Higher-order interference of low-coherenceoptical fiber sensors
Jun Yang,* Yonggui Yuan, Bing Wu, Ai Zhou, and Libo YuanPhotonics Research Center, School of Science, Harbin Engineering University, Harbin 150001, China
Fiber-optic sensing systems based on low-coherence in-terferometry have a lot of advantages, such as absolutemeasurement, high spatial resolution, easy multiplexing,and nondestructive testing [1–3]. Like conventional inter-ferometric fiber-optic sensors, the low-coherence basedfiber-optic sensing systems measure parameters such asstress, strain, or temperature through monitoring phasedifference (optical path difference). This kind of sensingsystem has high resolution due to the low-coherency ofthe light source. However, under the condition of a lowsignal-to-noise ratio (SNR), especially when the signal issubmerged by the noise, it is difficult to get a precisemeasurement. Therefore, research on the noise sourceand its suppression method in the low-coherence inter-ferometry is important for enhancing the measurementaccuracy and improving the practicality of the sensingsystems [4–7].In a low-coherence interferometric sensing system,
various noises, including shot noise [8], thermal noise [9],relative intensity noise (RIN) [10], and interference beatnoise [11] have been researched in previous works. How-ever, the effect of multireflected light beam interference(for example, the interference between the light beamsthat are reflected one and three times, or three and fivetimes) on a sensor array has not been discussed. In fact,the multireflect-based interference signal is a significantfactor which affects the multiplexing capacity of a sensorarray. If we define the nth-order reflection interferencepeak (nth-ORIP) as the interference signal whose ampli-tude is proportional to the nth power, for instance, theinterference signals obtained from light one time re-flected beams are called the first-ORIP and those causedfrom one and three times reflected light beams are calledthe second-ORIP, the amplitude of the nth-ORIP is higherthan those of any other kinds of noise in general con-dition (reflectivity is more than 10−5). Therefore, thenth-ORIP is the main factor that affects the final noiseamplitude and SNR of the low-coherence interferometricsensing system. In this Letter, we take the second-orderreflection interference peak as an example and useoptical path tracking method to research the generation,
amplitude, and quantity of the nth-ORIP and also give themethod of how to determine the position of interferencepeak and how to reduce its amplitude.
A typical low-coherence interferometric sensing sys-tem is shown in Fig. 1. Broadband light from light source(ASE or SLD) is coupled into the sensor array through C1and C2 ports of the circulator. The sensor array consistsof cascaded fiber-optic sensors segments Si (i ¼ 1…n)with different lengths, that is
Si ≠ Sj; i; j ¼ 1…n; Si − Sj ≥ Lc; ð1Þ
where Lc ¼ ð2 ln 2=πÞðλ20=ΔλÞ is the coherence length ofthe light source andΔλ is half spectrum width (FWHM) ofthe light source.
The signal light from the C2 port that passes throughthe sensor array is reflected by each end of the sensors,and the reflectivity is R0…Rn. When the reflected lightbeams return to the C2 port, a certain optical path differ-ence arises between beams which are reflected by theadjacent end surfaces. The light beams transmit fromC2 to the optical path autocorrelator through the portC3. Generally, the autocorrelator is a Michelson [12] orMach–Zehnder [13] interferometer that can achieve con-tinuous optical path scanning and introduce another op-tical path difference in order to compensate the opticalpath difference between the adjacent end surfaces. When
Fig. 1. (Color online) Low-coherence fiber-optic system ofsensor array.
the optical path autocorrelator continuously scans theoptical path, the signal processing unit can record aseries of white-light interference peaks. The positionof the light path scanning corresponds to the length ofsensors, so we can obtain strain or temperature by re-cording the scanning position change of each interfer-ence peak. As illustrated in Fig. 2, the signals enteringinto the optical path autocorrelator include beams thatare reflected one, two, three, and more times by theend surfaces of the different sensors. As long as the trans-mission direction of the multireflected light is the sameas the one time reflected signal and their optical path dif-ference is equal to the optical length of a sensor, thewhite-light interference pattern will appear on the detec-tor. For beams of the three time reflected light that is re-flected by the end surfaces of the sensor Si and the onetime reflected light from the distal end of the sensor Siþ2(optical path combination ②), the optical path of theautocorrelator is
Si þ Siþ1 þ Siþ2 − 2Si ¼ Siþ2 þ Siþ1 − Si
¼ Siþ2 þΔSi; Sn1 ¼ n − 2;
ð2Þ
where ΔSi ¼ Siþ1 − Si is the length difference of twoadjacent sensors and Sn1 is the number of these typeof peaks. So, the condition of getting a secondary reflec-tion coherent peak is at least three sensors in the fiber-optic array.Besides the optical path generated from the distal ends
of the ith and the (iþ 2)th sensors, optical path combi-nation ③ from the distal end of the (iþ 1)th sensor andthe proximal end of the (iþ 2)th sensor, as shown inFig. 2, can also produce the second-ORIP. The opticalpath is
Si þ Siþ1 þ Siþ2 − 2Si − 2Siþ1 ¼ −Si −ΔSiþ1;
Sn2 ¼ n − 2:: ð3Þ
Therefore, the total number of second-ORIP is
Sodd ¼ 2n3− 3n2
− 2nþ 312
; n ¼ 2k − 1;
Seven ¼ 2n3− 3n2
− 2n12
; n ¼ 2k: ð4Þ
From Eq. (4), there are 140 second-ORIPs in a sensorarray composed of 10 sensors and 1230 second-ORIP in a20-sensor array. The position of the second-ORIP isbefore or after the position of sensor's signal peak(first-ORIP) with a distance of the length difference be-tween the two sensors. When the lengths of sensors arestrictly arithmetic progression in the array, the positionof the second-ORIP coincides with the position of thefirst-ORIP.
In the white-light interference sensing system which isshown in Fig. 1, the amplitude of the interference peakenvelope (already converted to photo-current) of theith sensor (optical path matching ①) is [14]
Ii ¼ 2ρP0 · α · Ri ·Yi
k¼1
T2k−1;
Ti ¼ ð1 − RiÞβi; T0 ¼ 1; ð5Þ
where ρ is the detector’s responsivity, α is the opticalpath loss, except sensor array, R is the reflectivity ofthe end surface of sensor, β is the connection loss be-tween the two end surfaces of a sensor, T is transmit-tance, and P0 is the input light intensity.
If the second-ORIP is considered as noise, the SNR of asensor array which is composed of n sensors is
where In is the signal amplitude of the terminal sensor ofthe sensor array and Ii;i is the amplitude of second-ORIPof the ith sensor.If we define the minimum SNR as the rate of the
minimum amplitude of a reflected signal and the maxamplitude of the secondary reflected noise, we have
SNRmin ¼ InI1;1
¼ T2n−4
R: ð7Þ
From (7), we know SNR is inversely proportional tothe reflectivity and proportional to the transmissivity.The sensor array including three sensors was tested by
using the experimental setup shown in Fig. 1. The resultsare shown in Fig. 3. The power of the broadband lightsuperluminescent diode (SLD) is 1mW, the wavelengthis 1310 nm, spectral width is 50 nm, the scanning rangeof the optical path scanning arm is 0–100mm, the averageinsertion loss is 2 dB with a fluctuation range of less than�0:5dB, the single-pass insertion loss of the circulator is1dB, the length of the optical fiber sensor is about500mm, the length of sensors increases from the firstone to the last, the reflectivity of the end surface of eachsensor is 0.3%, and the insertion loss between two sen-sors is about 1dB.Shown in Fig. 3(a), S1, S2, and S3 are the white-light
interference peaks produced from a one time reflectedsignal at the proximal and distal ends of the three sensors,
respectively. The positions of these peaks are S1 ¼53472:4 μm, S2 ¼ 62736:2 μm, and S3 ¼ 71323:7 μm.Figure 3(b) shows the precise output signal and the peakposition of S2. We obtain the calculated positions S4 andS5 of the second-ORIPs from Eqs. (1) and (2), with S4 ¼44885:0 μm and S5 ¼ 80587:5 μm. They are in good accor-dance with S4 ¼ 44880:0 μm and S5 ¼ 80605:7 μm, whichare the positions of the scanning peaks. Figure 3(c) showsthe precision output signal and position of the peak S4.Similarly, S6 and S7 are the third-ORIPs. In addition, theviewpoint that S4 and S5 are the second-ORIPs can alsobe demonstrated by stretching the sensors S1 and S3.From experimental results, which are presented in Fig. 4,the peak positions of S4 and S5 decrease with the stretch-ing of the sensor S1 and increase with the stretching of thesensor S3.
In conclusion, when the number of sensors is large,say, more than 10 in the serial sensor, the large amountof higher-order reflection coherent peaks becomes themain factor affecting the SNR of the low-coherent sen-sing system. The higher-order reflection coherent peakscan be reduced by decreasing the reflectivity of the sen-sors’ ends, which will enhance the multiplexing capacityof the sensor array.
This work was supported by the key project ofNature Science Foundation of Heilongjiang Province(No. ZD200810) and key project foster program forUniversity and College Science and Technology In-novation (No. 708030) and partially supported by theNational Nature Science Foundation of China (NSFC),under grant numbers 60 877 046, 60 807 032 and 60 927008, and supported by special fund of central universitybasic scientific research (HEUCFZ1020), to the HarbinEngineering University.
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Stretching quantity (mm)
Stretching quantity (mm)
Fig. 4. (Color online) Mobility characteristics of white-lightinterference signal and second reflection noise, when stretch-ing different sensors in a three sensor system.
