1. Introduction

Terahertz technology has rapidly evolved from its first laser-based generation in the 1990s to a technology which is at the verge of being used for first applications. It is suggested to be applied in the areas of sensing, security, and future communication. THz time-domain sensing is due to its cost tag, however, today only accessible to industries in relatively rich market sectors. Examples are the pharmaceutical, automotive, paper production and semiconductor industries [1–4]. Nonetheless, among all novel application markets of THz spectroscopy, these niche market sectors seem to give the most prospect of any market integration. One, if not the field of application which can help this technology to prove itself is the inspection of paint on automotive bodies [3]. As paints dry, their thickness shrinks, and material properties change. For the automotive industry the final dry (so-called oven-dry) thickness d_dry is the quality parameter that has most relevance, as it is the only time-stable parameter. The earlier d_dry can be determined during the drying process, the greater the chance is that rework is still possible. Currently, inspection is performed manually at the end of the paint line, when the paint stack is oven-dried. Rework in this stage is impossible and globally averaged scrap rates are as high as 0.5-1%. Furthermore, the paint shop is the most expensive part of a car production, as the lead time is with 7 hours one third of the entire car production and the energy consumption the largest [5]. Therefore, by reducing the scrap rate and making the paint shop more efficient, very important cost and environmental savings can be achieved.

A real gamechanger would be to perform early quality control, i.e., on drying paint layers, before they enter the oven. In this stage, defects can be repaired on the same layer or by compensating the subsequent one. However, the technological requirements on a sensor for wet paint are stringent. It should (i) resolve the individual layer thickness and preferably consistency of paint multilayers, needs to be (ii) non-contact, (iii) of low energetic impact as not to influence the drying process and not to cause ignition or explosion of the evaporating solvents, (iv) not relying on material calibration properties as drying paints continuously change property and (v) robot-mountable. So far, and despite the longstanding wish of the automotive industry for such a sensor, no technology has been proven to fulfill these requests.

Here we report on the development and realization of a THz-based sensor for the determination of material properties of drying paints. In order to determine the physical states of matter during drying as well as their optical properties, we have built a model to describe the light-matter interaction with composite (multilayer) materials. For the first time, we find evidence of gelation followed by vitrification probed at THz frequencies. We use the model and these findings to reliably estimate dry thickness of a wet paint layer at any moment during the drying process, as requested by the application. We eventually report on the optical design of the robot-mounted sensor, which has been optimized to minimize effects of positional and angular misalignment, curved surfaces and mechanical vibrations, and we demonstrate the performance of the sensor as compared to state-of-the-art devices.

2. Results

2.1 Experiment

The bulk dynamics of as-applied dense irreversible and reversible colloidal dispersions, such as solvent borne and water borne automotive paints, respectively, have been studied with time-domain THz spectroscopy. Paints range from homogenous, so-called solid, to ones containing aluminum or mica particles, and are applied on steel substrates as described in Ref. [6]. The peak energy of the used THz radiation is around 2 meV, and therefore three orders of magnitude smaller than the minimum energy required for photopolymerization. The 10 μW average power is not able to induce temperature changes followed by an increased rate of crosslinking, and moreover the metal substrate, i.e., the car body, acts as a heat sink. For each paint layer stack, the interacted THz electric field E_refl(t), as well as the reference response E_ref(t) from a bare metal substrate were recorded in reflection geometry. For further experimental details, as well as for measured electric fields E(t), the reader is referred to Ref. [6] and Fig. 3.

2.2 Signal processing

We obtain the complex dielectric function ε_i(ω) at THz frequencies from each layer i by simultaneously fitting E_refl(t) and the complex reflectivity r(ω) = E_refl(ω)/E_ref(ω) to the simulated responses E_refl,sim(t) and r_sim(ω), respectively, using a signal processing scheme as sketched in Fig. 1. The core of the scheme is the stratified dispersive model [6,7], where the calculation of r_sim(ω) is based on a multilayer structure that mimics the experimental measurement configuration and a multilayer algorithm where the interaction of the THz radiation with the stack is simulated for a given polarization φ and angle of incidence θ. Within the multilayer structure, each layer i is characterized by a thickness d_i and a dielectric function ε_i(ω) (see Fig. 1). The optimization of the fitting parameters, that is, d_i and the parameters related to the parameterization of ε_i(ω) discussed in Refs. [6] and [7], takes place using the Levenberg-Marquardt algorithm [8]. Here, a gradient descent minimization approach is used as long as the parameters are distant from their final optima. With progressing risk minimization, the Gauss-Newton approach eventually takes over to converge the optimization process to its optimal solution. Curve fitting occurs in both the time-domain (on E_refl(t)) and the frequency-domain (on r(ω)) (see green areas in Fig. 1). This makes the best fit accurate with respect to details of the frequency spectrum situated at the extremes of the measurement range, where the signal-to-noise ratio is typically worse, as well as to geometrical thicknesses involved in the multilayer structure, respectively.

 

Fig. 1. Signal processing scheme to extract the optical material parameters ε_i(ω) and thicknesses d_i of each paint layer based on simultaneous fitting in the time- and frequency domain. Fast Fourier Transformation operations and its inverse are abbreviated by FFT and IFFT, respectively. The curve fitting path is indicated with red arrows, and functions directly involved in curve fitting are located in the green areas. Vectors used as input for operations are indicated next to black dashed lines.

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In order to properly simulate wet paint, consisting of a mixture of f solid and (1-f) volatile fractions, the dispersion of one or several layers of the multilayer structure is described by an effective medium approximation (EMA), as further discussed below. After determining ε_wet(ω) and ε_dry(ω), owing to the as-deposited and dry state, respectively, fitting of E_refl(t) using EMA provides f. The current scheme is highly optimized in order to obey to the process speed of the paint shop [9]. It reduces the time for a full conversion in less than ten iterations from 15 s for homogenous layers in Refs. [2]– [3] to below 70 ms here, thereby outperforming other reported schemes [10,11].

2.3 Physical states of matter

In this section we determine the physical states of matter of a drying coating, and find evidence of gelation, when bond-forming molecules span a percolating network, and vitrification, when the drying paint system becomes thermodynamically trapped. Hereto we deposit a layer of solvent borne primer onto a steel substrate and record E_refl(t) as a function of drying time τ. We consider each drying coating to consist of a single layer throughout the drying process, and do not consider bilayer formation [6], in order to avoid the span of fit parameters to become underdetermined. ε_i(ω) = ε_1,i(ω) + iε_2,i(ω) is parameterized by a series of Lorentzians. The number of these oscillators is at most three (accounting for a low and a high THz frequency resonance, as discussed later, as well as for the optical behavior at frequencies far beyond the THz range) and is fixed during the drying process. The data analysis scheme above readily provides ε(ω) and its parameterization parameters, the resonance frequency ω_0,j, the plasma frequency ω_p,j and the scattering rate γ_j, the layer thickness d and the distance between the sensor head and the layer d_air, without the need of any calibration or know-how about the paint composition [12]. The reaction progress of the drying coating is given by a conversion rate α, expressing the fraction of formed bonds between the polymer molecules, which is readily given by, and equal to f.

α(t) displays the typical behavior of chemical conversion, as expected for solvent borne paint (see inset Fig. 2(a)) [14,15]. At the onset of the reaction, ε₂(ω) features a pronounced band around 0.45 THz that slightly hardens (Fig. 2(a),(c)). Around these frequencies, physical and chemical glass formers often manifest a so-called boson peak, an excess of the vibrational density of states over the Debye level, of actively discussed origin [16–19]. With progression of the reaction, its mode parameters show a continuous jump around α= 0.42 (see Figs. 2(c)-(e)). Concomitantly, a second mode appears around 2.5 THz. We conjecture that, in analogy with Grigera et al. [20], the 0.45 THz mode is the boson peak that with increasing α manifests a phase transition to a solid phase, evinced by the 2.5 THz phonon mode. The relaxation rate of the boson peak also complements well the ones of the α, β and γ relaxations, which all four characterize a glass transition at frequencies below the infrared (see Fig. 2(b)). Therefore, α_gel= 0.42 corresponds to the gel point. As for chemical gels with high activation, also here the critical point is located at a greater conversion level than the inflection point of α(t) ≃ 0.14 (see inset Fig. 2). Furthermore, the power law behavior of the mode relaxation rate γ₁ with respect to (α_c – α) is in agreement with bond percolation on a Bethe lattice, which is representative of chemical gelation [21]. Upon advancement of the reaction, the parameters of both modes become invariant beyond α = 0.9, indicating that the material is frozen on the timescale of the experiment, most probably a metastable glass state. A clear slowdown of the reaction is also observed in behavior of the top layer thickness [7], dd_top/dα, which shows a minimum around α_glass= 0.9. In the paint shop, ε₂(ω) and α, as shown below, are readily obtained with our sensor and allow on-line inspection of the paint’s curing progress and consistency, expressed as the ratio of solid and volatile components. In the following we will use the knowledge about the states of matter of paint to predict the dry thickness of a wet coating.

 

Fig. 2. Optical material properties as a function of conversion rate α of a solvent borne automotive primer. (a) ε₂(ω). Dashed lines show a fit-based extrapolation of the experimental data. The inset shows α(t) with the gel and glass transition points marked as α_gel and α_glass, respectively. The lozenge indicates the inflection point of α(t). (b) Relaxation rate of the 0.45 THz mode (triangles) as compared to reported relaxation rates of the α, β and γ relaxations of physical and chemical glass formers (dots) from Ref. [13]. Fit parameters (c) ω₀, (d) γ and (e) spectral weight ω_p² of the 0.45 THz mode (triangles) and 2.5 THz mode (circles).

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2.4 Prediction of the dry state thickness

In order to predict d_dry from a spectroscopic THz measurement on a wet coating at an arbitrary moment of the drying process we first model the drying coating as an effective medium consisting of dry and wet domains with volume fractions f and (1-f), respectively. As the prediction should principally hold for the range where volume fractions are in the same ball park, rather than in the extreme regions where f ≳ 0 and f ≲ 1, we hereto choose to model the layer using the Bruggeman approximation [22,23]. The dry domains are solid fractions that remain during the drying process, whereas the wet domains contain volatile materials that evaporate during the drying process. In reality, and depending on the kind of bond formation, this picture may not be (entirely) accurate as for instance solvent borne paints use a small part of their solvent for polymerization [24]. However, in a first approximation, we consider this part to be close to zero. The predicted dry thickness d_dry,pred is thus the fraction of solid material f of the total thickness, i.e. d_dry,pred= f × d.

Similar as before, d at any instant of the drying process is determined as shown in Fig. 1. We now describe how to estimate f during the drying process. Dry (wet) domains are characterized by a dielectric function ε_dry (ε_wet), parameterized in Drude-Lorentz terms as before for ε(ω). The effective dielectric function of the coating ε_eff then satisfies the Bruggeman approximation [22], assuming spherical domains:

In the oven-dry state there is just one dry domain. Hence, ε_dry is simply determined in an automotive paint shop from E_refl(t) of an oven dried coating layer. However, ε_wet cannot be determined that easily, as the coating never exists just of volatile materials. As it would be cumbersome and unpractical—though not impossible—to determine the optical properties of the volatile part of the paint, we here describe how to determine ε_wet from the drying coating layer. However, before, we make a short intermezzo to evaluate the situation at the automotive paint shop, as to stay close to realistic situations. Early quality control there will likely be performed after the flash-off zone to avoid explosion danger, that is, one booth after the spraying booth. ε_wet thus needs to be determined at this stage which is between 20 min and 1 hour after spraying. In the current study, the samples are from the manual deposition onwards heated to 40 ℃ in order to avoid paint flowing. However, in an automotive paint shop, typical temperatures outside the ovens are around 20 ℃. That is, the paint at the flash-off zone is barely dryer than the as-deposited state. In line with this and in order to determine ε_wet we select a spectrum E’_refl(t) at any time τ’, preferably close to τ = 0 and thus at low α≪0.42 as to avoid determining ε_wet across either the gel or glass transition (see Fig. 2). The drying state of the paint at the chosen time τ can be revealed from the same measurement by determining ε₂(ω), as mentioned before, and comparing the dispersion to a reference data set, such as shown in Fig. 2(a). Similarly as for the oven-dried coating, we obtain for this wet layer ε(τ’) and d(τ’). Subsequently, we fit the Fresnel equations to E’_refl(t) using as dispersion ε_eff as described by Eq. (1). Hereto, ε_dry is as determined before and ε(τ’) is used as guess function for ε_wet, which is being optimized in the fit. We further require f’ ≡ d_dry / d(τ’). With ε_dry and ε_wet known, we obtain d_dry,pred at any τ by fitting the Fresnel equations to E_refl(t) with ε_eff as in Eq. (1) (Fig. 3(a)-(f)). The resulting fitting parameters are d(τ) and f(τ) (Fig. 3(g),(h)). For water borne paints f(0) ≃ 0.4 indicating that roughly 60% of the coating material before application consist of volatile parts, which agrees well with literature values [25]. Figure 3(i) shows d_dry,pred which is almost independent of τ. Consequently, |d_dry – d_{dry, pred}| < 2 μm, which is well within the requirements of the automotive industry. The reason for the kink around τ = 6 min may be an abrupt change of matter, such as the appearance of a spanning connected network of bonds, also shown by the abrupt change of d (Fig. 3(e)). We thus showed that independent of the kind of paint, our THz-based sensor can reliably predict the final oven-dry thickness of a drying paint layer at any stage of the drying process. No calibration is required other than information readily available from previous cars on the paint line using the same paint. Given that paints are typically kept for many years at a given automotive supplier, our method opens a realm of possibilities for early quality control, and as such reduces the rework and destruction of painted car bodies. The method works robustly for a wet paint layer either directly on a substrate or with several dry layers in between. It is also expected to work for modern spraying mechanisms according to the so-called wet-on-wet principle [26]. Here, a layer is sprayed onto another wet layer that has been air-dried for at least 15 min.

 

Fig. 3. Procedure of determining d_dry,pred for solvent borne and water borne coatings. (a-c) Experimental E_refl(t) of drying solvent borne primer on steel, E_ref(t) of steel, and the best result of the fitting procedure E_fit(t). (d-f) Idem for drying waterborne base coat on an oven-dry primer as used in panels (a-c). (g) total thickness d and solid volume fraction f as determined from the effective medium analysis (see text) for solvent borne primer. (h) Idem for water borne base coat on oven-dry primer. (i) d_dry,pred of solvent borne primer (), and water borne base coats: plain blue (), black with mica particles () (upshifted by 5 μm for clarity), gray with aluminum flakes ().

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3. Paint sensor design, development and validation

In the following, we report on the optical and mechanical design of the sensor demonstrator and discuss how self-alignment on curved surfaces and vibration robustness has been implemented. We also illustrate the performance of the sensor as compared to state-of-the-art paint sensors for dry paint.

3.1 Optical design

Figure 4 shows the external and internal sensor design (panels a-b). Inside the 3D printed housing, two photoconductive THz antennas are positioned on an alignment system with each a TPX lens in front. The antennas are connected to a THz time-domain spectrometer (Toptica Teraflash, Germany), which to date is among the most robust and cheapest on the market. Car bodies are almost everywhere curved to a certain extent, and in a paint shop the alignment of the sensor head relative to the probed area may not be perfect. The goal is therefore to minimize these effects, which propagate to errors on ε(ω) and d. The optimum optical design has been determined iteratively, first by evaluating the performance of two extreme beam designs: a collimated one and a focused one as compared to calculations using Gaussian beams. For each design we have built a demonstrator optical head, where the nature of the beam has been modified by varying the distance between the lens (TPX, f = 32.5 mm) and the emitter and receiver, respectively.

 

Fig. 4. Sensor design and performance. (a) External and (b) internal design. Visible are the laser-guided distance sensors as well as the THz lenses. Brown lines illustrate the laser beam paths, blue lines the THz beam paths. (c) Photograph of the sensor mounted on an industrial robot with beneath an automotive car part. (d) Surface thickness map (in μm) of a primer-covered automotive paint sample as measured by the sensor. A defect on the paint can be clearly identified in the upper right corner. (e) Measured distance (in μm) from the sensor head to the car part, after robot alignment, indicating the curvature of the sample. (f) Comparative thickness results of the sensor developed from this work () with an RMS of 1.1 μm and the state-of-the-art, Eddy-current based, layer thickness gauge (Elcometer 355) () with an RMS of 3.2 μm, taken across a multitude of different multilayers.

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As expected, the first design experimentally shows little variation with curvature and angular misalignment, which has both the same origin, but is sensitive to distance variations between the sensor head and the probed object (see Fig. 5). Oppositely, the collimated design is very sensitive to curvature and insensitive to positional misalignment. We thus designed the final demonstrator with a THz beam with a soft focus, having a beam waist of about 2.1 mm at 0.5 THz (slightly varying with frequency), of about 10 cm from to the sensor housing. Experimentally, we have observed that this design minimizes defocusing effects of curved surfaces, as for radii of curvature r < 0.5 m the error on d is typically below 0.9 μm, and furthermore makes the sensor least sensitive to positional alignments (see Fig. 5).

 

Fig. 5. Sensitivity of the sensor toward positional and angular misalignment, expressed in terms of a variation of the determined thickness, Δd, for three selected beam designs: collimated (c,f), soft focus (d,g) and focused (e,h), as compared to calculations shown as non-quantitative indications for a collimated beam (a,i) and a focused beam (b,j). Green marks show acceptable variations, red marks unacceptable variations.

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3.2 Limiting the influence of mechanical vibrations

In almost all automotive paint shops, mechanical vibrations are omnipresent. As the THz sensor operates in the time-domain, out-of-plane vibrations cause a non-uniform compression and dilatation of the THz pulse, depending on the vibration frequency relative to the sampling frequency of the THz spectrometer, and thus falsify determination of ε(ω) and d. In-plane vibrations, on the other hand, probe the spatial inhomogeneity relative to the vibration amplitude, which is expected to be of less influence on d. To obtain the vibration sensitivity of our sensor, we determined d first on a flat single layer paint sample (Fig. 6), then on a curved single layer paint sample (Fig. 7) and eventually for a multilayer flat paint sample (Fig. 8) as a function of the out-of-plane vibration frequency.

 

Fig. 6. Thickness variation Δd of a flat single paint layer as a function of the out-of-plane vibration frequency between 2 and 130 Hz. Blue data points are based on unaveraged time traces E(t). The orange curve is based on a moving average of 16 samples using the blue data points. The back line shows the vibration amplitude A_v as a function of vibration frequency, determined from E(t). Traces E(t) have been recorded with an acquisition frequency of 8.8 Hz.

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Fig. 7. Thickness variation Δd of a curved single paint layer with r = 0.5 m as a function of the out-of-plane vibration frequency between 2 and 130 Hz. Blue data points are based on unaveraged time traces E(t). The orange curve is based on a moving average of 16 samples using the blue data points. The back line shows the A_v as a function of vibration frequency, determined from E(t). Traces E(t) have been recorded with an acquisition frequency of 17.5 Hz.

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Fig. 8. Thickness variation of a flat paint multilayer as a function of the out-of-plane vibration frequency between 2 and 130 Hz, for (a) clear coat with d = 47 μm, (b) base coat with d = 15 μm and (c) phosphate with d = 38 μm. Blue data points are based on unaveraged time traces E(t). The orange curve is based on a moving average of 16 samples using the blue data points. The back line shows the vibration amplitude A_v as a function of vibration frequency, determined from E(t). Traces E(t) have been recorded with an acquisition frequency of 17.5 Hz.

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Figure 6 illustrates the thickness variation of a single layer paint sample of 40 μm thick on a flat metallic substrate that vibrates with an amplitude A_v = 57 μm. It shows the variation of the paint layer thickness Δd, determined according to the signal processing described in Fig. 1 using unaveraged time-domain traces E(t) (blue dots). We observe an additional error of 1.0 (2.5) μm at a 50 (100) Hz, which is significantly smaller than reported elsewhere [27]. There are several ways to reduce this effect. For relatively slow vibrations and small amplitudes, one can correct the time-axis of the THz trace E_refl(t) by performing a real-time measurement of A_v during its acquisition. As this method becomes unfeasible for fast vibrations, we found that another option is to record the (distorted) E_refl(t) several times, determining the thickness from each trace and then to average them. Such a post-averaging of 16 samples reduces the previously mentioned additional error to 0.3 (0.5) μm at a 50 (100) Hz vibration (see Fig. 6, orange curves).

This procedure, however, works less well at vibrations frequencies that match the frequency of the delay stage of the THz spectrometer, because of interfering signals. A solution to reduce this effect for a specific application, e.g. a specific paint line, is by detuning the delay stage frequency as compared to the principal vibration spectrum of the application. Figures 7 and 8 show an example of this effect, where the acquisition frequency has been doubled as compared to the one used in Fig. 6.

Interestingly, effects on d due to vibrations are not cumulative to the ones due to curved surfaces. For a curved vibrating surface, we only find (0.8 (1.0) μm error at 50 (100) Hz for a 36 μm paint layer with r = 0.5 m and A_v = 57 μm) (see Fig. 7). The effect on layers within a multilayer stack is similar to monolayers (see Fig. 8).

Eventually, the influence of out-of-plane vibrations is determined for a multilayer paint sample on a flat metallic substrate, consisting of a varnish top layer of so-called clear coat, a middle layer of so-called base coat, and a primer layer consisting of so-called phosphate. Figure 8 shows that Δd is similar to that of a single layer on a flat substrate (see Fig. 6).

3.3 Self-alignment and validation

A trend of automotive paint shops is to automatize the coating inspection, which today is still, apart from some test setups, entirely performed manually. We therefore mounted the sensor housing on an industrial robot (ABB IRB1600)(Fig. 4(c)). Three optical distance sensors, two above and one below the THz optics, provide the robot control software with the distance l between the sensor and the painted object, and, using a triangulation method, also the in-plane angular orientation of the object as two angles Θ and Φ. These parameters are used for automatic alignment of the sensor head relative to the car body. Figure 4(d) shows a surface map of d on an automotive car part as measured with the sensor, indicating the paint homogeneity. Hereto, ε_i(ω) of the individual paint layers have been measured earlier on flat samples using the same paint, comparable to a scenario where the sensor would be used at the end of the line. This enhances the accuracy of the layer thickness values, and in an industrial context is not a limitation as typically a specific paint is used in the paint shop for many years. Figure 4(e) shows from the same car part d_air, clearly displaying its convex shape. As constructed, our sensor has typical absolute RMS errors of on average 1.1 μm for individual (dry) coating thicknesses between 7 and 33 μm in multilayer configuration across a comprehensive palette of single, double and triple automotive paint types (see Fig. 4(f)). This is about three times smaller than state-of-the-art thickness gauges for dry layer paint inspection, based on the induction of eddy currents.

4. Conclusions

In conclusion, we reported on the development of the first sensor system to perform quality inspection of as-sprayed paint surfaces during their drying phase. The sensor utilizes THz time-domain technology, which so far is the only technology that does not alter the drying state of colloidal dispersions. We have developed a signal processing scheme that expands the stratified dispersive model for homogenous materials to include composite layers like wet paint, and drastically optimized its speed. Applied to solid borne coatings, this method revealed signatures of the colloidal dispersion crossing from a liquid phase to a gel and eventually entering a glass phase. In addition, it showed dynamic processes at THz frequencies. As such, our method is promising for the understanding of the physics of non-equilibrium systems in the THz range. Using the knowledge of these states of matter, the model gives an accurate estimate of the dry thickness probed at any stage during drying, for solvent borne and water borne coatings. We have built a demonstrator sensor system where the optical design and signal processing minimize perturbances from the application environment. Our sensor has typical total absolute errors of on average 2 to 3 μm, depending on the film thickness, the total stack composition, the level of vibrations and curvature, which is conform the requirements of the automotive industry. Our sensor system is of wide interest for the automotive industry and its signal processing opens a realm of novel applications on inhomogeneous media using THz technology.