Abstract

Porosity is one of the most important indicators for the characterization of the comprehensive performance of thermal barrier coatings (TBCs). Herein, we explored a fast, nondestructive porosity evaluation method based on the terahertz time-domain broadening effect. Different preparation process parameters were used to deposit the ceramic coatings, and the porosity ranged from 9.09% to 21.68%. Monte Carlo simulations were conducted to reveal the transitive relation between porosity and the terahertz time-domain broadening at different extinction coefficients and transmission distances. A transmission mode with an incidence angle of 0° was used to estimate the terahertz dielectric properties of ceramic coatings and the relative broadening ratio of terahertz pulses at different porosities. As a result, the Monte Carlo simulations showed that the time-domain broadening effect was enhanced when the extinction coefficient and transmission distances increased. As the porosity increased, the refractive index decreased and the extinction coefficient increased. The latter was more sensitive to minor porosity changes as demonstrated by linear fitting comparisons. Meanwhile, the relative broadening ratio increased when the porosity increased, and reserved the sensitivity of the extinction coefficient to porosity changes. The effect was more obvious on the relative broadening ratio which experienced multiple transmissions and reflections. Moreover, the relative broadening ratio could be obtained faster and in an easier manner compared to the dielectric parameters in both the transmission and reflection modes, based on single-step tests with the use of actual terahertz wave inspection. Finally, this study proposed a novel, convenient, online, nondestructive, and noncontact porosity evaluation method that could be potentially utilized to evaluate the integrity of TBCs in gas turbine blades.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Thermal barrier coatings (TBCs) are extensively applied to the hot sections of gas-turbine engines or aero-engines to protect the underlying metallic components from erosion, abrasion, and high-temperature degradation, thereby obtaining high-thrust–weight ratios and combustion efficiencies [1,2]. A state-of-the-art TBC system typically includes the superalloy substrate, the metallic bond coating (BC), and the brittle ceramic top coating (TC) [1,3]. However, the metallic bond coating of MCrAlY (M = Ni, Co, or Ni/Co) is easy to be oxidized in high-temperature environments. Once oxidized, it forms the thermal grown oxide (TGO) around the interface between the BC and TC layers. The thermal insulation capability of TBCs can be determined by the ceramic top coating which is deposited via plasma-spraying (PS) techniques or electron beam physical vapor deposition (EB–PVD). Among the various technologies for depositing TBCs, air plasma spray (APS) is extensively used owing to its relatively low cost and high efficiency [1]. Yttria-stabilized zirconia (YSZ) is generally chosen as the ceramic top coating material owing to its excellent comprehensive properties, such as its high-phase stability, low-thermal conductivity, and superior mechanical properties. The ceramic YSZ particles melt during the plasma spraying process, and serve as droplets toward the target substrate. These droplets solidify rapidly and form a splat-based microstructure with pores sandwiched between the splats when they impact the surface of the substrate. Owing to the presence of quenching stress that induces fast solidification, cracks and pores may occur [4,5]. The porosity is a vital parameter for the characterization of the internal microstructure of the ceramic top coating. Accordingly, the variation of porosity during service is closely related to the mechanical properties (elastic modulus, compressive stress) and the thermal conductivity of the ceramic top coating, which influences the performance and the service life of the TBCs directly [610]. Generally, APS–TBCs have typical porosity values which range from 3–20 vol% [11,12]. Hence, to monitor the porosity of TBCs quickly and nondestructively, fast and effective nondestructive testing (NDT) techniques ought to be explored.

Over the past few decades, a variety of NDT techniques, such as ultrasonic [1316], eddy current [1720], rare earth luminescence [2123], X-ray [24,25], and infrared [2629], have been developed to examine the TBCs. However, all these methods have their own weaknesses which are related with the thickness, and the type of the ceramic and metallic coatings. For example, ultrasound is limited to the size of the target object, the existence of edge effects, and the requirement of a liquid couplant [13,30,31]. Owing to the requirement of the lift-off operation step, eddy current suffers from manual scanning and large noise, and is not suitable for the evaluation of complex components in nonmetallic materials [18,20,32,33]. Rare earth luminescence suffers from the extra doping of rare earth elements and cannot be used for quantitative characterization [3436]. Increased radiant energy X-ray is harmful to the human body and special protection devices need to be used [37]. Infrared is affected considerably by the ambient temperature. As the depth of the defect increases, the detection sensitivity will decrease rapidly. Furthermore, it is also difficult to detect larger components owing to the limitations of the external heat source [3841].

Terahertz (THz) nondestructive testing technology has become a research hotspot in recent years as it has unique advantages based on the noncontact, nonionizing, real-time evaluation, high precision, and good penetration characteristics for nonmetallic dielectric materials compared to other inspection methods [42,43]. It has already been successfully used to determine the properties of materials with composite structures, such as glass fiber-reinforced plastic (GFRP) composites [44,45], integrated circuit packages [46], pharmaceutical tablets [47,48], and TBCs [4954]. Nevertheless, the accuracy of various NDT technologies is directly affected by noise and impurities in the surrounding testing environment to varying degrees. Compared to traditional NDT techniques, the typical terahertz pulse width is on the order of picoseconds, which makes it easy to perform time-resolved transient spectroscopy studies on various materials. The terahertz sampling measurement technology can significantly suppress the noise interference in the surrounding environment. But this does not mean that terahertz NDT technology is perfect. Most polar molecules, especially the common water molecules, have strong absorption of terahertz waves. This is the fatal disadvantage of terahertz NDT technology. As it happens, this is not a problem for TBCs in high temperature service, and then terahertz NDT technology is almost perfect for TBCs evaluation.

In our previous study, as the inner structures of the top coatings changed after the erosion test, the THz pulse broadening changed accordingly. Correspondingly, the broadening of the THz pulses is suggested as a possible measure for the porosity changes [53]. In this study, Monte Carlo simulations were conducted to reveal the transitive relation between the broadening and microstructural changes, and a THz time-domain spectroscopy (THz–TDS) system of the transmission mode was used to measure the porosity of TBCs.

2. Experimental and simulation methods

2.1. Preparation of coatings

In this study, fine and coarse ZrO2 8 wt.% Y2O3 (8YSZ) powders (Beijing Sunspraying Technology Co., Ltd., Beijing, China) with respective particle sizes in the ranges of 15–55 µm and 40–96 µm (shown as Fig. 1) were used to deposit the top coating. To obtain coatings with different porosities, fine and coarse powders with the plasma–spray distance ranges of 70, 80, 90, 100, 110 and 120 mm were used. YSZ ceramic coatings were deposited on a grit-blasted, disc-shaped, carbon steel substrate (Ø 25.4 mm × 3.1 mm) via a commercial APS system (APS–2000, Beijing Aeronautical Manufacturing Technology Research Institute, Beijing, China). During the entire spraying procedure, argon served as the primary plasma gas, and hydrogen was selected as an auxiliary gas. The pressure of argon and hydrogen were fixed at 0.4 MPa and 0.25 MPa, respectively. Argon was also used as the powder feed gas at a flow rate of 10 L/min. The plasma power was maintained at 36 kW (600 A/60 V) to deposit the YSZ ceramic coatings. The spray gun was operated by the manipulator (Asea Brown Boveri Ltd, Zurich, Switzerland) at a speed of 150 mm/s. To obtain the terahertz properties of samples, a deposited coating was stripped from its substrate. To minimize the electromagnetic scattering effect caused by surface roughness, both surfaces of the stripped coating were polished to make them smooth. The microstructure and porosity of coatings were examined by a scanning electron microscope (SEM, ZEISS EVO MA15, Carl Zeiss SMT Ltd, Oberkochen, Germany).

 

Fig. 1. Morphologies of the 8YSZ powders. (a) Particle sizes in the range of 15–55 µm; (b) Particle sizes in the range of 40–96 µm.

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2.2. Monte Carlo simulations

The real ceramic layer was a random porous medium which contained a large number of pores and crack scatterers. The terahertz pulse was scattered and absorbed as it propagated through the ceramic layer. Owing to the scattering effect of the pores and cracks, the ceramic layer channel could be described as a multichannel channel. Accordingly, the sum of the signals from different distance propagation paths constitutes the received signal, as shown by the schematic in Fig. 2. In this study, the Monte Carlo simulations were used to simulate the scattering motion of terahertz photons in the ceramic layer [55,56]. The transmission process of the terahertz signal in the ceramic layer was viewed as a photon transmission process. The transmission outcome of each photon was obtained statistically, and the transmission characteristics of the ceramic layer signal were obtained. Therefore, the following assumptions and instructions were postulated for the propagation of terahertz pulses in the ceramic layer: 1) The ceramic layer consisted of YSZ and pores, and the terahertz pulse consisted of a large number of photons. Terahertz photons propagated freely in YSZ and only absorption occurred (shown as area 1). When it propagated to the scatterer, scattering and absorption occurred simultaneously (shown as areas 2 and 3), and the effect of each scatterer on the photons was independent. The tracking ended when the photon diverged to the outer part of the receiving medium. 2) When the polarization of light was considered, the Stokes vector was used. However, in most cases, the reflected radiance and transmitted radiance obtained by the linear method were only slightly different from those obtained by the Stokes vector method. These differences were undoubtedly caused by statistical fluctuations in Monte Carlo simulations. Therefore, the polarization of light was temporarily ignored. 3) The statistical error was attributed to the fact that only a limited amount of photons were used in the calculation. To minimize the statistical error of the result, a large number of photon simulations was required. The number of photons used in the simulations was ten million. Assuming that the thickness of the ceramic coating prepared by the experiment was 300 µm, the geometric distances of the simulation was selected to be 300 µm, 900 µm, and 1500 µm, respectively, which corresponded to the geometric distances of the three transmission paths. 4) It was assumed that the terahertz pulse entering the ceramic layer was monochromatic and the refractive index of the YSZ coatings was equal to five [57,58]. This was equivalent to ignoring the dispersion effect of the ceramic layer on terahertz waves in simulations, and the influence of dispersion on broadening would be discussed in section 3.

 

Fig. 2. Schematic of the terahertz (THz) photonic motion trajectories in ceramic coatings.

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Based on the above assumptions and instructions, the Monte Carlo method was used to track the propagation of a large number of photons in the ceramic layer. By recording the coordinates, direction cosines and the motion time of the photons, the time-domain broadening energy extinction, and the arrival angle distribution of the terahertz pulse could be obtained by statistical processing. This simulation focused on the characteristics of the time domain broadening effect.

The state parameters S of the photon included the spatial position P(x, y, z), the direction cosine R(τx, τy, τz), and the length of the motion path L. A photon emitted from a light source after w collisions within the medium could be expressed as follows,

$${S_w} = ({P_w},{R_w},{L_w}).$$
Given that the photon flew in a straight line between two adjacent collisions, the direction of motion and the survival parameters were not changed. Therefore, the motion of this photon in the ceramic layer could be described by the state matrix, as follows:
$$\left( {\begin{array}{{c}{c}{c}{c}{c}} {{P_0}}&{{P_1}}&{\ldots }&{{P_{w - 1}}}&{{P_w}}\\ {{R_0}}&{{R_1}}&{\ldots }&{{R_{w - 1}}}&{{R_w}}\\ {{L_0}}&{{L_1}}&{\ldots }&{{L_{w - 1}}}&{{L_w}} \end{array}} \right).$$
The state matrix listed above recorded the history of the photon’s random walk. In this way, simulating the motion process of a photon became a problem for the determination of the state matrix. Figure 3 shows the coordinate system for studying the problem of photon propagation in a medium. The initial position O (0, 0, 0) of the photon was the origin of the coordinate, and the initial movement direction of the photon was the positive Z-axis. The initial position vector of a photon used a Cartesian coordinate system.

 

Fig. 3. Terahertz photon transmission coordinate system.

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After w collisions, the shift of the direction of the photon’s motion relative to the direction of the photon’s motion before this collision is represented by θw and φw, where θw is the scattering angle and φw is the azimuthal angle. Assuming that photons had undergone w collisions, the subsequent collision point is expected to be Pw+1. The position of the next collision point can be determined by its free path, which is the distance between the previous and the subsequent collision points. The distance L could be determined by Eq. (3), where α is the extinction coefficient of the ceramic layer, and ξ is a uniformly distributed random number between 0 and 1. Thus, the position of the next collision point can be estimated using Eq. (4).

$$L = - \frac{1}{\alpha }\ln (\xi ),$$
$$\left\{ {\begin{array}{{c}} {{x_{w + 1}} = {x_w} + {\tau_{xw}}\cdot \Delta {L_w},}\\ {{y_{w + 1}} = {y_w} + {\tau_{yw}}\cdot \Delta {L_w},}\\ {{z_{w + 1}} = {z_w} + {\tau_{zw}}\cdot \Delta {L_w}.} \end{array}} \right.$$
where $\Delta {L_w}$ is the free path between the wth and (w + 1)th collisions of the photon. The scattering angle of the moving direction of the photon after the wth collision relative to the moving direction of the photon before this collision could be obtained by sampling the phase function. Considering the terahertz wavelength range and the main distribution range of the pore diameter in the ceramic layer, Rayleigh scattering was dominant. Therefore, Eq. (5) was chosen to sample the scattering angle θ [59].
$$\theta = arc\cos (2\sigma - 1),$$
where σ was a random number between 0 and 1. Accordingly, φ could be sampled in the range between 0 and 2π. When the scattering angle θ and the azimuthal angle φ were obtained by random sampling, the new direction vector could be calculated after scattering based on the original photon moving direction vector $R({\tau _x},{\tau _y},{\tau _z})$, and can be expressed as follows,
$$\left\{ {\begin{array}{{l}} {{\tau_x}^\prime = {\tau_x}\cos \theta + \frac{{\sin \theta }}{{\sqrt {1 - {\tau_z}^2} }}({\tau_x}{\tau_z}\cos \varphi - {\tau_y}\sin \varphi ),}\\ {{\tau_y}^\prime = {\tau_y}\cos \theta + \frac{{\sin \theta }}{{\sqrt {1 - {\tau_z}^2} }}({\tau_y}{\tau_z}\cos \varphi - {\tau_y}\sin \varphi ),}\\ {{\tau_z}^\prime = {\tau_z}\cos \theta - \sin \theta \cos \varphi \sqrt {1 - {\tau_z}^2} ({\tau_x}{\tau_z}\cos \varphi - {\tau_y}\sin \varphi ).} \end{array}} \right.$$
If the direction of photon motion is close to the Z-axis, the new direction can be determined by Eq. (7).
$$\left\{ {\begin{array}{{l}} {{\tau_x}^\prime = \sin \theta \cos \theta ,}\\ {{\tau_y}^\prime = \sin \theta \sin \varphi ,}\\ {{\tau_z}^\prime = SIGN({\tau_z})\cos \theta .} \end{array}} \right.$$

2.3. THz time-domain system and inspection method

In this study, the THz TDS system (University of Shanghai for Science and Technology, China) was employed in this study to evaluate the porosity of TBCs. The main components of this system included a femtosecond laser, THz TDS, delay line, emitter, and receiver modules. The photoconductive antenna was excited by a femtosecond laser to produce THz pulses with bandwidths which extended from 0.06 THz to 3 THz. The laser provided 780 nm pulses with a pulse duration of 80 fs at a repetition rate of 76 MHz, and an average output power of 1.1 W. Herein, the THz TDS system was configured to operate in the transmission mode with an incidence angle of 0°. Each dataset contained 256 scans which were averaged to ensure reliability. Three samples were tested for the same spray process parameters, and each sample spectrum was acquired from three different, nonoverlapped tested areas. Additionally, to avoid water vapor absorption, dry air (with a relative humidity less than 1%) was supplied to the system. The test temperature was 20 °C. At the beginning of the experiment, the total transmission reference signal was obtained.

When THz waves were incident on the sample, the multiple transmissions could be detected as shown in Fig. 4. A part of the incident THz waves was reflected from the top surface of the ceramic layer, while another part was transmitted through the ceramic layer and was partly reflected at the bottom of this layer. Some of the reflected THz waves transmitted through the top surface from the bottom into air, and some of them were reflected back into the ceramic layer. Multiple reflections and transmissions took place between the top and bottom. Herein, T1, T2, and T3, were the first, second, and third transmissions, respectively. These transmissions embodied the inner message of the porous ceramic layer.

 

Fig. 4. Schematic of multiple terahertz transmission paths in the ceramic layer.

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From the transmission reference and sample time-domain signals, the frequency-domain information was extracted by calculating the fast Fourier transformation (FFT). Accordingly, the refractive index n(ω) and extinction coefficient α(ω) of the sample could be estimated using the methods proposed in references [6062]. Herein, the extinction coefficient accounted for the absorption and scattering of the electromagnetic waves owing to the sample ($\alpha (\omega ) = {\alpha _{absorption}}(\omega ) + {\alpha _{scattering}}(\omega )$).

To investigate the broadening effect of the porous ceramic layer on THz time-domain waveforms, the time difference Δt (peak-to-peak width) between the positive and negative peaks of each transmission pulse was extracted to evaluate the broadening effect of the porous ceramic layer with different porosities, as shown in Fig. 5.

 

Fig. 5. Time difference between positive and negative peaks of each transmission pulse.

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Following the increase of the optical path induced by multiple reflections inside the ceramic layer, scattering and dispersion accumulated, and the THz pulse spread over an increasingly broadened peak-to-peak width. It should be noted that the broadening time interval Δt which would be used to estimate the porosity was associated with the geometric thickness d through which THz waves passed through. This is considered in subsequent discussions in the next section.

3. Results and discussion

3.1. Porosity of coatings

Figures 6(a)–(c) and Figs. 7(a)–(c) show the typical microstructures of the as-sprayed YSZ coatings fabricated with different spray distances and powder sizes. Both of these coatings contained numerous large pores, non-bonded lamellar voids, and micro-cracks in the splat cracks. Large pores in the YSZ coatings were formed owing to the insufficient infiltration and wet-ability of the molten droplets that impacted on the substrate or the deposited layer, and the insufficient flattening of the semimolten particles. Non-bonded lamellar voids in the coating were generated owing to the trapped gas, the relatively low temperature of the deposited surface, and the rapid impingement between droplets and the previously formed under layers. It could also be observed that these YSZ coatings which were deposited with fine powder were denser than those deposited by coarse powder owing to the variation of the melting index [63,64] and the spraying speed. The sizes of the large pores were greater in the cases of the coatings which were deposited at the end of the process.

 

Fig. 6. Typical cross-sectional microstructures of the YSZ coatings with fine powder at different spray distances: (a) 80 mm, (b) 100 mm, (c) 120 mm.

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Fig. 7. Typical cross-sectional microstructures of the YSZ coatings with coarse powder at different spray distances: (a) 80 mm, (b) 100 mm, (c) 120 mm.

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The smaller pore scatterers exhibited Rayleigh scattering characteristics at all frequencies. The extinction coefficient $\alpha $ depends on the absorption and scattering and can be estimated as follows [65],

$${\alpha _{\textrm{absorption}}} = k\frac{{{\mathop{\rm Im}\nolimits} \{{{\varepsilon_{\textrm{air}}}} \}}}{{{\varepsilon _{YSZ}}}}\frac{{4\pi {a^3}}}{3}{\left|{\frac{{3{\varepsilon_{YSZ}}}}{{{\varepsilon_{\textrm{air}}} + 2{\varepsilon_{YSZ}}}}} \right|^2},$$
$${\alpha _{s\textrm{cattering}}} = \frac{{8\pi }}{3}{k^4}{a^6}|y{|^2},$$
where k = 2π/λ, $a$ was the radius of scatterer, y = (ɛairYSZ)/(ɛair+2ɛYSZ), ɛair and ɛYSZ are the permittivities of the air and YSZ medium, respectively, and Im{ɛair} is the imaginary part of ɛair. As the pore size increased, the absorption and scattering of the pore scatterer also increased, which led to the increase of the extinction coefficient of the YSZ coatings.

Figure 8 depicts the porosity of as-sprayed YSZ coatings, as shown in Figs. 6 and 7. For the coatings deposited with the same powder particle size, the porosity decreased slightly when the spray distance ranged between 70 mm and 100 mm, while the porosity increased significantly when the spray distance was greater than 100 mm. At the same spray distance, the coating deposited with the coarse powder yielded a larger porosity than the coating deposited with fine powder.

 

Fig. 8. Porosities of coatings with different particle sizes and spray distances.

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3.2 Terahertz pulse broadening induced by porosity

Figures 9(a)–(c) shows the Monte Carlo simulation results of the photon numbers and arrival time distributions at different extinction coefficients and transmission distances.

 

Fig. 9. Monte Carlo simulation results of photons numbers and arrival time distributions at different extinction coefficients and transmission distances: (a) 300 µm, (b) 900 µm, and (c) 1500 µm.

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The changes of the extinction coefficients were related to the variation of porosity, and the three different transmission distances respectively corresponded to the 1st, 2nd, and 3rd transmissions, as shown in Fig. 4. As the extinction coefficients and transmission distances increased, the arrival paths of the photons became increasingly tortuous, and the waveforms became chunkier. In the absence of scattering and dispersion, the ideal arrival time required for THz photons to pass through the YSZ coatings depicted in Figs. 9(a)–(c) should be 4 ps, 14 ps, and 24 ps, respectively. The simulation results showed [Figs. 9(a)–(c)] that only a few of the photons arrived at the end point with an ideal arrival time. All of these indicated that the scattering effect affected almost all the in-flight behaviors of photons that reduced the energy of the THz pulse and broadened the waveform. The stronger the scattering effect is, the more severe the extinction and broadening are. The change of pore structure was closely bound to the THz scattering effect, which made it possible to use the broadening effect to evaluate the change of porosity.

In order to quantify the influence of the extinction coefficient and transmission distances on the broadening of the pulse, as shown in Fig. 9, the full width at half maximum of the peak of the pulse was proposed to compare and analyze the influence between them. As shown in Fig. 10, linear models were set up, the broadening ratio ρ (the absolute broadening of sample with extinction coefficients of 30 cm−1 and thickness of 300 µm was used as the normalized denominator) was the dependent variable, and the extinction coefficient and transmission distances were independent variable in these models.

 

Fig. 10. Broadening ratio of the full width of the pulse at half maximum of the peak height at different extinction coefficients and transmission distances.

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In order to further improve the reliability of the analysis results, the origin was added for analysis. When the transmission distance was constant, the three same coloured linear Eqs. and their correlation coefficients showed a good linear correlation between the broadening ratio and the extinction coefficient, which made it possible to use the broadening ratio to characterize the porosity, owing to the close relationship between the extinction coefficient and porosity. It also could be seen from the increase of the slope that the longer the transmission distance was, the stronger the influence of the extinction coefficient on the broadening ratio was. It proved that the detection accuracy of the porosity may be increased by using a larger transmission distance. Similarly, when the extinction coefficient was constant, another six linear Eqs. and their correlation coefficients also showed a good linear correlation between the broadening ratio and the transmission distance. As the extinction coefficient increased, the slope increased, and the value of ρ/L increased accordingly. So based on this nine linear Eqs., it not only revealed the variation relation between the pulse broadening (broadening ratio), thickness (transmission distance), and the dielectric properties (extinction coefficient), but also provided a vital basis to define a parameter β (ρ/L) named relative broadening ratio (see section 3.2) for characterizing porosity in the experiment and a longer transmission distance was preferred.

As the porosity increased, the optically denser medium YSZ was droped with more optically thinner medium air, as shown in Fig. 11(a), thus reducing the refractive index of the ceramic layer. The refractive indices of the ceramic coatings at the frequencies of 1 THz and 1.5 THz were extracted and subjected to linear fittings to obtain linear Eqs. and correlation coefficients, as shown in Fig. 11(b). Based on these results, the refractive index can be used to estimate the variation of porosity. Nevertheless, Maxwell, Garnett, and Bruggeman models assumed that THz light scattering was absent, and that the spherical shapes of the pores which were distributed uniformly in the YSZ medium were attempted to be used to estimate the porosity [54]. Owing to the complex pore morphology inside the coatings, the current model that used spherical, ellipsoidal, or coin-shaped regular topographies could not conform to the actual pore morphology. Correspondingly, this resulted in a large error in the prediction of porosities [1,66].

 

Fig. 11. Refractive indices of ceramic layer at different porosities: (a) frequency spectrogram; (b) refractive indices at 1 THz and 1.5 THz.

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Obviously, these assumptions did not match the facts. The minor porosity change (9.09%–14.40%) could not be distinguished effectively on the basis of the refractive index, which was possible when the extinction coefficient was used as the criterion, as shown in Fig. 12. With the increase of porosity, the denser YSZ was doped with more air scatterers. This increased the extinction coefficient of the ceramic layer. The experiment results showed the close relationship between porosity and extinction coefficient, and the close relationship was in good agreement with the simulation hypothesis. The extinction coefficients of the ceramic coatings at the frequencies of 1 THz and 1.5 THz were extracted and subjected to linear fittings to obtain respective linear Eqs. and correlation coefficients, as shown in Fig. 12(b). Compared to the slopes of linear Eqs., the extinction coefficient was much more sensitive to the variation of porosity than the refractive index.

 

Fig. 12. Extinction coefficients of ceramic layer at different porosities: (a) frequency spectrogram, and (b) extinction coefficients at 1 THz and 1.5 THz.

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The results presented above showed that it was possible and more appropriate to utilize the extinction coefficient to inspect the porosity, especially the extinction coefficient at higher frequencies. However, in practice, the ceramic coating was deposited on the alloy, and the extinction coefficient of different frequency bands could not be obtained. Therefore, it is not practical to evaluate the porosity online by using directly the extinction coefficient. The Monte Carlo simulations showed that the extinction coefficient was related to the broadening of the THz pulse waveform. In fact, the dispersion effect also played a role in the broadening of the THz pulse waveform. The simulations assumed that the THz waves were monochromatic, and the dispersion effect was ignored. As shown in Fig. 11(a), the slopes of the plots of the refractive index n(ω) as a function of frequency have small values, and the dispersion effect occurs but is not strong. If the dense, nonporous YSZ medium with a thickness of d is homogeneous, and the broadening induced by the dispersion effect is ζ, then for the same medium with a thickness of kd, the broadening is expected to be equal to kζ. Nevertheless, because the scattering of photons followed longer routes than those that were transmitted directly, photons that underwent multiple scatterings also accumulated an increased dispersion. Therefore, there was no need to distinguish the synergistic broadening promoting effects of the scattering and dispersion, after all, the broadening was entirely rest with the variation of porosity. A relative broadening ratio β, which was normalized by the thickness d and the reference signal r, was corresponded to the ρ/L mentioned in section 3.2, was introduced to evaluate porosity. Accordingly, the definition of the relative broadening ratio β was expressed as follows,

$${\beta _{1,2,3}} = \frac{{\Delta {t_1}_{,2,3}}}{{\Delta {t_r}d}}.$$
As the porosity increased, the relative broadening ratio β of multiple transmissions (1st, 2nd, and 3rd) also increased, as shown in Fig. 13. The relative broadening ratio of each transmission was extracted and subjected to a linear fitting to obtain respective linear Eqs. and correlation coefficients. Compared to the slopes of the linear Eqs. in Figs. 13(a)–(c), the relative broadening ratio β reserved the sensitivity of the extinction coefficient α to the change in porosity. Specifically, β3 had experienced multiple scatterings and dispersions, and possessed the highest resolution of porosity variation. The experimental results were in good agreement with the simulation results by comparing the all the linear fitting models. Both the simulation and experimental results showed that the relative broadening ratio could be used to characterize the porosity and the long transmission distance could improve the porosity resolution.

 

Fig. 13. The relative broadening ratio of THz pulse waveforms normalized by the thicknesses and the reference signals at different porosities: (a) 1st transmission, (b) 2nd transmission, and (c) 3rd transmission.

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For the actual online porosity inspection, the THz TDS system with a reflection mode was more suitable, and Δt was also conveniently obtained in the reflection mode. The thickness d of the ceramic coatings deposited on the alloy could also be obtained. The details of the computation method have been presented in previous publications [49,53]. Hence, Δt and d could be obtained simultaneously with a single-step test, and β was recommended as a fast and effective criterion to evaluate the porosity in TBCs.

4. Conclusions

In this work, YSZ ceramic coatings were deposited with coarse and fine powders at different spray distances to obtain coating porosities in the range of 9.09% to 21.68%. Correspondingly, Monte Carlo simulations and the transmission THz time-domain spectroscopy were used to investigate the transitive relation and regularity between the dielectric parameters of the YSZ ceramic coatings and the broadening ratio of the THz pulse waveforms at different porosities. Simulation results showed that as the extinction coefficient and transmission distance increased, the total energy of photons was continually attenuated, and the broadening effect was enhanced. As the porosity increased, the refractive index n decreased, while the extinction coefficient α increased. Linear fitting analysis was performed by extracting the dielectric parameters, the minor porosity change between 9.09% and 14.40% could not be identified by the refractive index n. However, the slopes of each linear Eq. showed that the sensitivity of the extinction coefficient was approximately two orders of magnitude higher than the sensitivity of the refractive index. Linear fitting analysis of the relative broadening ratio of multiple transmissions at different porosities showed that as the transmission distances increased, scattering and dispersion accumulation and the porosity resolution increased, the linear fitting analyses based on experiment was in accordance with the results of simulation. Finally, not only was the sensitivity of the porosity estimation successfully reserved based on the relative broadening ratio, but the advantage of speed and convenience can be proved beneficial for the actual detection to improve efficiency. It is considered that THz NDT technology has provided a new, fast, and simple evaluation method for the detection of porous dielectric materials and the health monitoring of TBCs for the various forms of failure inspection owing to its nondestructive, noncontact, nonionizing, and rich feature information nature.

Funding

National Natural Science Foundation of China (51775189).

Acknowledgements

We thank the support from the Shanghai Key Laboratory of Modern Optical Systems and University of Shanghai for Science and Technology. We also thank OSA Publishing Language Editing Services (https://languageediting.osa.org) for its linguistic assistance during the preparation of this manuscript.

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4. S. Sampath, U. Schulz, M. O. Jarligo, and S. Kuroda, “Processing science of advanced thermal-barrier systems,” MRS Bull. 37(10), 903–910 (2012). [CrossRef]  

5. R. L. Jones, R. F. Reidy, and D. Mess, “Scandia, yttria-stabilized zirconia for thermal barrier coatings,” Surf. Coat. Technol. 82(1–2), 70–76 (1996). [CrossRef]  

6. X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018). [CrossRef]  

7. F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008). [CrossRef]  

8. S. Paul, “Assessing coating reliability through pore architecture evaluation,” J. Therm. Spray Technol. 19(4), 779–786 (2010). [CrossRef]  

9. N. Curry, N. Markocsan, X. H. Li, A. Tricoire, and M. Dorfman, “Next generation thermal barrier coatings for the gas turbine industry,” J. Therm. Spray Technol. 20(1–2), 108–115 (2011). [CrossRef]  

10. V. Teixeira, “Numerical analysis of the influence of coating porosity and substrate elastic properties on the residual stresses in high temperature graded coatings,” Surf. Coat. Technol. 146–147(2), 79–84 (2001). [CrossRef]  

11. P. Fauchais, M. Vardelle, and S. Goutier, “Latest researches advances of plasma spraying: From splat to coating formation,” J. Therm. Spray Technol. 25(8), 1534–1553 (2016). [CrossRef]  

12. M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017). [CrossRef]  

13. H. L. R. Chen, B. Zhang, M. A. Alvin, and Y. Lin, “Ultrasonic detection of delamination and material characterization of thermal barrier coatings,” J. Therm. Spray Technol. 21(6), 1184–1194 (2012). [CrossRef]  

14. A. I. Lavrentyev and S. I. Rokhlin, “An ultrasonic method for determination of elastic moduli, density, extinction and thickness of a polymer coating on a stiff plate,” Ultrasonics 39(3), 211–221 (2001). [CrossRef]  

15. Y. Zhao, L. Lin, X. Li, and M. Lei, “Simultaneous determination of the coating thickness and its longitudinal velocity by ultrasonic nondestructive method,” NDT&E Int. 43(7), 579–585 (2010). [CrossRef]  

16. S. Dixon, B. Lanyon, and G. Rowlands, “Coating thickness and elastic modulus measurement using ultrasonic bulk wave resonance,” Appl. Phys. Lett. 88(14), 141907 (2006). [CrossRef]  

17. A. N. Khan, S. Khan, F. Ali, and M. Iqbal, “Evaluation of ZrO2–24MgO ceramic coating by eddy current method,” Comput. Mater. Sci. 44(3), 1007–1012 (2009). [CrossRef]  

18. L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012). [CrossRef]  

19. D. Zhang, Y. Yu, C. Lai, and G. Tian, “Thickness measurement of multi-layer conductive coatings using multifrequency eddy current techniques,” Nondestr. Test. Eval. 31(3), 191–208 (2016). [CrossRef]  

20. B. Rogé, A. Fahr, J. Giguere, and K. McRae, “Nondestructive measurement of porosity in thermal barrier coatings,” J. Therm. Spray Technol. 12(4), 530–535 (2003). [CrossRef]  

21. J. I. Eldridge and T. J. Bencic, “Monitoring delamination of plasma-sprayed thermal barrier coatings by reflectance-enhanced luminescence,” Surf. Coat. Technol. 201(7), 3926–3930 (2006). [CrossRef]  

22. M. Gentleman and D. Clarke, “Concepts for luminescence sensing of thermal barrier coatings,” Surf. Coat. Technol. 188–189, 93–100 (2004). [CrossRef]  

23. J. I. Eldridge, J. Singh, and D. E. Wolfe, “Erosion-Indicating thermal barrier coatings using luminescent sublayers,” J. Am. Ceram. Soc. 89(10), 3252–3254 (2006). [CrossRef]  

24. I. Queralt, J. Ibañez, E. Marguí, and J. Pujol, “Thickness measurement of semiconductor thin films by energy dispersive X-ray fluorescence benchtop instrumentation: Application to GaN epilayers grown by molecular beam epitaxy,” Spectrochim. Acta, Part B 65(7), 583–586 (2010). [CrossRef]  

25. A. Carapelle, K. Fleury-Frenette, J.-P. Collette, H.-P. Garnir, and P. Harlet, “Portable x-ray fluorescence spectrometer for coating thickness measurement,” Rev. Sci. Instrum. 78(12), 123109 (2007). [CrossRef]  

26. R. Shrestha and W. Kim, “Evaluation of coating thickness by thermal wave imaging: A comparative study of pulsed and lock-in infrared thermography–Part II: Experimental investigation,” Infrared Phys. Technol. 92, 24–29 (2018). [CrossRef]  

27. M. Ferber, A. Wereszczak, M. Lance, J. Haynes, and M. Antelo, “Application of infrared imaging to the study of controlled failure of thermal barrier coatings,” Mater. Sci. 35(11), 2643–2651 (2000). [CrossRef]  

28. S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).

29. J. I. Eldridge, C. M. Spuckler, and R. E. Martin, “Monitoring delamination progression in thermal barrier coatings by mid-infrared reflectance imaging,” Int. J. Appl. Ceram. Technol. 3(2), 94–104 (2006). [CrossRef]  

30. C. Garnier, M. L. Pastor, F. Eyma, and B. Lorrain, “The detection of aeronautical defects in situ on composite structures using non destructive testing,” Compos. Struct. 93(5), 1328–1336 (2011). [CrossRef]  

31. E. Martin, C. Larato, A. Clément, and M. Saint-Paul, “Detection of delaminations in sub-wavelength thick multi-layered packages from the local temporal coherence of ultrasonic signals,” NDT&E Int. 41(4), 280–291 (2008). [CrossRef]  

32. Y. Li, B. Yan, W. Li, and D. Li, “Thickness assessment of thermal barrier coatings of aeroengine blades via dual-frequency eddy current evaluation,” IEEE Magn. Lett. 7, 1–5 (2016). [CrossRef]  

33. H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015). [CrossRef]  

34. W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014). [CrossRef]  

35. E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017). [CrossRef]  

36. A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016). [CrossRef]  

37. M. Kolbe, B. Beckhoff, M. Krumrey, and G. Ulm, “Thickness determination for Cu and Ni nanolayers: Comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis and X-ray reflectometry,” Spectrochim. Acta, Part B 60(4), 505–510 (2005). [CrossRef]  

38. C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016). [CrossRef]  

39. V. P. Vavilov and D. D. Burleigh, “Review of pulsed thermal NDT: Physical principles, theory and data processing,” NDT&E Int. 73, 28–52 (2015). [CrossRef]  

40. R. Shrestha and W. Kim, “Modelling of pulse thermography for defect detection in aluminium structures: Assessment on reflection and transmission measurement,” W. J. Mod. & Simul. 13(1), 45–51 (2017).

41. J. Y. Zhang, X. B. Meng, and Y. C. Ma, “A new measurement method of coatings thickness based on lock-in thermography,” Infrared Phys. Technol. 76, 655–660 (2016). [CrossRef]  

42. S. Zhong, “Progress in terahertz nondestructive testing: A review,” Front. Mech. Eng. 14(3), 273–281 (2019). [CrossRef]  

43. S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017). [CrossRef]  

44. C. H. Ryu, S. H. Park, D. H. Kim, K. Y. Jhang, and H. S. Kim, “Nondestructive evaluation of hidden multi-delamination in a glass-fiber-reinforced plastic composite using terahertz spectroscopy,” Compos. Struct. 156, 338–347 (2016). [CrossRef]  

45. D. H. Kim, C. H. Ryu, S. H. Park, and H. S. Kim, “Nondestructive evaluation of hidden damages in glass fiber reinforced plastic by using the terahertz spectroscopy,” Int. J. Precis. Eng. Manuf. Green Technol. 4(2), 211–219 (2017). [CrossRef]  

46. S. H. Park, J. W. Jang, and H. S. Kim, “Non-destructive evaluation of the hidden voids in integrated circuit packages using terahertz time-domain spectroscopy,” J. Micromech. Microeng. 25(9), 095007 (2015). [CrossRef]  

47. H. Lin, Y. Dong, Y. Shen, and J. A. Zeitler, “Quantifying pharmaceutical film coating with optical coherence tomography and terahertz pulsed imaging: an evaluation,” J. Pharm. Sci. 104(10), 3377–3385 (2015). [CrossRef]  

48. D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018). [CrossRef]  

49. T. Fukuchi, N. Fuse, M. Okada, T. Fujii, M. Mizuno, and K. Fukunaga, “Measurement of refractive index and thickness of topcoat of thermal barrier coating by reflection measurement of terahertz waves,” Electron. Commun. Jpn. 96(12), 37–45 (2013). [CrossRef]  

50. T. Fukuchi, N. Fuse, T. Fujii, M. Okada, K. Fukunaga, and M. Mizuno, “Measurement of topcoat thickness of thermal barrier coating for gas turbines using terahertz waves,” Elect. Eng. Jpn. 183(4), 1–9 (2013). [CrossRef]  

51. T. Fukuchi, N. Fuse, M. Okada, T. Ozeki, T. Fujii, M. Mizuno, and K. Fukunaga, “Topcoat thickness measurement of thermal barrier coating of gas turbine blade using terahertz wave,” Elect. Eng. Jpn. 189(1), 1–8 (2014). [CrossRef]  

52. C. C. Chen, D. J. Lee, T. Pollock, and J. F. Whitaker, “Pulsed-terahertz reflectometry for health monitoring of ceramic thermal barrier coatings,” Opt. Express 18(4), 3477–3486 (2010). [CrossRef]  

53. D. Ye, W. Wang, J. Huang, X. Lu, and H. Zhou, “Nondestructive interface morphology characterization of thermal barrier coatings using terahertz time-domain spectroscopy,” Coatings 9(2), 89 (2019). [CrossRef]  

54. M. Watanabe, S. Kuroda, H. Yamawaki, and M. Shiwa, “Terahertz dielectric properties of plasma-sprayed thermal-barrier coatings,” Surf. Coat. Technol. 205(19), 4620–4626 (2011). [CrossRef]  

55. S. L. Jacques, “Monte Carlo modeling of light transport in tissue (steady state and time of flight),” in Optical-thermal response of laser-irradiated tissue (Springer, 2010).

56. Y. M. Zhou, K. Q. Wu, J. L. Chen, Z. S. Wang, and H. H. Jiang, “Monte Carlo simulation of time-domain broadening of laser pulse propagating underwater,” Laser & Infrared 41(3), 10015078 (2011).

57. J. Zhu and Z. Liu, “Dielectric properties of YSZ high-k thin films fabricated at low temperature by pulsed laser deposition,” Mater. Lett. 57(26–27), 4297–4301 (2003). [CrossRef]  

58. D. Fork, D. Fenner, G. Connell, J. M. Phillips, and T. Geballe, “Epitaxial yttria-stabilized zirconia on hydrogen-terminated Si by pulsed laser deposition,” Appl. Phys. Lett. 57(11), 1137–1139 (1990). [CrossRef]  

59. J. R. Frisvad, “Importance sampling the Rayleigh phase function,” J. Opt. Soc. Am. A 28(12), 2436–2441 (2011). [CrossRef]  

60. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18(7), 1562–1571 (2001). [CrossRef]  

61. L. Duvillaret, F. Garet, and J. L. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38(2), 409–415 (1999). [CrossRef]  

62. L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996). [CrossRef]  

63. K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015). [CrossRef]  

64. Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015). [CrossRef]  

65. K. E. Peiponen, A. Zeitler, and M. Kuwata-Gonokami, Terahertz Spectroscopy and Imaging (Springer, 2012), Chap. 8.

66. U. Schulz, M. Peters, F.-W. Bach, and G. Tegeder, “Graded coatings for thermal, wear and corrosion barriers,” Mater. Sci. Eng., A 362(1–2), 61–80 (2003). [CrossRef]  

References

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    [Crossref]
  5. R. L. Jones, R. F. Reidy, and D. Mess, “Scandia, yttria-stabilized zirconia for thermal barrier coatings,” Surf. Coat. Technol. 82(1–2), 70–76 (1996).
    [Crossref]
  6. X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
    [Crossref]
  7. F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008).
    [Crossref]
  8. S. Paul, “Assessing coating reliability through pore architecture evaluation,” J. Therm. Spray Technol. 19(4), 779–786 (2010).
    [Crossref]
  9. N. Curry, N. Markocsan, X. H. Li, A. Tricoire, and M. Dorfman, “Next generation thermal barrier coatings for the gas turbine industry,” J. Therm. Spray Technol. 20(1–2), 108–115 (2011).
    [Crossref]
  10. V. Teixeira, “Numerical analysis of the influence of coating porosity and substrate elastic properties on the residual stresses in high temperature graded coatings,” Surf. Coat. Technol. 146–147(2), 79–84 (2001).
    [Crossref]
  11. P. Fauchais, M. Vardelle, and S. Goutier, “Latest researches advances of plasma spraying: From splat to coating formation,” J. Therm. Spray Technol. 25(8), 1534–1553 (2016).
    [Crossref]
  12. M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017).
    [Crossref]
  13. H. L. R. Chen, B. Zhang, M. A. Alvin, and Y. Lin, “Ultrasonic detection of delamination and material characterization of thermal barrier coatings,” J. Therm. Spray Technol. 21(6), 1184–1194 (2012).
    [Crossref]
  14. A. I. Lavrentyev and S. I. Rokhlin, “An ultrasonic method for determination of elastic moduli, density, extinction and thickness of a polymer coating on a stiff plate,” Ultrasonics 39(3), 211–221 (2001).
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  15. Y. Zhao, L. Lin, X. Li, and M. Lei, “Simultaneous determination of the coating thickness and its longitudinal velocity by ultrasonic nondestructive method,” NDT&E Int. 43(7), 579–585 (2010).
    [Crossref]
  16. S. Dixon, B. Lanyon, and G. Rowlands, “Coating thickness and elastic modulus measurement using ultrasonic bulk wave resonance,” Appl. Phys. Lett. 88(14), 141907 (2006).
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  17. A. N. Khan, S. Khan, F. Ali, and M. Iqbal, “Evaluation of ZrO2–24MgO ceramic coating by eddy current method,” Comput. Mater. Sci. 44(3), 1007–1012 (2009).
    [Crossref]
  18. L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012).
    [Crossref]
  19. D. Zhang, Y. Yu, C. Lai, and G. Tian, “Thickness measurement of multi-layer conductive coatings using multifrequency eddy current techniques,” Nondestr. Test. Eval. 31(3), 191–208 (2016).
    [Crossref]
  20. B. Rogé, A. Fahr, J. Giguere, and K. McRae, “Nondestructive measurement of porosity in thermal barrier coatings,” J. Therm. Spray Technol. 12(4), 530–535 (2003).
    [Crossref]
  21. J. I. Eldridge and T. J. Bencic, “Monitoring delamination of plasma-sprayed thermal barrier coatings by reflectance-enhanced luminescence,” Surf. Coat. Technol. 201(7), 3926–3930 (2006).
    [Crossref]
  22. M. Gentleman and D. Clarke, “Concepts for luminescence sensing of thermal barrier coatings,” Surf. Coat. Technol. 188–189, 93–100 (2004).
    [Crossref]
  23. J. I. Eldridge, J. Singh, and D. E. Wolfe, “Erosion-Indicating thermal barrier coatings using luminescent sublayers,” J. Am. Ceram. Soc. 89(10), 3252–3254 (2006).
    [Crossref]
  24. I. Queralt, J. Ibañez, E. Marguí, and J. Pujol, “Thickness measurement of semiconductor thin films by energy dispersive X-ray fluorescence benchtop instrumentation: Application to GaN epilayers grown by molecular beam epitaxy,” Spectrochim. Acta, Part B 65(7), 583–586 (2010).
    [Crossref]
  25. A. Carapelle, K. Fleury-Frenette, J.-P. Collette, H.-P. Garnir, and P. Harlet, “Portable x-ray fluorescence spectrometer for coating thickness measurement,” Rev. Sci. Instrum. 78(12), 123109 (2007).
    [Crossref]
  26. R. Shrestha and W. Kim, “Evaluation of coating thickness by thermal wave imaging: A comparative study of pulsed and lock-in infrared thermography–Part II: Experimental investigation,” Infrared Phys. Technol. 92, 24–29 (2018).
    [Crossref]
  27. M. Ferber, A. Wereszczak, M. Lance, J. Haynes, and M. Antelo, “Application of infrared imaging to the study of controlled failure of thermal barrier coatings,” Mater. Sci. 35(11), 2643–2651 (2000).
    [Crossref]
  28. S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).
  29. J. I. Eldridge, C. M. Spuckler, and R. E. Martin, “Monitoring delamination progression in thermal barrier coatings by mid-infrared reflectance imaging,” Int. J. Appl. Ceram. Technol. 3(2), 94–104 (2006).
    [Crossref]
  30. C. Garnier, M. L. Pastor, F. Eyma, and B. Lorrain, “The detection of aeronautical defects in situ on composite structures using non destructive testing,” Compos. Struct. 93(5), 1328–1336 (2011).
    [Crossref]
  31. E. Martin, C. Larato, A. Clément, and M. Saint-Paul, “Detection of delaminations in sub-wavelength thick multi-layered packages from the local temporal coherence of ultrasonic signals,” NDT&E Int. 41(4), 280–291 (2008).
    [Crossref]
  32. Y. Li, B. Yan, W. Li, and D. Li, “Thickness assessment of thermal barrier coatings of aeroengine blades via dual-frequency eddy current evaluation,” IEEE Magn. Lett. 7, 1–5 (2016).
    [Crossref]
  33. H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015).
    [Crossref]
  34. W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014).
    [Crossref]
  35. E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017).
    [Crossref]
  36. A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016).
    [Crossref]
  37. M. Kolbe, B. Beckhoff, M. Krumrey, and G. Ulm, “Thickness determination for Cu and Ni nanolayers: Comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis and X-ray reflectometry,” Spectrochim. Acta, Part B 60(4), 505–510 (2005).
    [Crossref]
  38. C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
    [Crossref]
  39. V. P. Vavilov and D. D. Burleigh, “Review of pulsed thermal NDT: Physical principles, theory and data processing,” NDT&E Int. 73, 28–52 (2015).
    [Crossref]
  40. R. Shrestha and W. Kim, “Modelling of pulse thermography for defect detection in aluminium structures: Assessment on reflection and transmission measurement,” W. J. Mod. & Simul. 13(1), 45–51 (2017).
  41. J. Y. Zhang, X. B. Meng, and Y. C. Ma, “A new measurement method of coatings thickness based on lock-in thermography,” Infrared Phys. Technol. 76, 655–660 (2016).
    [Crossref]
  42. S. Zhong, “Progress in terahertz nondestructive testing: A review,” Front. Mech. Eng. 14(3), 273–281 (2019).
    [Crossref]
  43. S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
    [Crossref]
  44. C. H. Ryu, S. H. Park, D. H. Kim, K. Y. Jhang, and H. S. Kim, “Nondestructive evaluation of hidden multi-delamination in a glass-fiber-reinforced plastic composite using terahertz spectroscopy,” Compos. Struct. 156, 338–347 (2016).
    [Crossref]
  45. D. H. Kim, C. H. Ryu, S. H. Park, and H. S. Kim, “Nondestructive evaluation of hidden damages in glass fiber reinforced plastic by using the terahertz spectroscopy,” Int. J. Precis. Eng. Manuf. Green Technol. 4(2), 211–219 (2017).
    [Crossref]
  46. S. H. Park, J. W. Jang, and H. S. Kim, “Non-destructive evaluation of the hidden voids in integrated circuit packages using terahertz time-domain spectroscopy,” J. Micromech. Microeng. 25(9), 095007 (2015).
    [Crossref]
  47. H. Lin, Y. Dong, Y. Shen, and J. A. Zeitler, “Quantifying pharmaceutical film coating with optical coherence tomography and terahertz pulsed imaging: an evaluation,” J. Pharm. Sci. 104(10), 3377–3385 (2015).
    [Crossref]
  48. D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
    [Crossref]
  49. T. Fukuchi, N. Fuse, M. Okada, T. Fujii, M. Mizuno, and K. Fukunaga, “Measurement of refractive index and thickness of topcoat of thermal barrier coating by reflection measurement of terahertz waves,” Electron. Commun. Jpn. 96(12), 37–45 (2013).
    [Crossref]
  50. T. Fukuchi, N. Fuse, T. Fujii, M. Okada, K. Fukunaga, and M. Mizuno, “Measurement of topcoat thickness of thermal barrier coating for gas turbines using terahertz waves,” Elect. Eng. Jpn. 183(4), 1–9 (2013).
    [Crossref]
  51. T. Fukuchi, N. Fuse, M. Okada, T. Ozeki, T. Fujii, M. Mizuno, and K. Fukunaga, “Topcoat thickness measurement of thermal barrier coating of gas turbine blade using terahertz wave,” Elect. Eng. Jpn. 189(1), 1–8 (2014).
    [Crossref]
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2019 (2)

S. Zhong, “Progress in terahertz nondestructive testing: A review,” Front. Mech. Eng. 14(3), 273–281 (2019).
[Crossref]

D. Ye, W. Wang, J. Huang, X. Lu, and H. Zhou, “Nondestructive interface morphology characterization of thermal barrier coatings using terahertz time-domain spectroscopy,” Coatings 9(2), 89 (2019).
[Crossref]

2018 (3)

D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
[Crossref]

X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
[Crossref]

R. Shrestha and W. Kim, “Evaluation of coating thickness by thermal wave imaging: A comparative study of pulsed and lock-in infrared thermography–Part II: Experimental investigation,” Infrared Phys. Technol. 92, 24–29 (2018).
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2017 (5)

M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017).
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D. H. Kim, C. H. Ryu, S. H. Park, and H. S. Kim, “Nondestructive evaluation of hidden damages in glass fiber reinforced plastic by using the terahertz spectroscopy,” Int. J. Precis. Eng. Manuf. Green Technol. 4(2), 211–219 (2017).
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S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

R. Shrestha and W. Kim, “Modelling of pulse thermography for defect detection in aluminium structures: Assessment on reflection and transmission measurement,” W. J. Mod. & Simul. 13(1), 45–51 (2017).

E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017).
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2016 (7)

A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016).
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C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
[Crossref]

J. Y. Zhang, X. B. Meng, and Y. C. Ma, “A new measurement method of coatings thickness based on lock-in thermography,” Infrared Phys. Technol. 76, 655–660 (2016).
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C. H. Ryu, S. H. Park, D. H. Kim, K. Y. Jhang, and H. S. Kim, “Nondestructive evaluation of hidden multi-delamination in a glass-fiber-reinforced plastic composite using terahertz spectroscopy,” Compos. Struct. 156, 338–347 (2016).
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P. Fauchais, M. Vardelle, and S. Goutier, “Latest researches advances of plasma spraying: From splat to coating formation,” J. Therm. Spray Technol. 25(8), 1534–1553 (2016).
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Y. Li, B. Yan, W. Li, and D. Li, “Thickness assessment of thermal barrier coatings of aeroengine blades via dual-frequency eddy current evaluation,” IEEE Magn. Lett. 7, 1–5 (2016).
[Crossref]

D. Zhang, Y. Yu, C. Lai, and G. Tian, “Thickness measurement of multi-layer conductive coatings using multifrequency eddy current techniques,” Nondestr. Test. Eval. 31(3), 191–208 (2016).
[Crossref]

2015 (6)

H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015).
[Crossref]

V. P. Vavilov and D. D. Burleigh, “Review of pulsed thermal NDT: Physical principles, theory and data processing,” NDT&E Int. 73, 28–52 (2015).
[Crossref]

S. H. Park, J. W. Jang, and H. S. Kim, “Non-destructive evaluation of the hidden voids in integrated circuit packages using terahertz time-domain spectroscopy,” J. Micromech. Microeng. 25(9), 095007 (2015).
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H. Lin, Y. Dong, Y. Shen, and J. A. Zeitler, “Quantifying pharmaceutical film coating with optical coherence tomography and terahertz pulsed imaging: an evaluation,” J. Pharm. Sci. 104(10), 3377–3385 (2015).
[Crossref]

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
[Crossref]

Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015).
[Crossref]

2014 (2)

T. Fukuchi, N. Fuse, M. Okada, T. Ozeki, T. Fujii, M. Mizuno, and K. Fukunaga, “Topcoat thickness measurement of thermal barrier coating of gas turbine blade using terahertz wave,” Elect. Eng. Jpn. 189(1), 1–8 (2014).
[Crossref]

W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014).
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2013 (2)

T. Fukuchi, N. Fuse, M. Okada, T. Fujii, M. Mizuno, and K. Fukunaga, “Measurement of refractive index and thickness of topcoat of thermal barrier coating by reflection measurement of terahertz waves,” Electron. Commun. Jpn. 96(12), 37–45 (2013).
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T. Fukuchi, N. Fuse, T. Fujii, M. Okada, K. Fukunaga, and M. Mizuno, “Measurement of topcoat thickness of thermal barrier coating for gas turbines using terahertz waves,” Elect. Eng. Jpn. 183(4), 1–9 (2013).
[Crossref]

2012 (3)

L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012).
[Crossref]

H. L. R. Chen, B. Zhang, M. A. Alvin, and Y. Lin, “Ultrasonic detection of delamination and material characterization of thermal barrier coatings,” J. Therm. Spray Technol. 21(6), 1184–1194 (2012).
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S. Sampath, U. Schulz, M. O. Jarligo, and S. Kuroda, “Processing science of advanced thermal-barrier systems,” MRS Bull. 37(10), 903–910 (2012).
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2011 (5)

N. Curry, N. Markocsan, X. H. Li, A. Tricoire, and M. Dorfman, “Next generation thermal barrier coatings for the gas turbine industry,” J. Therm. Spray Technol. 20(1–2), 108–115 (2011).
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C. Garnier, M. L. Pastor, F. Eyma, and B. Lorrain, “The detection of aeronautical defects in situ on composite structures using non destructive testing,” Compos. Struct. 93(5), 1328–1336 (2011).
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M. Watanabe, S. Kuroda, H. Yamawaki, and M. Shiwa, “Terahertz dielectric properties of plasma-sprayed thermal-barrier coatings,” Surf. Coat. Technol. 205(19), 4620–4626 (2011).
[Crossref]

Y. M. Zhou, K. Q. Wu, J. L. Chen, Z. S. Wang, and H. H. Jiang, “Monte Carlo simulation of time-domain broadening of laser pulse propagating underwater,” Laser & Infrared 41(3) (2011).

J. R. Frisvad, “Importance sampling the Rayleigh phase function,” J. Opt. Soc. Am. A 28(12), 2436–2441 (2011).
[Crossref]

2010 (4)

C. C. Chen, D. J. Lee, T. Pollock, and J. F. Whitaker, “Pulsed-terahertz reflectometry for health monitoring of ceramic thermal barrier coatings,” Opt. Express 18(4), 3477–3486 (2010).
[Crossref]

I. Queralt, J. Ibañez, E. Marguí, and J. Pujol, “Thickness measurement of semiconductor thin films by energy dispersive X-ray fluorescence benchtop instrumentation: Application to GaN epilayers grown by molecular beam epitaxy,” Spectrochim. Acta, Part B 65(7), 583–586 (2010).
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Y. Zhao, L. Lin, X. Li, and M. Lei, “Simultaneous determination of the coating thickness and its longitudinal velocity by ultrasonic nondestructive method,” NDT&E Int. 43(7), 579–585 (2010).
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S. Paul, “Assessing coating reliability through pore architecture evaluation,” J. Therm. Spray Technol. 19(4), 779–786 (2010).
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2009 (1)

A. N. Khan, S. Khan, F. Ali, and M. Iqbal, “Evaluation of ZrO2–24MgO ceramic coating by eddy current method,” Comput. Mater. Sci. 44(3), 1007–1012 (2009).
[Crossref]

2008 (2)

F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008).
[Crossref]

E. Martin, C. Larato, A. Clément, and M. Saint-Paul, “Detection of delaminations in sub-wavelength thick multi-layered packages from the local temporal coherence of ultrasonic signals,” NDT&E Int. 41(4), 280–291 (2008).
[Crossref]

2007 (1)

A. Carapelle, K. Fleury-Frenette, J.-P. Collette, H.-P. Garnir, and P. Harlet, “Portable x-ray fluorescence spectrometer for coating thickness measurement,” Rev. Sci. Instrum. 78(12), 123109 (2007).
[Crossref]

2006 (4)

J. I. Eldridge, J. Singh, and D. E. Wolfe, “Erosion-Indicating thermal barrier coatings using luminescent sublayers,” J. Am. Ceram. Soc. 89(10), 3252–3254 (2006).
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J. I. Eldridge and T. J. Bencic, “Monitoring delamination of plasma-sprayed thermal barrier coatings by reflectance-enhanced luminescence,” Surf. Coat. Technol. 201(7), 3926–3930 (2006).
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J. I. Eldridge, C. M. Spuckler, and R. E. Martin, “Monitoring delamination progression in thermal barrier coatings by mid-infrared reflectance imaging,” Int. J. Appl. Ceram. Technol. 3(2), 94–104 (2006).
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S. Dixon, B. Lanyon, and G. Rowlands, “Coating thickness and elastic modulus measurement using ultrasonic bulk wave resonance,” Appl. Phys. Lett. 88(14), 141907 (2006).
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2005 (2)

D. R. Clarke and S. R. Phillpot, “Thermal barrier coating materials,” Mater. Today 8(6), 22–29 (2005).
[Crossref]

M. Kolbe, B. Beckhoff, M. Krumrey, and G. Ulm, “Thickness determination for Cu and Ni nanolayers: Comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis and X-ray reflectometry,” Spectrochim. Acta, Part B 60(4), 505–510 (2005).
[Crossref]

2004 (1)

M. Gentleman and D. Clarke, “Concepts for luminescence sensing of thermal barrier coatings,” Surf. Coat. Technol. 188–189, 93–100 (2004).
[Crossref]

2003 (5)

B. Rogé, A. Fahr, J. Giguere, and K. McRae, “Nondestructive measurement of porosity in thermal barrier coatings,” J. Therm. Spray Technol. 12(4), 530–535 (2003).
[Crossref]

S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).

D. R. Clarke and C. G. Levi, “Materials design for the next generation thermal barrier coatings,” Annu. Rev. Mater. Sci. 33(1), 383–417 (2003).
[Crossref]

J. Zhu and Z. Liu, “Dielectric properties of YSZ high-k thin films fabricated at low temperature by pulsed laser deposition,” Mater. Lett. 57(26–27), 4297–4301 (2003).
[Crossref]

U. Schulz, M. Peters, F.-W. Bach, and G. Tegeder, “Graded coatings for thermal, wear and corrosion barriers,” Mater. Sci. Eng., A 362(1–2), 61–80 (2003).
[Crossref]

2002 (1)

N. P. Padture, M. Gell, and E. H. Jordan, “Thermal barrier coatings for gas-turbine engine applications,” Science 296(5566), 280–284 (2002).
[Crossref]

2001 (3)

V. Teixeira, “Numerical analysis of the influence of coating porosity and substrate elastic properties on the residual stresses in high temperature graded coatings,” Surf. Coat. Technol. 146–147(2), 79–84 (2001).
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A. I. Lavrentyev and S. I. Rokhlin, “An ultrasonic method for determination of elastic moduli, density, extinction and thickness of a polymer coating on a stiff plate,” Ultrasonics 39(3), 211–221 (2001).
[Crossref]

T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18(7), 1562–1571 (2001).
[Crossref]

2000 (1)

M. Ferber, A. Wereszczak, M. Lance, J. Haynes, and M. Antelo, “Application of infrared imaging to the study of controlled failure of thermal barrier coatings,” Mater. Sci. 35(11), 2643–2651 (2000).
[Crossref]

1999 (1)

1996 (2)

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
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R. L. Jones, R. F. Reidy, and D. Mess, “Scandia, yttria-stabilized zirconia for thermal barrier coatings,” Surf. Coat. Technol. 82(1–2), 70–76 (1996).
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1990 (1)

D. Fork, D. Fenner, G. Connell, J. M. Phillips, and T. Geballe, “Epitaxial yttria-stabilized zirconia on hydrogen-terminated Si by pulsed laser deposition,” Appl. Phys. Lett. 57(11), 1137–1139 (1990).
[Crossref]

Ali, F.

A. N. Khan, S. Khan, F. Ali, and M. Iqbal, “Evaluation of ZrO2–24MgO ceramic coating by eddy current method,” Comput. Mater. Sci. 44(3), 1007–1012 (2009).
[Crossref]

Alvin, M. A.

H. L. R. Chen, B. Zhang, M. A. Alvin, and Y. Lin, “Ultrasonic detection of delamination and material characterization of thermal barrier coatings,” J. Therm. Spray Technol. 21(6), 1184–1194 (2012).
[Crossref]

Amiel, S.

E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017).
[Crossref]

Antelo, M.

M. Ferber, A. Wereszczak, M. Lance, J. Haynes, and M. Antelo, “Application of infrared imaging to the study of controlled failure of thermal barrier coatings,” Mater. Sci. 35(11), 2643–2651 (2000).
[Crossref]

Bach, F.-W.

U. Schulz, M. Peters, F.-W. Bach, and G. Tegeder, “Graded coatings for thermal, wear and corrosion barriers,” Mater. Sci. Eng., A 362(1–2), 61–80 (2003).
[Crossref]

Bai, Y.

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
[Crossref]

Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015).
[Crossref]

Baraniuk, R. G.

Bardl, G.

H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015).
[Crossref]

Bawuah, P.

D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
[Crossref]

Beckhoff, B.

M. Kolbe, B. Beckhoff, M. Krumrey, and G. Ulm, “Thickness determination for Cu and Ni nanolayers: Comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis and X-ray reflectometry,” Spectrochim. Acta, Part B 60(4), 505–510 (2005).
[Crossref]

Bencic, T. J.

J. I. Eldridge and T. J. Bencic, “Monitoring delamination of plasma-sprayed thermal barrier coatings by reflectance-enhanced luminescence,” Surf. Coat. Technol. 201(7), 3926–3930 (2006).
[Crossref]

Bison, P.

S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).

Bison, P. G.

F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008).
[Crossref]

Booske, J.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Bøtker, J.

D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
[Crossref]

Bu, C.

C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
[Crossref]

Burleigh, D. D.

V. P. Vavilov and D. D. Burleigh, “Review of pulsed thermal NDT: Physical principles, theory and data processing,” NDT&E Int. 73, 28–52 (2015).
[Crossref]

Carapelle, A.

A. Carapelle, K. Fleury-Frenette, J.-P. Collette, H.-P. Garnir, and P. Harlet, “Portable x-ray fluorescence spectrometer for coating thickness measurement,” Rev. Sci. Instrum. 78(12), 123109 (2007).
[Crossref]

Carr, J.

X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
[Crossref]

Cernuschi, F.

F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008).
[Crossref]

S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).

Chen, C. C.

Chen, H. L. R.

H. L. R. Chen, B. Zhang, M. A. Alvin, and Y. Lin, “Ultrasonic detection of delamination and material characterization of thermal barrier coatings,” J. Therm. Spray Technol. 21(6), 1184–1194 (2012).
[Crossref]

Chen, J. L.

Y. M. Zhou, K. Q. Wu, J. L. Chen, Z. S. Wang, and H. H. Jiang, “Monte Carlo simulation of time-domain broadening of laser pulse propagating underwater,” Laser & Infrared 41(3) (2011).

Chen, Z.

L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012).
[Crossref]

Cherif, C.

H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015).
[Crossref]

Clarke, D.

M. Gentleman and D. Clarke, “Concepts for luminescence sensing of thermal barrier coatings,” Surf. Coat. Technol. 188–189, 93–100 (2004).
[Crossref]

Clarke, D. R.

D. R. Clarke and S. R. Phillpot, “Thermal barrier coating materials,” Mater. Today 8(6), 22–29 (2005).
[Crossref]

D. R. Clarke and C. G. Levi, “Materials design for the next generation thermal barrier coatings,” Annu. Rev. Mater. Sci. 33(1), 383–417 (2003).
[Crossref]

Clément, A.

E. Martin, C. Larato, A. Clément, and M. Saint-Paul, “Detection of delaminations in sub-wavelength thick multi-layered packages from the local temporal coherence of ultrasonic signals,” NDT&E Int. 41(4), 280–291 (2008).
[Crossref]

Collette, J.-P.

A. Carapelle, K. Fleury-Frenette, J.-P. Collette, H.-P. Garnir, and P. Harlet, “Portable x-ray fluorescence spectrometer for coating thickness measurement,” Rev. Sci. Instrum. 78(12), 123109 (2007).
[Crossref]

Connell, G.

D. Fork, D. Fenner, G. Connell, J. M. Phillips, and T. Geballe, “Epitaxial yttria-stabilized zirconia on hydrogen-terminated Si by pulsed laser deposition,” Appl. Phys. Lett. 57(11), 1137–1139 (1990).
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S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
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Liu, K.

Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015).
[Crossref]

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
[Crossref]

Liu, Y.

C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
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C. Garnier, M. L. Pastor, F. Eyma, and B. Lorrain, “The detection of aeronautical defects in situ on composite structures using non destructive testing,” Compos. Struct. 93(5), 1328–1336 (2011).
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Lours, P.

E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017).
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Lu, X.

D. Ye, W. Wang, J. Huang, X. Lu, and H. Zhou, “Nondestructive interface morphology characterization of thermal barrier coatings using terahertz time-domain spectroscopy,” Coatings 9(2), 89 (2019).
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J. Y. Zhang, X. B. Meng, and Y. C. Ma, “A new measurement method of coatings thickness based on lock-in thermography,” Infrared Phys. Technol. 76, 655–660 (2016).
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L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012).
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I. Queralt, J. Ibañez, E. Marguí, and J. Pujol, “Thickness measurement of semiconductor thin films by energy dispersive X-ray fluorescence benchtop instrumentation: Application to GaN epilayers grown by molecular beam epitaxy,” Spectrochim. Acta, Part B 65(7), 583–586 (2010).
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S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).

Marinetti, S. S.

F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008).
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D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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N. Curry, N. Markocsan, X. H. Li, A. Tricoire, and M. Dorfman, “Next generation thermal barrier coatings for the gas turbine industry,” J. Therm. Spray Technol. 20(1–2), 108–115 (2011).
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E. Martin, C. Larato, A. Clément, and M. Saint-Paul, “Detection of delaminations in sub-wavelength thick multi-layered packages from the local temporal coherence of ultrasonic signals,” NDT&E Int. 41(4), 280–291 (2008).
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Martin, R. E.

J. I. Eldridge, C. M. Spuckler, and R. E. Martin, “Monitoring delamination progression in thermal barrier coatings by mid-infrared reflectance imaging,” Int. J. Appl. Ceram. Technol. 3(2), 94–104 (2006).
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Massol, X.

E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017).
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Mauer, G.

M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017).
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B. Rogé, A. Fahr, J. Giguere, and K. McRae, “Nondestructive measurement of porosity in thermal barrier coatings,” J. Therm. Spray Technol. 12(4), 530–535 (2003).
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Mei, C.

C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
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Meng, X. B.

J. Y. Zhang, X. B. Meng, and Y. C. Ma, “A new measurement method of coatings thickness based on lock-in thermography,” Infrared Phys. Technol. 76, 655–660 (2016).
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Mess, D.

R. L. Jones, R. F. Reidy, and D. Mess, “Scandia, yttria-stabilized zirconia for thermal barrier coatings,” Surf. Coat. Technol. 82(1–2), 70–76 (1996).
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Mittleman, D. M.

Mizuno, M.

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T. Fukuchi, N. Fuse, T. Fujii, M. Okada, K. Fukunaga, and M. Mizuno, “Measurement of topcoat thickness of thermal barrier coating for gas turbines using terahertz waves,” Elect. Eng. Jpn. 183(4), 1–9 (2013).
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M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017).
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M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017).
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A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016).
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H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015).
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Okada, M.

T. Fukuchi, N. Fuse, M. Okada, T. Ozeki, T. Fujii, M. Mizuno, and K. Fukunaga, “Topcoat thickness measurement of thermal barrier coating of gas turbine blade using terahertz wave,” Elect. Eng. Jpn. 189(1), 1–8 (2014).
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T. Fukuchi, N. Fuse, T. Fujii, M. Okada, K. Fukunaga, and M. Mizuno, “Measurement of topcoat thickness of thermal barrier coating for gas turbines using terahertz waves,” Elect. Eng. Jpn. 183(4), 1–9 (2013).
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T. Fukuchi, N. Fuse, M. Okada, T. Fujii, M. Mizuno, and K. Fukunaga, “Measurement of refractive index and thickness of topcoat of thermal barrier coating by reflection measurement of terahertz waves,” Electron. Commun. Jpn. 96(12), 37–45 (2013).
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Ozeki, T.

T. Fukuchi, N. Fuse, M. Okada, T. Ozeki, T. Fujii, M. Mizuno, and K. Fukunaga, “Topcoat thickness measurement of thermal barrier coating of gas turbine blade using terahertz wave,” Elect. Eng. Jpn. 189(1), 1–8 (2014).
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D. H. Kim, C. H. Ryu, S. H. Park, and H. S. Kim, “Nondestructive evaluation of hidden damages in glass fiber reinforced plastic by using the terahertz spectroscopy,” Int. J. Precis. Eng. Manuf. Green Technol. 4(2), 211–219 (2017).
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C. H. Ryu, S. H. Park, D. H. Kim, K. Y. Jhang, and H. S. Kim, “Nondestructive evaluation of hidden multi-delamination in a glass-fiber-reinforced plastic composite using terahertz spectroscopy,” Compos. Struct. 156, 338–347 (2016).
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S. H. Park, J. W. Jang, and H. S. Kim, “Non-destructive evaluation of the hidden voids in integrated circuit packages using terahertz time-domain spectroscopy,” J. Micromech. Microeng. 25(9), 095007 (2015).
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D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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U. Schulz, M. Peters, F.-W. Bach, and G. Tegeder, “Graded coatings for thermal, wear and corrosion barriers,” Mater. Sci. Eng., A 362(1–2), 61–80 (2003).
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Pujol, J.

I. Queralt, J. Ibañez, E. Marguí, and J. Pujol, “Thickness measurement of semiconductor thin films by energy dispersive X-ray fluorescence benchtop instrumentation: Application to GaN epilayers grown by molecular beam epitaxy,” Spectrochim. Acta, Part B 65(7), 583–586 (2010).
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Qu, Y.

Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015).
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I. Queralt, J. Ibañez, E. Marguí, and J. Pujol, “Thickness measurement of semiconductor thin films by energy dispersive X-ray fluorescence benchtop instrumentation: Application to GaN epilayers grown by molecular beam epitaxy,” Spectrochim. Acta, Part B 65(7), 583–586 (2010).
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D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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R. L. Jones, R. F. Reidy, and D. Mess, “Scandia, yttria-stabilized zirconia for thermal barrier coatings,” Surf. Coat. Technol. 82(1–2), 70–76 (1996).
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D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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B. Rogé, A. Fahr, J. Giguere, and K. McRae, “Nondestructive measurement of porosity in thermal barrier coatings,” J. Therm. Spray Technol. 12(4), 530–535 (2003).
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D. H. Kim, C. H. Ryu, S. H. Park, and H. S. Kim, “Nondestructive evaluation of hidden damages in glass fiber reinforced plastic by using the terahertz spectroscopy,” Int. J. Precis. Eng. Manuf. Green Technol. 4(2), 211–219 (2017).
[Crossref]

C. H. Ryu, S. H. Park, D. H. Kim, K. Y. Jhang, and H. S. Kim, “Nondestructive evaluation of hidden multi-delamination in a glass-fiber-reinforced plastic composite using terahertz spectroscopy,” Compos. Struct. 156, 338–347 (2016).
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Saint-Paul, M.

E. Martin, C. Larato, A. Clément, and M. Saint-Paul, “Detection of delaminations in sub-wavelength thick multi-layered packages from the local temporal coherence of ultrasonic signals,” NDT&E Int. 41(4), 280–291 (2008).
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Scardi, P.

F. Cernuschi, P. G. Bison, S. S. Marinetti, and P. Scardi, “Thermophysical, mechanical and microstructural characterization of aged free-standing plasma-sprayed zirconia coatings,” Acta Mater. 56(16), 4477–4488 (2008).
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Schlossnikl, R.

D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016).
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S. Sampath, U. Schulz, M. O. Jarligo, and S. Kuroda, “Processing science of advanced thermal-barrier systems,” MRS Bull. 37(10), 903–910 (2012).
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U. Schulz, M. Peters, F.-W. Bach, and G. Tegeder, “Graded coatings for thermal, wear and corrosion barriers,” Mater. Sci. Eng., A 362(1–2), 61–80 (2003).
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Schulze, M.

H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, and R. Vetter, “Review on quality assurance along the CFRP value chain–non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques,” Composites, Part B 77, 494–501 (2015).
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E. Copin, X. Massol, S. Amiel, T. Sentenac, Y. Le Maoult, and P. Lours, “Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor,” Smart Mater. Struct. 26(1), 015001 (2017).
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Shan, Y.

W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014).
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J. I. Eldridge, C. M. Spuckler, and R. E. Martin, “Monitoring delamination progression in thermal barrier coatings by mid-infrared reflectance imaging,” Int. J. Appl. Ceram. Technol. 3(2), 94–104 (2006).
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Strobel, A.

D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, and K.-E. Peiponen, “Characterisation of pore structures of pharmaceutical tablets: A review,” Int. J. Pharm. 538(1–2), 188–214 (2018).
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Tang, J.

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
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Tang, Q.

C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
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M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen, “Correlation of splat morphologies with porosity and residual stress in plasma-sprayed YSZ coatings,” Surf. Coat. Technol. 318, 157–169 (2017).
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S. Marinetti, V. Vavilov, P. Bison, E. Grinzato, and F. Cernuschi, “Quantitative infrared thermographic nondestructive testing of thermal barrier coatings,” Mater. Eval. 61(6), 773–782 (2003).

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D. Ye, W. Wang, J. Huang, X. Lu, and H. Zhou, “Nondestructive interface morphology characterization of thermal barrier coatings using terahertz time-domain spectroscopy,” Coatings 9(2), 89 (2019).
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W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014).
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Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015).
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M. Watanabe, S. Kuroda, H. Yamawaki, and M. Shiwa, “Terahertz dielectric properties of plasma-sprayed thermal-barrier coatings,” Surf. Coat. Technol. 205(19), 4620–4626 (2011).
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W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014).
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Weightman, P.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Wellman, R.

A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016).
[Crossref]

Wereszczak, A.

M. Ferber, A. Wereszczak, M. Lance, J. Haynes, and M. Antelo, “Application of infrared imaging to the study of controlled failure of thermal barrier coatings,” Mater. Sci. 35(11), 2643–2651 (2000).
[Crossref]

Whitaker, J. F.

Williams, G.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Withers, P. J.

X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
[Crossref]

Wolfe, D. E.

J. I. Eldridge, J. Singh, and D. E. Wolfe, “Erosion-Indicating thermal barrier coatings using luminescent sublayers,” J. Am. Ceram. Soc. 89(10), 3252–3254 (2006).
[Crossref]

Wu, K. Q.

Y. M. Zhou, K. Q. Wu, J. L. Chen, Z. S. Wang, and H. H. Jiang, “Monte Carlo simulation of time-domain broadening of laser pulse propagating underwater,” Laser & Infrared 41(3) (2011).

Xiao, J.

X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
[Crossref]

Xuan, F.

W. Wang, J. Wei, H. Hong, F. Xuan, and Y. Shan, “Effect of processing and service conditions on the luminescence intensity of plasma sprayed (Tm3++ Dy3+) co-doped YSZ coatings,” J. Alloys Compd. 584, 136–141 (2014).
[Crossref]

Yamawaki, H.

M. Watanabe, S. Kuroda, H. Yamawaki, and M. Shiwa, “Terahertz dielectric properties of plasma-sprayed thermal-barrier coatings,” Surf. Coat. Technol. 205(19), 4620–4626 (2011).
[Crossref]

Yan, B.

Y. Li, B. Yan, W. Li, and D. Li, “Thickness assessment of thermal barrier coatings of aeroengine blades via dual-frequency eddy current evaluation,” IEEE Magn. Lett. 7, 1–5 (2016).
[Crossref]

Yang, Q.

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
[Crossref]

Ye, D.

D. Ye, W. Wang, J. Huang, X. Lu, and H. Zhou, “Nondestructive interface morphology characterization of thermal barrier coatings using terahertz time-domain spectroscopy,” Coatings 9(2), 89 (2019).
[Crossref]

Yong, L.

L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012).
[Crossref]

Yong, Q.

L. Yong, Z. Chen, Y. Mao, and Q. Yong, “Quantitative evaluation of thermal barrier coating based on eddy current technique,” NDT&E Int. 50, 29–35 (2012).
[Crossref]

Yu, F.

C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
[Crossref]

Yu, Y.

D. Zhang, Y. Yu, C. Lai, and G. Tian, “Thickness measurement of multi-layer conductive coatings using multifrequency eddy current techniques,” Nondestr. Test. Eval. 31(3), 191–208 (2016).
[Crossref]

Zeitler, A.

K. E. Peiponen, A. Zeitler, and M. Kuwata-Gonokami, Terahertz Spectroscopy and Imaging (Springer, 2012), Chap. 8.

Zeitler, J. A.

H. Lin, Y. Dong, Y. Shen, and J. A. Zeitler, “Quantifying pharmaceutical film coating with optical coherence tomography and terahertz pulsed imaging: an evaluation,” J. Pharm. Sci. 104(10), 3377–3385 (2015).
[Crossref]

Zhang, B.

H. L. R. Chen, B. Zhang, M. A. Alvin, and Y. Lin, “Ultrasonic detection of delamination and material characterization of thermal barrier coatings,” J. Therm. Spray Technol. 21(6), 1184–1194 (2012).
[Crossref]

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D. Zhang, Y. Yu, C. Lai, and G. Tian, “Thickness measurement of multi-layer conductive coatings using multifrequency eddy current techniques,” Nondestr. Test. Eval. 31(3), 191–208 (2016).
[Crossref]

Zhang, J. Y.

J. Y. Zhang, X. B. Meng, and Y. C. Ma, “A new measurement method of coatings thickness based on lock-in thermography,” Infrared Phys. Technol. 76, 655–660 (2016).
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K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
[Crossref]

Zhang, X.

X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
[Crossref]

Zhao, L.

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
[Crossref]

Y. Bai, L. Zhao, Y. Qu, Q. Fu, Y. Wang, K. Liu, J. Tang, B. Li, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and properties of supersonic-atmospheric-plasma-sprayed nanostructured thermal barrier coatings,” J. Alloys Compd. 644, 873–882 (2015).
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C. Bu, Q. Tang, Y. Liu, F. Yu, C. Mei, and Y. Zhao, “Quantitative detection of thermal barrier coating thickness based on simulated annealing algorithm using pulsed infrared thermography technology,” Appl. Therm. Eng. 99, 751–755 (2016).
[Crossref]

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S. Zhong, “Progress in terahertz nondestructive testing: A review,” Front. Mech. Eng. 14(3), 273–281 (2019).
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D. Ye, W. Wang, J. Huang, X. Lu, and H. Zhou, “Nondestructive interface morphology characterization of thermal barrier coatings using terahertz time-domain spectroscopy,” Coatings 9(2), 89 (2019).
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Y. M. Zhou, K. Q. Wu, J. L. Chen, Z. S. Wang, and H. H. Jiang, “Monte Carlo simulation of time-domain broadening of laser pulse propagating underwater,” Laser & Infrared 41(3) (2011).

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R. Shrestha and W. Kim, “Evaluation of coating thickness by thermal wave imaging: A comparative study of pulsed and lock-in infrared thermography–Part II: Experimental investigation,” Infrared Phys. Technol. 92, 24–29 (2018).
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J. I. Eldridge, J. Singh, and D. E. Wolfe, “Erosion-Indicating thermal barrier coatings using luminescent sublayers,” J. Am. Ceram. Soc. 89(10), 3252–3254 (2006).
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X. Zhang, J. Kulczyk Malecka, J. Carr, J. Xiao, and P. J. Withers, “3D characterization of porosity in an air plasma-sprayed thermal barrier coating and its effect on thermal conductivity,” J. Am. Ceram. Soc. 101(6), 2482–2492 (2018).
[Crossref]

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A. B. Schubert, R. Wellman, J. Nicholls, and M. M. Gentleman, “Direct observations of erosion-induced ferroelasticity in EB-PVD thermal barrier coatings,” J. Mater. Sci. 51(6), 3136–3145 (2016).
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J. Opt. Soc. Am. A (2)

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S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
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Laser & Infrared (1)

Y. M. Zhou, K. Q. Wu, J. L. Chen, Z. S. Wang, and H. H. Jiang, “Monte Carlo simulation of time-domain broadening of laser pulse propagating underwater,” Laser & Infrared 41(3) (2011).

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Mater. Lett. (1)

J. Zhu and Z. Liu, “Dielectric properties of YSZ high-k thin films fabricated at low temperature by pulsed laser deposition,” Mater. Lett. 57(26–27), 4297–4301 (2003).
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M. Ferber, A. Wereszczak, M. Lance, J. Haynes, and M. Antelo, “Application of infrared imaging to the study of controlled failure of thermal barrier coatings,” Mater. Sci. 35(11), 2643–2651 (2000).
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Mater. Sci. Eng., A (2)

K. Liu, J. Tang, Y. Bai, Q. Yang, Y. Wang, Y. Kang, L. Zhao, P. Zhang, and Z. Han, “Particle in-flight behavior and its influence on the microstructure and mechanical property of plasma sprayed La2Ce2O7 thermal barrier coatings,” Mater. Sci. Eng., A 625, 177–185 (2015).
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Figures (13)

Fig. 1.
Fig. 1. Morphologies of the 8YSZ powders. (a) Particle sizes in the range of 15–55 µm; (b) Particle sizes in the range of 40–96 µm.
Fig. 2.
Fig. 2. Schematic of the terahertz (THz) photonic motion trajectories in ceramic coatings.
Fig. 3.
Fig. 3. Terahertz photon transmission coordinate system.
Fig. 4.
Fig. 4. Schematic of multiple terahertz transmission paths in the ceramic layer.
Fig. 5.
Fig. 5. Time difference between positive and negative peaks of each transmission pulse.
Fig. 6.
Fig. 6. Typical cross-sectional microstructures of the YSZ coatings with fine powder at different spray distances: (a) 80 mm, (b) 100 mm, (c) 120 mm.
Fig. 7.
Fig. 7. Typical cross-sectional microstructures of the YSZ coatings with coarse powder at different spray distances: (a) 80 mm, (b) 100 mm, (c) 120 mm.
Fig. 8.
Fig. 8. Porosities of coatings with different particle sizes and spray distances.
Fig. 9.
Fig. 9. Monte Carlo simulation results of photons numbers and arrival time distributions at different extinction coefficients and transmission distances: (a) 300 µm, (b) 900 µm, and (c) 1500 µm.
Fig. 10.
Fig. 10. Broadening ratio of the full width of the pulse at half maximum of the peak height at different extinction coefficients and transmission distances.
Fig. 11.
Fig. 11. Refractive indices of ceramic layer at different porosities: (a) frequency spectrogram; (b) refractive indices at 1 THz and 1.5 THz.
Fig. 12.
Fig. 12. Extinction coefficients of ceramic layer at different porosities: (a) frequency spectrogram, and (b) extinction coefficients at 1 THz and 1.5 THz.
Fig. 13.
Fig. 13. The relative broadening ratio of THz pulse waveforms normalized by the thicknesses and the reference signals at different porosities: (a) 1st transmission, (b) 2nd transmission, and (c) 3rd transmission.

Equations (10)

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S w = ( P w , R w , L w ) .
( P 0 P 1 P w 1 P w R 0 R 1 R w 1 R w L 0 L 1 L w 1 L w ) .
L = 1 α ln ( ξ ) ,
{ x w + 1 = x w + τ x w Δ L w , y w + 1 = y w + τ y w Δ L w , z w + 1 = z w + τ z w Δ L w .
θ = a r c cos ( 2 σ 1 ) ,
{ τ x = τ x cos θ + sin θ 1 τ z 2 ( τ x τ z cos φ τ y sin φ ) , τ y = τ y cos θ + sin θ 1 τ z 2 ( τ y τ z cos φ τ y sin φ ) , τ z = τ z cos θ sin θ cos φ 1 τ z 2 ( τ x τ z cos φ τ y sin φ ) .
{ τ x = sin θ cos θ , τ y = sin θ sin φ , τ z = S I G N ( τ z ) cos θ .
α absorption = k Im { ε air } ε Y S Z 4 π a 3 3 | 3 ε Y S Z ε air + 2 ε Y S Z | 2 ,
α s cattering = 8 π 3 k 4 a 6 | y | 2 ,
β 1 , 2 , 3 = Δ t 1 , 2 , 3 Δ t r d .

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