AN INVESTIGATION OF FOCUSING AND ANGULAR TECHNIQUES FOR VOLUMETRIC IMAGES BY USING THE 2D CIRCULAR ULTRASONIC PHASED ARRAY

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1 AN INVESTIGATION OF FOCUSING AND ANGULAR TECHNIQUES FOR VOLUMETRIC IMAGES BY USING THE D CIRCULAR ULTRASONIC PHASED ARRAY S. Monal Lonon South Bank University; Engineering an Design 103 Borough Roa, Lonon SE1 0AA Abstract. New array instrumentation allows ultrasonic arrays to be use with increasing numbers of elements. This leas to the possibility of volumetric imaging of engineering components. In this paper, two imensional (D) ultrasonic transucer arrays are use to generate beams that can be steere an focuse throughout a three-imensional (3D) volume from a single location. A moel is evelope to generate time signals for all combinations of transmit an receive elements. Base on this moel, a theoretical investigation of the focusing an steering properties of D circular arrays is escribe. The imaging performance of a circular array is then quantifie from their point sprea functions. 1 Introuction Many ifferent techniques have been recently evelope for volumetric imaging [1-3]. They can be classifie into two categories: mechanical scanners an D ultrasonic phase arrays. In a mechanical scan, a single probe at a fixe angle is mechanically scanne over a component an for a efect to be etecte its orientation must be favourable with respect to the incient beam. In some cases, the orientation of likely efects can be estimate an the probe orientation chosen accoringly. However, in cases such as the etection of flattene inclusions in forge parts, the orientation of potential efects cannot be reliably anticipate an reliable etection requires many scans using probes at ifferent orientations. However, with a D phase array the complete ata set can be extracte from the array at a given location an a volume of the specimen can then be probe using offline post processing. Not only will this enable sensitivity to efects at unfavourable angles to be increase, but also once a efect ha been ientifie, its 3D lectivity function can be compute from the acquire ata. In this paper two post processing algorithms, terme the Focusing Metho (FM) an Angular Metho (AM) scan are presente. In the FM algorithm, an image is create in which the beam has been focuse, in turn, on every point within the fiel of view [4]. In the AM scan algorithm, an image is create in which the beam has been steere through a range of angles to inspect the volume of interest [5,6]. In orer to quantify the performance of these two imaging algorithms, a parameter calle Array Performance Inicator (API) is use. The performance of the FM an AM scan imaging algorithms are also compare using experimental ata. These experimental ata are obtaine by a D prototype circular phase array from flat bottom holes in aluminum.

2 Simulation of array ata The array ata are simulate by the response of a point lector that can be locate anywhere in the +z halfspace, as inicate in Figure 1. Array elements are uniformly space on the circumference of a circle of raius, r, in the x-y plane. A simulation program (written in Matlab) is use to generate time omain signals (time-traces) for all combinations of transmit an receive elements. For example, if n is the number of elements in the array then a maximum of n x n possible time-traces are available for all transmitter-receiver x Array element (x n, y n ) r y X Y z Z (x, y, z ) Point lector Figure 1 : Array elements are uniformly space on the circumference of a circle of raius, r, in the x-y plane an a point lector is in the x-y-z plane. combinations. However, the number of inepenent time-traces that actually nee to be n compute for the simulation is only n 1, because the time-trace when element 1 transmits to element is ientical to the time-trace when element transmits to element 1 ue to reciprocity. The first step in the simulation is to efine a transmitte signal f 0 (t) in the time, t, omain. Typically this is a Hanning winowe tone burst containing five cycles. The secon step in the simulation is to calculate the propagation istance associate with the lecte signal for each time-trace. For the - time trace( transmitter an receiver), the propagation istance,, from the transmitter to the lector an back to the receiver as shown in Figure 1 is calculate as follows: x x y y z x x y y z (1) where x, y, an z are the coorinates of the lector an x, x, y an y are the coorinates of the transmit an receive array elements respectively. The thir step in the simulation is to apply phase shifts to the spectrum of the input signal to simulate the propagation elays an compute the phase shifte spectrum, G, (). By ignoring the attenuation of the meium an the element irectivity effects it can be written :, ik q F e G, () 0

3 where q is a factor to account for the missing pitch-catch information (q = 1 for pulse-echo time-traces where the transmitter an receiver are the same an q = for pitch-catch timetraces), k is the circular wave number an F 0 () is the spectrum of the transmitte signal. Finally, the spectra G, () is returne to the time-omain to yiel the time trace g, (t). 3 Array ata processing Two post processing algorithms, terme the Focusing Metho (FM) an the Angular Metho (AM), were then use to generate the images. The FM algorithm procees by first iscretising any region of space in front of the array into a gri as shown in Figure. The beam is then focuse at every point in the gri to generate a fully focuse image. The intensity of the image, I(x,y,z) for the FM at any point in the gri is calculate by: I, (3), x x y, z g, cl where c l is the bulk longituinal velocity an x x y y z x x y y (4), z The AM scan algorithm procees by steering the beam through a range of angles, as shown in Figure. The intensity of the image, for the angular scan metho is calculate by: where x, y, z g t I,, (5) 1 z n n t, rcos cos sin (6) cl cos N N The nan n are the inices of the circular array element an N is the total number of elements. The raius of the circular array is r, the elevation angle is an the azimuth angle is as shown in Figure 1. Array probe Focus point Figure : Imaging algorithms a) TFM scan b) Angular scan

4 API value Near fiel API value Z () Z () X () X () Figure 3: B scan images when the lector point at x = 3.3, y =0, an z =10: a) TFM scan image b) Angular scan image. The scale shown to right of each image is in B. 4 Comparison of FM an AM scan performance In orer to quantify the performance of each scan algorithm a parameter calle the Array Performance Inicator (API) is efine. The API is a imensionless measure of the volume of the 3D point sprea function (PSF): V 6B API (7) 3 where V -6 B is the volume of PSF that is within 6B of its maximum value. A low API Distance along z axis () Steering angle (egrees) Figure 4: Comparison of TFM an Angular scan moel ata using API value a) API vs. lector z position; b) API vs. lector steering angle at z = 16.6 & z =5. value inicates that the beam from an array is well focuse.

5 The volume of the PSF is calculate by first computing I(x,y,z) over a 3D mesh of points aroun the lector location an then counting the number of voxels (a voxel is a three imensional pixel) within which the value of the PSF is within 6B of its maximum value. Even with current computing power, the calculation of intensity over a 3D mesh of points is computationally intensive an, theore, it is esirable for the pitch of the mesh an hence the voxel size to be as large as possible [7]. Figures 3a an 3b show the x-z plane images of the FM an AM scan respectively, from a single lector locate at a istance of x = 3.3 an z = 10. It can be seen by comparing Figure 3a with Figure 3b that the image resolution is increase when the FM algorithm use. The API value for the FM an AM scan was 0.95 an 1.56 respectively. Further comparison of the FM an AM scan was carrie out. Firstly, a point lector was move along the z axis from near to far fiel while the x an y positions remain constant an equal to zero. The API was calculate at each lector point. Moel ata from the two imaging algorithms are shown in Figure 4. The FM scan always emonstrates the lowest API value for lectors on the z axis (specially in the near fiel). Seconly, the point lector was move along an arcs of raius 16.6 an 5. Moel ata from the two imaging algorithms are shown in Figure 4. It again emonstrates lower API values for the FM. 6 Conclusion This paper has escribe an investigation into the performance of two imaging algorithms terme the FM an AM scan for post processing ultrasonic array ata. The imaging performance of the FM an AM scan algorithm has been quantifie by using the API value. Simulation results inicate that the image resolution is increase when the FM scan use an always emonstrate the lower API value than the AM scan, in both cases when the point lector was on the z axis (specially in the near fiel) an move along an arcs of raius 16.6 an 5. References 1. Huang, Q., Zheng, Y., Lu, M., an Chi, Z., 005, Development of a Portable 3D Ultrasoun Imaging System for Musculoskeletal Tissues, Ultrasonics, 40, pp Yen, J.T., an Smith, S.W., 00, Real Time Rectilinear Volumetric Imaging, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 49, no. 1, pp Menelsohn,Y., an Wiener-Avnear, E., 00, Simulations of Circular D Phase-Array Ultrasonic Imaging Transucers, Ultrasonics, 39, pp Holmes, C., Wilcox, P.D., an Drinkwater, B.W., 004, The Post Processing of Ultrasonic Array Data Using the Total Focusing Metho, Insight, 46, no.11, pp Daniel, H.T., an Stuart, F., 1991, Beam Steering with Pulse D Transucer Arrays, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 39, no. 4, pp Wooh, S.C., an Yijun, S., 1999 Optimum Beam Steering of Linear Phase Arrays, Wave Motion, 9, pp Monal, S.C., Wilcox, P.D., an Drinkwater, B.W., 005, Design of D Ultrasonic Phase Array Transucers, ASME J. of Press. Vess. Tech., 17 no.3, pp