digital demodulation system for low-coherence interferometric sensors based on highly birefringent...

Digital demodulation system for low-coherenceinterferometric sensors based on highlybirefringent fibers

Waclaw Urbanczyk, Magdalena S. Nawrocka, and Wojtek J. Bock

A new type of demodulation system for low-coherence interferometric sensors based on highly birefrin-gent fibers is presented. The optical path delay introduced by the sensor is compensated in fourdetection channels by quartz crystalline plates of appropriate thickness. The system can be used todecode a single-point sensor with a resolution of 2.5 � 10�3 or two serially multiplexed sensors withdecreased resolution. In a multiplexed configuration each sensor is served by two detection channels.By tilting the quartz plates, we can tune the initial phase shift between interference signals in successivechannels to differ by ��8 or ��4, respectively, for a single-point or a multiplexed configuration. Wetransferred the sinusoidal intensity changes into digital pulses by appropriate electronic processing,which eventually allows for an unambiguous phase-shift measurement with a resolution of 1�8 or 1�4 ofan interference fringe. The system performance for the measurement of hydrostatic pressure changesand simultaneous changes of hydrostatic pressure and temperature is demonstrated. The pressuresensors are based on side-hole fiber to ensure high sensitivity and an operation range of 2.4 MPa. A newconfiguration for temperature compensation of hydrostatic pressure sensors is proposed, which is bettersuited for dynamic pressure measurements. In this configuration the sensing and compensating fibersare located in the same compartment of the sensor housing. © 2001 Optical Society of America

OCIS codes: 060.2370, 060.4230, 060.2420, 120.3180.

1. Introduction

In recent years many sensing devices based on theprinciple of low-coherence interferometry have beendeveloped.1,2 Such devices are composed of sensingand receiving interferometers arranged in tandem,each having an optical path delay �OPD� greater thanthe coherence length of the source and almost equalto each other. If these conditions are fulfilled, thedifferential interference signal can be observed at theoutput of the receiving interferometer. An attrac-tive feature of the low-coherence methods is that theyallow for measurements of both absolute value andrelative changes of the measurand affecting the sens-ing interferometer. The absolute measurements are

performed by mechanical3 or electronic4,5 scanning ofthe OPD in the receiving interferometer until it is anexact match with that introduced by the sensing in-terferometer. An absolute measurement of the OPDcan also be realized by use of a spectrum analyzerinstead of a receiving interferometer as the decodingdevice. In this case, the absolute value of the OPD isdetermined from the spacing of peaks in the spectrumof light that emerges from the sensing interferome-ter.6,7

The demodulation method that we describe alsouses a low-coherence interferometric principle. Adecoding interferometer is composed of four detectionchannels that contain crystalline quartz plates tocompensate for the OPD introduced by the interro-gated sensor. The fading problem, which is themain difficulty in interferometric measurements, issolved when we tilt the quartz plates, thereby intro-ducing an initial phase shift between interferencesignals and eventually allowing for digital phasemeasurements with a resolution of 1�8 or 1�4 of aninterference fringe, depending on the number of mul-tiplexed sensors. The proposed solution of the fad-ing problem is to some extent similar to that by use oftwo wavelengths to create interference signals

W. Urbanczyk �[email protected]� and M. S.Nawrocka are with the Institute of Physics, Wroclaw University ofTechnology, Wybrzeze Wyspianskiego 27, Wroclaw 50-370, Poland.W. J. Bock is with the Laboratoire d’Optoelectronique, Departe-ment d’Informatique, Universite du Quebec a Hull, P.O. Box 1250,Station B, Hull, Quebec J8X 3X7, Canada.

Received 14 February 2001; revised manuscript received 13 July2001.

0003-6935�01�366618-08$15.00�0© 2001 Optical Society of America

6618 APPLIED OPTICS � Vol. 40, No. 36 � 20 December 2001

shifted in phase by ��2. Although the two-wavelength techniques have been successfully ap-plied in many practical devices,8–13 they have twolimitations. First, the wavelength difference be-tween detection channels must be tuned individuallyto ensure the quadrature condition. Second, adephasing problem arises when the OPD varies sig-nificantly from its initial value because of a change inmeasurand, which ultimately results in the depar-ture of a detection system from a quadrature condi-tion. These main limitations of the two-wavelengthmethod have been overcome to a certain degree byuse of three,14–16 four,17 or even five18 wavelengths tointerrogate the sensing interferometer. The five-wavelength method in particular brings about a sig-nificant reduction in measurement errors that aredue to measurand-induced changes in the OPD andrelaxes the conditions for phase differences betweenindividual interference signals.

In the proposed detection method the dephasingproblem does not appear at all. In contrast to themultiwavelength techniques, the phase differencesbetween detection channels remain the samethroughout the entire measurement range. Al-though the proposed method can be applied to anyfiber-optic sensor based on highly birefringent fibers,its performance was tested in hydrostatic pressureand temperature measurements.

It has already been shown that highly birefringentfibers can be used for the measurement of quasi-static changes of pressure, temperature, orelongation.19–22 However, there is also a need forreliable sensors to measure dynamic pressurechanges with a few kilohertz bandwidth. Such sen-sors could be used in civil engineering to monitorvibrations of bridges, dams, and large buildings withspecially developed hydraulic pads integrated withfiber-optic pressure sensors that serve as load-pressure transducers. This technology has alreadybeen used successfully to monitor quasi-staticloads.23

Highly birefringent fibers are sensitive to pressureand temperature, with the result that fiber-opticpressure sensors based on this type of fiber have to becompensated for temperature. Most often a refer-ence fiber located as close as possible to the sensingfiber is used to ensure temperature compensation.24

However, this method of compensation is not suitablefor sensors that are used to measure fast pressurechanges, which always induce temperature gradientsbetween the sensing and the reference fibers.Therefore we propose a new sensor configurationbased on highly birefringent side-hole fiber, whichprovides better temperature compensation than al-ready known solutions.

We also tested the sensor configuration that allowsfor the simultaneous measurement of pressure andtemperature changes. As sensing elements we usedside-hole and bow-tie fibers spliced together with po-larization axes rotation by an angle of 67.5°, whichensures the highest contrast for the interference pat-terns associated with the bow-tie fiber itself and for

the differential pattern produced by the two fibers.We used the bow-tie fiber as a temperature-sensingelement while information about pressure changewas decoded from the differential pattern producedby the side-hole fiber and the bow-tie fiber. The sen-sor characteristics and responses to simultaneouschanges in pressure and temperature are demon-strated.

2. Principle of Operation

The system shown in Fig. 1 is powered by a superlu-minescent diode from Anritsu, Ltd. and pigtailedwith 3M polarizing fiber. Linearly polarized lightfrom the polarizing fiber is coupled by a polarization-maintaining connector into one mode of the linkingfiber �Corning PMF-38�. The linking fiber and theactive part of the sensor are spliced to each other withpolarization axes rotation of �1 � 45°. Therefore,two polarization modes are excited in the first activeelement of the sensor. Figure 1 shows the construc-tion of the temperature-compensated sensor for themeasurement of pressure changes. The sensor iscomposed of side-hole and elliptical core fibers thatwere spliced with polarization axes rotation of �2 �90°. The differential configuration of the sensor en-sures compensation of the temperature effects. Thecompensating fiber was spliced with a highly birefrin-gent leading-out fiber with polarization axes rotationof �3 � 45°, and the output of the leading-out fiberwas aligned by �4 � 45° with respect to the polariza-tion axes of the quartz delay plates. These rotationsensure the maximum contrast of interference signalsin the detection channels.25–27 The interferencephenomenon can be observed in the detection chan-

Fig. 1. Scheme of the system with four detection channels fordecoding a temperature-compensated pressure sensor: SLD, su-perluminescent diode; PF, polarizing fiber; PMF-38, highly bire-fringent fiber from Corning; S1–4, beam splitters, P1–4, quartzdelay plates; A1–4, analyzers; D1–4, Dref, photodiodes.

20 December 2001 � Vol. 40, No. 36 � APPLIED OPTICS 6619

nel only if the total OPD �RS introduced by the sen-sor is compensated by OPD �RQ introduced by thequartz plates. The detection system is composed offour channels for the registration of interference sig-nals and one channel for the measurement of averageintensity at the sensor output. In the system thatserves only one sensor, all the plates have the samethickness �4 mm�. The plates can be tilted with re-spect to the incident beam to differentiate the initialphase shift of the interference signal in each decodingchannel. The intensity registered in the ith detec-tion channel can be represented by the followingequation:

Ii � I01 � VS��Q��RS � �RQ�sin��S � ��Qi��,

(1)

where I0 is the average intensity monitored by thereference detector, is a contrast function associatedwith the source spectrum, and VS��Q is the contrastat the center of the interference pattern. If the az-imuths of all the system elements are such as thoseshown in Fig. 1, VS��Q would reach a maximum valueequal to 0.5. The phase shifts ��Q

i introduced bythe quartz plates in successive channels differ by ��4,which corresponds to 1�8 of an interference fringe.At the same time, the contrast of all the interferencesignals remains practically the same because is aslowly changing function of OPD imbalance ��RS ��RQ� compared with the fast intensity variations as-sociated with interference fringes. Sinusoidal inten-sity changes registered in the detection channels areconverted into digital signals in such a way that ahigh level is generated when interference signal Ii isgreater than the average intensity I0 and a low levelis generated for Ii I0. This version of the detectionsystem allows for the measurement of fast phasechanges that occur in a sensing interferometer with aresolution of 1�8 of an interference fringe and for easyrecognition of the direction of phase changes �see Fig.2�. The counting speed is approximately 10 kHz andis limited by the computer board for data acquisitionand the p-i-n photodiodes.

We experimentally determined that for proper op-eration of the electronic unit that forms digitalpulses, the amplitude of the interference signal can-

not be lower than 10% of the average intensity.Therefore, to achieve the highest possible operationrange, the initial OPD of sensor �RS

0 �at atmosphericpressure� should satisfy the condition VS��Q��RS

0 � �RQ� � 0.1. When the sensor OPDchanges with applied pressure, the contrast of theinterference signal first increases to a maximumvalue equal to VS��Q and then starts to decay until itreaches the critical value on the other side of thepattern envelope, i.e., VS��Q ��RS

0 � �RSPmax �

�RQ� � 0.1, where �RSPmax constitutes the system

operation range. For the experiments described inthis paper we used a superluminescent diode fromAnritsu, Ltd. with �0 � 849 nm and �� 17 nm, forwhich we achieved an operation range of �RS

Pmax �52�0 �approximately 420 counts�, which was deter-mined primarily by the spectral width of the lightsource and by the value of the VS��Q contrast at thepattern center. Parameter VS��Q depends on preci-sion of angular alignment of successive sensor ele-ments ��5°� �Ref. 25� and on phase retardationuniformity introduced by the quartz plates over thewave-front cross section. To focus all the energythat comes from the sensor output on the p-i-n pho-todiodes, we used a convergent beam with an aper-ture angle of approximately 2°. Because of thevariations in crystal birefringence, in effective thick-ness with incident angle and the changes in orienta-tion of the plane of incidence with respect to thecrystal optical axis, the phase retardation for bound-ary rays differs from that for the central ray by �4°for a 4-mm thick quartz plate. As the photodiodesaverage intensity over the entire active area, such aretardation nonuniformity decreases the contrast VS��Q. By application of straightforward intensity av-eraging it can be shown that the drop in contrast isonly 2% in this case.

Another possible cause of contrast degradation canbe nonuniformity of the quartz plate thickness overthe wave-front cross section. The diameter of thebeam that passes through the plate is 3 mm. Weassume 0.4° as an acceptable variation of phase re-tardation across the beam caused by the change inplate thickness, which is ten times lower than thatcaused by beam convergence. This value allows usto estimate the tolerance for plate parallelism at �6arc sec, which is a modest requirement.

Technologically, we can control the length of thesensor elements to a precision of �2 mm, which cor-responds to ��0 in terms of retardation. There is noneed to control the retardation introduced by the de-coding plates to a much higher accuracy. For quartzplates, the thickness variation equivalent to retarda-tion ��0 equals �0.01 mm at �0 � 849 nm, which canbe used to determine the plate thickness tolerance indifferent detection channels.

3. Hydrostatic Pressure Measurements

The construction of the temperature-compensatedsensor for hydrostatic pressure measurements isshown in Fig. 1. The sensing element is composed ofside-hole fiber and elliptical-core fiber spliced with

Fig. 2. Response of digital outputs of a four-channel detectionunit to increasing and decreasing pressure.


polarization axes rotation of 90°. A high sensitivityto pressure KSH

P � �123.5 rad�MPa m and a lowsensitivity to temperature KSH

T � �0.78 rad�K mare characteristics of side-hole fiber.28 The sensitiv-ity of the elliptical-core fiber to pressure and temper-ature equals, respectively, KEC

P � 0.90 rad�MPa mand KEC

T � �0.87 rad�K m. The phase shift in-duced simultaneously by temperature and pressureon the two sensing elements is given by

��T, p� � ST�T � SP�p, (2)

where ST and SP are overall sensitivities to temper-ature and pressure as represented by the followingexpressions:

ST � KSHTLSH � KEC

TLEC, (3)

SP � KSHPLSH � KEC

PLEC. (4)

In Eqs. �3� and �4�, LEC and LSH are the lengths of theelliptical-core and side-hole fibers, respectively. Toensure the total temperature compensation of thesensors, the lengths of the side-hole and elliptical-core fibers must be inversely proportional to theirsensitivity to temperature:

KECT

KSHT �

LSH

LEC. (5)

One should note that, although the temperature-induced phase shifts in the two fibers are compen-sated, the pressure-induced phase changes add toeach other, because of opposite signs of pressure sen-sitivity in side-hole and elliptical-core fibers. Thisspecific feature of the side-hole fiber makes it possibleto locate the sensing and compensating fibers in thesame place on the sensor housing. Such sensor con-struction is better suited for compensation of temper-ature effects associated with fast compression anddecompression processes than for standard compen-sation configuration, in which pressure affects onlyon the sensing elements.24 Fast pressure changesalways cause temperature changes and thereforetemperature differences between sensing and com-pensating elements, if they are located in differentplaces.

Pressure that affects a sensor decreases its totalgroup delay. According to the operating principle ofour detection method, the total OPD introduced bythe sensor must satisfy the following condition toensure the maximum operation range:

�NSHLSH � �NECLEC � �NQ dQ1 � 0.5�RSmax

P, (6)

where �NEC � 3.70 � 10�4, �NSH � 3.84 � 10�4, and�NQ � 8.86 � 10�3 represent the group birefringenceof the elliptical-core fiber, the side-hole fiber, and thequartz plate, respectively, and dQ1 represents theplate thickness. For hydrostatic pressure measure-ments we used plates with a thickness of dQ1 � 4 mm,which introduced a group delay of approximately42�0.

Solving Eqs. �5� and �6�, we determined the lengths

of elliptical-core and side-hole fibers to be LEC �0.895 m and LSH � 0.998 m. The residual sensitiv-ity of the sensor to temperature ST is limited by theprecision of Eq. �5�. In practice, lengths LEC and LSHcan be controlled to within a tolerance of 2 mm.Substituting this value into Eq. �3� we obtained thetechnological limit for temperature sensitivity ST 2.4 � 10�3 rad�K. Such a small residual tempera-ture drift would generate a phase response equiva-lent to the system resolution equal to 0.785 rad �1�8of an interference fringe� for temperature changes ofapproximately 300 °C, a temperature range that ismuch higher than what is necessary for most techni-cal applications.

The sensing and compensating fibers were woundonto a 7-cm-diameter coil and placed in a steel hous-ing. Such a configuration diminishes the sensor sizeand makes it more suited for practical applications.Furthermore, as the sensing and compensating fibersfrom several loops inside the housing, the sensor be-comes much more resistant to temperature gradientsin comparison with sensing and compensating fibersthat are straight.

We investigated sensor performance by conductingseveral temperature and pressure tests. We testedthe sensor temperature stability at different pres-sures by using a Haake C temperature stabilizer witha precision of 0.1 °C. The sensor did not react totemperature changes from 10 °C to 50 °C at zeropressure even during fast heating, which introduceda temperature gradient of a few degrees across thesensor housing, which is certainly not the maximumtemperature gradient that can be accommodated bythe sensor. We did not complete the investigation ofthis problem because it is difficult to control the tem-perature distribution across the housing.

At a pressure of p � 2.4 MPa, the response totemperature was equal to one count, see Fig. 3. Thiseffect was most probably associated with a differencein second-order sensitivities �dependence of temper-ature sensitivity on pressure�29,30 in the side-hole andelliptical-core fibers. Therefore, the difference insecond-order effects constitutes a real physical limi-tation of the effectiveness of temperature compensa-tion in such sensors.

We calibrated the system for quasi-static pressurechanges by using a Harwood DWT-35 pressure gen-

Fig. 3. Sensor response to temperature at an applied pressure of2.4 MPa.


erator with a precision of 0.1% as a reference. Thecalibration results are shown in Fig. 4, where thenumber of counts registered by a computer �one countcorresponding to 1�8 of an interference fringe� areplotted versus applied pressure in the 0–2.4-MParange in 0.3-MPa steps. The calibration procedureallowed us to determine the sensor’s sensitivity topressure, which is equal to 151.3 counts�MPa �118.8rad�MPa� and is linear over the entire pressure rangethat we tested.

Figure 5 shows the response of the sensor to dy-

namic pressure changes generated in an oil chamber.The enlarged sections illustrate the time and pres-sure resolution. One count is equivalent to the min-imum detectable pressure change equal to 6.6 kPa.

4. Simultaneous Pressure and TemperatureMeasurements by use of Serially Multiplexed Sensors

The construction of a sensor for simultaneous mea-surement of pressure and temperature changes isshown in Fig. 6. The active part of the sensor iscomposed of bow-tie fiber �LBT � 0.265 m� and side-hole fiber �LSH � 0.575 m� spliced with polarizationaxes rotation of �2 � 67.5°. In the leading-in fiberonly one linearly polarized mode is excited. Thisfiber is spliced with the first active element of thesensor with polarization axes rotation of �1 � 45°,which ensures equal excitation of both polarizationmodes in the first active element of the sensor. Theleading-out fiber is spliced to the side-hole fiber withpolarization axes rotation of �3 � 22.5°. The phasechanges induced by pressure and temperature areretrieved from two interference patterns. The firstis a differential pattern produced by the side-hole andbow-tie fibers whereas the other is produced by thebow-tie fiber itself. Angular alignment of the sensorelements ensures the highest possible theoretical vis-ibility for the two interference patterns VBT��Q �0.25 and VSH�BT��Q � 0.3, respectively.26,27

The interference signals associated with the differ-ential pattern are registered in the first two detectionchannels in which we placed two retardation plateswith a thickness of dQ1 � 4 mm. By tilting thequartz plates we shifted these two signals in phase by��2, which ensures unambiguous fringe countingwith a resolution of 1�4 of an interference fringe.

The second interference pattern associated withthe bow-tie fiber is monitored in the third and fourthdetection channels. To balance the group delay in-troduced by the bow-tie fiber we placed compensatingplates with a thickness of dQ2 � 20 mm into thesechannels and again tilted the plates to introduce aphase shift of ��2.

High pressure sensitivity of the side-hole fibercauses the differential interference pattern to bemuch more sensitive to pressure than to tempera-ture. At the same time, the pattern produced by thebow-tie fiber itself is almost equally sensitive to tem-perature and pressure. We could easily retrieve in-formation about the changes in pressure �p andtemperature �T by solving a set of linear equations,if phase shifts ��BT �p, T� and ��SH�BT �p, T� are

Fig. 4. Calibration of the sensor for a quasi-static step-typechange of pressure in the range from 0 to 2.4 MPa in steps of 0.3MPa.

Fig. 5. Response of the sensor to dynamic pressure changes. En-larged sections illustrate the time and pressure resolutions of thesensor.

Fig. 6. Construction of a serially multiplexed sensor for simulta-neous measurements of pressure and temperature.


measured simultaneously and sensitivity coefficientsto pressure and temperature are known in advance.In respective interference patterns, these coefficientsare given by the following relations:

SBTP � KBT

PLBT, (7)

SBTT � KBT

TLBT, (8)

SSH�BTP � KSH

PLSH � KBTPLBT, (9)

SSH�BTT � KSH

TLSH � KBTTLBT. (10)

To determine the sensitivity coefficients we cali-brated the system for quasi-static pressure and tem-perature; see Fig. 7, which shows the number ofcounts registered by the computer versus appliedpressure and temperature. The response of the sen-sor to pressure and temperature is linear in bothdetected patterns. By fitting measurement data, wefound the coefficients SBT

P, SBTT, SSH�BT

P, andSSH�BT

T. In the differential pattern the sensitivi-ties are equal to SSH�BT

P � 48.18 counts�MPa �75.64rad�MPa� and SSH�BT

T � �0.568 counts�K ��0.892rad�K�, respectively. For the pattern produced bythe bow-tie fiber the sensitivities are equal to SBT

P ��1.329 counts�MPa ��2.087 rad�MPa� and SBT

T �0.817 counts�K �1.283 rad�K�.

Figure 8�a� shows the response of the sensor tosimultaneous step-type changes of pressure and tem-perature. Knowing the sensitivity coefficients, wecould solve the set of linear equations and determinesimultaneous changes of the two parameters Figs.

8�b� and 8�c��. The maximum difference between re-constructed and actual values of applied pressureand temperature is equal to 0.02 MPa and 1 °C, re-spectively, which in both cases corresponds to 1% of asensor’s full scale.

5. Summary

We have presented a flexible detection system basedon a fringe-counting method for decoding low-coherence interferometric sensors. The perfor-mance of the system was tested by measurements ofhydrostatic pressure changes with a singletemperature-compensated sensor and also by simul-taneous measurements of pressure and temperaturechanges with two serially multiplexed sensors. Inboth cases the side-hole fiber was used as one of thesensing elements. The unique features of this fiber,such as high sensitivity to pressure and the negativesign of the sensitivity, played an essential role insystem performance.

For a temperature-compensated sensor, the nega-tive sign of pressure sensitivity in the side-hole fibermade it possible to locate the sensing and compen-sating fibers in the same compartment of the sensorhead. This prevented temperature gradients be-

Fig. 7. Calibration of the multiplexed sensor to pressure andtemperature. The phase increases in the differential pattern�SH-BT� and the pattern associated with the bow-tie fiber �BT� arelinear versus �a� pressure and �b� temperature.

Fig. 8. Response of the multiplexed sensor to simultaneous step-type changes in �a� pressure and temperature in steps of 0.6 MPaand 15 °C, respectively, �b� reconstructed pressure values, �c� tem-perature.


tween the two elements and made the sensor almostinsensitive to temperature changes. The residualtemperature drift of the order of 0.2% of sensor’s fullscale for temperature change at 40 °C is most prob-ably associated with the second-order effects. Suchsensor construction is especially suitable for dynamicmeasurement, in which the fast compression or de-compression always induces temperature changesand could generate false readings if the sensing andcompensating elements were located at differentplaces in the sensor head. Optimization of the ini-tial OPD introduced by the sensor ensured a resolu-tion equal to 2.5 � 10�3, which is limited by thespectral linewidth of the source and precision of theangular alignment of the respective sensor elements.One count of the four-channel decoding unit corre-sponds to a ��4 rad phase increase. The operationrange of the tested sensor was equal to 2.4 MPa,which could easily be modified if one were to changethe lengths LSH and LEC of the two sensing elementsand also the thickness of the compensating quartzplate dQ1.

The feasibility of a decoding system for simulta-neous pressure and temperature measurements hasalso been demonstrated. However, for this mode ofoperation, the resolution of the system is significantlylower. One of the reasons is that only two detectionchannels are used to decode the phase changes asso-ciated with the interference pattern in question.For this configuration one count corresponds to ��2rad. Furthermore, for multiplexed systems, the the-oretical maximum contrast in both interference pat-terns is approximately 0.3 whereas for the single-sensor configuration it equals 0.5. Finally, formultiplexed systems the operation range associatedwith each interference pattern is used to registerpressure and temperature changes whereas forsingle-sensor systems it is assigned only to pressurechanges. The effect of these factors is to reduce theresolution of the two parameters in simultaneousmeasurements to the level of 10�2, which correspondsto 0.02 MPa and 1 °C, respectively, for temperatureand pressure readings.

This research was supported by the Polish Com-mittee for Scientific Research under grant 8T10C 02018 and by the Natural Sciences and Engineering Re-search Council of Canada.

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digital demodulation system for low-coherence interferometric sensors based on highly birefringent...

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