In-situ non-contact high-temperature measurement of an optical fiber up to the glass softening point

K. Mühlberger; C. M. Harvey; M. Fokine

doi:10.1364/OE.417175

1. Introduction

Optical fiber based sensors, such as fiber Bragg gratings (FBG), have found widespread use as temperature sensors for a number of different applications [1–3]. Certain types of FBGs can be used at extreme temperatures, well above of 1000 °C [4,5]. Using a high-temperature stable FBG, known as chemical composition grating (CCG), temperatures in excess of 1700 °C have been measured [6]. At these high temperatures, however, calibration becomes a significant challenge.

In this work we present a simple technique to locally measure the temperature of an optical fiber for temperatures approaching the softening point of glass. Viewing an optical fiber in the transverse plane, the circular cross-section forms a concentric Fabry-Pérot cavity interferometer (CCI), bound by the Fresnel reflections at the outer cladding surfaces. The optical path length (OPL) of this cavity is defined by the fiber diameter and the refractive index. Similar to the temperature response of the FBG wavelength ($\lambda _{\textrm {B}}$), the OPL depends on the thermo-optic and thermal expansion coefficient of the glass. For the CCI this results in a temperature-dependent phase ($\phi _{\textrm {OPL}}$) in the back-scattered interference pattern. Here, the concept of probing a CCI remotely using a HeNe-laser for in-situ temperature measurements is evaluated, similar to [7,8]. The detected phase response of the CCI was calibrated by comparison with a FBG temperature sensor. In particular, the phase response from the heating of a 125 µm diameter single-mode optical fiber with a CO$_2$-laser was measured. For calibration, the phase response was compared to the Bragg wavelength shift of an inscribed CCG in order to obtain a temperature reading. Temperatures between room temperature and 1400 °C were measured with a precision of $\pm 0.5\,\%$.

2. Sensing principle

A FBG temperature sensor relies on the change in Bragg wavelength with temperature coupled through the thermo-optic and thermal-expansion coefficients. The thermal response of the FBG wavelength is given by

(1)$$\lambda_\textrm{B}\left(T\right) = 2\Lambda\left(T\right)n\left(T\right),$$

where $\Lambda$ is the period of the grating and $n$ the refractive index.

Measuring temperature with a CCI is possible by monitoring the phase of the back-scattered interference pattern, given by:

(2)$$\phi_\textrm{OPL}\left(T\right) = \frac{2\pi}{\lambda_i}\cdot2L\left(T\right)n\left(T\right),$$

where $L$ is the cavity length corresponding to the fiber diameter, and $\lambda _i$ is the wavelength of the probing laser beam. Due to the size of the optical fiber and the wavelength of the probing laser, the light scattering can typically be treated using geometrical optics.

As shown in Fig. 1(a), the CCI is formed by the circular geometry of the optical fiber cross section. An axially focused laser beam, with the focus placed at the center of the fiber will be reflected due to Fresnel reflections at the air-glass interfaces at the front and back surfaces of the optical fiber. This results in the interference pattern shown in Fig. 1(b). Reflections at the cladding-core interfaces within in the fiber are orders of magnitude smaller than at the air-glass interface, because of the lower refractive index contrast. Thus, the source for reflected light are the two air-glass interfaces. The intensity response function in reflection for such a Fabry-Pérot cavity is

(3)$$I_\textrm{FP}\left(R, \phi\right) = \frac{2R\left(1-\cos\left(2\phi\right)\right)}{1+R^2-2R\cos\left(\phi\right)},$$

where $R$ is the reflectivity at the air-glass interface and $\phi$ the phase between the two interfering beams. Since the Fresnel reflections using a silica fiber in air are as low as $R\approx 3.5\,\%$, Eq. (3) can be approximated by the sinusoidal function

(4)$$I_\textrm{FP} \left(\phi\right) = I_0 + I_0\cos\left(2\phi\right).$$

Consequently, the phase change of the interference pattern can be measured using quadrature phase shift detection [9].

Fig. 1. (a) Schematic of the CCI illustrating the Fresnel reflection from the two opposite surfaces of the optical fiber. The fiber represents a low-finesse CCI with mirrors having a radius of half the fiber diameter. (b) Photograph of the back-scattered interference pattern of the optical fiber when exposed to a focused HeNe-laser.

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The interference signal of the reflections (illustrated in Fig. 1(b)) depends on the phase of the CCI, which itself is defined by the temperature-dependent OPL through the fiber. The temperature-dependent phase shift of the CCI can be written as

(5)$$\Delta\phi\left(T\right) = \phi_\textrm{OPL}\left(T\right)-\phi_\textrm{OPL}\left(T_{RT}\right) = \phi_0\left(\alpha + \frac{\beta}{n_0}\right)\cdot\Delta T + \phi_0 \left(\frac{\alpha\beta}{n_0}\right)\cdot\Delta T^2,$$

where $\phi _0=\phi _{\textrm {OPL}}\left (T_{RT}\right )=4\pi n_0 L_0\lambda _i^{-1}$ is the phase at room temperature, $\alpha$ is the thermal-expansion coefficient, $\beta$ is the thermo-optic coefficient, $n_0$ is the refractive index at room temperature and $\Delta T = T-T_{RT}$ is the temperature change relative to room temperature in °C. The assumptions made are a linear temperature dependence of:

• the cavity length $L\left (T\right )=L_0\left (1+\alpha \Delta T\right )$, and
• the refractive $n\left (T\right ) = n_0 + \beta \Delta T$,

where $L_0$ is the cavity length at room temperature. The characteristics of the CCG and of the CCI are summarized in Table 1.

Table 1. Comparison of the characteristics of the CCG and the CCI.

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3. Experimental setup

The CCI was calibrated for temperature measurements using a CCG by simultaneously monitoring the phase response of the CCI and the Bragg wavelength shift of the CCG during exposure to a CO$_2$-laser beam used to heat the fiber.

3.1 CCG temperature reading

First, the temperature-dependent Bragg wavelength shift of the CCG was determined. This was accomplished by putting the grating inside an oven (Carbolite CWF 1100) where the temperature was increased stepwise up to 988 °C. A K-type thermocouple was positioned adjacent to the grating inside the oven to monitor the temperature. Concurrently, the Bragg wavelength peak was detected by an optical spectrum analyzer (BaySpec FBGA-IRS).As the temperature increased the Bragg wavelength peak of the CCG shifted toward longer wavelengths, as illustrated in Fig. 2(a). The temperature-dependent Bragg wavelength shift of the CCG can be written as

(6)$$\Delta\lambda_\textrm{B}\left(T\right) = \lambda_\textrm{B}\left(T\right)-\lambda_\textrm{B}\left(T_{RT}\right) = \lambda_0\left(\alpha+\frac{\beta}{n_0}\right)\cdot\Delta T + \lambda_0\left(\frac{\alpha\beta}{n_0}\right)\cdot\Delta T^2,$$

where $\lambda _0=\lambda _{\textrm {B}}\left (T_{RT}\right )=1543\,\textrm{nm}$ is the Bragg wavelength at room temperature. This equation follows from Eq. (1) assuming a linear temperature dependence of the grating period $\Lambda \left (T\right )=\Lambda _0\left (1+\alpha \Delta T\right )$, where $\Lambda _0$ corresponds to the period of the grating at room temperature. Figure 2(b) shows the temperature-dependent Bragg wavelength shift. The data points were taken after the oven temperature was allowed to stabilize for more than 10 min. A second-order polynomial was fitted to the data:

(7)$$\Delta\lambda_\textrm{B} = 1.009 \cdot 10^{-2}\,{\textrm {nm}}^{\circ}\textrm{C}^{-1} \cdot \Delta T + 6.711 \cdot 10^{-6}\,\textrm{nm}^{\circ}\textrm{C}^{-2} \cdot \Delta T^2.$$

The R$^2$-value is 0.9998 and the root-mean-square error (RMSE) is ±87 pm corresponding to ${\pm 7.2}^{\circ}\textrm{C}$. The specified temperature accuracy of the thermocouple used at 1000 °C is $\pm 7.5^{\circ}\textrm{C}$. The calibration of the CCG was limited to temperatures below 1000 °C, because at temperatures approaching the glass transition region, the stability of the refractive index modulation and thus the stability of the Bragg wavelength decreases, resulting in larger errors [10,11].

Fig. 2. (a) Reflected Bragg wavelength of the CCG calibration at three example temperatures. (b) The CCG’s temperature-dependent Bragg wavelength shift.

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3.2 Sensor calibration

Following the CCG calibration, the Bragg wavelength change and the phase change of the CCI upon heating the fiber were recorded simultaneously in order to relate the phase response to the temperature response.

The optical fiber used in this study was fabricated by chemical vapour deposition. It was a silica-based single-mode fiber with a diameter of 125 µm, comprising a F-Ge$_2$-doped core. It is from the same batch as the fiber used in [11], labeled "fiber I". The core has an inscribed 2 mm-long CCG (see [12] for fabrication details). The CCG survived temperatures well above 1000 °C. The Bragg wavelength of the CCG was monitored in reflection using a super-continuum white-light source (Koheras SuperK) and an optical spectrum analyzer (BaySpec FBGA-IRS) sampling at 1 kHz. The fiber was heated by the vertically polarized beam of a CO$_2$-laser (Synrad Firestar ti100HS) operating at a wavelength of $\lambda =10.6\,\mathrm{\mu}\textrm{m}$, which was focused using a spherical lens ($f=101.6\,\textrm{mm}$). The fiber was positioned on the far side of the focus of the CO$_2$-laser beam. In perpendicular direction, a HeNe-laser beam was focused onto the fiber using a spherical lens ($f=50\,\textrm{mm}$). The combination of quarter waveplate and polarizing beamsplitter filtered out any reflections not originating from the fiber, ensuring that only the CCI Fresnel reflections of the fiber reach the two detectors $S_1$ and $S_2$. Both, the HeNe-laser beam and the CO$_2$-laser beam, were carefully aligned to overlap at the location of the CCG as illustrated in Fig. 3. The phase response was measured by the two sensors $S_1$ and $S_2$ sampling at 1 kHz. They were positioned 90° out of phase to detect the quadrature phase shift. After the two signals detected at $S_1$ and $S_2$ were offset around zero and normalized. The wrapped phase was extracted by simply using the arctangent function. Subsequent correction for phase jumps in the arctangent function revealed the unwrapped phase of the CCI (see [9] for details about the phase unwrapping algorithm). This measurement setup allowed for the recording of the Bragg wavelength shift of the CCG during CO$_2$-laser heating, while simultaneously measuring the corresponding phase response of the CCI.

Fig. 3. Schematic of the experimental layout. Note that the fiber under test (FUT) is the same on the left and on the right. Left: White-light source (WL) and optical spectrum analyzer (OSA) monitor the Bragg wavelength of the grating inscribed in the fiber. Right: Polarization and intensity control of HeNe-laser by half waveplate (HWP) and polarizer; M1 beam steering mirror; Quarter waveplate (QWP) and polarizing beamsplitter (PBS) ensuring only reflections from the fiber are incident on detectors $S_1$ and $S_2$; CO$_2$-laser to heat the fiber, vertically polarized and focused by a ZnSe lens.

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4. Results

The optical fiber was exposed to a CO$_2$-laser beam at the position of the calibrated CCG. Both the Bragg wavelength shift of the CCG and the corresponding phase response of the CCI upon heating the fiber for 2 s were recorded for 17 separate experiments, each with different power settings of the CO$_2$-laser, ranging between 5.8 W and 39.2 W. Figure 4 shows the normalized data for four different power settings. For clarity only every $100^{\textrm th}$ datapoint of the measured Bragg wavelength shift was plotted. The obtained relation between normalized Bragg wavelength change and normalized phase change is plotted in Fig. 5 and fitted by the linear regression:

(8)$$\Delta \lambda_\textrm{B} = 0.4230 \pm 0.0002\,\textrm{nm rad}^{-1} \cdot \Delta\phi.$$

Finally, the temperature calibration curve of the CCG (see Fig. 2(b)) and the linear relation between the CCG and the CCI (see Fig. 5) were combined to obtain the calibrated phase change of the CCI for a given temperature change. The data is plotted in Fig. 6 and fitted by Eq. (5) solved for $\Delta T$:

(9)$$\Delta T = a \cdot\left(\sqrt{1+b\cdot \Delta\phi} - 1\right).$$

Here, $a=7.771 \cdot 10^{2\circ}\textrm{C}$, $b=1.064 \cdot 10^{-1}\,\textrm {rad}^{-1}$, the R$^2$-value is 0.9998 and the RMSE is ±7.2 °C corresponding to ±0.5 %. The RMSE is within the same range as the temperature uncertainty of ±7.2 °C of the CCG calibration.

Fig. 4. Normalized Bragg wavelength shift and normalized phase change upon heating the optical fiber with a CO$_2$-laser for 2 s.

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Fig. 5. Measurement data showing the linear relation between the Bragg wavelength shift of the CCG and the phase change of the CCI.

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Fig. 6. Final CCI calibration curve for a 125 µm diameter fused silica optical fiber. The temperature change induced by the CO$_2$-laser was measured by monitoring the phase response $\Delta \phi$ of the CCI.

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5. Discussion and conclusion

Highly reproducible in-situ temperature measurements are demonstrated (see Fig. 4) by monitoring the phase response of the CCI. Except for small variations regarding the response times of the CCG and the CCI, both can be considered to respond identically to temperature variations. This allows for the deduction of a constant material-dependent relation between $\Delta \lambda _{\textrm {B}}$ and $\Delta \phi$. The ratio of $\Delta \lambda _{\textrm {B}}$ and $\Delta \phi$ is given by

(10)$$\frac{\Delta\lambda_\textrm{B}}{\Delta\phi} = \frac{\lambda_0\lambda_i}{4\pi n_0L_0} = 0.425\,\textrm{nm rad}^{-1},$$

where $\lambda _0=1543\,\textrm{nm}$, $\lambda _i=632.8\,\textrm{nm}$, $n_0=1.46$ and $L_0=125\,\mathrm{\mu}\textrm{m}$. The theoretical value for $\Delta \lambda _{\textrm {B}}/\Delta \phi = 0.425\,\textrm{nm rad}^{-1}$ is in good agreement with the experimentally determined value of $0.4230(2)\,\textrm{nm rad}^{-1}$ (see Fig. 5). It should be pointed out that, although the calibration of the CCG is limited to the long-term stability of the grating [6], the CCI technique itself is limited to temperatures below the softening point of glass (1600 °C to 1700 °C for fused silica). At those high temperatures, surface tension causes deformation of the fiber resulting in a change in fiber diameter and OPL of the CCI, which would result in an accumulation of error over time.

As illustrated in Fig. 6, the final CCI calibration curve is in good agreement with the theoretically expected square-root dependence on the phase-shift. The RMSE of $\pm 7.2^{\circ}\textrm{C}$ is a consequence of the CCG calibration, which is limited by the accuracy of the K-type thermocouple. However, the resolution of the CCI itself is only limited by the wavelength of the probing laser beam, the signal-to-noise performance of the sensor and the sampling rate of the sensor.

Moreover, the presented technique is not limited to optical fibers, but can be applied to any circular silica structure by scaling the respective diameter. Assuming a well-known diameter, any circular silica structure can work in and on itself as a CCI without needing an accompanying grating or recalibration. The technique is also applicable to structures of different optical materials; however, a custom calibration curve is needed for each material to account for the thermo-optic and thermal-expansion coefficients of the specific material.

In conclusion, a simple and reliable technique for in-situ non-contact high-temperature measurements of optical fibers was demonstrated. The technique is highly suitable for calibration of optical fiber sensors, for material characterization as well as for high-temperature process control, e.g. during fiber splicing, or as an optical sensor by itself.

Funding

Stiftelsen för Strategisk Forskning (RMA15-0135).

Disclosures

The authors declare no conflicts of interest.

References

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7. J. Jasapara, E. Monberg, F. DiMarcello, and J. W. Nicholson, “Accurate noncontact optical fiber diameter measurement with spectral interferometry,” Opt. Lett. 28(8), 601 (2003). [CrossRef]

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9. J. Wang and J. L. Pressesky, “Quadrature phase shift interferometer (QPSI) decoding algorithms and error analysis,” Proc. SPIE 5188, 71–79 (2003). [CrossRef]

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In-situ non-contact high-temperature measurement of an optical fiber up to the glass softening point

Abstract

1. Introduction

2. Sensing principle

3. Experimental setup

3.1 CCG temperature reading

3.2 Sensor calibration

4. Results

5. Discussion and conclusion

Funding

Disclosures

References

Cited By

Figures (6)

Tables (1)

Equations (10)

Optics Express