In this paper, a sensor system for measuring continuous Bragg wavelength distribution in a long-length fiber Bragg grating is newly proposed, using synthesis of optical coherence function (SOCF), which is one of the spatial resolving techniques used for reflectometry. Experimental results are also reported. In the process of synthesizing optical coherence function, it is found that an apodization scheme is necessary to obtain the reflection spectrum of local section in a long-length FBG around the coherence peak. As a verification of this method, the detection of local Bragg wavelength shift due to temperature change within a short section in a long-length FBG is demonstrated experimentally.
© 2008 Optical Society of America
FBG sensors are attractive for its capacity of measuring strain and temperature with high sensitivity. FBG acts as an optical filter that reflects the incident light at a particular wavelength (Bragg wavelength), and this reflection wavelength changes in proportion to the applied strain or temperature change. Many systems for multiplexing the FBGs have been proposed, using wavelength division schemes .
In recent years, types of multiplexing schemes with an array of the gratings having a same or similar Bragg wavelength have also been proposed and demonstrated for fabricating a quasi-distributed FBG sensor, such as systems using optical frequency domain reflectometry (OFDR) , and synthesis of optical coherence function (SOCF) . These sensors usually used FBGs as point sensors. Therefore, there would be behind points where strain or temperature change cannot be detected between the FBGs.
On the other hand, distributed sensing within a FBG has many advantages, including potentials for high spatial resolution and no dead zones. They can obtain crucial information on the structural integrity at important positions in the structure, and can be used as structural health monitoring systems. Recently, methods for measuring strain distribution within a long-length FBG based on low-coherent reflectometry [4–7] or OFDR  have been proposed. However, these sensing methods require mechanical moving parts, such as mirror sweep for adjusting the optical path difference, or signal processing including Fourier transformation, and extra interferometer for compensating the non-linearity of the tunable- laser.
The SOCF requires no mechanical moving parts, no signal processing, or no extra interferometer. Consequently, high-speed and random-accessible measurement with compact system becomes possible rather than OLCR and OFDR . In this paper, we have proposed to apply the SOCF to measuring the local reflection spectrum of a short section inside the long-length FBG. It is found that the basic SOCF technique can not work for this application, but the problem can be solved by introducing an apodization scheme to the SOCF. Measurement results of Bragg wavelength distribution within a FBG are demonstrated.
2. Principle of distributed sensing within a FBG by SOCF
Optical coherence function is a function that expresses the relation between the visibility of an interference pattern, which is also called “degree of coherence”, and the differential time delay between the two lightwaves forming the interference. The function can be given as the Fourier transform of the power spectrum of the light source. If a laser diode (LD) is used as a light source, the oscillating frequency can be modulated by modulating the injecting current into the LD; in other words, the arbitrary shape of the power spectrum can be synthesized. Hence, the arbitrary shape of the optical coherence function can be synthesized as well .
By modulating the optical frequency of the light source f(t) by Equation (2), where f 0 is the center frequency, f 1 the modulation amplitude, and f 2 the modulation frequency, the coherence function γ(τd) is synthesized as expressed in Equation (3), which is shown in Fig. 1(a).
The shape of the coherence function is a periodical series of delta-function-like peaks. The interference between the reference and signal light is observed only when the optical path difference between the two lights matches the position of the coherence peak. This means that lightwave reflected at a coherence peak position can be observed if we limit the measurement range so that there is only one peak in this range. In Fig.1(a), the interval between the neighboring coherence peaks, which is also the position of the 1st coherence peak, is expressed as 
where z is the optical path difference between the interfering two beams, n is the refractive index of the fiber(=1.45), c is the optical speed in vacuum. In the measurement using SOCF, the measurement range is determined by the interval as expressed in Eq. (4). It is easy to understand that the coherence peak position can be controlled by changing f 2. Thus, we can selectively and exclusively analyze the light reflected from a certain position.
Additionally, full-width at half maximum (FWHM) of the coherence peak δz shown in Fig. 1(b), which corresponds to the spatial resolution of the sensing system, is inversely proportional to f 1, as given by 
Then the shape of FBG reflection spectra at the coherence peak position can be obtained by sweeping f 0 in a saw-toothed-shape waveform .
Applying this technique to measuring the local reflection spectrum of a short section inside a long-length fiber Bragg grating, a distributed sensor system is expected to be realized. Sweeping the position of the coherence peak in the FBG while the center frequency (wavelength) of the modulated light source is swept around the Bragg wavelength, it is possible to observe the distribution of the FBG reflection spectrum, and determine the Bragg wavelength distribution as shown in Fig. 2. As a result, information about the strain or temperature distribution along the FBG can be obtained.
However, there are some expected problems in this newly proposed method. In the case of multiplexed short-length FBG sensors shown in Ref.  or , the SOCF is used to measure the total reflection spectrum of a short-length FBG. The width of the coherence peak is larger than the length of the FBG. This means that the side lobes of the coherence function around the main lobe (coherence peak), which is shown in Fig. 1(b), do not affect the measurement of the reflection spectrum of the FBG. On the other hand, in the case of the long-length FBG, the width of the coherence peak is much shorter than the length of the FBG. Therefore, the side lobes are inside the grating as well as the coherence peak and affect much the measurement of the local reflection spectrum of the FBG. These problems and solutions are discussed in the next section.
3. Experimental setup by SOCF with intensity modulation scheme
Measurement of Bragg wavelength distribution is implemented with the setup shown in Fig. 3. A distributed feed-back laser diode (DFB-LD), in which the oscillation frequency can be easily modulated by modulating the current injection into the LD, is used as a light source for the SOCF. We have used a three electrode DFB-LD having wider tunable range of about ~100GHz, so a few mm spatial resolution, calculated by Eq. (5), would be realized. The reference lightwave receives 40 MHz frequency shift by the acoust-optic modulator (AOM) and interferes with the signal lightwave reflected from the sensing arm. Therefore, the degree of coherence is observed by detecting the intensity of the heterodyne carrier, 40MHz, which is read by the band pass filter (BPF) and the square-low detector (SQD).
In the case of the distributed sensing with a long-length FBG, the width of the coherence peak must be much shorter than the length of the grating. As a result, there are side-lobes in the grating region as well as the coherence peak. The degree of coherence of the largest side-lobe in magnitude is about 40% (-4dB) of that of the coherence peak, so its influence on the spectra measurement is not negligible. Consequently, the side-lobes need to be suppressed for accurate distributed measurement in the long-length FBG.
Besides, the spectrum shape measured at each position is given by the convolution of the power spectrum of the modulated light source and the reflection spectrum of the FBG. In this method, the power spectrum bandwidth of the modulated light source is wider than that of the FBG’s reflection spectrum. Therefore, the obtained spectrum mainly depends on the shape of the power spectrum, which has two peaks at the edges as shown in Fig. 4 (the figure of power spectrum drawn between DFB-LD and IM). Then, it is impossible to determine the Bragg wavelength at each position with this shape of the modulation spectrum.
To solve the two problems mentioned above, the setup shown in Fig. 3 includes an intensity modulator (IM) after the DFB-LD. Coherence function can be apodized by the intensity modulation synchronized with the frequency modulation of the LD as shown in Fig. 4. Fig. 5 shows the apodized coherence function with this scheme. While the spatial resolution is degraded about twice as large as the one without the apodization, the side-lobe is suppressed to less than -20dB compared to the main peak. Furthermore, the shape of the power spectrum can be changed to the shape with only one peak as shown in Fig. 4 (the figure of power spectrum drawn after IM). Then, this apodization technique enables us to measure the Bragg wavelength.
4. Experimental results
First, measurement without the apodization scheme was tested. The frequency modulation amplitude f 1 was set to be 4.9GHz that synthesize the coherence peak with the FWHM about 9.8mm. A 100mm long uniform FBG, whose total reflectivity is about 90%, was used as a device under test, which was set at the position z=8.93[m]-9.03[m]. To measure this FBG section, the 1st coherence peak was swept from 8.91[m] to 9.05[m], which corresponds from -20[mm] to 120[mm] position in the 100mm length FBG. Thus the modulation frequency f 2 was swept from 11.60[MHz] to 11.42[MHz] according to the Eq. (4).
The measurement was done under the condition that uniform strain and temperature was applied to the whole FBG. The result is shown in Fig. 6(a), and an obtained shape of the spectrum at 30mm position in the grating is shown in Fig. 6(b). The center of the “Wavelength deviation” axis in the figure is 1552.34 nm. Both results show that the spectrum at each position has two peaks. As previously mentioned, this is due to the shape of the modulated power spectrum and the effect of the side lobe next to the coherence peak.
Next, measurement using the apodization scheme under the same condition as previous measurement was done. The results are shown in Fig. 7. The reflection spectrum at each position was improved to be a shape with only one peak, that enabled us to know the local Bragg wavelength. From these results, we can see that the Bragg wavelength distribution along the grating is varying in about 0.1nm while the strain or temperature distribution is uniform along the grating. This is due to the manufacturing non-uniformity.
To confirm more the ability of measuring Bragg wavelength distribution, the long-length FBG, which has local Bragg wavelength shift inside, was measured. The section from 30mm to 50mm position in the grating was heated by attaching a heated metal of 20 mm width to the grating to realize abrupt Bragg wavelength shift along the grating. The temperature in the heated portion is about 35 degrees Celsius, while that in the other portion is about room temperature, 25 degrees Celsius. The result is shown in Fig. 8(a), and peak wavelength distribution along the grating is plotted in Fig. 8(b). From the results, the local Bragg wavelength shift due to the temperature change in the heated portion (30mm–50mm position in the FBG) is clearly detected. Monitoring the Bragg wavelength “shift” compared to the result shown in Fig. 7, we can know the real strain or temperature distribution along the grating with this non-uniform FBG.
The plot in Fig. 8(b) corresponds to the wavelength where the highest value is shown in the measured local reflection spectrum. When the synthesized coherence peak with a finite spatial resolution is located just at the position where the abrupt temperature change takes place, the measured spectrum has two summits which have the same height. One summit corresponds to the Bragg wavelength at the heated portion, and another summit corresponds to that at the non-heated portion. Even when the coherence peak position shifts by quite a short length along the fiber, one summit becomes higher than the other. Thus the steep slope appears at the edges of the heated portion, as shown in Fig. 8(b).
The wavelength range is limited by the wavelength sweep-range of the DFB-LD. In our system, about 0.8nm range would be the maximum, when we use the wavelength change through the current modulation. And the wavelength resolution of our current measurement is estimated to be about 5pm, which is calculated by the ratio of the swept wavelength change to the total number of sampling points in one local spectrum measurement.
These results verified that the SOCF can be a useful technique for measuring Bragg wavelength distribution in a long-length FBG as well as multiplexing FBG sensors.
In this paper, we have proposed a method to realize the distributed FBG sensor system by the SOCF. The Bragg wavelength distribution in a long-length FBG was measured by use of the SOCF scheme. In the case of the long-length FBG, it is found that the side lobes in the synthesized coherence function affect much the measurement of the local reflection spectrum of the FBG. As a solution, we have proposed the apodization by intensity modulation synchronized with the frequency modulation of the light source, and succeeded in the measurement of the local reflection spectrum inside the long-length FBG. We have also succeeded in the detection of the Bragg wavelength shift due to the temperature change over 20mm region in the FBG. The spatial resolution is expected to be improved by widening the amplitude of the LD frequency modulation. This technique has a possibility applicable to a distributed strain or temperature sensing with a high sensitivity.
This work has been supported by the “Grant-in-Aid for Creative Scientific Research” from the Ministry of Education, Sports, Culture, Science and Technology, Japan.
References and links
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