temperature sensing system

Sensors and Actuators A 105 (2003) 40–46

Multiplexed Mach–Zehnder and Fizeau tandem white light interferometric fiber optic strain/temperature sensing system Libo Yuan∗ , Jun Yang Department of Physics, Harbin Engineering University, Harbin 150001, PR China

Abstract A novel multiplexed Mach–Zehnder and Fizeau tandem white light interferometric fiber optic sensing system permitting absolute length measurement in remote reflective sensor arrays is proposed. The sensor reflective signals characteristics have been analyzed and the relationship between light signals power and sensors total number was given for multiplexing potential evaluation. Experimentally, a three sensor array has been demonstrated. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Fiber optic sensor; Multiplexed sensor array; White light interferometer; Strain sensor; Temperature sensor

1. Introduction White light interferometry is an attractive technique for sensor measurements [1–9], it maintains the accuracy of monochromatic interferometry and avoids many of the limitations and problems associated with conventional interference technique. The advantage of the white light interferometry is that absolute fiber optic elongation or deformation can be measured. This is in contrast to monochromatic coherent interferometry where only relative changes can be measured. Also, due to the short coherence length of the sensing signals, undesirable time-varying interference from stray system reflections is eliminated. Another advantage is the ability to coherence multiplex many sensors onto a single optical signal without requiring the use of relatively complex time or frequency multiplexing techniques. These coherence-multiplexed schemes typically use separate receiving interferometers whose time delays are matched to the remote sensing interferometers [2]. The sensing interferometers are totally passive and demultiplexed interference signals are insensitive to any length changes in the connecting fiber leads. In present work, we design and demonstrate a novel white light multiplexed sensor system, which measures the absolute optical path lengths elongations between reflectors of each fiber segments. The new approach differs from previously demonstrated multiplexed schemes [2–9] in that only ∗ Corresponding author. Tel.: +86-451-251-9850; fax: +86-451-251-9391. E-mail address: [email protected] (L. Yuan).

a Mach–Zehnder non-balance interrogator is needed to generate adjustable differential optical path for matching the sensing gauges. And in the sensing part, only a single fiber lead is required to supply both input and output signals. This is advantageous since it greatly reduces the complexity and cost for a white light interferometric multiplexed sensor array.

2. Fiber optic interferometer configuration The multiplexed Mach–Zehnder and Fizeau tandem white light interferometer is illustrated in Fig. 1. A LED or SLD light source is coupled into the fiber sensor array by passing a non-balance Mach–Zehnder interrogator. Following optical modulation by the parameter, for instance, the elongations of the fiber optic segments, which connect each other, to be sensed at the sensor gauge (a segment of fiber), the reflected signals then again travel in same path towards the detection end. In this sensing system, the sensors consists of N sensing segments (N sensors) connected in series with partial reflectors in between the adjacent sensors, which forms a series fiber optic Fizeau interferometer tandem configuration. The reflectivities of the in-line reflectors are small (1% or less) to avoid depletion of the input optical signal. The fiber sensors lengths lj between adjacent reflectors have been chosen nearly equal the half of the differential optical path LDOP of the non-balance Mach–Zehnder interrogator. The adjustable non-balance Mach–Zehnder interrogator is used as the sensors gauge length matcher and tracer. It

0924-4247/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-4247(03)00062-1

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41

Fig. 1. Multiplexed fiber optic Mach–Zehnder and Fizeau tandem white light interferometer configuration.

is consist of two arms. One arm is direct a fiber line, and the other arm is a pair of fiber optic collimator, the two GRIN lens opposite each other forming an adjustable optical path gap. One of the GRIN lens is fixed on the solid frame, and the other one is mounted on a step moving translation stage, which positioning the scan distance. The interrogator is scanned about a small distance, which approximately equals the differences associated with the individual sensing fibers. In our experiment, the fiber sensor gauge lengths were approximately 500 mm long and the differential optical path LDOP of the Mach–Zehnder interrogator was set such that the difference between lj and LDOP was within 150 mm scan range. As the interrogator is scanned, white light interference signals occur whenever the path difference matches the distance between adjacent reflectors in the sensing array.

2nL1 + 2nL0 + 2n

j −1


lk

(2)

lk + 2nlj

(3)

k=1

2nL1 + 2nL0 + 2n

j −1
k=1

nL1 + nL2 + Xj + 2nL0 + 2n

j −1


lk

(4)

lk + 2nlj

(5)

k=1

nL1 + nL2 + Xj + 2nL0 + 2n

j −1
k=1

2nL2 + 2Xj + 2nL0 + 2n

j −1


lk

(6)

lk + 2nlj

(7)

k=1

3. Measuring principle 3.1. Optical path analysis

2nL2 + 2Xj + 2nL0 + 2n

j −1
k=1

The multiplexed sensors array is based on the aforementioned basic measuring principle. Assuming that the gauge lengths of the fiber sensors are l1 , l2 , . . . , lN , respectively, and the differential optical path of the non-balance Mach–Zehnder interrogator is fixed as shown in Fig. 1:

nL2 + Xj + nL1 + 2nL0 + 2n

L2 − L1 = LDOP

nL2 + Xj + nL1 + 2nL0 + 2n

(1)

The small distance between the two GRIN lenses is X. For the fiber optic sensor j, as shown in equivalent optical path, Fig. 2, the all inters and returns separate optical paths from sensor j are

j −1


lk

(8)

lk + 2nlj

(9)

k=1 j −1
k=1

Case 1. If chosen LDOP ≈ lsensor , and adjust Xj over a small range, then only path (3) and path (6) can match each other, unwanted interference signals associated with non-adjacent reflectors and non-matched reflectors lie outside the scan range and are not detected. For this circumstance, we have nLDOP + Xj = nlj ,

j = 1, 2, . . . , N

(10)

Case 2. If chosen LDOP ≈ 2lsensor , then it could be found that the match paths are (3) and (4), (3) and (8), (5) and (6), and (6) and (9). And the sum of the signals intensity is also much larger than Case 1 as shown after mention, thus we have Fig. 2. Equivalent optical paths for the sensor j.

nLDOP + Xj = 2nlj ,

j = 1, 2, . . . , N

(11)

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L. Yuan, J. Yang / Sensors and Actuators A 105 (2003) 40–46

The disadvantage in Case 2 is that there are N − 1 undesired signals come from each adjacent sensor pair like Case 1. The positions are described by nLDOP + Xi,j −1 = n(lj + lj −1 ),

j = 1, 2, . . . , N

(12)

Compare the signal intensity with Case 1, the undesired signals intensity is very small in Case 2.

at the temperature T0 . For sensor j, as the temperature changing from T0 to Tj , the optical path of the sensor gauge will be varied due to thermal expansion and the change of refractive index of the fiber core. The scanning displacement related with the ambient temperature Tj can be represents as follows in terms of Eq. (10):

Xj = n(T0 )1 + CT (Tj − T0 )lj (T0 )1 + αT (Tj − T0 ) ≈ n(T0 )lj (T0 )[αT + CT ](Tj − T0 ) = Slj (T0 )(Tj −T0 )

3.2. Quasi-distribution strain measurement For the sensors array, we suppose l1 change to l1 + l1 , l2 change to l2 + l2 , . . . , lN change to lN + lN , as distributed stresses are loaded in the sensing gauges. The step motor positioning system fine tunes the differential path length of the Mach–Zehnder interrogator to match and trace the variations of the sensors’ gauge lengths. Because it is a unique position for each individual sensor, therefore the distribution strains were measured as ε1 =

l1

l2

lN , ε2 = , . . . , εN = l1 l2 lN

From Eq. (10), due to LDOP is a constant length, therefore, the displacement of sensor j is corresponding to

Xj = n lj (εj ) + n(εj )lj

(13)

The first term in Eq. (13) represents the physical change of length produced by the strain, it is directly related axial strain ε through the expression

lj (εj ) = lj εj

(18) Then the ambient temperature can be measured as Tj =

Xj + T0 , Slj (T0 )

j = 1, 2, . . . , N

where n(T0 ) is the refractive index of fiber core at temperature T0 . Xj is the displacement recorded by the step moving stage which corresponds to the fiber sensor j. α T and CT are the thermal expansion coefficient and the refractive index temperature coefficient of the optical fiber, respectively. S is a sensitivity coefficient. For the standard commercial communication single mode fiber at wavelength λ = 1300 and 1550 nm the parameters are n = 1.4681, αT = 5.5 × 10−7 /◦ C, CT = 0.762 × 10−5 /◦ C and n = 1.4675, αT = 5.5 × 10−7 /◦ C, CT = 0.811 × 10−5 /◦ C are taken from Ref. [12]. Using these data, for the unit optical fiber length, the sensitivity coefficient S of this kind fiber optic temperature sensor can be calculated as 11.99 ␮m/(m ◦ C) at 1300 nm and 12.71 ␮m/(m ◦ C) at 1550 nm, respectively.

(14)

The second term, the change in optical path due to a change in the refractive index of the fiber core, is given by [10]

4. Multiplexing potential evaluation

n = − 21 n3 [(1 − µ)p12 − µp11 ]εj

4.1. Optical signal intensity analysis

(15)

Thus, we have

x = nlj εj − 21 n3 [(1 − µ)p12 − µp11 ]lj εj   = n − 21 n3 [(1 − µ)p12 − µp11 ] lj εj = nequivalent lj εj (16) where nequivalent represents the equivalent refractive index of the fiber core. For the silica materials at wavelength λ = 1300 nm, the parameters are n = 1.46, µ = 0.25, p11 ≈ 0.12, p12 ≈ 0.27 [11] and the equivalent index can be calculated as nequivalent ≈ 1.19. Thus, the strain can be measured by εj =

Xj , nequivalent lj

(19)

j = 1, 2, . . . , N

(17)

3.3. Quasi-distribution temperature measurement The fiber optic sensor array can also be used to measure the quasi-distribution temperature in free space. Assuming that the sensors gauge lengths are l1 (T0 ), l2 (T0 ), . . . , lN (T0 )

In the fiber optic sensor array the fraction of optical source power is coupled into the fiber and distributed over the sensor array via several splices and connectors. Each sensor elements absorbs or diverts a certain amount of power (insertion loss), typically between 0.1 and 0.5 dB. Calculating the sensor array power budget leads to the power margin, Ps , available at each sensor, which determines the possible dynamic range of the sensor and limits the maximum sensor number in the multiplexed sensing system. The light intensity I0 is split by the first 3 dB coupler into two branches. One branch goes to the arm L2 of the non-balance Mach–Zehnder interrogator, and passing through the GRIN lens pair. The intensity is P0 α1 η(x)/2, and then split by the second 3 dB coupler. In this branch, the intensity coupled into the sensor array is P0 α1 α2 η(x)/4. It undergoes lead fiber L0 and passing through j − 1 sensors get to the sensor j. Here, α 1 and α 2 represents the first and second 3 dB coupler insertion losses parameters, respectively. Similarly, the other branch goes along the arm L1 of the non-balance Mach–Zehnder interrogator, and is directly divided by the second 3 dB coupler and goes to sensor j.

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Fig. 3. Power fluxes of transmissive and reflective light signals in the multiplexed sensors array.

The intensity injected in the sensor array, in this branch, is P0 α1 α2 /4. It is larger than P0 α1 α2 η(x)/4 due to few decibels insertion losses of the GRIN lens pair in arm L2 . At each fiber sensors’ end surface, the light wave partly reflects and partly transmits. If the reflectively is R and transmission coefficient is T (with R + T ≤ 1), when the light wave undergoes a series sensors and get to sensor j, the transmitted light and reflective light intensity then are proportional to T j −1 and R, respectively, as shown in Fig. 3. Noted that all the losses included connection part insertion losses and other losses except reflective losses is δ j for the sensor j. For calculations convince, let log(βi ) = −δj /10. Then the reflective light signals intensity arrived to the detector of the jth sensor can be calculated as follows. Case 1. For the condition LDOP ≈ lsensor , only path (3) and path (6) are matched, then the light wave signal underwent path (3) and returned intensity will be given by  2 j    I0 Is (j +1) = βi , j =1, 2, . . . , N + 1 Rα12 α22 T 2j   16 i=1

(20) Similarly, the light wave signal undergone path (6) and returned intensity is  2 −1  j I0 2 Is (j ) = η (Xj )Rα12 α22 T 2j −2 βi ,   16 i=1

j = 1, 2, . . . , N + 1

(21)

The intensity of sensor signals used to perform measurement is the coherent mixing terms of the reflected light signals from the sensors’ two matching paths, i.e.:  ID (j ) = 2 Is (j +1)Is (j )  2 j −1 I0 = η(Xj )Rα12 α22 T 2j −1 βj  βi  , 8 i=1

j = 1, 2, . . . , N + 1

(22)

Case 2. For the condition LDOP ≈ 2lsensor , the match paths are (3) and (4), (3) and (8), (5) and (6), and (6) and (9). And

the sum of the coherent mixing terms of the reflected light signals can be calculated as  ID (j ) = 2 Is (j + 1)Is (j )|paths (3) and (4)  + 2 Is (j + 1)Is (j )|paths (3) and (8)  + 2 Is (j + 1)Is (j )|paths (5) and (6)  + 2 Is (j + 1)Is (j )|paths (6) and (9)  2 j −1  I0 = Rα12 α22 T 2j −1 βj  βi  η(Xj ){1 + η(Xj )} 4 i=1

(23) Similar to Case 1, the undesired signals intensities in Case 2 are also calculated:  2 j  I0 IUndesired (j, j + 1)= η(Xj,j +1 )Rα12 α22 T 2j −2  βi  , 8 i=1

j = 1, 2, . . . , N + 1

(24)

4.2. The maximum number of the multiplexed sensor If the detecting limit of the photodiode is Imin , then, the maximum number of the total fiber optic sensors can be evaluated by the condition ID (j ) ≥ Imin

(25)

For convenient calculating, we assume that α1 ≈ α2 = 0.98, corresponding to the typically 3 dB coupler excess insertion losses 0.06 dB, and typically fiber optic connection insertion losses coefficient βj = 0.9(j = 0, 1, 2, . . . , N ). Under the condition of perpendicular incidence, the reflectivity at the fiber end surface is given by Fresnel formula R = (n − 1)2 /(n + 1)2 , where n is the index of fiber core, the typical value is 1.46, corresponding to 4% reflectivity. For good connected fiber ends, the air gap is smaller than the wavelength, in that case the typically reflectivity R is nearly equal to 1%. Therefore, the transmission coefficient can be calculated as T = 0.89. We assume that the average attenuation of the moving GRIN lens part is 6 dB, i.e.

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L. Yuan, J. Yang / Sensors and Actuators A 105 (2003) 40–46

Fig. 6. Three fiber optic sensor array experimental scanning peak signals.

Fig. 4. Normalized optical signals intensities vs. fiber optic sensor number for Case 1 (LDOP ≈ lj ) and Case 2: (LDOP ≈ 2lj ).

η(Xj ) = 1/4. Then, the normalized optical signal intensity vs. the fiber optic sensor number j is plotted in Fig. 4. It is shown that the signals intensity of Case 2 is five times of Case 1. The undesired signals intensity in Case 2 is nearly equal to that sensors’ signals in Case 1, therefore, for the smaller signals beneath the dot line of Fig. 5, the sensors’ signal may be confused by the undesired signals. In fiber optic sensing system, the typical detecting capability of the photodiode is about 1 nW. Taking into account the noise floor and other stray signals from the system, the reasonable detect limit is assumed that Imin = 10 nW. Under the condition (25) and take account of the above data, for light source power I0 = 30 ␮W, the maximum number of the fiber sensor can be calculated as Nmax = 3 in Case 2 and Nmax = 0 in Case 1; while, for light source power I0 = 3 mW, we get Nmax = 14 in Case 2 and Nmax = 10 in Case 1, respectively. In fact, the maximum number of total fiber optic sensors is not only dependent on the light source power level, but also limited by the length of the longest moving distance of the scanning GRIN lens (or the length of translation stage). In addition, it should be noted that the receiver noise floor,

Fig. 5. Normalized signals intensities compared with the undesired signals in Case 2 (LDOP ≈ 2lj ).

and hence the detecting sensitivity, will be a function of the method of signal encoding and the required scanning speed of the moving GRIN lens, depending on the required detecting range and the multiplexing scheme. Thus, the maximum number, Nmax , of sensors are less than that given in above paragraph.

5. Experimental results A three sensor array was demonstrated in our experiments. In the sensing system, the LED light source power is 30 ␮W, the insertion losses of GRIN lens pair changes from 4 to 8 dB as the gap distance changes from 3 to 150 mm. The differential optical path of the non-balance Mach–Zehnder interrogator LDOP is chosen as twice of fiber optic sensor gauge length. And each individual sensor’s gauge length is about 500 mm. The scanning signals corresponding to the three white light interferometric peaks are plotted in Fig. 6. In order to demonstrate the applicability of the system in real distributed deformation or temperature measurements. The sensor array shown in Fig. 1 was used for quasi-distributed temperature measurements. Temperature calibration experiment was first carried out by emerging 500 mm long fiber segment into a hot water bath and measuring the shift in the fringe peak and at the same time the water temperature by using a thermal couple located near the sensing fiber. The linear relationship between the peak

Fig. 7. Temperature calibration results for a fiber of gauge length of 500 mm.

L. Yuan, J. Yang / Sensors and Actuators A 105 (2003) 40–46

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One method is by way of inserting a polarization controller to improve the ratio of the signal to noise. 6. Conclusion

Fig. 8. Results of the temperature distribution measurement.

shift of the white light interference fringe and the temperature given by the thermocouple over range from 35 to 85 ◦ C is plotted in Fig. 7. The calibration coefficient can be calculated as 10.17 ␮m/(m ◦ C). Therefore the resolution of the sensing system is about 0.5 ◦ C. We put two fiber optic sensors in separate water bath and cooling them done start from different temperatures, and let the third one keep in the room temperature (18 ◦ C). The testing results are plotted in Fig. 8. It can be seen that the sensor array can measure the variations of the temperature distribution. It should be mentioned that, the output signals of the sensors array are dependent on the polarization states. Fig. 9 shows the variation of the signals and the accompany noise when the polarization controller in the sensors array was adjusted. This is because the polarization states of the part of reflected light signals would be changed due to traveling through the long optical path length. When the light signals are of the same polarization, the light signal noise level at the output port would approach zero due to destructive interference. When the reflected signals are of different polarization states, the orthogonal polarization components would add up in intensity and result in a noise. And as the variation of deformation in each gauge length of the sensor starting from the first sensor would change the state of polarization. In that case, their multi-sensing capability would have been reduced. It may therefore necessary to control the polarization states in order to achieve the optimal results.

Fig. 9. The noise amplitude much reduced by adjusting the polarization state.

A white light fiber optic Mach–Zehnder and Fizeau tandem interferometer for performing multiplexed measurements on a fiber sensor array has been proposed and demonstrated. The sensor array is completely passive and absolute length measurements can be obtained for each sensing fiber. The proposed sensing scheme will be useful for the remote measurement of temperature or strain. An important application could be deformation sensing in smart structures. By incorporating fiber optic sensor arrays into structures such as bridges, building frames, dams, and tunnels, smart structures can be realized for situations where material strains must be monitored throughout the lifetime of the structures. This kind sensor array can also be addressed from both sides of the sensors chain introducing an interesting redundancy factor in the case of failures. Acknowledgements This work was supported by the National Natural Science Foundation of China, grant number 50179007, and the Teaching and Research Award Program for Outstanding Young Professors in Higher Education Institute, MOE, PRC, and the Science Foundation of Heilongjiang Province for Outstanding Youth, 1999, to the Harbin Engineering University. References [1] G. Beheim, Remote displacement measurement using a passive interferometer with a fiber-optic link, Appl. Opt. 24 (1985) 2335–2340. [2] J.L. Brooks, R.H. Wentworth, R.C. Youngquist, M. Tur, B.Y. Kim, H.J. Shaw, Coherence multiplexing of fiber optic interferometric sensors, J. Ligthwave Technol. LT-3 (1985) 1062–1071. [3] H.C. Lefevre, White light interferometry in optical fiber sensors, in: Proceedings of the Seventh Optic Fiber Sensors Conference, Sydney, Australia, 1990, pp. 345–351. [4] C.E. Lee, H.F. Taylor, Fiber-optic Fabry–Perot temperature sensor using a low-coherence light source, J. Ligthwave Technol. 9 (1991) 129–134. [5] A.B.L. Ribeiro, D.A. Jackson, Low coherence fiber optic system for remote sensors illuminated by a 1.3 ␮m multimode laser diode, Rev. Sci. Instrum. 64 (1993) 2974–2977. [6] D. Inaudi, A. Elamari, L. Pflug, N. Gisin, J. Breguet, S. Vurpillot, Low-coherence deformation sensors for the monitoring of civil-engineering structures, Sensors Actuators A 44 (1994) 125–130. [7] W.V. Sorin, D.M. Baney, Multiplexing sensing using optical low-coherence reflectometry, IEEE Photon. Technol. Lett. 7 (1995) 917–919. [8] L.B. Yuan, F. Ansari, White light interferometric fiber-optic distributed strain-sensing system, Sensors Actuators A 63 (1997) 177– 181. [9] L.B. Yuan, L. Zhou, W. Jin, Quasi-distributed strain sensing with white-light interferometry: a novel approach, Opt. Lett. 25 (2000) 1074–1076.

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[10] C.D. Butter, G.B. Hocker, Fiber optics strain gauge, Appl. Opt. 17 (1978) 2867–2869. [11] D.A. Pinnow, Elastooptical materials, in: R.J. Pressley (Ed.), Handbook of Lasers, CRC Press, Cleveland, OH, 1971. [12] L.B. Yuan, Effect of temperature and strain on fiber optic refractive index, Acta Opt. Sinica 17 (1997) 1713–1717.

Biographies Libo Yuan was born in 1962 and graduated with a BSc in Physics from Heilongjiang University in 1984 and an MEng in Electrical Engineering from Harbin Shipbuilding Engineering Institute in 1990. He joined Harbin Engineering University on August 1984 and as assistant in 1984; lecture in 1991, associate professor in 1992 and professor in 1996 at the Department of Physics. He has been invited as a

visiting research fellow doing research of fiber optic sensors for smart structure from October 1995 to April 1997 in New Jersey Institute of Technology, USA. He worked on optical waveguide theory, optoelectronic devices and fiber-optic sensors. His interests include fiber optic pressure detecting, temperature probe and fiber optic strain sensors based on white light interferometric techniques. Recently, as principal investigator, he has become involved in a number of projects on fiber optic sensors for smart structures. Over 120 of his research papers have been published. Jun Yang was born in 1976 and graduated with a BSc in Electronic Science and Technology in 1999 and an MEng in Optical Engineering in 2002 from Harbin Engineering University. He is a PhD candidate in Department of Physics, Harbin Engineering University. His current research interests concentrate on the design of O/E converter and embedded single chip CPU system and fiber optic white-light interferometers. 12 of his research papers have been published.