Conclusions of Chapter

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time tends to increase with the code length. This is because in order to obtain higher SNR, longer Walsh code must be used, which resulted in the increase in the number of code patterns. This obviously leads to a longer measurement time.

In contrast, for Golay code, regardless to the code length, only a pair of codes is used in the measurement. Therefore, if one aims to measure strain with fast measurement speed, combination no. 1) would be the best option.

On the other hand, as discussed in Chapter 6, when we have no information about the fiber type, there is a case where the total duration of continuously coded pulses happens to be twice longer than the time constant of the acoustic wave amplitude 𝜏𝑎. If this is the case for Golay code, it will cause the distortion in the decoded signal, which leads to the degradation of spatial resolution. Then, the employment of Walsh code would provide a better solution. In addition, compared to the discrete coding employing Walsh code, it was found that the maximum allowable Walsh code length for continuous coding is usually much shorter. In other words, the measurement time of the continuous Walsh coding would not be a problem for almost cases.

Let us give an example of a fiber of length 500m. In the case of discrete coding, regardless to the pulse width τ, the maximum code length is 32 bits. On the other hand, if we set 𝜏=0.2ns, in order to obtain spatial resolution that corresponds to the pulse width, the maximum allowable code length for continuous coding is also 32bits. For L of longer than 500m, however, the allowable code length increases for discrete coding, but remains unchanged for continuous coding. Consequently, the code length of the discrete coding can be often set longer than that of the continuous coding.

Furthermore, when using the 32 bits of Walsh code for the continuous coding, compared to that before code employment, the increase in the SNR is 15dB. In most cases of the continuous coding system, the SNR of 10dB cannot be achieved with the SNR improvement of 15dB (See Figs. 10.3 (b), 10.4 (b), 10.5 (b) and 10.6 (b)). Therefore, the implementation of signal addition process could be required additionally. Then, it takes the same time for both Walsh code and Golay code to reach the 10dB SNR.

Based on the above discussion, when there is variation in 𝜏_𝑎 along the fiber, the use of Walsh code in continuous coding would be preferable in order to obtain decoded signal with no degradation in spatial resolution. On the other hand, for discrete coding, in terms of fast measurement speed, Golay code would offer a more effective selection.

Therefore, it can be concluded that combination no. 2) provides a good tradeoff between the spatial resolution and measurement time. Since combination no. 3) is the opposite combination of no. 2), little merit of this combination can be found.

For combination no. 4), the measurement time would become a problem. In this study, since the goal is to perform the measurement of BFS with error of below 1MHz, the minimum required SNR of 10dB achievement was assumed. If we further want to perform a more accurate BFS measurement (much lower than 1MHz), however, the use of dual Walsh codes only would hardly obtain the required corresponding SNR. Thus, the signal addition process should be implemented additionally. In that case, as explained before, since there is no difference in the measurement time between Walsh code and Golay codes, combination no. 4) would be preferable for further obtaining smaller error in the BFS measurement with better spatial resolution.

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were performed so that the method to estimate the BFS should be as similar as possible with that of the actual measurement. Based on the results, in order to achieve BFS measurement error of below 1MHz, the required optical SNR was found to be about 10dB.

Next, the allowable maximum power of pump pulse and probe was discussed. For the pump case, the maximum optical power that can be used for the measurement is limited by the nonlinear effects in fiber: self-phase modulation effect, modulation instability (MI), Raman scattering etc. It was explained that the maximum allowable pump power that can be used without the influence of the nonlinear effects above was around 100mW. Therefore, in the simulations, the pump power was set to 20dBm (100mW).

For probe case, the maximum allowable power is influenced by the pump depletion effect. In this case, the probe input power depends on the fiber length L. Thus, the relationship between the BFS error and the probe power input was studied for two different fiber lengths, L=1km and L=10km. For L=1km case, in order to obtain BFS error of below 1MHz, the probe power was found to be less than 0dBm, while for L=10km case, the probe power should be less than -10dBm. These power settings were used to analyze the performance of the BOTDA employing code systems.

Based on the above considerations, the SNR of the conventional coded PSP-BOTDA (coded discrete- and coded continuous-PSP-BOTDAs) and the coded PSP-BOTDA employing code systems proposed in this thesis were analyzed and compared. In the simulations, fiber length L was set to 1km and 10km. In each fiber length case, the measurement with the spatial resolution zof 10cm and 2cm was considered. In this thesis, the employment of Walsh code and Golay code was proposed. The combinations of these codes that produce the dually coded system (dual Golay codes and dual Walsh codes) and the combined codes system are listed as follows.

1) discrete coding: Golay code + continuous coding: Golay code 2) discrete coding: Golay code + continuous coding: Walsh code 3) discrete coding: Walsh code + continuous coding: Golay code 4) discrete coding: Walsh code + continuous coding: Walsh code From the simulation results, it can be concluded that

i) Combination no. 1) provides the fastest measurement speed.

ii) If the variation in the BGS along the test fiber is anticipated in the measurement, the combination no. 2) would provide the best solution to obtain the good tradeoff between the spatial resolution and measurement time.

iii) Compared to other combinations, combination no. 3) has little merit.

iv) If BFS measurement error of much lower than 1MHz is required, the combination no. 4) would be appropriate.

References

[1] T. Horiguchi, T. Kurashima, and M. Tateda, “Nondestructive measurement of optical-fiber tensile strain distribution based on Brillouin spectroscopy”, IEICE Trans. B-I, vol. J.73-B-I, no. 2, pp. 144-152, Feb. 1990.

[2] H. Izumita, Y. Koyamada, S. Furukawa, and I. Sankawa, “The performance limit of coherent OTDR enhanced with optical fibre amplifiers due to optical nonlinear phenomena”, J. Lightwave Technol., vol. 12, no. 7, pp. 1230-1238, 1994.

[3] G. Agrawal, “Nonlinear Optics”, fourth ed. Academic Press, (2008).

[4] V. Lecoueche, D. J. Webb, C. N. Pannel, and D. A. Jackson, “25 km Brillouin based single-ended distributed fibre sensor for threshold detection of temperature or strain”, Optics Communications, vol.168, pp.95-102, Sept. 1999.

[5] D. Alasia, M. G. Herraez, L. Abrardi, S. M. Loppez, and L. Thevenaz, “Detrimental effect of modulation instability on distributed optical fibre sensors using stimulated Brillouin scattering”, 17th OFS (2005), in Proceedings of SPIE 5855, pp.

117 587-590.

[6] T. Horiguchi and M. Tateda, “BOTDA - Nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: Theory”, J. Lightwave Technol., vol.7, no.8, pp.1170-1176, Aug. 1989.

[7] T. Kurashima, T. Horiguchi and M. Tateda, “Distributed optical fiber sensor using Brillouin scattering”, IEICE Trans. C-II, vol.

J.74-C-II, no. 5, pp. 467-476, May 1991.

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