Influence of membrane surface shape change on theperformance characteristics of a
fiber optic microphone
Rui Li,1,2,* Nicholas Madamopoulos,2 and Wen Xiao1
1School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China2Optical Communications and Photonics Systems Laboratory, City College of City
University of New York, New York, New York 10031, USA
Interest in fiber optic microphones (FOMs) is quicklygrowing because of the advantages that an opticalsensor has over conventional sensors. These advan-tages include electrical and chemical passivenessand immunity to electromagnetic interference [1].In particular, the reflective intensity modulated(RIM) FOM , which has the advantages of simplestructure and low cost, is very attractive for applica-tions in surveillance, medicine, and noncontact ornondestructive essays [2–4].
For application of a RIM-FOM, its reflective inten-sity modulation model is a critical and importantstep for improving its sensitivity performance. Forexample, based on the development of the existing
model, some of the previously proposed solutionshave analyzed the influence of the system geometryparameters on performance, and they have opti-mized the structure [5,6]. RIM-FOMmodeling drawsmany modeling concepts and conclusions from fiberoptic displacement sensor (FODS) because of similarprinciple and structure [6]. Faria established themodel of two-fiber FODS with the assumption of aGaussian distribution of the output intensity, andanalyzed its sensitivity, the optimum operating dis-tance, and the linear operating range [7]. Based onthis model, the influence of the system geometryon the performance of FODS was evaluated [8–10].Further improvements led to an optimized structurefor RIM-FOMs and microphones with high perfor-mance [2,5,6]. However, there is an obvious differ-ence between a RIM-FOM and a FODS. That is,the reflector’s movement. In the case of the FODS,the reflector is the detected object, which is typically
flat and moves parallel [7–10]. On the other hand, inthe case of aRIM-FOM, the reflector is a flexiblemem-brane that senses the acoustic signal and vibrates.Hence, the movement of the membrane is a vibrationof the continuous surface shape change [11,12]. Thismovement will modulate the reflective intensity in adifferent way from that of a FODS. The existing mod-els for RIM-FOMs have not considered this influenceof surface shape change on the reflective intensitymodulation. In some papers [13,14], the membranesurface shape was mentioned, but they focused onthemembrane’s structural properties (e.g., thickness,size,material) andhow these structural properties af-fect the microphone performance. The membraneshape changes and the effect on the reflected opticalintensity is still an open issue.Hence, the focus of thispaper is themodeling of a RIM-FOMunder a realisticmembrane shape change and the analysis of its influ-ences on the microphone’s performance.
Section 2 analyzes the distribution of the mem-brane surface shape change caused by the acousticsignal and establishes the revised model of a RIM-FOM under this realistic membrane shape change.In Section 3, the microphone’s optimum operatingdistance and sensitivity are analyzed. An experimen-tal setup is used to validate our model and compareour analytical results with the existing model. InSection 4, we study the influences of the membraneshape change on the other microphone characteris-tics (e.g., the linearity, the distortion, and the dy-namic range). Finally, we conclude our work anddiscuss some future research directions in Section 5.
2. Modeling of RIM-FOM
A. Distribution of Membrane Surface Shape
In the RIM-FOM case, the membrane is usually a cir-cular plate with its boundary clamped. When theacoustic signal impinges on the membrane, the mem-brane vibrates. The vibration amplitude of any pointon the membrane surface, whose distance is r fromthe membrane’s center, is [15]
ηaðrÞ ¼Pa
k2T
�J0ðkrÞJ0ðkaÞ
− 1
�; ð1Þ
where a is the radius of the membrane, k ¼ 2πf =c isthe wavenumber, c is the velocity of the propagatingplane waves along the membrane, f is the frequencyof the acoustic signal, Pa is the acoustic pressure, T isthe tension on the membrane surface, and J0 is thezero-order Bessel function. When the frequency ofthe acoustic signal f is much lower than the mem-
brane’s first-order frequency f r1 ¼ 2:4052πa
ffiffiffiTσ
q, where σ
is the membrane surface density, then, by usingthe Bessel function expansion,
J0ðxÞ ¼X∞k¼0
ð−1Þk�x2
�2k
ðk!Þ2 ; ð2Þ
and, by keeping terms up to the second order, Eq. (1)can be simplified as
ηaðrÞ ¼Pa
k2T
�1 −
�kr2
�2
1 −
�ka2
�2 − 1
�
¼ Paa2
T½4 − ðkaÞ2� −Pa
T½4 − ðkaÞ2� r2; ð3Þ
when the parameter kr < ka < 0:5 [13]. Hence, thefrequency range of the acoustic signal for whichour approximation is valid is f < c=4πa. Note thatEq. (3) could be expanded to higher-order polyno-mials (e.g., fourth or sixth). In such a case, the opera-tion frequency for which the approximation would bevalid extends to higher frequencies. Note that, formost of the optical microphones, in order to get a flatresponse in the range of speech (from 300 Hz to 3kHz), the first-order frequency of the membrane isset to be larger than 3kHz [5,16,17]. Thus, using asecond-order approximation, which considers acous-tic frequencies in the range of speech for our analysisis adequate. As long as the geometric parameters ofthe membrane and the frequency of the acoustic sig-nal are known, Eq. (3) can be rewritten as
ηaðrÞ ¼ A0 þ B0r2; ð4Þ
where A0 ¼ Paa2
T½4−ðkaÞ2�, B0 ¼ −
Pa
T½4−ðkaÞ2�. Equation (4) isan expression of a parabolic curve. Meanwhile, be-cause of the boundary conditions ηaðaÞ ¼ 0, the coef-ficients in Eq. (3) can be further simplified toA0 ¼ ηað0Þ ¼ u, which is the vibration amplitude ofthe membrane center and is proportional to theacoustic signal pressure Pa. Correspondingly, B0 is−u=a2. Furthermore, Eq. (4) can be rezwritten asηaðrÞ ¼ Pa
T½4−ðkaÞ2� ða2− r2Þ, which shows the depen-
dency of the membrane vibration amplitude ηaðrÞon its radius a. In the rest of the paper, we useEq. (4) to describe the distribution of the membranesurface shape.
A realistic distribution of the microphone mem-brane is measured by a multiwavelength inter-ferometer [11] and a laser Doppler vibrometer [12].Figure 1 shows the measured result from [11] in cir-cles. The solid curve is the fitted curve and thedashed curve is the simulated result obtained byusing Eq. (4) for the same membrane parametersused in [11]. The two curves are very close to eachother, which indicates that the distribution of themicrophone membrane does follow the paraboliccurve and can be adequately described using Eq. (4).The small separation between the fitting curve andthe theoretical curve on the left side of the graph canbe explained by small rotation or misalignment ofthe membrane from the ideal symmetric positionaround its center.
B. Reflective Intensity Modulation Model of RIM-FOM
The reflective intensity modulation setup is shown inFig. 2(a). Because of the cylindrical symmetry, we fo-cus on the x–y plane. The x axis is along the radialdirection of the membrane and parallel to the line de-fined by the centers of the fibers. The y axis is normalto the membrane, crossing the membrane center. a isthe radius of the membrane, u is the vibration ampli-tude of the membrane when it senses the acousticsignal, and d is the operating distance of the fibertips along the y axis. The fiber radius and core radiusof the transmitting fiber (TF) and receiving fiber (RF)are R1, r1, and R2, r2, respectively. The distance be-tween the two fibers is D. The numerical aperture oftransmitting fiber is NA, and its maximum transmit-ting angle is θmax ¼ sin−1ðNAÞ.
We can assume that the transmitted light emergesfrom a point S, which is behind the TF tip at the dis-tance of M ¼ r1 cotðθmaxÞ, and it forms a cone withangle θmax. For any beam B1 with the angle θmax,we can assume that it is reflected by the point Ron the membrane. We can calculate the coordinateof the point R ðxR; yRÞ, using the coordinate of thepoint Sð0;−d −mÞ, the angle θmax, and Eq. (4). Thenthe slope of L, which is the normal of the membraneat point R, is expressed as
kL ¼ −1ηa0ðxRÞ
¼ −12B0xR
; ð5Þ
where ηa and B0 have been described in Eq. (4). Theslope of the corresponding reflected beam B2 is cal-culated by
k2 ¼ tan�2arctan kL −
π2− θmax
�: ð6Þ
Hence, the radius of the reflected circular pattern rRcan be obtained by
rR ¼����k2xR − yR − d
k2
����: ð7Þ
The overlap area between the reflected circularpattern and the RF tip, shown in Fig. 2(b), can beexpressed as [7,10]
S0 ¼Z
rR
R1þR2þD−r2
2αrdr; ð8Þ
where r is the radial distance and α can be evaluatedusing the law of cosines
α ¼ arccos�r2 þ ðR1 þ R2 þDÞ2 − r22
2rðR1 þ R2 þDÞ�: ð9Þ
Hence, the received power by theRF can be calcu-lated by
PR ¼Z
rR
R1þR2þD−r2
2αrIðrÞdr: ð10Þ
where IðrÞ is the radial intensity in the reflected cir-cular pattern, which is assumed to approximatelyobey Gaussian distribution [7,10,18].
Equation (10) differs from the previously reportedresult in [7], where the radius of the reflected circularpattern rR depends only on the vibration amplitudeof the membrane u. In our model, rR is calculated byEqs. (4)–(7) and depends on both the vibration ampli-tude u and another membrane shape factor B0, whichis inversely proportional to the a2. The dependency ofrR on B0 means that the membrane shape will affectthe intensity modulation.
Because, in our model, the membrane is supposedto follow a parabolic shape change, we refer to ourmodel as the parabolic surface change model (PSCM)in the rest of the paper. The existingmodel is referredto as the flat surface change model (FSCM) becauseof the assumption that the membrane surface is flatand moves parallelly.
3. Model Verification
In this section, two important issues for microphoneperformance, namely, the optimum operating dis-tance and the sensitivity, obtained by using thePSCM are analyzed and compared with the analyti-cal results obtained from the FSCM. Then some ex-periments are set up to verify the comparison results,to further validate our model.
Fig. 1. (Color online) Theoretical and experimental curves of themembrane surface shape.
Fig. 2. (Color online) Reflective intensity modulation model. (a)Intensity modulation model of the system with parabolic mem-brane. (b) Top view of the fiber tips showing the reflected circularpattern and the its overlap with the RF.
Initially using the model equation simulation is car-ried out for the ideal situation: the distance betweentwo fibers D is zero and the emerged power from theTF is 1mW. The RF and the TF are identical multi-mode fibers with cladding radius R1 ¼ R2 ¼ 125 μmand core radius r1 ¼ r2 ¼ 62:5 μm. Their NA is0.22. The original operating distance d is set at168 μm [19].
To simulate the membrane vibration caused by theacoustic signal, a small disturbance Δd ¼ u cosð2πf Þis added to d, where u is the vibration amplitude ofthe membrane center. The corresponding received in-tensity change, using u ¼ 200nm and f ¼ 1kHz, isshown in Fig. 3. The solid curve represents the re-sults obtained from the PSCM and the dashed curverepresents the results obtained from the FSCM. Forthe microphone, the received intensity change istransformed to an electrical signal by an optoelectro-nic device and then processed at the output. Usually,its output is proportional to the received intensitychange. Hence, we treat the calculated received in-tensity change as the microphone’s output. As shownin Fig. 3, the output results from the PSCM and theFSCM differ significantly. This difference also meansa significantly different sensitivity.
B. Sensitivity and Optimum Operating Distance
For the FSCM, the microphone’s sensitivity calcula-tion method is to evaluate the derivative of the re-ceived intensity PR with respect to the operatingdistance d [7,19]. This is shown in Fig. 4(a) (in cir-cles). The horizontal axis is the operating distance.Another alternative way to calculate the sensitivityis to add a small disturbance u cosð2πf Þ to the mem-brane. This will cause a received intensity changeΔPR. The sensitivity can be calculated by
Sen ¼ ΔPR=u: ð11Þ
The squares in Fig. 4(a) are the analytical resultsfrom Eq. (11) for u ¼ 100nm under different operat-ing distances. The overlap between the circles andthe squares indicates that calculating the sensitivityby adding a small disturbance is reasonable. Then,
some different disturbance magnitudes (u ¼ 10, 50,100nm) are examined. The analytical results ob-tained from the PSCM and the FSCM are shownin Fig. 4(b). For each of the models, the results onthe sensitivity for an undisturbed and a disturbedcase overlap with each other very well. This indicatesthat, when the disturbance amplitude u is not large,the sensitivity has no dependence on the disturbanceamplitude u, but it has only dependence on the mem-brane movement. The highest sensitivities and theoptimum operating distances obtained from thetwo models are also marked in Fig. 4(b) (in stars)and their values are listed in Table 1. We can con-clude from Table 1 that both the sensitivity and theoptimum operating distance are underestimated inthe FSCM. The highest sensitivity, obtained fromthe FSCM, is only 14.3% of the one obtained fromthe PSCM, and, for the optimum operating distance,the one obtained from the FSCM is 24 μm smallerthan the one obtained from the PSCM.
Because the optimum operating distance esti-mated by the FSCM is inaccurate, it will lead toan inappropriate microphone design and the micro-phone’s sensitivity will be greatly affected. For exam-ple, taking the data in Fig. 4(b), the sensitivity at theinaccurate optimum operating distance of 168 μm ob-tained from the PSCM is about 3:08 μW=μm, which is10% lower than the highest sensitivity 3:43 μW=μm.Note that this sensitivity is calculated by the PSCMbecause, for acoustic detection when the acoustic sig-nal is applied, the effect of membrane shape changeshould be considered.
C. Experimental Verification
To verify our theoretical results and, most impor-tantly, the improvement of the underestimation ofthe optimum operating distance and sensitivity bythe FSCM, we performed a series of measurementsusing the experimental setup in Fig. 5. A membraneof thin silver film is mounted on the bottom of amem-brane base. Two fibers are positioned parallel to eachother in a glass holder. The operating distance be-tween the membrane and the fibers is adjusted byFig. 3. Output signal comparison using the two models.
Fig. 4. (Color online) Comparison of the optimum operating dis-tances and the sensitivities obtained from two models. (a) Calcu-lated sensitivity from the FSCM: circles show the derivationresult; squares show the result obtained by adding small distur-bance. (b) Calculated sensitivities from the FSCM and PSCM byadding different disturbances: squares, circles, and trianglesare the results of adding disturbance of 10, 50, and 100nm,respectively. Stars are the optimum operating points.
a precision translation stage in steps of 5 μm [19].The acoustic pressure on the membrane is set to1Pa by adjusting the distance between the speakerand the membrane base. The frequency driving thespeaker is set at 1kHz. The received optical intensityis recorded by an optical power meter and trans-formed into an electrical signal, amplified, and ob-served at an oscilloscope.
We obtain the optimum operating distance of thissystem by using two different methods.
1. The first one is based on finding the relation-ship curve of the received intensity PR as a functionof the operating distance d, and evaluating the deri-vative of PR to d. Then the highest value of the deri-vative and its corresponding distance are calculated.Figure 6 shows the relationship of the received inten-sity results versus the operating distance, whenthere is no acoustic signal. Note that, in order toavoid the fibers from coming into contact with themembrane and, hence, destroying it, we offset thetip of the fibers from the membrane with an esti-mated start distance of 150 μm. In calculating the de-rivative of the received intensity, the optimumoperating distance is found to be at 165 μm, wherethe highest value of the derivative occurs. The corre-sponding received intensity is 87 μW at this distance.When the acoustic signal is applied, the output Vp−pobserved at the oscilloscope is 20mV at the distanceof 165 μm. Note that, since there is no acoustic signalto the membrane when we get the curve in Fig. 6, the
membrane remains flat and it corresponds to theassumption of the FSCM. Hence, the experimentalresults can be used to validate the FSCM.
2. The second method is to experimentally findthe optimum operating distance by finding the max-imum received optical power as we change the dis-tance between the fiber tips and the membrane.First, we position the fibers far from the membrane(e.g., 400 μm). Then we apply the acoustic signal andchange the operating distance from the original farpoint to as close as possible to the membrane (e.g.,150 μm). For each position we observe the outputVp−p. Its maximum value is measured at 30mV.When we remove the acoustic signal at the operatingdistance where the maximum Vp−p is obtained, thereceived intensity is at 117 μW. FromFig. 6 we obtainthe operating distance at 190 μm. In the second ex-perimental method, the membrane surface shapehas a continual change caused by the acoustic signal,which corresponds to the assumption of the PSCM.From Fig. 6 and Table 1, we see that there is verygood agreement between the estimated d ¼ 192 μmand the measured d ¼ 190 μm, which confirms thevalidity of our model. For a convenient analysis,the experimental results obtained by the two meth-ods and the simulated results obtained by two mod-els are listed in Table 2.
From Table 2, it can be found that there does existan offset of 25 μm between the experimental operat-ing distance of 190 μm obtained by the second meth-od (validation of the PSCM) and the analytical result165 μm obtained by the first method (validation ofthe FSCM). Because the only difference in the twomethods is the application of the acoustic signal,which corresponds to the membrane surface geom-etry (flat or not), we can conclude that this offset
Fig. 5. Experimental setup.
Fig. 6. Comparison of the experimental and theoretical optimumoperating distances.
Table 1. Optimum Operating Distance and the Highest SensitivityObtained from Two Models
is caused by the membrane surface shape differencein the two methods. In other words, the membranesurface change will give an experimental optimumoperating distance larger than the analytical resultfrom the FSCM, as it was predicted by our model(PSCM) and described in Subsection 3.B.
From the comparison between experimental re-sults and simulated results presented in Table 2,the experimental optimum distance offset of 25 μmis close to the simulated result of 24 μm, which alsovalidates our model. Furthermore, the ratio of theoutput amplitude obtained in method 2 and method1 is 1.5, which is close to the ratio of the highest sen-sitivities obtained from the PSCM to the one from theFSCM, which is 1.1. These two close ratios validateour model again. Note that the output amplitude20mV is obtained at the calculated optimum operat-ing distance, when the acoustic signal is applied.Hence, it corresponds to the simulated sensitivity3:08 μW=μm obtained from the PSCM.
4. Influence of Membrane Shape on MicrophoneCharacteristics
In this section, we use our experimentally verifiedmodel to analyze some additional microphone per-formance characteristics. The analytical results ob-tained from the two models are compared andthe differences are described, and we discuss theeffects of the membrane shape on the microphonecharacteristics.
A. Linearity
As we discussed earlier, the vibration amplitude ofthe membrane u is proportional to the acoustic signalpressure Pa. To study the response of the microphoneto different intensity levels of the acoustic signal, we
simulated the microphone’s response with vibrationdisturbances ranging from 0 to 3 μm. Figure 7(a)shows the peak-to-peak values (Vp−p) of the receivedoptical intensity changes for the different distur-bance amplitudes obtained using the two models.Both lines follow a linear response, which indicatesa linear relationship betweenmicrophone output andthe acoustic intensity level. The slopes of the twolines are calculated and their normalized slopesare shown in Fig. 7(b). For each line, the normalizedslope is the ratio of all the slope values to the max-imum value of them. If the microphone has good lin-earity, the slope of the curves in Fig. 7(a) should beconstant. Correspondingly, the normalized slopeequals to 1, which is a horizontal line parallel tothe x axis. However, we can see that the normalizedslopes obtained from the two models decrease withthe increase of the disturbance amplitude. Typically,the vibration amplitude of microphone membrane isless than 2 μm [11]. Hence, when the disturbance am-plitude added on the membrane is 2 μm, the normal-ized slope obtained from the FSCM is 0.999, whichis a decrease change of 0.1%. For the PSCM, the
Fig. 7. Comparison of the linearity and the linear operatingranges obtained from two models. (a) Peak-to-peak values (Vp−p)of the received intensity changes with the different disturbanceamplitudes obtained from the two models. (b) Linearity of the re-sponses and the linear operating ranges obtained from the twomodels.
Table 2. Experimental Results Obtained from Two Methods and Comparison with Simulated Results
Fig. 8. (Color online) Comparison of the frequency spectra ob-tained from the two models. (a) Received optical intensity changeswith disturbance of amplitude 1 μm and frequency 1kHz from twomodels. (b) Frequency spectra of the signals and (c) the zoom-in of(b) depicting the amplitude of the second-order frequency compo-nent amplitudes.
normalized slope is 0.986, which is a decrease changeof 1.4%. By using the slope change to indicate the mi-crophone’s linearity, we can see that the normalizedslope change obtained by the FSCM is less than theone obtained by the PSCM, which means that thelinearity is overestimated by the FSCM.
B. Distortion
Usually, the distortion of a microphone is measuredby analyzing the ratio of the high-order frequencycomponents to the first-order frequency componentunder an acoustic signal of 1kHz. This can be ex-pressed as
where U1 is the amplitude of the first-order fre-quency component (f ¼ 1kHz) and Un is the ampli-tude of the n-order frequency component.
In order to analyze the distortion and the dynamicrange (DR) due to the membrane, we ignore contri-butions from opto-electronics conversion and signalprocessing and focus only on the distortion generatedby the reflective intensity modulation. The compar-ison of the distortion analysis results from the twomodels is presented in Fig. 8, where we have applieda disturbance to the membrane with amplitude 1 μmand frequency 1kHz. The operating distance is sepa-rately set to be the optimum value, which is foundand validated in Subsection 3.B (shown in Fig. 4).As shown in Fig. 8(a), the amplitude of the receivedoptical intensity change from the PSCM is 3:0 μW,which is higher than the result of 0:27 μWobtained from the FSCM. The frequency spectrumis analyzed by fast Fourier transform [Fig. 8(b)],where the first-order frequency components areclearly shown at 1kHz. For the FSCM, it is0:13 μW, while, for our PSCM, it is 1:48 μW. To betterunderstand the results, Fig. 8(c) shows a zoom-in ver-sion of the high-order frequency components up to3kHz. The second-order frequency component isthe dominant contributor of the high-order frequencycomponents. By using Eq. (12) and assuming only theamplitude for the second-order components, we cal-
culate the distortion at 1.9% and 0.7% for the PSCMand the FSCM, respectively. This shows that ignor-ing the membrane surface shape change as consid-ered in the FSCM, leads to an underestimation ofthe distortion.
C. Dynamic Range
The DR, which is defined as an acoustic pressurerange in which the distortion is lower than a thresh-old valueDth, can be evaluated from the results of thedistortion analysis. Usually, the typical value of thethreshold value Dth in the microphone industry is3%. Following the method of the distortion calcula-tion shown above, we evaluate the effect of differentamplitudes to the output and, in particular, the am-plitude of higher-order components. Note that, sincethe added amplitude is proportional to the acousticpressure, the different amplitudes correspond to dif-ferent pressure levels. Table 3 shows the analyticalresults for the distortion. We see that the distortionresults obtained by considering the parabolic mem-brane shape change in the PSCM are higher thanthe ones from the FSCM. In comparison with thethreshold value of 3%, the actual DR obtained bythe PSCM is [0, 5 μm], which is much larger thanthe result [0, 1:5 μm] obtained by the FSCM. Thisshows again that the FSCM overestimates the micro-phone’s dynamic range.
5. Conclusion
The membrane of a RIM-FOM senses the acousticsignal and vibrates and modulates the reflective in-tensity. The acoustic signal makes the membranesurface shape change in a nonuniform way (e.g., aparabolic shape). To the best of our knowledge, thismembrane surface shape change has been ignored inthe existing models (FSCMs), which assume that theentire membrane has the same offset. In this work,the theoretical distribution of the membrane surfaceshape forced by the acoustic signal was analyzed byusing a parabolic surface shape assumption. Basedon this approximation, a revised model (PSCM) thattakes into account the effect of the membrane surfacechange on the reflected optical intensity modulationis developed. By comparing the analytical results ofthe microphone’s optimum operating distance and
Table 3. Comparison of the System Distortions at the Different Membrane Amplitudes
sensitivity obtained from the two models, we showthat the optimum operating distance and the sensi-tivity are underestimated by the FSCM, which canlead to an inappropriate microphone design. Wevalidate our PSCM model with experiments, wherewe show that our model is in very good agreementwith the experiment in estimating the optimumoperating distance, unlike the FSCM, which under-estimates this optimum operating distance. Our ex-periment also shows agreement with the simulationresults on the sensitivity estimation. Furthermore,we use our experimentally validated model to evalu-ate some additional microphone characteristics thatare affected by the membrane shape change. It isfound that the FSCM underestimates the distortion,while it overestimates the linearity and the dynamicrange, compared to the PSCM approach.
Future work will focus on the extension of ourmod-el to higher frequencies (e.g., beyond the first-orderfrequency of the microphone’s membrane), and theexperimental validation of the linearity and distor-tion results.
References1. J. Sakamoto and G. Pacheco, “Theory and experiment for
single lens fiber optical microphone,” Physics Procedia 3,651–658 (2010).
2. A. Paritsky and A. Kots, “Fiber optic microphone as a reali-zation of fiber optic positioning sensors,” Proc. SPIE 3110,408–414 (1997).
3. J. Chambers, D. Bullock, and Y. Kahana, “Developments inactive noise control sound systems for magnetic resonanceimaging,” Appl. Acoust. 68, 281–295 (2007).
4. M. NessAiver, M. Stone, and V. Parthasarathy, “Recordinghigh quality speech during tagged cine-MRI studies using afiber optic microphone,” J. Magn. Reson. Imaging 23, 92–97(2006).
5. J. Song and S. Lee, “Fiber-optic acoustic transducer utilizing adual-core collimator combined with a reflective micromirror,”Microwave Opt. Technol. Lett. 48, 1833–1836 (2006).
6. M. Feldmann and S. Buttgenbach, “Microoptical distancesensor with integratedmicrooptics applied to an optical micro-
phone,” in Proceedings of IEEE Conference on Sensors (IEEE,2005), pp. 769–771.
7. J. Faria, “A theoretical analysis of the bifurcated fiber bundledisplacement sensor,” IEEE Trans. Instrum. Meas. 47,742–747 (1998).
8. J. Zheng and S. Albin, “Self-referenced reflective intensitymodulated fiber optic displacement sensor,” Opt. Eng. 38,227–232 (1999).
9. W. Ko, K. Chang, and G. Hwang, “A fiber-optic reflective dis-placement micrometer,” Sens. Actuators A Phys. 49, 51–55(1995).
10. P. Buchade and A. Shaligram, “Influence of fiber geometry onthe performance of two-fiber displacement sensor,” Sens.Actuators A Phys. 136, 199–204 (2007).
11. C. Quan, C. Taya, and S. Wanga, “Study on defor-mation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun..197, 279–287(2001).
12. A. Degroota, R. MacDonald, and O. Richoux, “Suitability oflaser Doppler velocimetry for the calibration of pressuremicrophones,” Appl. Acoust. 69, 1308–1317 (2008).
13. K. Aiadi, F. Rehouma, and R. Bouanane, “Theoreticalanalysis of the membrane parameters of the fiber opticmicrophone,” J. Mater. Sci. Mater. Electron. 17, 293–295(2006).
14. A. Hu and F. Cuomo, “Theoretical and experimental study of afiber optic microphone,” J. Acoust. Soc. Am. 91, 3049–3056(1992).
15. L. Brechovskich and O. Godin, Acoustics of Layered Media(Springer, 1990).
16. K. Kadirvel, R. Taylor, and S. Horowitz, “Design and charac-terization of MEMS optical microphone for aeroacoustic mea-surement,” in Proceedings of 42nd Aerospace Sciences Meeting& Exhibit (American Institute of Aeronautics and Astronau-tics, 2006), paper 2004-1030.
17. J. Suh, “Measurement of resonance frequency and loss factorof a microphone diaphragm using a laser vibrometer,” Appl.Acoust. 71, 258–261 (2010).
18. A. Asadpour and H. Golnabi, “Fiber output beam shapestudy using imaging technique,” J. Appl. Sci. 10, 312–318(2010).
19. R. Li and W. Xiao, “Research on packaging technology forfiber optical acoustic sensor,” Proc. SPIE 7381, 73810U(2009).
