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Monitoring of air voids at plastic-metal interfaces by terahertz radiation
Infrared Physics and Technology 104 (2020) 103119
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Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Monitoring of air voids at plastic-metal interfaces by terahertz radiation a,⁎
b
b
b
T a
Norbert Pałka , Andrzej Rybak , Tomasz Jakubowski , Marek Florkowski , Marcin Kowalski , Przemysław Zagrajeka, Marek Życzkowskia, Wiesław Ciurapińskia, Leon Jodłowskia, Michał Walczakowskia a b
Military University of Technology, Institute of Optoelectronics, Warsaw, Poland ABB Corporate Research Center, Krakow, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Terahertz radiation Time domain spectroscopy Imaging Void detection
The time domain spectroscopy (TDS) setup in a reflection configuration was exploited for non-destructive measurements of four samples with a 10-mm (approx.) leaf-shaped air void at the interface between the plastic and metal structures. We identified and measured the material parameters of the samples required for precise determination of the voids’ thicknesses in the range of 125–500 μm. For high resolution measurements we selected the reflection TDS setup with a short focal length and developed a method for the accurate calculation of the incidence angle. We used a deconvolution-based method for thickness monitoring of voids and discussed its limitations. The two-dimensional thickness, amplitude and binary maps were exploited for imaging of the void areas. We also showed that the multiplication of the deconvolved and binarised maps can provide relevant information about the real thickness of the layer and the presence of the void in the single image. The correlation coefficient between the real and TDS measured shapes of the leaf in the range 0.8–0.9 suggests a good perspective for this technique in industrial applications.
1. Introduction Plastic-metal compositions are used in many demanding technical applications. During the overmolding or gluing process a heterogeneous layer of polymer material of a few millimetres is attached to a solid metal layer from one side. As a result, flat parallel two- or three-layer structures are created, in which, in the case of gluing, the thickness of the glue is usually below 500 μm, while the thickness of the metal layer is in the order of a few millimetres. All interfaces between the layers are smooth. The considered plastic-metal structures are very durable and are usually formed during the process of dielectric/insulation moulding around a metal terminal (e.g. bushing) of a high-voltage apparatus (e.g. transformer, inductor, capacitor, transducer, etc.). In such structures, it is necessary to monitor the quality of the contact zone, namely the thickness of the adhesive layer as well as detect and determine the shape of the voids (areas without glue). These result from imperfections in the production process, may have a surface of few millimetres and cause structural weakness of the structures. This may lead to degradation of high-voltage insulation due to partial discharges (PD) occurring in voids filled with gas. The non-destructive testing (NDT) techniques for monitoring the adhesive area should be fast, accurate and robust. Commonly used methods include X-ray computed tomography (CT) as
⁎
well as other indirect methods of PD measurement [1–2]. Currently, terahertz radiation (0.1–3 THz) has been the focus of a lot of interest as a competitive tool for NDT of plastic [3] and composite materials [4–5], steel plates [6], welds [7], electronic devices [8], paintings [9] and others [10]. THz waves are inherently non-ionising, easily penetrate plastics and are reflected by metals, which facilitates their application for the considered structures. Among many terahertz methods, Time Domain Spectroscopy (TDS) seems to be particularly useful because it can provide both thickness determination as well as void imaging [3–10]. Briefly, TDS is a synchronised system which, thanks to the use of a femtosecond laser, two photoconductive antennas and a delay line, provides synchronous generation and detection of about 1-ps long pulses of electromagnetic radiation. These pulses have a broad spectrum, usually in the range 0.1–3 THz. The detailed description of the TDS technique can be found in [11]. For NDT applications, TDS systems with a reflection configuration are usually exploited. The THz pulse propagating in a multilayer structure is reflected back at all interfaces due to the Fresnel phenomenon (change in the refractive indices). As a result, a pulse train is obtained, in which time differences between the consecutive reflected pulses depend on the thicknesses of the layers and their refractive indices. Therefore, knowing the refractive indices one can calculate the
Corresponding author. E-mail address: [email protected] (N. Pałka).
https://doi.org/10.1016/j.infrared.2019.103119 Received 8 August 2019; Received in revised form 8 October 2019; Accepted 11 November 2019 Available online 13 November 2019 1350-4495/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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thicknesses of the layers. Moreover, raster scanning of the sample point by point provides its 3D image, where heterogeneities, defects or voids can be imaged [3–10]. The main limitation of the determination of a layer’s thickness is the duration of the pulse propagating in the sample. For very thin layers (< 50 μm), e.g. automotive paints [12], the reflected pulses are heavily overlapped and it is impossible to distinguish between them. In this case, if the number of layers and their refractive indices are known, one can iteratively modify the thicknesses, and simulate the reflected signal until a satisfactory similarity to the measured signal is obtained [12–13]. This method is usually applied for surface layers, because for thicker samples, local fluctuations of the refractive indices can strongly influence the results. If the reflected signals are only partially overlapped, the deconvolution method can provide a separation of the individual pulses and, therefore, is broadly exploited [9,14–17]. Recently, also method based on matched field processing was proposed [18]. It is also worth mentioning that due to the dispersion of the materials, the propagating pulses are usually broadened, which limits thickness measurements in thicker samples. For the considered studies, we prepared four samples which mimic the real structures of the interface formed between metal and polymer surface during fabrication of the electrical devices by means of overmoulding or gluing. Such metal/polymer interfaces can be found for example in bushing structure where coper conductor is covered by polymer insulation during injection moulding process. Adhesion between metal and plastic is weak therefore primers (adhesion promotors) are used. Air voids can appear in the case of inhomogeneous coating with primer or appearance of bonding defect like delamination due to release of mechanical stresses. The primer/adhesive layer may have a thickness in the range of 125–500 μm. In each sample, the air void was formed as a characteristic leaf shape with dimensions of approximately 8 × 9 mm. Such sample design allowed to verify the limits of the selected method. Due to the presence of the metal layer, the samples can be illuminated only from the plastic layer side, which imposes the reflection configuration of the TDS system. In the reflection configuration, two approaches are mainly used: a normal incidence and a pitchcatch. The advantage of the first approach is easy signal processing, while its main drawback is the loss of at least 75% of power due to the use of a beam splitter. This results in a lower S/N ratio and, therefore, the second approach was selected for further studies. In the pitch-catch approach, due to the physical dimensions of the transmitter and receiver which are placed side by side, the angle of incidence is usually above 20°, which causes some signal processing issues. Detection of small voids requires a small THz beam spot, which could be provided only by short focal length optical systems, which in turn are characterised by a small depth of field. In this paper, based on theoretical considerations, we identified and measured all the parameters of the Rynite-based samples and the TDS setup, which are required to precisely and independently determine the thickness of the adhesive or voids. We also propose the novel method to accurately calculate the incidence angle of the TDS setup, which is needed for further calculations. Important factors connected with the experimental aspects, like focusing and depth of field, are also discussed. We developed a simple and robust terahertz method for determining the thickness of the adhesive layer and imaging of voids as well as to critically evaluate its performance for the considered samples. The presented set of signal and image processing with the discussions constitute the novelty of the manuscript.
Fig. 1. The photograph of the sample with 250-μm thick tape (a). Shape of the buried leaf (b). Scheme of the cross-section of the sample with reflections from the interfaces (c).
measurements. Each sample consists of three parts glued together: 1. 5450-μm thick metal base, which is smooth and reflects 100% of the THz radiation. 2. 3625 ± 5 μm thick plastic layer made of DuPont Rynite FR530 NC010 – A 30% glass reinforced, flame retardant, modified polyethylene terephthalate resin. This material is very durable, has outstanding temperature and mechanical properties and, hence, is often exploited in many fields [19]. 3. A glue fixing plastic and metal parts consists of 1, 2, 3 or 4 layers of a 125-μm thick double-sided adhesive tape with a polypropylene carrier coated with a transparent synthetic adhesive manufactured by Smart (4140 PP) [20]. This gives a nominal thickness of the tape layers equal to about 125, 250, 375 and 500 μm, respectively. A leaf shape with dimension 8.35 × 9.35 mm (Fig. 1b) was cut in the tape layers. This leaf-shaped lack of tape (void) is buried between the metal base and the plastic layer and is not visible. The use of tape layers instead of glue is connected with the ease of a void preparation with controllable thickness and shape. The samples are named using the thickness of the leaf gap: 125, 250, 375 and 500, respectively.
3. Propagation of the THz pulses in the sample Fig. 1c presents the scheme of the sample and the description of the parameters used in further analysis. Let’s consider a short THz pulse (P0) incident on the sample at an angle of θ0 relative to the normal. Part of the pulse propagates in the plastic region at an angle of θ1 = arcsin (sinθ0/n1), which was calculated by means of Snell’s law. Next, part of the pulse is reflected at interface 2 while rest of it, after refraction, propagates at an angle θ0 in the air gap or θ2 = arcsin(n1 sinθ1/n2) in the tape region. Finally, both pulses are totally reflected by the metal base and come back at the same angles. As a result, one can obtain three reflected pulses marked as P11, P12, P13 and P21, P22, P23 for the air gap and tape region, respectively. The thickness L can be independently calculated in two ways depending on the region [21]:
2. Description of samples As described in the Introduction samples design was selected in order to reproduce the real structures of the interface which can be formed between metal and polymer during the fabrication process of the electrical devices by means of overmoulding or gluing with adhesive. Fig. 1a shows one of four samples prepared for the THz
L=
2
c Δt1 for the air gap 2cosθ0
(1a)
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L=
c Δt2 for the tape 2n2 cosθ2
(1b)
where Δt1 is the time difference in the arrival of the pulses reflected from interface 2 (P12) and from the metal base (interface 3 – P13) for propagation in the air gap region, Δt2 is the time difference in the arrival of the pulses reflected from interface 2 (P22) and from the metal base (interface 3 – P23) for propagation in the tape region, and c is the speed of light in a vacuum. It can be also noted that the time differences Δt1(2) do not depend on the thickness of the plastic layer (d). We also define the ratio of the above described time differences as:
q=
Δt2 n cosθ2 = 2 Δt1 cosθ0
(2)
It is clear that to obtain the thickness L in line with reality for both Eqs. 1a and 1b, one needs precisely determined parameters in these formulas, namely n1, n2, θ0, Δt1, and Δt2. 4. Determination of the refractive indices Fig. 3. Measured and simulated (offset for clarity) signals (a). Calculated: refractive index n2 (b) and the absorption coefficient (c) of the tape.
We determined the refractive index (n) of both the plastic layer and the tape, which are needed for further calculations. The measurements were carried out in the standard TDS system with a transmission configuration using a TPS Spectra 3000 from Teraview. Additionally, we also present the absorption coefficients of the samples, which indicate the transmission properties of the considered materials.
of the sample were also determined using the standard TDS procedure [11] (Fig. 2c,d). The mean refractive index of the plastic layer (n1) corresponds to the refractive index spectrum at about 0.3 THz, which is connected with the maximum of the pulse spectrum. The absorption coefficient spectrum (Fig. 2d) indicates good penetration of the sample by the THz radiation and provides a good perspective for scanning in the reflection mode. To the best of our knowledge, the THz spectrum of Rynite has not yet been published.
4.1. Characterisation of the plastic material For the spectral characterisation of the plastic layer material, we used the 3625 ± 5 μm thick Rynite layer and put it in the focal point of the spectrometer. Fig. 2a,b show the TDS pulses – reference and transmitted though the plastic layer and their spectra, respectively. The pulse after transmission through the sample is stretched due to the dispersion of the material from 0.4 ps up to 0.8 ps and has five times lower amplitude due to its attenuation. The spectrum of the pulse transmitted through the sample is limited to 1.3 THz. Based on the time difference (Δt) between the reference and plastic pulses, we determined the mean refractive index of the plastic layer n1 = 1.884. The refractive index and the absorption coefficient spectra
4.2. Characterisation of the tape material For tape characterisation we used the sample which consisted of four layers of the tape with a total thickness of about 500 μm. Based on the time difference (Δt) between the reference and the tape pulses (0.86 ps), we determined the mean refractive index of the tape n2 = 1.53. However, for such relatively thin samples, a common error connected with the precise determination of the thickness can significantly influence the n calculation. Therefore, the transfer matrix method (TMM) [12–13] with a linear approximation of the parameters was applied. Fig. 3a shows the reference and sample signals measured in the spectrometer as well as the optimal simulated signal which was obtained using TMM. The calculated optimal thickness of the sample of 482 μm is close to the nominal value of 500 μm. The new thickness modified the mean refractive index of the tape to n2 = 1.537. The calculated characteristics of the refractive index (n2) and the absorption coefficient are presented in Fig. 3b,c. 5. Experimental setup For reflection experiments we used the commercially available TDS scanner TPS 3000 (TeraView) equipped with the reflection module with the angle of incidence (θ0) equal to about 22° [22]. Two off-axis ellipsoidal mirrors (OAEM) provide a short focal length of 50 mm (Fig. 4a), which in turn results in a small beam radius, which was determined using the knife-edge method (Fig. 5b) [23]. The THz part of the optical setup was purged with dried air to suppress the influence of water vapour. The reference TDS pulse and its spectrum measured with the reference gold mirror is shown in Fig. 4c-d. During the measurements, the samples were put on the stage and raster scanned horizontally point by point in X and Y directions. For such a short focal length, the setup is very sensitive to the position adjustment in the Z axis. Fig. 4c,d shows THz pulses and their spectra for 0.5 and 1-mm shifts from the optimal focal point (reference).
Fig. 2. Measured pulses (a) and their spectra (b). The refractive index (c) and the absorption coefficient (d) of the plastic layer. 3
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Fig. 4. TDS reflection setup: schema (a) and the beam radius as a function of frequency (b). Change in the reflected pulses (c) and their spectra (d) due to a shift from the focal point.
Fig. 6. The signals reflected from sample 500 when focusing on the front and back surfaces of the sample.
The new value of the angle of incidence θ0 = 22.86°, slightly higher than the manufacturer's data (22°), allows calculation of the required parameters, namely: θ1 = 11.91°, θ2 = 14.67°, and q = 1.612. 5.2. Focusing For the considered 4-mm (approx.) thick samples, the position of the focus of the THz beam is crucial for achieving meaningful results, especially for the short focal length of the optical system. If the THz radiation is focused on the front surface of the sample, the reflection from the back surface is distorted (Fig. 6), which hampers its further deconvolution. On the other hand, for the THz signal focused on the back surface, the reflections P12 and P13 are clearly seen and were then successfully used for deconvolution. In this case, the pulse coming from the front surface is heavily distorted, but it is not used in the further analysis. The sample was shifted by 2140 μm along the Z axis towards the setup, which corresponds to the time difference 13.14 ps and which agrees with the calculations using Eq. (1a). In the presented research, we only measured and analysed the pulses reflected from the back surface of the samples (P12 and P13), because simultaneous measurement of all pulses (P11, P12 and P13) in the setup is challenging due to the long scanning range (~70 ps). Moreover, use of only P12 and P13 provides better stability, because local thickness fluctuations and refractive index inhomogeneities of the plastic layers are avoided.
Fig. 5. Two pulses reflected from the two surfaces. Inset shows the rays diagram.
This deviation causes not only a decrease in the amplitude of the reflected pulses and their spectra but also an increase in the beam radius, which in turn results in a smaller resolution of the THz image, which will be shown in Section 6. 5.1. Angle of incidence
5.3. Deconvolution and thickness determination Precise determination of the angle of incidence (and reflection) θ0 is crucial for the accuracy of further calculations. Therefore, we modified the method presented in [21]. The THz pulse incidents on a step-edge between two flat and parallel smooth metal surfaces (mirrors). The distance between the mirrors b = 210 ± 5 μm. As a result, two pulses reflected from both surfaces (E1 and E2) are observed which are distant in time by Δt = 1.290 ± 0.005 ps (Fig. 5). In order to accurately determine Δt, the signals measured along the edge for 20 points were first deconvolved using the deconvolution algorithm presented in Section 5.3 and then averaged. The angle of incidence θ can be calculated as [21]:
c∙Δt ⎞ θ0 = arccos ⎛ ⎝ 2b ⎠
In the considered samples, our goal is to measure the distance (L) between interfaces 2 and 3 based on the time differences between the corresponding reflected pulses (Δt1(2)). However, achieving this goal is difficult due to two factors: dispersion-based stretching of the THz pulse (Fig. 2a) and the non-Gaussian shape of the pulse with two side lobes (Fig. 4c). As a result, both factors cause the reflected signal to be composed of partially overlapping and shifted in phase pulses. These phenomena significantly obstruct determination of the interfaces between media and, therefore, deconvolution methods are usually used to separate them and determine L. Knowing the reference signal incident on the sample (h) and the signal reflected from the sample (g), we can determine the response function (f) and, on this basis, find the interfaces between media [24].
(3) 4
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Fig. 7. Raw and deconvolved signals for: air gap (a) and tape (b) regions. The refractive index profile is below the signals.
After testing different algorithms [14–17], we used the inverse filtering algorithm coupled with a band pass double Gaussian filter. The unknown function f is calculated from the relation:
FFT (g ) ⎞ f = FFT −1 ⎛FFT (filter ) (h) ⎠ FFT ⎝ ⎜
⎟
(4)
FFT denotes Fast Fourier Transform. The operation of dividing in Eq. (4) often leads to the reinforcement of noise, which can be suppressed with the double Gaussian filter described as:
filter =
1 1 exp(−t 2/ HF 2) − exp(−t 2/ LF 2) HF LF
(5)
The filter is realised by subtracting two Gaussian functions with different widths described by two coefficients: low-frequency (LF) and high-frequency (HF). HF was equal to 4096 in the presented work, while LF = 160 was matched with the trial and error method, depending on the measured signals. To illustrate the benefits of the deconvolution, Fig. 7 shows exemplary row and deconvolved signals reflected from the air gap and tape regions for sample 500. First, the algorithm looks for the global minimum, which corresponds to the highly reflective interface 3. Next, it seeks for the maximum of the signal situated on the left side of the global minimum, because interface 2 is always in front of the interface 3. In both cases, the deconvolution process reveals the true reflections from the interfaces and decreases the amplitudes of the spurious side lobes and multiple reflections between interfaces 2 and 3. Additionally, we show the refractive index profile. Lower reflection from interface 2 in case of the tape region is explained by a lower refractive index contrast between n1 and n2. For both regions, the thickness L calculated based on Δt1(2) and Eq. (1) (505 and 503 μm for the air gap and tape regions, respectively) is compatible with the nominal value of 500 μm. The presented algorithm is dedicated to the case n1 > n2, due to features of real elements we imitated by our samples. Generally, the algorithm can also be applied for n1 < n2. In this case, reflections from interface 2 and 3 will have a form of negative pulses and the algorithm will look for the distance between their minima.
Fig. 8. Sample with the mirror set at an angle of 2.50: B-scan (a), A-scans for X = 4, 10, and 15 mm (b), and thickness calculated based on the deconvolution (c). Inset shows arrangement of the sample.
radiation was focused on interface 2. Fig. 8a presents a so-called B-scan – a set of reflected pulses versus position along the X axis (scanned with the 100-μm step). A-scans (time signals) for X = 4, 10, and 15 mm are depicted in Fig. 8b. Fig. 8c shows that the linear change of the thickness of the air gap calculated based on the deconvolution is in line with real values. However, for a threshold of 220 μm the reflected signals from interface 2 and 3 overlapped too much and cannot be separated using the deconvolution. This pretty low separability of the interfaces is connected with the fact that the THz pulses are extended in time due to back and forth propagation in the thick and dispersive plastic layer.
6. Experimental results and discussion The examined samples were installed in the holder of the scanner and adjusted in the Z axis (Fig. 4a) to reach the maximum of the reflection from interface 2. The coarse scanning with the 200-μm step lasted about 5 min. A resultant THz image of sample 250 (Fig. 9) shows its edges and the shadow of the leaf inside the image. Afterwards, the 12x12 mm square part of the samples with the centrally located leaf were scanned with a fine 100-μm step for 40 min. As the result, for each sample a 120 × 120 × 2048 matrix was obtained, where for each point
5.4. Limitation of deconvolution To analyse the practical limitations of thickness determination using the deconvolution, we arranged a sample consisting of the plastic layer with n = n1 and thickness d = 3625 μm and placed a flat mirror on it at an angle α = 2.50 (inset in Fig. 8b). This structure mimics the air gap region with thickness L varying in the range 0–630 μm. The THz 5
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Fig. 9. Coarse THz image of sample 250 with the leaf shadow in the middle. Fig. 10. 2D thickness maps calculated based on the deconvolution. The Z axis represents thickness in μm. The dotted lines indicate the cross-sections shown in Fig. 11. The real shape of the leaf is marked for comparison.
of the sample, the reflected 40-ps long signal was acquired.
6.1. Thickness maps
Table 1 Thicknesses of the samples.
Each signal was deconvolved and the time difference between the maximum and minimum was determined (Fig. 7). Next, the thickness L was calculated using Eq. (1b) and the previously determined parameters. Fig. 10 shows the 2D images of the samples, where the 1red/ yellow colour marked the region filled with the tape without any voids. The calculated thickness should be equal to the nominal values (125, 250, 375, and 500 μm). For the centrally located leaf-shaped air void (blue colour), the nominal thickness is lower by a factor of q = 1.612 (Eq. (2)) and should be equal to 77, 155, 233, and 310 μm (Table 1). For sample 125, due to strong pulses overlapping (Section 5.4), the shape of the leaf is hardy visible (Fig. 10a), while the mean thickness is equal to about 145 μm. This fact is consistent with the 220-μm threshold determined for the sample with the leaning mirror (Fig. 8b). For samples 250, 375, and 500, the shape of the leaf is clearly seen (Fig. 10b–d). The average thickness and its mean squared error (MSE) inside a rectangular region of the leaf area (Table 1: “Leaf ∙ q”) is in line with the nominal value. Since the thickness of the tape area is not uniform, we calculated the average thickness and MSE in a rectangular region in four corners of the samples (Table 1: “upper left” etc.). Next, all values from the rectangular regions from four corners were averaged and “mean (4 corners)” was calculated. The observed MSEs are rather small ( ± 7 μm) for samples 250 and 375, which suggests good homogeneity of the glued regions. For sample 500, the average values in the corners differs by about 60 μm (upper left vs. bottom right), which is probably connected with the fact that the metal base is not parallel to the plastic layer, because during preparation the sample might not have been uniformly glued. Since the thickness decreases uniformly from the upper left to the lower right corner, it proves the possibility of constant monitoring of the layers. Moreover, the mean thicknesses for the four corners are very similar to those determined for the leaf regions (Table 1 in bold). This fact suggests that the refractive indices (n1, n2) and the incidence angle (θ0) were precisely determined. The main source of error are instability of the TDS setup, error of the extrema determination and non-uniformity of glue thickness.
Thickness [μm] Nominal Nominal/q Leaf ∙ q upper left upper right bottom left bottom right mean (4 corners)
250 155 252 248 253 259 248 252
± ± ± ± ± ±
1 1 1 1 1 7
375 233 375 370 374 368 382 373
± ± ± ± ± ±
2 1 2 1 1 7
500 310 510 536 515 524 476 513
± ± ± ± ± ±
1 15 1 14 1 26
6.2. Thickness profiles Fig. 11 shows the cross-sections of the 2D images through the blade and stalk region of the leaves. For sample 125, as expected, only flat lines centred at 145 μm are visible. For samples 250, 375 and 500, the slope of the hollows becomes smaller for thicker air gaps. For the blade region (red lines), the nominal thickness (divided by q) is reached. This is not true for the stalk region (blue lines), where only for sample 250 can we observe so deep an incline. This phenomenon is connected with the change in resolution due to defocusing. The larger the distance L, the higher the beam radius which results in lower resolution and visibility of the leaf details as well as higher blurring of the shapes. For sample 500, the slope of the thickness for the 0–6 mm range is also visible for the stalk. It must be noted that the measured thickness inside the leaf should be multiplied by q to obtain its correct value, which can be easily applied for the presented samples with known thickness. However, this approach can lead to incorrect results when the thickness of the adhesive layer is not known, because the time difference-based algorithm cannot determine the type of the material (tape or air). To overcome this problem, we proposed a method which exploited both the time differences and amplitudes of the signals (Fig. 7). 6.3. Amplitude maps In addition to the 2D thickness map, the leaf-shaped voids can also be imaged as a map of extremes (minimum Amin and maximum Amax – see Fig. 7) of the deconvolved signals. We tested a few modes of imaging, including a peak to peak amplitude and integration of the signal
1 For interpretation of color in Figs. 10,11 and 14, the reader is referred to the web version of this article.
6
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Fig. 13. 2D binary maps of the samples. The real shape of the leaf and correlation coefficients are marked for comparison.
6.4. Binary maps
Fig. 11. Thickness profiles for two cuts: through the blade and stalk. Black solid lines indicate the widths of the stalk (0.8 mm) and blade (4 mm) regions.
The amplitude maps from Fig. 12 were next processed by the edge detection technique to find the boundaries of the objects within the images. After analysis and tests, we selected the Canny technique [25]. The resultant 2D binary images (Fig. 13) show only two regions (plastic layer and tape). The 2D correlation coefficient (corr) provided a quantitative shape similarity factor between the real (Fig. 1b) and binary images. In all cases, high similarity (corr > 0.8) proves that both the ratio amp and the edge detection technique were correctly selected. Moreover, the smaller the thickness of the air gap L, the higher the corr value (see Fig. 13), which is connected with the higher resolution discussed in the previous section. 6.5. Corrected thickness maps It can be noted that the binary map shows two regions which differ in the amplitude ratio of the reflected signals. This separation is connected with the different refractive indices of air and the tape. If we ascribe value 1 to the white region (tape) and value q to the grey region (air void), we can obtain a correction mask. Next, one can multiply it by the thickness map (Fig. 10), which leads to the results shown in Fig. 14. For samples 250, 375, and 500, both void and tape regions present the correct thicknesses, while the red colour (overestimated values) can be used for detection of the void’s edge. For sample 125, due to the limitation of the deconvolution, the thickness is not correctly determined, but shape of the void is clearly visible. To sum up, thanks to the developed processing scheme, one can display the relevant information in a single image, where both the real thickness and the presence of the void are marked. In the case of samples with a thinner L below the threshold, lack of thickness information is compensated by better visibility of the leaf details.
Fig. 12. 2D amplitude maps of the samples calculated based on the ratio amp = −Amax/Amin. The real shape of the leaf is marked for comparison.
between Amin and Amax, but the best results in terms of visibility of the details was obtained for the ratio: amp = −Amax/Amin (Fig. 12). In the case of sample 125, the leaf shape with fine details is now clearly seen. For other samples, the obtained results are generally similar to those presented in Fig. 10, but the stalks are slightly better visible. The lack of foil thinner than 125 mm prevented us from conducting experiments showing the minimum gap detectable with the amplitude map algorithm. However, based on the performance of the algorithm for sample 125, duration of the THz pulse after propagation in the plastic (about 2 ps), and instabilities of the THz pulse during the measurements, the minimum detectable gap is estimated at about 50–75 μm.
7. Conclusions The time domain spectroscopy setup in a reflection configuration was exploited for non-destructive monitoring of four samples with a 10mm (approx.) air gap in the shape of leaf buried between the 4-mm thick polymer layer and the metal plate. The thicknesses of the isolating 7
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indicate presence of the defect region. This algorithm worked well for 125-μm and its real detectability threshold was estimated at 50–75 μm. The binary map is based solely on the amplitude map and is mainly used for unambiguous determination of the void shape, calculation of the correlation coefficient and determination of the corrected thickness map. In summary, the results obtained in this research closely reflect the real thicknesses of voids and their shapes. Obviously, X-ray tomography can measure the voids with higher resolution and precision, but requires that the measured element to be installed on a rotating platform. On the contrary, TDS-based monitoring can be carry out in situ without the need to uninstall the element. Therefore, the TDS technique seems to have a good perspective as an alternative but also complimentary to X-ray CT tool for the non-destructive, non-ionising and contactless scanning of voids in plastic-metal samples in industrial applications. Declaration of Competing Interest The authors declare that there is no conflict of interest. Fig. 14. 2D corrected thickness maps calculated based on both amplitudes and time differences. The Z axis represents the thickness in μm.
References
layers of tape were equal to 125, 250, 375, and 500 μm. We identified and precisely measured the refractive indices of the constituent materials and obtained 1.884 and 1.537 for the plastic and tape layers, respectively. Due to the various thicknesses, we applied the standard procedure and TMM methods. After analysis, we selected the reflection TDS setup in a pitch-catch configuration with a short focal length for high resolution imaging. We showed that the radiation should be focused on the back surface of the sample to obtain optimal measurement conditions. We also developed a method for accurate calculation of the incidence angle in the TDS setup. High accuracy of both the refractive indices and the incidence angle measurements is crucial for further calculations, because it guarantees consistent thicknesses in the tape and air void regions calculated using Eqs. (1a-b). Next, we selected the optimal deconvolution method to separate overlapping impulses and calculate the time differences and amplitudes. We measured the sample with the inclined mirror to experimentally determine the minimum thickness threshold. The two-dimensional thickness, amplitude and binary maps were selected for imaging of the void areas. Mean thicknesses inside and outside the voids are similar, which proves the correctness of the applied approach. For sample 4, the difference in thickness between the corners is probably attributed to the fact that, due to small defects during the preparation process, the metal base is not parallel to the plastic layer. For sample 125, the shape of the leaf is not visible due to strong pulses overlapping, which is consistent with the previous measurements carried out for the inclined mirror. To overcome this problem, we exploited the information contained in the extremes of the deconvolved signals. We found that the ratio Amax/Amin provides the optimal visibility of the leaf details even for sample 125. For other samples, the images obtained for the thickness and amplitude mapping are similar, but the stalks are slightly better visible in the last method. Finally, the amplitude maps were binarised using the Canny edge detection technique. The correlation coefficient between the real and binarised images of the leaf in the range 0.8–0.9 proves the appropriate performance of the applied method for this class of samples. Finally, we showed that multiplication of the deconvolved and binarised maps can provide relevant information about the real thickness of the layer and the presence of the void in a single image. For the considered samples with 3.6-mm thick plastic layer, the thickness-based detectability is about 220 μm and thinner bonding defects cannot be determined. This limit is connected with sample-depending stretching of the pulse to about 2 ps due to dispersion, which reduces resolution. For thinner voids we can use the amplitude map to
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cpinfo.net/scissc/Rynite/FR530.pdf. [20] Characteristics of double-sided tape 4140 PP., 2019 (access from 2019). https:// www.totalmarket.pl/oferta/tasmy-specjalistyczne/tasmy-dwustronnie-klejace/ tasma-dwustronna-4140-pp/. [21] F. Vandrevala, E. Einarsson, Decoupling substrate thickness and refractive index measurement in THz time-domain Spectroscopy, Opt. Exp. 26 (2018) 1697–1702, https://doi.org/10.1364/OE.26.001697. [22] N. Palka, P. Rybak, E. Czerwinska, M. Florkowski, Terahertz detection of wavelength-size metal particles in pressboard samples, IEEE Trans. Terahertz Sci. Technol. 6 (2015) 99–107, https://doi.org/10.1109/TTHZ.2015.2504791.
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Contents lists available at ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Monitoring of air voids at plastic-metal interfaces by terahertz radiation a,⁎
b
b
b
T a
Norbert Pałka , Andrzej Rybak , Tomasz Jakubowski , Marek Florkowski , Marcin Kowalski , Przemysław Zagrajeka, Marek Życzkowskia, Wiesław Ciurapińskia, Leon Jodłowskia, Michał Walczakowskia a b
Military University of Technology, Institute of Optoelectronics, Warsaw, Poland ABB Corporate Research Center, Krakow, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Terahertz radiation Time domain spectroscopy Imaging Void detection
The time domain spectroscopy (TDS) setup in a reflection configuration was exploited for non-destructive measurements of four samples with a 10-mm (approx.) leaf-shaped air void at the interface between the plastic and metal structures. We identified and measured the material parameters of the samples required for precise determination of the voids’ thicknesses in the range of 125–500 μm. For high resolution measurements we selected the reflection TDS setup with a short focal length and developed a method for the accurate calculation of the incidence angle. We used a deconvolution-based method for thickness monitoring of voids and discussed its limitations. The two-dimensional thickness, amplitude and binary maps were exploited for imaging of the void areas. We also showed that the multiplication of the deconvolved and binarised maps can provide relevant information about the real thickness of the layer and the presence of the void in the single image. The correlation coefficient between the real and TDS measured shapes of the leaf in the range 0.8–0.9 suggests a good perspective for this technique in industrial applications.
1. Introduction Plastic-metal compositions are used in many demanding technical applications. During the overmolding or gluing process a heterogeneous layer of polymer material of a few millimetres is attached to a solid metal layer from one side. As a result, flat parallel two- or three-layer structures are created, in which, in the case of gluing, the thickness of the glue is usually below 500 μm, while the thickness of the metal layer is in the order of a few millimetres. All interfaces between the layers are smooth. The considered plastic-metal structures are very durable and are usually formed during the process of dielectric/insulation moulding around a metal terminal (e.g. bushing) of a high-voltage apparatus (e.g. transformer, inductor, capacitor, transducer, etc.). In such structures, it is necessary to monitor the quality of the contact zone, namely the thickness of the adhesive layer as well as detect and determine the shape of the voids (areas without glue). These result from imperfections in the production process, may have a surface of few millimetres and cause structural weakness of the structures. This may lead to degradation of high-voltage insulation due to partial discharges (PD) occurring in voids filled with gas. The non-destructive testing (NDT) techniques for monitoring the adhesive area should be fast, accurate and robust. Commonly used methods include X-ray computed tomography (CT) as
⁎
well as other indirect methods of PD measurement [1–2]. Currently, terahertz radiation (0.1–3 THz) has been the focus of a lot of interest as a competitive tool for NDT of plastic [3] and composite materials [4–5], steel plates [6], welds [7], electronic devices [8], paintings [9] and others [10]. THz waves are inherently non-ionising, easily penetrate plastics and are reflected by metals, which facilitates their application for the considered structures. Among many terahertz methods, Time Domain Spectroscopy (TDS) seems to be particularly useful because it can provide both thickness determination as well as void imaging [3–10]. Briefly, TDS is a synchronised system which, thanks to the use of a femtosecond laser, two photoconductive antennas and a delay line, provides synchronous generation and detection of about 1-ps long pulses of electromagnetic radiation. These pulses have a broad spectrum, usually in the range 0.1–3 THz. The detailed description of the TDS technique can be found in [11]. For NDT applications, TDS systems with a reflection configuration are usually exploited. The THz pulse propagating in a multilayer structure is reflected back at all interfaces due to the Fresnel phenomenon (change in the refractive indices). As a result, a pulse train is obtained, in which time differences between the consecutive reflected pulses depend on the thicknesses of the layers and their refractive indices. Therefore, knowing the refractive indices one can calculate the
Corresponding author. E-mail address: [email protected] (N. Pałka).
https://doi.org/10.1016/j.infrared.2019.103119 Received 8 August 2019; Received in revised form 8 October 2019; Accepted 11 November 2019 Available online 13 November 2019 1350-4495/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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thicknesses of the layers. Moreover, raster scanning of the sample point by point provides its 3D image, where heterogeneities, defects or voids can be imaged [3–10]. The main limitation of the determination of a layer’s thickness is the duration of the pulse propagating in the sample. For very thin layers (< 50 μm), e.g. automotive paints [12], the reflected pulses are heavily overlapped and it is impossible to distinguish between them. In this case, if the number of layers and their refractive indices are known, one can iteratively modify the thicknesses, and simulate the reflected signal until a satisfactory similarity to the measured signal is obtained [12–13]. This method is usually applied for surface layers, because for thicker samples, local fluctuations of the refractive indices can strongly influence the results. If the reflected signals are only partially overlapped, the deconvolution method can provide a separation of the individual pulses and, therefore, is broadly exploited [9,14–17]. Recently, also method based on matched field processing was proposed [18]. It is also worth mentioning that due to the dispersion of the materials, the propagating pulses are usually broadened, which limits thickness measurements in thicker samples. For the considered studies, we prepared four samples which mimic the real structures of the interface formed between metal and polymer surface during fabrication of the electrical devices by means of overmoulding or gluing. Such metal/polymer interfaces can be found for example in bushing structure where coper conductor is covered by polymer insulation during injection moulding process. Adhesion between metal and plastic is weak therefore primers (adhesion promotors) are used. Air voids can appear in the case of inhomogeneous coating with primer or appearance of bonding defect like delamination due to release of mechanical stresses. The primer/adhesive layer may have a thickness in the range of 125–500 μm. In each sample, the air void was formed as a characteristic leaf shape with dimensions of approximately 8 × 9 mm. Such sample design allowed to verify the limits of the selected method. Due to the presence of the metal layer, the samples can be illuminated only from the plastic layer side, which imposes the reflection configuration of the TDS system. In the reflection configuration, two approaches are mainly used: a normal incidence and a pitchcatch. The advantage of the first approach is easy signal processing, while its main drawback is the loss of at least 75% of power due to the use of a beam splitter. This results in a lower S/N ratio and, therefore, the second approach was selected for further studies. In the pitch-catch approach, due to the physical dimensions of the transmitter and receiver which are placed side by side, the angle of incidence is usually above 20°, which causes some signal processing issues. Detection of small voids requires a small THz beam spot, which could be provided only by short focal length optical systems, which in turn are characterised by a small depth of field. In this paper, based on theoretical considerations, we identified and measured all the parameters of the Rynite-based samples and the TDS setup, which are required to precisely and independently determine the thickness of the adhesive or voids. We also propose the novel method to accurately calculate the incidence angle of the TDS setup, which is needed for further calculations. Important factors connected with the experimental aspects, like focusing and depth of field, are also discussed. We developed a simple and robust terahertz method for determining the thickness of the adhesive layer and imaging of voids as well as to critically evaluate its performance for the considered samples. The presented set of signal and image processing with the discussions constitute the novelty of the manuscript.
Fig. 1. The photograph of the sample with 250-μm thick tape (a). Shape of the buried leaf (b). Scheme of the cross-section of the sample with reflections from the interfaces (c).
measurements. Each sample consists of three parts glued together: 1. 5450-μm thick metal base, which is smooth and reflects 100% of the THz radiation. 2. 3625 ± 5 μm thick plastic layer made of DuPont Rynite FR530 NC010 – A 30% glass reinforced, flame retardant, modified polyethylene terephthalate resin. This material is very durable, has outstanding temperature and mechanical properties and, hence, is often exploited in many fields [19]. 3. A glue fixing plastic and metal parts consists of 1, 2, 3 or 4 layers of a 125-μm thick double-sided adhesive tape with a polypropylene carrier coated with a transparent synthetic adhesive manufactured by Smart (4140 PP) [20]. This gives a nominal thickness of the tape layers equal to about 125, 250, 375 and 500 μm, respectively. A leaf shape with dimension 8.35 × 9.35 mm (Fig. 1b) was cut in the tape layers. This leaf-shaped lack of tape (void) is buried between the metal base and the plastic layer and is not visible. The use of tape layers instead of glue is connected with the ease of a void preparation with controllable thickness and shape. The samples are named using the thickness of the leaf gap: 125, 250, 375 and 500, respectively.
3. Propagation of the THz pulses in the sample Fig. 1c presents the scheme of the sample and the description of the parameters used in further analysis. Let’s consider a short THz pulse (P0) incident on the sample at an angle of θ0 relative to the normal. Part of the pulse propagates in the plastic region at an angle of θ1 = arcsin (sinθ0/n1), which was calculated by means of Snell’s law. Next, part of the pulse is reflected at interface 2 while rest of it, after refraction, propagates at an angle θ0 in the air gap or θ2 = arcsin(n1 sinθ1/n2) in the tape region. Finally, both pulses are totally reflected by the metal base and come back at the same angles. As a result, one can obtain three reflected pulses marked as P11, P12, P13 and P21, P22, P23 for the air gap and tape region, respectively. The thickness L can be independently calculated in two ways depending on the region [21]:
2. Description of samples As described in the Introduction samples design was selected in order to reproduce the real structures of the interface which can be formed between metal and polymer during the fabrication process of the electrical devices by means of overmoulding or gluing with adhesive. Fig. 1a shows one of four samples prepared for the THz
L=
2
c Δt1 for the air gap 2cosθ0
(1a)
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L=
c Δt2 for the tape 2n2 cosθ2
(1b)
where Δt1 is the time difference in the arrival of the pulses reflected from interface 2 (P12) and from the metal base (interface 3 – P13) for propagation in the air gap region, Δt2 is the time difference in the arrival of the pulses reflected from interface 2 (P22) and from the metal base (interface 3 – P23) for propagation in the tape region, and c is the speed of light in a vacuum. It can be also noted that the time differences Δt1(2) do not depend on the thickness of the plastic layer (d). We also define the ratio of the above described time differences as:
q=
Δt2 n cosθ2 = 2 Δt1 cosθ0
(2)
It is clear that to obtain the thickness L in line with reality for both Eqs. 1a and 1b, one needs precisely determined parameters in these formulas, namely n1, n2, θ0, Δt1, and Δt2. 4. Determination of the refractive indices Fig. 3. Measured and simulated (offset for clarity) signals (a). Calculated: refractive index n2 (b) and the absorption coefficient (c) of the tape.
We determined the refractive index (n) of both the plastic layer and the tape, which are needed for further calculations. The measurements were carried out in the standard TDS system with a transmission configuration using a TPS Spectra 3000 from Teraview. Additionally, we also present the absorption coefficients of the samples, which indicate the transmission properties of the considered materials.
of the sample were also determined using the standard TDS procedure [11] (Fig. 2c,d). The mean refractive index of the plastic layer (n1) corresponds to the refractive index spectrum at about 0.3 THz, which is connected with the maximum of the pulse spectrum. The absorption coefficient spectrum (Fig. 2d) indicates good penetration of the sample by the THz radiation and provides a good perspective for scanning in the reflection mode. To the best of our knowledge, the THz spectrum of Rynite has not yet been published.
4.1. Characterisation of the plastic material For the spectral characterisation of the plastic layer material, we used the 3625 ± 5 μm thick Rynite layer and put it in the focal point of the spectrometer. Fig. 2a,b show the TDS pulses – reference and transmitted though the plastic layer and their spectra, respectively. The pulse after transmission through the sample is stretched due to the dispersion of the material from 0.4 ps up to 0.8 ps and has five times lower amplitude due to its attenuation. The spectrum of the pulse transmitted through the sample is limited to 1.3 THz. Based on the time difference (Δt) between the reference and plastic pulses, we determined the mean refractive index of the plastic layer n1 = 1.884. The refractive index and the absorption coefficient spectra
4.2. Characterisation of the tape material For tape characterisation we used the sample which consisted of four layers of the tape with a total thickness of about 500 μm. Based on the time difference (Δt) between the reference and the tape pulses (0.86 ps), we determined the mean refractive index of the tape n2 = 1.53. However, for such relatively thin samples, a common error connected with the precise determination of the thickness can significantly influence the n calculation. Therefore, the transfer matrix method (TMM) [12–13] with a linear approximation of the parameters was applied. Fig. 3a shows the reference and sample signals measured in the spectrometer as well as the optimal simulated signal which was obtained using TMM. The calculated optimal thickness of the sample of 482 μm is close to the nominal value of 500 μm. The new thickness modified the mean refractive index of the tape to n2 = 1.537. The calculated characteristics of the refractive index (n2) and the absorption coefficient are presented in Fig. 3b,c. 5. Experimental setup For reflection experiments we used the commercially available TDS scanner TPS 3000 (TeraView) equipped with the reflection module with the angle of incidence (θ0) equal to about 22° [22]. Two off-axis ellipsoidal mirrors (OAEM) provide a short focal length of 50 mm (Fig. 4a), which in turn results in a small beam radius, which was determined using the knife-edge method (Fig. 5b) [23]. The THz part of the optical setup was purged with dried air to suppress the influence of water vapour. The reference TDS pulse and its spectrum measured with the reference gold mirror is shown in Fig. 4c-d. During the measurements, the samples were put on the stage and raster scanned horizontally point by point in X and Y directions. For such a short focal length, the setup is very sensitive to the position adjustment in the Z axis. Fig. 4c,d shows THz pulses and their spectra for 0.5 and 1-mm shifts from the optimal focal point (reference).
Fig. 2. Measured pulses (a) and their spectra (b). The refractive index (c) and the absorption coefficient (d) of the plastic layer. 3
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Fig. 4. TDS reflection setup: schema (a) and the beam radius as a function of frequency (b). Change in the reflected pulses (c) and their spectra (d) due to a shift from the focal point.
Fig. 6. The signals reflected from sample 500 when focusing on the front and back surfaces of the sample.
The new value of the angle of incidence θ0 = 22.86°, slightly higher than the manufacturer's data (22°), allows calculation of the required parameters, namely: θ1 = 11.91°, θ2 = 14.67°, and q = 1.612. 5.2. Focusing For the considered 4-mm (approx.) thick samples, the position of the focus of the THz beam is crucial for achieving meaningful results, especially for the short focal length of the optical system. If the THz radiation is focused on the front surface of the sample, the reflection from the back surface is distorted (Fig. 6), which hampers its further deconvolution. On the other hand, for the THz signal focused on the back surface, the reflections P12 and P13 are clearly seen and were then successfully used for deconvolution. In this case, the pulse coming from the front surface is heavily distorted, but it is not used in the further analysis. The sample was shifted by 2140 μm along the Z axis towards the setup, which corresponds to the time difference 13.14 ps and which agrees with the calculations using Eq. (1a). In the presented research, we only measured and analysed the pulses reflected from the back surface of the samples (P12 and P13), because simultaneous measurement of all pulses (P11, P12 and P13) in the setup is challenging due to the long scanning range (~70 ps). Moreover, use of only P12 and P13 provides better stability, because local thickness fluctuations and refractive index inhomogeneities of the plastic layers are avoided.
Fig. 5. Two pulses reflected from the two surfaces. Inset shows the rays diagram.
This deviation causes not only a decrease in the amplitude of the reflected pulses and their spectra but also an increase in the beam radius, which in turn results in a smaller resolution of the THz image, which will be shown in Section 6. 5.1. Angle of incidence
5.3. Deconvolution and thickness determination Precise determination of the angle of incidence (and reflection) θ0 is crucial for the accuracy of further calculations. Therefore, we modified the method presented in [21]. The THz pulse incidents on a step-edge between two flat and parallel smooth metal surfaces (mirrors). The distance between the mirrors b = 210 ± 5 μm. As a result, two pulses reflected from both surfaces (E1 and E2) are observed which are distant in time by Δt = 1.290 ± 0.005 ps (Fig. 5). In order to accurately determine Δt, the signals measured along the edge for 20 points were first deconvolved using the deconvolution algorithm presented in Section 5.3 and then averaged. The angle of incidence θ can be calculated as [21]:
c∙Δt ⎞ θ0 = arccos ⎛ ⎝ 2b ⎠
In the considered samples, our goal is to measure the distance (L) between interfaces 2 and 3 based on the time differences between the corresponding reflected pulses (Δt1(2)). However, achieving this goal is difficult due to two factors: dispersion-based stretching of the THz pulse (Fig. 2a) and the non-Gaussian shape of the pulse with two side lobes (Fig. 4c). As a result, both factors cause the reflected signal to be composed of partially overlapping and shifted in phase pulses. These phenomena significantly obstruct determination of the interfaces between media and, therefore, deconvolution methods are usually used to separate them and determine L. Knowing the reference signal incident on the sample (h) and the signal reflected from the sample (g), we can determine the response function (f) and, on this basis, find the interfaces between media [24].
(3) 4
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Fig. 7. Raw and deconvolved signals for: air gap (a) and tape (b) regions. The refractive index profile is below the signals.
After testing different algorithms [14–17], we used the inverse filtering algorithm coupled with a band pass double Gaussian filter. The unknown function f is calculated from the relation:
FFT (g ) ⎞ f = FFT −1 ⎛FFT (filter ) (h) ⎠ FFT ⎝ ⎜
⎟
(4)
FFT denotes Fast Fourier Transform. The operation of dividing in Eq. (4) often leads to the reinforcement of noise, which can be suppressed with the double Gaussian filter described as:
filter =
1 1 exp(−t 2/ HF 2) − exp(−t 2/ LF 2) HF LF
(5)
The filter is realised by subtracting two Gaussian functions with different widths described by two coefficients: low-frequency (LF) and high-frequency (HF). HF was equal to 4096 in the presented work, while LF = 160 was matched with the trial and error method, depending on the measured signals. To illustrate the benefits of the deconvolution, Fig. 7 shows exemplary row and deconvolved signals reflected from the air gap and tape regions for sample 500. First, the algorithm looks for the global minimum, which corresponds to the highly reflective interface 3. Next, it seeks for the maximum of the signal situated on the left side of the global minimum, because interface 2 is always in front of the interface 3. In both cases, the deconvolution process reveals the true reflections from the interfaces and decreases the amplitudes of the spurious side lobes and multiple reflections between interfaces 2 and 3. Additionally, we show the refractive index profile. Lower reflection from interface 2 in case of the tape region is explained by a lower refractive index contrast between n1 and n2. For both regions, the thickness L calculated based on Δt1(2) and Eq. (1) (505 and 503 μm for the air gap and tape regions, respectively) is compatible with the nominal value of 500 μm. The presented algorithm is dedicated to the case n1 > n2, due to features of real elements we imitated by our samples. Generally, the algorithm can also be applied for n1 < n2. In this case, reflections from interface 2 and 3 will have a form of negative pulses and the algorithm will look for the distance between their minima.
Fig. 8. Sample with the mirror set at an angle of 2.50: B-scan (a), A-scans for X = 4, 10, and 15 mm (b), and thickness calculated based on the deconvolution (c). Inset shows arrangement of the sample.
radiation was focused on interface 2. Fig. 8a presents a so-called B-scan – a set of reflected pulses versus position along the X axis (scanned with the 100-μm step). A-scans (time signals) for X = 4, 10, and 15 mm are depicted in Fig. 8b. Fig. 8c shows that the linear change of the thickness of the air gap calculated based on the deconvolution is in line with real values. However, for a threshold of 220 μm the reflected signals from interface 2 and 3 overlapped too much and cannot be separated using the deconvolution. This pretty low separability of the interfaces is connected with the fact that the THz pulses are extended in time due to back and forth propagation in the thick and dispersive plastic layer.
6. Experimental results and discussion The examined samples were installed in the holder of the scanner and adjusted in the Z axis (Fig. 4a) to reach the maximum of the reflection from interface 2. The coarse scanning with the 200-μm step lasted about 5 min. A resultant THz image of sample 250 (Fig. 9) shows its edges and the shadow of the leaf inside the image. Afterwards, the 12x12 mm square part of the samples with the centrally located leaf were scanned with a fine 100-μm step for 40 min. As the result, for each sample a 120 × 120 × 2048 matrix was obtained, where for each point
5.4. Limitation of deconvolution To analyse the practical limitations of thickness determination using the deconvolution, we arranged a sample consisting of the plastic layer with n = n1 and thickness d = 3625 μm and placed a flat mirror on it at an angle α = 2.50 (inset in Fig. 8b). This structure mimics the air gap region with thickness L varying in the range 0–630 μm. The THz 5
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Fig. 9. Coarse THz image of sample 250 with the leaf shadow in the middle. Fig. 10. 2D thickness maps calculated based on the deconvolution. The Z axis represents thickness in μm. The dotted lines indicate the cross-sections shown in Fig. 11. The real shape of the leaf is marked for comparison.
of the sample, the reflected 40-ps long signal was acquired.
6.1. Thickness maps
Table 1 Thicknesses of the samples.
Each signal was deconvolved and the time difference between the maximum and minimum was determined (Fig. 7). Next, the thickness L was calculated using Eq. (1b) and the previously determined parameters. Fig. 10 shows the 2D images of the samples, where the 1red/ yellow colour marked the region filled with the tape without any voids. The calculated thickness should be equal to the nominal values (125, 250, 375, and 500 μm). For the centrally located leaf-shaped air void (blue colour), the nominal thickness is lower by a factor of q = 1.612 (Eq. (2)) and should be equal to 77, 155, 233, and 310 μm (Table 1). For sample 125, due to strong pulses overlapping (Section 5.4), the shape of the leaf is hardy visible (Fig. 10a), while the mean thickness is equal to about 145 μm. This fact is consistent with the 220-μm threshold determined for the sample with the leaning mirror (Fig. 8b). For samples 250, 375, and 500, the shape of the leaf is clearly seen (Fig. 10b–d). The average thickness and its mean squared error (MSE) inside a rectangular region of the leaf area (Table 1: “Leaf ∙ q”) is in line with the nominal value. Since the thickness of the tape area is not uniform, we calculated the average thickness and MSE in a rectangular region in four corners of the samples (Table 1: “upper left” etc.). Next, all values from the rectangular regions from four corners were averaged and “mean (4 corners)” was calculated. The observed MSEs are rather small ( ± 7 μm) for samples 250 and 375, which suggests good homogeneity of the glued regions. For sample 500, the average values in the corners differs by about 60 μm (upper left vs. bottom right), which is probably connected with the fact that the metal base is not parallel to the plastic layer, because during preparation the sample might not have been uniformly glued. Since the thickness decreases uniformly from the upper left to the lower right corner, it proves the possibility of constant monitoring of the layers. Moreover, the mean thicknesses for the four corners are very similar to those determined for the leaf regions (Table 1 in bold). This fact suggests that the refractive indices (n1, n2) and the incidence angle (θ0) were precisely determined. The main source of error are instability of the TDS setup, error of the extrema determination and non-uniformity of glue thickness.
Thickness [μm] Nominal Nominal/q Leaf ∙ q upper left upper right bottom left bottom right mean (4 corners)
250 155 252 248 253 259 248 252
± ± ± ± ± ±
1 1 1 1 1 7
375 233 375 370 374 368 382 373
± ± ± ± ± ±
2 1 2 1 1 7
500 310 510 536 515 524 476 513
± ± ± ± ± ±
1 15 1 14 1 26
6.2. Thickness profiles Fig. 11 shows the cross-sections of the 2D images through the blade and stalk region of the leaves. For sample 125, as expected, only flat lines centred at 145 μm are visible. For samples 250, 375 and 500, the slope of the hollows becomes smaller for thicker air gaps. For the blade region (red lines), the nominal thickness (divided by q) is reached. This is not true for the stalk region (blue lines), where only for sample 250 can we observe so deep an incline. This phenomenon is connected with the change in resolution due to defocusing. The larger the distance L, the higher the beam radius which results in lower resolution and visibility of the leaf details as well as higher blurring of the shapes. For sample 500, the slope of the thickness for the 0–6 mm range is also visible for the stalk. It must be noted that the measured thickness inside the leaf should be multiplied by q to obtain its correct value, which can be easily applied for the presented samples with known thickness. However, this approach can lead to incorrect results when the thickness of the adhesive layer is not known, because the time difference-based algorithm cannot determine the type of the material (tape or air). To overcome this problem, we proposed a method which exploited both the time differences and amplitudes of the signals (Fig. 7). 6.3. Amplitude maps In addition to the 2D thickness map, the leaf-shaped voids can also be imaged as a map of extremes (minimum Amin and maximum Amax – see Fig. 7) of the deconvolved signals. We tested a few modes of imaging, including a peak to peak amplitude and integration of the signal
1 For interpretation of color in Figs. 10,11 and 14, the reader is referred to the web version of this article.
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Fig. 13. 2D binary maps of the samples. The real shape of the leaf and correlation coefficients are marked for comparison.
6.4. Binary maps
Fig. 11. Thickness profiles for two cuts: through the blade and stalk. Black solid lines indicate the widths of the stalk (0.8 mm) and blade (4 mm) regions.
The amplitude maps from Fig. 12 were next processed by the edge detection technique to find the boundaries of the objects within the images. After analysis and tests, we selected the Canny technique [25]. The resultant 2D binary images (Fig. 13) show only two regions (plastic layer and tape). The 2D correlation coefficient (corr) provided a quantitative shape similarity factor between the real (Fig. 1b) and binary images. In all cases, high similarity (corr > 0.8) proves that both the ratio amp and the edge detection technique were correctly selected. Moreover, the smaller the thickness of the air gap L, the higher the corr value (see Fig. 13), which is connected with the higher resolution discussed in the previous section. 6.5. Corrected thickness maps It can be noted that the binary map shows two regions which differ in the amplitude ratio of the reflected signals. This separation is connected with the different refractive indices of air and the tape. If we ascribe value 1 to the white region (tape) and value q to the grey region (air void), we can obtain a correction mask. Next, one can multiply it by the thickness map (Fig. 10), which leads to the results shown in Fig. 14. For samples 250, 375, and 500, both void and tape regions present the correct thicknesses, while the red colour (overestimated values) can be used for detection of the void’s edge. For sample 125, due to the limitation of the deconvolution, the thickness is not correctly determined, but shape of the void is clearly visible. To sum up, thanks to the developed processing scheme, one can display the relevant information in a single image, where both the real thickness and the presence of the void are marked. In the case of samples with a thinner L below the threshold, lack of thickness information is compensated by better visibility of the leaf details.
Fig. 12. 2D amplitude maps of the samples calculated based on the ratio amp = −Amax/Amin. The real shape of the leaf is marked for comparison.
between Amin and Amax, but the best results in terms of visibility of the details was obtained for the ratio: amp = −Amax/Amin (Fig. 12). In the case of sample 125, the leaf shape with fine details is now clearly seen. For other samples, the obtained results are generally similar to those presented in Fig. 10, but the stalks are slightly better visible. The lack of foil thinner than 125 mm prevented us from conducting experiments showing the minimum gap detectable with the amplitude map algorithm. However, based on the performance of the algorithm for sample 125, duration of the THz pulse after propagation in the plastic (about 2 ps), and instabilities of the THz pulse during the measurements, the minimum detectable gap is estimated at about 50–75 μm.
7. Conclusions The time domain spectroscopy setup in a reflection configuration was exploited for non-destructive monitoring of four samples with a 10mm (approx.) air gap in the shape of leaf buried between the 4-mm thick polymer layer and the metal plate. The thicknesses of the isolating 7
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indicate presence of the defect region. This algorithm worked well for 125-μm and its real detectability threshold was estimated at 50–75 μm. The binary map is based solely on the amplitude map and is mainly used for unambiguous determination of the void shape, calculation of the correlation coefficient and determination of the corrected thickness map. In summary, the results obtained in this research closely reflect the real thicknesses of voids and their shapes. Obviously, X-ray tomography can measure the voids with higher resolution and precision, but requires that the measured element to be installed on a rotating platform. On the contrary, TDS-based monitoring can be carry out in situ without the need to uninstall the element. Therefore, the TDS technique seems to have a good perspective as an alternative but also complimentary to X-ray CT tool for the non-destructive, non-ionising and contactless scanning of voids in plastic-metal samples in industrial applications. Declaration of Competing Interest The authors declare that there is no conflict of interest. Fig. 14. 2D corrected thickness maps calculated based on both amplitudes and time differences. The Z axis represents the thickness in μm.
References
layers of tape were equal to 125, 250, 375, and 500 μm. We identified and precisely measured the refractive indices of the constituent materials and obtained 1.884 and 1.537 for the plastic and tape layers, respectively. Due to the various thicknesses, we applied the standard procedure and TMM methods. After analysis, we selected the reflection TDS setup in a pitch-catch configuration with a short focal length for high resolution imaging. We showed that the radiation should be focused on the back surface of the sample to obtain optimal measurement conditions. We also developed a method for accurate calculation of the incidence angle in the TDS setup. High accuracy of both the refractive indices and the incidence angle measurements is crucial for further calculations, because it guarantees consistent thicknesses in the tape and air void regions calculated using Eqs. (1a-b). Next, we selected the optimal deconvolution method to separate overlapping impulses and calculate the time differences and amplitudes. We measured the sample with the inclined mirror to experimentally determine the minimum thickness threshold. The two-dimensional thickness, amplitude and binary maps were selected for imaging of the void areas. Mean thicknesses inside and outside the voids are similar, which proves the correctness of the applied approach. For sample 4, the difference in thickness between the corners is probably attributed to the fact that, due to small defects during the preparation process, the metal base is not parallel to the plastic layer. For sample 125, the shape of the leaf is not visible due to strong pulses overlapping, which is consistent with the previous measurements carried out for the inclined mirror. To overcome this problem, we exploited the information contained in the extremes of the deconvolved signals. We found that the ratio Amax/Amin provides the optimal visibility of the leaf details even for sample 125. For other samples, the images obtained for the thickness and amplitude mapping are similar, but the stalks are slightly better visible in the last method. Finally, the amplitude maps were binarised using the Canny edge detection technique. The correlation coefficient between the real and binarised images of the leaf in the range 0.8–0.9 proves the appropriate performance of the applied method for this class of samples. Finally, we showed that multiplication of the deconvolved and binarised maps can provide relevant information about the real thickness of the layer and the presence of the void in a single image. For the considered samples with 3.6-mm thick plastic layer, the thickness-based detectability is about 220 μm and thinner bonding defects cannot be determined. This limit is connected with sample-depending stretching of the pulse to about 2 ps due to dispersion, which reduces resolution. For thinner voids we can use the amplitude map to
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