N8511

When coherent light enters an optical fiber, the incident light is partly scattered inside the optical fiber and returns to the point of entry. This light is called back-scattered light. Fig. 1 shows a spectrum of back-scattered light for an optical fiber. Back-scattered light is classified into Rayleigh, Brillouin, and Raman scattered light. The scattering frequency of each type of light is different.



Back-scattered light generated by nonlinear interaction between acoustic lattice vibration and excitation light (incident light) is called Brillouin scattered light. It has an intensity about 20 dB lower than that of Rayleigh scattered light. It is known to have spectra that exhibit a Lorentzian profile as expressed by Equation (1):



where; g _B(ν) is a Brillouin scattering spectrum, ν is a frequency, Δν_B is a full width at half maximum (FWHM) of the Brillouin scattering spectrum, and g _B0 is the peak value of the Brillouin scattering spectrum. As shown in Fig. 2, the Brillouin scattering spectrum g _B(ν) shows the maximum value g _B0 at frequency ν = ν_B, where ν_B is called a frequency shift, as it is the frequency difference between the excitation light (incident light) frequency ν₀ and the Brillouin scattering spectrum peak frequency ν₀ + ν_B. The frequency shift ν_B is known to vary depending on strain and temperature.



The frequency shift is expressed by Equation (2):



where; n is the refractive index of an optical fiber, υ_A is an acoustic wave velocity in the optical fiber [m/s], and λ is a wavelength of incident light [mm]. Generally, the frequency shift ν_B of Brillouin scattered light of a quartz single-mode fiber is about 11 GHz (when λ = 1550 nm). The FWHM Δν_B with excitation by continuous light is 30 to 50 MHz. It is known that FWHM Δν_B increases to about 100 to 200 MHz with excitation by 10-ns pulse light.

When a strain occurs in a structure and it exerts a longitudinal stress on an optical fiber mounted in the structure, it will change the density and thereby change the acoustic wave velocity υ_A in the optical medium. It will also change the frequency shift ν_B of Brillouin scattered light. Equation (2) expresses the basic concept of using Brillouin scattered light for strain measurements.
The frequency shift ν_B(ε) with strain ε applied is given as a function of strain ε as expressed by Equation (3):



where; dν_B/dε is the rate of variation in the frequency shift to the variation in strain (strain sensitivity coefficient), and ν_B(0) is the frequency shift with no strain. The sensitivity coefficient dν_B/dε is a constant value determined by an optical fiber sensor. Therefore, strain ε can be determined by measuring the frequency shift with strain, ν_B (ε), and with no strain, ν_B(0). The strain coefficient dν_B/dε for a quartz single-mode fiber is about 500 MHz/%. For example, if the frequency shift ν_B(ε) is measured in repeated measurements over a long period of time, degrees of deterioration and damage of a structure can be monitored with a strain accuracy of 0.01% (measurement reproducibility).

As mentioned above, the Brillouin scattering spectrum has a range of about 100 to 200 MHz, which deteriorates the measurement accuracy of the frequency shift ν_B(ε). In actual strain measurements using Brillouin scattering phenomena, the frequency shift ν_B is determined by applying a Lorentz function type approximate calculation process to spectrum waveform data to improve the measurement accuracy of strain ε.

The frequency shift of Brillouin scattered light varies depending on strain locally applied to an optical fiber. If a single optical fiber simultaneously has sections with and without strain in a longitudinal direction, as shown in Fig. 3, these sections have different amounts of frequency shift, due to the nature of Brillouin scattering, and the amounts are proportional to the amounts of strain. Therefore, it is possible to determine the positions and amounts of strain applied to an optical fiber by continuously measuring frequency shifts at various distances along the optical fiber.