Ultrasonics 67 (2016) 85–93
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Passive focusing techniques for piezoelectric air-coupled ultrasonic transducers Tomás E. Gómez Álvarez-Arenas ⇑, Jorge Camacho, Carlos Fritsch ITEFI-CSIC, Serrano 144, 28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 29 May 2015 Received in revised form 16 November 2015 Accepted 5 January 2016 Available online 13 January 2016 Keywords: Air coupled ultrasound Ultrasonic transducers Focusing Newtonian Cassegrain
a b s t r a c t This paper proposes a novel passive focusing system for Air-Coupled Ultrasonic (ACU) piezoelectric transducers which is inspired by the Newtonian–Cassegrain (NC) telescope concept. It consist of a primary spherical mirror with an output hole and a flat secondary mirror, normal to the propagation axis, that is the transducer surface itself. The device is modeled and acoustic field is calculated showing a collimated beam with a symmetrical focus. A prototype according to this design is built and tested with an ACU piezoelectric transducer with center frequency at 400 kHz, high-sensitivity, wideband and 25 mm diameter flat aperture. The acoustic field is measured and compared with calculations. The presented prototype exhibit a 1.5 mm focus width and a collimated beam up to 15 mm off the output hole. In addition, the performance of this novel design is compared, both theoretically and experimentally, with two techniques used before for electrostatic transducers: the Fresnel Zone Plate – FZP and the off-axis parabolic or spherical mirror. The proposed NC arrangement has a coaxial design, which eases the transducers positioning and use in many applications, and is less bulky than off-axis mirrors. Unlike in off-axis mirrors, it is now possible to use a spherical primary mirror with minimum aberrations. FZP provides a more compact solution and is easy to build, but presents some background noise due to interference of waves diffracted at out of focus regions. By contrast, off-axis parabolic mirrors provide a well defined focus and are free from background noise, although they are bulky and more difficult to build. Spherical mirrors are more easily built, but this yields a non symmetric beam and a poorly defined focus. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Air-coupled ultrasound (ACU) sensing offers advantages over conventional fluid coupling techniques where the use of coupling fluids is not possible either for practical reasons or for the undesired effect they may have on the material under study. Applications appear in the fields of Non Destructive Testing (NDT) [1–9] materials characterization [10–14], wireless power and information transmission [15], sensing and analysis of cultural heritage [16,17], water control in agriculture [18,19], 3D surface profiling [20,21], quality control in the food industry [22,23] and computer gesture-based control [24,25]. Main drawbacks are the strong velocity and impedance mismatch between air and solids, which yields a very large reflection coefficient and a strong refraction at any air/solid interface and the high attenuation in the air. This imposes severe restrictions in the system dynamic range and in the alignment of sound beam axes ⇑ Corresponding author. http://dx.doi.org/10.1016/j.ultras.2016.01.001 0041-624X/Ó 2016 Elsevier B.V. All rights reserved.
and material surface, making difficult the inspection of non-flat components, rough surfaces and the use of focused beams. Improvements in the design of ACU transducers [2,26–33], high energy excitations, low noise amplification and digital signal processing [34–38], have enabled the applications previously mentioned. To further reduce losses and keep a reasonable signal to noise ratio (SNR), working frequency is usually kept below 1 MHz. Disk-shaped piezocomposites for these relatively low frequencies have a typical diameter from 15 to 25 mm, which produce a sound beam with poor lateral resolution. There are a number of focusing solutions available to mitigate this problem. Phased array techniques can be used to this purpose [39]. Direct generation of collimated ultrasound beams has been achieved with annular array transducers with radii set to produce non-diffracting Bessel beams [40,41]. Bessel-type transducers with selective ring poling have been also proposed [42]. A simpler collimated beam design has been achieved by shaping two electrodes in one face of a homogeneous poled ceramic to generate plane or edge waves by switching the excitation [43].
86
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
These ‘‘active” techniques require phasing multiple excitations and specifically designed multi-element transducers to get a single beam. By contrast, the same functions have been traditionally achieved with simpler ‘‘passive” means: refractive (lenses), apodization (horns), reflexive (mirrors) or interference devices (zone plates), schematically summarized in Fig. 1. In spite of their limitations, these low-cost approaches can be very effective for real-life ACU applications. For capacitive or electrostatic transducers, solutions based on the use of a spherical back plate and adapted Mylar foils [44] or shaped reflective optics solutions (parabolic mirror) [45] have been described. Refractive lenses are commonly used to focus immersion transducers (Fig. 1a). The most common are spherically focused, although collimator lenses with logarithmic shape to get a large focal depth have been also proposed [46]. In the past, sound focusing in air was carried out by confining CO2 in a thin wall container with a convex lens shape [47]. However, implementation of this solution results cumbersome. Apodization allows narrowing the ultrasound beam by attaching masks, horns or cones (Fig. 1b), while this eases transducers alignment and reduces reverberations [48], this is achieved at the expense of significant signal amplitude and SNR losses [49]. Among the reflective techniques, parabolic mirrors have been used to focus ultrasonic beams of capacitive transducers, Fig. 1c [45,50,51]. However, they tend to be bulky, require careful mirror grinding and are rather difficult to align due to the lack of an evident propagation axis. Fresnel Zone Plates (FZP) (Fig. 1d), consist of alternating transmitting and opaque rings and have been tried before for aircoupled capacitive transducers [52–56]. Diffraction at the transmitting rings produce constructive interferences at the focus by proper selection of their radii at the operating frequency. FZP are thin and flat, which represent a compact focusing element. However, only a fraction of the sound beam intensity reaches the focus due to the masking effect of the opaque rings. Comprehensive theoretical background and experimental data are available, but a comparative analysis for ACU beamforming is missed in the literature. Such study would be useful to choose among the different passive focusing alternatives that best fit a specific application. In this work three passive focusing techniques for ACU transducers are analyzed: the well known FZP and off-axis focused mirror are compared with a new arrangement proposed here, which derives from the Newtonian-Cassegrain telescope concept. These configurations are tried together with piezoelectric, instead of capacitive transducers, as it was done in previous works, showing the compatibility of the different focusing configurations with the multilayered configuration of air-coupled piezoelectric transducers required to optimize bandwidth and sensitivity. 2. Background on passive focusing techniques The typical diameter of air-coupled piezoelectric transducers based on 1–3 connectivity piezocomposites is about 15–25 mm for frequencies below 400 kHz. For many applications, some means
must be used to reduce the beam width and increase lateral resolution. The most frequently used technique is carving a spherical surface in the ceramic element and in the matching layers. This method provides a fixed focus and different transducers are required to get different focusing distances. Furthermore, accurate fabrication of the stack of matching layers required for ACU transducers may become unpractical. For a concave transducer with an aperture D = 2R, the Full Width at Half Maximum of the field (FWHM) at focal distance F within the near field region (F < D2 =4k) is given by [57]:
FWHM ¼ 1:4
kF ; 2R
ð1Þ
which determines the half-width lateral resolution. For some ACU applications, part of the focused beam arrives to the target exceeding the critical angle for which full reflection is produced and either Lamb or surface waves may be generated, thus reducing its efficiency. Large focal distances should be used to minimize this effect. On the other hand, external focusing devices could be attached to a general-purpose flat transducer to change the beam shape and the focal distance. This would involve the use of concave matching layers but this has the undesired effect of breaking the resonant condition which is critical for the optimum design of the ACU transducer. Given these problems, diffractive and reflective techniques have been used instead: the Fresnel Zone Plate (FZP) and the off-axis parabolic mirrors. We briefly describe their working principles and some of their properties by continuous wave simulations using the Monochromatic Transfer Matrix method [58]. 2.1. Fresnel Zone Plates (FZP) A FZP is a diffractive device composed of a series of alternate transmitting and blocking rings, with radii set at:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2 n2 rn ¼ kFn þ n ¼ 1; 2; 3; . . . 4
ð2Þ
where F is focal distance and k is wavelength. Starting from the center, the circle with radius r1 is transparent; the first blocking ring is from r1 to r2 and so on. It can be verified that the distances from consecutive rn to the focus differ by half wavelength. This way, alternating transparent with opaque rings leave signals producing constructive interferences at the focus. The focus position F should be set within the near field limit. Although designed for a specific focal distance and wavelength, it has been shown that a single FZP is able of focusing in air over a rather large frequency range [54]. This way, a FZP with wideband transducers will provide an increased depth of field. Simulated field distributions of a FZP designed for f = 400 kHz, R = 12.5 mm and F = 35 mm are shown in Fig. 2a. It can be compared with the field created by an ideal spherically focused transducer of the same diameter at the same depth (Fig. 2b). Bottom panels of Fig. 2a and 2b shows the lateral profile at the focal plane for FZP and spherically focused transducer, respectively. In both cases, maximum field amplitude is found at 35.3 mm, with an estimated FWHM of 1.3 mm and a depth of field of 11.5 mm at 3 dB.
Fig. 1. Passive focusing: (a) Lens for immersion transducer; (b) Apodization cone; (c) Off-axis parabolic mirror and (d) Fresnel zone plate.
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
87
Fig. 2. Simulated field distribution: (a) Top: plane transducer with a FZP; Bottom: lateral profile at the focal plane. (b) Top: spherically focused transducer; f = 0.4 MHz, F = 35 mm, Bottom: lateral profile at the focal plane. Linear color scale in arbitrary units. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
However, there are remarkable differences. First, the noise floor (sound level out of the main lobe) of a FZP is higher than that of an ideally focused transducer. It is a consequence of diffraction at the plate, which does not completely block the sound at off-focus regions, where some constructive interference arises. Differently from lenses and mirrors, sound is not concentrated at focus, but the field is created by waves diffracted in the transparent rings. In fact, a FZP can be regarded as a selective mask for those waves not arriving in phase to the focus. As a related effect, multiple secondary foci of lower amplitude appear between the plate and the main focus. Another difference is that field amplitude at the focus is lower with FZP than with a concave transducer, as only about 60% (or less) of the FZP is transparent. Advantages of FZP focusing are low cost and small size. In fact, FZPs are convenient to focus transducers integrated in silicon or made with cellular polymers (ferroelectrets), where the FZP can be one of the transducer electrodes [39,59]. 2.2. Off-axis parabolic mirror A revolution paraboloid is the 3D surface obtained by turning a parabola around its axis. It has the well known property that rays parallel to the axis are reflected to the focus. This property holds for any part of the paraboloid, so that the focus can be set at some selected angle to offset the ultrasound beam from the transducer axis (see Fig. 1c). From a practical point of view it is better to steer the beam by 90° in order to facilitate the transducers alignment. Fig. 3a shows schematically such geometry with a transducer aperture of diameter D = 2R located at the x = 0 plane and with center at the coordinates origin. The mirror is a section of a paraboloid
wide enough to concentrate all the sound emitted by the transducer. Its center is located at distance L off the origin along the x-axis and the focus is in the paraboloid axis at distance F from the vertex V. The focal distance H equals half the parabola latus rectum, that is, H = 2F. The revolution paraboloid equation is:
ðz þ 2F Þ2 þ y2 ¼ 4FðL þ F xÞ
ð3Þ
For x P 0, the following design constraints must be satisfied:
LP
ðR þ 2F Þ2 F 4F
ð4Þ
FP
R2 4ðL RÞ
ð5Þ
Fig. 3b–d shows the simulated field for a 90° steering parabolic mirror with F = 17.5 mm and L = 20 mm, which produces a focus at H = 35 mm, attached to a 25 mm diameter 400 kHz air-coupled transducer. The FWHM at focus is 1.3 mm and the depth of field is 10 mm, similar to those found for the FZP and spherically focused transducers at 35 mm. Fig. 4 shows the lateral and axial field pattern of the off-axis parabolic mirror. Unlike FZP, off-axis mirrors concentrate sound in the focal region without apparent loses and the beam is symmetric around the focal axis. However, they are bulky and more difficult to align due to their non coaxial design. Another issue is the need of machining the parabolic surface with enough accuracy. Sometimes, a parabolic surface can be replaced by a simpler to build spherical one, in spite of producing some aberrations. To test this possibility, we compute the field produced by a spherical mirror with center and radius that best fits the precedent parabolic
88
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
Fig. 3. (a) Geometry of a 90° off-axis parabolic mirror. Simulated field in planes: (b) XZ, (c) YZ and (d) XY. D = 25 mm, L = 20 mm, F = 17.5 mm, f = 400 kHz.
Fig. 4. Lateral (left) and axial (right) field pattern of the off-axis parabolic mirror shown in Fig. 3.
mirror. In the axis (y = 0, z = 0), geometric differences among both mirrors are below 80 lm, but they increase up to 0.73 mm towards the mirror border in the y-direction. Such error is in the order of one wavelength and will produce severe beam distortions. Fig. 5 shows the acoustic field created by such spherical mirror. The beam is deviated from the expected 90° steering angle (Fig. 5a) and is not symmetric. Fig. 5b–e indicates the presence of two beams due to aberrations at the mirror border in the y-direction. Fig. 5c shows the field at the focal plane, where it is seen that resolution is not isotropic, with a FWHM of 1.7 8 mm. These results deviate significantly from those given by the emulated parabolic off-axis mirror and, thus, we must conclude that off-axis spherical mirrors are not suitable for beam focusing. The key to limit aberrations when using spherical instead of parabolic mirrors is to keep incident angles on the surface near 90°. This approximation is not valid with off-axis mirrors, which demand the more complex parabolic construction, but can be used in the Newtonian–Cassegrain design addressed below.
3. A Newtonian–Cassegrain design for a focused air-coupled transducer Aimed to solve the mentioned problems of FZP and off-axis parabolic mirrors, we propose a design based on a variation of the Newtonian telescope. Originally, it was composed of a primary concave parabolic mirror with a secondary flat mirror in the optical axis tilted 45° to steer the rays 90° to the eyepiece mounted at the side of the telescope. A variation of this design is the Cassegrain telescope, where primary (parabolic) and secondary (hyperbolic) mirrors are coaxial and the eyepiece is attached to a centered hole in the primary mirror. Based on these ideas we propose an ACU focusing element completely coaxial, where the secondary mirror is flat, as in the Newtonian telescope, but normal to the propagation axis; in fact, we propose using the transducer surface itself as the secondary mirror. A hole in the center of the primary mirror allows the beam to propagate outside the device, like in Cassegrain telescopes (Fig. 6a). We
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
89
Fig. 5. Simulated field obtained with a spherical off-axis mirror: (a) XZ plane, (b) YZ plane, (c) XY plane at focal depth, (d) lateral (along X) field pattern, (e) lateral (along Y) field pattern and (f) axial field pattern.
call such focusing arrangement a Newtonian–Cassegrain design or NC in short. Waves generated by the transducer are reflected back by the primary mirror towards the transducer surface, which acts as the secondary mirror. After a second reflection, a focused beam is produced at the output hole. This way a compact and rotationally symmetric device is obtained, which facilitates the transducer alignment. With reference to Fig. 6a, the plane wave generated by a transducer of diameter D reaches the primary mirror located at a distance L. Ideally a parabolic shaped mirror should be used to focus the beam, but as it is shown, a spherical mirror produce acceptable aberration errors in this case, because the angle of incidence of rays in the primary mirror is near 90° (quite different to off-axis mirrors). With a curvature radius RP, a focus is produced at a distance F RP/2 from the mirror vertex; after reflection in the transducer surface, a focus is generated at a distance P from the device front:
P ¼ F 2L
ð6Þ
The minimum size of the output hole to do not intercept the focused wave-front can be approximated by:
aP
PD PD ; ðF þ PÞ F
FP
ð7Þ
Fig. 6b shows the simulated field of the NC focusing device with a primary mirror of RP = 70 mm, L = 16 mm and a = 5 mm. This results in F = 35 mm (from the transducer surface) and P = 3 mm. It is seen that the beam remains collimated with the maximum field amplitude within 3 dB up to a depth of 24 mm from the output hole (Fig. 6d) and the FWHM is 1.3 mm (Fig. 6c). Fig. 7 shows the geometrical differences between spherical and parabolic surfaces for the primary mirror specified above. It is seen
that they are below 20 lm, an error that is more than 40 times lower than the wavelength (k = 850 lm for f = 400 kHz). This way and, differently from the off-axis parabolic mirror, a simpler to build spherical surface can be used instead with little impact on the focusing properties. The proposed NC design presents losses due to the reduction of the primary mirror surface by the area of the output hole. These losses are proportional to the ratio of the hole to the transducer aperture surface. For the considered case, these represent about 1.5 dB. Another subject is the time it takes the main beam to reach the output hole. When the transducer is triggered, a first pulse arrives at the output at time t1 = L/c, where c is the sound propagation velocity (c 340 m/s in air). The time-of-flight of the main focused pulse is about three times that figure, that is, t2 = (3L + P)/c. The first pulse has small amplitude, since it results from an apodization of the order (a/D)2. For the example design, t1 = 47 ls, t2 = 141 ls and the relative amplitude of the first pulse is 0.16 (16 dB in relation to the focused pulse). The longer acquisition time will rarely affect the pulse repetition rate, mainly limited by the time required to damp reverberations. In general, the presence of both pulses does not disturb measurements because they are well separated in time, even when emitting with large bursts of 8–16 periods. They are separated by a constant time, so that are easily discriminated from other indications.
4. Experimental verification Experiments were carried out using a pair of wideband 400 kHz ACU transducers of own design (k 0.85 mm). They were built with a 25 mm diameter, 1–3 connectivity piezocomposite made
90
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
Fig. 6. (a) Newtonian–Cassegrain focusing principle; (b) calculated acoustic field; (c) calculated lateral field pattern and (d) calculated axial field pattern.
Fig. 7. Geometric differences between spherical and parabolic surfaces.
of randomly embedded piezoceramic fibers (PZT5A) in an epoxy matrix, 65% ceramic volume fraction. A stack of three impedance matching layers were attached following the techniques described in [31,32] with the purpose of optimizing both bandwidth and sensitivity simultaneously. Transducer housing is a 30 mm diameter aluminum cylinder. To measure transducers performance, transmitter (Tx) to receiver (Rx) separation was set to 20 mm, Tx was driven using a Panametrics 5077 pulser/receiver, pulse amplitude 200 V, and Rx was connected to the receiver stage, gain set to 0 dB. Signal was acquired using a digital oscilloscope (Tektronix DPO 7054) in high
Fig. 8. Impulse response and sensitivity of a pair of 400 kHz ACU transducers in through transmission mode.
resolution mode, sampling frequency 10 MHz. Sensitivity (SNS) is defined as:
SNS ¼ 20 logðjFFTðV Rx Þj=jFFTðV Tx ÞjÞ
ð8Þ
where VRx and VTx are the voltage measured across receiver and transmitter transducers terminals, respectively, and || represents the absolute value. The transducers impulse response and sensitivity band are shown in Fig. 8. Peak sensitivity of 29 dB is achieved at 478 kHz.
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
91
Fig. 9. Three passive focusing devices: (a) FZP and (b) off-axis spherical mirror, both attached to a 30 mm diameter 400 kHz air-coupled transducer and (c) interior of the NC design showing primary mirror, spacer and output hole.
For beam characterization, emission and reception was carried out with an AirScope instrument (Dasel, S.L, Madrid, Spain), which provides programmable burst excitation (voltage up to 400 V, frequency and length), signal conditioning in reception (up to 120 dB amplification and selectable filter bandwidth from 20 kHz to 3 MHz). The instrument is controlled through an Ethernet link from a conventional computer. A XYZ scanner DIS-800 (Dasel S. L., Madrid, Spain) allows performing field measurements. As receiver we used a transducer identical to that used as transmitter but, in this case, with a 0.75 mm pinhole mask to obtain a wide field of view. All measurements were carried out with passive focusing devices attached externally to the emitter transducer. We built three prototypes: (a) FZP: 30 mm diameter, 400 kHz and a focal distance of 35 mm (Fig. 9a). The FZP was micro-machined in a 0.1 mm thick stainless steel sheet and bonded to a cylinder to facilitate its attachment to the transducer case.
(b) A 45° spherical mirror with a best fit to a parabolic surface, with a focal distance H = 35 mm and L = 20, as described before (Fig. 9b). (c) A NC coaxial design with a primary mirror of RP = 70 mm (focal distance 35 mm), a spacer to set L = 16 mm and output hole diameter a = 8 mm (Fig. 9c), where the transducer surface acts directly as the secondary mirror (not shown). Fig. 10a shows the measured field for the FZP arrangement. A focus is observed at 33.5 mm (nominal 35 mm), as well as secondary foci at other ranges. The ‘‘noise floor” resulting from diffraction and interference at positions different from the focus can also be appreciated. Measured FWHM is 2.5 mm (theoretical 1.3 mm) and depth of focus is 8 mm (theoretical 11.5 mm). Differences are more noticeable in FWHM, which are explained by increased diffraction at the ring zone plate boundaries due to the mask thickness, considered zero in the simulation.
Fig. 10. Measured field: (a) FZP, (b) 45° spherical mirror in YZ, (c) 45° spherical mirror in XZ, (d) 45° spherical mirror in XY. Amplitude in arbitrary units.
92
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
Fig. 11. (a) Measured acoustic field of the NC arrangement and (b) theoretical-experimental comparison of the lateral field profile at focal distance.
Fig. 10b–d shows the measured field distribution for the off-axis spherical mirror in the YZ, XZ and XY planes. Experimental results agree with the theoretical ones shown in Fig. 5 with minor deviations. Among them, the twin-foci expected in the YZ plane become merged in a 10 mm wide focus. In the XZ plane, the field shape is similar to that obtained by simulation, with the exception of the enhanced sidelobes on the latter case computed for continuous wave. Resolution, as explained before, is not isotropic in the XY plane, finding a FWHM of 3 10 mm. Resolution anisotropy and field distortion are the major drawbacks of this configuration. Fig. 11a shows the measured field provided by the NC arrangement. Results show a good agreement with the theoretically expected ones (see Fig. 6b). Fig. 11b shows a comparison between calculated and measured lateral profiles; measured FWHM from Fig. 11b is 1.5 mm (1.3 mm expected). The beam remains collimated up to 15 mm off the output hole. The larger mismatch with theory is the increased sidelobe width (Fig. 11b), probably due to reflections/diffraction in the thickness of the primary mirror at the output hole, theoretically considered zero. The NC arrangement provides lower noise than FZP and has lower losses, mainly due to the relation of hole to PZT areas. On the other hand, and unlike the off-axis spherical mirror, it provides a symmetrical beam, like an off-axis parabolic mirror, but with lower mechanical complexity and with a smaller coaxial design. 5. Conclusions Passive focusing devices for Air-Coupled Ultrasound (ACU) transducers provide simple methods to concentrate the sound beam into a focus. This helps to improve lateral resolution and increase sensitivity. This work analyzed both theoretical and experimentally the behavior of three passive focusing devices: Fresnel Zone Plates (FZPs), off-axis parabolic and spherical mirrors and a new design derived from the Newtonian–Cassegrain (NC) telescope concept. For the experimental work air-coupled piezoelectric transducers with center frequency at 400 kHz and 25 mm diameter aperture has been used and all designs shared a 35 mm focal distance. FZPs are small devices easy to build, although they present a relatively high noise floor due to diffraction and interference of signals at out-of-focus regions. However the resulting arrangement is coaxial, which facilitates transducer alignment and integration. Off-axis parabolic mirrors provide well collimated beams with a symmetrical focus. By contrast, off-axis spherical mirrors produce large aberrations, deforming the beam shape and focus. Both are bulky and parabolic mirrors require careful grinding. Alignment of these devices is, in general, more complicated.
The proposed NC solution has a coaxial design, uses an easy to build spherical primary mirror with a sound output hole, while the ceramic itself acts as the secondary mirror. It is less bulky than offaxis mirrors but more than FZPs. The NC arrangement is easily aligned and produces a well collimated beam with a symmetrical focus at the specified range. It has slight losses due to the hole in the primary mirror. Acknowledgements This work was supported by a R&D contract with Dasel, S.L. in the framework of the EuroStar E!8929 Nuthic project, funded by the E. U. and by the DPI 2011-22348 project funded by the National R&D program, Spanish Ministry of Economy and Competitivity. We want also to acknowledge the assistance of L. Díez, E. Villanueva and J.C. Liébana in the development of the transducer prototypes. References [1] M. Luukkala, P. Heikkila, J. Surakka, Plate wave resonance – a contactless test method, Ultrasonics 9 (4) (1971) 201–208. [2] M. Deka, Air-coupled ultrasonic transducers for NDE, in: Proc. IEEE Ultrason. Symp, 1987, pp. 543–546. [3] C.M. Fortunko, J.O. Strycek, W.A. Grandia, Nondestructive testing of thick aerospace honeycomb structures using through-transmitted ultrasonic guided waves, Rev. Prog. Quant. NDE 8B (1990) 1643–1650. [4] D. Reilly, G. Hayward, Through air transmission for ultrasonic nondestructive testing, in: Proc. IEEE Ultrason. Symp., 1991, pp. 763–766. [5] A.J. Rogovsky, Development and application of ultrasonic dry-contact and aircontact C-scan systems for nondestructive evaluation of aerospace composites, Mater. Eval. 49 (1991) 1491–1497. [6] W. Grandia, C.M. Fortunko, NDE applications of air-coupled ultrasonic transducers, in: Proc. IEEE Ultrason. Symp., 1995, pp. 697–709. [7] W. Hillger, R. Meier, Inspection of CFRP components by ultrasonic imaging with air coupling, in: 8th ECNDT, Barcelona, Spain, 2002. [8] R.E. Green, Non-contact ultrasonic techniques, Ultrasonics 42 (2004) 9–16. [9] D.K. Hsu, Nondestructive testing using air-borne ultrasound, Ultrasonics 44 (2006) 1019–1024. [10] D.A. Hutchins, W.M.D. Wright, Ultrasonic measurements in polymeric materials using air-coupled capacitance transducers, J. Acoust. Soc. Am. 96 (3) (1994) 1634–1642. [11] B. Hosten, D.A. Hutchins, D.W. Schindel, Measurement of elastic constants in composite materials using air-coupled ultrasonic bulk waves, J. Acoust. Soc. Am. 99 (4 Pt.1) (1996) 2116–2123. [12] T.E. Gómez Álvarez-Arenas, F.R. Montero, M. Moner-Girona, E. Rodrı´guez, A. Roig, E. Molins, Viscoelasticity of silica aerogels at ultrasonic frequencies, Appl. Phys. Lett. 81 (7) (2002) 1198. [13] T.E. Gómez Álvarez-Arenas, Air-coupled ultrasonic spectroscopy for the study of membrane filters, J. Membr. Sci. 213 (1–2) (2003) 195–207. [14] M.D. Fariñas, D. Sancho-Knapik, J.J. Peguero-Pina, E. Gil-Pelegrín, T.E. Gómez Álvarez-Arenas, Shear waves in vegetal tissues at ultrasonic frequencies, Appl. Phys. Lett. 102 (10) (2013) 103702. [15] T. Ishiyama, Y. Kanai, J. Ohwaki, M. Mino, M. Wakamiya, Impact of a wireless power transmission system using an ultrasonic air transducer for low-power mobile applications, in: Proc. IEEE Ultrason. Symp., 2003, pp. 1368–1371.
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93 [16] F.J. García-Diego, J.M. Bravo, J. Pérez-Miralles, H. Estrada, A. FernándezNavajas, Development of a low-cost airborne ultrasound sensor for the detection of brick joints behind a wall painting, Sensors (Basel, Switzerland) 12 (2) (2012) 1299–1311. [17] J. Bravo, J. Sánchez-Pérez, M. Ferri, J. Redondo, R. Picó, Application of ultrasound phase-shift analysis to authenticate wooden panel paintings, Sensors 14 (5) (2014) 7992–8002. [18] D. Sancho-Knapik, T.E. Gómez Alvarez-Arenas, J.J. Peguero-Pina, E. Gil-Pelegrín, Air-coupled broadband ultrasonic spectroscopy as a new non-invasive and non-contact method for the determination of leaf water status, J. Exp. Botany 61 (5) (2010) 1385–1391. [19] D. Sancho-Knapik, H. Calás, J.J. Peguero-Pina, A. Ramos Fernandez, E. GilPelegrín, T.E. Gómez Alvarez-Arenas, Air-coupled ultrasonic resonant spectroscopy for the study of the relationship between plant leaves’ elasticity and their water content, IEEE Trans. Ultrason., Ferroelectr. Freq. Control 59 (2) (2012) 319–325. [20] D.J. Roth, E. Kautz, J.L. Hendricks, 3-D surface depression profiling using high frequency focused ultrasonic pulses, NASA/TM-1999-209053, 1999. [21] T.E. Gomez Alvarez-Arenas, F. Montero, A.P. Pozas, Air-coupled ultrasonic scanner for Braille, in: Proc. IEEE Ultrason. Symp., vol. 1, 2001, pp. 591–594. [22] T.H. Gan, D. Hutchins, D.R. Billson, Preliminary studies of a novel air-coupled ultrasonic inspection system for food containers, J. Food Eng. 53 (2002) 315– 323. [23] E. Corona, J.V. Garcia-Perez, T.E. Gomez Alvarez-Arenas, N. Watson, M.J.W. Povey, J. Benedito, Advances in the ultrasound characterization of dry-cured meat products, J. Food Eng. 119 (3) (2013) 464–470. [24] R. Mcmillan, The technology and applications of gesture-based control, RTO lecture series on Alternative Control Technologies: Human Factor Issues, 4, 1998, pp. 1–11. [25] T. Chiu, H. Deng, S. Chang, Implementation of ultrasonic touchless interactive panel using the polymer-based CMUT array, IEEE Sensors (2009) 625–630. [26] T. Yano, M. Tone, A. Fukumoto, Range finding and surface characterization using high-frequency air transducers, IEEE Trans. Ultrason., Ferroelec. Freq. Control 34 (2) (1987) 232–236. [27] B T. Khuri-Yakub, J. H. Kim, C. Chou, P. Parent, G.S. Kino, A new design for air transducers, in: Proc. IEEE Int’l Ultrason. Symp., 1988, pp. 503–506. [28] W. Manthey, N. Kroemer, V. Mágori, Ultrasonic transducers and transducers arrays for applications in air, Measur. Sci. Technol. 3 (1992) 249–261. [29] D.W. Schindel, D.A. Hutchins, L. Zou, M. Sayer, The design and characterization of micromachined air-coupled capacitance transducers, IEEE Trans. Ultrason., Ferroelectr. Freq. Control 42 (1) (1995) 42–50. [30] D.W. Schindel, D.A. Hutchins, W.A. Grandia, Capacitive and piezoelectric aircoupled transducers for resonant ultrasonic inspection, Ultrasonics 34 (6) (1996) 621–627. [31] S.P. Kelly, G. Hayward, T.E.G. Alvarez-Arenas, Characterization and assessment of an integrated matching layer for air-coupled ultrasonic applications, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51 (10) (2004) 1314–1323. [32] T.E. Gómez Alvarez-Arenas, Acoustic impedance matching of piezoelectric transducers to the air, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51 (5) (2004) 624–633. [33] T.E. Gómez Alvarez-Arenas, Wide-band air-coupled ultrasonic piezoelectric transducers, in: International Symposium on Piezocoposite Applications, Dresden, Germany, September 22–23, 2011. [34] A. Turo, J. Salazar, J.A. Chavez, H.B. Kichou, T.E. Gomez, F. Montero de Espinosa, M.J. Garcia-Hernandez, Ultra-low noise front-end electronics for air-coupled ultrasonic non-destructive evaluation, NDT & E Int. 36 (2) (2003) 93–100. [35] L. Svilainis, A. Chaziachmetovas, V. Dumbrava, Efficient high voltage pulser for piezoelectric air coupled transducer, Ultrasonics 51 (1) (2012) 225–231. [36] D. Hutchins, P. Burrascano, L. Davis, S. Laureti, M. Ricci, Coded waveforms for optimised air-coupled ultrasonic non destructive evaluation, Ultrasonics 54 (2014) 1745–1759.
93
[37] T.H. Gan, D.A. Hutchins, R.J. Green, Swept frequency multiplication (SFM) techniques for improved air-coupled ultrasonic NDE, Rev. Progr. Quant. Nondestruct. Eval. 22 (2003) 620–627. [38] J. Buckley, Air-coupled ultrasound: A Millennial Review, in: 15th WCNDT, Rome, Italy, 2000. [39] J. Ealo, J. Camacho, C. Fritsch, Airborne ultrasonic phased arrays using ferroelectrets: a new fabrication approach, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 (4) (2009) 818–858. [40] J.Y. Lu, Ultrasonic nondiffracting transducer for medical imaging, IEEE Trans. UFFC 37 (5) (1990) 438–447. [41] J.Y. Lu, J.F. Greenleaf, Ultrasonic nondiffracting transducer, US. Pat. 5,081.995, January 21, 1992. [42] J. Eirás et al., Vibration Modes in Ultrasonic Bessel Transducer, in: Proc. IEEE Ultrason. Symp., 2003, pp. 1314–1317. [43] D. De Vadder, A. Lhémery, N. Gengembre, A new ultrasonic combining three modes: high axial resolution, high transverse resolution and standard modes, Rev. Progr. Quant. Nondestruct. Eval. 15 (1996) 979–986. [44] J. Song, D.E. Chimenti, Design, fabrication and characterization of a spherically focused capacitive air-coupled ultrasonic transducer, Int. J. Appl. Sci. Eng. 4 (1) (2006) 1–19. [45] B. Hosten, M. Castaigns, Parabolic mirror and air-coupled transducer for multimodal plate wave detection, Rev. Progr. Quant. Nondestruct. Eval. 22 (2003) 1243–1250. [46] A. Karpelson, Piezotransducers with acoustic lenses forming narrow weakly diverging ultrasonic beams, ECNDT, Mo.2.7.2, Berlin, Germany, 2006. [47] T. Tarnockzy, Sound focussing lenses and waveguides, Ultrasonics (1965) 115– 127. [48] J. Peters, V. Kommareddy, Z. Liu, D. Fei, D. Hsu, Non-contact inspection of composites using air-coupled ultrasound, Rev. Progr. Quant. Nondestruct. Eval. 22 (2003) 973–980. [49] A. Vladišauskas, R. Raišutis, E. Zˇukauskas, Air-coupled ultrasonic transducers with collimators, Ultragarsas 64 (1) (2006) 24–28. [50] X. Dai, J. Zhu, Y.-T. Shai, Use of parabolic reflector to amplify in-air signals generated during impact-echo testing, J. Acoust. Soc. Am. 130 (4) (2011) 167– 172. [51] T.H. Gan, D.A. Hutchins, D.R. Billson, D.W. Schindel, High-resolution, aircoupled ultrasonic imaging of thin materials, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (11) (2003) 1516–1524. [52] B. Hadimioglu, E.G. Rawson, R. Lujan. M. Lim, J.C. Zesch, B.T. Khuri-Yakub, C.F. Ouate, High-efficiency Fresnel acoustic lenses, in: Proc. IEEE Ultrason. Symp., 1993, pp. 579–582. [53] M.Z. Sleva, W.D. Hunt, R.D. Briggs, Focusing performance of epoxi and airbacked polyvinylidene fluoride Fresnel zone plates, J. Ac. Soc. Am. 96 (3) (1994) 1627–1633. [54] D.W. Schindel, A.G. Bashford, D.A. Hutchins, Focussing of ultrasonic waves in air using a micromachined Fresnel zone-plate, Ultrasonics 35 (1997) 275–285. [55] D.W. Schindel, A.G. Bashford, D.A. Hutchins, Chromatic aberration of an aircoupled ultrasonic Fresnel zone-plate, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46 (1) (1999) 242–246. [56] W.J. Hugues, J.R. Craig, The focusing properties of an acoustic thin lens and zone plate, Tech. Report TR 96–003, Penn. State University, Applied Research Lab, April 1996. [57] R.S.C. Cobbold, Foundations of Biomedical Ultrasound, Oxford Univ. Press, Inc., 2007. [58] A. Ibáñez, C. Fritsch, M. Parrilla, J. Villazón, Monochromatic transfer matrix method for acoustic field simulation through media boundaries, Phys. Proc. 3 (2010) 883–890. [59] S. Bauer, S. Bauer-Gogonea, M. Dansachmüller, I. Graz, H. Leonhartsberger, H. Salhofer, R. Schwödiauer, Modern electrets, in: Proc. IEEE Ultrason. Symp., 2003, pp. 370–376.
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Passive focusing techniques for piezoelectric air-coupled ultrasonic transducers Tomás E. Gómez Álvarez-Arenas ⇑, Jorge Camacho, Carlos Fritsch ITEFI-CSIC, Serrano 144, 28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 29 May 2015 Received in revised form 16 November 2015 Accepted 5 January 2016 Available online 13 January 2016 Keywords: Air coupled ultrasound Ultrasonic transducers Focusing Newtonian Cassegrain
a b s t r a c t This paper proposes a novel passive focusing system for Air-Coupled Ultrasonic (ACU) piezoelectric transducers which is inspired by the Newtonian–Cassegrain (NC) telescope concept. It consist of a primary spherical mirror with an output hole and a flat secondary mirror, normal to the propagation axis, that is the transducer surface itself. The device is modeled and acoustic field is calculated showing a collimated beam with a symmetrical focus. A prototype according to this design is built and tested with an ACU piezoelectric transducer with center frequency at 400 kHz, high-sensitivity, wideband and 25 mm diameter flat aperture. The acoustic field is measured and compared with calculations. The presented prototype exhibit a 1.5 mm focus width and a collimated beam up to 15 mm off the output hole. In addition, the performance of this novel design is compared, both theoretically and experimentally, with two techniques used before for electrostatic transducers: the Fresnel Zone Plate – FZP and the off-axis parabolic or spherical mirror. The proposed NC arrangement has a coaxial design, which eases the transducers positioning and use in many applications, and is less bulky than off-axis mirrors. Unlike in off-axis mirrors, it is now possible to use a spherical primary mirror with minimum aberrations. FZP provides a more compact solution and is easy to build, but presents some background noise due to interference of waves diffracted at out of focus regions. By contrast, off-axis parabolic mirrors provide a well defined focus and are free from background noise, although they are bulky and more difficult to build. Spherical mirrors are more easily built, but this yields a non symmetric beam and a poorly defined focus. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Air-coupled ultrasound (ACU) sensing offers advantages over conventional fluid coupling techniques where the use of coupling fluids is not possible either for practical reasons or for the undesired effect they may have on the material under study. Applications appear in the fields of Non Destructive Testing (NDT) [1–9] materials characterization [10–14], wireless power and information transmission [15], sensing and analysis of cultural heritage [16,17], water control in agriculture [18,19], 3D surface profiling [20,21], quality control in the food industry [22,23] and computer gesture-based control [24,25]. Main drawbacks are the strong velocity and impedance mismatch between air and solids, which yields a very large reflection coefficient and a strong refraction at any air/solid interface and the high attenuation in the air. This imposes severe restrictions in the system dynamic range and in the alignment of sound beam axes ⇑ Corresponding author. http://dx.doi.org/10.1016/j.ultras.2016.01.001 0041-624X/Ó 2016 Elsevier B.V. All rights reserved.
and material surface, making difficult the inspection of non-flat components, rough surfaces and the use of focused beams. Improvements in the design of ACU transducers [2,26–33], high energy excitations, low noise amplification and digital signal processing [34–38], have enabled the applications previously mentioned. To further reduce losses and keep a reasonable signal to noise ratio (SNR), working frequency is usually kept below 1 MHz. Disk-shaped piezocomposites for these relatively low frequencies have a typical diameter from 15 to 25 mm, which produce a sound beam with poor lateral resolution. There are a number of focusing solutions available to mitigate this problem. Phased array techniques can be used to this purpose [39]. Direct generation of collimated ultrasound beams has been achieved with annular array transducers with radii set to produce non-diffracting Bessel beams [40,41]. Bessel-type transducers with selective ring poling have been also proposed [42]. A simpler collimated beam design has been achieved by shaping two electrodes in one face of a homogeneous poled ceramic to generate plane or edge waves by switching the excitation [43].
86
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
These ‘‘active” techniques require phasing multiple excitations and specifically designed multi-element transducers to get a single beam. By contrast, the same functions have been traditionally achieved with simpler ‘‘passive” means: refractive (lenses), apodization (horns), reflexive (mirrors) or interference devices (zone plates), schematically summarized in Fig. 1. In spite of their limitations, these low-cost approaches can be very effective for real-life ACU applications. For capacitive or electrostatic transducers, solutions based on the use of a spherical back plate and adapted Mylar foils [44] or shaped reflective optics solutions (parabolic mirror) [45] have been described. Refractive lenses are commonly used to focus immersion transducers (Fig. 1a). The most common are spherically focused, although collimator lenses with logarithmic shape to get a large focal depth have been also proposed [46]. In the past, sound focusing in air was carried out by confining CO2 in a thin wall container with a convex lens shape [47]. However, implementation of this solution results cumbersome. Apodization allows narrowing the ultrasound beam by attaching masks, horns or cones (Fig. 1b), while this eases transducers alignment and reduces reverberations [48], this is achieved at the expense of significant signal amplitude and SNR losses [49]. Among the reflective techniques, parabolic mirrors have been used to focus ultrasonic beams of capacitive transducers, Fig. 1c [45,50,51]. However, they tend to be bulky, require careful mirror grinding and are rather difficult to align due to the lack of an evident propagation axis. Fresnel Zone Plates (FZP) (Fig. 1d), consist of alternating transmitting and opaque rings and have been tried before for aircoupled capacitive transducers [52–56]. Diffraction at the transmitting rings produce constructive interferences at the focus by proper selection of their radii at the operating frequency. FZP are thin and flat, which represent a compact focusing element. However, only a fraction of the sound beam intensity reaches the focus due to the masking effect of the opaque rings. Comprehensive theoretical background and experimental data are available, but a comparative analysis for ACU beamforming is missed in the literature. Such study would be useful to choose among the different passive focusing alternatives that best fit a specific application. In this work three passive focusing techniques for ACU transducers are analyzed: the well known FZP and off-axis focused mirror are compared with a new arrangement proposed here, which derives from the Newtonian-Cassegrain telescope concept. These configurations are tried together with piezoelectric, instead of capacitive transducers, as it was done in previous works, showing the compatibility of the different focusing configurations with the multilayered configuration of air-coupled piezoelectric transducers required to optimize bandwidth and sensitivity. 2. Background on passive focusing techniques The typical diameter of air-coupled piezoelectric transducers based on 1–3 connectivity piezocomposites is about 15–25 mm for frequencies below 400 kHz. For many applications, some means
must be used to reduce the beam width and increase lateral resolution. The most frequently used technique is carving a spherical surface in the ceramic element and in the matching layers. This method provides a fixed focus and different transducers are required to get different focusing distances. Furthermore, accurate fabrication of the stack of matching layers required for ACU transducers may become unpractical. For a concave transducer with an aperture D = 2R, the Full Width at Half Maximum of the field (FWHM) at focal distance F within the near field region (F < D2 =4k) is given by [57]:
FWHM ¼ 1:4
kF ; 2R
ð1Þ
which determines the half-width lateral resolution. For some ACU applications, part of the focused beam arrives to the target exceeding the critical angle for which full reflection is produced and either Lamb or surface waves may be generated, thus reducing its efficiency. Large focal distances should be used to minimize this effect. On the other hand, external focusing devices could be attached to a general-purpose flat transducer to change the beam shape and the focal distance. This would involve the use of concave matching layers but this has the undesired effect of breaking the resonant condition which is critical for the optimum design of the ACU transducer. Given these problems, diffractive and reflective techniques have been used instead: the Fresnel Zone Plate (FZP) and the off-axis parabolic mirrors. We briefly describe their working principles and some of their properties by continuous wave simulations using the Monochromatic Transfer Matrix method [58]. 2.1. Fresnel Zone Plates (FZP) A FZP is a diffractive device composed of a series of alternate transmitting and blocking rings, with radii set at:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2 n2 rn ¼ kFn þ n ¼ 1; 2; 3; . . . 4
ð2Þ
where F is focal distance and k is wavelength. Starting from the center, the circle with radius r1 is transparent; the first blocking ring is from r1 to r2 and so on. It can be verified that the distances from consecutive rn to the focus differ by half wavelength. This way, alternating transparent with opaque rings leave signals producing constructive interferences at the focus. The focus position F should be set within the near field limit. Although designed for a specific focal distance and wavelength, it has been shown that a single FZP is able of focusing in air over a rather large frequency range [54]. This way, a FZP with wideband transducers will provide an increased depth of field. Simulated field distributions of a FZP designed for f = 400 kHz, R = 12.5 mm and F = 35 mm are shown in Fig. 2a. It can be compared with the field created by an ideal spherically focused transducer of the same diameter at the same depth (Fig. 2b). Bottom panels of Fig. 2a and 2b shows the lateral profile at the focal plane for FZP and spherically focused transducer, respectively. In both cases, maximum field amplitude is found at 35.3 mm, with an estimated FWHM of 1.3 mm and a depth of field of 11.5 mm at 3 dB.
Fig. 1. Passive focusing: (a) Lens for immersion transducer; (b) Apodization cone; (c) Off-axis parabolic mirror and (d) Fresnel zone plate.
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
87
Fig. 2. Simulated field distribution: (a) Top: plane transducer with a FZP; Bottom: lateral profile at the focal plane. (b) Top: spherically focused transducer; f = 0.4 MHz, F = 35 mm, Bottom: lateral profile at the focal plane. Linear color scale in arbitrary units. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
However, there are remarkable differences. First, the noise floor (sound level out of the main lobe) of a FZP is higher than that of an ideally focused transducer. It is a consequence of diffraction at the plate, which does not completely block the sound at off-focus regions, where some constructive interference arises. Differently from lenses and mirrors, sound is not concentrated at focus, but the field is created by waves diffracted in the transparent rings. In fact, a FZP can be regarded as a selective mask for those waves not arriving in phase to the focus. As a related effect, multiple secondary foci of lower amplitude appear between the plate and the main focus. Another difference is that field amplitude at the focus is lower with FZP than with a concave transducer, as only about 60% (or less) of the FZP is transparent. Advantages of FZP focusing are low cost and small size. In fact, FZPs are convenient to focus transducers integrated in silicon or made with cellular polymers (ferroelectrets), where the FZP can be one of the transducer electrodes [39,59]. 2.2. Off-axis parabolic mirror A revolution paraboloid is the 3D surface obtained by turning a parabola around its axis. It has the well known property that rays parallel to the axis are reflected to the focus. This property holds for any part of the paraboloid, so that the focus can be set at some selected angle to offset the ultrasound beam from the transducer axis (see Fig. 1c). From a practical point of view it is better to steer the beam by 90° in order to facilitate the transducers alignment. Fig. 3a shows schematically such geometry with a transducer aperture of diameter D = 2R located at the x = 0 plane and with center at the coordinates origin. The mirror is a section of a paraboloid
wide enough to concentrate all the sound emitted by the transducer. Its center is located at distance L off the origin along the x-axis and the focus is in the paraboloid axis at distance F from the vertex V. The focal distance H equals half the parabola latus rectum, that is, H = 2F. The revolution paraboloid equation is:
ðz þ 2F Þ2 þ y2 ¼ 4FðL þ F xÞ
ð3Þ
For x P 0, the following design constraints must be satisfied:
LP
ðR þ 2F Þ2 F 4F
ð4Þ
FP
R2 4ðL RÞ
ð5Þ
Fig. 3b–d shows the simulated field for a 90° steering parabolic mirror with F = 17.5 mm and L = 20 mm, which produces a focus at H = 35 mm, attached to a 25 mm diameter 400 kHz air-coupled transducer. The FWHM at focus is 1.3 mm and the depth of field is 10 mm, similar to those found for the FZP and spherically focused transducers at 35 mm. Fig. 4 shows the lateral and axial field pattern of the off-axis parabolic mirror. Unlike FZP, off-axis mirrors concentrate sound in the focal region without apparent loses and the beam is symmetric around the focal axis. However, they are bulky and more difficult to align due to their non coaxial design. Another issue is the need of machining the parabolic surface with enough accuracy. Sometimes, a parabolic surface can be replaced by a simpler to build spherical one, in spite of producing some aberrations. To test this possibility, we compute the field produced by a spherical mirror with center and radius that best fits the precedent parabolic
88
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
Fig. 3. (a) Geometry of a 90° off-axis parabolic mirror. Simulated field in planes: (b) XZ, (c) YZ and (d) XY. D = 25 mm, L = 20 mm, F = 17.5 mm, f = 400 kHz.
Fig. 4. Lateral (left) and axial (right) field pattern of the off-axis parabolic mirror shown in Fig. 3.
mirror. In the axis (y = 0, z = 0), geometric differences among both mirrors are below 80 lm, but they increase up to 0.73 mm towards the mirror border in the y-direction. Such error is in the order of one wavelength and will produce severe beam distortions. Fig. 5 shows the acoustic field created by such spherical mirror. The beam is deviated from the expected 90° steering angle (Fig. 5a) and is not symmetric. Fig. 5b–e indicates the presence of two beams due to aberrations at the mirror border in the y-direction. Fig. 5c shows the field at the focal plane, where it is seen that resolution is not isotropic, with a FWHM of 1.7 8 mm. These results deviate significantly from those given by the emulated parabolic off-axis mirror and, thus, we must conclude that off-axis spherical mirrors are not suitable for beam focusing. The key to limit aberrations when using spherical instead of parabolic mirrors is to keep incident angles on the surface near 90°. This approximation is not valid with off-axis mirrors, which demand the more complex parabolic construction, but can be used in the Newtonian–Cassegrain design addressed below.
3. A Newtonian–Cassegrain design for a focused air-coupled transducer Aimed to solve the mentioned problems of FZP and off-axis parabolic mirrors, we propose a design based on a variation of the Newtonian telescope. Originally, it was composed of a primary concave parabolic mirror with a secondary flat mirror in the optical axis tilted 45° to steer the rays 90° to the eyepiece mounted at the side of the telescope. A variation of this design is the Cassegrain telescope, where primary (parabolic) and secondary (hyperbolic) mirrors are coaxial and the eyepiece is attached to a centered hole in the primary mirror. Based on these ideas we propose an ACU focusing element completely coaxial, where the secondary mirror is flat, as in the Newtonian telescope, but normal to the propagation axis; in fact, we propose using the transducer surface itself as the secondary mirror. A hole in the center of the primary mirror allows the beam to propagate outside the device, like in Cassegrain telescopes (Fig. 6a). We
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
89
Fig. 5. Simulated field obtained with a spherical off-axis mirror: (a) XZ plane, (b) YZ plane, (c) XY plane at focal depth, (d) lateral (along X) field pattern, (e) lateral (along Y) field pattern and (f) axial field pattern.
call such focusing arrangement a Newtonian–Cassegrain design or NC in short. Waves generated by the transducer are reflected back by the primary mirror towards the transducer surface, which acts as the secondary mirror. After a second reflection, a focused beam is produced at the output hole. This way a compact and rotationally symmetric device is obtained, which facilitates the transducer alignment. With reference to Fig. 6a, the plane wave generated by a transducer of diameter D reaches the primary mirror located at a distance L. Ideally a parabolic shaped mirror should be used to focus the beam, but as it is shown, a spherical mirror produce acceptable aberration errors in this case, because the angle of incidence of rays in the primary mirror is near 90° (quite different to off-axis mirrors). With a curvature radius RP, a focus is produced at a distance F RP/2 from the mirror vertex; after reflection in the transducer surface, a focus is generated at a distance P from the device front:
P ¼ F 2L
ð6Þ
The minimum size of the output hole to do not intercept the focused wave-front can be approximated by:
aP
PD PD ; ðF þ PÞ F
FP
ð7Þ
Fig. 6b shows the simulated field of the NC focusing device with a primary mirror of RP = 70 mm, L = 16 mm and a = 5 mm. This results in F = 35 mm (from the transducer surface) and P = 3 mm. It is seen that the beam remains collimated with the maximum field amplitude within 3 dB up to a depth of 24 mm from the output hole (Fig. 6d) and the FWHM is 1.3 mm (Fig. 6c). Fig. 7 shows the geometrical differences between spherical and parabolic surfaces for the primary mirror specified above. It is seen
that they are below 20 lm, an error that is more than 40 times lower than the wavelength (k = 850 lm for f = 400 kHz). This way and, differently from the off-axis parabolic mirror, a simpler to build spherical surface can be used instead with little impact on the focusing properties. The proposed NC design presents losses due to the reduction of the primary mirror surface by the area of the output hole. These losses are proportional to the ratio of the hole to the transducer aperture surface. For the considered case, these represent about 1.5 dB. Another subject is the time it takes the main beam to reach the output hole. When the transducer is triggered, a first pulse arrives at the output at time t1 = L/c, where c is the sound propagation velocity (c 340 m/s in air). The time-of-flight of the main focused pulse is about three times that figure, that is, t2 = (3L + P)/c. The first pulse has small amplitude, since it results from an apodization of the order (a/D)2. For the example design, t1 = 47 ls, t2 = 141 ls and the relative amplitude of the first pulse is 0.16 (16 dB in relation to the focused pulse). The longer acquisition time will rarely affect the pulse repetition rate, mainly limited by the time required to damp reverberations. In general, the presence of both pulses does not disturb measurements because they are well separated in time, even when emitting with large bursts of 8–16 periods. They are separated by a constant time, so that are easily discriminated from other indications.
4. Experimental verification Experiments were carried out using a pair of wideband 400 kHz ACU transducers of own design (k 0.85 mm). They were built with a 25 mm diameter, 1–3 connectivity piezocomposite made
90
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
Fig. 6. (a) Newtonian–Cassegrain focusing principle; (b) calculated acoustic field; (c) calculated lateral field pattern and (d) calculated axial field pattern.
Fig. 7. Geometric differences between spherical and parabolic surfaces.
of randomly embedded piezoceramic fibers (PZT5A) in an epoxy matrix, 65% ceramic volume fraction. A stack of three impedance matching layers were attached following the techniques described in [31,32] with the purpose of optimizing both bandwidth and sensitivity simultaneously. Transducer housing is a 30 mm diameter aluminum cylinder. To measure transducers performance, transmitter (Tx) to receiver (Rx) separation was set to 20 mm, Tx was driven using a Panametrics 5077 pulser/receiver, pulse amplitude 200 V, and Rx was connected to the receiver stage, gain set to 0 dB. Signal was acquired using a digital oscilloscope (Tektronix DPO 7054) in high
Fig. 8. Impulse response and sensitivity of a pair of 400 kHz ACU transducers in through transmission mode.
resolution mode, sampling frequency 10 MHz. Sensitivity (SNS) is defined as:
SNS ¼ 20 logðjFFTðV Rx Þj=jFFTðV Tx ÞjÞ
ð8Þ
where VRx and VTx are the voltage measured across receiver and transmitter transducers terminals, respectively, and || represents the absolute value. The transducers impulse response and sensitivity band are shown in Fig. 8. Peak sensitivity of 29 dB is achieved at 478 kHz.
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
91
Fig. 9. Three passive focusing devices: (a) FZP and (b) off-axis spherical mirror, both attached to a 30 mm diameter 400 kHz air-coupled transducer and (c) interior of the NC design showing primary mirror, spacer and output hole.
For beam characterization, emission and reception was carried out with an AirScope instrument (Dasel, S.L, Madrid, Spain), which provides programmable burst excitation (voltage up to 400 V, frequency and length), signal conditioning in reception (up to 120 dB amplification and selectable filter bandwidth from 20 kHz to 3 MHz). The instrument is controlled through an Ethernet link from a conventional computer. A XYZ scanner DIS-800 (Dasel S. L., Madrid, Spain) allows performing field measurements. As receiver we used a transducer identical to that used as transmitter but, in this case, with a 0.75 mm pinhole mask to obtain a wide field of view. All measurements were carried out with passive focusing devices attached externally to the emitter transducer. We built three prototypes: (a) FZP: 30 mm diameter, 400 kHz and a focal distance of 35 mm (Fig. 9a). The FZP was micro-machined in a 0.1 mm thick stainless steel sheet and bonded to a cylinder to facilitate its attachment to the transducer case.
(b) A 45° spherical mirror with a best fit to a parabolic surface, with a focal distance H = 35 mm and L = 20, as described before (Fig. 9b). (c) A NC coaxial design with a primary mirror of RP = 70 mm (focal distance 35 mm), a spacer to set L = 16 mm and output hole diameter a = 8 mm (Fig. 9c), where the transducer surface acts directly as the secondary mirror (not shown). Fig. 10a shows the measured field for the FZP arrangement. A focus is observed at 33.5 mm (nominal 35 mm), as well as secondary foci at other ranges. The ‘‘noise floor” resulting from diffraction and interference at positions different from the focus can also be appreciated. Measured FWHM is 2.5 mm (theoretical 1.3 mm) and depth of focus is 8 mm (theoretical 11.5 mm). Differences are more noticeable in FWHM, which are explained by increased diffraction at the ring zone plate boundaries due to the mask thickness, considered zero in the simulation.
Fig. 10. Measured field: (a) FZP, (b) 45° spherical mirror in YZ, (c) 45° spherical mirror in XZ, (d) 45° spherical mirror in XY. Amplitude in arbitrary units.
92
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93
Fig. 11. (a) Measured acoustic field of the NC arrangement and (b) theoretical-experimental comparison of the lateral field profile at focal distance.
Fig. 10b–d shows the measured field distribution for the off-axis spherical mirror in the YZ, XZ and XY planes. Experimental results agree with the theoretical ones shown in Fig. 5 with minor deviations. Among them, the twin-foci expected in the YZ plane become merged in a 10 mm wide focus. In the XZ plane, the field shape is similar to that obtained by simulation, with the exception of the enhanced sidelobes on the latter case computed for continuous wave. Resolution, as explained before, is not isotropic in the XY plane, finding a FWHM of 3 10 mm. Resolution anisotropy and field distortion are the major drawbacks of this configuration. Fig. 11a shows the measured field provided by the NC arrangement. Results show a good agreement with the theoretically expected ones (see Fig. 6b). Fig. 11b shows a comparison between calculated and measured lateral profiles; measured FWHM from Fig. 11b is 1.5 mm (1.3 mm expected). The beam remains collimated up to 15 mm off the output hole. The larger mismatch with theory is the increased sidelobe width (Fig. 11b), probably due to reflections/diffraction in the thickness of the primary mirror at the output hole, theoretically considered zero. The NC arrangement provides lower noise than FZP and has lower losses, mainly due to the relation of hole to PZT areas. On the other hand, and unlike the off-axis spherical mirror, it provides a symmetrical beam, like an off-axis parabolic mirror, but with lower mechanical complexity and with a smaller coaxial design. 5. Conclusions Passive focusing devices for Air-Coupled Ultrasound (ACU) transducers provide simple methods to concentrate the sound beam into a focus. This helps to improve lateral resolution and increase sensitivity. This work analyzed both theoretical and experimentally the behavior of three passive focusing devices: Fresnel Zone Plates (FZPs), off-axis parabolic and spherical mirrors and a new design derived from the Newtonian–Cassegrain (NC) telescope concept. For the experimental work air-coupled piezoelectric transducers with center frequency at 400 kHz and 25 mm diameter aperture has been used and all designs shared a 35 mm focal distance. FZPs are small devices easy to build, although they present a relatively high noise floor due to diffraction and interference of signals at out-of-focus regions. However the resulting arrangement is coaxial, which facilitates transducer alignment and integration. Off-axis parabolic mirrors provide well collimated beams with a symmetrical focus. By contrast, off-axis spherical mirrors produce large aberrations, deforming the beam shape and focus. Both are bulky and parabolic mirrors require careful grinding. Alignment of these devices is, in general, more complicated.
The proposed NC solution has a coaxial design, uses an easy to build spherical primary mirror with a sound output hole, while the ceramic itself acts as the secondary mirror. It is less bulky than offaxis mirrors but more than FZPs. The NC arrangement is easily aligned and produces a well collimated beam with a symmetrical focus at the specified range. It has slight losses due to the hole in the primary mirror. Acknowledgements This work was supported by a R&D contract with Dasel, S.L. in the framework of the EuroStar E!8929 Nuthic project, funded by the E. U. and by the DPI 2011-22348 project funded by the National R&D program, Spanish Ministry of Economy and Competitivity. We want also to acknowledge the assistance of L. Díez, E. Villanueva and J.C. Liébana in the development of the transducer prototypes. References [1] M. Luukkala, P. Heikkila, J. Surakka, Plate wave resonance – a contactless test method, Ultrasonics 9 (4) (1971) 201–208. [2] M. Deka, Air-coupled ultrasonic transducers for NDE, in: Proc. IEEE Ultrason. Symp, 1987, pp. 543–546. [3] C.M. Fortunko, J.O. Strycek, W.A. Grandia, Nondestructive testing of thick aerospace honeycomb structures using through-transmitted ultrasonic guided waves, Rev. Prog. Quant. NDE 8B (1990) 1643–1650. [4] D. Reilly, G. Hayward, Through air transmission for ultrasonic nondestructive testing, in: Proc. IEEE Ultrason. Symp., 1991, pp. 763–766. [5] A.J. Rogovsky, Development and application of ultrasonic dry-contact and aircontact C-scan systems for nondestructive evaluation of aerospace composites, Mater. Eval. 49 (1991) 1491–1497. [6] W. Grandia, C.M. Fortunko, NDE applications of air-coupled ultrasonic transducers, in: Proc. IEEE Ultrason. Symp., 1995, pp. 697–709. [7] W. Hillger, R. Meier, Inspection of CFRP components by ultrasonic imaging with air coupling, in: 8th ECNDT, Barcelona, Spain, 2002. [8] R.E. Green, Non-contact ultrasonic techniques, Ultrasonics 42 (2004) 9–16. [9] D.K. Hsu, Nondestructive testing using air-borne ultrasound, Ultrasonics 44 (2006) 1019–1024. [10] D.A. Hutchins, W.M.D. Wright, Ultrasonic measurements in polymeric materials using air-coupled capacitance transducers, J. Acoust. Soc. Am. 96 (3) (1994) 1634–1642. [11] B. Hosten, D.A. Hutchins, D.W. Schindel, Measurement of elastic constants in composite materials using air-coupled ultrasonic bulk waves, J. Acoust. Soc. Am. 99 (4 Pt.1) (1996) 2116–2123. [12] T.E. Gómez Álvarez-Arenas, F.R. Montero, M. Moner-Girona, E. Rodrı´guez, A. Roig, E. Molins, Viscoelasticity of silica aerogels at ultrasonic frequencies, Appl. Phys. Lett. 81 (7) (2002) 1198. [13] T.E. Gómez Álvarez-Arenas, Air-coupled ultrasonic spectroscopy for the study of membrane filters, J. Membr. Sci. 213 (1–2) (2003) 195–207. [14] M.D. Fariñas, D. Sancho-Knapik, J.J. Peguero-Pina, E. Gil-Pelegrín, T.E. Gómez Álvarez-Arenas, Shear waves in vegetal tissues at ultrasonic frequencies, Appl. Phys. Lett. 102 (10) (2013) 103702. [15] T. Ishiyama, Y. Kanai, J. Ohwaki, M. Mino, M. Wakamiya, Impact of a wireless power transmission system using an ultrasonic air transducer for low-power mobile applications, in: Proc. IEEE Ultrason. Symp., 2003, pp. 1368–1371.
T.E. Gómez Álvarez-Arenas et al. / Ultrasonics 67 (2016) 85–93 [16] F.J. García-Diego, J.M. Bravo, J. Pérez-Miralles, H. Estrada, A. FernándezNavajas, Development of a low-cost airborne ultrasound sensor for the detection of brick joints behind a wall painting, Sensors (Basel, Switzerland) 12 (2) (2012) 1299–1311. [17] J. Bravo, J. Sánchez-Pérez, M. Ferri, J. Redondo, R. Picó, Application of ultrasound phase-shift analysis to authenticate wooden panel paintings, Sensors 14 (5) (2014) 7992–8002. [18] D. Sancho-Knapik, T.E. Gómez Alvarez-Arenas, J.J. Peguero-Pina, E. Gil-Pelegrín, Air-coupled broadband ultrasonic spectroscopy as a new non-invasive and non-contact method for the determination of leaf water status, J. Exp. Botany 61 (5) (2010) 1385–1391. [19] D. Sancho-Knapik, H. Calás, J.J. Peguero-Pina, A. Ramos Fernandez, E. GilPelegrín, T.E. Gómez Alvarez-Arenas, Air-coupled ultrasonic resonant spectroscopy for the study of the relationship between plant leaves’ elasticity and their water content, IEEE Trans. Ultrason., Ferroelectr. Freq. Control 59 (2) (2012) 319–325. [20] D.J. Roth, E. Kautz, J.L. Hendricks, 3-D surface depression profiling using high frequency focused ultrasonic pulses, NASA/TM-1999-209053, 1999. [21] T.E. Gomez Alvarez-Arenas, F. Montero, A.P. Pozas, Air-coupled ultrasonic scanner for Braille, in: Proc. IEEE Ultrason. Symp., vol. 1, 2001, pp. 591–594. [22] T.H. Gan, D. Hutchins, D.R. Billson, Preliminary studies of a novel air-coupled ultrasonic inspection system for food containers, J. Food Eng. 53 (2002) 315– 323. [23] E. Corona, J.V. Garcia-Perez, T.E. Gomez Alvarez-Arenas, N. Watson, M.J.W. Povey, J. Benedito, Advances in the ultrasound characterization of dry-cured meat products, J. Food Eng. 119 (3) (2013) 464–470. [24] R. Mcmillan, The technology and applications of gesture-based control, RTO lecture series on Alternative Control Technologies: Human Factor Issues, 4, 1998, pp. 1–11. [25] T. Chiu, H. Deng, S. Chang, Implementation of ultrasonic touchless interactive panel using the polymer-based CMUT array, IEEE Sensors (2009) 625–630. [26] T. Yano, M. Tone, A. Fukumoto, Range finding and surface characterization using high-frequency air transducers, IEEE Trans. Ultrason., Ferroelec. Freq. Control 34 (2) (1987) 232–236. [27] B T. Khuri-Yakub, J. H. Kim, C. Chou, P. Parent, G.S. Kino, A new design for air transducers, in: Proc. IEEE Int’l Ultrason. Symp., 1988, pp. 503–506. [28] W. Manthey, N. Kroemer, V. Mágori, Ultrasonic transducers and transducers arrays for applications in air, Measur. Sci. Technol. 3 (1992) 249–261. [29] D.W. Schindel, D.A. Hutchins, L. Zou, M. Sayer, The design and characterization of micromachined air-coupled capacitance transducers, IEEE Trans. Ultrason., Ferroelectr. Freq. Control 42 (1) (1995) 42–50. [30] D.W. Schindel, D.A. Hutchins, W.A. Grandia, Capacitive and piezoelectric aircoupled transducers for resonant ultrasonic inspection, Ultrasonics 34 (6) (1996) 621–627. [31] S.P. Kelly, G. Hayward, T.E.G. Alvarez-Arenas, Characterization and assessment of an integrated matching layer for air-coupled ultrasonic applications, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51 (10) (2004) 1314–1323. [32] T.E. Gómez Alvarez-Arenas, Acoustic impedance matching of piezoelectric transducers to the air, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51 (5) (2004) 624–633. [33] T.E. Gómez Alvarez-Arenas, Wide-band air-coupled ultrasonic piezoelectric transducers, in: International Symposium on Piezocoposite Applications, Dresden, Germany, September 22–23, 2011. [34] A. Turo, J. Salazar, J.A. Chavez, H.B. Kichou, T.E. Gomez, F. Montero de Espinosa, M.J. Garcia-Hernandez, Ultra-low noise front-end electronics for air-coupled ultrasonic non-destructive evaluation, NDT & E Int. 36 (2) (2003) 93–100. [35] L. Svilainis, A. Chaziachmetovas, V. Dumbrava, Efficient high voltage pulser for piezoelectric air coupled transducer, Ultrasonics 51 (1) (2012) 225–231. [36] D. Hutchins, P. Burrascano, L. Davis, S. Laureti, M. Ricci, Coded waveforms for optimised air-coupled ultrasonic non destructive evaluation, Ultrasonics 54 (2014) 1745–1759.
93
[37] T.H. Gan, D.A. Hutchins, R.J. Green, Swept frequency multiplication (SFM) techniques for improved air-coupled ultrasonic NDE, Rev. Progr. Quant. Nondestruct. Eval. 22 (2003) 620–627. [38] J. Buckley, Air-coupled ultrasound: A Millennial Review, in: 15th WCNDT, Rome, Italy, 2000. [39] J. Ealo, J. Camacho, C. Fritsch, Airborne ultrasonic phased arrays using ferroelectrets: a new fabrication approach, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 (4) (2009) 818–858. [40] J.Y. Lu, Ultrasonic nondiffracting transducer for medical imaging, IEEE Trans. UFFC 37 (5) (1990) 438–447. [41] J.Y. Lu, J.F. Greenleaf, Ultrasonic nondiffracting transducer, US. Pat. 5,081.995, January 21, 1992. [42] J. Eirás et al., Vibration Modes in Ultrasonic Bessel Transducer, in: Proc. IEEE Ultrason. Symp., 2003, pp. 1314–1317. [43] D. De Vadder, A. Lhémery, N. Gengembre, A new ultrasonic combining three modes: high axial resolution, high transverse resolution and standard modes, Rev. Progr. Quant. Nondestruct. Eval. 15 (1996) 979–986. [44] J. Song, D.E. Chimenti, Design, fabrication and characterization of a spherically focused capacitive air-coupled ultrasonic transducer, Int. J. Appl. Sci. Eng. 4 (1) (2006) 1–19. [45] B. Hosten, M. Castaigns, Parabolic mirror and air-coupled transducer for multimodal plate wave detection, Rev. Progr. Quant. Nondestruct. Eval. 22 (2003) 1243–1250. [46] A. Karpelson, Piezotransducers with acoustic lenses forming narrow weakly diverging ultrasonic beams, ECNDT, Mo.2.7.2, Berlin, Germany, 2006. [47] T. Tarnockzy, Sound focussing lenses and waveguides, Ultrasonics (1965) 115– 127. [48] J. Peters, V. Kommareddy, Z. Liu, D. Fei, D. Hsu, Non-contact inspection of composites using air-coupled ultrasound, Rev. Progr. Quant. Nondestruct. Eval. 22 (2003) 973–980. [49] A. Vladišauskas, R. Raišutis, E. Zˇukauskas, Air-coupled ultrasonic transducers with collimators, Ultragarsas 64 (1) (2006) 24–28. [50] X. Dai, J. Zhu, Y.-T. Shai, Use of parabolic reflector to amplify in-air signals generated during impact-echo testing, J. Acoust. Soc. Am. 130 (4) (2011) 167– 172. [51] T.H. Gan, D.A. Hutchins, D.R. Billson, D.W. Schindel, High-resolution, aircoupled ultrasonic imaging of thin materials, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (11) (2003) 1516–1524. [52] B. Hadimioglu, E.G. Rawson, R. Lujan. M. Lim, J.C. Zesch, B.T. Khuri-Yakub, C.F. Ouate, High-efficiency Fresnel acoustic lenses, in: Proc. IEEE Ultrason. Symp., 1993, pp. 579–582. [53] M.Z. Sleva, W.D. Hunt, R.D. Briggs, Focusing performance of epoxi and airbacked polyvinylidene fluoride Fresnel zone plates, J. Ac. Soc. Am. 96 (3) (1994) 1627–1633. [54] D.W. Schindel, A.G. Bashford, D.A. Hutchins, Focussing of ultrasonic waves in air using a micromachined Fresnel zone-plate, Ultrasonics 35 (1997) 275–285. [55] D.W. Schindel, A.G. Bashford, D.A. Hutchins, Chromatic aberration of an aircoupled ultrasonic Fresnel zone-plate, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46 (1) (1999) 242–246. [56] W.J. Hugues, J.R. Craig, The focusing properties of an acoustic thin lens and zone plate, Tech. Report TR 96–003, Penn. State University, Applied Research Lab, April 1996. [57] R.S.C. Cobbold, Foundations of Biomedical Ultrasound, Oxford Univ. Press, Inc., 2007. [58] A. Ibáñez, C. Fritsch, M. Parrilla, J. Villazón, Monochromatic transfer matrix method for acoustic field simulation through media boundaries, Phys. Proc. 3 (2010) 883–890. [59] S. Bauer, S. Bauer-Gogonea, M. Dansachmüller, I. Graz, H. Leonhartsberger, H. Salhofer, R. Schwödiauer, Modern electrets, in: Proc. IEEE Ultrason. Symp., 2003, pp. 370–376.
