development of a parallel demodulation system used for extrinsic fabry-perot interferometer and...

Development of a parallel demodulation systemused for extrinsic Fabry–Perot interferometer andfiber Bragg grating sensors

Junfeng Jiang, Tiegen Liu, Yimo Zhang, Lina Liu, Ying Zha, Fan Zhang,Yunxin Wang, and Pin Long

A parallel demodulation system for extrinsic Fabry–Perot interferometer (EFPI) and fiber Bragggrating (FBG) sensors is presented, which is based on a Michelson interferometer and combines themethods of low-coherence interference and a Fourier-transform spectrum. The parallel demodulationtheory is modeled with Fourier-transform spectrum technology, and a signal separation method withan EFPI and FBG is proposed. The design of an optical path difference scanning and sampling methodwithout a reference light is described. Experiments show that the parallel demodulation system hasgood spectrum demodulation and low-coherence interference demodulation performance. It can real-ize simultaneous strain and temperature measurements while keeping the whole system configura-tion less complex. © 2006 Optical Society of America

OCIS codes: 060.2370, 120.3180, 300.6300, 120.6200.

1. Introduction

In recent years, optical fiber sensors have been thesubject of a good deal of research because they can beeasily embedded into the structure and provide struc-ture health monitoring services. Structure healthmonitoring usually demands two-parameter or mul-tiparameter measurements, such as simultaneousstrain and temperature measurement, which can berealized through the combination of optical fiber sen-sors. The combination makes use of the difference inoptical fiber sensors’ sensitivity to different measur-ands to construct a sensing matrix and then to obtainthe measurands through inverse calculation.1 Amongthem, the combination of extrinsic Fabry–Perot in-terferometer (EFPI) and a fiber Bragg grating (FBG)is one of the most promising sensor groups for theirsuccess in each application. However, in previous re-search, the combination was mainly focused on the

special sensor design, i.e., the research was carriedout from the aspect of sensor fabrication.2,3 The com-plicated fabrication technique has the disadvantagesof poor consistency and high cost. Furthermore, usu-ally two sets of demodulation systems are needed forEFPI and FBG sensors, respectively, making thewhole sensing system complex that in turn discour-ages the application of specially designed sensors.Considering that some companies have begun to pro-vide commercial FBG and EFPI sensors, the combi-nation from the aspect of demodulation is anotherresearch direction deserving more attention.

Since the EFPI sensor encodes measurand infor-mation with cavity length and the FBG sensor en-codes measurand information with wavelength, theproblem of sensor demodulation is transformed toobtain the cavity length of the EFPI and the wave-length of the FBG. There is a good deal of literatureabout EFPI or FBG sensor demodulation. For theFBG, the research includes passive ratio demodula-tion with an edge filter or its variant, a tunable nar-rowband filter, interferometer demodulation,4 etc.The demodulation methods for the EFPI are mainlyclassified into two categories5: low-coherence inter-ference and a method based on the reliability of thespectrum transfer character of a Fabry–Perot cavityon cavity length. However, little research has beendone on parallel demodulation of the EFPI and FBG.

The authors are with the College of Precision Instrument andOpto-Electronics Engineering and the Key Laboratory of Opto-Electronics Information and Technical Science, Tianjin University,Ministry of Education, Tianjin 300072, China. The e-mail addressfor J. Jiang is [email protected].

Received 8 December 2004; revised 31 May 2005; accepted 7June 2005.

0003-6935/06/030528-08$15.00/0© 2006 Optical Society of America

528 APPLIED OPTICS � Vol. 45, No. 3 � 20 January 2006

In Ref. 6 we describe a new parallel demodulationsystem and signal processing method for EFPI andFBG sensors, which combines the methods of low-coherence interference or spectrum demodulation ofthe EFPI and Fourier-transform spectrum demodu-lation of the FBG. In this paper the design of theparallel system will be discussed in detail, and thecorresponding experiments are presented.

2. Parallel Demodulation Method of the ExtrinsicFabry–Perot Interferometer and Fiber Bragg Grating

A. Fourier-Transform Demodulation ofa Fiber Bragg Grating

An optical signal from a FBG array will contain aseries of weak narrowband spectrum components ifthe FBG array consists of FBGs with different Braggwavelengths. The case is similar to the application ofFourier-transform spectroscopy, and it is easy to as-sociate a Fourier-transform spectrum with FBGwavelength demodulation, as was done by Davis andKersey in 1995.7 The Fourier-transform spectrometeris based on a Fourier relationship existing betweenthe light source spectrum S�k� and the ac term of itsinterferogram I��:

I��

�

S�k�cos�2�k��dk, (1)

S�k� ��

�

I��cos�2�k��d�, (2)

where k is the wavenumber of the light source and �is the optical path difference (OPD). If the opticalsignal from the FBG array is regarded as light sourceS�k�, then the wavelength of the FBG can be obtainedwhen the interferogram is acquired.

B. Low-Coherence Interference of the ExtrinsicFabry–Perot Interferometer

If an optical signal from an EFPI is led into a Fourier-transform spectrometer, a low-coherence interfer-ence sensing system is established. This kind ofsystem has been described with a geometric opticalpath match method.5 Here we will describe it withFourier-transform spectrum technology to keep themodeling of the parallel demodulation system consis-tent for both the EFPI and the FBG.

The output of a low-finesse EFPI can be regardedas two-beam interference. The two-beams interfer-ence intensity of a monochrome light source, as afunction of OPD, can be expressed as

I�k, �� I1�k� � I2�k� � 2�I1�k�I2�k�cos�2�k��,(3)

where I1�k� and I2�k� are the intensities of the twobeams. Assuming that the intensities are propor-tional to the power spectrum of the light source S(k),

I1�k� � pS�k�, (4)

I2�k� � qS�k�, (5)

where p and q are proportion coefficients. ThenEq. (3) can be rewritten as

I�k, �� p � q�S�k� � 2�pqS�k�cos�2�k��. (6)

For a given EFPI, the OPD �s is fixed and is equalto two times the cavity length; its output from anideal Fourier-transform spectrometer when a broad-band source is used can be expressed as

I��

�

��p � q�S�k�

� 2�pqS�k�cos�2�k�s��cos�2�k��dk

� �p � q��

�

S�k�cos�2�k��dk

� 2�pq��

�

S�k�cos�2�k�s�cos�2�k��dk.

(7)

The second term can be rewritten as8

2�pq��

�

S�k�cos�2�k�s�cos�2�k��dk

� �pq��

�

S�k�cos�2�k��dk � �� s�

� �� s��, (8)

where � represents the convolution operation and �is the Dirac delta function.

For a broadband source, the ac term I�� in Eq. (1)can be rewritten with a coherent function g��:

I�� 2g��cos�2�k0��, (9)

where k0 is the mean wavenumber of the light sourceand g�� will be nonzero only at a small region near� � 0.

Substituting Eqs. (1), (8), and (9), Eq. (7) can berewritten as

I�� 2�p � q�g��cos�2�k0�� 2�pq�g��cos�2�k0�� s�� s��. (10)

Equation (10) shows that three similar interferencefringe packets will exist in the output of the Fourier-transform spectrometer and center on � � 0, �� s, � � ��s, respectively. The three centers are

20 January 2006 � Vol. 45, No. 3 � APPLIED OPTICS 529

also the peaks of interference fringe packets. Thusthe distance between the peaks gives the informationof an EFPI cavity length.

C. Parallel Demodulation System and Data Processing

The above analysis shows that the Fourier-transformspectrometer can obtain the wavelength of a FBGwhen the Fourier-transform result of the interfero-gram is used and can obtain the cavity length of theEFPI when the interferogram is used directly. So aparallel demodulation system can be establishedwith a Fourier-transform spectrometer as the base,as shown in Fig. 1.

After the interferogram is acquired, three process-ing methods are adopted according to different appli-cation situations. When only the EFPI sensor needsdemodulating, the low-coherence interference can beused to obtain the absolute cavity length directly;when only the FBG sensor needs demodulating, theabove-mentioned Fourier-transform is used; for thecase where both a FBG and a EFPI sensor are used,a special signal process method is proposed here. Aswe know, the signal obtained in the detector is theoverlapping result of the EFPI low-coherence inter-ference fringe and the interferogram of the FBG; butthe phenomenon of the signal from the EFPI is anarrow support function in the spatial domain whilethe signal from the FBG is a narrow support functionin the spectrum domain, as shown in Fig. 2, whichwill help signal separation. The characteristics of anarrow bandwidth of the FBG reflecting spectrummake the interference fringe visible at 1 cm, whilethe interference fringe of the EFPI low-coherence in-terference is visible only at �100 �m; so it is possibleto separate the region in which the interferencefringe relates only to the FBG signal in the spatialdomain. We call this part of interference fringe thelocal interferogram. The Fourier transform of the lo-cal interferogram gives the wavelength of the FBG.The Fourier-transform result of the whole interfero-

gram is the overlapping spectrum of the FBG andEFPI reflecting spectrum. Again, the feature of a nar-row bandwidth of the FBG can be used to separatethe EFPI reflecting spectrum from the FBG reflectingspectrum in the spectrum domain, i.e., the spectrumpart away from the FBG spectrum is used for theEFPI demodulation. With this signal processingmethod, the cavity length of the EFPI and the wave-length of the FBG can be obtained simultaneously.

3. Design of a Parallel Demodulation System

A parallel demodulation system is based on theFourier-transform spectrometer, and the design of itsoptical components can be carried out according tothe design of a conventional Fourier-transform spec-trometer. However, the fact that Fourier-transformspectrum technology and low-coherence interferencehave different requirements on the OPD samplinginterval demands that the interference fringe sampleinterval of a parallel demodulation system be adjust-able. We will now discuss the recording method of theinterference fringe of a parallel demodulation systemin detail to solve the problem.

A. Uniform Time Sampling without Reference Light

In a Fourier-transform spectrometer, any periodicvariations of the real recorded signal, including am-plitude of the light source (intensity caused by align-ment and sampling position), will give rise to a ghostspectrum. Among them, sampling position accuracywill be the main system error source after carefuladjustment. If the system is subject to a periodicsampling position error,

� 0 cos�2�� 0�, (11)

Fig. 1. Parallel demodulation system of an EFPI and FBGsensor.

Fig. 2. Interference fringes in the spatial domain and the corre-sponding spectrum character in the spectrum domain: (a) EFPI,(b) FBG. FFT, fast Fourier transform.


where � is the frequency of the position error, 0 is theamplitude of the position error, and �0 is the randomphase. Then the calculation spectrum of a mono-chrome light with wavenumber k1 is9

S��k� ��0

�M

cos�2�k1��cos�2�k��d�

� �k10�0

�M

sin�2��k1 � ��cos�2�k��d�

� �k10�0

�M

sin�2��k1 � ��cos�2�k��d�.

(12)

Equation (12) means that two ghost spectrum lineswill appear at the position k1 � and k1 � , and itsamplitude is �k1.

To reduce this error, a reference light (a He–Nelaser) is usually used. To sample the interferogram atthe zero crossing of the reference laser fringes is anusual method and can achieve high sampling positionaccuracy, but the free spectral range will be restrictedby the Nyquist limit. If we want to have a widerspectral range, some schemes should be employed tosubdivide the reference laser fringe, but it is easy tointroduce other periodic errors that are caused bynonuniform subdivision into the system at the sametime.10 Sampling in uniform time both in the refer-ence channel and in the target channel and thencorrecting the target channel with the referencechannel in postprocessing is an effective method toovercome the problem encountered by sampling inthe uniform space interval.11,12 However, this methodstill needs a stable reference He–Ne laser and is un-suitable for an optical fiber sensing system.

We want to have an interferogram in a uniformsample time without reference light when the posi-tion stage is well controlled in scanning movement, sothe system can have a suitable resolution for both theEFPI and the FBG at the same time through theadjustment of the sampling interval. This methodwill have periodic sampling position errors as men-tioned above; but considering the fact that the wave-length of the FBG sensor is mainly in the C � L waveband �1525–1610 nm�, the Fourier-transform spec-trometer system with some sampling position errorscan still be used for demodulation of the FBG sensorsif the ghost spectrum fails to appear in the usefulspectrum region.

To avoid overlapping of the true spectrum and theghost spectrum, the frequency � should be largeenough while the restriction on the amplitude of thesampling position error can be loosened to a certainextent according to Eq. (12). The value of frequency �is mainly determined by the stage itself after carefulcalibration of proportional, integral, and differential(PID) control parameters. Through the weight ad-justment of the movable part of the stage, � can be

tuned. The position error is mainly caused by thespeed error since the timer used for the sample timeinterval is accurate enough. If the speed error is pe-riodic, the relationship between � and the frequencyof the speed error f� can be expressed as

f� � 2V, (13)

where V is the nominal speed of the stage. The spec-trum region of concern is the C � L wave band, andits spectral range is 85 nm; thus the ghost spectrumis at least 85 nm away from the true spectrum, i.e.,the position of the right side of the ghost spectrum ofthe spectrum line at 1525 nm should be greater than1610 nm while the position of the left side of the ghostspectrum of the spectrum line at 1610 nm shouldless than 1525 nm, which requires � greater than386.926 cm�1.

B. Practical Realization

The performance of position stages with a stagecontroller has improved greatly and the cost hasdecreased in recent years, making the system pos-sible to realize. Figure 3 is a schematic diagram ofthe measurement and control system. A positionstage produced by Bayside Motion Group is used forthe OPD scanning stage. The stage uses precisioncrossed-roller bearings to provide enough stiffnessand is driven by linear piezomotor, reducing theservo dither. A linear encoder is mounted down thestage center to provide position feedback for themovement control card. The encoder resolution is50 nm and the stroke of the stage is 160 mm. Thestage is controlled by a miniature programmablemultiaxis controller (mini-PMAC) control card, whichcan provide PID control, velocity forward and feed-back control, and acceleration forward and feedbackcontrol. The interference fringe is detected by an In-GaAs detector and acquired with a 16 bit acquisitioncard.

We can use the encoder output to analyze the move-ment of the stage. The encoder outputs a rectangle-wave signal with a spatial period of 0.2 �m, and the

Fig. 3. Schematic diagram of the measure and control systemused in the parallel demodulation system.


frequency will be 8 kHz when the stage speed is at1.6 mm�s under closed-loop control. If a periodicspeed error exists, then the corresponding frequencycomponents will be found. We acquire the rectangle-wave signal of the encoder with 10 �s sample inter-vals to analyze the speed error. According to Eq. (13)and the condition for � to be fulfilled, only low fre-quency is needed to be analyzed because it accountsfor the overlapping between the true spectrum andthe ghost spectrum. Figure 4(a) shows the measuredrectangle-wave signal of the encoder and Fig. 4(b)provides the power spectrum of the speed error. Thefrequency of the speed error is 161.743 Hz and thecorresponding � is 505.45 cm�1, satisfying our needs.

4. Experiments and Results

A. Spectrum Calculation

To verify the system, a set of experiments were car-ried out. The sampling time interval of the paralleldemodulation system is 50 �s; the correspondingOPD sampling interval is 0.16 �m with a stage speed

at 1.6 mm�s. First, a FBG with a central wavelengthof 1566.36 nm and a bandwidth of 0.2 nm is con-

Fig. 4. Movement analysis of the scanning stage: (a) rectangle-wave signal of the encoder, (b) power spectrum of the speed error.

Fig. 5. Spectrum demodulation of a FBG: (a) interferogram ob-tained from the parallel demodulation system, (b) local magnifica-tion of (a), (c) calculation spectrum of the FBG.


nected to the system. Figure 5(a) is an interferogramwith 8192 data points output by the parallel demod-ulation system. Figure 5(b) is the part of Fig. 5(a)showing that the interference fringe approximates asine wave because of the FBG’s narrow bandwidth.Figure 5(c) is the calculation spectrum; it can be seenthat two main ghost spectra appear at 1452.873 and1699.709 nm, respectively. The corresponding wave-numbers are 6882.914 and 5883.36 cm�1, so themean value of � is 499.777 cm�1. According to Eq.(13), the frequency of the speed error is 159.929 Hz,which approximates the value of 161.743 Hz ob-tained at the stage movement analysis. There existsome other minor ghost spectra, which result fromdetector noise, noise in the acquisition card, and soon. Second, an amplified spontaneous emission (ASE)light source with an output power of 10 mW is con-nected to the interferometer system directly to inves-tigate the effect of minor ghost spectra. Figure 6shows the experiment results. Figure 6(a) is the in-terference fringe output from the parallel demodula-tion system. Figure 6(b) is the calculated spectrumfrom the data in Fig. 6(a). The ghost spectra appear atthe two sides of the true spectrum as in Fig. 5(c).Figure 6(c) shows the calculated true spectrum. Fig-ure 6(d) is the spectrum measurement result from anAgilent spectrometer (Model 86142B). From Figs. 6(c)and 6(d), it can be seen that the spectrum measure-ment result with the parallel demodulation systemagrees with the result obtained with the Agilent spec-trometer. The correlation coefficient is 0.9788, whichshows that the parallel demodulation system hasgood spectrum demodulation performance.

The difference between FBG wavelength measure-ment errors by a whole interferogram and a localinterferogram, respectively, is investigated and the

results are shown in Fig. 7. In the experiment, twoFBGs are used; one FBG with a wavelength of1569.062 nm is used for the spectrum line positionreference and the other is used as a FBG sensor.Figure 7(a) is a whole interferogram with 218 data;points. Figure 7(b) is its calculation spectrum with ameasurement error of 17.8 pm. Figure 7(c) is the localinterferogram with 216 data points selected from thewhole interferogram with the center position offset65,000 sample points away from zero OPD its calcu-lation spectrum is shown in Fig. 7(d). Figure 7(e)shows the measurement errors with different posi-tion offsets. It can be seen that measurement errors ofa local interferogram are related to position offsetsand vary from 9.0 to 32.9 pm with a mean value of21.0 pm when the position offset of the local inter-ferogram is less than 75,000 sample points which isclose to the measurement error of 17.8 pm of thewhole interferogram. The measurement error is�70 pm when the position offset of the local inter-ferogram is greater than 75,000 sample points. Thedegradation is caused by a signal-to-noise ratio de-

Fig. 6. Spectrum demodulation of an ASE light source: (a) inter-ferogram obtained from the parallel demodulation system, (b) cal-culation spectrum including ghost spectrum, (c) useful spectrumselected from (b), (d) measurement result with Agilent spectrom-eter.

Fig. 7. Comparison of FBG wavelength measurement errors by awhole interferogram and a local interferogram: (a) whole interfero-gram, (b) calculation spectrum of (a), (c) local interferogram se-lected from (a) with center position offset 65,000 sample pointsaway from zero OPD, (d) calculation spectrum of (c), (e) relation-ship between measurement error and position offset.


crease and coherence length limit of the FBG. Be-cause the cavity length of the EFPI is usually lessthan 500 �m, the distance between the center of theselected local interferogram and zero OPD needs onlyto be larger than 6.4 mm in our experiments, whichcan be fulfilled when the minimum position offset is40,000 sample points. When the maximum positionoffset is set as 75,000 sample points, the FBG wave-length measurement error is �20 pm.

B. Low-Coherence Interference Demodulation

A low-coherence interference demodulation experi-ment was carried out with an ASE light source andan EFPI, which is constructed with two ends of asingle-mode optical fiber. The OPD sampling intervalis 0.16 �m. A Morlet wavelet is used to retrieve theprofile of an interference fringe. Figure 8 shows thelow-coherence interference fringe and retrieved pro-file. The distance between peaks of 0 order and 1order gives a cavity length of 246.08 �m and themeasure error is 0.203 �m.

C. Parallel Demodulation of an Extrinsic Fabry–PerotInterferometer and Fiber Bragg Grating Sensor

In Ref. 6 we showed simultaneous measurement ofEFPI cavity length and FBG wavelength with theparallel demodulation system; here an elementaryexperiment on simultaneous strain and temperaturemeasurement is presented. An EFPI sensor and aFBG sensor are bonded on an equal-intensity canti-lever. The strain of an equal-intensity cantilever isscaled with a resistance strain gauge. Then the can-tilever is placed into a temperature-controllable dry-ing stove, the temperature variance magnitude ofwhich is less than 1 °C around the target tempera-ture. In practical applications, the temperature usu-ally varies slowly, so it is reasonable that theexperiment temperature is set at a certain tempera-ture and stays constant while the strain varies. Toavoid the effect of glue characteristics on our mea-surement, the temperature is set at 40 °C and the

strain varies at a range of 0–768 � when the equal-intensity cantilever is loaded with different weights.The data processing method proposed above is usedto obtain the cavity length of the EFPI and the wave-length of the FBG. The strain and temperature can beobtained through the inverse calculation of a sensingmatrix. Figure 9 shows the measurement result. Thestrain measure error is 24.36 � and the temperaturemeasure error is 1.61 °C.

5. Conclusions

A novel parallel demodulation system used for anEFPI and FBG sensor is presented. On the basis ofthe Michelson interferometer, the parallel demodu-lation system combines the method of a Fourier-transform spectrum and low-coherence interference.Parallel demodulation theory is modeled withFourier-transform spectrum technology. The designof an OPD scanning stage and sampling method isdescribed in detail. Experiments show that the sys-tem has good spectrum demodulation and low-coherence interference demodulation performance.An elementary simultaneous strain and temperaturemeasurement experiment with a strain measure er-ror of 24.36 � and a temperature measure error of

Fig. 8. Low-coherence demodulation experiment with the paralleldemodulation system.

Fig. 9. Experimental result of strain and temperature measure-ment.


1.61 °C further verify effectivity the parallel demod-ulation system. The system can realize multiplexingof EFPIs and FBGs through coherence multiplexingof an EFPI and wavelength division multiplexing of aFBG, respectively. A FBG array with different wave-lengths can be demodulated with a Fourier transformof a local interferogram. After the wavelengths of theFBGs are obtained, the FBG spectrum lines can befiltered with a digital filter function in a spectrumcalculated from the whole interferogram. Then theinverse Fourier transform of the filtered spectrumwill have only a low-coherence interference fringe ofthe EFPIs. If the EFPI array consists of differentcavity lengths, the inverse Fourier transform will re-sult in multiple low-coherence interference packets,which are separated from each other by two times thecavity length difference. Then the cavity lengths areobtained through the distance between those peaks oflow-coherence interference packets and zero OPD.

This work is supported by the National NaturalScience Foundation of China (60077023) and the Nat-ural Science Foundation of Tianjin (013601711).

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development of a parallel demodulation system used for extrinsic fabry-perot interferometer and...

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