ~ 775- exp ( - j ( k r . + dp.)). the beam width is almost independent of the nffil V l n number of elements when selected above a The program allows for focusing, i.e. ad- very low number of five elements in this case. justment of 4~, and amplitude weighting by The existence of grating lobes may cause image distortion. The grating lobe depends on means of a weighting factor A,. The total soundpressure in point A may be the interelement distance. In these calculations on arrays for sectorscanning the written as: calculated grating lobe level, which arises if element spacing is larger than ~ wavelength, is PA N M C , .ffi, .-, ~ exp ( - j ( k r . . + qb.,)). high for interelement distance larger than 1 wavelength. The strength of the grating lobe A comparison between calculated and depends on its off-axis position. Reduction of experimental values, obtained with a practical this strength in the calculations is due to the reduced off-axis sensitivity of the individual array, is shown in Fig. 3. This figure shows the calculated and elements. As may be observed from Fig. 4 measured beamwidth of a dynamically the definition of beamwidth becomes invalid focused system. This system, the Fociscan, when the grating lobe increases above the was developed in 1977 at the Erasmus Uni- - 1 0 dB level. The point has been indicated with crosses. It is shown that the grating lobe versity, Rotterdam. will cause distortion when the number of elements is selected too small, particularly SECTORSCANNER when the beam is steered at an angle. The The sectorscanner is illustrated for the in- position of the grating lobes can be derived dicated fixed parameters and calculation ap- from the following equation: proximations. In Fig. 4 the beam width of the sectorscanner is shown vs the number of q = - ~ ( s i n 0 - sin qO = Nzr (5) elements in the aperture for various scan angles. The individual element width is equal to 1 wavelength in all situations with less than where N is an integer. 32 elements in the aperture. The individual They arise if in formula (3) both numerator elements have been equally spaced over the and denominator are zero. with: k = 2¢r/;t ; r = X/(x 2 + y:); c~ = constant; qb, = phase of the line source. The soundpressure in A for one array element m is given by

=

Measured and calculated

b e a m w l d t h at - 6 a n d - 2 0 d B l e v e l as F u n c t i o n oF

axial dlstance

----

measured calculated

I

-s

'-"

~

Ni~ 2 a~

i 1

| 2

I

,

I

I

I r

I I

I I

d8

f

~

. . ~ - - - 6 d

3

v 5

J 6

I 7

i 8

I

i 9

i 10

I

r 11

i 12

~3

14

B i 15

t 16,

A x l a l d i s t a n c e (cm)

Fig. 3. A comparison between calculated and experimental values, obtained with a dynamically focused system, the Fociscan.

Transducer design considerations in dynamic focusing

191

~ectorscan

Beomwidth (rrirr~) X = - I O dB intensity level of grating Io~e - 1 0 dB level

scon angle 5-

45 ° i=1

4-

30 ° 15o 0o

3" 2.

element width = ~ ~

1.

element width < k

/ 30

10

Point focussing in transmisJlion and reception

Distance : 10 cm Frequency = 2 MHz Aperture = 2.5 cm

4O number of elements

Fig. 4. Beam width as function of number of elements for the sectorscanner. The element width has been kept 1 wavelength or less. The crosses indicate the points where the grating lobe has increased to an inacceptable level chosen at - 1 0 dB in this example.

As stated before, this formula and the graphs of Fig. 4 are based on continuous wave calculation. The broad spectrum of pulsed echo signals tends to decrease the grating lobe level. In the examples therefore a grating lobe is accepted up to where it increases to a level of - 1 0 d B . The example illustrated in Fig. 4 shows that for the sectorial electronically steered scanner important design considerations are: • For an appreciable suppression of the grating lobe the number of individual elements in the aperture of a sectorscanner must be relatively high. 32 elements is the lower limit and 64 elements may result in optimal beam forming. • For each beam all elements are activated. The entire sectorial image format is obtained with these elements.

• The lateral resolution of a sectorscanner decreases with angle. Optimal resolution is obtained in the 0 ° direction. LINEAR SCANNER

The linear array is also discussed for an active aperture of 2.5 cm and a frequency of 2 MHz. For the linear array there does not exist a rigid prescription for the individual element width within the aperture. For optimal sensitivity it seems therefore allowed to fully occupy the active surface minus a practical sawing width as separation between the element of 150~m. In Fig. 5 the beam width at 10 cm depth is represented as function of number of individual element in the aperture. In this situation however, the elements do not have a fixed width. Given the fixed parameters, 10

Lineor t.~n

Ikmmwidt~ (mm) x = - 1 0 dB intensity level of grating Io~e

- l0 dB |evel

6 .

\ \

Grating lobe I level I L 0 I (dB) - -5

5' L -15 I - -20 I --25

4, 3 2

I

Point focussing ;~ tranlmls$1on and rer..ept ;0.

\ \ \ 10 Distonce = l0 cm Frequency = 2 /V~Jz Aperture = 2.5 cm

Ir - 3 0 40 number of element1 ( e l e r ~ t t e ~ m t ; ( ~ = 150 pro)

Fig. 5. Beam width for the linear scanner shown vs number of elements used in the subset. The individual element varies in width such that the full aperture (minus an interelement sawing width) is occupied. The dotted line indicates the level of the grating lobe.

192

J. VOGEL et al.

elements on the x-axis of Fig. 5 corresponds to an element width of 3 wavelengths and 30 elements correspond to an element width of 1 wavelength. As may be observed the beam width hardly varies with the number of elements. In the Fig. 5 the dotted line indicates the grating lobe level in dB. In order to minimize the grating lobe the number of elements thus has to be selected greater than 10. Thus: • For the linear array exists a larger freedom in selection of individual element width. • In order to obtain a reasonable beam width and suppression of the grating lobe in this example the individual element number in the subset may be as low as 10 elements. • To obtain a field of view of 8 cm in lateral orientation a transducer of about 10cm is required and the linear array will consist of a minimal number of 40 transducer elements in total.

W. Smith and Von Ramm (1978) described a system in which two different arrays with a slightly different central frequency are used in transmission and reception. Herewith the grating lobe in transmission is localized in another direction than in reception. Besides techniques for array processing and beamforming, final images are largely influenced by signal processing and display techniques. Appreciation and clinical usefulness of ultrasound images depends also on the number of images per second, the number of lines per image, grey scale besides other factors.

CONCLUSION

For the given fixed set of parameters a beam width between 3 and 4ram can be obtained in both sectorial scanning and linear scanning. For optimal beam forming both methods require between 32 and 64 individual EFFECTOr eROCESSlNC elements in the transducer array. The sectorIt has not.been the purpose of this article scanner uses for each scan all individual to describe and compare all parameters which elements "at the same time" to form the influence diagnostic capabilities. These sectorial beams. The probe is relatively small. should have also included probe size and The beam width, and thus the lateral resoluaiming capabilities; image line density; image tion, decreases with scanning angle. In the format; frame rate; video compatibility etc. linear array scanning each beam is formed However, when the beam width and grating with a subset of elements. Although each lobes are presented for various configurations subset may consist of a low number of eleand design criteria are discussed some atten- ments a large number of elements is required tion should be paid to some processing tech- to form all necessary scans. In linear array niques which directly influence beam pat- scanning the resolution will be equal at a given depth over the entire image. The interns. A number of techniques exist to diminish dividual element width must be small in sectorscanning in order to provide "around the side lobes. Some practical methods are: (a) Logarithmic compression for each array corner" sensitivity whereas no such~r~stricelement which introduces a multiplicative tion results for the linear array systems. It aspect in array processing (Von Ramm and appears that the sectorscan system is more Thurstone, 1976; Ligtvoet et al., 1977). Aside sensitive to effects resulting from the grating from side lobe reduction, the dynamic range lobe. It has been realised that a useful clinical of echo signals is compressed, so that diffuse system is not completely determined by the and specular reflectors are displayed together discussed array parameters. Image format, probe mobility, signal processing and display on the monitor. (b) Additive array processing, where by method are some of the factors that conaddition of the echo information for more tribute to successful diagnosis in clinical routhan one focal point, also side lobe sup- tine. pression is obtained (Bom et al., 1975; Lanc6e and Born, 1977). REFERENCES (c) An array design with an increased eleBorn, N., Lanc~e, C. T. and Honkoop, J. et aL (1971) ment density towards the center of the active Ultrasonic viewer for cross-sectional analysis of moving cardiac structures. Bio-med. Engng 6, 500-503. transducer surface and or similar amplitude Born, N., Lanc6e, C. T., Ridder, J.,Ligtvoet, C. and weighting (Miller and Thurstone, 1977). Roelandt, J. (1975) The technology of miniature The effect of grating lobes can be very acoustic elements. Proc. o/ the Conf. Cardiovascular Image Processing, Stanford University, 11-15 July. troublesome in phased ultrasound systems. S.

Transducer design considerations in dynamic focusing Lanc6e, C. T. and Born, N. (1977) Some signal processing aspects in medical ultrasound. Aspects of Signal Processing, part 2, NATO Advanced Study Inst. Series (Edited by Tacconi), pp. 649-657. Reidel Publishing Company, Dordrecht, the Netherlands. Ligtvoet, C. M., Ridder, J. and Lanc6e, C. T. (1977) A dynamically focused multiscan system. Echocardiology (Edited by Born, N.), pp. 313-324. Martinus Nijhoff, the Hague, the Netherlands. Ligtvoet, C. M., Ridder, J., Hagemeijer, F. and Wladimiroff, J. W. (1977) Ultrasonics, Brighton, Conf. Proc. pp. 111-120. McLeod, J. H. (1954) The Axicon: a new type of optical element. J. Optical Soc. Am. 44(8), 592-597. Miller, E. B. and Thurstone, F. L. (1977) Linear ultrasonic array design for echosonography. J.A.S.A. 61, 1481-1491.

193

O'Neill, H. T. (1949) Theory of focusing radiators. J.A.S,A. 21,516-528. Skolnick, M. I. (1%2) Introduction to Radar Systems, pp. 347-349. McGraw-Hill, Tokyo. Smith, S. W. and Von Ramm, O. T. (1978) Improved imaging with a wide band array. Ultrasound in Medicine 4 (Edited by White D. N. and Lyons E. A.), pp. 433-438. Plenum Press, New York. Somer, J. C. (1%8) Electronic sector scanning for ultrasonic diagnosis. Ultrasonics 6, 153-159. Thurstone, F. L. and Von Ramm, O. T. (1973) Electronic beam scanning for imaging. Ultrasonics in Medicine (Edited by deVlieger, M., White, D. N. and McCready, V. R.), pp. 43-48. Excerpta Medica, Amsterdam. Von Ramm, O. T. and Thurstone, F. L. (1976) Cardiac imaging using a phased array ultrasound system. Circulation 53, 258-262.

Transducer design considerations in dynamic focusing.

Ultrasound in Med & Biol.. Vol. 5. p p 187-193 Pergamon Press Ltd.. 1979. Printed tn Great Britain TRANSDUCER DESIGN CONSIDERATIONS DYNAMIC FOCUSING...
482KB Sizes 0 Downloads 0 Views