THE STUDY of the art objects paint layer stratigraphy

Transcription

1 3082 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Three-Dimensional Nondestructive Sampling of Art Objects Using Acoustic Microscopy and Time Frequency Analysis Georgios Karagiannis, Dimitrios S. Alexiadis, Student Member, IEEE, Argirios Damtsios, George D. Sergiadis, Member, IEEE, and Christos Salpistis Abstract The microsampling destructions, which are caused by the sampling procedures of analytical spectroscopic methods, are, in most cases, not permitted to art objects, which are extremely valuable, rare, and fragile. Consequently, the development of nondestructive analysis techniques becomes a necessity. In this paper, we present a technique and method for the nondestructive identification of the stratigraphic structure of the paint layers of art objects. Using acoustic microscopy, in combination with time frequency representations, the continuous or discrete wavelet transform, or the Hilbert Huang transform, the depth profile of the stratigraphy is determined. Index Terms Acoustic microscopy, art objects, nondestructive testing (NDT), time frequency (TF) analysis, ultrasounds, wavelet transform (WT). I. INTRODUCTION THE STUDY of the art objects paint layer stratigraphy is crucial for their documentation since it provides important information related to the painting technique and to previous restoration attempts. Analytical spectroscopic methods, which require a microsampling operation, applied in conservation science were well established during the last 20 years [1]. However, the nondestructive analysis of art objects becomes a necessity, because the microdestructions caused by the sampling procedure are, in most of the cases, not permitted to the objects under study, which are extremely valuable, rare, and fragile. The nondestructive analysis techniques are generally not so effective, compared with the analytical microsampling techniques. However, the support of these methods with soft-computing techniques can minimize their ambiguity. In this paper, we propose an acoustic micro- Manuscript received October 12, 2010; revised January 17, 2011; accepted January 28, Date of publication April 19, 2011; date of current version August 10, This work was supported by the CHARISMA and InfrArtSonic Projects, which are funded by the European Commission. The Associate Editor coordinating the review process for this paper was Dr. Robert Gao. G. Karagiannis, G. D. Sergiadis, and C. Salpistis are with Aristotle University of Thessaloniki, Thessaloniki, Greece. D. S. Alexiadis is with the Department of Electronics, Technical Education Institute, Thessaloniki, Greece. A. Damtsios is with Ormylia Foundation, Ormylia, Greece. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TIM scope supported by a set of soft-computing methods, which are based on time frequency (TF) signal processing techniques for the nondestructive depth profiling of the stratigraphies of art objects. Up to now, there is a lot of work done in the field of artworks documentation with respect to material identification [1], [2]. The most widely used analytical methods are given here. 1) Multispectral imaging from the visible up to the near infrared area of the spectrum, providing surface information and information from the underlayers. The method is nondestructive since no contact with the artwork is required, but it provides only qualitative and not quantitative results [4] [7]. 2) Ellipsometry, providing mainly surface information and also information from the underlayers, in the case that they are optically transparent. No information is provided for pigment materials, which are not optically transparent. This method is nondestructive, but it provides only qualitative results [8], [9]. 3) Unilateral nuclear magnetic resonance: The information provided by this method is mainly associated with the structural stability and not with pigment identification. The method is nondestructive since no contact with the artwork is required. It is still under research but very promising to provide rich qualitative and quantitative results [10], [11]. 4) X-ray fluorescence, providing mainly elemental analysis information from the surface, as well as information from the under-layers. No depth profiling information is provided since it is not known from which layer the information is received. The method is nondestructive, and it provides qualitative results. The possibility to acquire quantitative results is under research [12]. 5) Raman, providing mainly information related to the surface information and to inorganic materials. In order to acquire information from the depth profile, usually microsampling is required. It provides only qualitative results, while the extraction of quantitative results is under research. 6) Fourier-transform infrared spectrometry: The information it provides is mainly related to the surface and to /$ IEEE

2 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3083 organic materials. In order to acquire information from the depth profile, usually microsampling is required. The methodologies in this category provide mostly qualitative results. The possibility to produce quantitative results is under research. 7) Laser induced breakdown spectroscopy, providing rapid elemental analysis results. It is applicable in situ and is almost a nondestructive technique since only microdestructs (ablates) to the layers are generated, in order to reach the underlayers. It provides qualitative results, whereas the possibility to acquire quantitative results is under research [13]. 8) Optical coherence tomography is lately used in the field providing depth profiling images from the paint layers of art objects [14]. Nevertheless, there is a significant restriction: due to the radiation used in the visible area of the spectrum, the depth profile of the underlayers can successfully be revealed only in the case that the upper layers are transparent to the electromagnetic radiation, which is something that is not happening using the ultrasonic technique. The main objective of the work presented in this paper is the determination of the depth profile of the artworks stratigraphy, using ultrasound, combined with TF tools. Ultrasounds, combined with TF analysis, have been extensively used in the field of nondestructive testing (NDT) [15] [25]. For example, Andria et al. [15] studied the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) as suitable TF tools to detect reflected pulse echoes and estimate their time of flight (TOF). They also perform a characterization of the methods in terms of systematic and random errors. However, they do not study the problem of overlapping echoes, and they present results only with simulated data. In [16], the use of basis pursuit (BP) for adaptive TF decomposition is proposed, in order to improve ultrasonic-based flaw detection. The BP decomposes the signal into a superposition of dictionary elements using an overcomplete dictionary. Zhang et al. [16] found that the use of the real Gabor dictionary and the Daubechies Wavelet Packets dictionary was well suited to the ultrasonic nondestructive evaluation problem. However, they present results only with simulated data, without considering overlapping echoes. Drai et al. [17] used the STFT and the discrete wavelet transform (DWT) for the extraction of appropriate time/frequency features. The extracted feature vectors are fed to appropriate classifiers in order to characterize the nature of defects (planar or volumetric). Furthermore, they propose the application of the STFT and Smoothed Pseudo Wigner-Ville (SPWV) distribution to the problem of thickness measurement. For the latter, however, they present results only for a simple experiment with simulated A-scans, without overlapping echoes. In [18], the use of the DWT is proposed for the detection of echoes from multilayer structures. The argument in [18] that supports the use of DWT is based on the fact that the DWT basis function has constant relative bandwidth, in contrast to the STFT s functions, which have constant bandwidth, independent to the center frequency. Therefore, for high signal-to-noise ratios (SNRs), they propose the use of a small wavelet scale (high center frequency and large bandwidth), which offers good time resolution. On the other hand, for low SNRs, they propose the use of a large scale (low center frequency and low bandwidth), which leads to reduced time resolution but also eliminates the effect of noise. However, this argument ignores the fact that the signal to detect (echo) has a specific frequency support, and the selection of scale has to take into account this signal s frequency support. Therefore, the arbitrary selection of scale based on the SNR does not seem to be reasonable. Furthermore, the DWT is not a time-invariant transform, which constitutes a limitation in signal analysis problems. Finally, the authors present results on simulated A-scans and an A-scan taken from a flat Perspex target. Rodríguez et al. [19] proposed an interesting approach for flaw detection in the non destructive evaluation of scattering materials using ultrasounds combined with the wavelet transform (WT) or the Wigner-Ville (WV) distribution. However, they study the detection of a single flaw echo, and they present results only on simulated A-scans. The use of Lamb waves, which are generated and received by an ElectroMagnetic Acoustic Transducer (EMAT), combined with the DWT is proposed in [20] for the detection of cracks in high-pressure metallic reservoirs. The use of an EMAT is permitted by the metallic nature of the studied objects and overrides the necessity of using a coupling medium between them and the transducer. The main drawback in using EMATs is the low SNR, due to small amplitudes of the generated signals. Therefore, in [20], the DWT is used for signal denoising by pruning (hard thresholding) the DWT coefficients and applying the inverse DWT. The use of the DWT as a denoising tool has also been proposed in [21] for the pipe inspection with ultrasonic guided waves. The use of the empirical mode decomposition (EMD) for the processing of ultrasound signals has been proposed in [22]. However, EMD is used only for denoising of the ultrasound signal, by rejecting the noise-containing intrinsic mode functions (IMFs) and reconstructing the signal. An interesting approach for the detection of defects in electronic devices by means of ultrasounds and the WT has been proposed in [23]. However, the presented experimental results do not include the case of overlapping echoes. Although the use of acoustic microscopy accompanied with TF analysis tools has been extensively studied in the field of nondestructive evaluation, it has never been used for the documentation of artworks and paintings but only initially in the Ph.D. thesis of one of the authors in 2008 [26], [27]. In this paper, we propose the employment of acoustic microscopy, combined with five different TF analysis-based methodologies, for the depth profiling of the artworks stratigraphies. This paper is organized as follows: The wave propagation simulations, supporting the development of the acoustic microscope device and the device itself, are described in Sections II and III, respectively. In Section IV, the proposed system was tested with reference materials and samples. In Section V, the proposed signal processing techniques used for the stratigraphy depth profile estimation are described. In Section VI, we present experimental results on simulated and real A-scans. A comparative study between the presented methodologies is performed. Finally, the conclusions are given in Section VII.

3 3084 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 II. SIMULATION OF THE WAVE PROPAGATION IN THE STRATIGRAPHIES, TARGETING TO THE OPTIMAL DESIGN OF THE SYSTEM A. State of the Art of Wave Propagation Technology Pertaining to the Proposed Research Application The propagation of the acoustic waves in multilayered structures has been extensively studied in [28] [34], involving analytical ray tracing and matrix techniques to simulate the propagation of the acoustic waves in the structures. In [30], the ray-tracing technique has been used to extend the simulation of the wave propagation to the calculation of ray reflection and diffraction in consecutive surfaces (resembling wave propagation in a layered medium). Moreover, an extensive study and the corresponding simulations are presented, concerning the ultrasound-wave propagation in layered media, which are inhomogeneous in each layer and the surfaces between adjacent layers are not planar. Furthermore, the various transmission losses in each layer are also calculated; these are mainly caused by reflections in boundary surfaces, by wave-front mitigations, and by absorption in the material of each medium. The stratigraphies of artworks are rather complicated structures with inhomogeneous and grainy materials in each layer. The size of the grains distributed in the layers varies from the order of several tenths of nanometers, up to the order of micrometers, depending on the pigment. The simulation of the wave propagation in such structures using the aforementioned analytical techniques would require significant effort without ensuring the reliability of the results. The appropriate numerical methods for calculating the field in cases of difficult structures, like the grainy materials of our case, are the finite-difference ones, which are well established in the specific research field [35]. Therefore, in our case, the finite difference method (FDM) was also used. The simulations are performed in two dimensions (2-D), which are mainly developed for planar objects. However, if the third dimension is large enough, the same theory can be applied in full-3-d cases. B. Simulation Method: FDM Applied to the Elastic Wave Equation We suppose that, when an acoustic wave excites a solid stratigraphy, its particles are being displaced. This displacement is related to the local materials properties. For a specific point (i, j), the particles displacement is provided by the following equation: u(t + t, i, j) = c 1 (i, j)u x (t, i, j)+c 2 (i, j)u x (t t, i, j) + c 3 (i, j)u x (t, i +1,j)+c 4 (i, j)u x (t, i 1,j) + c 5 (i, j)u x (t, i, j +1)+c 6 (i, j)u x (t, i, j 1) + c 7 (i, j)u y (t, i, j)+c 8 (i, j)u y (t, i +1,j+1) + c 9 (i, j)u y (t, i 1,j+1)+c 10 (i, j)u y (t, i 1,j 1) + c 11 (i, j)u y (t, i +1,j 1) + c 12 (i, j)u y (t, i +1,j) + c 13 (i, j)u y (t, i, j +1) + c 14 (i, j)u y (t, i 1,j)+c 15 (i, j)u y (t, i, j 1) where u =[u x,u y,u z ] T are the displacements of particles of the material in three dimensions, and c(i, j) are the coefficients that depend on the properties of the materials existing in the cells around the point (i, j), in the grid model structure using the FDM method. The precise equation that is used for the calculation of this displacement in each point of the solid stratigraphy for each time instance t is the approximation of the elastic wave equation provided in [35] [ ρ 2 ũ 2 t = λ + µ + φ t + η ] [ ( ũ)+ µ + η ] 2 ũ 3 t t where ρ is the density of the material (in kilograms per cubic meter), λ and µ are the first and second regularly Lamé (in Newton per square meter), η stands for the shear viscosity (in Newton-second per square meter), and φ is the bulk viscosity (in Newton-second per square meter). The variables λ and µ describe the relation between the pressure (T ) and the strain (S) that is present in an isotropic material when excited by an acoustic wave. This equation is valid for the isotropic material cells, like the grains of the pigments, which also collectively build up heterogeneous materials, like the stratigraphies of art objects. This acoustic equation applies not only to isotropic materials but also to flexible ones, when the viscous losses are also taken into consideration. 1) Reference Samples for the Sound Speeds Measurement and the Proposed System s Evaluation: The parameters of (1), as well as the densities of the materials, can be derived from the ultrasound speed inside them [31]. In order to measure the preceding characteristics, special reference pellets were fabricated [Fig. 1(b)]. At the same time, an adequate number of experimental stratigraphies were developed with pure pigments or mixtures of them, resembling the paint layers of byzantine iconography (Fig. 2). In the reference samples, the pigments in the paint layers and the pellets are mixed with the medium, which is egg tempera. For the creation of the pellets, initially, the mixture of pigment with the medium is spread on a sleek surface (glass) and is left to dry. The dehydrated mixture of pigment and medium is collected, and the necessary quantity is formulated into a pellet under an applied pressure of 100 bars. The type of the reference stratigraphies and pellets, as well as their purpose of fabrication, is shortly summarized in Table I and in more detail in [36]. Using the pellets and the setup displayed in Fig. 1, the ultrasound speed inside the materials was measured: An ultrasound signal is sent to the pellet of thickness d, and the reflected echo from the bottom of the pellet is received after a TOF t. The speed is provided by the following simple equation: C u = 2d t. (2) The results of these measurements are summarized in Table II. The probe used for the measurement is a Panametrics transducer (V2012) with central operating frequency of 5 MHz. The acoustic impedance of the materials can be calculated,

4 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3085 Fig. 1. (a) Setup for the measurement of the sound speed of the materials. (b) Transducer above the reference pellet before the measurement. (For the measurement, a coupling gel is used.) Fig. 2. (a) Reference panels stratigraphies containing different combinations of successive paint layers of pure pigments or mixtures of them. (b) Way of their fabrication. (c) Detail with an artificial scratch. TABLE I REFERENCE SAMPLES based on the measured speeds and the materials density P, using the following equation: Z = P C u. (3) The density of the pellets materials is calculated as the quotient of their mass to their volume. 2) Application of the Wave Propagation Simulation to the Reference Materials: Using the aforementioned analysis, we converted optical microscopy digital images of the cross section of the stratigraphies to a coded gray level image as follows: Each pigment in the cross-section images is represented by a specific gray level, which corresponds to different ultrasound speeds and, consequently, to different acoustic properties; the higher the resolution of the optical microscopy images, the more precisely the acoustic characteristics of the materials are described, resulting to a more precise wave calculation. If the paint layer contains only one pigment, a unique gray level is assigned to all the pixels in the corresponding region. If we have a mixture of two pigments, then the pixels of the corresponding

5 3086 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 TABLE II MEASURED SOUND SPEEDS OF THE MATERIALS Fig. 3. (Left) Optical microscopy image of a reference stratigraphy. (First layer) Ultramarine (thickness 49 µm). (Second layer) Ultramarine + Lead White ( 47 µm). (Third layer, upper): Lead White ( 53 µm). (Right) Corresponding PCX gray level image model. region are separated in two gray levels with proportions equal to the proportions of the mixture, according to the optical microscopy images (Fig. 3). To the gray levels that correspond to a pigment, we assigned as sound-speed and density values the geometric mean of the values that correspond to the medium and the pigment. We attributed to the bigger grains, compared to the probing ultrasonic wavelength, the sound speed, which was calculated experimentally. The simulated waves, emitted by focused and unfocused sources, are of frequencies 150, 250, and 350 MHz. A pulse echo technique was used, where the source-receiver consists of a focused piezoelectric crystal that is 2 mm long and placed in a specific height above the surface of the reference material that simulates the distance of the transducer from the measurement point. The source emits an exponentially attenuating sinus Gaussian pulse, which is similar to the output pulse that the system Pulser Transducer produces, i.e., p(t) =A e (t pw /2) 2 (2πft) a 2 sin(2πft) (4) where f is the central operating frequency of the transducer; A is the amplitude of the pulse, which is selected to be equal to unity; and p w is the pulsewidth (duration), which is selected to be equal to 20 and 40 ns, similar to the expected time width of the pulse that the transducer with the expected operating spectral range provides. The different operating frequencies and the focusing of the transducer are two of the main issues that were examined during the application of these simulations. Some indicative captures of the wave distribution in specific time instances, as well as the corresponding A-scans, are presented in Fig. 4. In the presented A-scans, the echo times are roughly indicated using dashed vertical lines. The blue line indicates the time when the echo from the surface is received, and the black line indicates the time when the echo from the interface between the first and second layers is received. The red line indicates the time when the echo from the interface between the second and third layers is received, and finally, the magenta line indicates the time when the echo from the interface between the third and preparation layers is received. 3) Conclusions From the Simulations: The echoes resulting from the interface between the first and second layers are evident for all the used frequencies. The presence of microechoes, which are distributed between significant echoes, indicates the change of grain distribution and, therefore, eventually that of

6 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3087 Fig. 4. Wave propagation in the reference stratigraphy in a specific time instance when the first echo from the surface and the echo of the interface between the first and second layers are displayed (with (left) focused source and (right) unfocused source). The corresponding simulated A-scans have echoes at 269, 348,418, and 480 ns. (Dashed line) Time instances on which the echoes have been received from the interfaces between the layers. a layer. This is also a strong indication that the crossed layer is grainy with relatively bigger grains or that a grain mixture is present. The phenomenon becomes more evident as the frequency of the source increases. The echo of the received signal from the interface between the first and second layers, compared with that of the source signal, is attenuated approximately 20 db. This attenuation and the power of the wave radiated from the transducer to the artwork was one of the criteria for the determination of the output dynamic range of the preamplifiers and the analog-todigital (A/D) converter that were chosen. The resolution of the system, i.e., capability to reveal existing grains, is much higher using 350-MHz focused transducers. The received echoes for higher frequencies are sharper and distinct from the internal grains of the layers, particularly when a focused transducer is used. At the same time, the echoes from the inner interfaces are significantly attenuated in general. In Table III, we present TABLE III ACOUSTIC IMPEDANCE OF THE PIGMENTS THAT ARE PRESENT IN REFERENCE 90 OR P03_04_01_03 the acoustic impedances of the materials that are present in the stratigraphy of Fig. 2(c). When lower-than-100-mhz frequencies are used, usually no distinct echoes from the internal structures in the layers can be determined. The use of focused transducers operating in higher frequencies will also help discriminate the low-signal echoes

7 3088 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 5. Acoustic microscope device block diagram. The pulser receiver excites the transducer. The received signal is amplified and then fed to the pulser receiver. Then, the output of the pulser receiver is fed to the 2GS/s A/D converter. from the deeper layers or grains. The chosen micropositioning system of the transducer takes into consideration the micromovements that are needed to increase the resolution in the Z direction to more easily discriminate the layers. For this reason, the drive step resolution is 1 µm. Taking into consideration that previously mentioned, there was an effort to optimize the efficiency/cost ratio of the system. This compelled us to choose either a high-frequency transducer or a lower frequency transducer, discriminating better the interfaces of the layers, and develop appropriate algorithms, which would reveal as best as possible the time instances of the echo arrivals. III. PROTOTYPE DEVELOPMENT A. State of the Art of High-Frequency Transducers Taking into consideration the results of the simulations, one of the most crucial parts of the system is the transducer, which determines the frequency of the wave that will be emitted to the paint layers, as well as the geometry of the wave front. The progress and development of acoustic microscopy systems, particularly advanced in the field of medical diagnosis, is shown in [36] [47]. Manufacturing of high-frequency piezoelectric transducers and acoustic microscopes is presented in [41] and [44], some of which operate at frequencies up to 200 MHz, providing images from the depth of the object under study. The use of higher frequencies is mainly used for surface imaging since the penetration depth dramatically decreases. The use of frequencies up to 200 MHz can provide axial resolution of approximately 12 and 14 µm for analyzing tissues with characteristic sound wave propagation speed of 1540 m/s. In the context of the current work, sound speeds for different materials vary around an average value of 1660 m/s, as tested and verified in laboratory experiments. In [41], it is also stated that piezoelectric materials for high-frequency applications, such as Lead Zirconate Titanate (PZT) and Piezoelectric polymers (PVDF) materials, show reduced efficiency at frequencies above 100 MHz. In the same reference, LiNbO 3 has been used for manufacturing a high-efficiency focused transducer of 200 MHz, with a focal length of 4 mm. Using LiNbO 3 is advantageous, due to its mono-crystal nature; hence, efficiency problems are avoided due to the material s granules [47]. The image quality acquired by such a transducer (in the range of 200 MHz) depends on the beam distribution of the transmitted wave and on the pulse bandwidth [36], [38], [47]. For example, for a 10-µm resolution system, the operating frequency must be 120 MHz, when the ratio of the focal length to the diameter of the acoustic lens F = z 0 /D is unity. It is crucial to receive the echoes from the target point when this is at the focal length. Therefore, to increase the resolution, the transducer is vertically moved during the scanning procedure [39]. B. Experimental Setup and Measurements A basic overview of our first prototype of acoustic microscope device is displayed in Fig. 5. The thickness of the paint layers is expected to be around µm; therefore, the corresponding TOF of the acoustic wave is on the order of 100 ns (considering the sound speeds of Table II). The pulser receiver of 400-MHz bandwidth is exciting the transducer. The pulsewidth of the pulser is equal to 2.5 ns, which is less than the TOF in a very thin paint layer (5 10 µm). Our transducer is broadband with central operating frequency of 110 MHz, focal length of 6 mm, and spherically shaped lens for focusing the wave in the stratigraphic structure. The signal waveform and the spectrum of the transducer are provided in Fig. 6. As a coupling medium with the painting, we used carboxyl methyl cellulose (CMC), which has the unique capability of fully evaporating after a few minutes, without leaving any traces to the device under test. Its sound speed was measured, and its contribution to the final focal length was experimentally estimated. The received signal from the transducer is amplified using a low-noise broadband preamplifier and is finally sent to the A/D converter, which can collect 4 GSamples/s. The highspeed A/D converter ensures the safe separation of the echoes from the thin paint layers. The system is modular, allowing the use of various probes to observe the object in different frequencies.

8 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3089 Fig. 6. Transducer waveform and corresponding spectrum. Fig. 7. (a) Raster of strip lines. (b) C-scan of the strip lines. The scanning step is 5 µm. The widths of the reconstructed strip lines are in accordance with those observed under the optical microscope. IV. APPLICATION OF THE SYSTEM ON REFERENCE MATERIALS, PAINTED STRATIGRAPHIES, AND A WALL PAINTING FRAGMENT: COMPARISON WITH THE SIMULATED A-SCANS Initially, in order to evaluate the resolution of the system, a pattern of strip lines with controlled widths (ranging from 50 µm up to hundredths of micrometers) was created and scanned with the acoustic microscope. Using an optical stereomicroscope, the pattern of the strip lines was photographed with a microscale on it [Fig. 7(a)]. The generated C-scan image of the strip lines is provided in Fig. 7(b). The width of the reconstructed strip lines is in accordance with those that appear in the optical microscope images. Then, the developed system was tested using painted stratigraphy reference samples. Here, we present the measurements for the sample in Fig. 2(c), which includes an artificial defect scratch between the borders. The scanned area is mm. The measured A-scan signals with the simulated ones are in good agreement [Fig. 8(b)]. The absolute instances of the reception of the echoes are also produced at the very specific instances that correspond to interfaces between the paint layers (Table IV). The received A-scans collect the echoes from the upper layer of the stratigraphy to the preparation layer Fig. 9(a). The analysis of the echoes received from the interfaces between the various combinations of the paint layers of the reference stratigraphy is presented in Fig. 9: There is a clear distinction between the echoes coming from the surface and the next layers. A second measurement was also acquired from the combination of the two underlying layers (marked with blue, green, and yellow). The instances on which the echoes are received are in accordance with the first measurement. The third echo in the A-scan from the scratch area (in blue) is received delayed, as expected, since it is located further than the other layers from the transducer. Furthermore, we used the system to analyze a wall painting fragment by scanning an area of 4 4 mm that includes two brush strokes (Fig. 10). In the same figure, the rectified corresponding A-scans are displayed for different points of measurement, with one over the brushstrokes, in which the second echo from the sublayer is also evident, and one over the surface without the brushstrokes, where we can observe only one echo. It is also obvious that, in the second case, the echo is received later, because the surface at this point is located further away from the transducer, compared with the point where the brush strokes are located. V. P ROCESSING OF ULTRASOUND-MICROSCOPE SIGNALS FOR THE EXTRACTION OF PAINT LAYERS PROFILES The idea is based on the fact that the transducer s ultrasound signal can be seen as a dumped oscillation and, consequently, as an amplitude-modulated (AM) harmonic signal. Let this be denoted as x 0 (t) =a(t)cos(f 0 t), where a(t) stands for its envelope. In this paper, we use a transducer with center frequency f 0 = 110 MHz. The transducer s signal and the corresponding spectrum are given in Fig. 6. Let the transducer s frequency response be denoted as H t (f). The produced wave initially propagates through the CMC gel, which is used for the coupling of the transducer with the artwork. The gel acts as a low-pass filter with impulse response H g (f). Therefore, the spectrum of the signal, corresponding to the propagated wave, is determined from the product H f (f) H g (f). Fig. 11 shows a received A-scan containing a clear echo in the time and frequency domains. One can verify that the center frequency of the echo is approximately f c =60MHz, whereas its 6 db bandwidth is about 25 MHz. This verification shows that the get acts as a relatively strong low-pass filter, with a cutoff frequency approximately equal to MHz.

9 3090 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 8. Simulated A-scan and the corresponding measured one from the layers of the reference stratigraphy no (a) Captures of the simulations, as well as the transducer s position according to the stratigraphy, are presented. (b) Simulated and measured signals. The time instances of the echo arrival are presented. TABLE IV EXPECTED TOF OF THE ECHOES GENERATED FROM REFERENCE SAMPLE NO. 119 OR P03_ ACCORDING TO THE SIMULATIONS AND THE CORRESPONDING MEASURED ONES The wave is reflected due to the discontinuities in the medium it travels (gel first paint layer second layer, etc.), resulting to the various echoes in the received signal (A-scan). Therefore, the latter can be modeled by x(t) = M a m (t T m )cos(f c (t T m )+φ m (t)) (5) m=1 where the envelopes a m (t) are attenuated and distorted versions of a(t), whereas φ m (t) are used to characterize frequencymodulated (FM) (frequency-distortion) effects, due to various distortion phenomena. The time delays T m refer to the time instances in which the various echoes arrive back to the transducer, i.e., to the TOFs of the signal. According to the simple model previously described, in each A-scan, we expect to detect signals that have well-localized characteristics in both frequency (around frequency f c ) and time (at time instances T m ). The separation of the different echoes and the estimation of the corresponding TOFs are challenging tasks, particularly when neighbor echoes overlap. However, TF analysis of each A-scan can reveal the TOFs T m, as described in the next paragraphs. The idea is based on the fact that the useful signal, i.e., the echoes, has known and well-localized frequency characteristics. On the contrary, noise is spread over the whole frequency axis, whereas other kinds of distortion have frequency components that may be inside but also outside the frequency range of the useful signal. Therefore, the proposed methods are more or less based on the estimation of an instantaneous energy (IE) measure, which exploits the aforementioned fact. A. Using TFRs As an appropriate tool for TF analysis, we select the TF representations (TFRs) [48] [51] and, specifically, the SPWV distribution, described here. 1) WV Distribution: Among all the quadratic TFRs, the WV distribution is the most important one, satisfying a large number of mathematical properties. It has been extremely popular in

10 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3091 Fig. 9. Echoes received from the interfaces between the various combinations of the paint layers of the reference stratigraphy. the electrical engineering community. The WV distribution of a signal x(t) is defined by W x (f; t) = x(t + τ/2) x (t + τ/2) e j2πfτ dτ (6) where x (t) represents the conjugate of x(t). By definition, it is the Fourier transform of the signal s central covariance function x(t + τ/2) x (t + τ/2). WV distribution is always real valued and can be loosely interpreted as a 2-D distribution of the signal s energy over the TF plane. For a single linear FM signal, it is ideally concentrated along the instantaneous frequency (IF), i.e., x m (t) =e j2π(f 0m+γ m t)t W xm (f; t) = δ(f f 0m 2γ m t). (7) While the WV distribution presents the best TF localization among all the quadratic distributions, in the case of multicomponent signals, the WV distribution presents the most emphatic cross terms. However, cross terms have oscillatory nature, which is a key point in the introduction of the

11 3092 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 10. Echoes from a wall painting fragment. Fig. 11. (a) A-scan taken using the transducer of 110 MHz and (b) its corresponding Fourier transform. The gel used for the coupling of the transducer with the artwork acts as a low-pass filter. Therefore, the center frequency of the received A-scan is approximately 60 MHz. reduced interference distributions, which are directly discussed here. 2) SPWV Distribution: Using a 2-D TF smoothing (lowpass) kernel Π c (f; t), one can obtain a smoothed version of the WV distribution as follows: C x (f; t) = Π c (ξ f; s t)w (ξ; s) ds dξ. (8) Equation (8) gives the general form of Cohen s class TFRs [48], [49]. The oscillatory form of the cross terms is attenuated using time and/or frequency smoothing operations. However, this comes at the cost of a loss of TF localization. Sophisticated designs of the smoothing kernel, in order to attenuate the cross terms while preserving TF localization, led to many important Cohen s class TFRs, such as the Butterworth, the Choi-Williams, the cone-kernel, and the Page distributions [48] [50]. We use the SPWV. The SPWV is defined by a separable 2-D kernel Π c (f; t) =H( f)g(t), where H(f) is the Fourier transform of an 1-D smoothing window h(t). Introducing separable smoothing actions allows controlling the smoothing in time and frequency freely and independently to each other. The wider the time (frequency) smoothing window that is chosen, the more the time (frequency) smoothing that can be achieved. For H(f) =δ(f), i.e.,h(t) =1and g(t) =δ(t), one simply obtains WV. 3) Application of the SPWV Distribution: According to the given analysis, the used systematic procedure for the extraction of the TOFs is summarized here. 1) Calculate the SPWV distribution of each A-scan, using Gaussian windows as smoothing windows along time and frequency, i.e., g(t; σ) = 1 t 2 2πσ 2 e 2σ 2 (9) and, similarly, for h(t; σ). The window g(t; σ) is selected to be relatively weak, with σ = ms (ten samples for f s = 4000 MHz), in order to maintain good resolution along time. The window h(t; σ) is

12 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3093 selected slightly stronger, with σ = ms (20 samples for f s = 4000 MHz). 2) In order to calculate an IE function, one can find the projection of C x (f; t) to the temporal axis. However, according to the presented model of the A-scans, the regular components of x(t) are expected to have frequency contents around the center frequency f c. We therefore, calculate the projection: IE c (t) = f max f min C x (f; t)df (10) where f min =30and f max =90MHz. 3) Find the peaks of IE c (t). The time locations of these peaks correspond to the TOFs T m. B. Using the CWT 1) CWT and Complex Morlet Wavelet: An alternative tool for time scale analysis (scale is inversely proportional to frequency) is the WT. For a detailed analysis on the WT and the DWT, the reader is referred to [52] and [53]. The CWT of a signal x(t) is defined as an expansion along two parameters scale a and time shift t [52], i.e., CWT x (a, t) = + x(τ) ψ a,t(τ) dτ. (11) The wavelet functions ψ a,t (τ) are obtained by shifting and scaling the mother wavelet ψ(τ), i.e., ψ a,t (τ) = 1 a ψ ( τ t a ), a,t R(a 0). (12) As a mother wavelet, one can consider any square-integrable oscillating function, which has bandpass characteristics and zero mean (the latter condition is simplification of the wavelet admissibility condition [52]). The parameter a is the scale factor, and t is the shift factor. For small a(a <1), ψ a,t (τ) is short and of high frequencies, whereas, for large a, thewavelet function is long and of low frequencies. Considering real-valued wavelets, since the CWT of a signal is calculated as a convolution of the signal with the scaled wavelets (oscillating waveforms), the CWT has oscillatory characteristics along t for a given scale a. Therefore, we use complex wavelets and, specifically, complex Morlet wavelets [54]. The mother complex Morlet wavelet is given by the following: where ψ(t) =g(t) e j 2π t (13) g(t) = 1 πσ1 e t2 /σ 1 (14) is a Gaussian function. In particular, the mother complex Morlet wavelet is a modulated Gaussian waveform with a normalized center frequency that is equal to unity. The complex Morlet wavelets are very similar with the basis functions of the short-time (windowed) Fourier transform (STFT). They are both windowed complex exponentials. However, the main difference is that the window size changes as scale a changes, in contradiction to the fixed window size (independent of the center frequency) in STFT. 2) Application of the CWT: The selection of the bandwidthrelated parameter σ 1 [(14)] is based on the following arguments. According to Fig. 11, the 6-dB bandwidth of the received echo is approximately 25 MHz, whereas its center frequency is f c =60 MHz. The relative bandwidth is equal to 25/ , i.e., if the center frequency is normalized to unity, the 6-dB bandwidth becomes B =0.42. It is known that the Gaussian function g(t) in (14) is also Gaussian with 6-dB bandwidth equal to B = ln(2)/π σ 1. Therefore, we conclude that σ 1 should be approximately σ 1 = (ln 2/π 2 B 2 ) 0.4. Since the mother complex Morlet wavelet has a center frequency equal to unity, the approximate wavelet scale a for which we will have maximum correlation of the scaled wavelet with a received echo is a c = f s 1/f c 65. Notice that we have multiplied with the sampling frequency f s since f s should have been considered in the wavelet analysis. Therefore, the CWT scales used in our experiments were selected in the interval between a min =0.5a c and a max =1.5a c. Our application of the CWT for the extraction of the TOFs can be summarized here. 1) Calculate the complex Morlet CWT of the A-scan, for scales between a min =0.5a c and a max =1.5a c. Let this be denoted as CWT x (a, t). 2) An IE function can be obtained by calculating the projection of squared modulus CWT x (a, t) 2 to the temporal axis, i.e., IE w (t) = a max a min CWT(a; t) 2 da. (15) 3) Estimate the TOF T m by finding the peaks of IE w (t). C. Using the DWT 1) Wavelet Series and DWT: In the wavelet series expansion of a signal, we do not have continuously scalable and shifted functions. Instead, the wavelets are scaled and shifted in discrete steps. In other words, samples of the continuous transform are calculated on a sampling grid. The wavelet series expansion of a signal x(t) is given by where WS x (s; t) = + x(τ) ψ s;t(τ)dτ (16) ψ s;t (τ) =2 s/2 ψ ( 2 s (τ t) ) (17)

13 3094 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 13. Symlet-14 wavelets in the frequency domain, for various scales, considering a sampling frequency of f s = 4000 MHz. Studying this figure, together with Fig. 11(b), one can conclude that the DWT at scales s =5and s =6contains the most energy of the signal. Fig. 12. Division of the TF plane by the DWT. is the mother wavelet at scale 2 s and shifted by t. For a discrete signal x[n], we have the DWT, where the scale factor s takes integer values s {1, 2,...,J 1), whereas the shift values t n are multiples of 2 s, i.e., t k = k 2 s.in particular, in the DWT, we have samples of the CWT, with the CWT time-scale parameters (a, t) sampledonaso-called dyadic grid: (2 s,k 2 s ). The fast implementation of the DWT is based on the use of a bank of filters [53]. The DWT can be calculated only for compactly supported wavelets, e.g., for the Daubechies, Symlets, and Coiflets wavelet families [52], [53]. Each stage of this scheme consists of two digital filters h 0 and h 1, i.e., a low-pass and a high-pass filter, followed by downsampling by 2. The filter h 1 is related to the mother wavelet of the corresponding wavelet-series expansion, whereas h 0 is orthogonal (or almost orthogonal) to h 1. The output of each stage is the approximation (low-pass) coefficients x (s) [n] and the detail (high-pass) coefficients y (s) [n]. In each next stage, the low-pass coefficients x (s) [n] are further processed. Based on the scale property of the Fourier transform, the scale 2 s is inversely proportional to the frequency. Therefore, the division of the TF plane, as introduced by the DWT, is dyadic, as shown in Fig. 12. The higher the scale, the better the frequency resolution and the lower the time resolution. 2) Application of the DWT: According to the diagram of Fig. 11(b), the center frequency of a received echo is approximately 60 MHz. Assuming a sampling frequency of f s = 4000 MHz, the frequency supports of the Symlet14 wavelets for various DWT s scales s are depicted in the diagram of Fig. 13. One can find that, with respect to the frequency support, the appropriate scale factors of the DWT are s =5 and s =6. This can also be verified from the diagrams of Fig. 14, where we give the absolute value of the DWT detail coefficients in four consecutive scales. For s<5, the DWT has better temporal resolution as the scale decreases, but the detail coefficients correspond to higher noise-containing frequencies. The amplitude of the DWT for s = {5, 6} is greater than that for s {5, 6}, verifying that the scales corresponding to the signal s frequency content are s = {5, 6}. Since using the lower scale one obtains better time resolution, we use the DWT scale factor s =5. Based on the preceding discussion, the used DWT-based approach can be summarized here. 1) Calculate the DWT of the A-scan x(t). In our study, we have experimented with many wavelet families. Since the echo signals present a relative symmetry, our experiments also showed that the use of near-symmetric wavelets (e.g., Symlets) leads to better performance, compared with wavelets that are far from symmetric. Therefore, we present various results with respect to the Symlets wavelets family. However, a detailed analysis is beyond the scope of this paper. 2) Take the absolute value of the DWT detail coefficients at the appropriate scale 2 s. For our experimental settings, s =5. Let this vector be denoted as y (s) (t k ). 3) Find the peaks of y (s) (t k ). Let the sample locations of the peaks be denoted as p m, m =1,...,M. The corresponding estimated TOFs are T m = p m 2 s. D. Using the DSWT 1) DSWT: The DWT is a critically sampled transform (i.e., the number of the transform coefficients is equal to the input signal s samples number), in contrast to the CWT, which is extremely redundant. This constitutes an advantage for signal compression/coding applications. Furthermore, in contrast to the CWT, it has a fast implementation using filter banks. On the other hand, the classical DWT as an analysis tool suffers a serious drawback: It is not a time-invariant transform, i.e., the DWT of a translated version of a signal x(t) is not, in general, the translated version of the DWT of x(t). The desirable translation-invariance property in signal analysis, which is lost by the classical DWT, is restored in the discrete stationary WT (DSWT), which also has a filter-bank-based fast implementation. For a detailed analysis, the reader is referred to [55]. Translation invariance is achieved by removing the downsamplers of the DWT and upsampling the filter coefficients by a factor of 2 s 1 in the sth level of decomposition. Consequently, the DSWT is an inherently redundant scheme since the output at each decomposition level contains the same number of samples as the input. This algorithm is also known as algorithme à trous. 2) Application of the DSWT: Our DSWT-based approach for the estimation of the TOFs is similar to the DWTbased one. However, there is a significant difference: At each

14 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3095 Fig. 14. Symlet-14 DWT coefficients (absolute value) in four consecutive scales, for the A-scan in Fig. 11. According to Fig. 13, the most appropriate scales, corresponding to the signal s frequency content, are s =5and s =6. Therefore, the amplitude of the DWT for these scales is greater than s {5, 6}.However, the smaller the scale, the better the time resolution. Therefore, we use s =5. decomposition level, the DSWT transform coefficients present oscillating characteristics along t [55]. This can be explained based the fact that the DSWT is obtained from the CWT with a redundant sampling along t and the CWT has oscillatory characteristics for a given scale (considering real-valued wavelets). Let the DSWT at a given scale 2 s be denoted as y (s) (t) =DSWT x (s; t). In order to estimate the echoes TOFs from y (s) (t), we have to find the envelope (instantaneous amplitude, IA) of y (s) (t). Therefore, we calculate the analytic signal z (s) (t) =y (s) (t)+j ỹ (s) (t) =a(t)e jφ(t) (18) where ỹ (s) (t) is the Hilbert transform of y (s) (t). The analytic signal is calculated in the Fourier transform domain by simply replacing those FFT coefficients of y (s) (t) that correspond to negative frequencies with zeros and calculating the inverse FFT. Summarizing, the used DSWT-based approach is given here. 1) Calculate the DSWT of the A-scan x(t). We present results using the Symlets wavelet family, similarly to the DWT-based approach. 2) Calculate the analytic signal z (s) (t) for the wavelet scale factor s =5. 3) Find the peaks of z (s) (t). The locations of these peaks correspond to the TOFs T m. E. Using the Hilbert Huang Transform Hilbert et al. [56] introduced a general empirical method, which is referred to as the Hilbert Huang Transform (HHT), for the TF analysis of nonstationary data, which are generated by nonlinear processes. This method requires two steps in analyzing the data, the EMD, and the Hilbert transform. For a detailed analysis on the HHT, the reader is referred to [56] and [57]. 1) EMD: The first key part of the HHT is the EMD, which decomposes the time-series signal into a finite generally small number of IMFs components. In particular, the signal is expanded onto a basis derived from the signal itself. Let M denote the number of the IMFs. Then, the signal is written as follows: x(t) = M x m (t) (19) m=1 where x m (t) stands for the mth IMF. The requirement for the IMFs is to admit well-behaved Hilbert transforms. In fact, this means that each IMF should be an AM FM harmonic signal, i.e., where x m (t) =a m (t)cos(φ m (t)) (20) φ m (t) = t τ=0 2πf m (τ)dτ (21) is the instantaneous phase of the mth AM-FM component, and π/2 is the corresponding IF. Practically, this requirement means that an IMF should satisfy the two conditions: 1) the number of its extrema and the number of its zero crossings must either equal or differ at most by one and 2) at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. A systematic procedure for the extraction of the IMFs, which is also known as the Sifting process, can be summarized in five steps. 1) Identify all extrema of x(t). 2) Interpolate between minima (respectively maxima) to construct the lower envelope e min (t) (respectively e max (t)). 3) Compute the local mean c(t) =(e min (t)+e max (t))/2. 4) Extract the detail d(t) =x(t) c(t). This is the first extracted IMF. 5) Iterate on the residual c(t), until the number of the minima or maxima is less than two (the residual is a monototic function), or the maximum number of iterations (extracted IMFs) is achieved. Studying the previously described Sifting process, one can conclude that each next IMF contains lower frequencies.

15 3096 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 15. A-scan and the corresponding IMFs. IMF 1 contains the high-frequency noise. IMFs 2 and 3 contain most of the useful signal (corresponding to the echoes). IMFs 5 and 6 contain low-frequency distortion components. (a) A-scan taken at position 1 of the reference stratigraphy panel (see Fig. 24). (b) Corresponding IMFs obtained by the EMD. In addition, two succesive IMFs may never contain congener frequencies at the same time interval, although this is possible for different time intervals. An example of the EMD application to one of our experimental A-scans is given in Fig. 15. Applying the EMD to the received A-scans of our experiments, in practice, one observes the following: 1) the first extracted IMF (higher frequency IMF) always contains only weak noise components (additive noise, quantization noise, etc.); 2) the last extracted IMFs (low frequency IMFs) contain only weak slowly ac components, i.e., the local mean value of the A-scans; and 3) strong components, at frequencies related to the actual transducer signal, appear in the second to fourth IMFs. 2) Hilbert Spectrum: Given that the signal was decomposed into AM FM components (IMFs), the second step is the application of the Hilbert transform to each of the separate components. The goal is the construction of a frequency-time energy distribution. Since the extracted IMFs is considered to be of the form of (20) and (21), the application of the Hilbert transform aims at the extraction of the IFs f m (t) and the IAs a m (t). Considering the component signal x m (t) =a m (t)cos(φ m (t)), the Hilbert transform produces a signal that is π/2 delayed in phase, i.e., y m (t) =a m (t)sin(φ m (t)). Thus, the analytical signal z m (t) =x m (t)+jy m (t) =a m (t)e jφ m(t) (22) in its polar form, directly gives the IA and the IF of the IMF component. Then, the amplitude and the frequency can be represented as functions of time in a 3-D plot, in which the amplitude can be contoured on the frequency time plane. This frequency time distribution of the amplitude is designated as the Hilbert Huang spectrum H x (f; t). 3) Hilbert Huang IE Density: With the use of the Hilbert Huang spectrum H(f; t), one can define the function of time IE H (t) = Hx(f; 2 t)df (23) f i.e., the projection to the temporal axis, which serves as an IE function and can be used to check the energy fluctuation, during time. 4) Application of the HHT: The EMD and, consequently, the HHT method is adaptive and therefore can be very efficient. For example, a significant advantage of HHT is that the HHTbased analysis is not restricted by the Heisenberg uncertainty principle f t c ( f is the frequency resolution, t is the time resolution, and c is a constant). This means that HHTbased analysis may offer both good and frequency and time resolutions. We use an approach that is similar to the presented WV one. The used HHT-based systematic approach for the extraction of the TOFs is summarized here. 1) Construct the Hilbert Huang spectrum H x (f; t) of the signal x(t). 2) Considering that the useful signal s frequency content is between f min =30 and f max =90 MHz [see

16 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3097 Fig. 11(b)], calculate the Hilbert Huang IE function IE H (t) = f max f min H 2 x(f; t)df. (24) 3) Apply a smoothing operation to the IE function, convolving with a relatively weak Gaussian filter. The used Gaussian filter is as in (9), with σ =0.004 ms (16 samples for a sampling frequency of f s = 4000 MHz). This helps the identification of the function s peaks and, consequently, the estimation of the echoes arrival time. VI. EXPERIMENTAL RESULTS A. Simulations In order to test the accuracy of the presented methods and their ability to resolve overlapping echoes in the presence of noise, we performed a series of simulation experiments. The Gaussian pulse of the pulser was simulated based on (4) with A =1, a =0.007 ms, and f = 110 MHz. With these values, we obtained a Gaussian pulse very similar with the actual one of Fig. 6. The low-pass behavior of the coupling gel was simulated as a Butterworth low-pass filter of order N =5and a cutoff frequency equal to 50 MHz. When the pulser s signal passes through such as the filter produces a waveform with the spectral characteristics of the one in Fig. 11. Let the low-pass-filtered signal be denoted as x 0 (t). Note that the low-pass-filtered signal x 0 (t) corresponds to a Gaussian pulse with almost twice the extent of the original pulse (a ms ). We simulated a received A-scan in additive white Gaussian noise as x(t) =x 0 (t T 1 )+x 0 (t T 2 )+n(t). (25) The distance between the echoes DT = T 2 T 1 is varying from 0.02 to 0.06 ms, with a step equal to ms. Such a noise-free simulated A-scan with DT = ms is plotted in the diagram of Fig. 16(a). The received echoes have a significant overlap. We considered a sampling frequency equal to f s = 4000 MHz, which is equal to the sampling frequency of our A/D converter and the total time duration of the A-scan is equal to 0.36 m. The methods were evaluated for three cases: 1) without noise; 2) SNR =5dB; and 3) SNR = 5 db. For the SNR calculation, the mean signal power in the effective width of the low-pass-filtered pulse was considered. As effective width, we refer to the time interval in which the envelope of the pulse is not smaller than 20 db of its maximum value. The noisefree case with DT = ms and the corresponding SNR = 5 db case are presented in Figs. 16(a) and 17(a), respectively. The corresponding results of the presented methods are given in the same figures. All methods achieved to resolve two peaks, even in the case with strong noise, with different accuracies however. In order to quantify the accuracy of the detection methods, we present the diagrams of Fig Fig. 18 refers to the noise-free case. In the left column, we present the estimated difference of TOFs (DTOFs) DT with respect to the actual ones. In the right column, we present the Absolute estimation Error (AE) with respect to the actual DT. We have to highlight the behavior of the DWT-based approach: The corresponding AE presents some kind periodicity. This periodicity arises from the fact that the DWT coefficients at scale 2 s correspond to time instances that are multiples 2 s, and the DWT is not time invariant. This phenomenon is not present with the DSWTbased approach. For all methodologies, except from the DWTbased one, the AE decreases as the actual DT increases. We also have to highlight that the HHT-based approach showed the best performance in the noise-free case. This arises from the fact that it is not restricted by the Heisenberg uncertainty principle, as explained. In the diagrams of Figs. 19 and 20, we present the corresponding results for SNR =5dB and SNR = 5 db. For each noise level, we performed 20 experiments, and we present the mean absolute error (MAE) with respect to the actual DT. For all methods, the MAE remains in low levels, even in the SNR = 5 db case, except from the DWT-based methodology due to its lack of time invariance. With the presented simulation experiments, the most accurate methods seem to be the SPWV- and CWT-based ones, with the SPWV-based performing slightly better. The DSWT- and HHT-based ones follow. In all cases, the DWT-based approach presents the worst accuracy. Some conclusions about which method to use are given in the next paragraph. B. Real Data With Known Ground-Trough We also have experimented with real A-scans, obtained using coatings of exactly known thicknesses and sound velocity, traceable according to the ISO standards provided by De- Felsko Corporation. The system was tested using two coatings with thicknesses of and mm and corresponding sound velocities equal to 2640 and 2650 m/s. The received A-scans contain three echoes, i.e., two strong echoes and one weak echo, with equal time distances, which were produced according to the explanation of Fig. 21. For the thin coating (39.71 mm), the three echoes have a great overlap, and the third weak one is almost hidden [see Fig. 22(a)]. For each thickness, a set of A-scans were captured. Two examples and the corresponding results of the five presented methodologies are presented in Figs. 22 and 23. In all cases, the methodologies achieved to resolve the three echoes, except from the DSWTbased approach, which could not resolve the weak echo for the thin coating (39.71 mm). Comparing the results, we have to highlight the great capability of the HHT-based approach in resolving the overlapping echoes [see Fig. 22(f)]. The statistic results (MAE and standard deviation (STD) of the error), which were obtained based on all the = 121 measurements, for both thicknesses, are given in Tables V and VI. Comparing the results, one can conclude that the best performance is obtained using the SPVW distribution, followed by the CWT. The HHT-based approach also produced relatively accurate results and managed to effectively resolve the three echoes. The DSWT produced very accurate results but could not resolve the weak echo in the case of the thin coating. The

17 3098 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 16. Simulations for the noise-free case. See text for details. The actual distance of the echoes is m. Results of the five presented methodologies. (a) Simulated A-scan with two overlapping echoes for the noise-free case. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14, scale =5). (e) DWT-based results (Symlet14, scale =5). (f) Extracted IMFs of the EMD procedure (Huang). (g) HHT-based results. worst performance with respect to accuracy was shown by the DWT-based approach, as expected. C. Related Conclusions Based on the experimental results presented so far, one can verify that almost, in all cases, the presented methodologies can effectively resolve and accurately identify different echoes, overlapping or not. Furthermore, based on the experimental results and the discussion so far, some related conclusions can be extracted. 1) The SPVW-based approach and the CWT-based one present the highest estimation accuracy. According to the presented model, these are the most straightforward and the most intuitive approaches. They are also based on a strict mathematical analysis, and therefore, their effectiveness is more or less the same for all A-scans. Compared to the CWT-based approach, the SPVW-based

18 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3099 Fig. 17. Simulation for the SNR = 5 db case. See text for details. The actual distance of the echoes is m. Results of the five presented methodologies. (a) Simulated A-scan with two overlapping echoes for the SNR = 5 db case. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWTbased results (Symlet14, scale =5). (e) DWT-based results (Symlet14, scale =5). (f) Extracted IMFs of the EMD procedure (Huang) applied to the simulated A-scan of (a). (g) HHT-based results. one performs slightly better, due to its quadratic nature. However, according to our experiments, the computation effort for the SPWV calculation is relatively higher than the one for the CWT. 2) The presented HHT-based approach presents relatively accurate results when used with the given settings/parameters. The HHT approach is an empirical and self-adaptive method. Therefore, its performance significantly depends on the selection of the related parameters, but it can also become very efficient. An advantage of the HHT is that is not restricted by the Heisenberg uncertainty principle and therefore could offer both good and frequency and time resolutions. We feel that the advantages of the HHT are not fully explored in the presented methodology, and a part of our future research will be toward this direction.

19 3100 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 18. Simulations for the noise-free case. See text for details. (Left column) Estimated DTOFs with respect to the actual DTOFs. (Right column) Corresponding MAEs for the five presented methodologies. (a) SPVW-based results. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) CWT-based results (complex Morlet). (e) DSWT-based results (Symlet14,scale=5).(f) DSWT-based results (Symlet14,scale=5).(g) DSWT-based results (Symlet14, scale =5). (h) DSWT-based results (Symlet14,scale=5).(i) HHT-based results. (j) HHT-based results. 3) The DSWT-based approach presents slightly worse (but comparable) accuracy than the SPWV- and CWT-based approaches. An advantage however is that the DSWT can be rapidly calculated based on the use of filter banks, similarly with the DWT. The DWT, although the faster approach, presents the worst accuracy among all the presented methods, due to its critically sampling and, consequently, its lack of time invariance.

20 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3101 Fig. 19. Simulations for SNR =5dB. See text for details. The MAEs in DTOF estimation for the five presented methodologies, with respect to the actual DTOF, are shown. (a) SPVW-based results. (b) CWT-based results (complex Morlet). (c) DSWT-based results (Symlet14,scale=5).(d) DWTbased results (Symlet14,scale=5).(e) HHT-based results. We have to mention that a strict theoretical analysis about the computational effort of the presented methodologies is beyond the scope of this paper. We also preferred not to present the run time of the presented approaches since they were implemented and ran with Matlab. Therefore, the run time strongly depends Fig. 20. Simulations for SNR = 5 db. See text for details. The MAEs in DTOF estimation for the five presented methodologies, with respect to the actual DTOF, are shown. (a) SPVW-based results. (b) CWT-based results (complex Morlet). (c) DSWT-based results (Symlet14,scale=5).(d) DWTbased results (Symlet14,scale=5).(e) HHT-based results. on the optimization of the Matlab code, and we feel that such a presentation would be unfair. Based on the preceding conclusions, two observations hold. 1) When computation time is not an issue, we suggest the use of the SPWV-based approach. For example, the

21 3102 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 21. Three echoes (two strong and a weak one) are expected in the experiment for the DeFefelsko Certificate of Calibration. The origination of these echoes is explained in this figure. implementation of the approaches on hardware (e.g., field-programmable gate arrays) or the use of the parallel computing architecture of graphical processing units (GPUs) could render these approaches real-time operating. A direction of our future work is the GPU-assisted implementation of the approaches using the NVIDIA Compute Unified Device Architecture [58]. 2) When the run time constitutes an issue, we propose the use of DSWT, which presents relatively accurate results and very small run time, compared with the SPWV- and CWT-based approaches. D. Real Data From Paint Layers The A-scans that we use here were taken from the reference panel of Fig. 24. The panel consists of two paint layers in a stairs-like configuration. A scratch was intentionally created. A set of measurements was taken in the region of interest (ROI) indicated by the black rectangle. 1) Processing Single A-Scans: We present results of the five presented methodologies at six representative points of measurements. These points are given in Fig. 24(c). Three of them (points 1, 2, and 3) are located in the region with three paint layer discontinuities, and consequently, we expect three distinct echoes. Point 4 is located in the region of the scratch, and therefore, only one clear echo is expected. Points 5 and 6 lie in the region with two paint layers, and consequently, two distinct echoes are expected. In many cases, however, due to multiple reflections from the rough upper layer, there appear two echoes with a very small TOF distance (very overlapping echoes), at the time interval where the first strong echo should appear. Given that the paint layers cannot be arbitrary thin, the TOF distance of two echoes coming from different paint layers cannot be arbitrary small. Assuming a minimum of 25 mm Fig. 22. DeFefelsko experiment for the Certificate of Calibration (thickness: mm). Results for the five presented methodologies are shown. (a) A-scan with three overlapping echoes. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5).(e) DWTbased results (Symlet14,scale=5).(f) HHT-based results.

22 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3103 TABLE V EXPERIMENT DEFELSKO NO. 1:ACTUAL THICKNESS: mm, ACOUSTIC SPEED: 2640 m/s, MAEs, AND STD OF THE ERROR TABLE VI EXPERIMENT DEFELSKO NO. 2:ACTUAL THICKNESS: mm, ACOUSTIC SPEED: 2650 m/s, MAEs, AND STD OF THE ERROR Fig. 24. Reference panel stratigraphy. Artificial scratch was intentionally created. (a) and (b) Panel and pseudo-3-d view. The rectangles denote the region of measurements. (c) and (d) Measurements region. The numbers in (c) denote the positions of the measurements referred in Figs Fig. 23. DeFefelsko experiment for the Certificate of Calibration (thickness: mm). Results for the five presented methodologies are shown. (a) A-scan with three distinct echoes. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results. for the paint layers and a mean sound velocity equal to 1600 m/s, we conclude that the minimum accepted TOF distance of two echoes from different paint layers is approximately 2 25/ ms. Therefore, found echoes with TOF distances smaller than 0.03 ms are considered as one echo, with TOF equal to the TOF of the strongest one. This can be verified in Figs. 25 and 26.

23 3104 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 25. Position 1: experimental results. See text for details. (a) A-scan at position 1. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results. Fig. 26. Position 2: experimental results. See text for details. (a) A-scan at position 2. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results.

24 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3105 Fig. 27. Position 3: experimental results. See text for details. (a) A-scan at position 3. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results. Fig. 28. Position 4: experimental results. See text for details. (a) A-scan at position 4. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results.

25 3106 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 Fig. 29. Position 5: experimental results. See text for details. (a) A-scan at position 5. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results. Fig. 30. Position 6: experimental results. See text for details. (a) A-scan at position 6. (b) SPVW-based results. (c) CWT-based results (complex Morlet). (d) DSWT-based results (Symlet14,scale=5). (e) DWT-based results (Symlet14,scale=5).(f) HHT-based results.

26 KARAGIANNIS et al.: SAMPLING OF ART OBJECT USING ACOUSTIC MICROSCOPY AND TF ANALYSIS 3107 Fig. 31. Results based on the SPVW and spatial median filters of sizes 5 5, 12 12, and for the upper, second, and third surfaces, respectively. Fig. 33. Results based on the DSWT (Symlet 14, s =5) and spatial median filters of sizes 5 5, 12 12, and for the upper, second, and third surfaces, respectively. Fig. 32. Results based on the CWT (complex Morlet wavelet) and spatial median filters of sizes 5 5, and for the upper, second, and third surfaces, respectively. Results for the six points of measurements are presented in Figs One can verify that the all the presented methodologies can effectively identify the different echoes coming from the different paint layers. A quantitative comparison cannot be performed since the actual thicknesses of the paint layers are not exactly known. 2) Integration of the Results Within a Spatial Region: Let that the proposed approaches are applied to a set of N x N y A-scans, taken in an ROI of the artwork. Each of the proposed methodologies produces a set of estimated TOFs, and let T m (x, y),x=1,...,n x, y =1,...,N y, and m =1,...,M. If, for a given point (x, y) only, M 1 <Mpeaks were detected, then the TOFs T m (x, y) for m>m 1 are assigned the label NaN (Not-a-Number). If the A-scans were taken in a small spatial neighborhood (a few millimeters by a few millimeters), the TOFs are expected to smoothly/slowly vary in space for a given m. This is based on the assumption that the structure of the paint layers cannot significantly vary between neighborhood points. Based on this fact, a smoothing (meanlike) spatial operation may be used for the extraction of the final layers depth profile. Additionally, since some estimates may be very wrong for some points (x, y), a robust approach should be taken, which rejects those outliers. Based on this discussion, we apply a spatial median filter of size N rx N ry for each m. For the presented experiments, where N x N y =75 50, we selected N rx N ry =5 5 for the upper layer (m =1), N rx N ry =12 12 for the second layer (m =2), and N rx N ry =16 16 for the third Fig. 34. Results based on the DWT (Symlet 14, s =5) and spatial median filters of sizes 5 5, 12 12, and for the upper, second, and third surfaces, respectively. Fig. 35. Results based on the HHT-based methodology and spatial median filters of sizes 5 5, 12 12, and for the upper, second, and third surfaces, respectively. paint layer (m =3). This decision is based on the fact that, for the upper layer, the pointwise estimates are obviously better. For the test panel of Fig. 24, the results corresponding to the presented approaches are given in Figs VII. CONCLUSION In this paper, we have presented the use of acoustic microscopy, which is supported by a set of soft-computing methods, for the nondestructive depth profiling of the stratigraphies of art objects. The proposed soft-computing methods are based

27 3108 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 9, SEPTEMBER 2011 on signal-processing techniques that exploit TF tools, such as the SPWV, CWT, DWT and its Stationary version (DSWT), and HHT. We have presented all the details for the construction of our acoustic microscopy system. Additionally, a comparison among the proposed accompanying signal-processing methodologies has been performed. Acoustic microscopy is a novel method in the field of nondestructive identification of art objects, determining the stratigraphy in ROIs of them and, particularly, in the most delicate case of painted artworks. Ultrasonic, combined with TF analysis tools, such as those presented, have been commonly used in the NDT field. However, according to our knowledge, acoustic microscopy, together with signal-processing techniques, is applied for first time in the field providing nondestructive identification of art objects. 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Waterway, Port, Coastal, Ocean Eng., vol. 132, pp , Sep./Oct [58] NVIDIA CUDA, Compute Unified Device Architecture. [Online]. Available: Georgios Karagiannis was born in Thessaloniki, Greece, in He received the Diploma degree and the Ph.D. degree in electrical and computer engineering from Aristotle University of Thessaloniki (AUTh), Thessaloniki, in 1997 and 2008, respectively. He is a Research Scientist/Engineer with the ORMYLIA Foundation, where he is responsible for the Nondestructive Testing (NDT) Technique Application and Development Department and the Information Processing and Database Development Department. Since 1998, he has been a principal participant and Coordinator in R&D projects related to NDT technique development and application in art objects, diagnosis and documentation, knowledge management, and image and signal processing. Since 1998, he has been with the School of Engineering, AUTh, where he teaches the Master s degree in conservation and restoration of art objects. He is the holder of two national patents and an international patent. His research interests include NDT, signal processing, and knowledge management. Mr. Karagiannis is a member of the Technical Chamber of Greece. Dimitrios S. Alexiadis (S 03) was born in Kozani, Greece, in He received the Diploma degree and the Ph.D. degree in electrical and computer engineering from Aristotle University of Thessaloniki (AUTh), Thessaloniki, Greece, in 2002 and 2009, respectively. Since 2002, he has been involved in several research projects and has been a Research and Teaching Assistant with the Telecommunications Laboratory, Department of Electrical and Computer Engineering. During 2010, he was a Research Assistant with the School of Science and Technology, International Hellenic University (IHU), Thessaloniki. Since March 2010, he has been a Full-Time Adjunct Lecturer with the Department of Electronics, Technical Education Institute, Thessaloniki. His research interests include still- and moving-image processing, motion estimation; stereo television (TV), high-definition TV, and 3-D TV; detection, estimation, and classification algorithms; and medical image and biomedical signal processing. Dr. Alexiadis is a member of the Technical Chamber of Greece. Argirios Damtsios received the M.Sc. degree from Macedonia University, Thessaloniki, Greece, in 2008 and the Engineering Diploma degree from Aristotle University of Thessaloniki (AUTh), Thessaloniki, in Since 2007, he has been a Research Associate with Ormylia Foundation, Ormylia, Greece. His research interests include nondestructive testing and image and signal processing. George D. Sergiadis (M 88) was born in Thessaloniki, Greece, in He received the Diploma degree in electrical engineering from Aristotle University of Thessaloniki (AUTh), Thessaloniki, in 1978 and the Ph.D. degree from Ecole Nationale Superieure des Telecommunications, Paris, France, in He was with Thomson CsF, in France, until 1985, participating in the development of the French Magnetic Resonance Scanner. Since 1985, he has been with AUTh, teaching telecommunications and biomedical engineering, and is currently as a Full Professor. For three years, he served as the Director of the Telecommunications Department. He has developed the Hellenic TTS engine Esopos and designed the mobile communications for the Athens Olympic Games in During the academic year , he was a Visiting Researcher with Media Laboratory, Massachusetts Institute of Technology, Cambridge. His current research interests include fuzzy image processing and wireless communications. Dr. Sergiadis is the President of the Hellenic Society of Biomedical Engineering, and a member of the Technical Chamber of Greece, A Toroidal Large hadron collider Apparatus (ATLAS), the Society of Magnetic Resonance in Medicine, the European Society for Magnetic Resonance in Medicine, the IEEE Engineering in Medicine and Biology Society, and Soft Computing in Image Processing (SCIP). Christos Salpistis was born in Katerini, Greece, in He is currently an Electrical Engineer and Assistant Professor with the Department of Mechanical Engineering, Aristotle University of Thessaloniki (AUTh), Thessaloniki, Greece. He is a member of the laboratory of stress analysis and machine elements He teaches electronics, mechatronics, nondestructive testing (NDT) techniques in the Faculty of Mechanical Engineering, AUTh. He is the holder of two patents (one national and one international). His research interests include experimental stress analysis and NDT techniques.