Novel auto-correction method in a fiber-optic distributed-temperature sensor using reflected anti-Stokes Raman scattering

Dusun Hwang; Dong-Jin Yoon; Il-Bum Kwon; Dae-Cheol Seo; Youngjoo Chung

doi:10.1364/OE.18.009747

1. Introduction

Optical fiber sensors have attracted interests for decades because they can offer the capability of easy handling to apply harsh environment and reduced operational risks (no electrical shocks or sparks), and optical fiber is inherently immune to electromagnetic interference (EMI). Some of these sensors have the prominent feature of fully distributed measurement through the optical fiber. For the distributed temperature sensor (DTS), the Raman DTSs have been most widely used and investigated [1].

Raman DTS is essentially a variant of an optical time domain reflectometry (OTDR) technique. When a short pulsed light is launched in one end of a sensing fiber, this pulsed light travels through the fiber. This light is scattered everywhere and partially guided back to the launching end. The scattering lights are categorized into three wavelength bands, i.e., Rayleigh, Brillouin, and Raman scatterings. For the conventional DTS system, these three components are involved. The ratio of temperature sensitive anti-Stokes intensity to temperature-insensitive Rayleigh or Stokes intensities is used to determine the values of temperature through the sensing optical fiber. Because these ratio are independent of the laser power, the launch conditions and the composition of the fiber (provided no fluorescence occurs), thus the only correction required is a small allowance for differences in the fiber attenuation at each wavelength when long length of fiber is used [1].

But recently the critical issue of the DTS systems has been an ambiguity in the backscattered intensity profile, which is the function of local attenuation affected by physical perturbations as well as that of pure temperature effects. To avoid the measurement error due to this ambiguity, the effect of local attenuations should be eliminated at the time of installation and afterward continuously. This is mainly due to the inherent attenuation difference in Stokes wave and anti-Stokes wave owing to their wavelengths difference which ranges from 100nm to 200nm and depends on the wavelength of pump light source. The fibers which are made under different manufacturing process have different attenuation profiles. Moreover, these differential attenuations are increased when the fiber undergoes perturbations such as bends, tensions, compressions, radiation, and chemical contamination. For the case of bending or compression, the differential attenuation is relatively small so it can be compensated by Rayleigh or Stokes wave. So the γ-ray radiation in nuclear infrastructures [2] and hydrogen darkening in oil well [3] are typical origins of temperature error due to the differential attenuation problem. Some modification methods have been proposed using Rayleigh and anti-Stokes bands, but the wavelength difference was still remained thus the differential attenuation couldn’t be completely eliminated [4].

The dual-ended (DE) configuration was proposed for the automatic correction of differential attenuation. In this configuration, both ends of sensing fiber are connected to DTS unit to cancel out common attenuations [5]. This method also has an advantage of redundancy in the case of fiber breakage in a section of sensing fiber. But there are some issues related to this scheme, which require double length of sensing fiber and extra DTS channel. To avoid these disadvantages, a dual-light source scheme has been proposed [6]. This method utilizes two light sources with different wavelengths, such that the wavelength of the primary source’s return anti-Stokes component overlaps with the incident wavelength of the secondary light source to cancel out the non-identical attenuations generated by the wavelength differences between Stokes and anti-Stokes. But this configuration requires one additional light source, an optical switch, and still two Avalanche photodiodes (APDs).

In this paper, a simpler and fully automatic correction method is presented, which just requires only one light source and only one APD. The key concept of our scheme is attachment of a reflecting mirror at the end of sensing fiber so that the reflected anti-Stokes wave cancels out the effect of local attenuation of fiber.

2. Theory

Anti-Stokes which is the most important component of Raman scattering is attributed to the simultaneous annihilation of one photon of the incident radiation and on thermally excited phonon followed by the creation of a new photon with higher energy [7]. The probability for this anti-Stokes scattering process is proportional to the number of phonons at a given fiber position x and can be deduced from Bose-Einstein statistics. Similar expression also can be derived for the Stokes process where a phonon with energy hcΔν is created and the photon loses the same amount of energy. The differential cross section for anti-Stokes and Stokes scattering depends on the temperature at position z [8]:

\frac{d σ_{A S}}{d Ω} ≅ \frac{1}{λ_{A S}^{4}} \frac{1}{\exp (\frac{h c Δ ν}{k_{B} T (z)}) - 1}, \frac{d σ_{S}}{d Ω} ≅ \frac{1}{λ_{S}^{4}} \frac{1}{1 - \exp (- \frac{h c Δ ν}{k_{B} T (z)})},

where h is Planck’s constant, c is the velocity of light in vacuum, Δν is the Raman shift in transmission medium, and k_B is Boltzmann’s constant. If we assume that the all transmission-related background features, such as absorption, splice loss, connectors loss, bending loss and so forth, are included in α_x(z) (subscript p, AS, and S mean pump, anti-Stokes, and Stokes, respectively) the intensity of anti-Stokes signal I_AS and the intensity of Stokes signal I_S can be expressed by [4]

I_{A S} (z, T) = P_{0} A_{A S} (T) \exp (- \int_{0}^{z} α_{P} (z) d z - \int_{0}^{z} α_{A S} (z) d z) + C,

I_{S} (z, T) = P_{0} A_{S} (T) \exp (- \int_{0}^{z} α_{P} (z) d z - \int_{0}^{z} α_{S} (z) d z) + D,

where P₀ is the incident pump power, C and D are constant background dark currents of photodiodes for anti-Stokes and Stokes wave, respectively. A_AS(T) and A_S(T) are the temperature-dependent Raman scattering cross section for anti-Stokes and Stokes, respectively. These values are proportional to the differential cross sections,

d σ_{A S} / d Ω

and

d σ_{S} / d Ω

averaged over the capture fraction S for anti-Stokes and Stokes Raman scattering, respectively [8]. Thus, assuming no Raman scattering induced attenuation and the same capture fraction of anti-Stokes and Stokes wave in the fiber, the ratio between two backscattered Raman components, R(z) is given by

R (z) = \frac{I_{A S} - C}{I_{s} - D} = \frac{\exp (- \int_{0}^{z} α_{P} (z) d z - \int_{0}^{z} α_{A S} (z) d z) \frac{d σ_{A S}}{d Ω} (z)}{\exp (- \int_{0}^{z} α_{P} (z) d z - \int_{0}^{z} α_{S} (z) d z) \frac{d σ_{S}}{d Ω} (z)} .

Assuming α_AS(z) ≈ α_S(z), the exponential terms are reduced and R(z) can be simplified as

R (z) \approx \frac{d σ_{A S}}{d Ω} (z) / \frac{d σ_{S}}{d Ω} (z) = \frac{λ_{S}^{4}}{λ_{A S}^{4}} e^{- \frac{h c Δ ν}{k_{B} T (z)}} .

To calculate the absolute temperature, the reference fiber coil located in a DTS unit is maintained at a known temperature T(z₀). The unknown temperature T(z) along the arbitrary section of the sensing fiber can be calculated by rearranging the above equation as

T (z) = {(\frac{k_{B}}{h c Δ ν} \log (\frac{R (z_{0})}{R (z)}) + \frac{1}{T (z_{0})})}^{- 1} .

The final equation is the temperature equation for typical DTS system. The assumption (α_AS(z) ≈ α_S(z)) holds true when there is no differential attenuation or the length of fiber is sufficiently short to neglect the effect of differential attenuation. But for the case of hydrogen darkening or γ-ray irradiation, this approximation is not true anymore.

In the proposed system, a mirror was located at the end of the sensing fibers (See Fig. 1 ). In our system, we considered only the anti-Stokes component for the scattered light.

Fig. 1 Normal back scattered beam and reflected back scattered beam.

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In the Fig. 1, we can express the normal back scattered signal, I_n and reflected back scattered signal, I_r as

I_{n} (l) = P_{0} g (l, T) \exp (- \int_{0}^{l} α_{P} (z) d z - \int_{0}^{l} α_{A S} (z) d z) + C,

I_{r} (l) = P_{0} R_{p} R_{A S} g (l, T) \exp (- \int_{0}^{L} α_{P} (z) d z - \int_{l}^{L} α_{P} (z) d z - \int_{0}^{L} α_{A S} (z) d z - \int_{l}^{L} α_{A S} (z) d z) + C,

where the g(l,T) is the Raman cross section captured by the sensing fiber at l with temperature T. R_p and R_AS are the reflectivity of mirror at the pump wavelength and anti-Stokes wavelength, respectively. By multiplying Eqs. (7) and (8), the integration terms get together and become a constant for the location l and we can get

I_{f} (l) = \sqrt{(I_{n} (l) - C) (I_{r} (l) - C)} = A R g (l, T) P_{0}

where the

A = \exp (- \int_{0}^{L} (α_{p} (z) + α_{s} (z)) d z)

and the

R = \sqrt{R_{p} R_{s}} .

In left side of Eq. (9) the location dependences of all transmission related losses are removed and the temperature dependent g(l,T) is remained. Namely, any local attenuation affects to the whole range of signal with same amount (note that the A is the integration over the whole range of sensing fiber), and it can be considered constant. Thus we can eliminate the other environmental effect from the acquired signal except the information of temperature. If we solve the Eq. (9) for g(l,T) and substitute l to the arbitrary location z, then we can get

g (z, T) = \frac{I_{f} (z)}{A R P_{0}} .

Because g(z,T) is proportional to differential cross section of anti-Stokes scattering, left side of Eq. (10) can be replaced as follow,

\frac{S}{λ_{A S}^{4}} \frac{1}{\exp (\frac{h c Δ ν}{k_{B} T (z)}) - 1} = \frac{I_{f} (z)}{A R P_{0}},

where S is the proportional coefficient which means the fraction of scattering captured by numerical aperture (N.A.) of sensor fiber. With the Eq. (11), we can construct the temperature equation with procedure similar to the conventional DTS as follows:

T (z) = {(\frac{k_{B}}{h c Δ ν} \log (\frac{I_{f} (z_{0})}{I_{f} (z)} (e^{\frac{h c Δ ν}{T (z_{0}) k_{B}}} - 1) + 1))}^{- 1} .

From above Eq. (12) we can evaluate the absolute temperature of a specific point from only the anti-Stokes component not from the ratio of different components.

3. Experiment

For the verification of the proposed method, temperature and bending experiments were performed. The experimental setup was shown in Fig. 2 .

Fig. 2 Schematics of single wavelength auto-correction experiment.

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The pulsed laser light was generated at 50 ns of pulse width and 5 kHz of repetition rate. This pulse was amplified by erbium-doped fiber amplifier with 20 dB gain. The amplified pulsed laser light was launch to the sensing fiber (SMF-28) by passing through the optical circulator. The launched laser pulse propagates through the sensing fiber and is reflected at the end of the sensing fiber by mirror. The reflected light comes back to the circulator and finally terminated by Raman filter. The reflectivities of mirror at the pump wavelength and anti-Stokes wavelength were both about 99%. During the pulsed laser propagation, the anti-Stokes wave was generated and guided back to the APD. When the pulsed laser propagates in forward direction (from the circulator to the mirror), the back-scattered light is detected by APD as a typical DTS system. But when the pump laser propagates in backward direction (from the mirror to the circulator) after reflected by the mirror, the back-scattered light is also reflected by the mirror. The reflected back-scattered light passes through the sensing fiber and is detected by APD. Between these normal scattered light and reflected scattered light, all forward scattered light which propagated with the pump light is arrived at the APD. The whole signals which include the normal back-scattered anti-Stokes light, forward scattered light, and reflected back-scattered anti-Stokes light, were measured by APD and was averaged 10000 times during the 47 sec. The averaged signal was shown in Fig. 3 . In this signal the normal back-scattering, forward scattering (peak), reflected back-scattering are located in sequence. For the case of normal back scattered light, the time t and the location z have the relation as follow,

I_{n} (z) = I_{s} (t) = I_{s} (2 z / v_{g}),

where v_g is the group velocity of pump and scattered light in the fiber, I_s(t) is the signal which is measured at time t, and 0<t<2L/v_g.

Fig. 3 (a) Acquired raw signal from proposed DTS. (10⁴ times averaging), the change of temperature profiles of 4.3km-long fiber sensor at different oven temperature for (b) full range profile, and (c) enlarged temperature profile over the 2.1km-2.35km.

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But for the case of reflected scattering wave, the locations are mapped on the reverse of time like,

I_{r} (z) = I_{s} (t) = I_{s} (2 (2 L - z) / v_{g}),

where 2L/v_g<t<4L/v_g.

For the temperature test, we measured the anti-Stokes Raman scattering signal as a function of time by increasing the temperature from the room temperature, 23 °C to 100 °C. During heating up the oven, the temperature of reference fiber was also measured. This results are shown in Fig. 3(a). The splicing loss induced signal attenuations can be observed near the 22 μs and 61 μs due to splicing points between fiber spools and 50 m-long test fiber in the oven. The forward scattering beam was observed at 42 μs. The increasement of scattering signal due to the temperature increase can be observed near the 22 μs and 61 μs in this figure. The differences among the total level of signals are thought to be originated from the incident power decay due to the long time operation. We used the signal between 2 μs and 3 μs as a reference signal which coincide with the fiber ranging from 200 m to 300 m from the circulator to compensate the incident power decay. After the signal process which was described in section 2, we extracted the temperature information along the fiber location z. The temperature distribution of the fiber was presented in Figs. 3(b) and 3(c). From the Fig. 3(c) we can validate that the proposed temperature equation, Eq. (12) is working properly.

To prove the auto-correction properties of the proposed method, the bending experiment was performed while maintaining the same temperature. At the room temperature, we applied bending at the point A and B. The changes of signal due to the bending are presented in Figs. 4(a) and 4(b).

Fig. 4 (a) Change of acquired signal for DTS due to the bending. (b) Magnified signal of (a) near the bending point. (c) Calculated temperature.

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The black curve stands for the original signal without intentional bending and the red and green curves stand for the signals which were measured when we applied bending at the location A and at the location A and B, respectively. Despite of the applied bending, the measured temperature from the proposed method in Fig. 4(c) was invariant. From the above bending experiment, we can confirm the auto-correction properties of proposed method. Moreover, because we used only the light at the anti-Stokes wavelength to calculate the temperature, there was no differential attenuation effect which is originated from the usage of lights in two different wavelengths.

The considerable problem of proposed method is the degradation of signal-to-noise ratio (SNR). For the comparison between proposed method and two well known conventional methods, we measured the temperature resolution of each method. In each method the worst temperature resolution appears at different point of sensing fiber. For the case of conventional DTS, the SNR decreases as the measurement location is far from the DTS system [9]. And for the dual ended scheme, the SNR has the lowest value at the both ends of sensing fiber. But in the proposed scheme, the SNR has lowest value at the beginning of sensing fiber and is increased as it goes to fiber end. This nature is originated from the signal processing method. In the proposed method, the temperature at the beginning point is calculated from the product of intensity between the strongest signal and the weakest signal so the result gives the noisiest signal. The same effect occurs in the case of dual ended method. The product of intensity between the strongest signal and the weakest signal occurs at the both end of fiber, so the worst SNR appears at these points. Any physical perturbation at the downstream of fiber doesn’t affect the SNR or temperature resolution of upstream of fiber in the single ended operation. But in the dual ended method and proposed method, SNR of all points are affected by every loss (attenuation, bending loss, splice loss, connector loss, etc.) at entire fiber. To compare both methods fairly, we just measured the maximum temperature resolution (the worst temperature resolution) in the previous experimental condition. For single ended operation the maximum temperature resolution was 2.37 °C, for the dual ended operation it was 1.45 °C, and for proposed operation it was 2.95 °C at room temperature with 4.2 km of conventional single mode fiber with 3 splicing points with the same amount of averaging (10000 times). The amount of SNR improvement is different for each measurement setup and condition but dual ended scheme usually gives a better SNR and temperature resolution than the single ended scheme. The proposed method gives the slightly better result than the single ended operation only at the end of fiber, because the proposed method has an effect similar to multiplication of two substantially identical signals at this point. Except this point the proposed method gives worse temperature resolution. Our proposed method has some analogue with dual ended operation. Neglecting the signal degradation at the reflecting mirror and the noise of Stokes wave, the minimum SNR of proposed method is identical to the conventional dual ended operation with double length of sensing fiber. Additionally the reflectivity of reflecting mirror degrades the SNR of proposed system with a factor of R². The bending applied at A and B made the signal weaker and induced a worse temperature resolution. From original signal the temperature resolution (usually expressed by standard deviation, σ) was 2.95 °C and it degraded as 3.03 °C and 3.45 °C for the A-point bending and the AB-points bending, respectively. Besides temperature resolution itself, the measurement time is also an important factor of DTS. For the 10000 times average, proposed method took 47seconds while the single ended operation took only 25 seconds. The measurement time for 10000 records averaging of proposed method (47 sec.) is nearly twice that of single ended operation(25 sec.) but it is not exactly twice because of rearming time of data acquisition board.

Generally in DTS, the temperature resolution can be improved by increasing the measurement time. The noise of the signal is nearly random, so if we increase the number of averaging by N times then the noise are reduced by 1/N times. The noise of proposed scheme is 1.24 times higher than that of single ended system, so 2(double record length) × 1.24² = 3.08 times longer measurement time is required for the similar quality of conventional single ended methods for our 4.2km SMF system. Thus our proposed setup would be a good solution for auto correction of differential attenuation with lower cost and simpler setup but in which the measurement time doesn’t much matter.

4. Conclusion

We proposed and experimentally demonstrated a simple and novel auto-correction distributed temperature measurement method by detecting only the anti-Stokes Raman back scattering of the fiber. This system is able to work with single light source and single APD without any optical switch or additional APD, which ensures that the system is highly cost-competitive. In this measurement method intrinsically there is no differential attenuation, because it measures anti-Stokes wave only. And the auto-correction characteristics of proposed method were confirmed by bending experiment successfully. The proposed method is expected to be a good solution for the systems which require auto-correction functionality for the continuous measurement and cost-effectiveness.

Acknowledgements

This work is financially supported by Ministry of Education & Science Technology through the Project of “Development of advanced measurement technology for public safety” (KRISS-10-011-131)

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Novel auto-correction method in a fiber-optic distributed-temperature sensor using reflected anti-Stokes Raman scattering

Abstract

1. Introduction

2. Theory

3. Experiment

4. Conclusion

Acknowledgements

References and links

Cited By

Figures (4)

Equations (14)

Optics Express