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Enhancement of Dynamic Range of Optical Fiber Sensor Using Fiber Bragg Grating Fabry–Pe´rot Interferometer With Pulse-Position Modulation Scheme: Compensation of Source Wavelength-Sweep Nonlinearity Volume 5, Number 4, August 2013 Atsushi Wada Satoshi Tanaka, Member, IEEE Nobuaki Takahashi, Member, IEEE

DOI: 10.1109/JPHOT.2013.2276971 1943-0655 Ó 2013 IEEE

IEEE Photonics Journal

Enhancement Of Dynamic Range For FBG-FPI Sensor

Enhancement of Dynamic Range of Optical Fiber Sensor Using Fiber Bragg Grating Fabry–Pe´rot Interferometer With Pulse-Position Modulation Scheme: Compensation of Source Wavelength-Sweep Nonlinearity Atsushi Wada, Satoshi Tanaka, Member, IEEE, and Nobuaki Takahashi, Member, IEEE Department of Communications Engineering, National Defense Academy of Japan, Yokosuka 239-8686, Japan DOI: 10.1109/JPHOT.2013.2276971 1943-0655 Ó 2013 IEEE

Manuscript received July 2, 2013; revised August 1, 2013; accepted August 1, 2013. Date of publication August 7, 2013; date of current version August 27, 2013. This work was supported by KAKENHI-JSPS 23760379. Corresponding author: A. Wada (e-mail: [email protected]).

Abstract: A fiber optic vibration sensor using a fiber Bragg grating Fabry–Pe´rot interferometer with a wavelength-swept laser diode source, which works well for the case of small strain-amplitude vibration, exhibits inaccuracies in the interrogation caused by the nonlinearity of the wavelength modulation in the source when the strain amplitude due to vibration is large. With increasing the frequency of the wavelength sweep, the span of the wavelength sweep is reduced and the nonlinearity is pronounced. We experimentally characterize the nonlinearity, and by using a fiber Fabry–Pe´rot interferometer as a wavelength reference, we compensate it to enhance the accuracy of the interrogation for large strainamplitude vibration. p The ffiffiffiffiffiffi proposed sensor achieves vibration measurement with a strain resolution of 0.3 n= Hz, measurement time of 10 s, and maximum measurable value of 34 at the wavelength-sweep frequency of 100 kHz under the present condition. The measurement time is limited by the capability of the laser diode driver, and the maximum measurable strain would be easily enhanced by increasing the wavelength-modulation current amplitude. Index Terms: Fiber Bragg grating, optical fiber sensor, strain sensor, Fabry–Pe´rot interferometer.

1. Introduction Recently fiber Bragg grating (FBG) sensors have been intensively developed and widely used for various applications [1]–[5]. The reflection spectrum of an FBG experiences a wavelength shift as a result of physical influence such as temperature change and applied strain. The wavelength shift can accordingly be used to measure temperature, strain, acoustic pressure, and vibration of solid. In comparison to electrical sensors, an FBG sensor has the following advantages: It is light and compact. It can be then placed in a small space. Furthermore, an optical wave in a fiber is not subject to electromagnetic interference. Using a Fabry–Pe´rot interferometer with FBGs as reflectors (FBG-FPI) instead of using a FBG itself as a sensor, it has been shown that the sensor resolution can be improved [6]–[10]. This is

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because a steeper slope in the reflection spectrum peaks results in higher-resolution in determining the wavelength shift. There are various ways to measure the wavelength shift in the light reflected from an FBG-FPI under influence of dynamic strain caused by mechanical vibration of solid, which is of our primary interest: First, locking a laser oscillation wavelength to an FBG-FPI transfers the wavelength shift of the FBG-FPI to the laser wavelength-shift [6], [9]. The FBG-FPI wavelength-shift is then interrogated from the error signal of the active feedback loop for the laser lock. In this method, the dynamic range is determined by the linewidths of a FBG-FPI and wavelength reference pffiffiffiffiffiffi device. J. H. Chow et al. achieved vibration sensing at 216 Hz with the resolution of 360 f= Hz using the laser locking method [6], where is dimensionless unit of strain applied to a fiber. Since they used a FBG-FPI with the linewidth of 0.8 pm and a wavelength reference with the linewidth of 0.3 pm, the measurement range of their sensor is estimated to 0.4 . In the intensity modulation method, second, a narrowband light source is used and its wavelength is tuned to the wavelength of a sloped region of the reflection spectrum of the FBG-FPI [7]. In this scheme, the wavelength shift gives rise to an intensity change in the reflected light. This scheme has a simple setup and short measurement time. The measurement speed is higher than 10 kHz [7]. However, the measurement range is limited to a few because of the narrow spectral range in which a linear approximation is valid [7]. In the third method, a transmittance peak is converted into an optical pulse by sweeping a laser source wavelength, i.e., the FBG-FPI wavelength modulation is transformed into the pulseposition modulation [8], [10]. The wavelength shift and therefore the applied physical influence can be obtained by demodulation of a shift in the temporal position of the pulse. Since the measurement range in this method is larger than those in the first two methods described above and is only limited by the wavelength sweep range, we adopt the third method. In the pulse-position modulation (PPM) method, dynamic-strain measurement requires fast and precise sweep of the laser wavelength. The measurement time is limited by the sweep period. The resolution of the measurement depends on the linewidth of the sensing FBG-FPI transmittance peaks and the precision of the laser wavelength modulation. Lasing wavelength of a laser diode can be modulated by changing its injection current. The injection current can be precisely modulated at high frequency up to 1 MHz using a laser-diode controller and fast wavelength sweep can be then easily achieved with a laser diode. However, the wavelength of a laser diode changes nonlinearly when the injection current is swept at a frequency higher than 1 kHz as shown later. If one is interested in a limited range of dynamic strain, say smaller than a few , which causes a few pm of the wavelength shift, the nonlinearity is not significant and may be neglected even for sweep frequency as high as 10 kHz [10]. If one wants to measure fast and large dynamic strain, say faster a 10 kHz and larger than 10 , which causes the wavelength shift larger than 10 pm, however, one has to face the nonlinearity of the wavelength modulation of the laser source and solve the problem associated with it. In this paper, we first characterize the nonlinear wavelength modulation of a distributed feedback laser diode (DFB-LD) used as an optical source quantitatively based on the experiment, in which the instantaneous laser wavelength is estimated by using a fiber Fabry–Pe´rot interferometer as a wavelength reference. Next we propose a compensation method to correct the distorted sensor output resulted from the nonlinearity. Finally, we perform the experiment and demonstrate the validity of the method.

2. Sensing Principle Two FBGs having identical reflection spectra placed with some separation in a fiber form a Fabry– Pe´rot interferometer [11], [12]. The resonance effect of the Fabry–Pe´rot interferometer produces sharp transmittance peaks in the reflection band of the FBGs. Fig. 1(a) shows the reflection spectrum of the fabricated FBG-FPI. The fabrication was performed by exposing a single-mode fiber to ultraviolet light fringe while blocking the light in the central potion of 4 mm length out of the total length of 20 mm. In Fig. 1(a), three dips corresponding to the FPI resonance peaks are seen in the range from 1549.8 to 1550.0 nm, whose wavelength bandwidths are much narrower


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Fig. 1. (a) Reflectance spectrum of FBG-FPI and (b) schematic diagram of PPM method. LS is a light source, PD is a photodetector, and OC is an optical circulator.

Fig. 2. Experimental setup for characterization of wavelength modulation. PD1 is a photodetector for laser intensity monitoring, FFPI is a fiber Fabry–Pe´rot interferometer, and PD2 is a photodetector for measuring transmitted light waveform through FFPI.

than that of the FBG. The static strain response of the FBG-FPI resonant peak is measured to be 1.17 pm=. Fig. 1(b) shows a schematic diagram of PPM method. The source wavelength is periodically swept over the range which includes a transmittance peak wavelength of the FBG-FPI. Light from the laser source enters the FBG-FPI through an optical circulator. Light reflected from the FBG-FPI passes through the optical circulator again and reaches a photodetector. If the wavelength increases from min to max in the period T , a dark optical pulse is produced in the reflected light when the laser wavelength matches with the transmittance peak (reflectance dent) wavelength of the FBG-FPI. The occurrence time of the pulse is modulated if the FBG-FPI is under influence of strain due to mechanical vibration. Therefore, the vibration strain applied to the FBG-FPI can be retrieved from temporal shifts of the pulses if one knows how the laser source wavelength varies with time within the period. The measurement range and speed of the sensing are limited by max min and the period T , respectively.

3. Wavelength-Modulation Characteristics In this section, we analyze experimentally the wavelength-modulation characteristics of the DFB-LD used for the sensor. As seen from the previous section, the precise knowledge of the source wavelength variation with time is important for knowing the wavelength shift, i.e., for the demodulation in the sensor system, when the laser source wavelength is modulated with a sawtooth wave as a modulation signal. The instantaneous wavelength is estimated using an external fiber Fabry– Pe´rot interferometer as a wavelength reference. Fig. 2 shows the experimental setup used for the characterization. The laser source is a DFB-LD (FITEL FRL15DCWD-A81-19340) and its wavelength is modulated through the injection current modulation. A laser diode driver (ILX Lightwave LDX-3220) drives the DFB-LD and allows an external voltage to be superimposed on the injection current with transfer rate of 50 mA/V. Without


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Fig. 3. Current modulation signal and photodetector outputs at 1 kHz. (a) Signal for current modulation and output of PD1. (b) Output of PD2.



the modulation, the injection current is set to 200.0 mA and the output wavelength is 1549.9 nm. Light from the DFB-LD is divided into two by an optical coupler. One beam is detected by a photodetector (New Focus MODEL 2053) in order to monitor the laser intensity. Another beam enters a reference Fabry–Pe´rot interferometer. The reference interferometer is a fiber Fabry–Pe´rot interferometer (FFPI; Micron optics FFP-I-1550-100M0010-3.5dB-065) and consists of a Fabry– Pe´rot interferometer with a single-mode fiber between two multilayer mirrors. The free spectral range (FSR) of the FFPI is 1 GHz, which corresponds to 8.04 pm of a light wavelength at 1549.9 nm, and the finesse is 11. The beam passed through the FFPI is detected by a photodetector (New Focus MODEL 1811). Figs. 3–5 show the modulation signal and the photodetector outputs when the injection current is swept by applying to the driver the sawtooth voltage signal having an amplitude of 250 mV and a frequency of 1, 10, and 100 kHz, respectively. It is seen from the output waveform of PD1 in Figs. 3–5 that as the driver input voltage increases, the laser intensity lineally increases with time except for small distortion in the beginning of the period at 100 kHz. It may be then deduced that the injection current follows basically the sawtooth signal, i.e., the modulation signal voltage applied to the laser driver. When the sweep frequency


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Fig. 6. Wavelength variation in sawtooth-wave current modulation. (a) 1 kHz. (b) 10 kHz. (c) 100 kHz.

Fig. 7. Experimental setup for FBG-FPI sensor. OC is an optical circulator, PD1 is a photodetector for reflected light from sensor FBG-FPI, FG1 is a function generator used for current modulation, FFPI is a fiber Fabry–Pe´rot interferometer for wavelength reference, PD2 is a photodetector for transmitted light through reference FFPI, and FG2 is a function generator for PZT driving.

becomes as high as 100 kHz, however, the laser output shows time delay as well as the small distortion in the waveform. These results are considered to be caused by the finite bandwidth of the laser driver signal transfer, which is 1 MHz in the present case. Unlike the variation in the laser output intensity for the sawtooth wave modulation of the LD current, the laser wavelength variation exhibits a complicated behavior that seems not to be in proportion to the LD current. If the wavelength variation would follow the modulation current like the intensity, we should have equally-spaced optical pulses after passing through the FFPI. However, the waveform has the peculiar region of dense peaks, where the modulated wavelength is decreasing and the longer interval, where the wavelength of the laser output is considered to be minimum in the period of the modulation and begin to increase again. In addition, the interval of the peaks after the longer interval is decreased as the time approaches the end of the period. Since it is not easy to use the peaks in the peculiar region as a wavelength reference to obtain correct data of the wavelength shift, we adopt the peaks after the longer interval as the reference. From the occurrence time of the peaks, we have obtained the wavelength-current characteristics of the DFB-LD for various sweep frequencies. Fig. 6(a)–(c) show the wavelength variations obtained from the trains of optical pluses shown in Figs. 3–5. It is seen from Fig. 6 that the wavelength sweep width decreases as the sweep frequency increases. It is also seen that the relationship between the wavelength variation and time is not linear and the wavelength changes more as the time approaches the end of the period. If one wants to calibrate the wavelength data even only with the optical pluses after the longer interval, therefore, one cannot assume the linearity between the wavelength variation and time and has to take the nonlinearity into account.

4. FBG-FPI Sensor With External Wavelength Reference Fig. 7 shows experimental setup for the present sensor. The source is the DFB-LD. The FFPI is used as a wavelength reference. A beam from the DFB-LD is divided into two by an optical coupler.


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Fig. 8. Outputs of the photodetectors for (a) reflected light from the sensor FBG-FPI and (b) transmitted light through the reference FFPI.

One beam is passed through an optical circulator and enters an FBG-FPI which is used as a sensor head. Light reflected from the FBG-FPI is detected by a photodetector (New Focus MODEL 2053). Another beam reaches a photodetector (New Focus MODEL 1811) after passing through the FFPI used as a wavelength reference. The wavelength of the DFB-LD is swept through injection current modulation using a sawtooth wave with an amplitude of 250 mV and a frequency of 100 kHz. Fig. 8(a) shows the output of the photodetector used for the reflected light from the FBG-FPI. In Fig. 8(a), a dip can be shown at 7 s, which corresponds to a transmittance peak of the FBG-FPI. Since the wavelength sweep of DFB-LD is not proportional to time, as described in the previous section, the peak wavelength is estimated from its appearance time td with nonlinearity compensation using the transmitted light waveform through the reference FFPI. Fig. 8(b) shows the output of the photodetector receiving the FFPI transmitted light. Several peaks are shown in Fig. 8(b), corresponding to transmittance peaks of the reference FFPI. As discussed in the previous section, the peculiar region, i.e., the beginning part of the sweep period that is full of dense pulses, is a region of high nonlinearity and cannot be easily used for the wavelength compensation. We adopt then as a wavelength reference the peaks appearing after the longer interval, i.e., in the time range from 3 to 10 s in the case of Fig. 8(b). The compensation method for the wavelength modulation nonlinearity is as follows. Let the wavelengths and the appearance time of the nth peak in each period to be n and tn , respectively, where n is an integer. An integer m is chosen so that the time tm is to be closest to the time td , i.e., so that the relations jtm td j jtmþ1 td j;

jtm td j jtm1 td j

(1)

are to be fulfilled. Using the quadratic interpolation, the peak wavelength p is estimated by p ¼ m þ FSR

ðt1 þ t2 Þtd2 ðt1 2 þ t2 2 Þtd t1 t2 ðt2 t1 Þ

(2)

where FSR is the FSR of the reference FFPI and t1 , t2 , and td are defined as t1 ¼ tm1 tm , t2 ¼ tmþ1 tm , and td ¼ td tm , respectively. The appearance times td , tm1 , tm , and tmþ1 are estimated using the quadratic curve fitting method given in Ref. [13]. This method uses a least squares method to fit a quadratic to several P data points near a peak. Approximating the peak by a second order polynomial ð ck tjk Þ, the error j in the jth point satisfies P 2 @ ð Þ j j ¼0 for k ¼ 0; 1; 2 (3) @ck P where j ¼ Ij ck tjk and Ij represent the sampled intensity. The appearance time is estimated from the peak position of the fitted polynomial. The measurement range of the sensor is determined by a difference between the maximum and minimum and of n . In this experiment, the difference is equal to 6 1 ¼ 5FSR ¼ 5 8:04 pm ¼ 40:20 pm, which corresponds to the measurement range of 34 . The range can be easily extended by increasing the amplitude of the wavelength sweep.


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Fig. 9. Input signal and sensor output. (a) PZT driving voltage and (b) demodulated wavelength-shift when a sinusoidal signal of 1 kHz and 5 V is applied to the PZT.

Fig. 10. Evaluation for linearity of sensor responce. (a) Fourier spectrum of demodulated wavelengthshift signal when a sinusoidal signal of 1 kHz and 5 V is applied to the PZT. (b) Amplitude of demodulated wavelength-shift v.s. amplitude of applied strain when the PZT is driven with a frequency of 1 kHz or 10 kHz .

For a demonstration of dynamic-strain measurement, a multi-layer piezoelectric transducer (PZT; NEC TOKIN AE0203D44H40) is used to apply dynamic strain to the FBG-FPI. Wavelength modulation of the DFB-LD is achieved in the same manner as described above. A sinusoidal signal is applied to the PZT which is glued on the whole of the FBG-FPI. An amplitude of the PZT driving signal is varied from 10 mV to 10 V for the frequency 1 and 10 kHz. The displacement of the PZT is measured with the laser Doppler vibrometer (GRAPHTECH AT3700) with accuracy of 5% and the dynamic strain applied to the fiber is calculated. The response of the dynamic strain induced by the PZT is 1.05 =V at 1 kHz and 0.466 =V at 10 kHz. Fig. 9 shows a PZT driving signal and the wavelength-shift demodulated from a train of dark optical pulses, using the compensation method described above. A frequency and amplitude of the signal applied to the PZT are 1 kHz and 5 V, respectively. The demodulated wavelength-shift in Fig. 9(b) is a sinusoidal signal having same frequency and phase as the PZT driving voltage in Fig. 9(a). An amplitude of the demodulated signal is 5.82 pm. Since the strain response of the FBGFPI is 1.17 pm=, this corresponds to the mechanical vibration with an amplitude of 4.97 . The result is in good agreement with the amplitude obtained from the calibration using the laser Doppler vibrometer within its accuracy 5%. Fig. 10(a) shows the Fourier spectrum of the demodulated wavelength-shift shown in Fig. 9(b). A noise floor of the spectrum is 5 fm. The Fourier spectrum is obtained from the discrete Fourier transform with resolution of 125 Hz. Thus the noise floor corresponds to a spectral density pffiffiffiffiffiffi 0.3 fm= Hz. In Fig. 10(a), three peaks can be seen at 1 kHz, 2 kHz, and 3 kHz. The peak at 1 kHz corresponds to the fundamental component and other peaks correspond to the harmonics. Since the amplitudes of the peaks are 5.82 pm at 1 kHz, 0.0433 pm at 2 kHz, and 0.0288 pm at 3 kHz, the total harmonic distortion of the demodulated wavelength-shift signal is less than 1%. Fig. 10(b) shows the plot of the amplitude of the demodulated wavelength-shift as a function of the amplitude of the applied strain. A dashed line indicates a linear function based on the strain response of the FBG-FPI. The linear response of the present sensor is shown in the range of the


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applied strain from 10 n to 10 . As seen from Fig. 10(b), the experimental results are in good agreement with the linear function except for the case that the amplitude of applied strain is as low as 4.7 n. Although the amplitude of the wavelength-shift is expected to be 5.4 fm, in that case, 7.9 fm is obtained from the experiment. This is considered to be due to the noise floor of 5 fm shown in Fig. 10(a).

5. Conclusion We have presented a dynamic-strain sensor using an FBG-FPI and laser wavelength sweep with the compensation of the wavelength sweep nonlinearity. A DFB-LD was used as the source and its wavelength was swept by the injection current sweep at a frequency of 100 kHz. The modulation characteristics of the laser wavelength was evaluated experimentally pffiffiffiffiffiffiand compensated using an external fiber Fabry–Pe´rot interferometer. The resolution of 0.3 n= Hz and measurement time of 10 s were experimentally demonstrated in the present sensor. The total harmonic distortion of the sensor output is less than 1%. The linear response of the proposed sensor were demonstrated in the range of the input dynamic-strain from 10 n to 10 in the experiment.

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