Ultrashort fiber Bragg gratings (US-FBGs) have significant potential as weak grating sensors for distributed sensing, but the exploitation have been limited by their inherent broad spectra that are undesirable for most traditional wavelength measurements. To address this, we have recently introduced a new interrogation concept using shifted optical Gaussian filters (SOGF) which is well suitable for US-FBG measurements. Here, we apply it to demonstrate, for the first time, an US-FBG-based self-referencing distributed optical sensing technique, with the advantages of adjustable sensitivity and range, high-speed and wide-range (potentially >14000 με) intensity-based detection, and resistance to disturbance by nonuniform parameter distribution. The entire system is essentially based on a microwave network, which incorporates the SOGF with a fiber delay-line between the two arms. Differential detections of the cascaded US-FBGs are performed individually in the network time-domain response which can be obtained by analyzing its complex frequency response. Experimental results are presented and discussed using eight cascaded US-FBGs. A comprehensive numerical analysis is also conducted to assess the system performance, which shows that the use of US-FBGs instead of conventional weak FBGs could significantly improve the power budget and capacity of the distributed sensing system while maintaining the crosstalk level and intensity decay rate, providing a promising route for future sensing applications.
© 2016 Optical Society of America
Weak fiber Bragg gratings (FBGs) based distributed optical fiber sensing is particularly attractive for engineer monitoring due to its significant advantages such as large capacity and low cost. [1,2]. Even thousands of identical weak FBGs nowadays can be rapidly fabricated along a single optical fiber using the well-established on-line writing methods . These FBG sensors can be simultaneously interrogated through a single measurement system assisted by some spatial domain multiplexed techniques such as time-division multiplexing (TDM)  and optical frequency domain reflectometry (OFDR) , allowing one to conveniently monitor the target parameters over a long range. These have been extensively applied in civil engineering  and structural status monitoring in automobile and aerospace [7, 8]
In the formation of conventional weak FBGs, a slight refractive index (RI) modulation will be applied during the grating writing, while the grating length will be relatively long to approach a narrow reflection spectrum simultaneously (normally less than 0.2 nm ). This spectral characteristic of an FBG sensor is a critical requirement for many traditional wavelength detections. Particularly, for most common spectrum-construction based interrogation schemes involving the spectral peak or notch location (such as using an optical spectrum analyzer (OSA) and a tunable laser), narrow spectra of the grating sensors could yield a high measuring resolution and a fast measurement speed ; interferometric detection needs a sufficient coherence length of the reflected pulses ; and edge filtering scheme requires that the bandwidth should not exceed the linear portion of the filter response . Using these conventional weak FBGs for distributed measurements may result in a relatively low signal-to-noisy ratio (SNR) because of their narrow reflection spectra. Another issue for such gratings is the vulnerability of the measurement to no-uniform measurand field, due to their long effective sensing lengths. For example, to realize 0.1 nm full width at half maximum (FWHM) grating spectrum, the grating length should generally reach several centimeters . Such a long grating length could make the FBG sensor very easily exposed to no-uniform distribution of strain or temperature, which could distort the spectrum considerably and thus affect the measurement accuracy . Those in fact usually happen in structural health monitoring applications with events such as multiple damage states in composite material  and transverse cracks .
There also exists another type of weak FBGs, namely, ultrashort fiber Bragg gratings (USFBGs), with typical grating lengths scaled to only hundreds or even tens of microns . Different from the conventional low RI modulation induced weak FBGs, the low-reflectivity for US-FBGs mainly results from the ultrashort lengths . Nevertheless, their short lengths can also broaden the reflection spectra significantly, typically several (or even tens of) nm . Figure 1 illustrates the characteristic comparison between US-FBGs and the conventional weak FBGs. The fabrication of US-FBGs is similar to that of common uniform FBGs, and therefore can be cost-effective and efficient . By placing a tunable slit between the phase mask and the fiber, ultra-short grating lengths can be easily obtained by carefully adjusting the slit width . However, due to their inherent broad spectra which are unfavorable for many spectral interrogation techniques as previously mentioned, such US-FBGs have rarely been used as sensors. However, several important advantages can be envisaged if US-FBGs can be used as weak grating sensors for distributed measurements. Their ultrashort lengths could fundamentally solve the mentioned non-uniform measurement problem. More importantly, they could provide significant benefits in terms of the system power budget and the sensing capacity, as discussed in the paper (Sect. 4).
Very recently, we have introduced a new interrogation concept that uses shifted optical Gaussian filters (SOGF)  with a differential detection scheme, and proposed it for wavelength detection of US-FBGs . It can well take advantage of wide spectra of such gratings, and offers several remarkable features of high flexibility, self-referencing capability, and relatively wide measurement range, opening up the possibility of the exploitation of US-FBG sensors.
In this paper, through exploiting this SOGF concept in distributed measurements, we propose and demonstrate an identical US-FBG based distributed microwave-photonic sensing system.
The multiplexing approach is essentially based on microwave-network analysis: the spatial/time domain information can be resolved by analyzing the frequency response of the entire network [21–23]. This multiplexing method would offer several important advantages including more stable and easier controlled measurements (owing to its operation in microwave rather than optical domain ), a remarkable spatial resolution, and more importantly, a better SNR since a continuous-wave light instead of a short-pulse source can be used , which is certainly important for this intensity detection-based distributed sensing. In the proposed system, to achieve the SOGF interrogation of distributed US-FBG sensors, the microwave network is implemented as a multi-tap microwave-photonics filter (MPF), and the SOGF with a delay-line between the two arms is incorporated into the MPF structure. By this way, the power differential detections of the cascaded US-FBGs can be performed individually by resolving the tap weights of the MPF which can be obtained from the analysis of its frequency response. Compared with conventional wavelength-based detections, using SOGF interrogation concept owing to its intensity-based detection nature allows a much faster, simpler and cheaper distributed monitoring. Furthermore, the significant advantages of adjustable sensitivity and range, wide measuring range, self-referencing ability, and strong resistance to no-uniform measurand field of US-FBG sensors make the proposed system particularly attractive for various distributed sensing applications.
Numerical studies of the dependence of several important system parameters on grating bandwidth are also carried out in the present work, to investigate how the use of US-FBGs affects the distributed measuring performance. Relationship between weak FBG-based distributed sensing performance with the grating reflectivity has been already well established [1, 2], but little has been learned about the correlation between that with the grating bandwidth. Our results show that the use of US-FBGs instead of conventional weak FBGs for distributed sensing will lead to considerable improvements in terms of the system power budget and capacity, while maintaining the crosstalk level and intensity decay rate of the reflected signals, clearly highlighting the advantages of such US-FBG based sensing networks.
2. Concept of the proposed sensing network
Figure 2 illustrates the schematic and the fundamental concept of the sensor network. The light from a broadband source is modulated by a frequency scanning microwave signal, which is introduced by a vector network analyzer (VNA). The modulated light is then sent into an optical fiber with cascaded identical US-FBG sensors, by an optic fiber circulator. Wide spectrum reflections are created at these gratings, reflected back, and directed to the SOGF interrogation part via the circulator again. The configuration of the SOGF interrogator is similar with the previous one except for a slight fiber delay-line added between the two arms [19,20]. An optical fiber coupler first splits each reflected signal into two arms. Two optical Gaussian filters with shifted transmission spectra, i.e., with the same Gaussian spectra but a slight offset between their center wavelengths, are placed at the two fiber arms respectively (denoted as Gaussian filter 1 (GF 1) and Gaussian filter 2 (GF 2), respectively). The two arms have a slight difference in their lengths, allowing their signals to be separated in the spatial-domain, thereby enabling the differential detection of each grating, as we will see latter. A second fiber coupler is used to combine the two arm signals. The optical signals from the SOGF interrogation part are then collected by a photo-detector (PD) and transferred to the RF signals, which are finally sent to another port of the VNA to be analyzed in the RF domain.
This way, a microwave-photonics network, composed of the grating array, the light director (circulator), and the SOGF interrogation part, is constructed, with an operation that is equivalent to a discrete-time MWP filter as shown in Fig. 2(b). The gratings sampling the original RF signal act as multiple tap points, and give time-delays between them according to their fiber positions. Then, because of the shifted filters and the time-delay ΔT between the two arms, each sample is divided in two, which are weighted by shifted filters respectively and delayed again. Finally, all the samples are combined together by means of a combiner.
Therefore, the frequency response H(ω) of such a multi-tap microwave filter can be expressed as 
The VNA is actually used to acquire the frequency response of the entire microwave network (including both magnitude response, i.e., |H(ω)|, and phase response). After complex and inverse Fourier transform operation to the obtained frequency response, the network impulse response, i.e., the time-domain response of the MWP network can be resolved as
From this equation, one can find that, in the time-domain response, all the samples with their weights and time-delays are revolved at discrete time-positions. They will appear as a series of discrete peaks, and their time-positions can be used to ascertain the locations of the gratings, while the heights which actually represent the sample weights can be utilized to determine the corresponding signal power.
Due to the slight time-delay between the two arms (ΔT), for each grating, it will have a pair of adjacent peaks in the time-domain response, which correspond to its two reflected signals passed through the different filters (GF 1 and GF 2)Fig. 2(d).
As mentioned before, the peak heights can actually be used to determine the corresponding signal power. Therefore, for the kth grating, we in the time-response can obtain the power ratio (in dB) of its two signals filtered by the different filters, from the ratio of its two adjacent peak heights, hereafter referred to as peak-to-peak ratio (PPR)
Our previous studies have already shown that for a SOGF interrogation scheme, the responses of the two filtered power to the Bragg wavelength (that is P1,k(λk) and P2,k(λk) for the kth grating in our case) will follow two delayed Gaussian functions, and the ratio of them will give a linear behavior, with a slope that is proportional to the shifted filter wavelength offset [19,20].
Thus, the obtained PPR of the kth grating (PPRk) can be used to linearly determine its Bragg wavelength (λk), with an adjustable sensitivity through tuning the filter offset λos, i.e.
Therefore, when any grating is affected by measurands, as shown in Fig. 2(c), the resultant spectrum shifts will linearly change the corresponding PPRs, as depicted in Fig. 2(d), and thus, the Bragg wavelengths can be tracked rapidly by simply monitoring their PPRs in the system time-domain response.
Also, the differential detection nature of the measurement will give it a self-referencing capability. In other words, it will be insensitive to any intensity fluctuations resulted by bend loss of the fiber, light source variations, among others, making the system even more attractive for large-range and harsh environment sensing.
3. Experimental demonstration
3.1. System implementation
We have conducted preliminary experimental studies based on the setup depicted in Fig. 2(a). A C-band amplified spontaneous emission (ASE) source was used to provide illumination to the sensor system. A 10 GHz intensity-modulator was used for the modulation, which was driven by the port 1 of a 6 GHz VNA. Eight US-FBGs with ultrashort lengths of ∼500 μm and identical Bragg resonances of near 1531.2 nm were fabricated and cascaded along a single fiber; their reflectivity are 1–3 %, and FWHMs are ∼1.36 nm. The spectrum of the first grating is shown as Fig. 3(a). The fiber separations between the neighboring gratings are ∼8m.
Two 3 dB optical fiber couplers were used as the splitter and combiner in the SOGF interrogation part, respectively. We used two programmable optical filters (Waveshaper, 4000s) as the shifted Gaussian filters: both the transmission characteristics were set to be Gaussian, and the FWHMs were 1.36 nm that are equal to those of the used US-FBGs; the center wavelengths were 1531.2 nm (GF 1) and 1531.6 nm (GF 2), respectively, which leads to a wavelength offset of 0.4 nm, as shown in Fig. 3(b). The fiber arm with the GF 2 was longer by ∼0.92 m than that with the GF 1, acting as the fiber delay-line between them.
Figures 3(c) and 3(d) show the amplitude and phase response of the whole network respectively, captured by the VNA. The scanning frequency range was 9 kHz to 4 GHz, giving a spatial resolution of ∼2.5 cm, which can be estimated by the following equation 
After inverse Fourier transform operation to the complex response, the system impulse response, that is the time-domain response, can be obtained as shown in Fig. 3(e), where the x axis has been converted to the location. Eight pairs of closed peaks can be clearly seen in the system time-domain response with a high SNR. As mentioned before, due to the slight time-delay introduced by the SOGF interrogator, each reflected signal from any US-FBG will be slightly separated in the time-domain and be filtered by the different filters. Therefore, the eight consecutive pairs of peaks appeared in Fig. 3(e) individually correspond the eight US-FBGs cascaded along the fiber, with the peak height representing the corresponding signal power. The separation between each pair of peaks in Fig. 3(e) has been found to be near 0.9 m, which, within the 2.5 cm spatial resolution, matches well with the delay-line of ∼0.92 m employed. For each pair of adjacent peaks, we hereafter refer to the peaks related to GF 1 and GF 2 as peak 1 and peak 2, respectively, and refer to PPR as the peak 2-to-peak 1 height ratio (dB). The heights for the different peak pairs are not the same but show a general trend of decrease, which is because of insertion loss of the gratings. However, since all the gratings have near the same Bragg resonances, for the eight pairs of peaks they present nearly the same PPRs.
3.2. Self-referencing capability demonstration
Experiments to validate the self-referencing capability of the distributed measurement were then carried out. The change of the reflection intensity in practice should mainly come from two sources: light-source fluctuations, and long transmission-fiber related intensity change, including fiber bend loss, transmission loss, etc. The later could very easily happen for large-scale distributed measurements where long transmission-link and harsh environment are inevitably involved.
The impact of source fluctuations on the measurement was first investigated. We decreased the power of the optical source by 3.3 dBm through tuning the intensity of the ASE, and then compared the normalized time responses obtained before and after the power decrease. The comparison result is shown in Fig. 4(b), where the blue waveform shows the original time-domain response, while the red one represents the response after the test. As can be seen, all the peak levels drop significantly, which is apparently due to the reduction of the optical source power that directly leads to the decrease of the power for all the reflections. The decreases of the peak values in Fig. 4(b) have been found to be about 3.4 dB, which agrees well with the variation value of the source power. However, it also can be seen in Fig. 4(b) that, despite the considerable changes of the peak values, all the PPRs appear to be relatively unchanged during the source power change. Figure 4(c) plots the variations of the PPRs, where it can be found that the changes are near zero level on this scale, confirming that the source variation has little influence on the measurement.
Then, to verify the immunity of the distributed measurements to transmission-link related intensity changes, we introduced bend loss between the 3rd and the 4th gratings, by winding the fiber of that section around a cylinder, as illustrated in Fig. 4(d), and compared the two time-responses again. This bend point would lead to a considerable power attention of the light that propagates through it. Therefore, it could be expected that the power of the reflections from the gratings locating after the bending point (i.e. the 4th–8th US-FBGs) would decrease, while the others should not be affected. The experimental result is given in Fig. 4(e), where it can be found that the peak level decreases in this time occur only for the 4th–8th US-FBGs, while the levels for the gratings locating before the bending point (the 1st–3rd gratings) remain nearly unchanged, as expected. However, we can also find in Fig. 4(e) that the PPRs for all the eight US-FBGs are still seen to be unchanged. The calculated PPR changes for the all the gratings are plotted in Fig. 4(f). The changes are as small as just less than 0.2 dB, and we attributed these tiny changes to the small background-strain variations for the gratings during the fiber winding.
3.3. Distributed strain measurements
The wavelength interrogation of the distributed US-FBG sensors was then carried out, in the case of applied strain. To fully perform the interrogation and to acquire a better sensitivity, before the measurement, we shifted the whole shifted transmission spectrum to longer wavelength, and slightly increased the filter offset: the center wavelengths of GF 1 and GF 2 were tuned from 1531.2 to 1532.2 nm and from 1531.6 to 1532.8 nm, respectively. In this way, the interrogation of the strain-tuned grating can be started when the grating spectrum is located at the short-wavelength edge of the whole shifted transmission spectrum, and the filter offset can also increase to 0.6 nm. The 7th US-FBG was firstly measured, and glued to a micrometric translation stage with a resolution of 2 μm to be applied with strain.
Figure 5(a) shows enlarged 3D view of the evolution of the two adjacent peak height changes for the 7th US-FBG as the applied strain increases, and Fig. 5(b) plots the normalized change curves of them. Two delayed Gaussian behaviors are observed, as expected. By dividing these two curves, the PPR versus strain can be obtained, as shown in Fig. 5(c). A typical measurement curve of a SOGF interrogator is observed, where a relatively wide linear range of ∼2800 με with a high sensitivity of 0.004 dB/με is obtained.
However, beyond the linear range, we can find that the slope rapidly deceases for both the ends of the measurement curve, that is, when the sensor spectrum is located at the edges of the whole shifted-spectrum. These flat trends are essentially due to the side lobes of the grating spectrum. These spectra, because of their narrow bandwidths relative to the transmission window, can be considered as background or ”dark” noise in the measurement, and have a tendency to decrease the sensitivity. Despite their much lower energy compared with the main lobe, when the grating spectrum shifts nearly outside one of the transmission windows, they will begin to play a role in the measurement that can not be neglected. When this occurs, the sensitivity begins to decrease, with the maximal linear range occurring.
Therefore, in real implementations, it is important that the sensor spectrum should be limited in a range in which it is not too far to the main-body of the shift-transmission, so that those ”dead regions” can be avoided and the linear behavior of the measurement can be ensured.
Nevertheless, since the FWHMs of the US-FBGs used here are only ∼1.36 nm, the current linear range (∼2800 με) can be still improved a lot when shorter US-FBGs with wider spectra are employed. As a reference example, the simulation shows that if a more typical ultrashort grating with FWHM of 3.5 nm is employed, the maximum linear range (using a small filter offset of 0.2 nm) can be greatly improved to ∼14600 με, which would be a quite wide measurement range and should cover the needs of the most sensing applications
Repeating the measurement for the 3rd and the 5th gratings then gave similar results, as depicted in Figs. 6(a) and 6(c), where the inset in each figure shows the response curves of the two peaks during the measurement. The PPRs of other gratings were also monitored during the two measurements shown in Figs. 6(b) and 6(d). As can be seen, for both the measurements, only the PPR of the grating with the strain changes obviously, while others remain relatively stable, and no appreciable crosstalk is observed. This suggests a considerable potential of the system for large-scale distributed sensing applications.
3.4. Sensitivity and measurement range tuning
Finally, the important feature of adjustable sensitivity for the sensing system was verified. Measurements of the strain-turned gratings were accomplished at the different filter offsets of 0.8 and 1.0 nm. The offset change was realized via tuning the GF 2 center wavelength (1533 nm and 1533.2 nm for the two cases, respectively) while leaving the GF 1 wavelength (1532.2 nm) unchanged. Figure 7 plots the measurement results for the different gratings, where the measurement curves at the offset of 0.6 nm are also included for comparison. As can be seen, the slopes for each grating increases significantly as the filter offset used becomes larger, agree well with the theory.
However, this improved sensitivity is also accompanied with a reduced linear sensing range, as shown in Fig. 7 and summarized in Table. 1, which is consistent with the previous observation . This dependence can be explained by noting that when the distance between the shifted transmissions increases, the shift range of the Bragg wavelength in which the sensor spectrum can cover most of both the transmission spectra, necessary for linear measuring characteristic as mentioned before, will decrease, which then lead to a reduced linear measuring range. Therefore, there exists a trade-off between sensitivity and measurement range for the interrogation. Nevertheless, it suggests a very easy way to make any adjustment towards high-sensitivity detections or broad range sensing, by just tuning one of the filter wavelength. This high flexibility should be very attractive for many distributed measurements where the sensors are required to be embedded into structures or used in harsh or remote environments, and the reconfigurations of them to fit the changing requirements and environments are very difficult [15, 16].
4. Numerical study of the US-FBGs based sensing network performance
After the preliminary experimental studies, in this section, we will compare theoretically the system performances between this new distributed sensing network employing US-FBG sensors and previous ones using conventional narrow-band weak FBGs. Since the main difference between these two are the difference in the spectrum bandwidth of the grating sensors used in the network, in order to make the performance comparison, in this section we will thoroughly study the dependence of the distributed sensing network performance on the sensor bandwidth.
The remainder of this section is organized as follows. In section 4.1, the dependence of multi-reflection crosstalk level in the sensing network on the grating bandwidth is analyzed, and the relationship between the crosstalk level and the grating reflectivity is also given in this part for comparison. In section 4.2, we investigate how the spectral shadowing crosstalk of the network impacts the measurement accuracy of the SOGF interrogation, followed by the analysis of the relationships between this impact and the grating bandwidth and reflectivity. Then, in section 4.3, we explore whether the increase of the grating bandwidth would increase the intensity decay speed of the returned signals. Finally, the dependence of the capacity of the sensing network on grating bandwidth is analyzed in section 4.4.
4.1. Multi-reflection crosstalk
Just like traditional identical weak FBG based sensor networks, the measurement of the proposed system will suffer from multiple-reflection crosstalk , which refers to the interference by the false signal that undergoes multiple reflections between the upstream FBGs and arrives at the detector at the same time with the real signal of the downstream FBGs.
It is well known from the previous studies that using higher reflectivity gratings will improve the average signal power but also significantly raise the multi-reflection crosstalk level [1, 2]. The employment of US-FBG sensors, owing to their much wider spectra, should also improve the reflected signal power in the system, and in the next, we will investigate whether using US-FBGs as sensors will increase the network crosstalk
For the proposed sensing system using intensity-based interrogation, the first-order multi-reflection crosstalk level of the kth FBG can be expressed as 
The returned signal power from the kth grating can be calculated asEqs. (9)–(12), the relationship between the crosstalk level with the grating bandwidth (B) and the reflectivity (r) can be established. Figure 8(a) shows the calculated crosstalk level as a function of the sensor reflectivity, when the FWHM of each sensing unit is 0.2 nm and the total sensor number is 200. Figure 8(b) plots the relationship between that and the grating FWHM, when the same sensor number of 200 and the grating reflectivity of −30 dB are used.
It can be found in Fig. 8(a) that the crosstalk level significantly increase with the grating reflectivity, which is agree with the previous studies. However, we can find in Fig. 8(b) that the crosstalk remains unchanged as the grating FWHM increases. This indicates that there exists little dependence of the crosstalk on the grating bandwidth, and also means that the adoption of wide-spectrum US-FBGs as sensors instead of conventional ones would not increase the crosstalk level of the network.
Based on the analysis above, it can be concluded that when the identical grating reflectivity, total sensor number, detections and light source are used, the networks with US-FBGs as sensors would have the same multi-reflection crosstalk level compared with conventional ones using narrow band FBGs, while possessing higher average signal power at the receivers due to the boarder spectra of the reflections, highlighting the power-budget advantage of the US-FBGs based sensing network.
4.2. Spectral shadowing effect
Another form of crosstalk in identical grating-based sensing networks is spectral shadowing, which is defined as distortion of a downstream FBG’s spectrum due light having to pass twice through an upstream FBG . Then the returned spectrum from that grating will not be a true representation of its spectrum but will be the multiplication of the upstream gratings and the interrogation spectrum.
When conventional wavelength-domain detections (such as using an optical spectrum analyzer (OSA), tunable laser, etc.) are used, the distorted reflected spectrum will increase uncertainty when determining the spectrum center, and thus introduce errors to the measurement. In our case, however, this spectral-distortion will be transferred to a response curve change of the SOGF interrogator, which then, if not be re-calibrated, affects the accuracy of the measurements.
Numerical studies were conducted to investigate the impact of such spectral distortion on the response curve of the SOGF interrogator. In the simulation, shifted Gaussian filters are located at 1550 and 1550.6 nm, respectively, corresponding to a filter offset of 0.6 nm. The total identical US-FBG number is 800, each grating reflectivity is −36 dB, and the FWHM is 2.3 nm. The Bragg wavelengths of all the upstream gratings are randomly centered around 1550.3 nm with a range of 3 nm (i.e. randomly distributed from 1548.8 to 1551.8 nm) to better simulate the real situation.
Figure 9(a) gives the comparison between the reflection spectra of the 800th grating and the first one. Due to spectral shadowing effect, the spectrum for the 800th grating is clearly different from the 1st one: it becomes wider, and the reflectivity appears lower. Figure 9(b) compares the simulated measurement curves between these two gratings. The slope of the curve for the 800th grating is slightly smaller than the 1st one, and the linear range is reduced a little. The decreased slope could be explained by the broadened spectrum (our previous study has shown that the slope of the response cure for the SOGF interrogation is actually inversely proportional to the square of the grating FWHM ), while the reduced linear range should come from the increased mismatch between the distorted spectrum with the Gaussian filter spectrum. However, it can be found that the measuring curve still maintain a good linear behavior.
Simulations were also performed to explore the relationship between the degree of this response curve change with the grating parameters. Figures 10(a)–10(c) compare the calculated measurement curves of the 1st and the 800th gratings for the different grating reflectivity of −36, −32, and −28 dB, respectively, with the grating bandwidth assumed to be 1.8 nm. Figures 10(d)–10(f) illustrate the measurement curve comparisons at the different bandwidths of 1.8, 2.3 and 2.8 nm, respectively, when the grating reflectivity is − 36 dB. We can first find the degree of the difference between the two curves becomes larger when the grating reflectivity used is higher. However, for the case of the different bandwidths, the degree of the difference appear similar to each other, suggesting that it is not highly related to the grating bandwidth.
Therefore, it can be concluded that using wide-spectrum US-FBG as sensing units would not increase the interference level from spectral shadowing crosstalk significantly, while the opposite is true for the use of higher reflectivity gratings, which is a similar result to that obtained from the multi-reflection crosstalk analysis above.
It is worth noting that although the curve slope and the liner range could be considerably changed due to spectral shadowing, the desirable linear behavior of the measurement is still maintained, even when a relatively high grating reflectivity of −28 dB is used, see Fig. 10(c). More importantly, the response curve change due to this effect in principle can be completely compensated. It is because when re-calibrating the kth grating sensor, the Bragg wavelengths of all the previous k − 1 gratings are known. The ”new” spectrum of the kth grating then can be calculated with these data, and the response curve thus can be re-constructed. These calculations for re-calibrations in practice can be accomplished in real-time by some efficient and low-cost digital signal processing (DSP) devices.
4.3. Intensity decay rate
In this part, we focus on another important parameter of large-scale sensing networks, namely, intensity decay rate of the reflected signals from a serial array, which can directly determine the performance balance of the grating sensors in the array . In practice, when all the instruments in a sensing network, including light source and optical receivers, have been implemented and the dynamic range of the detection system has been given, it is highly desirable to have similar reflected power from each of the FBG sensors. This, however, is generally difficult to be realized for an identical weak grating-based sensing network, where the insertion loss of each grating for the light would make the signal power become lower as it is from the grating more distant positions along the fiber. Nevertheless, it is still very important to achieve a low power decay rate of the returned signals, in order to better balance the power of the reflected signals.
It has been suggested that this power decay rate is strongly related to the grating reflectivity, which can be readily explained as that will directly affect the insertion loss of each grating. Here, we will explore the dependence of the decay rate on the grating bandwidth.
Using Eqs. (10) and (11), we can construct the curves of the reflected power change with the sensor number when different grating parameters are used. Figure 11(a) plots the calculated reflected power as a function of the sensor number when the different grating reflectivity are employed, with the FWHM assumed to be 0.2 nm, while Fig. 11(b) presents the power change curves for the case of different grating bandwidths when the reflectivity is −30 dB. One can clearly find that the decay rate becomes faster as higher reflectivity gratings are employed, but appears unchanged for the different grating bandwidths. These results clearly suggest that the use of wider gratings will not make the power decay rate faster, and thus not increase the performance difference between the identical sensors with in an array.
4.4. Sensing system capacity
Finally, we explore how the increase of the grating sensor bandwidth impacts the maximum number of sensors that can be multiplexed in a distributed sensing network. To study this point, in this part, we will theoretically characterize the relationship of the sensing network capacity on the grating bandwidth. The capacity of a distributed sensing network would depend on many factors including insertion loss of the instruments, performance of the detections, etc. For most cases, however, it is the minimum optical power determined by a specific SNR requirement that sets a limit to the maximum number of sensors that can be multiplexed [23, 26]. In these cases, the sensor number needs to be chosen so that the power from each sensor can be higher that minimum power, and in the following numeral studies, the maximum multiplexing number of the gratings in distributed sensing networks will be determined based on this criterion.
Figure 12(a) plots the simulated reflection power change with the grating number for a sensor array at different grating bandwidths, where from black to origin there is a gradual increase of the grating FWHM from 0.2 to 2.3 nm with a step of 0.35 nm. The grating reflectivity in the calculation is assumed to be −25 dB, and the source power density is 0 dBm/nm.
When the minimum power is given as, for example, −34 dBm, see the horizontal dashed line in Fig. 12(a), the maximum multiplexing sensor number then can be obtained by comparing the power level of the sensor with the minimum power. By this way, we can find that when the grating spectrum is wider, the overall signal power level becomes higher, and the maximum multiplexing sensor number increases. Figure 12(b) shows the plot of the capacity as a function of the grating bandwidth. We can find that using a typical 3 nm FWHM US-FBG as the sensing unit will allow a capacity of near 1500, which is even more than ten times better than that of 120 from the employment of traditional ones with FWHMs of 0.2 nm.
Therefore, according to these results, it can be concluded that when using wide-spectrum USFBGs as the sensor units instead of conventional narrow-band weak FBGs, the average signal power at the receiver would increase greatly, which then significantly improve the maximum multiplexing number of the sensing network.
It should be noted that in real practice, the maximum multiplexing number of the network would also be influenced by other factors, such as transmission loss of the fiber, Rayleigh scattering, and a specific accuracy requirement. Thus, the maximum multiplexing number of US-FBGs should still need to be evaluated according to a specific implementation with particular requirements. Nevertheless, as the power budget is the key factor that determines the maximum number of gratings in a distributed sensing network [23, 26], the results from the numeral studies above still directly highlights the great capacity advantage of US-FBGs based sensing networks over conventional ones.
5. Conclusion and future work
An US-FBG-based distributed optical sensing using SOGF and microwave network analysis has been reported. The whole sensing system is implemented as a multi-tap microwave-photonics filters, and shifted Gaussian filters with a fiber delay-line between the two arms are incorporated into the filter structure as the fast and cheap intensity-based interrogation. By this way, in the impulse response of the microwave-network, which can be obtained by analyzing its frequency response, each grating will be resolved as two adjacent discrete peaks. The differential detection of each grating thus can be achieved by calculating peak-to-peak ratio of the corresponding pair of closed peaks.
Eight US-FBGs have been fabricated and used to prove the concept. The self-referencing capability of the distributed sensing has been verified and the application for distributed strain measurement has been demonstrated. Relatively wide linear measurement range of near 2800 με has been realized with the current ∼1.36 nm FWHM US-FBGs, which could be further improved to more than 10000 με by using shorter US-FBGs which have broader spectra. No appreciable crosstalk has been observed during the measurements. The tuning of sensitivity and measurement range has also be demonstrated. The remarkable features of high flexibility, self referenced capability, wide measuring range, and fast and simple interrogation make the system very attractive for various large-scale distributed measuring applications.
Numerical studies to investigate how the system crosstalk impacts the accuracy of the SOGF interrogation, and how the use of wide-spectrum US-FBGs as the sensing units affects the sensing network performance have also been conducted. The spectral-shadowing crosstalk of the sensing network will distort the reflection spectrum of the downstream grating sensors, and thus slightly change their response curves of the SOGF interrogation. The ”new” response curve still maintains a good linear behavior but with a slightly reduced linear range and slope. Nevertheless, the response curve change in principle can be compensated completely by some low-cost DSP devices. More importantly, our studies have shown that using US-FBGs instead of conventional weak FBGs can considerably improve the sensing system power budget and the capacity (potentially by more than ten times) while maintaining the crosstalk level and the intensity decay rate. This, along with their inherent robustness against non-uniform measurand field, implies that such gratings may be more suitable as weak FBG sensors for distributed measurements than conventional ones.
In real implementations, reliable and stable Gaussian optical filters are very essential for a high-performance SOGF interrogation. Nevertheless, cheap and well-performed Gaussian filters have already been readily available, and can be easily fabricated based on different means, such as using thin-film , optical-waveguide , and fiber gratings . Furthermore, the resonance wavelength for most of these optical filters can be easily and precisely tuned, by a thermo-optic or electro-optic effect , which greatly facilitates the adjustment of sensitivity & measurement-range for the SOGF interrogation.
Future work will focus on extending the current system to multi-wavelength channel USFBG based sensing network. It can be noted that there actually exists some planar waveguide spectrometers for which the spectral characteristic of each channel is naturally very similar to Gaussian, including arrayed waveguide gratings (AWGs) and Echelle diffractive gratings (EDGs) [31, 32]. These devices can be essentially considered as multichannel Gaussian filters. Then, employing two of such filters with a wavelength offset between their transmission spectra could yield shifted Gaussian transmissions at multiple wavelength channels. When this could be achieved, multiple wavelength channel US-FBGs could be multiplexed and interrogated simultaneously by such multichannel shifted optical Gaussian filters, thereby further improving the capacity of the sensing system.
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