Optical microphone with fiber Bragg grating and signal processing techniques

Optical microphone with fiber Bragg grating and signal processing techniques

Daniele Tosi*a, Massimo Oliveroa, Guido Perronea

aDept. of Electronics, Politecnico di Torino, c.so Duca degli Abruzzi 24, Torino, ITA 10129

ABSTRACT

In this paper, we discuss the realization of an optical microphone array using fiber Bragg gratings as sensing elements. The wavelength shift induced by acoustic waves perturbing the sensing Bragg grating is transduced into an intensity modulation. The interrogation unit is based on a fixed-wavelength laser source and - as receiver - a photodetector with proper amplification; the system has been implemented using devices for standard optical communications, achieving a low-cost interrogator. One of the advantages of the proposed approach is that no voltage-to-strain calibration is required for tracking dynamic shifts. The optical sensor is complemented by signal processing tools, including a data-dependent frequency estimator and adaptive filters, in order to improve the frequency-domain analysis and mitigate the effects of disturbances. Feasibility and performances of the optical system have been tested measuring the output of a loudspeaker. With this configuration, the sensor is capable of correctly detecting sounds up to 3 kHz, with a frequency response that exhibits a top sensitivity within the range 200-500 Hz; single-frequency input sounds inducing an axial strain higher than ~10nε are correctly detected. The repeatability range is ~0.1%. The sensor has also been applied for the detection of pulsed stimuli generated from a metronome.

Keywords: Fiber optic sensors, Fiber Bragg gratings, Vibro-acoustic sensor, Optical instrumentation, Optical microphone, Multisensor system, Adaptive signal processing, Frequency estimation.

1. INTRODUCTION Over the last few years, the usage of fiber Bragg gratings (FBG) for sensing applications has received an increased interest from several research groups, as they combine advantageous properties typical of optical fibers, such as safety, immunity to electromagnetic interferences, low invasiveness and remote sensing capability, with the specific characteristics of this technology, such as in-fiber integration, high sensitivity and possibility to easily realize multiplexed sensor networks [1-2]. For these reasons, FBG are emerging as a successful replacement of standard electrical and mechanical instrumentation, which is inapplicable in rugged or radiation-prone environments. One of the target applications is the detection of acoustic waves through optical sensors, in order to provide an alternative instrument capable of working under the effect of strong electromagnetic fields, e.g. for monitoring medical parameters of a patient during a Computerized Tomography (CT) scan. Some implementations of FBG microphones, targeted for medical applications, have been documented in literature [3-5], using principles of operation based on matched-filters demodulation or spectral scanning with a tunable laser. The possibility of detecting acoustic signals through optical hydrophones is also a key issue in underwater sensing [6-7].

In this paper we discuss the realization of a fiber Bragg grating microphone, derived from the approach initially proposed by Morey [8] and subsequently extended by Wilson et al. [9]. This configuration, whose principle of operation is based on the intensity modulation, does not involve any scanning or moving element that limits the overall sampling frequency and increases the costs and mechanical instability, and can be implemented using off-the-shelf components developed for optical communications. In order to improve the performances of the interrogation unit, the optical sensor has been complemented by signal processing techniques: adaptive filters are used to mitigate the effects of disturbances arising both from the sensor itself and from external interferences, while a suitable frequency estimator permits dealing successfully also with weak and pulsed signals embedded into noise.

*daniele.tosi @polito.it; phone 39 011 2736-311; fax 39 011 564-4099

Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, edited byEnrico Primo Tomasini, Proc. of SPIE Vol. 7098, 70981E, (2008) 0277-786X/08/$18 doi: 10.1117/12.803184

Proc. of SPIE Vol. 7098 70981E-1

Entering spectnim Transmitted

Reflected spectrUm

FB 0sp e ctru in

FBG

Laser

Photodetector

2. PRINCIPLE OF OPERATION A fiber Bragg grating is a periodic modulation of the refractive index within the core of a photosensitive optical fiber, which yields to a frequency-selective response, as depicted in Fig 1 [10]. The FBG behaves as a stop-band filter, in which the central wavelength is

λB0 = Λeffn2 (1)

where neff is the effective refractive index of the fiber and Λ is the period of the index modulation. The peak wavelength, and consequently the whole spectrum, linearly shifts upon application of stresses either due to mechanical forces or temperature variation, according to the following relation [11]:

( ) TkkT TBB ∆++=∆ ελελ ε0, (2)

where ∆T is the temperature variation with respect to the reference value, ε is the axial strain applied to the FBG, and kT and kε are the temperature and strain coefficients respectively. Of course (2) is valid for stress intensity not exceeding the range in which the grating spectral response is not distorted. In our application the axial strain is applied to the FBG by an acoustic excitation, yielding a wavelength shift proportional to the pressure [12]. On the other hand, since the sensor is targeted to the detection of dynamic phenomena, temperature static fluctuations can be neglected.

Fig. 1. Wavelength-selective behavior of a FBG.

Fig. 2. Principle of operation of the interrogator. The light emitted by a narrow-linewidth laser is filtered through the FBG,

yielding an output power proportional to the FBG transmission coefficient. When the FBG is strained, its spectrum shifts and the laser intercepts a different spectral slice, changing the output voltage.

The FBG is interrogated by means of a fixed-wavelength narrow-linewidth laser source, exploiting the spectral shift induced by the axial strain to produce an intensity modulation proportional to the spectral shift and therefore to the


FBG arrayPD Amp

PD Amp

PD Amp

PD Amp

Photodiodes Amplifiers

DAQ

Sampling (fs)

lIJY'Ii IAEII IV-+sI _____1 IJ?I Ar

I IV—

I I Ar V—+s

I I Ar V—+s

MVE Adaptive Voltagefiltering to strain

Laser

meFiber

fter

SENSOROUTPUT

1111111 II

1111111 II

—H 111111Buffers

applied stress, as schematized in Fig. 2. The measured output power is approximately proportional to the FBG transmission coefficient evaluated at the laser wavelength, but an alternative scheme based on the reflected power is also possible. In both cases, with these arrangements, the unambiguous range suitable for interrogation is approximately half of the FBG full bandwidth; however it is important to note that the response is non-linear and thus a preliminary characterization is necessary in order to find the calibration curve.

3. EXPERIMENTAL SETUP The actual experimental setup of the FBG interrogator is and extension of the principle shown in Fig. 2 and is depicted in Fig. 3. The light source is a laser diode for telecom applications, packaged in a convenient butterfly case, with an emission wavelength close to 1560 nm and an output power of 140µW @ I = 180 mA. The laser is controlled by a ILX laser controller that includes a current source and temperature stabilization by a thermo-electric cooler (TEC). The light source is followed by a high quality isolator (> 30dB), in order to reduce the self-mixing (SM) effect due to the power reflected by the FBG [13]. However, despite the isolation, the SM is not completely removed, and introduces a slow and chaotic fluctuation perturbing the optical signal that are removed/attenuated thanks to the employment of adaptive filters, as will be further detailed in the next section. All the FBG employed in the experiments have been fabricated in our lab, with the phase mask technique [14], using a photosensitive fiber with coefficients kε = 1.10 pm/µε and kT = 10.2 pm/°C showing a Bragg wavelength close to 1560 nm using a phase mask with pitch 2Λ = 1071.46 nm. In order to protect the FBGs and, at the same time, preserve their strain sensitivity to sound pressure, the FBGs have been embedded in a suitable package, consisting in a thin double layer of polyimide tape with glue for glass. The chosen FBG is linked to the source and the receiver by means of two fiber spans of about 5m, in order to simulate a remote sensing application. The optoelectronic receiver is implemented with a PIN photodiode for low bit-rate communications, followed by a transimpedance amplifier and a low-noise voltage amplifier.

Fig. 3. Schematic of the optical microphone, arranged for multiple FBG interrogation.


I' III.

'.1

5

0

-5

10

15

MVE - L500— MVE - L800 -

FF1— PWeIch -

NIw-o

0(-I)a-Da)N(t

0z

ii

— — —.

'I'j\

20

25

Rso 360 370 380 390

Frequency (Hz

This interrogation system can be extended to a multiplexed structure, by splitting the input signal into multiple channels and replicating the receiver; however this extension requires the employment of wavelength-matched FBG. In any case this feature is limited to a small amount of sensing points, since the signal-to-noise ratio (SNR) decreases with the splitting ratio.

The output voltages of the N channels are read by a NI-6036 data acquisition (DAQ) card with sampling rate fS. The maximum sampling frequency of the DAQ card is 200 kS/s, but it is unfeasible in a multiple channel configuration since the sampling intervals are not equally distributed if the DAQ is forced to switch between different channels at the highest speed. A LabVIEW 8.2 interface has been developed in order to collect the received data, store them in a buffer and perform the further elaboration routines detailed in the next section.

In our experiments, the optical sensor has been applied without any calibration, supposing a linear relationship between voltage and strain. This is correct since the strain induced by input sounds is typically very low (<< 1 µε), and the sensor is supposed to detect weak sounds. The working point is chosen approximately in the middle of the useful range, corresponding to the steepest part of the calibration curve, in order to get the maximum strain sensitivity.

4. SIGNAL PROCESSING 4.1 Frequency estimation

The choice of the frequency estimation technique is fundamental for transferring the data analysis in the frequency domain. Standard methods, such as Fast Fourier Transform (FFT) and Bartlett/Welch periodogram [15], suffer by strict limitations in terms of frequency resolution and are strongly biased, hence are not suitable for the accurate estimation of weak or pulsed sounds embedded into noise. In order to overcome these restrictions, we applied the Minimum Variance Estimator (MVE), proposed by Capon in 1969 [16], for the estimation of the power spectral density (PSD) of the measured sound. This algorithm builds, for every frequency point arbitrarily chosen, the bandpass finite impulse response (FIR) filter with L taps that minimizes the output power without distorting the pitch frequency. The Capon estimator computes the optimum FIR coefficients directly from the input data, hence shaping the profile of the filters in order to reduce the bias affecting the estimate. Moreover, because of the arbitrary choice of the frequency points, the MVE has no intrinsic limitation in terms of resolution; this permits a fine monitoring of both a narrow frequency range and the full spectrum.

Fig. 4. Comparison of spectral estimators for measurement of a 370 Hz reference tone, with an integration interval of 2s;

MVE with 500 and 800 taps, FFT and Welch periodogram have been computed.


10

8

6

R4m

S 2

0

-2

2 4 6 8 10n x I o4

Figure 4 reproduces the comparison of the spectral estimators when applied to a reference measure of a sinusoidal signal with resonance frequency of 370 Hz. The MVE provides a clear spectrum, due to the strong reduction of the bias affecting the estimate. On the other hand, the behavior of the FFT algorithm is strongly limited by bias, hence the resulting spectrum fluctuates, making the quality of estimation inaccurate; the Welch periodogram reduces the effect of biasing because of its windowed filtering, but it also exhibits a worse resolution and, for this reason, it does not return an accurate estimation of the peak position. Although the MVE exhibits a more accurate spectral reconstruction, the selectivity of the designed FIR filters is lower than the FFT even using a huge number of taps, making the MVE unable to resolve thin spectral slices. Our measurements confirmed than the -3dB bandwidth of the estimated spectral response of a sinusoidal signal decreases proportionally to 1/L. The noise floor level also depends on the number of taps: Fig. 4 shows a difference of ~2dB between L=500 taps and L=800 taps: as a consequence, the threshold SNR for correct detection has a slight dependence on the choice of the filter length. The minimum operative SNR for the MVE with 500 taps is approximately -25dB, while FFT requires a SNR higher than -15dB, due to its intrinsic fluctuating noise floor.

4.2 Adaptive equalization

The FBG interrogation unit is affected by three main disturbances: SM effect due to the optical power backreflected by the FBG into the laser source; power supply-related disturbances, affecting the non-ideally shielded optoelectronic receiver; external disturbances captured by the FBG. Hence, in absence of input sound and external disturbances, the resulting signal is perturbed by a highly chaotic and low-frequency noise combined with the 50Hz and higher-order harmonics injected by the power supply system. Fig. 5 plots the autocorrelation rx[n] of a typical acquired signal x[n] in absence of input sound waves, with fS=5kS/s: disturbances are strongly correlated even after 20 seconds, exhibiting a trend that follows the slow oscillations of SM. This strongly correlated noise pattern suggests the application of adaptive filters to mitigate the effects of disturbances on the input signals [17].

Fig. 5. Autocorrelation of a typical acquired signal when no input sound is applied to the FBG.

The principle of operation of adaptive filtering is shown in Fig. 6. The easiest way to implement the equalization is to acquire the training set in a silent condition, hence measuring only disturbances. Alternatively, a calibrated broadband signal can be sent as reference, but this requires a harder implementation and an accurate synchronization. The measured signal x[n] is compared to the desired signal d[n], which is simply a constant signal equal to the average of x[n]. The length of the training set NT is chosen as a reasonable trade-off between convergence time of the adaptive algorithm, coherence time of disturbances to be mitigated and constraints of the applicative context of the optical sensor. At each iteration k, k=1,…,NT, the adaptive algorithm updates the coefficients w(k) of the FIR filter that approximates the ideal compensator, returning the correspondent filtered signal y[n]. The training phase is accomplished at the NT-th iteration; then, all the next measured data are filtered through the w(NT) FIR. The algorithm is initialized by setting w(0) as an all-pass filter.

In order to obtain a fast convergence, hence reducing the training length, we applied the exponentially weighted recursive least square (RLS) algorithm. The most effective noise that limits the SNR of the system is low-frequency self-mixing that can be mitigated even with a low number of taps; high-frequency disturbances (e.g. harmonics of the power supply frequency) instead require a better selectivity of the FIR filters, therefore requiring long filters. Fig. 7 reports the behavior of the RLS adaptive algorithm with different numbers of taps (5, 20, 60), all having the same forgetting factor


Measured data

Nr-th iteration coefficients

0.9, and with a training sequence length of 20 seconds. As expected, the time plots confirm the noise removal of SM-related fluctuations even for a low number of taps. On the other hand, the efficiency in mitigating high-frequency noise when the filter w(NT) is applied depends on the FIR length: while for a 5-tap equalizer the PSD is almost the same, the increase of number of taps progressively clears out the noise surrounding the frequency peaks.

Fig. 6. Principle of operation of adaptive equalization.

We define two indicators in order to give a quantitative measure of the efficiency of adaptive filters. The noise removal, during the training phase, hence in absence of input sounds, is measured by the following parameter, which accounts the ratio between the noise variance before and after the RLS:

GAF [dB] = [ ]( )[ ]( )TEE

TEE

NNNyNNNx

,,,var,,,var

log101

110

K

K

+

+ (3)

in which NE is the FIR transient length. In order to measure the efficiency of the adaptive filter when applied to an input sound, according to Fig. 6, we define the following parameter that evaluates the spectral efficiency as the ratio between the PSD related to the input sound and the PSD related to the surrounding noise level:

GPSD =

( )

( ) ( )

( )

( ) ( ) ⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+

⋅

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+ ∫∫

∫

∫∫

∫

∆+

∆−

∆+

∆−

∆+

∆−

∆+

∆−

−

b

a

b

a

f

fy

f

fy

f

fy

f

fx

f

fx

f

fx

dffPdffP

dffP

dffPdffP

dffP1

(4)

where Px(f) and Py(f) are the estimated PSD values (in linear units) of the measured sound x[NT+NE+1,…,NF] and the RLS-filtered signal y[NT+NE+1,…,NF], with NF correspondent to the final sample; the frequency range [f-∆ – f+∆] is the spectral portion belonging to the input sound, while the intervals [fa, f-∆] and [f+∆, – fb] refers to the noise surrounding the sound spectrum. As reported in Fig. 7, GFA is approximately the same for each case (17.7 dB – 19.9 dB); this means that the RLS is capable of reducing the noise variance by ~20dB even with a low number of taps. On the other hand, GPSD is close to 1 for a 5-tap FIR filter, but grows up to 3.23 for 60 taps, confirming that a greater selectivity of the FIR filter yields a better reduction of the high-frequency noise, improving the extinction ratio.

An alternative technique for equalization, based on the same training set but limited to the frequency domain, is to exploit the MVE as flattening filter, by applying the spectral estimator to the training set and then setting the inverse of this PSD as gain coefficient of the correspondent frequency.


a) 5 taps-5.48

19.6dB-5.49

-55

b) 20 taps

-5.52

-5530

c) 60 taps

5 10

Time (s)15

-5.48

-549

00,C,

-5.51>

-5.52

-5.5320

19.9dB

5 10

Time (s)15 2

0

x[l...NT]-y[l...NT]

P(f)

-10-20

-300-

-40

400 450 500

Frequency (Hz) Frequency (Hz)

- 00 350 400 450 500

Frequency (Hz)

b)

Fig. 7. Application of the RLS adaptive filter to a reference measurement of a 370 Hz tone, with a training phase of 20s. A

RLS filter has been applied using 5 (a), 20 (b) and 60 (c) taps, obtaining the resulting plots (a-c) of the measured and filtered signals during the training sequence. Then, the resulting filters have been applied to the 370 Hz tone, estimating the spectrum of the signals with a 500-tap MVE (d-f). GPSD has been computed with the following settings: fa = 300Hz, fb = 500Hz, f-∆ = 360 Hz, f+∆ = 380 Hz.

5. RESULTS The optical microphone has been validated in a laboratory framework, using purposely poor setups in order to assess the effectiveness of the proposed approach. The sensing FBG have been pre-strained and fixed on a loudspeaker controlled by an arbitrary waveform generator; alternatively, the FBG have been applied to the output of a notebook PC, as shown in Fig. 8.

Fig. 8. Experimental setup for sound detection: a) the packaged FBG is strained and locked to the edges of a loudspeaker

with scotch-tape, without contact between the FBG and the membrane; b) the FBG is fixed to the poor-quality speaker of a notebook PC with scotch-tape.


o o

.0 0

=

0

0 =

C)

01

lo

N 0 N

J 01

0 0

PS

D (

dB/H

z)

0)

01

a o

o 0

0) 0

NJ

- 0

0 0

01 0 0 N

J 0 0 0

—70'.. . I I I I I I

372Frequency (Hz)

-70

1sf 0.45Hzy

I I

370 372

-75

80

369 370 371

-85

369Frequency (Hz)

371

5.1 Frequency response

We measured the spectral response of the optical microphone, arranged in the configuration of Fig. 8a, obtaining the response curve plotted in Fig. 9. The maximum sensitivity occurs at a low frequency range (50-480 Hz), with a peak response at 250 Hz. The range 600-950 Hz exhibits a good response, approximately 20 dB lower than the previous region. The FBG sensor is capable of detecting intense sounds up to 3 kHz, with a sensitivity 50 dB lower than the top response.

The measured spectral sensitivity depends on the transfer functions of the loudspeaker and the FBG package, on the energy coupling between the FBG and the speaker, on the propagation of the acoustic waves from the membrane to the FBG cover and on the spectral response of the optoelectronic circuit. However, further measurements show that the trend of Fig. 9 is qualitatively replicated in all the typical configurations.

Fig. 9. Spectral response of the optical microphone, evaluated by changing the resonance frequency of the loudspeaker (with

a fixed driving voltage) and recording the correspondent PSD peak level.

Fig. 10. Measure of the repeatability range of the FBG sensor before and after the RLS equalization, evaluated from 10

different measures of a 370 Hz pure tone generated through a loudspeaker.


5.2 Repeatability

Figure 10 plots the repeatability of the optical sensor, evaluated from 10 different measurements of a sinusoidal tone of 370 Hz at the same acoustic power; the signal length is 0.4s, with sampling rate fS = 5kS/s. The PSD is evaluated on a frequency span of 0.01 Hz applying the MVE with 500 taps. The frequency pitch estimate lies within a range of 0.46 Hz, corresponding to a relative interval of 0.12%. The application of the RLS adaptive filter does not improve the repeatability of the peak frequency estimate, since the low frequency selectivity intrinsic in the Capon algorithm does not permit an improvement of the peak estimation sharpness when dealing with narrow spectra.

5.3 Detection of short pulses

In order to simulate a medical context, in which the optical sensor is expected to detect pulsed stimuli such as the heartbeat, we probed the capability of the system to react to periodic beats. For this experiment the FBG has been fixed as shown in Figure 8b and an online-metronome [18] has been used to generate acoustic pulses via PC and the beat rate has been chosen to closely match a typical heartbeat signal. The results of this test are shown as time-plot in Fig. 11: the sensor clearly detects beats, reproducing the selected rate without distortion.

2 3 4 5 6 7-0.5

0

0.5

2 3 4 5 6 7-0.5

0

0.5

2 3 4 5 6 7-1

-0.5

0

0.5

2 3 4 5 6 7-0.5

0

0.5

Time (s)

Stra

in (a

.u.)

60 beat/min

92 beat/min

112 beat/min

144 beat/min

Fig. 11. Measurement of the vibro-acoustic excitation provided by a metronome, with 60, 92, 112 and 144 beat/min

respectively.


5.4 Voice detection

The good sensitivity exhibited in the low-frequency range 300-500 Hz, in which the principal part of the spectrum of human voice is concentrated, opens up to the application of the optical microphone for voice detection. We performed a preliminary test, using a recorder speech as input sound played by the PC speaker and reconstructing the voice from the FBG sensor. The achieved results show that the sound measured by the sensor, although distorted, maintains the clear intelligibility of the speech. A better result is obtained if the sensor output is normalized by the spectral sensitivity shown in Fig. 9, in order to remove the dependence on the transfer function of the acousto-optical system.

6. CONCLUSIONS In this paper we described the realization of an optical microphone based on fiber Bragg gratings; the dynamic wavelength shift induced by sound axial pressure is transduced into an intensity modulation and then detected with an optoelectronic circuit. This arrangement, applied to detection of weak and dynamic phenomena, permits selecting the optimal working point to maximize the sensitivity, and avoiding precalibration. Moreover, the application of advanced signal processing routines has demonstrated to be effective in mitigating disturbances and increasing performances and robustness of the interrogator.

The proposed sensor is mainly oriented to medical and biomedical target applications, with the purpose of providing an alternative instrument capable of working in rugged environment. Compactness, immunity to electromagnetic disturbances and compatibility are expected to make this sensor a useful tool for measurement of voice, breath and heartbeat of patients during exams where more common electrical sensors are not allowed, such as during Computerized Tomography scans. Preliminary tests, involving sound generation from loudspeakers and contact detection, highlight encouraging results and a good potential, which can be raised by adaptive noise canceling techniques.

REFERENCES

[1] Kersey, A. D., Davis, M. A., Patrick, H, J., LeBlane, M., Koo, K. P., Askins, C. G., Putnam, M. A. and Friebele, E. J., "Fiber grating sensors," J. Lightw. Technol. 15, 1442-1463 (1997).

[2] Rao, Y. R., "In-fibre Bragg grating sensors," Meas. Sci. Technol. 8, 355-375 (1997). [3] Mohanty, L., Koh, L. M. and Tjin, S. C., "Fiber Bragg grating microphone system," Appl. Phys. Lett. 89(16),

(2006). [4] Bezombes, F. A., Lalor, M. J. and Burton, D. R., "Contact microphone using optical fibre Bragg grating

technology," J. Phys.: Conf. Ser. 76, (2007). [5] Gurkan, D., Starodubov, D. and Xiaojing Yuan, "Monitoring of the heartbeat sounds using an optical fiber Bragg

grating sensor," IEEE Sensors, (2005). [6] Fisher, E., Webb, D. J., Pannell, C. N., Jackson, D. A., Gavrilov, L. R., Hand, J. W., Zhang, L. and Bennion, I.,

"Ultrasonic hydrophone based on short in-fiber Bragg gratings," Appl. Opt. 37(34), (1998). [7] Cusano, A., D’Addio, S., Cutolo, A., Giordano, M., Campopiano, S., Balbi, M. and Balzarini, S., "Plastic coated

fiber Bragg gratings as high sensitivity hydrophones," IEEE Sensors, 166-169 (2006). [8] Morey, W. W.., "Distributed fibre grating sensors," Proc. 7th Optical Fiber Sensors Conf., 285-288 (1990). [9] Wilson, A., James, S. W. and Tatam, R. P., "Time-division-multiplexed interrogation of fibre Bragg grating sensors

using laser diodes," Meas. Sci. Technol. 12(2), 181-187 (2001). [10] Erdogan, T., "Fiber grating spectra," J. Lightw. Technol. 15(8), 1277-1294 (1997). [11] Othonos, A., and Kalli, K., [Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and

Sensing], Artech House, 98-99 (1999). [12] Iida, T., Nakamura, K. and Ueha, S., "A microphone array using fiber Bragg gratings," OFS Conf. Digest Tech. 1,

239-242 (2002). [13] Giuliani,G., Norgia, M., Donati, S. and Bosch, T., "Laser diode self-mixing technique for sensing applications," J.

Opt. A: Pure Appl. Opt. 4, 283-294 (2002). [14] Hill, K. O., Malo, B., Bilodeau, F., Johnson, D. C. and Albert, J., "Bragg gratings fabricated in monomode

photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993). [15] Oppenheim, A. V. and Schafer, R. W., [Digital Signal Processing], Prentice Hall, 532-562 (1975). [16] Capon, J., "High-resolution frequency-wavenumber spectrum analysis," Proc. IEEE 57(8), 1408-1418 (1969).


[17] Haykin, S., [Adaptive Filter Theory], Prentice Hall, 562-572 (2001). [18] Metronome Online, http://www.metronomeonline.com/.


Documents

Optical microphone with fiber Bragg grating and signal processing techniques