Ultrasonics 54 (2014) 1745–1759

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Ultrasonics

journal homepage: www.elsevier .com/locate /ul t ras

Coded waveforms for optimised air-coupled ultrasonic nondestructiveevaluation

http://dx.doi.org/10.1016/j.ultras.2014.03.0070041-624X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: D.A.Hutchins@warwick.ac.uk (D. Hutchins).

David Hutchins a,⇑, Pietro Burrascano b, Lee Davis a, Stefano Laureti a,b, Marco Ricci b

a School of Engineering, University of Warwick, Coventry CV4 7AL, UKb Polo Scientifico Didattico di Terni, Università degli Studi di Perugia, 05100 Terni, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 19 June 2013Received in revised form 28 February 2014Accepted 13 March 2014Available online 24 March 2014

Keywords:UltrasonicAir-coupledCoded waveformsCross-correlationNon-destructive evaluation

This paper investigates various types of coded waveforms that could be used for air-coupled ultrasound,using a pulse compression approach to signal processing. These are needed because of the low signal-to-noise ratios that are found in many air-coupled ultrasonic nondestructive evaluation measurements, dueto the large acoustic mismatch between air and many solid materials. The various waveforms, includingboth swept-frequency signals and those with binary modulation, are described, and their performance inthe presence of noise is compared. It is shown that the optimum choice of modulation signal depends onthe bandwidth available and the type of measurement being made.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Air-coupled ultrasound is a non-contact technique that is ofinterest to nondestructive evaluation (NDE), because it can be usedto test a wide range of materials, from polymers and composites tometals [1,2], It can also be used in harsh environments, where con-tamination is an issue, and when rapid scanning is required. Thetechnique has been proposed for application in many areas, includ-ing the inspection of composites [3–5], the detection of contamina-tion and changes in food quality [6] and for imaging many othermaterials [7]. In all cases, it is the fact that air is used as the cou-pling medium which makes the technique attractive.

In pioneering work by Bernard Hosten and his colleagues atCNRS Bordeaux, this approach has been used for the inspectionof polymer composite plates using Lamb waves [8,9]. Work wasalso done on the determination of the elastic constants of carbonfibre reinforced polymer (CFRP) composites [10–12]. Here, thecomposite sample was positioned between an ultrasonic capacitivesource/receiver pair, and the angle of incidence changed byrotation of the sample relative to the ultrasonic beam axis. Theultrasonic waveforms were recorded at each angle, and the longi-tudinal and shear wave arrival times calculated in real time (thelatter created by mode conversion within the composite plate).Changes in arrival time were then compared to theoretical

predictions, and an optimum fit between the two allowed the cal-culation of elastic constants to take place. Moreover in [12], thetransmission coefficients at different angles were measured andused as input for an inverse procedure capable of inferring thecomplex viscoelastic moduli of Perspex and composite materials.The elastic properties of other materials such as wood have alsobeen examined [13]. Note that the design of the electrostatic (or‘‘capacitive’’) transducer is also important in determining perfor-mance [14].

Although air-coupled transducers can be scanned to formimages, a higher resolution can be obtained if the transducer beamis focused. A convenient way to do this is to use external optics.This can be achieved using a Fresnel zone plate, which is alignedso as to focus on-axis at a pre-selected frequency [15]. More com-monly, however, a good focus in air can be obtained across a widebandwidth using external off-axis parabolic mirrors, which can beused for imaging thin materials and other samples [16]. It is worthmentioning that off-axis parabolic mirrors have also beenexploited to increase the angular aperture of air-coupled transduc-ers used to collect Lamb mode waves radiating from plates, allow-ing therefore a faster reconstruction of the dispersion curves ofunknown materials [17,18].

There is, however, a problem which must be overcome if air isused to transmit ultrasonic energy into and out of a solid sample– there is a need to overcome the large acoustic impedance mis-match between air and the solid object being tested. This causesseveral problems. The first is that a large fraction of the incident

1746 D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759

energy is reflected at the air/solid interface. This reduces theamount of energy both entering and leaving the sample. It alsomeans that a large reflection from the incident surface results,meaning that pulse-echo operation becomes more complicated.In through-transmission, there are two basic approaches to solvingthe lack of signal. The first is to choose a very narrow bandwidthexcitation whose central operation frequency is tuned to thethrough-thickness resonance of the sample, so as to maximizetransmission [19]. This lack of bandwidth is a problem when itcomes to conventional imaging, as discrimination of defects, forexample, becomes very difficult.

The second approach is to use a wider bandwidth, togetherwith some method of retrieving very small ultrasonic signalsthat have passed through two separate air/sample boundaries.This second method has been investigated by several authors[20–24], and the general approach is to use a form of cross-correlation to detect the signal. The resulting technique is knownas pulse compression. The incident waveform, with a bandwidthusually defined by the transduction method used, is chosen sothat this type of signal processing can be performed most effec-tively for a particular measurement. There are many types of sig-nal that can be used, but they can be broadly classified withintwo main types: a swept-frequency ‘‘chirp’’ signal or a form ofbinary sequence. Fig. 1 gives an example of a chirp signal buriedin noise to illustrate the pulse compression process. Cross-corre-lation between the output ‘‘noisy’’ signal and a reference wave-form, known in the literature as a matched filter, allows thissignal to be detected, with the smoothed rectified output shown.The resulting pulse compression operation has allowed the signalto be enhanced in terms of the signal to noise ratio (SNR), allow-ing air-coupled measurements to be made. Usually, the matchedfilter coincides with a replica of the sent signal. Moreover,depending on the specific application, the pulse compression pro-cedure can use either periodic or aperiodic signals; the cross-cor-relation step is then realized in either cyclic or non-cyclic moderespectively.

The operation shown in Fig. 1 is an example of a pulse compres-sion operation that is not optimised. The purpose of this paper is toinvestigate different forms of signal modulation, and to determinethe best approach for air-coupled ultrasound for a given bandwidthof transducer. To accomplish this aim, Section 2 briefly describesthe basic principles behind pulse compression, and elaborates themain differences between cyclic and non-cyclic operation. Section 3then details the various types of waveform used. Section 4 reportsthe results of numerical simulations that demonstrate the influ-ence of the transducer bandwidth on the choice of the optimumwaveform, whilst Section 5 illustrates experimental results thatdemonstrate the validity of the numerical results. Finally, conclu-sions are drawn in Section 6 and some further possible develop-ments are indicated.

Fig. 1. (a) Example of a linear chirp signal embedded in noise, and (b)

2. Basic principle of the pulse-compression approach and themeasurement protocols

Pulse compression is a measurement technique developed forestimating the impulse response h(t) of Linear Time Invariant Sys-tems (LTI). The basic principle at the heart of the technique can beexpressed as follow: if exists a pair of signals {s(t), W(t)} such thattheir convolution sðtÞ �WðtÞ ¼ dðtÞ ’ CdðtÞ is a good approxima-tion of the Dirac delta function d(t), then the impulse responseh(t) can be estimated by exciting the LTI system with the signals(t) and then by convolving the system output y(t) with W(t):

yðtÞ ¼ hðtÞ � sðtÞ; sðtÞ �WðtÞ ¼ dðtÞ ’ C � dðtÞ;hðtÞ ¼ yðtÞ �WðtÞ ¼ hðtÞ � sðtÞ �WðtÞ ’ C � ðhðtÞ � dðtÞÞ ¼ C � hðtÞ

ð1Þ

The better the approximation of d(t), the higher the quality of theestimation of h(t). In addition, the theory of matched filters statesthat, in presence of Additive White Gaussian Noise (AWGN), i.e.when y(t) = h(t) � s(t) + e(t) (where e(t) is the noise term), thechoice of W(t) that maximizes the SNR uses the time-reversed rep-lica of the input signal W(t) = s(�t) as the matched filter [25]. Withthis choice, the approximation dðtÞ of d(t) coincides with the auto-correlation function Us(s) of the input signal. In order to optimisethe SNR and to ensure a good measurement resolution, Us(s) hastherefore to be d-like. This requirement is fulfilled if s(t) is a wide-band signal with a bandwidth that spans as much as possible theentire frequency range of response of the LTI system.

A more formal description of the pulse compression theory liesbeyond the scope of the present paper and the reader is referred tothe literature on this topic (see for example [22]); here, it is worthstressing that a d-like feature of the signal autocorrelation can beassured both by single-shot or periodic signals, leading to twomain pulse compression schemes: Acyclic Pulse Compression(APC) and Cyclic Pulse Compression (CPC), as depicted in Fig. 2.The particular features of these two approaches are highlighted be-low, together with a computational representation of the two pro-cedures in terms of Discrete Fourier Transforms, to provide ageneral framework. Then, in Section 3, the properties of the variouscodes will be reviewed in the light of the differences between thetwo measurement methods, where specific hardware and softwaretools to perform the pulse compression will also be discussed.

2.1. Acyclic vs Cyclic Pulse Compression

A pulse compression measurement scheme can exploit eithersingle-shot or continuous (periodic) excitation. Depending on thischoice, the impulse response of the system under test can be re-trieved by using either cyclic or acyclic convolution between thesystem output signal and the matched filter.

the resultant pulse compression output from a cross-correlation.

Fig. 2. Sketches of the Acyclic (left) and Cyclic (right) Pulse Compression procedures.

D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759 1747

To gain some insight into this process, let us suppose that forthe APC and CPC cases respectively there exist pairs of signals thatguarantee the expression

s1ðtÞ � s1ð�tÞ ¼ dðtÞ; �s2ðtÞ � �s2ð�tÞ ¼ �dðtÞ; ð2Þ

where s1(t) is a coded waveform defined in t e [0, Ts1], �s2ðtÞ is s peri-odic coded waveform with period Ts2 and �dðtÞ consist of a periodictrain of d(t)0s spaced by Ts2 as illustrated in Fig. 2.

In the APC case, if the output signal in a LTI system is convolvedwith the matched filter, we obtain exactly the impulse responseh(t), while for the CPC case we obtain the convolution betweenh(t) and �dðtÞ. This shows the main difference between the twoschemes. Indeed, if h(t) is shorter than the input signal period,the convolution between h(t) and �dðtÞ produces a periodic trainof non-overlapping h(t)

0s, whereas if h(t) is longer than the input

signal period, the convolution between h(t) and �dðtÞ is no longerperiodic and presents pile-up between the h(t)0s. Therefore theCPC approach should be used only if a priori information aboutthe maximum length of h(t) is known; in this case h(t) is easy re-trieved by cutting out a single period, to prevent time-aliasing inthe reconstructed h(t). Conversely, in APC, the input signal durationTS1 of s1 is not constrained by the duration of Th. This could be con-sidered a strong limitation on the use of the cyclic scheme butactually, in air coupled ultrasonic inspection, the signal length isusually significantly longer than that of the impulse response (orat least longer than that part of h(t) that produces effects abovethe noise level). This is so as to achieve a sufficient SNR to over-come the large acoustic impedance mismatch between air andthe solid object being tested, For this reason henceforth we con-sider (Ts1, Ts2) > Th.

From an experimental point of view, there exist differences be-tween the two approaches. In the APC case, the coded signal s1(t) oflength TS1 excites the system that produces an output signal y1-

(t) = h(t) � s1(t) of duration Ty1 = Ts1 + Th. If all the h(t) should bereconstructed, the output signal has to be recorded for timeTrec P Ty1 and the pulse compression is implemented by filtering,i.e. convolving, the output signals with the matched filter; in thecase of continuous-periodic excitation, a periodic signal �s2ðtÞ ofperiod Ts2 > Th is switched on at t = 0 and excites the system thatproduces an output signal y2ðtÞ ¼ hðtÞ � �s2ðtÞ. For a transient ofduration Ts2, the output signal will be periodic with the same per-iod Ts2 and, by performing the cyclic convolution between a singleperiod ys.s. of the steady-state of y2 and a single period of the inputsignal �s2ðtÞ, h(t) is retrieved. In practice, it is sufficient to transmittwo periods of the excitation signal and to record the output corre-sponding to the second excitation period only.

Mathematically, once that the signals have been digitalized inAPC, the matched filter can be applied by performing standard con-volution or Fast Fourier Transform (FFT)-based convolution algo-rithms, such as overlap-add, overlap-save [26,27]; in cyclic modethe matched filter is applied by computing the cyclic convolutionbetween the output signal and the matched filter. By exploiting

the Convolution Theorem for Discrete Signal, the cyclic convolutioncan be efficiently implemented in the frequency domain as follow:

ys:s:½n� ��s2½n� ¼ IFFTfFFTfys:s:½n�g � FFTfs2½n�gg ð3Þ

where IFFT is the Inverse Fast Fourier Transform [26,28].For completeness, it should be noted that the convolution the-

orem for a discrete signal can be used also in the single-shot case,provided that the discrete input and output signal are padded withzeroes up to double the number of samples of the input signal, hav-ing assumed Th < Ts1.

At this point of discussion, it is therefore fair to ask whetherthere are any advantages of the cyclic approach over the acyclicone. The first concerns the SNR attainable. By considering the opti-mised APC procedure in which the output is recorded for the min-imum time needed to recover all the impulse response, itstraightforward to see that the energy is delivered to the systemfor a fraction pEX = (TS1/(TS1 + Th)) of the measurement time, andthat the final SNR is given by SNR(pEX) = pEX � SNRmax, whereSNRmax is the limit value achievable for TS1� Th. On the otherhand, in the cyclic (CPC) case, the excitation is always active dur-ing the measurement, thus saturating the SNR for a given excita-tion power once the condition TS2 > Th is satisfied. Moreover, inorder to increase the SNR of APC for a given pEX value, averagescan be executed by sending a train of single-shot excitations,but the minimum repetition time of these must be TS1 + Th; forCPC systems, averages are easily performed by considering severalconsecutive periods of the steady state output signal, making itmore time-efficient. From a computational point of view, the inputand output signals to be processed are equal in length and usuallyshorter (if the assumption Th < Ts1 is still valid) for the CPC thanthe APC case, and therefore the convolution with the matched fil-ter is less time-consuming; moreover the cyclic convolution ad-mits an efficient implementation through the FFT that is also atthe heart of fast convolution algorithms such as overlap-add usedin acyclic mode.

In summary, CPC methods can only be used if a priori informa-tion about the duration of the impulse response to be measured isavailable; therefore its application is limited when compared tostandard APC approaches. Nonetheless, when applicable, it assuresthe optimal SNR and computational savings for selected measure-ments, as will now be demonstrated.

3. The choice of waveform for pulse compression

In the previous Section, it was assumed that signals exist withan ideal d-like auto-correlation. Unfortunately, such a property isnot exhibited by any kind of finite-duration waveform; hence,researchers have devised strategies that use signals approximatingto this condition as well as possible for pulse compression applica-tions. Two main families of waveforms have been suggested: bin-ary codes and frequency modulated (chirp) waveforms. In thispaper, various forms of both chirp signals and binary sequences

1748 D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759

are investigated. In particular, the performances of linear and non-linear chirps in terms of maximum achievable SNR and resolutionare compared to two types of binary sequence, namely MaximumLength Sequences (MLS) and Golay Complementary Sequences(GCS). In this Section the main features of the various waveformsare briefly listed, highlighting the pros and the cons of each ofthem.

For the sake of clarity, henceforth the normalised autocorrela-tion (both acyclic and cyclic) function of the various signals willbe denoted either by dðtÞ or by d½n� to indicate that they representonly an approximation of the ideal Dirac-delta and Unit Impulsefunctions respectively.

3.1. Linear and Non-linear Chirp signals

A generic Chirp signal is defined as

sCHIRPðtÞ ¼ A sinðUðtÞÞ; ð4Þ

where U(t) is a non-linear phase function of t [29]. The key quantityof a Chirp signal is represented by the instantaneous frequencyfist(t) that is related to U(t) by the expression:

fistðtÞ ¼ 1=2p � ðdUðtÞ=dtÞ ð5Þ

By defining a proper trajectory fist(t) in a given time intervalt e [0, Ts], a chirp signal is obtained via Eq. (4) and by invertingEq. (5).

The instantaneous frequency is important because it is strictlyrelated to the Power Spectral Density (PSD) of the resulting func-tion. Indeed if the duration Ts of the Chirp signal is large enough,the PSD is confined within the frequency interval spanned by fist(t)and, for a given frequency value, PSD is inversely proportional tothe rate of change of fist(t) at that frequency [20,30]. For instance,if fist(t) = fstart + (B/T) � t with B = fstop � fstart and t e [0, T], the usualLinear Chirp (LChirp) is retrieved, where U(t) = 2p(fstartt +(B/2T) � t2) is quadratic and the PSD is almost flat and confinedwithin the interval f e [fstart, fstop]. In general, the frequency canbe swept in either a linear or non-linear way with respect to time.Two such signals sweeping from 150 kHz to 450 kHz are shown inFig. 3. While at first sight the waveforms do not appear to be very

Fig. 3. Examples of chirp signals in the form of (a) linear and (b) non-linear frequency sright.

different, their spectra indicate that the two signals have very dif-ferent properties. This can be illustrated further by looking at thetrajectory followed by fist(t) in the Time–Frequency plane, asshown in Fig. 4. In particular, the LChirp is associated with astraight line in this type of plot, whereas the trajectory of theNon-Linear Chirp (NLChirp) can be any continuous monotoniccurve, defined by the type of sweep function used.

A NLChirp can be defined to satisfy particular requirements, forexample chirps having exponential instantaneous frequency havebeen used for several years to characterize non-linear systems[33,34]. Here two main aspects of NLChirps are investigated: (i)using them with knowledge of the transfer function of a probe tomaximize the SNR, and (ii) generating an NLChirp by applying awindow function to the PSD of an LChirp [30]. The latter casewas developed to implement only in frequency domain what iscommonly performed in both time and frequency domains for anLChirp by applying windowing functions [30]. It is usual to ampli-tude modulate an LChirp to produce spectral-windowing, in orderto reduce the level of side-bands of dCHIRPðtÞ. With the generalassumption W(t) = s(�t), dðtÞ is in fact proportional to the InverseFourier Transform of the PSD, according to the Wiener–Khinchintheorem. A non-windowed LChirp exhibits abrupt changes in thePSD, in proximity to the limit frequencies fstart and fstop, and this re-sults in slowly- attenuating side-bands [31,32]. By applying a win-dow function in time-domain to an LChirp, a smoothing of the PSDis obtained, thereby producing a faster decay of side-bands at thecost of reducing the signal energy. This is a result of losing the con-stant envelope feature and the effective bandwidth of the signal,causing a broadening of the main lobe of the cross-correlation.There are many different types of window that can be used, andthis work has investigated three types: Gaussian, Blackman andTukey [33,34]; here, numerical and experimental results are re-ported for the Tukey case only, as this is reputed to assure thatan optimal trade-off exists between side-band reduction, resolu-tion achievable and SNR. Note, however, that by applying spectralwindowing through an NLChirp, the constant envelope feature ispreserved, and then also the SNR, and at the same time side-bandsof dðtÞ are reduced with respect to an un-windowed LChirp. In thiscase, the effective bandwidth is also reduced. To quantify this

weeps. Waveforms are on the left, and corresponding frequency spectra are on the

Fig. 4. Trajectories in the Time–Frequency planes of linear (a) and non-linear (b) chirps.

Fig. 5. Comparison of autocorrelation functions of chirp signals to the non-windowed linear case (black). This is for the windowed linear Tikey (left) and windowed non-linear Tukey (right), both in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759 1749

reduction, the following definition can be used for the effectivebandwidth [35]:

Beff ¼ffiffiffiffiffiffi12p Z fstop

fstart

ðf � fcÞ2PSDðf Þdf ; ð6Þ

where fc is the central frequency and the factorffiffiffiffiffiffi12p

is a normaliza-tion constant used to achieve Beff = B = fstop � fstart in the case of anideal LChirp.

As an example, Fig. 5 illustrates the effect of time and the spec-tral windowing applied to a Lchirp signal. Time windowing pro-vides the best reduction in side-bands both in the near and inthe far region but, as expected, exhibits the largest central lobe.On the other hand, spectral windowing ensures a resolution thatis almost the same as for the un-windowed Lchirp, and providesa significant reduction of the side-bands in the near region whilein the far region the side-bands levels coincide.

As mentioned above, a further application of the NLChirp tonoisy environments is the possibility that the excitation signalhas a PSD that matches the overall transfer function Hset-up of thehardware set-up, i.e. transmitter + receiver transducers and op-tional amplifiers [20]. In this case, the energy-bandwidth productof the output signal is optimised for a given spanned frequencyrange [fstart, fstop] assuring an enhancement of the SNR. Here the en-ergy-bandwidth product is defined as

ðB� EÞoutput ¼Z fstop

fstart

ðf � fcÞ2jHset-upðf Þj2PSDðf Þdf ð7Þ

Note, however, that the measurement resolution is notoptimised.

3.2. Binary sequences

The other type of waveforms used for pulse-compressionapplication is represented by binary sequences. Although manydifferent types of code exist, mainly for Spread Spectrum commu-nication protocols and error-correction schemes, here only thoseexhibiting the d-like autocorrelation property are considered:Golay Complementary Sequences (GCS) and Maximum LengthSequences (MLS or m-sequences).

GCS consists of two binary sequences, sAGCS½n�; sB

GCS½n�, defined byrecursion from two seed sequences, with the peculiar property thattheir out-of-phase aperiodic and periodic autocorrelation coeffi-cients sum to zero:

dAGCS½n� ¼ �dB

GCS½n� 8 n–0 ; dAGCS½n� þ dB

GCS½n� ¼ 2L� d½n�; ð8Þ

where L is the sequence length. GCS were first introduced by MarcelJ.E. Golay in 1949 for infrared spectroscopy and some years later thesame author gave several methods for constructing sequences oflength 2N and gave examples of complementary sequences oflengths 10 and 26 [36]. The complementary property of the auto-correlation can be usefully exploited in pulse compression by takingadvantage of the linear hypothesis at the heart of the method, tomodify the procedures described in Section 2.1 as follows: (i) thetwo complementary sequences are both used as input of the LTIsystem under test; (ii) the matched filter is applied separately toeach output to obtain the two estimates hA

GCS½n� ¼ dAGCS½n� � h½n�;

hBGCS½n� ¼ dB

GCS½n� � h½n�; (iii) the impulse response is reconstructedwithout any approximation by adding the two contributions to ob-tain 2L� h½n� ¼ ðhA

GCS½n� þ hBGCS½n�Þ. In spite of the fact that it is neces-

sary to use two distinct sequences, GCS are the only codedwaveforms that theoretically exhibit a perfect pulse compression

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at the end of the overall procedure. This is why they are popular inultrasonic measurements [20,37,38]. Moreover, as stated above, thecomplementary feature holds both for APC and CPC cases, so onecan decide to choose one of the two approaches depending on thespecific application. A further advantage of the GCS approach isthe existence of a fast algorithm to perform correlation–convolutionbetween a generic signal and a Golay pair with length L. Such analgorithm is known in the literature as a Fast-Golay-Correlationand it exhibits a computational complexity similar to the FFT oper-ation but it is less demanding since it mainly involves sums andsubtractions instead of multiplications [39]. This feature openedthe way to digital hardware implementation of GCS pulse compres-sion procedure for ultrasonic NDT applications [40,41].Despite theabove attractive properties, there are other types of binary se-quences of interest to air-coupled ultrasonic inspection. One isMLS, and here we try to highlight the main differences with respectto GCS above. MLS are periodic sequences that are generated by aLinear Feedback Shift Register (LFSR) machine and, as illustratedby Golomb [42], they exhibit the maximum period length for a gi-ven register depth. In particular for a register with N cells, the per-iod of the MLS[n] is L = 2N � 1. The configuration of the LFSRmachine is derived by the theory of Galois finite fields and it assuresseveral useful mathematical properties to those codes. For ultra-sonic pulse compression applications, the most useful one is repre-sented by the normalised cyclic auto-correlation function of thesesequences that consists of a train of unit pulses with added a DCbias whose amplitude decreases inversely proportional to L:�sMLS½n� � �sMLS½�n� ¼ �d½n� � ð1=LÞ. If the h[n] can be assumed to havea zero mean (where h[n] takes into account also the transfer func-tion of the transducers), and the considerations about the h[n] dura-tion are satisfied, then it is straightforward to see that by adoptingthe cyclic operation a perfect estimate of h[n] can be retrieved. For-tunately, this hypothesis is true in almost all cases, so that MLS canbe fully exploited in CPC application. Indeed, after the work of Go-lomb [43], MLS-based impulse response schemes were successfullyintroduced into acoustic measurements. Nevertheless, even in themost general case, by adopting the cyclic protocol, h[n] can be per-fectly retrieved by applying specific processing [44] or by slightlymodifying the amplitude of MLS[n] to attain a ‘‘Perfect Sequence’’[45]. MLS are therefore equivalent to GCS if CPC is possible, andin fact may be preferred since only one sequence is necessary.Moreover as for GCS, there exists a fast algorithm to perform cycliccorrelation with MLS sequences derived by Hadamard Transform:the so-called Fast-m-Transform [46]. Note that, if APC has to beused, MLS methods are not suitable, since consistent self-noise ap-pears in the aperiodic autocorrelation function and therefore GCSare highly preferable. A further advantage of MLS with respectGCS, provided by the decimation property, is the possibility inCPC to under-sample the output signal of any factor 2k attainingafter 2k periods exactly the original signal, thus allowing the useof Analog to Digital Converters with sampling rate equal or lowerthan the signal bandwidth itself [47]. Note also that MLS can beused in multi-input/multi-output systems by exploiting their pseu-do-orthogonality [48,49].

It should also be noted that Legendre sequences [43] have verysimilar properties to MLS. However, they cannot be generatedrecursively, and a fast algorithm for their correlation does not ex-ist; hence, the MLS approach has historically been preferred. More-over it has been shown recently how both GCS and MLS pulsecompression schemes are extremely robust against quantizationnoise introduced by ADC’s, and they both allow the measurementof impulse responses with dynamics well below the quantizationstep [24,50].

For both GCS and MLS, it is important to stress that the autocor-relation properties aforementioned hold for numerical sequencesbut, when changing sequences of numbers into practical voltage

signals, some aspects should be considered. In particular, at any‘‘1’’ or ‘‘�1’’ of the codes, a voltage level exists with a finite dura-tion dT related to the update rate of generation Rgen of the se-quences by dT = (Rgen)�1. At the same time, the correlation stepneeded for pulse compression depends on the sampling rate RADC

of the ADC process. To correctly apply pulse compression, RADC

must be a multiple of Rgen, i.e. RADC = m Rgen with m e N, and somepre-processing has to be performed when m > 1, so as to exploitthe fast correlation algorithms. Usually this is the case since whileRgen determines the actual PSD of excitation, a greater RADC isneeded to faithfully reconstruct output signals. Indeed, the gener-ated signals have power spectra close to that of a boxcar pulse ofwidth dT, so that it is better to choose Rgen in order to concentratethe energy in the actual bandpass of the system. In the following, itwill be shown that a good criterion is 2fc < Rgen < 4fc where fc is thecentral frequency of the transducers. At the same time, as a generalrule RADC should be at least 5–10 times greater than the upper fre-quency of interest. Of course, it is possible to choose Rgen = RADC toconsider the input signal as the ideal numeric sequences, but at thecost of exciting a bandwidth larger than the effective one. Thiscould waste a lot of energy, due to the band-pass behaviour of atypical ultrasonic experimental system. In contrast to this, chirp-based pulse compression schemes allow Rgen and RADC to be chosenindependently, providing that the matched filter is sampled atRADC.

From an experimental point of view, in most of the cases thetransducers have a bandwidth B that is a fraction of the central fre-quency fc. The spectra of binary sequences thus do not fit very wellwith the frequency range of interest, causing a decrease of theeffective energy delivered to the system. For this reason, in orderto increase the energy transfer ratio by better matching the systembandpass, it has been proposed in literature to modulate the GCS orMLS sequences by replacing ‘‘1’’ or ‘‘�1’’ with short sequences ofbinary values to perform some spectral shaping [51]. The easiestsolution here considered it to replace each ‘‘1’’ with the combina-tion ‘‘1, �1’’ and each ‘‘�1’’ with the opposite sub-code ‘‘�1, 1’’.This technique is largely adopted in acoustics where it has beennamed Inverse Repeated Sequences (IRS) [52].

Examples of waveforms and spectra of GCS and MLS sequencesand their respective IRS’s are shown in Figs. 6 and 7, where it is evi-dent how the IRS signal spectra match the transfer function of atypical ultrasonic transducer more effectively.

In the following Sections, all the various signals introduced willbe compared for use in air-coupled ultrasound. Their performancewill be determined for various levels of noise first numerically byconsidering measurement systems with different bandwidth ofoperation and then experimentally, so that their suitability inNDE can be determined.

4. Numerical investigation of modulation scheme performance

The optimal choice of the coded waveforms for air-coupledultrasonic NDE strongly depends on the transfer function of themeasuring system utilized [52]. For instance, on the basis of thatillustrated in Section 3, intuitively one can expect that for narrow-band transducers it is better to use a chirp, tailored to the systemresponse, rather than that of a flat excitation provided by binarysequences. In this Section, in order to quantify the effectivenessof one excitation with respect to the others, the results of numer-ical simulations executed considering the various types of excita-tion are reported. In particular, the maximum SNR attainable fora fixed excitation duration and peak power is investigated by vary-ing the transducer bandwidth and the noise level.

In order to make the analyses as general as possible, the simu-lations assumed normalised frequencies. In particular, the band-width B of the overall Tx–Rx system is given as a percentage of

Fig. 6. Examples of waveforms useful for ultrasonic air-coupled signals derived from Standard and Inverse Repeated Golay and MLS sequences. The ‘‘standard’’ waveformswere optimised for a central frequency of 300 kHz, see Fig. 7, and the waveforms were generated to all have the same duration.

Fig. 7. Power Spectral Density curves for the waveforms of Fig. 6. The red line in the Golay cases represents the sum of the two PSD that exhibits the complementary propertyas the autocorrelation. It can be seen that, unless for the DC component, the PSD of MLSs is half the sum of the PSD of the two Golay sequences, as expected, since the overallGolay duration is double.

Fig. 8. Examples of impulse responses and Power Spectral Densities of FIR filters used to simulate the effect of measurement set-up (Tx–Rx transducers + amplifier) atdifferent values of bandpass width.

D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759 1751

the central frequency fC of the system varying from 10% to 200%,which represents the limit case of an almost-ideal broadbandsystem in the range [0,B]. The sampling rate considered wasRADC = 20fC. The system impulse response is simulated by a bandpass

FIR filter and some examples of the corresponding impulse responseand of the magnitude of the transfer function are reported in Fig. 8.

The following combinations of waveforms and pulse compres-sion schemes are considered, which represent the most promising

1752 D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759

cases, both for easiness of the procedure, maximum available SNR,computational resources, etc.:

1. Acyclic Pulse Compression & Tukey-windowed Linear Chirp(LChirpAPC).

2. Cyclic Pulse Compression & Tukey-windowed Non-Linear Chirp(NLChirpCPC).

3. Acyclic Pulse Compression & Golay (GCS–APC).4. Cyclic Pulse Compression & MLS (MLS–CPC);5. Acyclic Pulse Compression & IRS-Golay (IRSGCS–APC).6. Cyclic Pulse Compression & IRS-MLS (IRSMLS–CPC).

For this comparison, each waveform has appoximately the sameduration (GCS and CHIRPs defined with k29 samples while MLSwith k(29 � 1) samples with k = 5) and the same peak amplitude.This assures that binary sequences have a doubled power and anadditional 3 dB of SNR with respect to chirps. Moreover, Golay-based codes lead to another factor of 3 dB in the theoretical SNR,since they use of a pair of sequences. The binary sequences wereoptimised to cover the bandwidth [0–2fC], the IRS-binary sequencewere defined to have the maximum of the PSD at fC, Chirp signalsinstead were defined both with a fixed bandwidth B = 2fC and witha varying B following the one of the Tx–Rx transducers system. Thislatter case is denoted as a ‘‘Matching Chirp’’ (MChirp).

Four main quantities were calculated in presence of noise toconsider different aspects related to detection, resolution, etc.:(a) the width of the main lobe (‘‘MLW’’); (b) the SNR in the mainlobe (‘‘ML-SNR’’); (c) the near side-lobe level (‘‘NSL’’) and (d) thefar side-lobe level (‘‘FSL’’). Each quantity is computed within a dis-tinct region of the measured signal; to gain deeper insight, con-sider the three regions labelled in Fig. 9 by the capital letters A,B, C: A indicates the main lobe, that is the region outside of whichthe envelope of the expected signal is 20 dB below the maximum;B indicates near side-lobes, i.e. two regions at the sides of the mainlobe, each with the same width as the main lobe; C indicates farside-lobes, that is the outer regions beyond near side-lobes.

MLW provides a measure of the resolution of the pulse com-pression procedure, and can be defined as:

MLW ¼minfD s: n t: hex½n < n1;n > n1 þ D� < 0:1 Maxðhex½n�Þ;8ngð9Þ

Here, the smaller the MLW, the better the temporal-spatial res-olution of the measurement, so that this parameter is of particularinterest in Time-of-Flight measurement or in range detection. ML-SNR expresses the capability of detecting a signal in presence ofnoise and it is defined as the ratio between the energy of the ex-pected impulse response after pulse compression without noisehex[n] = hFIR[n] � s[n] �W[n] to the Energy of the noise inside themain lobe:

ML-SNR ¼P

n�MainLobeðhex½n�Þ2P

n�MainLobeðhex½n� � hm½n�Þ2

; ð10Þ

Fig. 9. Definition of MainLobe (A), Near Side

where hFIR[n] is the FIR impulse response used to simulate the sys-tem, and hm[n] = (hFIR[n] � s[n] + e[n]) �W[n] is the measured im-pulse response in presence of noise e[n]. NSL is defined as theratio (in dB) between the maximum absolute amplitude of hex[n]and the mean value of the envelope of hm[n] in the Near Sidelobesregion, given by

NSL ¼ Maxðhex½n�ÞMeanðEnvðhm½n�ÞÞn�NearSidelobes

ð11Þ

Also in a similar way to NSL, FSL is defined as the ratio (in dB) be-tween the maximum absolute amplitude of hex[n] and the maxi-mum value of the envelope of hm[n] in the far side-lobes region

FSL ¼ Maxðhex½n�ÞMaxðEnvðhm½n�ÞÞn�FarSidelobes

ð12Þ

NSL and FSL quantify the level of noise and at the same time ex-press the limit value that a secondary signal should not be de-tected. These quantities are of utmost importance when compleximpulse responses have to be measured, as in the case of multi –path reflection, multi-layered structures, etc.

Fig. 10 shows surface plots of the ML-SNR versus the noisepower and the bandwidth of the Tx–Rx system. The results arequite similar for all the cases and in general higher SNR are at-tained with broadband systems, as expected for this choice of exci-tations. Moreover with respect to ‘‘standard’’ Linear Chirp, GCS andMLS, some improvements are attained by using a non-linear chirpand the IRS approach. The IRS sequences, both GCS and MLS, attainthe highest value of ML-SNR.

If we let the bandwidth of the chirp follow that of the experi-mental system, then an improvement of the SNR of the Chirp isachieved, as expected from our previous discussion. Fig. 11 showsthe surface plot of the ML-SNR for the MChirp compared to that ofthe IRSGCS–APC and in particular the subplot on the right maps theNoise Power – System BW region for which IRSGCS–APC exhibits aSNR higher than MChirp. The area where IRSGCS–APC is betterthan MChirp is coloured white, otherwise is black. For BW P 90%fC

(approximately), the IRSGCS (and also the IRSMLS) perform betterthan Matched Chirp; for BW < 90%fC a higher SNR is attained byusing a Chirp (Linear or Non-linear) ‘‘matched’’ with the systemband-pass. This result is reasonable, since almost half of the inputenergy is filtered out by the transducers for BW = fC, erasing there-fore the theoretical advantage of binary sequences

At the same time, the matched chirp has the worst resolutionamong the various schemes, corresponding to a large MLW, asshown by Fig. 12 that reports the trends of the MLW for all theexcitation types considered. While all the various codes with fixedbandwidth have practically the same resolution, the matched chirpachieves a better SNR, with a significant decrease of the resolutionthat is accentuated for BW < 90%fC.

Figs. 13 and 14 report a comparison analogous to thatillustrated in Fig. 11 for the NSL and the FSL respectively.

lobes (B) and Far Sidelobes (C) regions.

Fig. 10. ML-SNR versus the noise power and the system bandpass width for various pulse compression schemes.

Fig. 11. Comparison of the ML-SNR achievable for IRSGCS–ACP and MChirp schemes. In the plot on the right, in white is evidenced the Noise-BW region in which the IRSGolay attains higher SNR than matched chirp.

Fig. 12. Main lobe width (MLW) versus the system band-pass width for variouspulse compression schemes.

D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759 1753

In summary, the numerical simulations show that for suffi-ciently-broadband systems, the binary sequences are preferableboth in terms of resolution, SNR and side-lobe levels.

Conversely, a chirp signal matching the bandwidth of the exper-imental system outperforms binary sequences in terms of the SNR

of the main lobe detection when the bandwidth of the measuringsystem is below the central frequency value, i.e. when B < fC, evenat the cost of deteriorating the resolution.

Indeed, the band-pass behaviour of chirp signals counterbal-ances the higher energy carried within binary sequences by fittingbetter to the overall transfer function of the experimental system.This effect becomes even more relevant if narrow-bandwidth sys-tems are used. In this case, by using a standard binary sequence,only a small portion of the input energy can be transferred to themeasured system. In contrast to this, the energy spectrum of achirp signal can be tailored to the transducer bandwidth. Hence,the input energy in this case is always almost effectively deliveredto the system, so that chirp signals are a good choice for transduc-ers with a narrow bandwidth. In any case, since it is desirable touse binary signals both for hardware and computational reducedcosts, sub-modulation and spectrum design techniques can be ap-plied also to this case, in order to further improve the SNR.

It is worth stressing that, among the binary sequences, the IRSapproach achieves the best results, so it is could be useful to extendthis approach in various applications of air-coupled ultrasonicNDE, and at the same time optimizing the performances by intro-ducing more complex modulation of the sequences [51]. By using

Fig. 13. Comparison of the NSL achievable for IRSGCS–ACP and MChirp schemes. In the plot on the right, in white is evidenced the Noise-BW region in which the IRS Golayattains higher NSL than MatchedChirp.

Fig. 14. Comparison of the FSL achievable for IRSGCS–ACP and MChirp schemes. In the plot on the right, in white is evidenced the Noise-BW region in which the IRS Golayattains higher FSL than MatchedChirp.

1754 D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759

such techniques the binary sequences approach could out-performchirps, even with narrow-band transducers. In general, MLS andGCS attained very close results, so that when CPC can be used,there could be advantages in terms of measurement and computa-tional efficiency in using MLS instead of GCS.

5. Experimental investigation of modulation schemeperformance

The initial data was collected using a pair of air-coupledtransducers from The Ultran Group (Boston, USA), centred atfc = 200 kHz and aligned on-axis in air. The transmitter was directlydriven by an Arbitrary Function Generator PXI NI-PXI 5412 fromNational Instruments Inc., providing a voltage signal of ±6 V on aload of 50 X, while the receiving transducer was directly digital-ized by an ADC NI-PXI 5105 having 12bit of resolution and60 MS/s of maximum sampling rate. Different levels of SNR were

Fig. 15. Experimental characterisation of the Tx–Rx system by using broadband GCS

reproduced by placing sheets of various materials: wood, plastic,steel, etc. between the transducers. The transducer pair presentsa quite irregular transfer function, characterised by two mainlobes, as depicted in Fig. 15, where high-rate ‘‘Standard’’ GCS–APC and MLS–CPC were used to characterize the system transferfunction.

It can be seen that, after proper normalization, GCS and MLSgave very similar results, as expected from simulations. In the fol-lowing experimental comparisons, all the binary sequences types(GCS–APC, MLS–CPC, IRSGCS–APC, IRSMLS–CPC) were used whilefor the Chirp waveforms a LChirp-APC and a NLChirp-CPC withfc = 200 kHz and BW = 120,000 = 60%fc were considered. Moreover,due to the peculiar transfer function of the system, also a Non-lin-ear chirp designed to have the same PSD of the system itself wasemployed in CPC [20], labelled henceforth as NLChirpT-CPC.Fig. 16 compares the results in air with the aforementionedschemes; also Figs. 17–19 compares the results when a wood

and MLS. On the left the impulse response h(t) is reported, on the right the PSD.

Fig. 16. Comparison of performaces in air for different excitaion schemes.

Fig. 17. Comparison of performaces through wood for different excitaion schemes.

Fig. 18. Comparison of performaces through plasitc for different excitaion schemes.

Fig. 19. Comparison of performaces through steel for different excitaion schemes.

D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759 1755

sample, a plastic sample and a steel plate are placed between theprobes respectively. The plots show the envelopes of the recon-structed impulse response, and the scale is normalised so that1Volt of amplitude corresponds to 0 dB. In all these Figures, theupper subplot refers to the chirp waveforms (Black: LChirp-APC,Red: NLChirp-CPC and Blue: NLChirp-CPC) while the lower subplotrefers to binary sequences (Black: GCS–APC; Red: MLS–CPC;Blue:IRSGCS–APC and Green:IRSMLS–CPC). Note that the Golay-

based schemes are expected to have 3db over the MLS’s and Chirp’sschemes due to the use of two sequences that actually double theenergy delivered to the system. Finally, to better compare Chirpand Binary waveforms, in Fig. 20 a direct comparison of LChirp-APC with IRSGCS–APC and IRSMLS–CPC is reported for the woodand plastic samples respectively. In these cases, the envelopeswere normalised to their relative maxima, so as to better appreci-ate the differences in resolution and side-lobe levels.

In agreement with the numerical simulations, the bandwidth ofthe transducers makes the chirp the optimal choice in terms ofside-lobe levels. On the other hand, IRS sequences maintain a bet-ter resolution with respect to the chirp case in the presence ofstrong attenuation, as demonstrated by the width of the main lobe.In particular, the rise-time of the signal in the IRS case is signifi-cantly shorter than for the chirp, making such strategies preferableif time-of-flight is to be measured with high precision.

To further investigate the differences between the various exci-tations, data were also recorded using a pair of capacitive transduc-ers, which have been described elsewhere [1,2]. They use a thinmetallised Mylar membrane attached to a micromachined back-plate, so as to operate in air with a high efficiency. The experimen-tal impulse response of the devices used in the current experi-ments is shown in Fig. 21. It can be seen that the experimentalamplitude response for a pair of transducers peaks at approxi-mately 250 kHz, which was assumed as fC in this case. The re-sponse also led to the choice of a frequency sweep range of 100–400 kHz for the chirp signals. The voltage drive signals were gener-ated in LabView™ software, and sent to the transmitter via a Na-tional Instruments PXI system. Note that a DC bias was appliedto the transmitter via a decoupling circuit and a charge amplifierwas used to provide amplification and a DC bias to the receiver, be-fore being recorded via the PXI system. Moreover, although thecentral frequency is near to that of the previous results, the im-pulse response for the capacitive transducers is significantly short-er, due to their broadband nature with respect to the ULTRANprobes described earlier.

The initial experiments again recorded signals that were trans-mitted by each of a set of sequences across a simple air gap. Thiswas done to determine the initial properties of the recorded signalsin ideal conditions. The ultrasonic waveforms will not be the sameas those provided by the driving voltage sequences, due to theamplitude and phase response of the transducers, the effect of dif-fraction by the finite apertures of the transducer themselves, andfrequency-dependent ultrasonic attenuation in air. Moreover in thiscase two further steps of amplification were introduced, that affectthe overall system transfer function. The experimental results can

Fig. 20. Left: comparison of performaces through wood for LChirp (black) and IRSGCS (blue). Right: comparison of performaces through plastic for LChirp (black) and IRSMLS(green). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 21. Experimental characterisation of the capacitive transducers Tx–Rx system by using pulse excitation. On the left the impulse response h(t) is reported, on the right thePSD.

1756 D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759

be illustrated by looking at two particular examples – a LChirp-ACPand a MLS–CPC. The chirp had a bandwidth defined by the chosenstart and finish frequencies (100–400 kHz), whereas the MLS se-quence had a generation rate of a single bit is Rgen =107/17 600 kHz, in compliance with the empirical rule is 2fc <Rgen < 4fc previously introduced, see Section 3.2. These signals wereused to drive the ultrasonic air-coupled transmitter, and the signalsdetected by the receiver after propagation through air fc recorded.The received experimental spectra in each case are shown in Fig. 22.

Note that, as stated above, the system exhibited a wider propor-tional bandwidth with respect to the experiments with ULTRANtransducers, and for the MLS case non-vanishing components ex-tends for all the region f e [0, 2fC]. The pulse-compression outputis therefore expected to be very concentrated in a small time inter-val, as shown in Fig. 23. It was found that the received MLS signalamplitude was approximately twice that of the LChirp-APC, andthat the width of the main cross-correlation peak was narrower.The broadband feature of the transducer makes them very suitablefor performing thickness measurement by resonance, which repre-sents an important application of air-coupled ultrasonic systems inthe NDE of solid samples.

Fig. 22. Experimental spectra measured with the capacitive transduce

To illustrate such application, samples of Plexiglas with differ-ent thickness (0.1 mm, 1 mm and 5 mm) were placed normal tothe ultrasonic beam. This material has a longitudinal velocity of2700 ms�1, corresponding to a wavelength at the central fre-quency of 10.8 mm. Since resonance appears when the thicknessD of the sample contains an integer number of half-wavelengthsfor some frequency, and since the effective bandwidth extend from100 kHz to 400 kHz, resonance should appear when

D �[

n

nk1

2;nk2

2

� �; ð13Þ

where k1 ¼ 2700½m=s�400;000½cycles=s� ’ 6:75½mm=cycles�; k2 ¼ 2700½m=s�

100;000½cycles=s� ’27½mm=cycles�.

The only experimental object that should exhibit resonance istherefore the last one with D = 5 mm, and this was confirmed bythe results reported in Fig. 24, where the impulse responses re-trieved for all the Plexiglas samples and by using both LChirp-APC and MLS–CPC were depicted. The two responses are effectivelysimilar for the two thinner samples. This is because their thicknessis small enough that the frequency of the sample’s fundamentalresonance (at 1.3 MHz for a 1 mm thickness) is above that of

rs Tx–Rx system by using (left) LChirp-APC and (right) MLS–CPC.

Fig. 24. Impulse response for three different thicknesses of Plexiglas: (a) 0.1 mm, (b) 1 mm and (c) 5 mm and fo LChirpAPC (left) and MLS–CPC (right).

Fig. 25. Frequency spectra arising from the impulse responses for the 5 mm thick Plexiglas plate: (left) LChirp-APC (right) MLS–CPC solid black with superimposed LChirp-APC dashedred. All vertical scales are normalised to the maximum values of the spectra.

Fig. 23. Experimental impulse response envelopes reconstructed with the capacitive transducers Tx–Rx system by using (left) LChirp-APC and (right) MLS–CPC.

D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759 1757

the highest frequencies transmitted. At a thickness of 5 mm,however, where the solid plate through-thickness resonancewould be expected at 267 kHz, the impulse response is that ofa decaying resonance. This is exactly what would be expected fromsuch a system.

It is interesting to look at the frequency spectra correspondingto the impulse responses for the 5 mm thick Plexiglas sample,and these are shown in Fig. 25 for the two signals. Both have pro-duced a good spectral response, indicating that the frequency ofresonance could be estimated from the peak value.

1758 D. Hutchins et al. / Ultrasonics 54 (2014) 1745–1759

Indeed in the right subplot of Fig. 25, the spectra of both MLSand the linear chirp are normalised and plotted together: it canbe seen that the narrow peak corresponding to the resonancefrequency coincides in the two cases and give thickness valuesof 5.2 mm, assuming a longitudinal velocity of 2700 ms�1. How-ever, the larger received amplitude of the impulse response forthe MLS sequences (Fig. 24) can make these codes preferablefor thickness measurements were the sidelobes level is lessimportant.

6. Conclusions

This paper has revised through numerical and experimentaldata most of the types of signal used for air-coupled ultrasoundand their relative measurement procedures. The results have dem-onstrated that it is extremely important that the type of excitationsignal used is chosen so as to match the bandwidth available in theexperimental system. With respect to the enhancement of the SNR,binary and Chirp signals achieve very similar results for widebandwidth measurements even if binary codes assure high SNRvalues. For a narrower available bandwidth, a chirp signal wouldbe preferred; alternatively, some spectral shaping must be intro-duced into binary codes, as shown by the Inverted Repeated Se-quences approach. For time-of-flight and thickness measurement,the binary codes have been seen to be the best choice. They givethe highest received amplitude, and the shortest impulse responsewhen used in a through-transmission measurement. For defectdetection purpose, where very low side-bands level are needed,linear windowed chirps appear to be the best solution for narrow-band systems, at the cost of reducing the resultant spatialresolution.

Acknowledgements

DAH acknowledges financial support via EPSRC United King-dom. PB, SL and MR acknowledge PRIN 2009 project ‘‘Diagnosticanon ditruttiva ad ultrasuoni tramite sequenze pseudo-ortogonaliper imaging e classificazione automatica di prodotti industriali’’and ‘‘Fondazione CARIT’’ Italia for financial support.

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