Song Li，F(xiàn)erhati Mokhtar，Li-Bo Yuan

(Photonics Research Center，School of Science，Harbin Engineering University，Harbin 150001，China)

1 Introduction

White light interferometry，as a technique employing low coherence broadband light source，has been considered as a very active area of research in recently years［1－4］.The technique for distributed strain or temperature sensing in advanced composite or other structural materials［5－8］uses a scanning interferometer(e.g.，Michelson or Mach-Zehnder interferometer)to match the optical path of signal light for getting white light interference fringes.An advantage of fiber optic white light interferometer is the ability to multiplex，in coherent domain，many sensors into a single optical signal without using the relative complex techniques of time or frequency multiplexing.In order to respond the increasing request，from a number of application fields，of fiber-optic sensors with multiplexing capacities［9－12］，the significant effort has been devoted to the development of sensor arrays.In general，multiplexing involves the concepts of network topology，sensor addressing，and sensor interrogation［13］.

In most of the practical applications，the distance incorporated into white light interferometer measure may be as long as several kilometers.Therefore，we work out for a reflective ladder topology network(RLT)based on white light fiber-optic Mach-Zehnder interferometer.Moreover，exotic sensing，topologies have also been considered in various literatures in terms of the recursive series topology［14］and the tapped serial array［15］.We are focused on the reflective ladder topology network，which，to our knowledge，has not been yet analyzed.In this paper，we have discussed the main principle of operation and optimization criterion and numerical results are also addressed with the aim to analyze the multiplexing capacity of the network.Practical setup is also built up for demonstrating the theoretical analysis.The absolute length measurement can be obtained for each sensing fiber.Considering the results，the proposed sensing schemes would likely be useful for the remote measurement of temperature or strain.

2 Experimental Details

In general scheme，the network system comprises an optical transmitter，an input bus，an output bus，a number of sensing elements and a receiver［12］.Fig.1 shows the designed ladder topology，in which the multiple sensors are arranged in parallel.The sensor interrogation is achieved through the use of a Mach-Zehnder interferometer(MZI)powered by a superluminescent diode(SLD)light source.The optical path-length difference(OPD)of the MZI is tuned by using a scanning prism-Graded Index(GRIN)lens system.When the prism moves to a position where the OPD is matched to the gauge length of a particular sensor(one signal reflected by the proximal end of the sensor and the other one reflected by the distal end)，a low-coherence interferometric pattern is generated.The topology network consists of N rungs sensing elements linked by N－1 couplers.In multi-sensor arrays，an important consideration is the method used to identify each sensor at the receiver.For this purpose，the gauge lengths of the sensors are chosen to be slightly different one from another but approximately the same as the optical path-length difference(OPD)of the MZI.Taking sensor Suvas an example，the pairs of matching paths are shown in Fig.2.

Fig.1 Reflective ladder topology network configuration

Fig.2 Optical path and reflective signals analysis diagram for the fiber-optic sensor Suv

The light from the SLD is split by the first 3 dB coupler into two branches.The upper branch goes to the arm 2X+nL2(L2means the length of the upper arm and X means the distance of the mirror’s scanning)of the MZI and passing through the second 3dB coupler，gets to the u-th column and v-th row sensor Suvconnecting interface，and reflected by the proximal end reflector Ru，v－1，its total optical path may be described by:

Similarly，the light wave along the lower branch and reflected by the distal end reflector Ruvof the sensor Suvis written as Eq.(2)，here L1means the length of the lower arm

If we make the MZI to satisfy the condition:

Then we adjust X by moving the position of the scanning prism，and let the optical path Eqs.(1)and(2)matching.Thus，we have:

Eq.(4)shows that the white light interference patterns will be appeared as X changing with scanning prism moving from one end to another end on the translation stage.And each interference pattern corresponds to a unique fiber optic sensor(or a fiber segment)，which can be used to measure the variations of the fiber optic sensor topology network.

The signal intensity of the upper branch turns back to the detector may be expressed as:

And the signal intensity of the lower branch may be:

The power which can be detected by the photodiode is:

where the two couplers are assumed to be 3dB couplers and the insertion losses are neglected;kiis the power splitting ratio of the coupler;βuvrepresents the excess insertion loss associated with u-th column and v-th row is connected interface between the adjacent sensors due to stray scattering and absorption.Tuvand Ruvare respectively the transmission and reflection coefficients of the u-th column and v-th row connection interface between the adjacent sensors;β'uvand T'uvrepresent，respectively，the excess insertion loss and the transmission coefficient from the opposite direction;f(Xuv)is the loss associated with the scanning prism and fiber optic collimator systems and is a function of Xuv.

3 Results and Discussion

The practical setup is shown in Fig.3.The wavelength of the SLD light source is 1310 nm，and the spectral bandwidth is 60 nm.The insertion loss of the fiber optic GRIN lens collimator is from 4 dB to 8 dB as the gap distance between the fiber optic collimator end and the scanning prism position changing from 0 to 100 mm.The fiber optic segment length is chosen as almost the same as optical path difference of the Mach-Zehnder interrogator and each individual fiber optic segment length is about 100mm.Theoretical simulations are conducted for typical parameters:β=β'=0.9，R=R'=1%，T=T'=0.89.The loss of the scanning mirror and the GRIN lens part is taken as f(Xuv)=0.25.We carried out a simulation of the maximum number of sensors by using one fiber optic sensor in each branch，with different power ratios of couplers.Fig.4 shows that for coupler power ratio of k=0.2，the medium number of sensors for(Io=1 mW，3 mW，6 mW)is the biggest，so we choose(k=0.2 or k=20%)for the next simulations.

Fig.3 Practical setup

Fig.4 Maximum number of sensors vs.power ratio of couplers

The topology network consists of 6 rungs sensing elements linked by 5 couplers was investigated under two different cases:one is equal coupling ratio，and the other is tailored coupling ratio.Here we introduce optimization criterion into our experiments and the tailored equation is given as:

If the detecting power limit of the photodiode is Imin，then，the maximum number of the total fiber optic sensors can be evaluated by the condition:

Taking into account the noise floor and other stray signals from the system，the power detection limit is assumed to be Imin=10 nW.Under the condition，Eq.(11)and taking account of the above data，the maximum number of sensors can be calculated as N=19，using equal coupling ratio shown in Fig.5，and N=20，using tailored coupling ratio shown in Fig.6.

Fig.5 Normalized returned power per sensor as a function of sensor number with equal coupling ratio

Fig.6 Normalized returned power per sensor as a function of sensor number with tailored coupling ratio

The power coupled into the input fiber is 1 mW with drive current 100 mA.The scanning gap distance is from 0 mm to 30 mm.The length of each fiber optical sensor is about 1000 mm，but they are slightly different to corresponding to a unique interferometric signal.The sensors are named as S11，S12，…S1M，S21，S22，…S2M，…，SN1，SN2，…SNM.

In Case 1，the power ratio of couplers is taken as mentioned before k=0.2，but the last coupler whom the power ratio is k5=0.5，as shown in Fig.7.The maximum number of sensors which can be multiplexed is 8，including 6 sensors in the first step and 2 sensors in the second step.

Fig.7 Output signal powers of 8 sensors linked by 5 couplers with equal ratio

For the second case where the couplers are tailored by Eq.(10):k1=1/5，k2=1/4，k3=1/3，k4=1/2，k5=1/2.

As shown in Fig.8，the maximum number which can be multiplexed is 12 fiber optic sensors，including 6 sensors in the first step and 6 sensors in the second step.We note that in this case we have better results as compare to the first case.The intensity in the same column are not the same as the simulation results due to difficult criteria to ensure each reflective surfaces the same as one value.Normally it is highly desirable that all sensors return the same level of average optical power to the detection block.This is true only when the network losses are neglected［11］.

Fig.8 Output signal powers of 12 sensors linked by 5 couplers with tailored ratio

On the other side，comparing the results in Figs.7 and 8，it is obvious that the multiplexing capacity of using tailored coupler ratios is much better than that of using equal coupler ratio.This agrees with our simulation analysis as shown in Figs.5 and 6.The x-coordinate of Figs.7 and 8 means displacement of scanning prism，which is corresponding to the length of the sensors.That means the sensor whose signal on the left side of Figs.7 and 8 is shorter than that whose signal on the right side of Figs.7 and 8.In practical application，we can observe which x-coordinate location of a signal changes，and then we know the corresponding sensor is disturbed.For the moment，y-coordinate is not considered.

4 Conclusions

Reflective ladder topology network(RLT)based on white light fiber-optic Mach-Zehnder interferometer is studied and analyzed in this paper.An optical path matching technique is used to demodulate each sensor.The topology network consists of N rungs sensing elements linked by N－1 couplers.Optimization criterion and numerical results are addressed，and the multiplexing capacity of the network has been analyzed.The results show that the multiplexing ability will be enhanced after using optimization criterion.Practical setup is also built up for demonstrating the theoretical analysis.The experimental results have a good agreement and the performance is matched with the numerical simulation.Therefore，it is useful to incorporate RLT into structures like buildings，grounds，bridges，dams，tunnels，highways and perimeter security.

［1］Rao Yunjiang，Ning Yanong，Jackson D A.Synthesized source for white-light sensing systems.Optics Letters，1993，18(6):462－464.

［2］Yuan Libo，Zhou Limin，Jin Wei.Recent progress of white light interferometric fiber optic strain sensing techniques.Review of Scientific Instruments，2000，71(12):4648－4654.

［3］Yuan Libo.Department and applications of white light interferometric optic sensing techniques.Journal of Natural Science of Heilongjiang University，2005，22(2):172－187.

［4］Xue Hui，Shen Weidong，Gu Peifu，et al.Thickness measurement of thin film based on white-light spectral interferometry.Acta Optica Sinca，2009，29(7):1877－1880.

［5］Yuan Libo，Ansari F.White light interferometric fiber optical distribution strain sensing system.Sensors and Actuators A，1997，63(3):177－181.

［6］Li Xinhong，Zhang Haijun，Zhang Dongxian.Quantitative phase imaging system with active phase stabilization based on white-light interferometry.Acta Optica Sinca，2008，28(7):1279－1282.

［7］Yuan Libo，Zhou Limin，Jin Wei.Quasi-distributed strain sensing with white-light interferometry:a novel approach.Optics Letters，2000，25(15):1074－1076.

［8］Peng Feng，Yang Jun，Wu Bing，et al.Compact fiber optic accelerometer.Chin Opt Lett，2012，10(1):011201.

［9］Sorin W V，Baney D M.A simple intensity noise reduction technique for optical low-coherence reflectometry.IEEE Photonics Technology Letters，1992，4(12):1404－1406.

［10］Michie W C，Culshaw B，Thursby G，et al.Optical sensors for temperature and strain measurement.SPIE，1996，2718:134－146.

［11］Brooks J L，Wentworth R H，Youngquist R C，et al.Coherence multiplexing of fiber-optic interferometric sensors.Journal of Lightwave Technology，1985，LT－3(5):1062－1072.

［12］Jiang Haili，Yuan Yonggui，Yang Jun，et al.Theoretical and experimental study on white light interferom etric fiber optic sensors network configuring by tandem of Michelson and Mach-Zehnder interferometers.Journal of Harbin Engineering University，2011，32(2):60－265.

［13］Ribeiro A B L，Caleya R F，Santos J L.Progressive ladder network topology combining interferometric fiber-opticbased sensors.Applied Optics，1995，34(28):6481－6488.

［14］Moslehi B，Layton M R，Shaw H J.Efficient fiber-optic structure with application to sensor arrays.Journal of Lightwave Technology，1989，7(2):236－243.

［15］Kersy A D，Dandridge A.Transmissive serial interferometric fiber sensor array.Journal of Lightwave Technology，1989，7(5):846－854.