Aw

I

1

Tvotvimalaodwthsawsaud

tTBcd

2

bsolute strain measurements madeith fiber Bragg grating sensors

n C. Song, Sun K. Lee, Sung H. Jeong, and Byeong H. Lee

A strain sensor system based on optical fiber Bragg gratings �FBGs� is proposed with a new matched-filterdesign. The strain variation on the sensor FBG is continuously followed and matched by a filter FBGby use of a feedback control loop that produces an identical strain condition on the filter FBG. Thematched strain on the filter FBG is then determined from the resonance vibration of the fiber pieceembedding the filter FBG. The implementation and the performance of the proposed system aredescribed. It is demonstrated that the proposed system can distinguish strain variation on the sensorFBG with resolution of one microstrain. © 2004 Optical Society of America

OCIS codes: 060.2370, 120.0280, 050.2770, 000.2170.

somf

tFmsfTcttositsateqaoi

2

Fpfogp

. Introduction

he refractive index of the core of an optical fiber isaried upon exposure to ultraviolet light. When theptical fiber is irradiated by an ultraviolet laser beamhrough a phase mask, a periodic refractive indexariation along the core can be produced that resultsn a fiber Bragg grating �FBG�. When light is trans-

itted through the FBG, a strong reflection occurs atcertain wavelength, known as the Bragg wave-

ength ��B� and determined by �B � 2ne�, where nend � are the effective refractive index and the periodf the grating, respectively. Owing to its depen-ency on the spatial period of the grating, the Braggavelength of a FBG shifts as the strain and�or the

emperature of the optical fiber is changed.1 Theigh sensitivity of the Bragg wavelength to externaltrain offers a good possibility for a FBG to be used asstrain sensor. For detection of the shift of Braggavelength of a FBG sensor, tunable bandpass filters

uch as a Fabry–Perot filter2 or a FBG-based filter3,4

nd different types of interferometers have beensed.5,6 In the case of tunable filters, however, theifficulties in interrogating the filter parameters,

C. Song, S. K. Lee, and S. H. Jeong �shjeong@kjist.ac.kr� are withhe Department of Mechatronics, Kwangju Institute of Science andechnology, 1 Oryong-dong, Buk-gu, Kwangju 500-712, Korea.. H. Lee is with the Department of Information and Communi-ations, Kwangju Institute of Science and Technology, 1 Oryong-ong, Buk-du, Kwangju 500-712, Korea.Received 23 May 2003; revised manuscript received 15 October

003; accepted 20 November 2003.0003-6935�04�061337-05$15.00�0© 2004 Optical Society of America

uch as the separation between Fabry–Perot mirrorsr the nonlinearity of piezoelectric transducer �PZT�aterial during actuation, degrade the system per-

ormance.In this paper, we report on a new matched-filter

ype strain-measurement system consisting of twoBGs, one as the strain sensor and another as theatched filter. By use of a closed control loop, the

train on the filter FBG is continuously adjusted toollow the strain on the sensor FBG in real time.herefore the strain information on the sensor partan be achieved by monitoring the matched strain onhe filter FBG. For determination of the strain onhe filter FBG, the mechanical resonance frequencyf the fiber piece embedding the filter FBG is mea-ured. Because the resonance frequency of a vibrat-ng optical fiber is a unique function of the strain onhe fiber string, we can absolutely determine thetrain of the filter FBG, eliminating the nonlinearitynd the hysteresis effects observed in conventionalunable filters for which PZT voltage is measured tostimate the filter FBG strain. The resonance fre-uency of the vibrating filter FBG is determined withspecially designed string resonator. Performance

f the proposed strain measurement system is exper-mentally examined.

. Principle of the Strain Sensor System

igure 1 shows the schematic diagram of the pro-osed strain measurement system consisting of twoeedback control loops, a PZT-driven fiber stretcher,ptical fibers embedded with the sensor and filterratings, and a string resonator. Light from a su-erluminescent LED �SLED� enters the system

20 February 2004 � Vol. 43, No. 6 � APPLIED OPTICS 1337

tslwpPetmwmfimoabcF

mtfidPgnscfidseolrl

A

Fswq

s

mf

w�TtSetttw

wtbfi

A�wa

EmF

trnfiaiTas

wlStts

FI

1

hrough a 3-dB coupler and is transmitted into theensor fiber. A narrow band of the transmittedight, whose wavelength is centered at the Braggavelength of the sensor FBG, will be reflected, de-ending on the strain condition of the sensor FBG.art of the reflected light then enters the filter fibermbedding the filter FBG via the coupler. The op-ical power transmitted through the filter FBG iseasured with a photodiode. When the centeravelengths of the sensor and filter FBGs areatched, the reflection of the incident light by the

lter FBG would become maximum, resulting in theinimum measured power on the photodiode.7 The

ptical fiber embedding the filter FBG is attached toPZT-driven stretcher and controlled with a feed-

ack loop so that the strain on the filter FBG can beontinuously adjusted to match that of the sensorBG.Because the strain on the filter FBG is controlled toatch that of the sensor FBG, the strain condition on

he sensor FBG can be monitored from that of thelter FBG. The strain on the filter FBG may beetermined from the strain-voltage relation of theZT-driven fiber stretcher. However, because aeneral piezo material exhibits large hysteresis andonlinear characteristics, the accuracy of the mea-ured strain degrades if the PZT-driving-voltage ishosen as a method to determine the strain of thelter FBG. To overcome this problem, we intro-uced a string resonator that measures absolutetrain of the filter fiber. Specifically, the fiber piecembedding the filter FBG is forced to vibrate at itswn resonance frequency using a feedback controloop and then the resonance vibration frequency iselated to the applied strain as described in the fol-owing section.

. Feedback Control of the String Resonator

eedback control of the string resonator to match thetrain of the filter FBG to that of the sensor FBGhile the filter fiber is vibrated at its resonance fre-uency is done as follows.7When the intensity of the light transmitted into the

ensor FBG is equal to I ���, the total light power

ig. 1. Schematic diagram of the strain measurement system.MG, index-matching gel; LPF, low-pass filter.

i

338 APPLIED OPTICS � Vol. 43, No. 6 � 20 February 2004

easured on the photodiode, Pd, is expressed by theollowing equation:

Pd � �0

�

Id���d� ��1 � ��

4 �0

�

Ii��� Rs���Tr���d�,

(1)

here Id��� is the light intensity into the photodiode,is the loss occurring in the light path, and Rs��� andr��� are the spectral reflectance and the transmit-

ance of the sensor and filter FBGs, respectively.ubscripts s and r in Eq. �1� and in the followingquations represent the sensor and filter, respec-ively. Assuming that the spectral distribution ofhe reflected light at the sensor grating is Gaussian,he sensor grating’s reflectance Rs��� in Eq. �1� can beritten as

Rs��� � Rmax exp��� � �s�

2

s2 � , (2)

here Rmax is the maximum reflectance measured athe Bragg wavelength �s of the sensor FBG having aandwidth s. Similarly, the transmittance of thelter FBG can be expressed as

Tr��� � 1 � Rr exp��� � �r�

2

r2 � . (3)

ssuming that the spectrum of the input light sourceSLED� is approximately flat over the spectral band-idth of the sensor FBG and defining �� � �s �rnd � �s

2 r2�1�2, Eq. �1� can be rewritten as

Pd �1 � �

4Ii��s� Rss���1 � Rr

r

exp�

��2

2 �� .

(4)

quation �4� shows that the optical power Pd becomesinimum when the strain on the sensor and the filterBGs are the same, that is, �� � 0.Note that the optical power in Eq. �4� is propor-

ional to the square of the wavelength mismatch,esulting in an identical effect for both positive andegative ��. To decide the direction of control of thelter FBG, a small amplitude sinusoidal signal withfixed frequency �o, called the dithering signal, is

ntentionally added to the driving voltage of the PZT.hen the wavelength mismatch between the sensornd the filter gratings is described as the sum of thetrain-induced part and the dithering-induced part:

�� � ��o � �d sin �o t � ��s � �ro� � �d sin �o t, (5)

here �ro is the averaged filter grating’s peak wave-ength and �d is the amplitude of the dithering signal.ubstitution of Eq. �5� into Eq. �4� makes Pd a func-ion of a constant term, a sin �ot term, and a sin2 �oterm. When Pd is multiplied by the same ditheringignal for demodulation and passed through a low-

pp

wpAotdt

BF

AemTbsdbbt

wialrb

qc

wittmsbDmbooa

qtt

iamkaTqth

vsfiwFrpfibdvs

3

Fuw1awwFtm

Fw

Fb

ass filter, only the sin �ot term remains, and thehotodiode output �voltage� signal becomes

Vo���o� � constantr

3 2��o�d, (6)

here the constant includes a conversion factor of thehotocurrent into voltage and a demodulation factor.ccordingly, through observation of the photodiodeutput signal represented by Eq. �6�, the direction ofhe feedback control �that is, either an increase or aecrease of the strain on the filter FBG� can be de-ermined.

. Determination of Absolute Strain from the Resonancerequency of a Fiber Piece

s mentioned above, the strain condition of the fibermbedding the filter FBG is determined throughonitoring its resonance frequency during vibration.heoretically, the resonance frequency of a vibratingeam element with clamped ends is a function of thetrain applied to the beam. Neglecting system-amping effects, the optical fiber can be modeled as aeam element subjected to an axial force and its vi-ration amplitude w at a point x can be expressed byhe following equation8:

EI�4w� x, t�

� x4 � �A�2w� x, t�

�t2 � P�2w� x, t�

� x2 � 0, (7)

here E is the elastic modulus, I is the moment ofnertia, � is the density, A is the cross-sectional area,nd P is the tension on the beam. The detailed so-ution procedure to derive the relation between theesonance frequency and the applied strain to theeam was reported in Ref. 8.From the solution of Eq. �7�, the resonance fre-

uency of the fiber element embedding the filter FBGan be written as a function of strain as follows:

fi2 �

Di�εo � ε�

�1 � εo � ε�2 �fo,i

2

�1 � εo � ε�3 ,

�Di��εo � ε� � �εo � ε�2� � fo,i

2

1 � 3�εo � ε�, (8)

here fi and fo,i are the resonance frequencies of theth mode with and without strain, respectively, εo ishe initial strain applied to the filter FBG, and Di ishe mode coefficient of the ith vibration mode. Theode coefficient Di includes the effects of material

tiffness, geometry, and the vibration modes of theeam on the resonance frequency and is expressed byi � EA��4�2, where � is a coefficient matrix of theode-shape function of the transversely vibrating

eam. Because E and A are constant for a specificptical fiber, Di is determined by the vibration modef the beam during a measurement and increases athigher vibration mode.Figure 2 shows the variation of resonance fre-

uency fi, calculated by use of Eq. �8�, with respect tohe applied strain for different vibration modes. Forhese calculations, the mechanical properties of a typ-

cal single-mode optical fiber consisting of core, clad,nd coating layers are used as the effective Young’sodulus is 3.55 � 109 Pa, the effective density is 1594

g�m3, the clad diameter is 125 �m, the coating di-meter is 250 �m, and the fiber length is 56 mm.9he calculation results show that the resonance fre-uency increases for increasing strain, and its sensi-ivity with respect to the applied strain improves atigher modes.Note that Eq. �8� is useful only when the fiber is

ibrating at its resonance frequency. For this rea-on, another feedback control loop that enables theber piece embedding the filter FBG to vibrate al-ays at its own resonance frequency is adopted.igure 3 shows the functional diagram of thisesonance-maintaining feedback loop in which ahoto interrupter measures the displacement of theber while the feedback loop controls the PZT to vi-rate a fiber end with the same phase as the fiberisplacement. This scheme maintains a resonantibration of the fiber regardless of the variation in thetrain applied to the fiber.

. Results and Discussion

igure 4 shows the resonance frequency measured byse of the proposed strain-measurement systemhile varying the strain on the sensor FBG up to700 �ε. For these experiments, commerciallyvailable polyimide recoated fiber Bragg gratingsere utilized �Koheras, Birkerød, Denmark; centeravelength, 1555.0 nm at 24 °C, spectral width atWHM, 0.18 nm�. To examine the effects of vibra-ion mode on the resonance frequency, the measure-ents were carried out for two different vibration

ig. 2. Variation of the resonance frequency of a vibrating beamith respect to strain for different modes.

ig. 3. Functional diagram of the resonance-maintaining feed-ack loop.

20 February 2004 � Vol. 43, No. 6 � APPLIED OPTICS 1339

mriomt

tttti

astq

�acco0Tmtifiadcucmdh

ssstttsl0vimsIm1sfqc

tiwftadc

Fa

Ft

1

odes, namely, the first and third modes. The dataepresented by the closed circles were obtained dur-ng increasing the strain while the open circles werebtained during decreasing it. Both the measure-ents and the fitted curve are well matched within

he size of the data point with almost no hysteresis.On the contrary, the driving voltage of the PZT of

he string resonator showed �10% hysteresis be-ween the increasing and the decreasing courses overhe same strain range �Fig. 5�. As explained in Sec-ion 2, this hysteresis is attributed to the character-stics of the piezo material. It is clear from Figs. 4

ig. 4. Measured resonance frequency with respect to the strainpplied to the sensor FBG: �a� first mode, �b� third mode.

ig. 5. PZT driving voltage with respect to the strain applied onhe sensor FBG.

340 APPLIED OPTICS � Vol. 43, No. 6 � 20 February 2004

nd 5 that the accuracy of the matched-filter typetrain-measurement system can be improved withhe proposed method of measuring resonance fre-uency.The measured data in Fig. 4 are fitted by use of Eq.

8� �solid line in Fig. 4�. The mode coefficient �Di�nd the initial strain value �εo� for the closest-fittingurve are listed in Table 1. The curve fitting wasarried out with MATLAB software, and the coefficientsf determination �r2� values were 0.999992 and.999971 for the first and third modes, respectively.he natural frequencies fo,i for the first and thirdodes were measured as 225 and 1380 Hz, respec-

ively. The measured value of Di for the third modes approximately nine times greater than that for therst mode, implying that a higher sensitivity can bechieved for the third-mode operation. Although airect comparison between the measured and the cal-ulated resonance frequencies is difficult owing to thenavailability of material properties of the commer-ial fiber, the variation of resonance frequency in theeasured results is consistent with the calculated

ata in Fig. 2; that is, a higher vibration mode has aigher sensitivity to strain.To examine the sensitivity of the system, we mea-

ured the response of the resonance frequency to amall stepwise variation of strain. The strain on theensor FBG was increased by tiny steps of 1 �ε, andhe increment was done every 1 s. Figure 6 showshat the system can distinguish strain variation onhe sensor with a resolution better than 1 �ε. Thetandard deviations of the data in Fig. 6 were calcu-ated to be 0.28 and 0.33 Hz, which correspond to.254 and 0.095 �ε in strain for the first and the thirdibration modes, respectively. The system sensitiv-ty of the third mode is better than that of the first

ode. However, note that the first mode operationhows better frequency stability than the third mode.n other words, the resonance frequency of the thirdode shows a greater increase or decrease over the

-s period than that of the first mode. This is con-idered to be due to the characteristics of an analogeedback control circuit that shows a higher fre-uency fluctuation as the operation frequency in-reases.

Figure 7 shows the system response to tempera-ure variation on the sensor FBG. The sensor FBGs heated with a thermal pad, and its temperatureas monitored with a thermometer. The resonance

requency was measured for the first mode while theemperature was varied over a range between 25 °Cnd 123 °C. From the curve fitting of the measuredata, the mode coefficient and initial strain are cal-ulated to be D � 107920 �Hz2� and ε � 127 ��ε�,

Table 1. Coefficients of the Fitting Equation, Eq. �8�, Calculatedwith the Measured Data

Mode Di�hz2� εo��ε�

First 10426 1533.7Third 89812 1496.5

i o

rftmsoi

tss

4

Apmhsieotfieotshfetsrds

Et

R1

2

3

4

5

6

7

8

9

Fs

Ftc

espectively. The maximum deviation of the curverom the measured data is �7 Hz, which correspondso a temperature change of 0.7 °C. Because theode coefficient represents the sensitivity of the FBG

ensor to strain and�or temperature, from the valuesf Di for the strain and temperature measurements,t can be said that the FBG sensor is approximately

ig. 6. Resonance frequency response to stepwise increments oftrain on the sensor grating: �a� first mode, �b� third mode.

ig. 7. Measured resonance frequency with respect to tempera-ure variation at the sensor FBG and its deviation from the fitting

en times more sensitive to the temperature mea-ured in degree than the strain measured in micro-train ��ε�.

. Conclusion

matched-filter type strain sensor system that em-loys a string resonator for absolute strain measure-ent is proposed. To avoid the nonlinearity andysteresis of a PZT fiber stretcher, the matchedtrain on the filter FBG is measured through a mon-toring of the resonance frequency of the fiber piecembedding the filter FBG. From the measurementf strain over a range of 0–1700 �ε, it was found thathe system operates with almost no hysteresis at therst and the third vibration modes of the fiber piecembedding the filter FBG. Quasistatic resolutionsf 0.254 and 0.095 �ε were achieved for the first andhe third vibration modes, respectively, as a small-tep response. The measurement system showed aigher sensitivity at the third vibration mode, but therequency stability was better for the first-mode op-ration. The system shows an accuracy of 0.7 °C forhe temperature measurement. The proposedtrain-measurement system may be used to accu-ately measure an absolute strain of a structure orynamic deformation of a system owing to varyingurrounding conditions.

This work was supported by Korea Science andngineering Foundation and partially by the Minis-

ry of Education-Brain Korea 21 Project.

eferences. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo,

C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber gratingsensors,” J. Lightwave Technol. 15, 1442–1463 �1997�.

. A. D. Kersey, T. A. Kerkoff, and W. W. Morey, “Multiplexed fiberBragg grating strain-sensor system with a fiber Fabry–Perotwavelength filter,” Opt. Lett. 18, 1370–1371 �1993�.

. D. A. Jackson, A. B. Lobo Ribeiro, L. Reekie, and J. L. Archam-bault, “Simple multiplexing scheme for a fiber-optic gratingsensor network,” Opt. Lett. 18, 1192–1194 �1993�.

. M. A. Davis and A. D. Kersey, “Matched-filter interrogationtechnique for fibre Bragg grating arrays,” Electron. Lett. 31,822–823 �1995�.

. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolutionfibre-grating based strain sensor with interferometricwavelength-shift detection,” Electron. Lett. 28, 236–238 �1992�.

. G. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, andJ. L. Archambault, “Simultaneous inerrogation of interferomet-ric and Bragg grating sensors,” Opt. Lett. 20, 1340–1342 �1995�.

. B. H. Lee, “Absolute strain measurement using fiber Bragggratings,” Ph.D. dissertation �University of Colorado, Boulder,Colo., 1996�.

. Y. K. Lee, I. C. Song, S. H. Jeong, B. H. Lee, and S. K. Lee,“Absolute strain measurement for fiber Bragg grating sensorusing a string resonator with high accuracy,” in Proceedings ofthe Sixteenth Annual Meeting of the American Society for Pre-cision Engineering �American Society of Precision Engineers,Raleigh, N.C., 2001�, pp. 180–183.

. Y. K. Lee, “Real-time monitoring of the precision machine struc-ture using fiber Bragg grating �FBG� sensors,” M.S. thesis�Kwangju Institute of Science and Technology, Kwangju, Korea,2000�.

urve.

20 February 2004 � Vol. 43, No. 6 � APPLIED OPTICS 1341