Double-modulation reflection-type terahertz ellipsometer for measuring the thickness of a thin paint coating

Tetsuo Iwata; Hiroaki Uemura; Yasuhiro Mizutani; Takeshi Yasui

doi:10.1364/OE.22.020595

1. Introduction

The terahertz (THz) frequency band, ranging from around 0.1 THz to several tens of THz, is located at the boundary region between the electric- and optical-frequency regions, or at the intermediate region between the microwave and the mid-infrared wavelength regions. THz waves exhibit promising properties, such as propagation in free-space, high transmittance through materials, low scattering, and non-invasiveness to living bodies. These properties are of use not only for nondestructive testing of industrial materials but also for electronics, photonics, materials science, and medical applications [1]. One of the most practical applications in the industrial field is non-contact and in-line measurement of the thickness of a paint film on cars, airplanes, ships, and other transportation means. Although such measurement would appear to be simple, it is not always easy to determine coating thicknesses of several micrometers or less with precision. The reason is that the paint material is usually not transparent to light in the optical-frequency region. Conventional methods [2], such as ultrasonic methods, eddy-current methods, and electromagnetic-induction methods, are hard to use for measuring a wet paint film; these methods are “destructive” ones, which means that one has to contact the sensor probe against the sample.

In light of this situation, THz-wave techniques have been introduced. For thickness measurement, a time-of-flight (TOF) technique based on THz time-domain spectroscopy (THz-TDS) has been developed [3]. In THz-TDS, a photoconductive antenna (PCA) is used as an excitation light source, and the time difference of the two THz pulses that are reflected from the surface of a paint film and the film–metal interface is measured. Therefore, it is difficult to apply the TOF method to the measurement of a thin paint coating because of the large temporal overlapping of the two pulses. For example, when the pulse width of the THz pulse and the group refractive index are 1.2 ps and 1.6, respectively, the measurable thickness of the paint film is 100 µm or more. Although a numerical deconvolution technique and a mathematical multivariate method have been proposed to determine the thickness of such thin films [4–6], they are still difficult to apply to the measurement of film thicknesses of less than 20 µm. In addition, one has to know the frequency-dependent group-refractive-index of the paint film in advance.

For such a situation, the ellipsometric technique seems promising [7]. Although a THz ellipsometer employing a backward wave oscillator [8] and one using synchrotron radiation [9] as the THz light source have reported, simultaneous broadband measurement is difficult. Therefore, a frequency-domain (FD)-THz ellipsometer is usually employed [10]. With a FD-THz ellipsometer, one can obtain the spectroscopic information all at once; a time-series waveform of the electric-field strength of the THz pulse is Fourier transformed, which allows the frequency dependence of the ellipsometric parameters, ∆ and Ψ, to be calculated directly [10].

In an FD-THz ellipsometer, an essential point for precise measurement is to enhance the signal-to-noise ratio (SNR). At present, however, SNR enhancement is limited by low-frequency flicker noise, due to the femtosecond laser used as a pump (and/or a probe) for the PCA used as the THz pulse emitter (and/or detector). Therefore, a lock-in light-detection method is commonly used, where the THz pulse trains incident on the detector should be modulated at as high a frequency as possible.

In the ellipsometric measurements, one has to derive the complex-amplitude reflection ratio ρ, which is defined as the ratio of the complex-amplitude reflectivity of the p-polarized light to that of the s-polarized one. Therefore, two measurements are required, and two scans of a mechanical time-delay stage are necessary [10], which is apt to introduce errors due to changes in the sample and/or the instrument conditions as time passes. In order to eliminate such errors, a single-scan measurement is desirable. Therefore, a polarization modulation technique in combination with a quadrature-phase-detection method should be introduced. As described later, a two-phase lock-in amplifier (LA) operated in the quadrature-phase-detection mode enables us to obtain two signals simultaneously: one is an in-phase signal and the other is an out-of-phase signal, from which we can derive the two ellipsometric parameters simultaneously. Cancelation of the common-mode noise in the measurement is another bonus. One way to conduct polarization modulation in the THz frequency range is to use a mechanically rotating wire-grid polarizer (RWGP). However, the upper modulation frequency is limited to 30 Hz [11–13]. At such a low frequency, the flicker noise cannot be eliminated sufficiently.

To this end, in order to construct an FD-THz ellipsometer, we have to employ a double-modulation method; in this method, combined use of high-frequency modulation of the bias voltage of the PCA and relatively low-frequency polarization modulation by the RWGP is indispensable. The double-modulation method retains the advantages of both methods while compensating for their disadvantages. To carry out double modulation, the output signal from the detector should be fed into two LAs connected in tandem: one LA works in synchronization with the modulation frequency of the bias voltage for the PCA with a time constant τ₁, and the other LA works in synchronization with the polarization modulation frequency with a time constant τ₂. The two time constants should be set so that τ₁ < τ₂, and τ₂ should be at least one order of magnitude larger than τ₁. Such a double-modulation technique has been used for spectroscopy in the optical-frequency region [14] and has also been considered for the THz region [15]. A trial to measure polarization Stokes parameters also has been reported recently [13]. However, the former system is based on the THz-TDS method for obtaining the optical constants of materials through transmission measurements. The latter one is a transmission type-polarimeter for measuring the optical constants. Neither instrument was intended for thickness measurement of paint films, and the instruments were not described in sufficient detail. In addition, the modulation frequency was not so high, and quadrature-phase detection has not been introduced yet. As far as polarization measurements are concerned, new ideas have been proposed, such as a PCA emitter (and/or detector) that has multiple electrodes [16–18]. A method that uses a rotating electro-optical (EO) crystal has also been reported [19]. Although the proposed methods work well, specially designed components or devices are required.

In the present paper, we focus on the construction of a double-modulation reflection-type THz ellipsometer for measuring the thickness of a paint film coated on a metal surface. We also discuss ellipsometric measurement of Jones matrixes for anisotropic materials.

2. Instrument

Figure 1 shows a schematic diagram of the double-modulation reflection-type THz ellipsometer, and Fig. 2 shows a timing diagram explaining its operation. A laser beam from a mode-locked Ti:sapphire laser (Spectra-Physics, Mai Tai; wavelength, 800 nm; pulse width, 100 fs; repetition frequency, 80 MHz) was divided into a pump beam and a probe beam by a 9:1 beam splitter (BS). The pump beam, shown in Fig. 2(a), was focused on the PCA (Gigaoptics GmbH, TERA-SED) for emitting THz pulses. The bias voltage of the PCA was modulated by a 20 V_pp modulation signal, as shown in Fig. 2(b), where the duty ratio and the frequency of the modulation signal were 50% and 100 kHz, respectively. The THz pulse trains emitted from the PCA, as shown in Fig. 2(c), were collimated by a lens (TL1; focal length, 50 mm) and passed through four wire-grid polarizers (WGP1–4; frequency range, 0.1–1.5 THz; wire diameter, 50 µm; spacing, 125 µm) sequentially and a rotational WGP (RWGP; frequency range, 0.1–1.5 THz; wire diameter, 50 µm; spacing, 125 µm; motor, model HM2669E18H, Technohands Co., Ltd.). The orientation angles (or transmission axes) of WGP1, WGP2, RWGP, WGP3, and WGP4 are indicated by θ₁, θ_P, θ_R, θ_A, and θ₄, respectively, where θ = 0° means p-polarized light (parallel to the plane of the figure), and θ = 90° means s-polarized light (perpendicular to the plane of the figure). For the measurement of the anisotropic sample, we set θ₁ = 45° and θ₄ = −45°. The role of WGP1 was to fix the polarization of the incident light at 45°. WGP4 was used for EO sampling, described later.

Fig. 1 Schematic block diagram of the double-modulation reflection-type THz ellipsometer. PCA: photoconductive antenna, TL1,2: THz lens, WGP1–4: wire grid polarizer, OAP: off-axis parabolic mirror, RWGP: rotational wire-grid polarizer, QWP: quarter-wave plate, RP: Rochon prism, OSC: oscillator, LA1,2: lock-in amplifier.

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Fig. 2 Timing diagram explaining the operation of the double-modulation THz ellipsometer. (a) Output pulse trains obtained from the Ti:Sapphire laser with a repetition frequency of 80 MHz, (b) bipolar-modulation signal with a frequency of 100 kHz applied to the PCA, (c) THz pulse trains emitted from the PCA, (d) THz pulse trains modulated by the RWGP (whose orientation angles are shown), (e) waveform of the THz pulse trains after passing through WGP3, (f) output signal obtained from LA1, and (g) and (h) the in-phase and out-of-phase reference signals, respectively, which were fed into LA2 for quadrature-phase detection and whose modulation frequency was 200 Hz.

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The THz pulses were focused on the sample with an incident angle ϕ of 60° by an off-axis parabolic mirror (OAP; focal length, 101.6 mm). The THz pulses reflected from the sample were collimated again by another OAP and then passed through the RWGP, which was rotated at a frequency f = 100 Hz. Thus, the frequency of the polarization modulation was 2f = 200 Hz. Figures 2(d) and 2(e) show the waveforms of the THz pulse trains after passing through the RWGP and WGP3, respectively. To clarify the illustration, the waveforms drawn in Fig. 2 are schematic ones obtained with no paint coating on the metal and θ_P = θ_A = 0°. Typical orientation angles of the RWGP as time passed are depicted at the lower part of the waveform in Fig. 2(d).

In order to detect the pulsed THz light, we used the EO sampling technique [20, 21]. The THz pulses were focused into a ZnTe EO crystal. The probe beam reflected by the BS, after being polarized, was also incident on the same crystal. A slight change in its polarization state by the Pockels effect due the electric field of the THz pulses was detected by a balanced light detector (New Focus Corp., Model 2007) followed by a quarter-wave plate (QWP) and a Rochon prism (RP). The output signal from the detector was fed into the LA1 (NF Corp., LI5640), whose reference signal was derived from the PCA bias modulation-signal shown in Fig. 2(b). The output signal from the LA1, shown in Fig. 2(f), was fed again into the LA2 (NF Corp., LI5640), which worked in synchronization with the phase modulation signal, so that quadrature phase detection was carried out. Figures 2(g) and 2(h) show the in-phase and out-of-phase reference signals used for the quadrature-phase detection procedure, respectively.

The in-phase signal obtained from the LA2 was proportional to the difference between the two electric-field strengths when θ_R = 0° and when θ_R = 90° for the output of LA1 shown in Fig. 2(f). Similarly, the out-of-phase signal was proportional to the difference between the two electric-field strengths when θ_R = 45° and when θ_R = −45°. The two component signals were recorded as a function of the time delay given by the movement of the mechanical stage. Finally, by Fourier transformation, we could obtain two complex electric-field components in the frequency domain: the in-phase component, Eⁱⁿ(ω), and the out-of-phase component, E^out(ω).

In the present system, the incident angle was fixed at ϕ = 60°, which was near the Brewster angle of ϕ = 61.3° for the air/paint film interface, where the refractive index of the paint film at f = 1.02 THz was assumed to be n = 1.83. The time span of the optical delay was 27.3 ps, and its step interval was 53.4 fs, which corresponded to a frequency resolution of ∆f = 36.6 GHz. The overall frequency range in the present system was limited by that of the WGP, which was from 0.1 to 1.5 THz. The time constants of the LA1 and the LA2 were τ₁ = 300 µs and τ₂ = 300 ms, respectively.

3. Ellipsometric measurements

3.1 Quadrature signal detection

In this section, we derive mathematical expressions for the output signals obtained from the LA2 in the quadrature-phase detection method for several combinations of θ_P and θ_A; these expressions will be used in the next section.

The Jones polarization-matrix for the ellipsometric measurement is given by

[\begin{matrix} E_{p} (θ_{R}, ω) \\ E_{s} (θ_{R}, ω) \end{matrix}] = P_{θ_{A}} \cdot P_{θ_{R}} \cdot S \cdot P_{θ_{P}} \cdot [\begin{matrix} E_{p}^{0} (ω) \\ E_{s}^{0} (ω) \end{matrix}],

where the WGP1 and the WGP4 are not taken into account, because they should be included in the input and output parts of the optical system, respectively. In Eq. (1), E⁰(ω) is the electric-field strength at the angular frequency ω; E_p(θ_R, ω) and E_s(θ_R, ω) stand for the p- and the s-polarized light components, respectively, when θ = θ_R; and P_θ (θ = θ_P, θ_R, or θ_A) represents the Jones matrix for the polarizer with orientation angle θ, which is given by

P = [\begin{matrix} \cos^{2} θ & \cos θ \sin θ \\ \cos θ \sin θ & \sin^{2} θ \end{matrix}] .

Therefore, we have

P_{0^{\circ}} = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}]

,

P_{90^{\circ}} = [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}]

,

P_{45^{\circ}} = \frac{1}{2} [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]

, and

P_{- 45^{\circ}} = \frac{1}{2} [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]

.

The Jones matrix, S, for the sample is given by

S = [\begin{matrix} {\tilde{r}}_{p p} (ω) & {\tilde{r}}_{p s} (ω) \\ {\tilde{r}}_{s p} (ω) & {\tilde{r}}_{s s} (ω) \end{matrix}],

where

{\tilde{r}}_{i j} (ω)

(i, j = p or s) is Fresnel’s complex-amplitude reflectivity of the sample for the i-polarized incident light and the j-polarized reflected light.

In Eq. (1), E_s(θ_R, ω) = 0 when θ_A = 0þ. Then, the output signal from the LA1 is proportional to E_s(θ_R, ω) only. Also, E_p(θ_R, ω) = 0 when θ_A = 90°. Then, the output signal from the LA1 is proportional to E_s(θ_R, ω) only. Therefore, the in-phase signal Eⁱⁿ(ω) is given by

E^{in} (ω) = E_{i} (0^{\circ}, ω) - E_{i} (90^{\circ}, ω),

which means that Eⁱⁿ(ω) is given by the difference between the electric-field strengths when θ_R = 0° and θ_R = 90°. In Eq. (4), when θ_A = 0°, i = p, and when θ_A = 90°, i = s. Similarly, the out-of-phase signal E^out(ω) is given by

E^{out} (ω) = E_{i} (45^{\circ}, ω) - E_{i} (- 45^{\circ}, ω) .

By using the same procedure, we can calculate Eⁱⁿ(ω) and E^out(ω) for the situations (θ_P, θ_A) = (0°, 0°), (90°, 0°), (45°, 0°), (45°, 90°), (90°, 0°), and (90°, 90°). Table 1 summarizes the calculated results. Note that the non-diagonal elements of the Jones matrix, S, become zero for the case of an isotropic sample:

{\tilde{r}}_{p s} (ω)

=

{\tilde{r}}_{s p} (ω)

= 0.

Table 1. Expressions for Eⁱⁿ(ω) and E^out(ω) derived from Eqs. (4) and (5), respectively, for various combinations of (θ_P, θ_A).

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3.2 Measurement of an isotropic sample

In reflection-type ellipsometry of an isotropic sample, the ratio ρ is measured, which is the ratio of the complex amplitude reflectivity of the p-polarized light to that of the s-polarized light:

ρ (ω) = \frac{{\tilde{r}}_{p p} (ω)}{{\tilde{r}}_{s s} (ω)} = \tan [Ψ (ω)] \exp (i Δ (ω)),

where Ψ and ∆ are the amplitude-ratio angle and the phase difference, respectively. Now, if we measure Eⁱⁿ(ω) and E^out(ω) in the setup with (θ_P, θ_A) = (45°, 0°), we can derive the following expression from Table 1:

\frac{E^{in} (ω)}{E^{out} (ω)} = \frac{\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) \cdot ({\tilde{r}}_{p p} (ω) + {\tilde{r}}_{p s} (ω))}{\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) \cdot ({\tilde{r}}_{s p} (ω) + {\tilde{r}}_{s s} (ω))} .

Because of the isotropic sample, we have

{\tilde{r}}_{p s} (ω) = {\tilde{r}}_{s p} (ω) = 0

, and thus

\frac{E^{in} (ω)}{E^{out} (ω)} = \frac{{\tilde{r}}_{p p} (ω)}{{\tilde{r}}_{s s} (ω)} = ρ (ω) .

Therefore, the ellipsometric parameters ∆ and Ψ can be derived from Eq. (6) as a function of ω.

Similarly, when (θ_P, θ_A) = (45°, 90°), the following relation can be derived:

ρ (ω) = \frac{{\tilde{r}}_{p p} (ω)}{{\tilde{r}}_{s s} (ω)} = \frac{\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) \cdot ({\tilde{r}}_{p p} (ω) + {\tilde{r}}_{p s} (ω))}{\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) \cdot ({\tilde{r}}_{s p} (ω) + {\tilde{r}}_{s s} (ω))} = - \frac{E^{out} (ω)}{E^{in} (ω)} .

Once the two ellipsometric parameters are derived, the thickness d of the film and/or its complex refractive index can be estimated by a usual manner used in ellipsometry [22].

3.3 Measurement of an anisotropic sample

For the case of an anisotropic sample, the following ratio ρ_ij should be measured:

ρ_{i j} (ω) = \frac{{\tilde{r}}_{i j} (ω)}{{\tilde{r}}_{s s} (ω)} = \tan [Ψ_{i j} (ω)] \exp (i Δ {}_{i j}{(ω)}), i, j = p, s .

In order to determine the element

{\tilde{r}}_{i j} (ω)

of the Jones matrix, for a given orientation angle, we have to carry out two measurements. First, a measurement should be carried out in the setup with (θ_P, θ_A) = (0°, 0°). Then, two elements of the first column in the Jones matrix S can be obtained from Table 1:

(\begin{matrix} {\tilde{r}}_{p p} (ω) \\ {\tilde{r}}_{s p} (ω) \end{matrix}) = \frac{1}{E_{p}^{0} (ω)} (\begin{matrix} E^{in} (ω) \\ E^{out} (ω) \end{matrix}) \begin{matrix} . \end{matrix}

Next, a measurement should be carried out in the setup with (θ_P, θ_A) = (90°, 90°). Then, two elements of the second column in the matrix can be obtained:

(\begin{matrix} {\tilde{r}}_{p s} (ω) \\ {\tilde{r}}_{s s} (ω) \end{matrix}) = \frac{1}{E_{s}^{0} (ω)} (\begin{matrix} E^{out} (ω) \\ - E^{in} (ω) \end{matrix}) .

Similarly, we can derive the four elements of the matrix S by using other setups: (θ_P, θ_A) = (0°, 90°) and (90°, 0°). The two combinations of setups mentioned above work well under the condition where

E_{p}^{0} (ω) = E_{s}^{0} (ω)

. Therefore, we set the orientation angle of the WGP1 to θ₁ = 45°. In addition, we set the orientation angle of the WGP4 to θ₄ = −45° to cancel the polarization dependency of the incident light on the EO crystal.

The four elements of the Jones matrix can be determined by another two combinations of setups: (i) (θ_P, θ_A) = (0°, 0°) and (90°, 0°), and (ii) (θ_P, θ_A) = (0°, 90°) and (90°, 90°). In these two setups, although the condition $E_{p}^{0} (ω) = E_{s}^{0} (ω)$ is still required, the WGP4 can be removed. This is because the orientation angle θ_A is kept constant for the two sequential measurements.

4. Experiments

4.1 Measurement of the complex refractive index of a Si substrate

In order to compare the measurement precision of the proposed double-modulation THz ellipsometer with that of a single-modulation one without the polarization modulation technique, we measured the complex refractive index, $\tilde{n} (ω) = n (ω) - i κ (ω)$ , where n(ω) is the refractive index and κ(ω) is the extinction coefficient, of a high-purity, polycrystalline Si substrate. The value of $\tilde{n} (ω)$ for such an isotropic sample without multiple reflections can be obtained from the following relation [10]:

\tilde{n} {(ω)}^{2} = {n (ω) - i κ (ω)}^{2} = \sin^{2} ϕ [1 + \tan^{2} ϕ {(\frac{1 - ρ (ω)}{1 + ρ (ω)})}^{2}],

where ρ(ω) is measured using the setup with (θ_P, θ_A) = (45°, 0°), and ϕ is the incident angle, which is set to ϕ = 60°.

Figures 3(a) and 3(b) show n(ω) and κ(ω), respectively, which were obtained from the double-modulation ellipsometer. Error bars attached to the plot indicate the standard deviation obtained from twenty repeated measurements. Figures 3(c) and 3(d) show those measured by the single-modulation ellipsometer. The horizontal solid lines in the figure show a value reported in the literature for undoped Si [23], namely, $\tilde{n} (ω) = 3.415 - 0 i$ . The measured values agreed well with the literature ones. The averaged relative standard deviation (RSD) over the frequency range from 0.1 to 1.5 Hz was 2.6%. By introducing the double-modulation technique, the RSD value was reduced by two times in comparison with that without the double-modulation technique.

Fig. 3 Complex refractive index, $\tilde{n} (ω) = n (ω) - i κ (ω)$ , of a Si substrate as a function of frequency, where (a) and (b) show n(ω) and κ(ω) measured by the double-modulation THz ellipsometer, and (c) and (d) show those measured by the conventional single-modulation ellipsometer.

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4.2 Measurement of the complex refractive index of a paint coating

Next, we measured a black lacquer paint film coated on an Al substrate. Because the complex refractive index of the paint film in the THz frequency range is not known, we prepared a similar but thicker paint film to measure the value accurately. The thickness of the coating was d = 170 ± 1.5 µm, which was obtained from thirty measurements by using an eddy-current thickness meter (LZ-300C, Ketto Kagaku).

Figures 4(a) and 4(b) show the in-phase time-domain waveform, Eⁱⁿ(ω), and the out-of-phase time-domain waveform, E^out(ω), respectively, which were obtained from the setup with (θ_P, θ_A) = (45°, 0°). Figures 4(c) and 4(d) show the amplitude and the phase spectrum obtained from Fourier transformation of Eⁱⁿ(ω) and E^out(ω), respectively, from which the ellipsometric parameters Ψ(ω) and ∆(ω) were calculated, as shown in Figs. 4(e) and 4(f), respectively. Finally, the real part, n(ω), and the imaginary part, κ(ω), of the complex refractive index, $\tilde{n} (ω)$ , of the paint film were estimated from Ψ(ω) and ∆(ω), as shown in Figs. 4(g) and 4(h), respectively. Here, we used a three-layer (air/film/Al substrate) optical model for the estimation. In the calculation, the complex refractive index of the Al substrate was derived from the Drude model [24]:

\tilde{n} {(ω)}^{2} = ε_{\infty} - \frac{ω_{p}^{2}}{ω^{2} - i Γ ω},

where ω_p is the plasma frequency, Γ the damping constant, and ε_∞ the dielectric constant at ω → ∞; the values were ω_p = 2π × c × 1.19 × 10⁷ rad/s, Γ = 2π × c × 6.47 × 10⁴ rad/s, and ε_∞ = 1.

Fig. 4 Time-domain waveforms (a) Eⁱⁿ(ω) and (b) E^out(ω) obtained from the LA2 as the in-phase and the out-of-phase output signals. Amplitude and phase spectra of (c) Eⁱⁿ(ω) and (d) E^out(ω), which were obtained from Fourier transformation of (a) and (b), respectively. (e) Ψ and (f) ∆ as a function of frequency, which were calculated from Eqs. (7) and (8), respectively. (g) Real part, n(ω), and (h) imaginary part, κ(ω), of the complex refractive index of the paint film as a function of frequency.

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4.3 Measurement of the thickness of a thin paint coating

In the previous section, we obtained the complex refractive index of the paint film as a function of ω. Using these values, we measured the thicknesses of thin paint coatings. The left column and the right column in Fig. 5 show Ψ(ω) and Δ(ω), respectively, which were measured for five thicknesses of paint coatings: (a) and (b) d = 102 µm, (c) and (d) d = 20.0 µm, (e) and (f) d = 10.4 µm, (g) and (h) d = 5.3 µm, and (i) and (j) d = 4.3 µm. The solid lines in the individual plots are mathematically fitted results obtained by using a three-layer model. Table 2 summarizes the estimated thicknesses. For reference, thickness values measured by an eddy-current meter thirty times are also shown. Both values agreed well. For the thickness of the 4.3 µm-thick paint film, the RSD in twenty repeated measurements using the double-modulation THz ellipsometer was 1.4%.

Fig. 5 The ellipsometric parameters, Ψ(ω) (left column) and Δ(ω) (right column), for various thicknesses of paint coatings: (a) and (b) d = 102 µm, (c) and (d) d = 20.0 µm, (e) and (f) d = 10.4 µm, (g) and (h) d = 5.3 µm, and (i) and (j) d = 4.3 µm.

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Table 2. Measurement results of thicknesses of five paint coatings with an eddy-current meter and the double-modulated THz ellipsometer. unit: [µm]

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5. Conclusions

We constructed a double-modulation reflection-type THz ellipsometer for measuring the thickness of a paint film coated on a metal surface. The double-modulation technique, together with a quadrature-phase detection method using a two-phase lock-in amplifier, enabled us to obtain the ellipsometric parameters Ψ(ω) and Δ(ω) at the same time with a single measurement. For a 4.3 µm-thick paint coating, the relative standard deviation (RSD) value in twenty measurements was 1.4%. We also discussed the possibility of measuring all elements of the Jones matrix for an anisotropic material. Although we have measured single-layer films with good precision, in future work we will attempt to measure the thicknesses of multi-layer coatings and to analyze inhomogeneous paint films that include impurity materials such as metal flakes.

Acknowledgements

This work was supported by a Grand-in-Aid for Scientific Research B (No. 26289066) from the Japan Society for the Promotion of Science. The authors are grateful to Dr. Shinichi Watanabe of Keio University for fruitful discussions on rotational wire-grid polarizer. We also thank Mr. Hiroyasu Furukawa of Nippon Steel and Sumitomo Metal Corporation, Japan, for preparation of the paint samples.

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(θ_P, θ_A)	$E^{i n} (ω)$	$E^{o u t} (ω)$
(0°, 0°)	$E_{p}^{0} (ω) {\tilde{r}}_{p p} (ω)$	$E_{p}^{0} (ω) {\tilde{r}}_{s p} (ω)$
(0°, 90°)	$- E_{p}^{0} (ω) {\tilde{r}}_{s p} (ω)$	$- E_{p}^{0} (ω) {\tilde{r}}_{p p} (ω)$
(45°, 0°)	$\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{p p} (ω) + {\tilde{r}}_{p s} (ω))$	$\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{s p} (ω) + {\tilde{r}}_{s s} (ω))$
(45°, 90°)	$- \frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{s p} (ω) + {\tilde{r}}_{s s} (ω))$	$\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{p p} (ω) + {\tilde{r}}_{p s} (ω))$
(90°, 0°)	$E_{s}^{0} (ω) {\tilde{r}}_{p s} (ω)$	$E_{s}^{0} (ω) {\tilde{r}}_{s s} (ω)$
(90°, 90°)	$- E_{s}^{0} (ω) {\tilde{r}}_{s s} (ω)$	$E_{s}^{0} (ω) {\tilde{r}}_{p s} (ω)$

Eddy-current meter	104.5 ± 0.9	20.4 ± 0.8	10.0 ± 1.0	5.6 ± 0.6	4.4 ± 0.7
Ellipsometer	105.20 ± 0.12	20.58 ± 0.14	10.39 ± 0.06	5.66 ± 0.09	4.39 ± 0.069

(θ_P, θ_A)	$E^{i n} (ω)$	$E^{o u t} (ω)$
(0°, 0°)	$E_{p}^{0} (ω) {\tilde{r}}_{p p} (ω)$	$E_{p}^{0} (ω) {\tilde{r}}_{s p} (ω)$
(0°, 90°)	$- E_{p}^{0} (ω) {\tilde{r}}_{s p} (ω)$	$- E_{p}^{0} (ω) {\tilde{r}}_{p p} (ω)$
(45°, 0°)	$\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{p p} (ω) + {\tilde{r}}_{p s} (ω))$	$\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{s p} (ω) + {\tilde{r}}_{s s} (ω))$
(45°, 90°)	$- \frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{s p} (ω) + {\tilde{r}}_{s s} (ω))$	$\frac{1}{2} (E_{p}^{0} (ω) + E_{s}^{0} (ω)) ({\tilde{r}}_{p p} (ω) + {\tilde{r}}_{p s} (ω))$
(90°, 0°)	$E_{s}^{0} (ω) {\tilde{r}}_{p s} (ω)$	$E_{s}^{0} (ω) {\tilde{r}}_{s s} (ω)$
(90°, 90°)	$- E_{s}^{0} (ω) {\tilde{r}}_{s s} (ω)$	$E_{s}^{0} (ω) {\tilde{r}}_{p s} (ω)$

Eddy-current meter	104.5 ± 0.9	20.4 ± 0.8	10.0 ± 1.0	5.6 ± 0.6	4.4 ± 0.7
Ellipsometer	105.20 ± 0.12	20.58 ± 0.14	10.39 ± 0.06	5.66 ± 0.09	4.39 ± 0.069

Double-modulation reflection-type terahertz ellipsometer for measuring the thickness of a thin paint coating

Abstract

1. Introduction

2. Instrument

3. Ellipsometric measurements

3.1 Quadrature signal detection

3.2 Measurement of an isotropic sample

3.3 Measurement of an anisotropic sample

4. Experiments

4.1 Measurement of the complex refractive index of a Si substrate

4.2 Measurement of the complex refractive index of a paint coating

4.3 Measurement of the thickness of a thin paint coating

5. Conclusions

Acknowledgements

References and links

Cited By

Figures (5)

Tables (2)

Equations (14)

Optics Express