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Optics Communications 281 (2008) 94–101

An investigation of a fiber-optic air-backed mandrel hydrophone

Kai Yin a,c,*, Min Zhang b,c, Tianhuai Ding c, Liwei Wang b,c,Zhenguo Jing b,c, Yanbiao Liao b,c

a Department of Electronic Engineering, Tsinghua University, Beijing 100084, Chinab Laboratory on Integrated Optoelectronics, Tsinghua University, Beijing 100084, China

c State Key Laboratory of Precision Measurement Technology and Instruments, 9003 Building, Tsinghua University, Beijing 100084, China

Received 12 April 2007; received in revised form 3 September 2007; accepted 7 September 2007

Abstract

In this work, a optical-fiber air-backed mandrel hydrophone is proposed and investigated both analytically and experimentally. Thetwo-dimensional and three-dimensional quasistatically theoretical models of the hydrophone is created and compared, and the phasesensitivity of the hydrophone is analyzed. The theoretical result of phase sensitivity with three-dimensional model is �153.3 dB rerad/lPa. Twenty-two hydrophones of this type according to the model presented are constructed and tested. The experiment results showthat experimental results of mean values of phase sensitivity are about �153 ± 0.5 dB re rad/lPa and have the close agreement with theestimation of theoretical models. The size of the fiber sensor is B12 · 55 mm, the normal phase sensitivity achieves �308 dB re 1 lPa�1,the 3 dB effective bandwidth of the frequency response is 30 kHz, and the responsivity decreases less than 0.5 dB when static pressure is2 MPa (200 m water depth). The hydrophone is easy to constructed at low cost with simple structure, and some new type of it with therequired performances could be designed according to the model presented.� 2007 Elsevier B.V. All rights reserved.

Keywords: Hydrophone; Fiber-optic sensor; Phase sensitivity

1. Introduction

The optical-fiber hydrophone is one of the most success-ful applications in the optical-fiber sensor area [1,2]. Theoptical-fiber hydrophones were proposed as early as late1970s [3–7], and have been developed for more than 20years.

Optical-fiber hydrophones based on air-backed mandrelhave been successfully constructed and analyzed, and thistype of hydrophone is based on Michelson or M–Z inter-ferometer, in which the acoustic pressure is changed intothe optical phase difference and demodulated. McMahonand Cielo reported and briefly analyzed the optical-fiber

0030-4018/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2007.09.029

* Corresponding author. Address: East Main Building 11#303, Tsing-hua University, Beijing 100084, China. Tel./fax: +86 10 62781372.

E-mail address: yinkai@tsinghua.org.cn (K. Yin).

mandrel hydrophone with air-filled end-capped thin-walledcylinder [6], McDearmon analyzed the former transducerin more detail later [8]. Knudsen had researched on the fre-quency response of the air-backed mandrel hydrophone[9,10]. This type hydrophones had been used to constructthe optical-fiber interferometric hydrophone arrays [11]due to the high phase sensitivity and large frequencybandwidth.

In former work, the model was based on plane strainassumption elastic model, and the model using multilayeranalyses. Due to the fact that the elastic tube does not haveinfinite length and is not in pure plane strain, the axialstress is not equal to zero. Thus the analytical results ofphase sensitivity are higher than real situation, when theelastic tubes are not long enough – and without a thin-wall.Early work on the hydrophone had always been designedwith complex structure. The fibers and couplers need tobe produced specially due to the multilayer, specific

Fig. 2. Cross section of the air-backed fiber-optic mandrel hydrophone.

K. Yin et al. / Optics Communications 281 (2008) 94–101 95

materials or special optical properties, and it results that tomake the hydrophones in low cost and to produce at large-scale commercially difficultly.

In our work, a fiber-optic air-backed mandrel hydro-phone is investigated and a two-dimensional and a three-dimensional quasistatic model are created, which are alsobased on plane stain assumption. The three-dimensionmodel could improve the accuracy estimation of the phasesensitivity compared to the two-dimensional model.Twenty-two hydrophones of the type are designed accord-ing to the proposed model, which is with high phase sensi-tivity and large bandwidth. The fiber used is not withspecial thick coating to improve the performance, onlythe ordinary bend-insensitive fiber at low cost and easyto produce. The structure of our designed hydrophone issimple, and all key devices used in the hydrophone arecommercial production, which means the hydrophone isconstructed at low cost and could be produced at large-scale in commercial use. Finally the performances couldbe estimated according to the model mentioned above,which is analyzed in detail in the following.

2. Theory

2.1. The general principle of the hydrophone

The general principle is shown in Fig. 1. The hydropho-ne transducer is a Michelson interferometer essentially,which is the shadow parts in Fig. 1 with all-optical compo-nents. The light interrogates into the interferometer thougha 2 · 2 optical-fiber coupler, the acoustic pressure to bemeasured is applied to the sensing arm of the interferome-ter and converted to the optical phase difference (OPD).The OPD is detected by the optic detector and demodu-lated. The fibers of reference arm and sensing arm are usingbend-insensitive single fibers with low attenuation, and theFaraday mirrors are used as reflecting mirrors at the end ofthe fibers of reference and sensing, and the polarizationfading in the fiber-optic interferometers is minimized. Thestructure is simple and easy to be constructed, and the com-ponents are commercial productions. That means thehydrophone is at low cost and has potential large-scaleproduction.

The cross section of the air-backed mandrel hydrophoneis schematically shown in Fig. 2, which is under severalconsiderations and assumptions in these analyses. The

Fig. 1. Principal structure of the air-backed fiber-optic mandrelhydrophone.

model is constructed from a linear elastic theory so thatsmall displacements and low-frequency are required, whichmeans the wavelengths are much larger than the dimen-sions of the hydrophone, so the analyses are suitable forthe quasistatic model and acoustic scattering would notbe considered in low-frequency. All the materials of thecomponents of the hydrophone are assumed to be linear,and thermal noise are neglected due to the high thermalconductive of the material. The reference fibers are isolatedfrom the acoustic pressure and the phase difference in theinterferometer results from the phase shift of the sensingfiber. The sensing fibers with jacket are assumed to bebonded to the thin-wall elastic tube perfectly so that thefiber would be in a state of the plane strain [4], in whichthe phase shift due to two effect: the first is the radial strainof the thin-wall elastic tube to which the acoustic pressureand the fiber tension force apply; the second is the photo-elastic effect including the axial strain due to the pressureand the change of reflective index of the fiber, with tensionand bending-induced birefringence is normally much smal-ler than acoustic effect. Therefore it is neglected [4],together with the Sagnac effects which are neglected too[12]. The axial strain of sensing fiber is converted to theOPD in the interferometer.

2.2. Analysis of the elastic tube

The theoretical schematic map of the hydrophone is cre-ated and shown in Fig. 3. First the state of the elastic tubewill be analyzed. The symmetric load applies to the elastictube with isotropic material. Hence the equilibrium equa-tion in cylindrical coordinates could be written as [14]

Fig. 3. The theoretical schematic map of the air-backed fiber-opticmandrel hydrophone.

Fig. 4. The boundary condition of the hydrophone. (rR is the symmetricalstress, rz is axial pressure, H is the height of the fiber which is wound onthe elastic tube, a and b are the inner and outer radius of the elastic tube,respectively.)

Fig. 5. The mechanical situation of the elastic tube and mandrel. (Pt is theupper pressure, F is the pressure force of the elastic tube and F* is thepressure force of the mandrel.)

96 K. Yin et al. / Optics Communications 281 (2008) 94–101

orror þ 1

rosrhoh þ

rr�rhr þ br ¼ 0

orzoz þ

osrzor þ

srzr þ bz ¼ 0

(ð1Þ

where r, h, z are cylindrical coordinates, rr, rh, rz are nor-mal stress, srh, srz are shear stresses, br, bz are body forces.This is in axisymmetric elastic and plane strain state, so thesrh, srz are equal to zero. No body forces are applied thatmeans the acceleration is neglected. And rz could be deter-mined according Eq. (1) and the assumptions above:

uz ¼ C3z ð2Þwhere C3 is a constant. Eq. (1) means rz is a constant, sothe axial displacement uz does not have relationship be-tween r or h, and be direct ratio to z. The strain-displace-ment relationship in the state is [13]:

er ¼ our=dr

eh ¼ 1r

ouhoh þ ur=r

ez ¼ C3

crh ¼ ourrohþ

ouhor �

uhr

8>>><>>>:

ð3Þ

where er is radial strain, eh is circumferential strain, ez isaxial strain, crh is one of the tangential strains. Accordingto constitutive equation in elastic theory, given therelationship between e and r, the equation about radialdisplacement ur by (1) and (3):

o2ur=or2 þ 1

r� our=or � ur

r2¼ 0 ð4Þ

The general solution of the (4) is

ur ¼ C1r þ C21

rwhere C1 and C2 are two constant like C3. Then the dis-placement could be expressed as

ur ¼ C1r þ C21r

uh ¼ 0

uz ¼ C3z

8><>: ð5Þ

And the stresses could be derived as

rr ¼ E1þl

C1þlC3

1�2l �C2

r2

� �rh ¼ E

1þlC1þlC3

1�2l þC2

r2

� �rz ¼ E½2lC1þC3ð1�lÞ�

ð1þlÞð1�2lÞ

8>>>><>>>>:

ð6Þ

where E and l is the elastic modulus and Possion’s ratio ofthe elastic tube. Ci will be determined by boundaryconditions.

The boundary condition is shown in Fig. 4. The sensingfiber is bonded to the elastic tube. When the radial dis-placement of the elastic tube occurs, the length of the sens-ing fiber changes and a part of the phase shift is generated.rR applies to the outer radial surface of the tube, and theaxial direction is also applied by the pressure rz which iscaused by the acoustic. The inner radial surface of the tubeis not applied to pressure because of the air-filled betweenthe tube and mandrel.

Then the boundary conditions (BC) could be expressedas

rrjr¼a ¼ 0

rrjr¼b ¼ �rR

uzjz¼H ¼ C3H

u�zjz¼H ¼ uzjz¼H

8>>><>>>:

ð7Þ

where u�z is the axial displacement of the mandrel. The firstand second boundary conditions denote the inner and out-er stress of the tube. The third condition comes fromassumption (2). The fourth condition means because thetube and mandrel are all pressed by a nut which is treatedlike rigid body, the tube and the mandrel have the same ax-ial displacements. The sketch map of the situation is shownin Fig. 5.

The nut of the hydrophone is applied to three forces: theforce caused by Pt, F and F*, hence the three forces arebalanced.

Due to the assumption that the elastic tube and the man-drel have same axial displacement because of both of them

K. Yin et al. / Optics Communications 281 (2008) 94–101 97

are pressed by the nut, the following expression could beobtained:

ezjz¼H ¼ e�zjz¼H

The pressure force of the elastic tube is

F ¼ rzHpðb2 � a2ÞThe pressure force of the mandrel is

F � ¼ C3E�S�;

where E* and S* are elastic modulus and the effective areaof the mandrel. The balance equation of the nut could bewritten as

P tSn ¼ rzHpðb2 � a2Þ þ C3E�S� ð8Þwhere Sn is the effective area of the upper surface of thenut. And Sn is

Sn ¼ pb2

In this situation, the upper pressure Pt is equal to theacoustic pressure Ps.

Then C1, C2, C3 could be got by Eqs. (6)–(8):

C1 ¼ � b2fE�S�ð1þlÞð1�2lÞrRþEpðb2�a2Þ½P slþð1�lÞrR �gE½Epðb2�a2ÞþE�S��ðb2�a2Þ

C2 ¼ � a2b2ð1þlÞrR

Eðb2�a2Þ

C3 ¼ b2pðP sþ2lrRÞEpðb2�a2ÞþE�S�

8>>><>>>:

ð9Þ

The radial stress rR is comprised of the acoustic pressure Ps

and the fiber tension Pf which is wrapped around the tubeand acts on the tube when the radius of the tube changes.

The fiber used is ordinary bend-insensitive fiber, withoutthick coating. The coating is so thin that the fiber could beregarded as quasi-solid fiber with effective elastic modulusand effective area. It means that the multilayer consider-ation could be neglected, and the radial stress rR couldbe expressed as [14]:

rR ¼ P s þ P f ¼ P s þEfSfND

b2Hð10Þ

where Dr is the radial displacement, Ef and lf are elasticmodulus and Possion’s ratio of the optical-fiber core.

According to (5), the Dr is

Dr ¼ urjr¼b

A constant v* could be supposed as

v� ¼ EfSf NH¼ EfSf

tf

where N is the numbers in which the sensing fiber wrappedto the elastic tube, and tf is the diameter of the fiber. Thenthe expression of rR is

rR ¼ P sfEbðb2 � a2Þ½pðb2 � a2ÞE þ E�S� � pbv�l�g=f½E�S� þ pðb2 � a2ÞE�½ðb2 � a2ÞbE þ ða2 þ b2Þv��� ðb2 � a2Þ½E�S� þ pðb2 � a2ÞE�v � l� 2b2E�S�v�l2g

ð11Þ

So the stresses of the elastic tube are determined under thepress.

And when a constant x* is supposed as

x� ¼ b2f½pa4Eð1þ lÞ � a2ðE�S�ð1þ lÞ þ pb2ElÞ� b2ðpb2E þ E�S�ð1þ lÞð1� 2lÞÞ�g=f½E�S� þ pðb2 � a2ÞE� � ½ðb2 � a2ÞðbE � v � lÞþ ða2 þ b2Þv�� � 2b2E�S�v�l2g

The Dr could be expressed by Eqs. (9)–(11):

D ¼ P sx� ð12Þ

2.3. Analysis of the phase sensitivity of three-dimensionalmodel

The phase shift is

D/ ¼ b � DLþ L � Db ð13Þwhere b is transmission coefficient, b = 2pn/k, n is therefractive index of the fiber core, L is the length of the sens-ing fiber, and k is the wavelength of the optical light. Plus bthe function of n and diameter of the fiber core: b = b(n,D).

Thus the (13) could be expressed as

Du ¼ b � L � DLL

� �þ L � ob

on

� �� Dnþ L � ob

oD

� �� D � DD

D

� �

In the above, the first item at right denotes the phase shiftcaused by the change of the length of the fiber, the seconditem denotes the phase shift caused by the change of therefractive index of the fiber core, and the third item denotesthat caused by the change of the diameter of the fiber core.In general, the effect caused by the change of the diameterof the fiber core is neglected [15].

In the following analyses, the phase shift D/ has twocomponents D/1 which is due to the radial displacementof the elastic tube and D/2 which is because of the changeof the refractive index of the fiber.

Du1 ¼ 22pnDL

k¼ 2

4p2nDNk

ð14Þ

The normal phase sensitivity of the fiber which is underdirect pressure which is expressed as [15]

DuuDP

¼ 1

DPezf �

1

2n2½erfðP 11 þ P 12Þ þ ezf P 12�

� �ð15Þ

where ezf and erf are the axial strain and radial strain of thefiber, DP is the pressure directly applying to the fiber, Pij

(i, j = 1,2) is the Pockels’ coefficients of the fiber core.In the certain boundary condition, the fiber is applied to

the axial load with the axial displacement DL, and the D/2

could be expressed according to (15):

Du2 ¼ �22pnDL

kP c ¼ �2

4p2nDNk

P c ð16Þ

Fig. 6. Diagram of the measurement setup. (A panel is diagram ofmeasurement in which the frequency is between 10 and 1000 Hz, B panel isthat of between 1 k and 40 kHz.)

98 K. Yin et al. / Optics Communications 281 (2008) 94–101

where Pc is the photonic elastic coefficient:

P c ¼1

2n2

eff ½�lf P 11 þ ð1� lfÞP 12�

Then

Du ¼ Du1 þ Du2

The phase sensitivity of three-dimensional model could bewritten as

DuP s three

¼ D/1

P s

þ D/2

P s

¼ 24p2nN

kx�ð1� P cÞ ð17Þ

And the normal phase sensitivity is

DuuP s three

¼ 2pb

x�ð1� P cÞ ð18Þ

Table 1Air-backed mandrel hydrophone performance example

Elastic tube E (GPa) l a (mm) b (mm)6.5 0.35 5 6

Mandrel E Æ (GPa) S Æ (mm2)71 37.7

Fiber (SM) Ef (GPa) SF (mm2) n L (m) H (mm)73 1.23 · 10�2 1.456 5.18 25.8tf (l) P11 P12 lf

190 0.121 0.270 0.17

Optical light k (nm)1550

E and l is the elastic modulus and Possion’s ratio of the elastic tube, a andb is the inner and outer radius of the elastic tube, respectively, E* and S*

are elastic modulus and the effective area of the mandrel, Ef and lf areelastic modulus and Possion’s ratio of the optical-fiber core, n is therefractive index of the fiber core, L is the length of the sensing fiber, H isthe height of the fiber which is wounded on the elastic tube, tf is the outerdiameter of the fiber, P1 and P2 is the Pockels’ coefficients of the fiber core,and k is the wavelength of the optical light) is the elastic modulus andPossion’s ratio of the elastic tube, a and b is the inner and outer radius ofthe elastic tube, respectively, E* and S* are elastic modulus and theeffective area of the mandrel, Ef and lf are elastic modulus and Possion’sratio of the optical-fiber core, n is the refractive index of the fiber core, L isthe length of the sensing fiber, H is the height of the fiber which iswounded on the elastic tube, tf is the outer diameter of the fiber, P1 and P2

is the Pockels’ coefficients of the fiber core, and k is the wavelength of theoptical light.

2.4. Analysis of the phase sensitivity of two-dimensional

model

The two-dimensional model is different from three-dimensional model in axial strain:

uz ¼ 0

The deduced processes like above, and the phase sensitivityof two-dimensional model could be expressed as

DuP s two

¼ 24p2nNð1� P cÞy�kðE þ Ef SfNHy�Þ ð19Þ

where

y� ¼ bð1þ lÞ½a2 þ b2ð1� 2lÞ�b2 � a2

The expression of the phase sensitivity and the normal sen-sitivity are achieved, some examples hydrophones of thistype are made and tested in experiments later.

3. Experimental methods

Some experiments are taken to testify our theory anddesign. A schematic description of the phase sensitivitymeasurement is shown in Fig. 6. ‘‘A’’ panel in Fig. 6 showsa standard hydrophone test tank which is used to providethe low-frequency (10–1000 Hz) test environment for thefiber-optic hydrophone. For the high-frequency range of1 k–40 kHz, the hydrophones are mounted in the freeacoustic field measurement cistern and inspired by ahigh-frequency acoustic projector shown in the ‘‘B’’ panelin Fig. 6. For the phase sensitivity measurements, theapplied acoustic pressure was increased until the inducedpeak phase shift of the sensor reached 2p, a value easilydetectable with an oscilloscope. The laser FLSA-25-3-1550 (NP Photonics), the shaker is HTBISE 2202 whichis driven by Agilent 33120A signal generator, the referencehydrophone is RHA2-0205 (made by Hangzhou AppliedAcoustics Research Institute, China), the oscilloscope isAgilent 54622D, the free field measurement is tested in

National Defence Underwater Acoustic Metrology Centerin Hangzhou Applied Acoustics Research Institute.

4. Theoretical and experimental results

The following example illustrates the example of thetype of the air-baked mandrel hydrophone according toour model. The design parameters and the calculationresults are shown in Table 1.

According to the parameters above and the model,phase sensitivity of three-dimensional model is

DuP s three

¼ 0:0217 rad=Pa ¼ �153:2657 dB re rad=lPa

The normal phase sensitivity of three-dimensional model is

Du/P s three

¼ �292:9403 dB re rad=lPa

Fig. 8. Phase sensitivity versus length of the sensing fiber. (ai and bi are theinner and outer radius of the elastic tube, respectively which are defined inFig. 4. The other designing parameters are same as that in Table 1.)

K. Yin et al. / Optics Communications 281 (2008) 94–101 99

The phase sensitivity of two-dimensional model is

DuP s two

¼ �149:8111 dB re rad=l Pa

The theory determination of the example shows that thehydrophone is smart, lightweight and very sensitive.

Then some parameter analyses could be made accordingto the three-dimensional model.

The theoretical analyses of phase sensitivity versus elas-tic modulus of elastic tube are shown in Fig. 7. It could begained that phase sensitivity would be higher when elasticmodulus of elastic tube become smaller, thus choose amaterial with small elastic modulus could improve the per-formance of phase sensitivity. Three situations with thick-ness of elastic tube 1.25 mm, 1 mm, 0.75 mm areanalyzed, and the conclusion is that the thickness is smal-ler, the phase sensitivity is higher. It gives a indication thatthe thickness of the elastic tube could be produced smallerto improve the performance.

The theoretical analyses of phase sensitivity versuslength of the sensing fiber are shown in Fig. 8. It couldbe gained that phase sensitivity would be higher whenlength of the sensing fiber become longer, and the relation-ship between phase sensitivity and length of the sensingfiber is linear in both of logarithmic coordinates. Also itgives a indication that the thickness of the elastic tubecould be produced smaller to improve the performance.

Experimental results of the phase sensitivity of twenty-two air-backed hydrophones are shown in Fig. 9. Thelow-frequency (10–1000 Hz) test is in a standard hydropho-ne test tank shown in ‘‘A’’ panel in Fig. 6, and 1000–3000 Hz test is mounted in the free acoustic field shownin ‘‘B’’ panel in Fig. 6. The results show that the phase sen-sitivities of twenty-two hydrophones are distributedbetween �151 dB re rad/lPa and �155 dB re rad/lPaapproximately, and most effective experimental results con-

Fig. 7. Phase sensitivity versus elastic modulus of elastic tube. (ai and bi

are the inner and outer radius of the elastic tube, respectively whichare defined in Fig. 4. The other designing parameters are same as that inTable 1.)

Fig. 9. Experimental results of phase sensitivity of the twenty-twohydrophones over the 10–3000 Hz range.

centrated between �152 dB re rad/lPa and �154 dB rerad/lPa, and very flat in 3 kHz bandwidth. Thus thedesigned hydrophones satisfy most commercial and lowcost special applications.

Fig. 10 shows that the mean values of each hydropho-ne’s phase sensitivity over the 10–3000 Hz range inFig. 9, and the analytical results of both three-dimensionalmodel and two-dimensional model. The figure shows thatanalytical results of two-dimensional model are about2 dB re rad/lPa higher than the highest phase sensitivityof the measurement results, while that of three-dimensionalmodel is matching to the real results approximately. Thedistribution of the results denotes our model improve onthe accuracy of estimation of the phase sensitivity muchbetter.

Root mean square (RMS) in Table 2 show that only thatof 1 (4.5%) hydrophone is about 0.6 dB re rad/lPa, that of

Fig. 10. The mean values of each hydrophone’s phase sensitivity over the10–3000 Hz range. (The data error bars represent root mean squaresshown in Table 2.)

Fig. 11. Frequency responsivity of the F-A-9 hydrophone.

Fig. 12. Pressure responsivity of the F-A-8 hydrophone.

100 K. Yin et al. / Optics Communications 281 (2008) 94–101

2 (9.1%) hydrophones are between 0.1 and 0.2 dB re rad/lPa, that of 19 (86.4%) hydrophones are below 0.1 dB rerad/lPa. The results denote that uniformities of the hydro-phones are very high, thus the hydrophones could be pro-duced successfully following theoretical model andprinciples of design.

An experiment was executed for testing the frequencyresponsive bandwidth of the air-backed mandrel hydro-phone. The experimental result of the F-A-9 hydrophoneis shown in Fig. 11, and the intersection of two dash lineindicates the 3 dB bandwidth point. The testing frequencyis from 1.6 kHz to 40 kHz, and the result shows that themean phase sensitivity of the hydrophone is about�152 dB re rad/lPa, and the bandwidth of the frequencyresponse is at least 30 kHz @3dB.

An experiment was executed for testing the pressureresponsive of the air-backed mandrel hydrophone. Theexperimental result of the F-A-8 hydrophone is shown inFig. 12 in 800 Hz measurement. The responsive results ofthe experimental is relative to responsive in normal pres-sure which is set to 0 dB. The results show that the respon-sive is decreasing while pressure is increased. When thepressure is 2 MPa (200 m water depth), the responsivedecreases less than 0.5 dB, and decreased less than 3 dBwhile pressure is 4 MPa (400 m water depth). The reasonfor decreasing of the responsive could be the change ofmaterial character of encapsulant, the bucking pressure

Table 2RMS (Root Mean Square) of mean values of the twenty-two hydrophones se

Hydrophone number 1 2 3 4 5RMS (dB re rad/lPa) 0.6035 0.1354 0.0205 0.0961 0.03

Hydrophone number 12 13 14 15 16RMS (dB re rad/lPa) 0.0435 0.0599 0.0077 0.0336 0.01

of the sensing fiber, and so on. If the hydrophone is usedas towed array in shallow sea or bottom array on the shorebottom, the hydrophone designed could satisfy therequirement.

5. Conclusion

An optical-fiber air-backed mandrel hydrophone is pro-posed and investigated. The phase sensitivity of the hydro-phone is analyzed according to a two-dimensional and athree-dimensional quasistatic model, and experiment

nsitivity over the 10–3000 Hz range

6 7 8 9 10 1130 0.0128 0.0763 0.0060 0.0059 0.0411 0

17 18 19 20 21 2216 0.0030 0.1371 0.0945 0.0068 0.1900 0.0127

K. Yin et al. / Optics Communications 281 (2008) 94–101 101

results prove the correctness of the theory. The resultsshow that estimation of the three-dimensional model is bet-ter than that of two-dimensional model. The normal phasesensitivity achieves �308 dB re 1/ lPa, the 3 dB effectivebandwidth of the frequency response is 30 kHz, and theresponsivity decreases less than 0.5 dB when static pressureis 2 MPa (200 m water depth). The performance is shownthat the hydrophone could be used in general applica-tions.The size of the hydrophone is about B12 · 55 mm,thus the smart structure and performances of the hydro-phone shows that the air-backed mandrel hydrophonecould satisfy most applications in these fields. The analysesshow that using a proper material with low elastic moduluscould improve the performance of phase sensitivity greatly,also increase the length of the sensing fiber could achievethe purpose. But excessive long fiber is hard to wraparound the elastic tube, even wrapping two or more layersis not a better choice, due to complex production and poorperformance. Also the materials of the elastic tube andmandrel must be chosen carefully, because the phase sensi-tivity, frequency bandwidth or other performance are con-cerned with them. The hydrophone is produced bycommercial parts and simple structure, thus the hydropho-ne could be produced at low cost and applied in large-scalecommercial areas. This is more, it could be designedaccording to the model above to achieve the requiredperformances.

Acknowledgements

Kai Yin thanks the support of China National OffshoreOil Corp. China National 863 Program 2003AA602110-1,

Ke Guo, Hongfu Zhou, and Applied Acoustics ResearchInstitute, Hangzhou, China.

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