PHASE STEERING AND FOCUSING BEHAVIOR OF ULTRASOUND IN CEMENTITIOUS MATERIALS

Transcription

1 PHAS STRING AND FOCUSING BHAVIOR OF ULTRASOUND IN CMNTITIOUS MATRIALS Shi-Chang Wooh and Lawrence Azar Department of Civil and nvironmental ngineering Massachsetts Institte of Technology Cambridge, MA INTRODUCTION Deterioration of civil infrastrctre system (CIS) raises not only safety isses bt also socio-economic concerns. In order to meet the high demand of strctral condition assessment and health monitoring, development of qick, reliable and accrate ND methods became critical isses recently. Compared to metal strctres, ND for cement-based materials is still prematre and reqires frther development. Concrete strctres, which are the poplar basic bilding blocks of civil infrastrctre systems, degrade with time de to a variety of physical and chemical processes. Composition of cement-based materials is complex, making it difficlt to evalate their strctral conditions. In particlar, it is challenging to se ltrasonic techniqes to assess these materials primarily becase concrete is natrally poros, inhomogeneos, highly attenative and scatters ltrasond. More importantly, it is reqired to scan large area qickly. Compared to the static natre of conventional transdcers, phased arrays provide dynamic capabilities. These arrays, consisting of mltiple elements excited at predetermined times, can be sed to steer and focs ltrasonic beams dynamically. Low freqency phased array transdcers may enjoy the merits of less labor-intensive operations, redced inspection time, increased field of view, and improved signal to noise ratios. More detailed description can be fond in the companion paper [I] pblished elsewhere in this volme. In this paper, we focs on showing the merits of focsing over steering in the near field. Qality of beam steering and focsing can be characterized by the featre "beam directivity," defined by the distribtion of pressre as a fnction of azimthal angle. A phased array developed for assessing concrete strctres has an inherently large apertre size de to the reqirement of tilizing low freqency ltrasond. This reslts in a large near field or "dead zone" where the qality of beam steering is very mch deteriorated. Simlation stdies show that focsing in the near field combined with steering greatly improves the near field directivity and redces this dead zone. It is also shown that Review of Progress in Qantitative Nondestrctive valation. Vol. 18 dited by Thompson and Chimenti, Klwer AcademiclPlenm Pblishers,

2 the characteristics of the focsed beam approaches that of steering when the focal spot is located in the far field. This phenomenon allows for efficient fll filed assessment of concrete strctres. The simlation reslts agree well with experimental measrements, as shown in the companion paper [I]. OPTIMIZATION LIMITATIONS OF BAM STRING FOR CONCRT Sectorial diagnostic images are sally constrcted by sweeping an ltrasonic beam throghot the area of interest and transforming the retrn signals into an image. This reqires phase steering that is accomplished by seqentially plsing the array elements. The analytical pressre distribtion regarding beam steering was previosly derived by Wooh and Shi [3,4]. This analytical model is crcial in resolving the key parameters for these arrays. By analyzing the directivity patterns, beam steering characteristics were stdied and optimm transdcer parameters were determined. The fndamental transdcer parameters stdied inclde freqency (f), the element width (a), the center-to-center spacing of the elements (d), the nmber of elements (N), the total apertre dimension (D), and the elevation dimension (L). It was conclded from this stdy that increasing N greatly improves the beam steering characteristics and also sppresses other detrimental effects. At the same time, increasing d improves the sharpness of the beam, p to a critical vale. It is therefore desirable to se the largest nmber of elements spaced by the maximm allowable distances. This immediately poses a problem since it reqires increased overall dimension, reslting in blky transdcers. More importantly, high vales of these parameters increases transition zone that separates the near field from the far field of the array. (1) For linear arrays, maximm allowable inter-element spacing withot introdcing sprios grating lobes is given [5] as A N-l 1 + sin(o.)max N d m a x = - - ~ - - : - - (2) where A is the wavelength of the acostic medim and (O.)max is the reqired maximm steering angle. For large N and a, and assming D2» A, (O.)max = 90 0, dmax approaches A/2 so that the overall dimension becomes D ~ N d. Therefore, the transition zone can be expressed in terms of N as (3) For concrete, this transition can be significantly increased. For example, wavespeed of sond in a well-cred concrete can be in the range of 4,000 km/sec. If the transdcer parameters are chosen sch that N = 16 and f = 100 khz, then the wavelength A becomes approximately 4 cm and the corresponding optimm inter-element spacing is approximately 2162

3 )../2 = 2 em. With this design, the transition zone calclated from eq. (3) is 64 cm. Considering the fact that signals retrned from this zone is nstable, this area beneath the transdcer can be considered as nsable or "dead" zone, making it nattractive. This paper deals with an approach to remedy this problem by redcing the transition zone. DYNAMIC FOCUSING AND TH PRSSUR FILD If targets within the near field of the array apertre are imaged, that is, at distances less than ZTR, then focsing may be employed to increase the system resoltion. In order to explain how focsing improves the resoltion over steering, it is very critical to nderstand the behavior within this transition zone. Focsing of the transmitted beam is accomplished by combining a parabolic timing relationship with a linear one to prodce a beam which is focsed at a given range and propagated at a specific azimthal angle. The following generalized focsing formla was derived to compte the reqired time delays: F{[ (Nd)2 2Nd ]1/2 tn = ~ 1 + Ii" + F sin B. [ ((n_n)d)2 2(n-N)d. ]1/2} F - F smb. (4) for any nmber of elements N, where tn is the reqired time delay for element n = 0,..., N -1, N = (N - 1)/2, d is the center-to-center spacing between elements, F is the focal length from the center of the array, B. is the steering angle from the center of array, and c the wavespeed. This generalized focsing time delay formla is valid for any nmber of array elements (even or odd). Frthermore, by eliminating the constant to, the formla garantees positive time delays which do not have to be larger than necessary. The analytical pressre distribtion for the beam focsing was obtained as [4]: p(r,b,t). (kasinb) = (PO)! sm ex (_jkasinb) r kasmb p 2 ( ~ e X P + [ Bn j ( A n 2 )]) exp[j(wt - kr)], 2 (5) where k is the wave nmber, w is the anglar freqency, Po is a fnction of k, j is the nit imaginary nmber, and c(n - 1) 2 A = F 2 B ~ TO - W ~ TO + kd sm B, 2 tan s B = C ~ T g 2Ftan 2 Bs (6) 2163

4 This expression is sefl for stdying the far field characteristics of the beam focsed beyond the transition range, as discssed later. However, it shold be noted from eq. (5) that the pressre distribtion for beam focsing can not be simplified into a closed form. This means that the analytical method is not possible; instead, the nmerical method to simlate the acostic field is desirable and powerfl. Nmerical Simlation A nmerical simlation program was developed to attain directivity and image pressre profiles for ltrasonic linear phased arrays. This software simlates wave propagation fields for either steering or focsing, in both the near and far fields, and prodces directivities at any specified distance. The pressre along the steered direction when steering or focsing was also simlated. The simlation is based pon Hyghen's principle, which states that wave interactions can be analyzed by smming the phases and amplitdes contribted by a nmber of simple line sorces. The pressre at a given distance form the sorce is compted as follows: P (r, t) = r 1 exp[j (wt - kr) - or] (7) ( ~ O where a is the attenation coefficient (Np/m) and r is the radial distance from the sorce (m). Or simlation rotine is similar to that tilized by Bchanan [7], in that they modeled the transdcer as an evenly spaced array of simple sorces (a «A), whereas or model treats it as an ensemble of elements of finite width. More simlation reslts for steering can be fond in or paper fond elsewhere in this volme [8]. RSULTS AND DISCUSSION A nmerical simlation of the fll-field acostic pressre distribtion is tilized to demonstrate some key effects of focsing within and beyond the transition range of a linear phased array. A comparison between steering and focsing is ndertaken, revealing a distinct benefit of focsing over steering within the near field. The array simlated is made p of 16 elements, with a freqency of 170 khz, center-to-center element spacing of A/2, and a wavespeed of 3,650 mls. The transition range for this array is calclated to be 50 em. The array is consistent with one that wold be sed for the ND of concrete strctres, bt the conclsions broght forth are valid for other applications inclding metal applications and medical evalation. A directivity plot is sed to show the pressre along a radial distance from the center of the array, and is an accepted standard to demonstrate the accracy of steering and focsing behavior. An ideal plot shold have a very good directivity, characterized by a very narrow main lobe width [3]. 'They are derived from the image of pressre distribtion, which maps the contribtions of pressre from each element via Hyghen's principle. These contribtions incorporate the respective phase shifts, which lead to constrctive and destrctive interference of the ltrasond. 2164

5 Figre 1 (a) shows an image of the pressre distribtion for a beam steered at 30 degrees, and Fig. l(c) shows the directivity at r = 20 cm. Since the directivity is taken in the near field of the array, the beam steering qality is qite poor, characterized by the wide and irreglarly shaped main lobe. A received signal from this region cold not be properly mapped to the appropriate location on an image, becase the resoltion of which is determined by the sharpness ofthe main lobe. By contrast, Fig. l(b) shows an image pressre distribtion as the beam is steered at the same angle and is also being focsed at a distance F = 20 cm. The directivity shown in Fig. l(d), which passes throgh this focal point (r = F), shows a dramatic improvement over that of steering. Looking at the respective pressre distribtion images, the focsing effect in the near field is qite obvios. Focsing enables the acqisition of data from within a region not previosly attainable by steering only, and contribtes to increased resoltion capabilities within the transition zone of the array. Referring back to eq. (5), when the focal length is infinitely large, i.e., F -+ 00, then A -+ -wllrg + kdsino, and B -+ o. In this case, it can be easily shown that the pressre distribtion for focsing becomes exactly that of the steering [4]. This means that if the focal length is sfficiently large, i.e., beyond the transition range, the pressre distribtion for focsing will converge to that of steering. Figre 2 illstrates this concept. Figre 2(a) shows the pressre field of the beam steered at 30 while the corresponding directivity taken at r = 1 m is shown in Fig. 2(c). This is beyond the transition zone, and as sch, the directivity is good. On the other hand, Fig. 2(b) shows the pressre field ofthe array now being focsed in the far field at F = 1 m, which now resembles that of steering. Taking a directivity at r = F = 1 m, the benefit over focsing is negligible as shown in Fig. 2(d). This is critical, becase this means that at the locations beyond the transition zone, the se of only steering is sfficiently adeqate. Since focsing reqires analysis of a large nmber of scanned points, it does introdce a cost, namely scanning time. Steering is mch more efficient, as each sectorial line can be analyzed at a time. Directivities are not the only criteria that shold be considered when evalating the importance offocsing. Simlating the pressre along the steered direction, Fig. l(e) and 1(0, 2(e) and 2(0 respectively shows how the pressre of focsing compares to that of steering in the near and fat fields. Within the transition range, the pressre with focsing is more concentrated than that with steering. This added pressre contribtion improves the resoltion when acqiring data from the near field. Figre 2(e) and 2(0 also show that beyond the transition range, the pressre along the steered direction when focsing will also converge to that of steering. This compliments the observations made analytically and tilizing the directivity plots. Figre 1 also demonstrates another important fact, that the maximm pressre does not necessarily occr at the focal point. For example, Figre 1(0 shows that the maximm pressre occrs at approximately 15 cm when the focal point is set at 20 cm. Despite the fact that the maximm pressre occrs elsewhere than the focal spot, it is important to note that the focal length is the distance that defines the best directivity. CONCLUSION An attempt was made to reach an analytical soltion to the pressre distribtion with focsing, reslting in an nleosed form. Therefore, a nmerical simlation was 2165

6 x(m) (a) x(m) (b) Q) 0.8 :! 0.7 «0.5 Q) ~ Z 0.2 Q) 0.8.e 0.7 «0.5 Q) ~ Z Angle, O(deg) (e) 1.0 Q) 0.8. ~ «Q) ~ z 0.2 Q) 0.8 ~ «Q) ~ Z L Distance along steered angle (m) (e) 0.0 L Distance along steered angle (m) (t) Figre 1. Comparisson of beam steering (left) and focsing (right), with directivities (c, d) taken in the near field, and comparing the pressre profiles along the steered angle (e, f). (r = 20 em, F = 20 em (focsing only), N = 16, c = 3,650 mis, f = 170 khz, (). = 30, and d = >./2). 2166

7 (m). (m) (a) G) 0.8 Ql 0.8 ~ 0.7 ~ 0.7 ««O.S Ql O.S ~ 0.4 ~ Z 0.2 Z eo -eo Angle, O(deg) Ce) Ql 0.0 (b) Angle, O(deg) Cd) G) 0.8 G) ~ ««G) Ql ~ 0.4 ~ Z 0.2 Z L --==========::J 0.0 L..- --' Distance along steered angle em) Distance along steered angle em) Ce) (I) Figre 2. Comparisson of beam steering (left) and focsing (right), with directivities (c, d) taken in the near field, and comparing the pressre profiles along the steered angle (e, 0. (r = 1 m, F = 1 m (focsing only), N = 16, c = 3,650 mis, f = 170 khz, 8. = 30, and d = >./2). 2167

8 recommended to attain the pressre field, based on Hyghen's principle for a discrete nmber of simple sorces. Nmerical directivity and image pressre profiles were tilized to compare the behavior of focsing and steering within, and beyond, the transition zone of the phased array. This demonstrated the importance of focsing in the near field, as the directivity for steering is qite poor, while that of steering is very well defined. This transition range is proportional to the sqare of the overall dimension of the array. As the nmber of elements increases, there is a sbseqent increase in the region where steering cannot be sed. To benefit from the added nmber of elements, focsing mst be sed in this "dead" zone. Althogh the maximm pressre along the steered direction when focsing does not always coincide with the focal point, focsing does demonstrate better directivity at that point and an overall improvement over steering. The nmerical simlation proved or analytical conclsion that as the focal length goes to infinity, the pressre distribtion of focsing converges to that of steering. This validates the se of steering beyond the transition zone, which enable faster acqisition over focsing. Althogh there is still some improvement beyond this zone, those improvements are negligible, since the convergence applies to a focal length approaching infinity. ACKNOWLDGMNTS This stdy was spported by the Korea Highway Corporation. We are gratefl to Dr. Chang-Gen Lee, Program Manager and Mr. Keon-Chang Cho, Director of Highway Research Institte of the KHC, for their encoragement and spport. RFRNCS 1. L. Azar and S. C. Wooh, "A novel ltrasonic phased arrays for the nondestrctive evalation of concrete strctres," in Review of Progress in Qantitative Nondestrctive valation, eds. D. O. Thompson and D.. Chimenti, (Plenm Press, New York 1999), in this volme. 2. M. G. Silk, Ultrasonic Transdcers/or Nondestrctive Testing" (Adams Hilger, Bristol, 1984). 3. S. C. Wooh, and Y. Shi, "Optimization of ltrasonic phased arrays," Review of Progress in Qantitative Nondestrctive valation, op. cit., (1998), p Y. Shi, Modeling of acostic waves for linear phased arrays, MIT MS thesis (1998). 5. S. C. Wooh and Y. Shi, "Design Strategies for Phased Arrays," in Review 0/ Progress in Qantitative Nondestrctive valation, op. cit., (1999), in this volme. 6. O. T. Von Ramm and S. W. Smith, "Beam steering with linear arrays," I Trans. on Biomedical ngineering BM-30, 8 (1983), p M. T. Bchanan and K. Hynynen, "Design and experimental evalation of an intracavity ltrasond phased array system for hyperthermia," I Trans. on Biomedical ngineering 41,12 (1994), p S. C. Wooh, and Y. Shi, "Simlated pressre fieldand directivity of phased arrays," Review of Progress in Qantitative Nondestrctive valation, op. cit., (1999), in this volme. 2168