elliptical-tukey chirp signal for high-resolution, air-coupled ultrasonic imaging

1530 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 54, no. 8, august 2007

Elliptical-Tukey Chirp Signal forHigh-Resolution, Air-Coupled

Ultrasonic ImagingPrakash Pallav, Tat Hean Gan, and David A. Hutchins, Member, IEEE

Abstract—A new signal processing method, which usesa modified chirp signal for air-coupled ultrasonic imaging,is described. A combination of the elliptical and Tukeywindow functions has been shown to give a better perfor-mance than the Hanning windowing used in most pulse-compression algorithms for air-coupled applications. Theelliptical-Tukey chirp signal provides an improvement inboth the resolution of images and signal-to-noise ratios. Inaddition, this type of signal also reduces the level of sig-nal voltages required to drive the source transducer whilemaintaining the performance of the system. This approach,thus, may have wide interest in all forms of wide bandwidthultrasonic imaging.

I. Introduction

In air-coupled ultrasonic experiments, the signal-to-noiseratio (SNR) within the received waveform is often poor

due to the large difference in acoustic impedance betweenair and the test sample. In some cases, the reduction inreceived signal level is so high that the received signal iscompletely embedded within the noise floor. These factorsbring about the need for signal processing techniques forimproving the accuracy of the measurement system, whilealso trying to improve the SNR of the received signal. Dueto the relatively high ultrasonic attenuation in air, espe-cially at frequencies above 1 MHz, it also is imperativeto find an approach whereby the chosen waveform shapeoptimizes the amount of transmitted signal energy.

It is difficult to detect the air-coupled, ultrasonic signaltransmitted through solid objects in air without using asuitable type of signal processing technique to recover thewanted signal. Tone bursts can be used, tuned to the res-onant frequency of the sample [1]. However, it is difficultto apply these techniques for inspecting multilayered ma-terials or those with changing structures. This is becausethe resonant frequencies of these materials may lie outsidethe bandwidth of the narrow bandwidth ultrasonic trans-ducer. In this case, a wideband ultrasonic signal such asswept frequency chirp signal has been found to be more ap-propriate [2]–[4]. In addition, with the chirp signal, a pulsecompression technique can be applied to improve the SNR[5], [6].

Manuscript received June 27, 2006; accepted December 3, 2006.The authors are with the School of Engineering, University

of Warwick, Coventry CV4 7AL, UK (e-mail: [email protected]).

Digital Object Identifier 10.1109/TUFFC.2007.423

The principles of pulse compression were originally de-veloped by radar engineers. They were in search of a way toovercome the problem of extending the operating range ofradar by increasing the average transmitted power, whilestill maintaining the range resolution [7]. Later this tech-nique was adopted within the field of ultrasound, to solveSNR problems [2]–[4]. Iizuka [5] showed that an improve-ment of the SNR of more than 20 dB could be achieved us-ing the pulse-compression technique compared to the con-ventional ultrasonic testing systems using a transient sig-nal. In the application of subsurface radar [6], pulse com-pression was shown to improve SNRs by more than 40 dB.The pulse compression technique uses coded signals withlarge time bandwidth (TB) products, such as a chirp andpseudo random signals [8], [9]. Research shows that uti-lization of these coded signals enable the improvement ofSNR up to 15–20 dB [10].

High resolution and penetration depth are the primarycriteria for a signal to be used for air-coupled ultrasonicimaging application. A good choice for ultrasonic imag-ing would be a very short pulse, which gives good rangeresolution due to its large bandwidth and insensitivity tovariable resonant frequencies within the transmitted wave-form. The main disadvantage of short-pulse excitation isthat it provides low transmitted energy and a low TB prod-uct. A large TB provides good SNR [11], which in turngives optimal detection capability and measurement accu-racy. The use of a swept-frequency signal, instead of a tran-sient pulse, allows a high-power, broad-bandwidth signalto be used when combined with suitable processing suchas pulse compression. The technique gives excellent timeresolution [9]. In addition, a swept frequency signal hasthe advantage of measuring the full spectral response ofa test sample across the available bandwidth. This avoidsthe need of frequency scanning, as would be needed fortone burst excitation [12].

There are three primary reasons why pulse compres-sion is potentially a useful technique when applied in con-junction with air-coupled measurement systems [3]. First,because a chirp signal is a complex, coded waveform, itcorrelates well only at well-defined points in time, thusimproving the accuracy of a measurement system. Second,a coded waveform such as a chirp has the advantage ofbeing detectable using cross-correlation techniques (as inpulse compression) when the received signal level is wellbelow the noise level of the detector. Third, high ultra-sonic energy levels can be transferred into the test sample

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pallav et al.: elliptical-tukey chirp signal for high-resolution, air-coupled ultrasonic imaging 1531

by using a chirp signal, due to its long duration, leadingto better SNR in the received signal.

Various types of swept-frequency signals—such as chirpsignals (both linear and non-linear), Barker codes, andGolay codes, and their applications of pulse compressiontechnique—have been studied [13]–[15]. Misaridis et al.[13] found that the linear modulated (FM) signal had thebest results for SNR improvement and the most robustperformance for attenuation effects of the test medium. Inthis paper, we investigate a swept-frequency signal com-bined with a rectangular modulation envelope. This typeof signal allows both maximum utilization of the full sys-tem bandwidth and an improvement in signal power. Inaddition, the required input voltage to the source can bereduced as a result of maximizing the acoustic power inthe waveform.

II. Simulation and Theoretical Modeling

A linear swept-frequency chirp signal, as used typicallyin pulse compression, can be represented as:

C(t) = sin(

2πfst +πB

Tt2

)0 ≤ t ≤ T, (1)

where T is the time duration of the chirp with a bandwidthB and a start frequency fs; t is time varying from zero toduration of chirp signal. An example is plotted in Fig. 1(a).The signal shown in Fig. 1(a) has values of fs = 100 kHz,B = 300 kHz, and T = 400 µs. The spectrum of the signal,shown in Fig. 1(b) has a rectangular shape, with ripples atthe band edges. These ripples are known as Fresnel ripplesand contribute toward the generation of side lobes on thepulse compression output, thus reducing the quality andcontrast of the ultrasonic images. Development of suppres-sion techniques for these side lobes is an area of interest[14]. It also can be observed from the spectrum that thebandwidth of the signal extends beyond the actual band-width of the chirp signal, which has its lower cut-off limitat 100 kHz and higher cut-off limit at 400 kHz. These dis-advantages can be overcome by using suitable weightingwindow functions.

The efficiency of windowing is based on the concept ofshaping a rectangular spectrum to smooth out the side-lobes in the time domain. Window functions such as theKaiser-Bessel [16], Dolph-Chebyschev [17], and Hanning[3] are the most widely used in medical ultrasonic imag-ing. Fig. 2(a) shows the type of windows used by variousresearchers in the past. However, due to the shape of thesewindows, the full spectrum of the chirp waveform is notproperly used when they are used to modulate a codedchirp signal. This is because the signal energy is only amaximum at the center frequencies, and it is a minimumat higher and lower frequencies, thus reducing the effec-tive signal energy level. Due to the effect of frequency-dependent ultrasonic attenuation in many media, theretends to be an increased attenuation of the higher frequen-cies in the transmitted signal in real experiments [13]. This

(a)

(b)

Fig. 1. (a) Simulated broadband chirp signal with a duration (T ) of400 µs, a start frequency (fs) of 100 kHz, and a bandwidth (B) of300 kHz. (b) Corresponding frequency spectrum.

will further restrict the amplitude of higher frequencies,effectively causing a decrease in the mean frequency. Italso will result in a reduction of effective time-bandwidthproduct, and would thus lead to degradation in SNR [18].The linear FM is a good candidate as long as appropri-ate weighting assures good range resolution and side lobesuppression.

The frequency spectrum of a linear chirp signalapodized by various signal windows is shown in Fig. 2(b),where it will be seen that the Tukey window has the spec-trum closest to a rectangular window. The Tukey window,Fig. 2(a), was formed from three sections: a tapering in-crease in amplitude, a central constant amplitude, and fi-nal tapering decrease in amplitude. Because the spectrumof the Tukey window is close to rectangular, we can as-sume that it provides the optimum time-bandwidth prod-uct and thus gives highest energy and maximum SNR. Thepeak of the pulse compression output using a Tukey win-dowed chirp signal as input also would become sharper,due to the high time-bandwidth product. This leads to anincrease in both time resolution of the output signal and


(a)

(b)

Fig. 2. (a) Various types of signal windows for the chirp of 400 µsduration, shown in Fig. 1(a). (b) Frequency spectra resulting fromapodization of the chirp with the various signal windows of Fig. 2(a).

spatial resolution for ultrasonic imaging. However, the useof such a window also will cause a rise and fall overshootin the frequency spectrum, due to nonsmooth transition inthe central frequency region. These overshoots are visiblein Fig. 2(b) as an abrupt increase in signal energy in thefrequency spectrum at the lower and higher ends of thefrequency spectrum. This gives the motivation for shapingthe Tukey window with a smooth transition at the cen-tral region, thus making it most suitable for air-coupledimaging applications.

Such a procedure can be illustrated by considering theform of a Tukey window, as given by:

Tukey (n) =⎧⎪⎪⎨⎪⎪⎩

12

[1 + cos

(4π

(nN

(N−1) − 14

))], 0 ≤ n ≤ a

1 a < n < b12

[1 + cos

(4π

(nN

(N−1) − 34

))], b ≤ n < N

, (2)

where:

a = floor(0.25(N − 1)) + 1, (3)b = N − a + 1, (4)

n = 0, 1, 2, . . . , N − 1, (5)

and the operation floor means a rounding down of theresultant value to the nearest integer. N is the length ofthe signal window.

Fig. 3. An elliptical-Tukey window of 400 µs duration.

Although this window has a near rectangular spectrum,leading to an increased time-bandwidth product and SNRcompared to other commonly used signal windows, the riseand fall overshoots are observed in the signal spectrum.This degrades the resolution of the signal for imaging ap-plications. These overshoots are attributed to the steeptransition in the signal spectrum from tapered to constantamplitude and vice versa. It was observed that, on smooth-ing out this transition and reshaping the Tukey windowinto a bell shape, these overshoots could be removed. Toachieve a bell-shaped Tukey window, the original windowfunction was modified using an elliptical function to give:

Tukey (n) =⎧⎪⎪⎨⎪⎪⎩

√1−x2

2

[1 + cos

(4π

(nN

(N−1) − 14

))], 0 ≤ n ≤ a

√1 − x2 a < n < b

√1−x2

2

[1 + cos

(4π

(nN

(N−1) − 34

))], b ≤ n < N

,

(6)

where:

x = −1 + 2n/(N − 1), (7)

and a, b, and n are as defined in (3)–(5). Again, N is thelength of the signal window.

The result is shown in Fig. 3 as the elliptical-Tukeywindow function. It can be seen that the original uniformcentral response of the Tukey window [Fig. 2(a)], which re-sulted in steep transition in the central frequency region,has been replaced by an elliptical curve. This provides amore smooth transition in the frequency spectrum whenthe elliptical-Tukey window is applied to a chirp signal.The results of applying various window functions to a lin-ear chirp with a 100 kHz start frequency, 300 kHz band-width, and 400 µs duration is shown in Fig. 4, in whicha comparison of the elliptical-Tukey window with threeother commonly-used signal windows (Hanning, Tukey,and Kaiser-Bessel) is presented. Figs. 4(a)–(d) show theresulting chirp waveform after being weighted with differ-ent window functions, together with their corresponding


(a)

(b)

(c)

(d)

Fig. 4. Broadband chirp signals apodized with (a) Hanning, (b) Kaiser-Bessel, (c) Tukey, and (d) elliptical-Tukey windows. In each case,the time waveform is shown on the left, and the corresponding frequency spectrum is on the right.

frequency spectra. Comparison of Fig. 4(d) to 4(a) and(b) indicates that the elliptical-Tukey window had a muchbroader frequency spectrum than the Hanning and Kaiser-Bessel windows, giving it a broader effective bandwidth. Italso could be observed that the elliptical-Tukey chirp hada smooth frequency spectrum, with no abrupt increases inthe signal energy at any frequency. This is not the casewith the Tukey chirp, Fig. 4(c). This was due to the factthat there were no steep transitions in the time signal asseen in Fig. 4(d). From Fig. 4 it also can be seen that theelliptical-Tukey window came closest to the Tukey window

in producing a rectangular frequency spectrum. Thus, theelliptical-Tukey window gave an effective bandwidth thatwas closest to a nonweighted chirp but had no ripples inthe frequency domain. When used as a pulse compressionsignal, the elliptical-Tukey chirp would thus be expected togive an improved SNR when compared to the Hanning andKaiser chirps and lower side-lobe levels when compared toa Tukey window.

The degree of side-lobe suppression can be estimatedby performing an autocorrelation of each window function,the results being shown in Fig. 5. Here it was observed that


Fig. 5. The results of autocorrelation of chirp signals apodized withfour different window functions.

Fig. 6. Simulated pulse-compression output for a chirp waveformmodulated with four different signal windows.

the elliptical-Tukey (peak = 113 dB) window exhibits a 4–8 dB increase in main-lobe amplitude compared to thoseof the commonly used Kaiser-Bessel (peak = 109 dB) andHanning windows (peak = 105 dB). It also had a higherpeak main lobe to side lobe ratio (of ∼7.5 dB) when com-pared to Tukey chirp signals. Due to its broad spectrum, itwas expected to give a higher total signal power than theother apodized functions, when used in air-coupled appli-cations. Such applications require a SNR improvement (asused in pulse compression) by cross correlation of receivedsignals with a replica of the transmitted chirp waveform. Inthe simulated pulse-compression output, shown in Fig. 6,it can be observed that the output peak for a chirp modu-lated with an elliptical-Tukey window is higher than thosemodulated with Kaiser-Bessel or Hanning windows. This isthe direct result of the signal having a higher TB product.

A simulation also was performed to illustrate the be-havior of the various windowing functions in the pres-ence of high noise levels. This was achieved by mixing thewindowed chirp signal with higher amplitude (+23 dB)random noise. Fig. 7(a) shows three types of simulated

chirp signals embedded in noise. These signals (Hanning,Kaisser-Bessel, and elliptical-Tukey) were delayed by 1 msin time to simulate propagation across an air gap. It can beseen from Fig. 7(a) that the signals were completely em-bedded in noise in each waveform. The noise in the wave-forms then was reduced using a band-pass filter, with apass-band equal to the bandwidth of the original chirp sig-nal. The filtered waveform is shown in Fig. 7(b). Althoughthe noise has been reduced, it is still difficult to determinethe time of arrival of the wanted chirp signals. The filteredsignals then were correlated with a replica reference sig-nal of its own type. The correlated results are shown inFig. 7(c). The magnitude of the compressed-pulse wave-form is shown in Fig. 7(d). It can be seen from Fig. 7 thatthe noise has been clearly removed. The elliptical-Tukeychirp signal gives a higher and sharper peak when com-pared to Hanning and Kaiser chirp signals and a betterSNR when compared to a Tukey window. Table I showsa comparison of both the SNR and width of the cross-correlation peak, measured as the full width at half maxi-mum (FWHM), for three window functions.

It can be seen from Table I that the elliptical-Tukeysignal provides the best SNR. This type of signal also hasthe narrowest compression width of the correlated pulsecompared to Hanning and Kaiser-Bessel functions. Thisshows that the elliptical-Tukey function should be ableto provide good accuracy in velocity measurements whenused for material characterization and imaging.

III. Apparatus and Experiment

Experiments have been performed to investigate theperformance of the new windowing approach for air-coupled, ultrasonic imaging. Of interest was whether theimprovements in performance seen in the simulations wereobservable experimentally in terms of signals transmit-ted across an air gap. Also of interest was the radiatedfield pattern of transducers and whether the use of differ-ent windowing functions affected their characteristics (andhence the spatial resolution for imaging).

The experimental arrangement used for plotting the ra-diated fields of the ultrasonic transducer, excited with vari-ous types of chirp signals, is shown in Fig. 8. The capacitivetransducers used for ultrasonic generation and detectionwas constructed using a micromachined silicon back-plateand a metallized Mylar membrane. The characteristics ofthese transducers have been described in earlier publica-tions [19], [20]. The transducer acting as source had a 10-mm aperture with a 5-µm thick Mylar membrane; thisthickness was able to withstand the required excitationvoltages without damage. The windowed driving wave-form, together with a +100 V direct current (DC) biasvoltage (to attract the membrane to the backplate and toensure linear operation) was used to generate the signalsin air from the source transducer.

The pulse compression approach was implemented us-ing a PXI unit from National Instruments Ltd., Newbury,


(a) (b)

(c) (d)

Fig. 7. A comparison of performance of a chirp signal (start frequency = 100 kHz, bandwidth = 300 kHz, duration = 400 µs) using differentsignal windows in a pulse-compression technique. (a) Four types of chirp signals delayed in time by 1 ms and embedded in noise. (b) Noisysignal after band-pass filtering within the chirp bandwidth. (c) Resultant cross-correlated signals. (d) The magnitude of the compressed-pulsesignals.

TABLE IComparison of SNRs and FWHM of Different Types of Window Functions Applied to a Chirp Signal.

Main lobe to sidelobe ratio of the SNR of the pulse Pulse-cross-correlated compression compression

Signal window signal (dB) output (dB) peak (dB) FWHM (µs)

Hanning 34.21 41.02 116.02 6.2Kaiser-Bessel 37.23 44.53 118.95 5.8Elliptical-Tukey 34.09 46.84 121.15 5.8Tukey 29.05 42.84 123.17 5.4

UK, in conjunction with custom-built software using theLabVIEWTM programming language from the same com-pany. Signal amplification prior to transmission was per-formed using a 40 W broadband power amplifier of vari-able gain. This PXI unit contained an on-board personalcomputer for data processing and a high-speed and high-frequency data acquisition card for data transmission andreception. All aspects of signal generation and digital sig-

nal processing and display, post-reception, were controlledusing customized LabVIEWTM-based scanning software.The radiated fields were measured by recording the ul-trasonic waveform at various locations using a second ca-pacitive device fitted with a 2-mm aperture. The 2-mmaperture helps to improve the resolution of the image andprovide accurate signal measurement at a particular point.The detector had a membrane thickness of 3 µm and was


Fig. 8. Experimental arrangement used for plotting the radiatedfields of the air-coupled ultrasonic transducer source for various ex-citation waveforms.

connected to a Cooknell CA6/C charge amplifier (Wey-mouth, England) with a gain of 250 mV/pC and a 100 Vbias. A thinner membrane allowed the detection of higher-frequency signals. Additional processes such as signal av-eraging, filtering, and cross correlation were applied tothe received signal using dedicated software, leading to acompressed-pulse output.

Radiated fields from the source transducer were mea-sured by scanning the receiver horizontally, using an X-Ystage controlled by the LabVIEWTM system, as shown inFig. 8. A typical scan used a 1-mm step size, over an areaof 70-mm radially and 140-mm axially away from the frontface of the transmitter. Data in the form of the radiatedwaveform or the cross-correlation output could be recordedat each spatial location.

In addition to the radiated fields, through-transmittedimages also were obtained using different types of windowfunctions to determine their performance in air-coupled,ultrasonic imaging. Here the source and receiver remainedaligned axially, and the scanning system was used to movethem at a constant separation, 74 mm, across the surface ofsolid samples, placed between the two transducers, 20 mmfrom the receiver. The ultrasonic beam was at normal inci-dence to the sample surface. Two test samples were inves-tigated. The first contained a hole of 5-mm diameter and63-mm length, drilled into a 20.3-mm thick Plexiglas plate.A similar size hole was drilled on the other side along thelength of the sample. These side-drilled holes, being em-bedded within the thickness of the Plexiglas plate, acted asan internal defect. The second sample was a 3-mm thick,carbon-fiber reinforced composite plate, containing barelyvisible impact damage.

(a)

(b)

Fig. 9. Four different types of chirp signals transmitted across a 140-mm wide air gap. (a) Time waveforms. (b) Corresponding frequencyspectra.

IV. Results and Discussion

The first experiment involved transmitting a signalacross an air gap of 140 mm from the capacitive sourceto the receiver, to demonstrate the effectiveness of thenew window functions and to demonstrate improvementsin the SNR of the pulse-compression technique. Fig. 9(a)shows four types of chirp signals (modulated with dif-ferent window functions) transmitted across the air gap,with the corresponding frequency spectra being shown inFig. 9(b). The transmitted chirp signals have a bandwidthB of 300 kHz and start frequency fs of 100 kHz. It can beseen from Fig. 9(b) that the elliptical-Tukey window func-tion has a wider bandwidth at the −3 dB level comparedto either the Hanning or Kaiser-Bessel window functions.


Fig. 10. Compressed-pulse signals (after cross correlation) for fourdifferent types of chirp signals.

TABLE IIComparison of Peak Amplitude and FWHM of Three

Different Types of Compressed-Pulse Signals Across Air at

140 mm.

Pulse-compression FWHM valueSignal window peak value (dB) (µs)

Hanning 53.3 12.2Kaiser-Bessel 54.1 11.8Elliptical-Tukey 57.8 10.3Tukey 59.6 10.0

Fig. 10 shows the correlated, compressed-pulse signalsweighted with four different types of window functions.The signal was again transmitted across an air gap of140 mm. Table II shows the peak value and FWHM ob-tained for each signal. It can be seen from Table II thatthe peak amplitude of the elliptical-Tukey chirp signal ismuch higher compared to those obtained using the Han-ning and Kaiser-Bessel window functions. This agrees withthe results predicted in the theoretical simulation, shownin Table I. It also can be seen that the peak is sharper (i.e.,has a smaller FWHM value) than Hanning and Kaiser-Bessel window functions. In an experiment, this would beexpected to lead to an improvement in accuracy of time-based measurements.

The radiated field of the 10-mm aperture, air-coupledtransducer, when excited by Hanning, Kaiser-Bessel, andelliptical-Tukey functions, was measured using the scanned2-mm diameter detector to illustrate any changes in direc-tivity and beam profile. The results are shown in Fig. 11. Itcan be seen from the result that the elliptical-Tukey chirpsignal has higher effective amplitude across the test re-gion compared to Hanning and Kaiser-Bessel chirp. Theelliptical-Tukey function also had lower sidelobe levelscompared to Hanning, Kaiser-Bessel, and Tukey functions.In addition, Fig. 11(c) also shows that the radiated field

(a)

(b)

(c)

(d)

Fig. 11. Radiated field plots from four different types of window func-tions. (a) Hanning window. (b) Kaiser-Bessel. (c) Elliptical-Tukey.(d) Tukey.


(a) (b)

(c) (d)

Fig. 12. Ultrasonic pulse-compression imaging of Plexiglas plates with internal side-drilled hole of 5-mm diameter using (a) elliptical-Tukey,(b) Kaiser-Bessel, (c) Hanning, and (d) Tukey windowing of the chirp signal.

Fig. 13. A line scan of the Plexiglas plate across the 5-mm internaldefect, showing data from the four windowing functions.

for elliptical Tukey is more uniform in the nearfield, with alower side-lobe level, than the other windowing functions.

Further experiments were carried out to illustrate theeffectiveness of the elliptical-Tukey chirp signal in provid-ing a higher resolution for air-coupled, ultrasonic imaging

when used in conjunction with the pulse-compression tech-nique. Various types of samples were tested and imaged.The first sample tested was a Plexiglas plate of thickness20.3 mm with an internal defect of 5 mm. The results ofthe ultrasonic scans are shown in Fig. 12. In Fig. 12, theelliptical-Tukey chirp signal shows a better contrast com-pared to Kaiser-Bessel and Hanning functions. This is dueto the high SNR and greater transmission power given bythe elliptical-Tukey signal. In order to compare the reso-lution of the scan, a cross section of the image was gath-ered. Fig. 13 shows the cross section at y = 20 mm, whichindicates that the elliptical-Tukey signal gives a sharperdetection capability compared to the other two techniquesdue to its good SNR. (Note that the Kaiser-Bessel func-tion was found to be better than the Hanning window formost imaging applications, and it is the only one shownhere for comparison.)

A second imaging experiment was carried out on thecarbon-fiber reinforced composite plate containing real im-pact damage not visible from the surface. The resultsfrom ultrasonic imaging using the Kaiser-Bessel, elliptical-Tukey chirp, Tukey chirp, and elliptical-Tukey chirp sig-nals are shown in Fig. 14. It can be seen that the elliptical-Tukey signal produces higher contrast between the dam-aged area and the background, due to the greater power


(a) (b)

(c) (d)

Fig. 14. Ultrasonic imaging of impact damage within a composite structure using (a) elliptical-Tukey, (b) Kaiser-Bessel, (c) Hanning, and(d) Tukey windows.

Fig. 15. A line scan of the composite structure across the impactdamage region.

level achieved by this window function. The cross section,Fig. 15, across the middle of the sample again indicatesthat the elliptical-Tukey signal gives a sharper detectioncapability compared to the other two techniques due to itsgood SNR.

V. Conclusions

A new elliptical-Tukey windowing technique has beeninvestigated for application in air-coupled, ultrasonicimaging applications. It was compared with the commonlyused Hanning and Kaiser-Bessel windowing techniques andwas found to be better in terms of SNR and resolution.It was found that, for the same peak amplitude sourceexcitation voltage, the elliptical-Tukey chirp produced ahigher energy transmitted signal. This, in turn, meantthat a lower input signal voltage was required to pro-duce a similar effective acoustic output. When comparedto other common windowing techniques (such as Hanningand Kaiser-Bessel), the approach was seen to lead to otheradvantages in simulations, in terms of desirable character-istics in pulse-compression output, namely, the width ofthe main peak and the presence of side lobes.

Experiments using capacitive ultrasonic transducers inair confirmed the desirable characteristics seen in the simu-lations. It was further noted that the radiated beam profiletended to have a more directional main lobe, and a lowerlevel of spatial side lobes, than seen with other windowfunctions. This would be expected to lead to a better spa-tial resolution in air-coupled imaging, and indeed this was


observed in experiments with two types of solid samplescontaining both artificial and real defects.

The authors feel that this new windowing technique isboth simple to apply to existing air-coupled measurementsand able to lead to improvements in measurement capa-bility. Thus, it should be of interest to workers in this fieldand to others such as medical imaging where cross corre-lation for SNR and image enhancement is becoming morecommonplace.

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Prakash Pallav received his B.Eng. degreein Computer Engineering from the Univer-sity of Mumbai, Mumbai, India in December2002. He then continued with his postgrad-uate studies at the University of Warwick,Coventry, UK, where he obtained his M.Sc.degree in advanced electronics engineering inJanuary 2005. Prakash Pallav is currentlypursuing his Ph.D. degree in engineering atthe University of Warwick. His research inter-est includes applications of both contact andnon-contact air coupled ultrasonic transduc-

ers, materials evaluation and nondestructive evaluation, and otherimaging techniques and signal processing. He is a member of theIEE, UK.

Tat Hean Gan received his B.Eng. (Hons)degree in Electrical and Electronics Engineer-ing from the University of Nottingham, UK,in July 1997. He then continued with his post-graduate studies at the University of War-wick, UK, where he obtained his M.Sc. in Ad-vanced Mechanical Engineering and Ph.D. inJanuary 1999 and July 2002, respectively.

From 2002 to 2006, Dr. Gan was a Post-doctoral Research Associate at the Universityof Warwick. His research interest included ap-plications of both contact and non-contact air

coupled ultrasonic transducers, materials evaluation and NDE, ul-trasonic tomography, and other imaging techniques and signal pro-cessing. He is currently Section Manager for long-range ultrasoundwithin the NDT Technology Group at TWI Ltd., Cambridge, UK.Dr. Gan is a member of the IEE, UK.

David A. Hutchins (M’81) obtained hisB.Sc. and Ph.D. degrees from the Univer-sity of Aston, Birmingham, UK. After sev-eral postdoctoral positions he joined the fac-ulty of Queen’s University, Ontario, Canada.He then moved to the University of War-wick, UK, where he is currently a Professorin the School of Engineering. His research in-terests include non-contact ultrasound, mi-cromachined transducers, ultrasonic imaging,and non-destructive evaluation.

elliptical-tukey chirp signal for high-resolution, air-coupled ultrasonic imaging

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