Ultrasonic Analytic-Signal Responses From Polymer-Matrix Composite Laminates

Ultrasound has been used to inspect composite laminates since their invention but only recently has the response from the internal plies themselves been considered of interest. This paper uses modeling techniques to make sense of the fluctuating and interfering reflections from the resin layers between plies, providing clues to the underlying inhomogeneities in the structure. It shows how the analytic signal, analyzed in terms of instantaneous amplitude, phase, and frequency, allows 3-D characterization of the microstructure. It is found that, under certain conditions, the phase becomes locked to the interfaces between plies and that the first and last plies have characteristically different instantaneous frequencies. This allows the thin resin layers between plies to be tracked through various features and anomalies found in real composite components (ply drops, tape gaps, tape overlaps, and out-of-plane wrinkles), giving crucial information about conformance to design of as-manufactured components. Other types of defects such as delaminations are also considered. Supporting evidence is provided from experimental ultrasonic data acquired from real composite specimens and compared with X-ray computed tomography images and microsections.


I. INTRODUCTION
I N THE composites manufacturing environment, the nondestructive testing (NDT) profession is increasingly criticized for being unable to provide sufficient information about the defects it detects and the conformance of as-manufactured components to the design [1], [2]. A consequential reduction in confidence that the component will perform adequately leads to risk mitigation in terms of increased thickness of the design and a reluctance to concede defects, thus increasing weight, numbers of repairs, and scrappage rates. Examples of the desirable additional NDT information are: 3-D maps of fiber volume fraction, porosity, out-of-plane ply wrinkling, in-plane fiber waviness, ply-drop and ply-overlap locations, and ply stacking sequence [3].
The body of research aimed at extracting these material characteristics from NDT outputs is evidence for its Manuscript  current importance. Methods have been applied to various NDT modalities such as: X-ray computed tomography (X-ray CT) [4]- [7], terahertz imaging [8], [9], eddy currents [10], [11], ultrasonic guided waves [12], near infrared [13], optical [14]- [17], and ultrasound [18]- [21]. Many of these methods are limited to specific material characteristics or are difficult to deploy due to sample-size limitations or data acquisition constraints. Manufacturers are reluctant to deploy additional NDT methods and, of the above methods, only pulse-echo ultrasonic inspection is already routinely used in industrial settings to detect inclusions, delaminations, and porosity in carbon-fiber reinforced plastic (CFRP) components. Extending its use to detect other features (ply wrinkling, fiber orientation, etc.) is, therefore strongly desirable, but has been limited due to the lack of understanding of the interaction of ultrasound with the internal plies and fibertows that is required to image such features reliably. The information about the composite that would increase confidence in its fitness for purpose is at the scale of a ply or a fiber tow in the laminate; individual fibers do not have to be tracked and no defects smaller than 0.1 mm in size have been shown to be significant. Plies are commonly 0.125, 0.189, or 0.250 mm in thickness. Fiber tows-bundles of fibers from which preimpregnated (pre-preg) plies are formed-can contain from 1000 to 12 000 fibers of diameter approximately 0.007 mm, making fiber tows within a ply between 0.5-and 6-mm wide. Thus, the range of ultrasonic wavelengths (0.2-2 mm) and manageable focal beamwidths (0.5-3 mm) commonly used for ultrasonic NDT should be capable of resolving any irregularities on the required scale. It is not due to insufficient resolution that the desired ultrasonic NDT capabilities have not been forthcoming for composite materials. The shortcomings of NDT are, instead, explained by a lack of inversion methods for linking the ultrasonic response to the microscopic variations in the material, due to a lack of understanding of the ultrasonic interaction with composite plies, fiber tows, and defects. Increased computational power, coupled with recent advances in ultrasonic modeling methods [22]- [25], has enabled this paper, which provides a deeper understanding of the ultrasonic interaction with composite laminates. This paper builds on previous empirical attempts to extract ply-specific information such as in-plane fiber-tow orientation to determine ply stacking sequence [26]- [28], out-of-plane ply wrinkling, and in-plane fiber-waviness mapping [28]- [30]. This previous work used either the "RF" ultrasonic waveform 0885-3010 © 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See ht. tp://ww. w.ieee.org/publications_standards/publications/rights/index.html for more information. or its envelope. Whilst this is adequate for measuring misaligned plies through wrinkles, it is unreliable for tracking ply drops and overlaps because amplitude variations can be caused by many other phenomena such as porosity and layerthickness changes, so a different method is required. Pain and Drinkwater [31], [32] and Li et al. [33] have shown the potential for using the instantaneous phase to track plies in composites, which was developed further by Smith et al. [34]. Zardan et al. [20] detected and identified out-of-plane ply waviness by considering the deviation of the ultrasonic beam through resin wedges. However, they have yet to propose an inversion method to map the ply locations and quantify the angular deviations.
The aim of this paper is to demonstrate that characteristic signatures from microstructural variations that exist in the reflected analytic signals from composite laminates and that an automated process can be used for mapping these variations.
Following a background section in which the analytic signal, ultrasonic model, and previous modeling predictions are described with reference to published literature, the novel modeling predictions of characteristic signatures are shown. This paper uses a 1-D analytical model, which shows that instantaneous phase, amplitude, and frequency can be used to distinguish between various changes in the laminate and to track and map those variations. The analytic-signal response is studied for several different defect types including ply drops, delaminations, tape gaps and overlaps, and out-of-plane ply wrinkling. Finally, the resulting analysis method is demonstrated on real specimens and compared with microsections and X-ray Micro-CT scans.

A. Ultrasonic Model
An ultrasonic model has been implemented in MATLAB and used to simulate the pulse-echo response of a composite laminate. It is one of a number of ways of obtaining the exact solution to a 1-D wave-propagation problem and is based on the recursive analytical multilayer model developed in [22], which had been benchmarked against various other models and experiment; it is described more fully in [34]. The Hashin mixture rules for long-fiber composites [35] are applied to determine effective-medium properties for the composite plies based on a fiber volume fraction which is allowed to vary to compensate for ply-thickness variations, such as in wrinkled regions. The transverse compression modulus is used for ultrasonic propagation across plies, for which case the isotropic-fiber expressions of Hashin [35] still apply-as shown by Hashin [36]. Interply layers are modeled as pure resin. The model calculates the frequency-dependent response of a laminate and includes attenuation due to visco-elastic damping in the interply resin layers and the resin phase of the composite plies. In this paper, two scenarios are used for embedding the composite laminate either: 1) in water as for immersion scanning or 2) in a matched homogeneous, isotropic medium with the same effective-medium bulk properties as a carbon fiber composite with a 60% fiber volume fraction, to view the ply responses without any interference from the front and back surfaces.
A plane-wave input-pulse is simulated using a Gaussianweighted spectrum with a constant phase, φ 0 at all frequencies, making φ 0 the phase at the time of the peak in the envelope. This input pulse accounts for both the transmission and reception responses of the transducer. It is applied by multiplication in the frequency domain prior to the use of an inverse Fourier transform to determine a realistic time-domain analytic-signal response of the laminate. Zero time is at the time-of-flight for the front-surface reflection. No artificial noise was added for the simulations presented here.
In order to investigate how the normal-incidence reflected response varies over a structural feature such as a ply drop, wrinkle, or delamination, the 1-D model has been applied for the set of layer thicknesses and properties under each point on the surface of the structure and a pseudo B-scan image is built up from the adjacent waveform responses. Whilst this is an over-simplification for laminates with very local variations, it is a reasonable assumption for most nonwoven composites when inspected with focal beamwidths of 2 mm or less, as used in this paper. An investigation of more local effects will be the subject of a future project and publication.

B. Analytic Signal
The analytic signal was defined by Gabor [37] in 1946. Gammell [38] demonstrated that it is "the optimal estimator of interface location for echo signals of the type commonly used in ultrasound analysis." As such, it is a useful formulation for interpreting the ultrasonic response from composite laminates and locating the echoes from the various layers. It is a complex function describing the time dependence of the acoustic signal received at a pulse-echo transducer and comprises a measurable (real) component and an imaginary component in quadrature phase with it. As shown by Heyser [39], the analytic signal accurately describes the energy rate-of-arrival whilst the real part is unable to do this alone. During each cycle, the energy transfers between the real and imaginary components like it does between particle velocity (kinetic energy) and particle displacement (potential energy) in an acoustic wave. The mathematical form used in this paper is where A(t) is the instantaneous amplitude and φ(t) is the instantaneous phase at time t. The imaginary part of the analytic signal is calculated by applying a Hilbert transform to the measured (real) waveform [40]. The instantaneous frequency, f (t), is the rate of change of phase at time t in the response at the measurement location and is given [41] by The instantaneous amplitude, A(t), is the magnitude, or envelope, of the signal [42].

C. Previous Modeling Predictions
The simulated analytic signal shown in Fig. 1 corresponds to the ultrasonic response of an 8-ply composite embedded in a matching infinite homogenous medium. In the context of this result, the predictions previously proposed in [34] can be summarized as follows.
1) Internal reflections occur primarily at the resin-rich layers between plies, giving rise to a weak resonant behavior and peaks in the instantaneous amplitude as shown by the red line in Fig. 1(a). 2) At the fundamental ply resonance frequency, one wavelength is equal to the round-trip path length through a ply; the instantaneous phase traverses approximately 2π radians for each ply in the laminate as seen in Fig. 1 where each turn of the helix about the time axis corresponds to 2π radians change of instantaneous phase.
3) The instantaneous phase at the time of the reflection from a resin layer appears to be close to φ 0 -π/2 radians, shown as red dots in Fig. 1(b), where φ 0 is the instantaneous phase at the peak instantaneous amplitude of the input pulse and is zero for Fig. 1. 4) The phase tracks the location of resin layers well when center frequency and pulse-echo bandwidth are both at approximately the fundamental ply resonance frequency. 5) A narrower bandwidth allows too little variation in resonance frequency to track varying thickness plies because the input-pulse center frequency dominates over the ply resonance. 6) A wider bandwidth allows the second resonance of a ply (termed the second harmonic) to be excited to a sufficient amplitude for a phase change of 4π radians to be observed for a thicker ply, implying a double ply instead of a thicker single ply.
This paper explores the validity of the above predictions quantitatively and proposes using the instantaneous frequency f (t), (2) to improve the distinction between different microstructural features, defect types, and causes of ultrasonic-response variations. A simple example is that a significant second-harmonic amplitude in the response, due to a thick ply, would be clearly visible as a doubling of the instantaneous frequency and would be distinguishable from two thin plies because the instantaneous amplitude is lower in the middle of a ply than at a resin layer.

A. Ply Interactions
All modeling in this paper uses a nominal ply spacing (one ply thickness plus one resin-layer thickness) of 0.25 mm, which has a fundamental resonance frequency of approximately 6 MHz such that a single cycle fits in the time of a round-trip through a ply and back. The resulting predictions can be applied to other ply spacings by simple scaling using the methods described below. Fig. 2(a) shows the frequency response (frequency-dependent reflection coefficient) of a single ply between two resin layers, all embedded in matching entry/exit media. This is the product of the single-ply response (a "half-wave resonator" with maxima at integer multiples of the half-wave resonance frequency, including a peak at zero frequency) and the 0.01 mm resin-layer response (a "quarterwave resonator," which is zero at zero frequency and rises monotonically to its first maximum at 72 MHz) [22]. Over the frequency range from 0 to 15 MHz, the overall response exhibits maxima at 6 MHz, termed here the fundamental resonance, and 12 MHz, termed the second harmonic. These correspond to the half-and full-wave resonances of the ply, respectively. There is also a maximum at approximately 1.5 MHz, termed the subharmonic, which is merely a result of the above multiplication of two responses and only exists locally for each ply because it destructively interferes with reflections from adjacent plies.
The nth harmonic frequency for other ply spacings can be calculated by a simple scaling of frequency where f n is the frequency of the nth harmonic resonance, c is the sound velocity in the composite ply, and l is the ply spacing. n takes the value 1 for the fundamental resonance and 2 for the second harmonic.
The three resonance peaks shown in Fig. 2(a) effectively define three resonance modes in the pulse-echo response of a single ply, the dominant mode depending on the input-pulse characteristics and the ply thickness. These modes need to be understood for optimized characterization of composites. Fig. 2(b) illustrates how the dominant mode (black dot) varies with ply thickness using the simulated amplitude response of a single ply between two resin layers with matched entry/exit media. The modes can be described as follows, with reference to (3) and Fig. 2(b), where f c is the input-pulse center frequency, f 1 is the fundamental resonance frequency (n = 1) for the ply: 0 cycles are reflected per ply. Fig. 2(c)-(f) illustrates the analytic-signal response for a single ply between resin layers with matching entry/exit media, so starting and ending with a phase of φ 0 −π/2 radians. The instantaneous frequency is shown as the color of the dots, spaced in time at the sample rate where green is approximately the input-pulse center frequency of 6 MHz, red is an increase and blue a decrease. Fig. 2(d) shows the fundamental resonance mode-the center frequency is near the nominal ply resonance. The instantaneous frequency increases as the ply becomes thinner in Fig. 2(c) and decreases as it gets thicker, eventually forming an additional loop opposite the resin-layer phase, corresponding to the middle of a ply as in Fig. 2(e). This loop accommodates the same phase progression within a longer time period. At this stage, the instantaneous frequency is negative and the amplitude is very low as the analytic signal approaches the origin. If the ply thickens further, the loop suddenly goes beyond and encloses the origin in Fig. 2(f), adding 2π to the phase progression in the ply and indicating the dominance of the second-harmonic mode. This is a significant discovery as such sudden changes in instantaneous frequency are observed experimentally in the middle of plies.
The three components of the analytic-signal response are illustrated in Fig. 3 for 8 plies of thickness 0.24 mm and resin layers of 0.01-mm thickness, immersed in water. Instantaneous amplitude and frequency both increase at each resin-layer echo and decrease in the middle of each ply, as in Fig. 2(d) where amplitude is the radius from the origin and frequency is represented by changes in the color and spacing of the dots as they progress from the resin-layer echo at φ 0 −π/2 to the mid-ply region at φ 0 + π/2.
The prediction that either a particular instantaneous phase or an amplitude peak will be locked to the resinlayer interfaces is considered quantitatively in Fig. 4 as a function of depth in the laminate and thickness of the resin layers. Fig. 4(a) clearly shows that phase is more stable than amplitude for tracking plies, especially where amplitude is affected by the strong surface signal. As the reflection coefficient of a resin layer is approximately proportional to its thickness, this explains the breakdown in phase tracking for very thin resin layers. But, in general, resin-layer thicknesses only vary between 5% and 15% of the ply spacing. For this range, Fig. 4(b) shows there is an underestimate in resinlayer phase-tracking of approximately 15% of the resin-layer thickness (e.g., slope of the thick solid line), combined with a systematic error of less than ±1.5% of the ply spacing. The resolution of the ply tracking is limited by the time resolution of the phase data set; this result was obtained with a time resolution of 0.4 ns, giving a ply-tracking resolution of 0.24% of the ply spacing. In this case, a digitization sample rate of 2.5 GS/s was used, although a lower rate could be used in practice, with interpolation of the phase data to achieve the required resolution. The input-pulse center frequency and bandwidth were equal to the fundamental ply resonance.
The deviations from perfect ply tracking in the absence of noise, shown in Fig. 4, can be explained in terms of two competing influences on the phase of the response. In the absence of interfaces, the phase progression (instantaneous Fig. 3. Analysis of the simulated response to an input signal with center frequency and bandwidth at the fundamental ply resonance of 6 MHz and an input-signal phase, φ 0 = 0, of (a) eight 0.24-mm-thick plies with 0.01-mm-thick resin layers, embedded in water, (b) instantaneous amplitude with a gain of 1 (solid curve) and 20 (dashed curve), (c) wrapped instantaneous phase, and (d) instantaneous frequency. Note that the phase at the front-surface peak in amplitude (0 on horizontal axis) is zero for an input-pulse phase (φ 0 ) of zero, whilst the phase at the back-surface peak (ply 8) is at −π radians (i.e., φ 0 −π ). frequency) at a particular depth would be solely dictated by the spectrum of the ultrasound incident at that depth, whilst the resonance frequency of the resin-layer interfaces increases in influence with resin-layer thickness. As the resonance-frequency amplitude is gradually more attenuated with depth and with greater resin-layer thickness, this will also affect the trade-off between these two influences on phase.

B. Front-Surface Echo in Water
In the authors' previous work, the echo from the water-tocomposite (front-surface) interface was considered to provide little useful information [34], but it can actually define: 1) the exact time-of-flight to the front surface, set as t = 0; 2) the input-pulse instantaneous phase φ 0 [at t = 0 in Fig. 3(c)]. Simulated responses have shown that the front-surface echo from a composite laminate with a thin surface resin layer is very similar in the time domain to the echo from a frequency-independent reflector such as a single interface. This implies a close similarity of center frequency, phase, and pulse-echo bandwidth to the input pulse. Therefore, the phase at the peak amplitude of the front-surface echo is a useful estimate of φ 0 . Simulation has shown this to be within ±0.1 radians of the actual φ 0 for surface resin-layer thicknesses up to 10% of a wavelength and for a center frequency and bandwidth close to the ply resonance.
Given that the wrapped phase at the peak of the reflection from the resin layer between plies 1 and 2 is at φ 0 -π/2 radians (predicted in Section III-A), it follows that the instantaneous phase only increases by 3π/2 radians in the first ply, implying a significantly lower instantaneous frequency following the front-surface echo than between deeper resin layers (as illustrated in Fig. 3(d).

C. Back-Surface Echo
At the back surface of the laminate, the resin-to-water boundary again dominates over the composite-to-resin boundary. In the case of water, or any low-impedance medium, beyond the back surface, the reflection coefficient for acoustic pressure will be negative, resulting in an instantaneous phase at the peak of the reflection of φ 0 -π radians, as seen in Fig. 3(c). As with the front-surface echo, if the phase at the peak of the reflection from the last resin layer (between the last two plies) is at φ 0 -π/2 radians, it follows that the instantaneous phase again only increases by 3π/2 radians in the last ply. This has proved to be a useful classifier for the back-surface echo as phase and amplitude are insufficient to distinguish it from an unusually thick resin layer.

IV. CHARACTERISTIC SIGNATURES IN COMPOSITE
For the purposes of investigating characteristic signatures, the ultrasonic plane-wave propagation has been modeled in a series of independent 1-D analytical models with parallel planar interfaces, producing a sequence of waveforms combined as B-scan cross-sectional slices. The structure modeled in Fig. 5 contains a ply drop (on the left) where ply 7 stops and resin fills the gap until adjacent plies join, a wrinkle of amplitude equal to a ply thickness (middle), and a delamination between plies 5 and 6 (right), modeled as 100% porosity in ply 6. Color palettes are chosen deliberately, throughout the paper, as follows. Grayscale is used for amplitude so additional results can be superimposed in color. The Hue Fig. 6. Illustration of the "analytic-signal gates" on the response from an 8-ply laminate in immersion with an input pulse of phase φ 0 = π /6 radians. For interface-classification: red for front-surface (φ 0 ), blue for back surface (φ 0 −π ), and green for resin layers (φ 0 −π /2). Colored dots show gate trigger points. axis of the "HSV" (hue, saturation, value) color space is used for phase because it uses a cylindrical geometry where angle represents Hue, so it wraps in the same way as phase angle [43]. The "Jet" palette is used for frequency to show the fundamental resonance frequency as central green, with increases as yellow-red and decreases as cyan-blue [44]. Fig. 6 illustrates the classification of interfaces using analytic-signal "gates" on a simulated response from an 8-ply laminate in immersion; a gate is a defined surface in complex space through which the analytic signal may pass, marking the time when the gate was "triggered." The front-surface gate (red), at the input-pulse phase φ 0 (φ 0 = π/6 radians in this case), begins at the start of the waveform with a minimum instantaneous-amplitude threshold at a userprescribed percentage of the predetermined maximum in each waveform. When the analytic signal passes through this gate (red dot in Fig. 6), it triggers that time as the time-of-flight of the front-surface echo. After the amplitude has subsided below another prescribed proportion of the front-surface maximum, the back-surface (blue) and resin-layer (green) gates start, with phases of φ 0 -π radians and φ 0 -π/2 radians, respectively. Trigger events in the green gate (green dots in Fig. 6) indicate the times-of-flight of the middle of the resin layers. This happens once per cycle of the analytic signal until the backsurface (blue) gate's amplitude threshold (at a predetermined percentage of the front-surface signal) is surpassed (blue dot in Fig. 6) and there has also been a characteristic reduced instantaneous frequency in the previous ply, indicating the time-of-flight of the back surface.

A. Classification of Interfaces
In Fig. 5(e), resin-layer locations are superimposed on amplitude data at all points with phase within ±π/4 radians of the resin-layer gate's phase by plotting a color representing instantaneous frequency there, whilst front and back surfaces are shown as magenta lines.

B. Delaminations
The reflection at a delamination, assuming it has a volume of air within it, is similar to the water-backed back-surface echo in all but its larger amplitude [ Fig. 5(b)]. As a reduced instantaneous frequency exists in the ply before a delamination, it will be detected as if it is a back-surface echo. Fig. 5(d) shows a characteristic instantaneous frequency rise and fall before the delamination and Fig. 5(e) has it marked as a magenta line on the right, also showing the larger amplitude echo from a delamination than the back surface, and even larger than the front-surface echo. A potential application for this is in automated 3-D mapping of impact damage and generation of 3-D finite-element analysis models [45], [46].

C. Resin-Filled Ply Drops, Tape Gaps, and Overlaps
Tape gaps and overlaps are effectively two ply drops in close proximity and opposite orientation. Therefore, it is sufficient to consider them all as resin-filled ply drops, as modeled by Smith et al. [34]. For the ply drop in Fig. 5(b) at location 3-10 mm and a time of approximately 1.1 μs, the instantaneous amplitude is higher at the front and back of the resin wedge than at a normal resin layer. This is because the reflection coefficient of a single composite-toresin interface is much greater than for a thin resin layer. The model predicts that the peak amplitude is when the resin wedge is 0.2 wavelengths (in resin) thick -0.1 mm in this case for an input pulse with bandwidth equal to its center frequency. Up to this point, the phase at the peak of the signal reflected from the resin wedge is φ 0 -π/2 radians, as normal [see Fig. 7(a)]. But, for the thicker part of the resin wedge-between 0.2 and 0.5 wavelengths thickness-the front and back echoes separate out; the phase at the peak from the front of the resin wedge is φ 0 -π radians and from the back it is φ 0 , as shown in Figs. 5(c) and 7(c). This causes just a 3π/2 radians phase progression in the plies before and after Large black dots at localmaxima in instantaneous-amplitude show that the front and back wedge echoes split as it thickens; phases move from φ 0 −π /2 for a thin resin layer to φ 0 + π and φ 0 . the ply drop, which can be seen in Fig. 5(d) as a drop in instantaneous frequency in these plies. The consequence is that the phase progression in the resin wedge is π radians in a gradually increasing propagation time [ Fig. 7(c)-(d)]. This is why there is a minimum in amplitude. A negative instantaneous frequency occurs close to the dropped plyat location 3 mm and time 1.1 μs in Fig. 5-caused by a second-harmonic loop in the phase response and a minimum in the amplitude response (an antiresonance) [see Fig. 7(d)]. The loop grows as the wedge thickens and the π radians phase progression has to fit a longer time period. Fig. 5(e) shows that the resin layers, and front and back surfaces of the resin wedge, can be tracked well from their characteristic signatures.

D. Out-of-Plane Ply Wrinkling
As out-of-plane wrinkling is accompanied by changes in ply thickness, the result is a change in the instantaneous frequency. Fig. 5(d) demonstrates a frequency increase above the wrinkle in the squashed plies and a decrease where the plies are thicker.
The ability of instantaneous phase to track resin layers and map out-of-plane wrinkles [34] works only in the fundamentalresonance mode (see Fig. 2). If the ply becomes too thick, the second-harmonic mode is entered, in which two cycles of phase are traversed per ply; if the ply becomes too thin, the subharmonic mode is entered. This effect on wrinkle imaging can be seen in Fig. 5(c). Where plies are thinner, above the wrinkle, instantaneous frequency increases but stays in the fundamental resonance mode [ Fig. 2(c)]. A negative instantaneous frequency occurs when the ply is thicker but not enough to enter the second-harmonic mode [ Fig. 2(e)]. If the second-harmonic mode is entered [ Fig. 2(f)], a sudden change from negative to high positive frequencies occurs as the loop crosses the origin, giving zero amplitude and causing a phase singularity [47] where phase is unknown. It is important to determine the potential accuracy of plyinterface tracking as a function of ply spacing within a wrinkle for a range of bandwidth/center-frequency ratios. Analytically modeled quantitative information is shown in Fig. 8 for 8 plies in water, where all plies change in thickness whilst the center frequency is kept at the fundamental resonance of the nominal ply spacing. Fig. 8(b) shows that the depth error for the middle resin layer is predicted to be less than ±1% of the nominal ply spacing across the bandwidth range.

E. Summary of Modeling Predictions
The characteristic analytic-signal features of these defects are summarized in Table I and their use to detect and characterize these features is demonstrated in Fig. 5(e) and the following section on experimental applications. Fig. 9. Wedge specimen containing ply-drops, made from 0.189-mm plies and incorporating 0.04-mm resin layers. (a) X-ray CT slice. (b) Ultrasoundderived front-surface (red), back-surface (red), and resin-layer (green) locations (c) overlaid on X-ray CT data. The ultrasound scan used a 38-mm spherical-focus 7.5-MHz probe.

V. EXPERIMENTAL APPLICATION
All of the experimental data presented below was acquired using single-element normal-incidence focused probes in immersion with the focal plane at the mid-plane of the sample. A 38-mm focal-length in water has been shown to be a good compromise for probes with center frequencies of 5, 7.5, and 10 MHz. The 7.5-MHz probe reported here was 12.5 mm in diameter so the −6-dB focal spot size in composite was calculated to be 1.2 mm, with a −6-dB focal range (depth of field) of 11 mm in composite. The probe was chosen to have a measured center frequency closest to the fundamental plyresonance frequency. Olympus Videoscan probes were used because they have a bandwidth approximately equal to the center frequency and this has been shown to be optimal [34]. Pulse-echo full-waveform data was acquired over a 2-D raster scan with a 0.2-mm step size controlled by scanner software from Ultrasonic Sciences Ltd. The data acquisition rate was at least 100 MS/s in all cases.

A. Determining Input-Pulse Phase
The above modeling exercise has demonstrated that phase is effectively "locked" to the interply resin layers and that it is crucial to know the phase, φ 0 , at the peak instantaneous amplitude of the input pulse for correct location mapping of interfaces. It has also been shown that the front-surface echo can be used to determine the input phase. For the following experimental analysis, the phase was determined at the peak instantaneous amplitude for the mean analytic signal from a large number of waveforms near the middle of the scan.

B. Ply Tracking: Front and Back Surfaces and Resin-Layers
Once the input-pulse phase is known, the analytic-signal formulation allows automatic classification of front surface, back surface, and resin-layer interfaces based on the criteria for instantaneous amplitude, phase and frequency listed in Table I. Fig. 9 shows the result, compared with optical cross sections and X-ray CT, for a wedge specimen with several ply-drop locations. Fig. 10 shows the stages in the process.
Agreement is very good for all but the interface between the last two plies where the attenuation due to the 0.04-mm resin layers has caused a significant signal reduction.
This wedge specimen was manufactured with a 0.189-mm ply spacing inclusive of 0.04-mm toughened resin layers.  I   SUMMARY OF THE PREDICTED CHARACTERISTIC ANALYTIC-SIGNAL RESPONSE TO VARIOUS FEATURES IN A COMPOSITE LAMINATE FOR THE SCENARIO  WHERE THE CENTER FREQUENCY OF THE INPUT PULSE IS AT THE FUNDAMENTAL PLY RESONANCE FREQUENCY. φ 0 IS THE INSTANTANEOUS  PHASE AT THE TIME OF THE PEAK AMPLITUDE OF THE INPUT PULSE AND IS SET TO ZERO FOR THE IMAGES IN THE ANALYTIC SIGNAL  COLUMN. THE BLACK DOTS IN THOSE IMAGES ARE AT THE PEAKS IN INSTANTANEOUS AMPLITUDE The fundamental resonance will be approximately 8 MHz and the reflection coefficient of each resin layer will be four or five times larger than for nontoughened resin layers, which will generally have a thickness of 0.005-0.010 mm. Fig. 11 illustrates characteristic features in the instantaneous frequency at a ply-drop as the resin layer thickens. Where it starts to thicken [red line, Fig. 11(a)], the plies immediately above and below have a lower instantaneous frequency [cyan color in Fig. 11(b)]. The harmonic frequencies continue to reduce until [green line, Fig. 11(a)] a negative-frequency region appears at the end of the dropped ply in Fig. 11(c) because the second-harmonic frequency has become significant in the bandwidth of the probe (the second-harmonic mode). The dropped ply is thinner at its endpoint [yellow line, Fig. 11(a)], resulting in a band of increased instantaneous frequency between two more closely-spaced resin-layer depths as seen in Fig. 11(d).

C. Delaminations
The same process was applied to data from an impactdamaged region in a nontoughened composite with 0.25-mm ply spacing and thin (approximately 0.01-mm thick) resin layers. The classic cone-shaped delamination-damage region can be seen in Fig. 12.
It is important that multiple reflections after a delamination are not misinterpreted as actual deeper delaminations; these have been correctly interpreted by the automated process  which stops looking for interfaces after the first delamination or back-wall echo. Note that the delaminations appear to have been tracked right to their edges in the data.

D. Tape Gaps, Tape Overlaps, and Wrinkles
Gaps or overlaps created at the edges of tapes during the tape lay-up manufacturing process can cause stress concentrations and need to be tracked through a laminate. Wrinkles can be created as a side-effect; the 25-ply sample shown in Fig. 13 was manufactured to exhibit all of these features using IMA/M21 (fiber/matrix) material with 0.189-mm ply spacing incorporating approximately 0.02-mm thick resin layers. Tape gaps are in the upper part of the center wrinkle with overlaps in the lower part, whilst this is reversed for the left and right wrinkles. It demonstrates how well the process outlined above can be used to track the resin layers (plotted as colors on an instantaneous frequency scale) and identify tape gaps and overlaps as reductions in instantaneous frequency because they are either thick resin-filled layers or thick doubleply layers. Note that the thin resin layers, which are less reflective, allow adequate transmission through the full 25-ply laminate.

VI. DISCUSSION
Although many composite laminates are uniform over the lateral scale of a focused ultrasonic beam and are therefore suitable for modeling using a 1-D model, certain defect types such as ply drops and any 2-D or 3-D woven composites vary significantly within this scale. Future work by the authors will be focused on the use of 3-D finite-element analysis modeling for woven composites including a comparison with the 1-D model used here [48]. The inversion methods developed in this paper do not rely on the model for their operation but a 3-D model may well help to understand effects of focusing and nonnormal-incidence propagation.
The 1-D model predictions presented in this paper have increased understanding of the ultrasonic response from flat laminates sufficiently to propose new methods to invert the ultrasonic data. These methods have been shown to work well with a few flat samples containing ply drops, tape gaps and overlaps, wrinkles, and delaminations. However, in these results there is evidence that this is not yet the complete picture. For example, in Fig. 9, the ply tracking appears to become confused beyond about 8 plies in depth in this sample with 0.04-mm resin layers, whereas the tracking is good until about ply 20 in Fig. 13 where the resin layers are only 0.02-mm thick. This is thought to be caused by phononic band gaps, where the resonance frequency is selectively attenuated due to its stronger reflection from thicker plies. This effect is undergoing further investigation; an explanation and further results are published in [49]. The authors are also investigating solutions to this problem in terms of signal processing or detection and correction of the effects in the data.
There are also several outstanding issues to do with the setting of thresholds and other parameters for the gates used for ply tracking shown in Fig. 6. The primary concern here is the ability to distinguish between resin-layer reflections and the back surface or delamination signals but without erroneously classifying a ply-drop as a delamination. The proposed criteria on instantaneous amplitude may be difficult to calculate on a very wide range of materials, numbers of plies, attenuations, and entry/exit media. The drop in instantaneous frequency in the last ply before the back surface or a delamination is a crucial clue here, but this also exists before a ply drop and may be subject to other ply-thickness variations in the structure. Further work is being undertaken to investigate rigorous methods for calculating these thresholds.
Finally, there is evidence in Fig. 13 that there is a limit to the out-of-plane ply angle that can be tracked consistently through the structure. The previous work has suggested a maximum measurable angle of 15°and, below this, an accuracy of ±(2°+ 17%) [30], but this has yet to be verified for the latest ply-tracking algorithms. Future work will include a new investigation of limitations and measurement uncertainties.

VII. CONCLUSION
The aim of this paper was to develop an automated process for characterizing composite laminates based on characteristic signatures of microstructural features. Use of the analyticsignal formulation of the ultrasonic response has added three metrics to the conventional armory of ultrasonic NDT measurements-instantaneous amplitude, instantaneous phase, and instantaneous frequency. In composite laminates, these metrics have been shown by 1-D analytical modeling to be sensitive to small variations in layer thicknesses, which are characteristic of features and defects that are of great interest to manufacturers, such as ply drops, tape gaps and overlaps, outof-plane wrinkles, and delaminations. Depending on the ply spacing in the composite, the transducer center frequency and bandwidth can be chosen to optimize the enhanced imaging of these characteristic signatures.
A process has been demonstrated for automatically recognizing, measuring, and mapping the times-of-flight to the front surface, back surface, and all resin-rich layers between plies. This results in a significant enhancement in the 3-D ultrasonic imaging of composite laminates. The maps of these interface locations from experimental data have been qualitatively compared with both optical micrographs and X-ray CT scans for components containing ply drops, delaminations, and wrinkles.
Two different resin-rich interply layer thicknesses were tested experimentally and the automated processing was applied. Agreement with X-ray CT and microsectioning was good for the sample with 0.02 mm resin layers, throughout 25 plies to the back surface. It was also good for the first plies of the sample with thick (0.04 mm) resin layers, but became poorer deeper than approximately 10 plies. This is due to the increased attenuation of the resonance frequency; the reflection coefficient from resin layers increases approximately linearly with resin-layer thickness.
The tracking of interfaces through ply drops, tape gaps, tape overlaps, and wrinkles is a severe test of the process, which has performed well in all of these cases provided the optimum data acquisition parameters for center frequency and bandwidth are used. However, there is still further work to do to unambiguously differentiate delaminations from ply drops because they both show a reduction in instantaneous frequency and an increase in amplitude compared with resin layers.