Theory and experiment for single lens fiber optical microphone

Transcription

1 Available online at Physics Physics Pocedia 3 (010) 00 (009) ntenational Congess on Ultasonics, Univesidad de Santiago de Chile, Januay 009 Theoy and expeiment fo single lens fibe optical micophone João Macos Salvi Sakamoto *, Gefeson Mendes Pacheco nstituto Tecnológico de Aeonáutica, Paça Maechal Eduado Gomes, 50 Vila das Acácias, CEP , São José dos Campos, SP, Basil Elsevie use only: Received date hee; evised date hee; accepted date hee Abstact This wok epots a theoy fo the single lens fibe optical micophone. Computational simulation and expeimental esults wee compaed pesenting good ageement. t is shown that the opeating pinciple of this micophone is based in membane tilt angle vaiation athe than membane longitudinal displacement. PACS:43.38+n, z Keywods: fibe optical micophone; acoustic senso; nondestuctive essay 1. ntoduction nteest on fibe optical micophone, FOM, is elated to the advantages that an optical senso has ove conventional sensos, such as electical and chemical passiveness and electomagnetic intefeence immunity. n addition, long distances between the micophone and the electonic cicuit ae suppoted due to the low loss chaacteistic of optical fibe. These featues make feasible the employ of a FOM as an altenative way to applications in suveillance, militay, medicine, obotics, and noncontact o nondestuctive essays [1]-[4]. n the FOM configuation poposed in this wok, diffeently fom classic configuations [5], [6] a lens is used and the pinciple of opeation based in back and fowad movement of membane is not valid anymoe. Feldmann and Büttgenbach [7] developed a two lens fibe optical micophone and used the classical appoach to explain the behavio of this micophone, but unlike suggested by these authos, a back and fowad movement will not cause the light modulation since lens focus the paallels beams at the same point. The theoetical analysis pesented in an ealy wok by the authos [8], povided the computational simulation and in this wok it is compaed to expeimental data. * Coesponding autho. Tel.: ; fax: addess: jmss@ita.b doi: /j.phpo

2 65 J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco/ Physics Pocedia 00 (010) Theoy.1. Micophone scheme The poposed fibe optical micophone consists of two optical fibes (tansmitting and eceiving ones), one positive lens, and one eflective membane, as shown in Fig. 1. The light emeges fom the tansmitting fibe in a conical shape limited by the citical angle o, until it eaches the lens. The distance, d o, between the lens and the tansmitting fibe is set to obtain a collimated beam afte lens. Supposing that membane is tilted by an angle elative to y axis, the collimated beam eaches the membane with incidence angle elative to the membane nomal, and is eflected with the same angle. Total deviation is equal to. Afte going though the lens again, the beam is focused eaching the eceiving fibe coe. The tilt of the membane is necessay to light impinge the coe of eceiving fibe since tansmitting and eceiving fibes ae spatially sepaated. Fig.1 Detailed scheme of fibe optical micophone head with a single lens and tilted membane. The paametes shown in Fig. 1 ae the following: a, b and c ae coe adius, cladding adius, and cladding thickness of tansmitting fibe; n 1 and n ae the efactive indexes of coe and cladding, espectively; a, b and c ae coe adius, cladding adius and cladding thickness of eceiving fibe; m is the distance between the cente of fibes and is the gap between fibes; d 1 is the distance between lens and eflective membane; P is the total powe of the beam incident in the entance plane of eceiving fibe, z = 0, and P o is the powe coupled to eceiving fibe coe; y 1 and 1 ae the height and angle of the cente ay at membane, o plane z = d o + d 1 ; y and ae the height and angle of the cente ay at fibes plane, o z = 0. The angle o is given by sin 1 NA n (1) o / whee n is the ai efactive index and NA is the tansmitting fibe numeical apetue, given by NA () n 1 n The distance d o is given by do f a tan o (3) whee f is the lens focal distance. n the next section powe tansfe coefficient,, i.e., the atio between the powe coupled to the eceiving fibe, P o, and the total powe incident on its suface, P, is calculated to detemine how amplitude modulation of light occus in this micophone.

3 .. Pinciple of opeation J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco / Physics Pocedia 00 (010) Powe tansfe coefficient The intensity distibution pofile of the optical beam fom tansmitting fibe can be egaded as gaussian and can be witten in cylindical coodinate as w e (4) whee is the adial coodinate, is the optical intensity at the cente of the coss section plane, is a constant elated to the modal powe distibution in the fibe, and w is the beam (o spot) adius. ntegating (4) ove the total spot aea, S, one can find the elation between the optical powe P and the optical intensity on the entance plane of eceiving fibe, as follows: P w ds d d 0 0 (5) whee ds is the aea diffeential element of S. Then the optical intensity distibution in tems of P can be witten as w P e (6) w The optical powe coupled to the eceiving fibe can be calculated integating (6) ove incident light aea on coe: P o ds R P w 1 e w d (7) whee ds R is the aea diffeential element of the intesection aea, S R, between spot and fibe coe. The angle between y axis and the line connecting the cente of spot to the intesection point of coe and spot is given by 1 d a cos (8) d Finally, egading tansmission losses in inteface ai-eceiving fibe as a constant, the powe tansfe coefficient is as follows: 1 w Po e d (9) P w With (9) it is possible to calculate fo each spot position elative to the cente of eceiving fibe. Such position detemines the integation limits. The two paametes which the authos take in account as the cause of vaiations in spot positions ae d 1 and. n Fig., the x and y axis have the oigin in cente of tansmitting fibe coe. The x and y axis ae placed in the cente of spot and move with it. The paamete d is the distance between cente of eceiving fibe coe and cente of spot, and is given by d m (10) y

4 654 J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco/ Physics Pocedia 00 (010) whee the distance m is m a a c c (11) R R Fig. Geometic scheme showing tansmitting and eceiving fibes and the light spot impinging eceiving one.... Spot position Analyzing only the cental ay of the eflected beam, knowing its position and angle (y 1, 1 ) at the membane and using ABCD matix, it is possible to detemine the position and angle (y, ) at the eceiving fibe. Since is quite small, a paaxial appoximation and the following ABCD matix can be used: y 1 0 d o f d1 y1 1 1 As can be seen in Fig. 1, it was stated that y 1 = 0 and 1 =. With (1) one can vay d 1 o paamete to find the spot position y...3. ntegation limits n ode to detemine the integation limits 1 and, the spot position was divided in fou egions. The fist egion initiates when the spot stats to ente the coe of eceiving fibe and it ends immediately afte spot entes completely on coe, which means a w d a w (1)

5 and the integation limits ae J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco / Physics Pocedia 00 (010) d a w The second egion occus when spot is completely on coe until the cente of spot each the cente of coe, i.e., and the integation limits ae 0 d a w, 1 w w The integal is consideed symmetic fo d < 0 and the thid and fouth egions ae symmetic to fist and second, espectively. 3. Results The esults pesented in this section efe to static calibation cuves of micophone. The fist cuve was obtained vaying the tilt angle of membane,, to a fixed position d 1. The second cuve was obtained vaying the position d 1 to a fixed angle Micophone paametes The fibe optical micophone mounted in laboatoy was built using a light souce, two step-index optical fibes, a lens, a eflective membane mounted ove tanslation and otation stages, and a photodetecto. This system is shown in Fig. 3. (13) (14) Fig.3 Photogaphy of the fibe optical micophone. The light souce in this case was an He-Ne lase with 633 nm wavelength and 30 mw powe. A PN photodiode OPF480 was employed as photodetecto. The eflective membane used was a dielectic mica film with 19.4 mm adius and 60 m thickness. The membane was mounted in a cicula suppot, fixed at the bodes. The pupose of this wok was not a membane analysis, and then its paametes wee not subject of concen. The tansmitting fibe has the following chaacteistics: monomode, 1330 nm opeating wavelength, a = 4 m, b = 60 m, and efaction indexes n 1 = (coe) and n = (cladding), esulting in NA 0.1. The eceiving fibe has the following elevant chaacteistics: multimode, a R = 13 m, and b R = 60 m. The gap between fibes is egaded as = 0, then

6 656 J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco/ Physics Pocedia 00 (010) m = 10 m. The lens had a focal distance f = 8 mm. As mentioned befoe y 1 = 0, 1 =. The calculated paametes ae o 11 mad and d o 7.96 mm. The spot adius was consideed as w = 1 m and =. Expeimental and simulation esults ae compaed in the next sections. 3.. Tilt angle vaiation Fistly, to evaluate the vaiation as a function of tilt angle vaiation, fo a given constant d1, it was used (1) to detemine the y position, d position with (10) and the integation limits 1 and with (13) o (14). Then was calculated using (9). This calculation was done though compute simulation to each value, and the esult was nomalized. The set of the following paametes wee used: d 1 = 60 mm, and anges fom 5 to 10 mad. Fig. 4 displays the simulation esult fo as function of in the black solid line. The measuement was done using a otation stage to vay membane angle, maintaining distance d 1 = 60 mm. The photodetecto output was measued to each angle, measued with the otation stage scale, and the esult was nomalized. The expeimental esult is shown in Fig. 4 in the ed makes. Fig.4 Expeimental and simulation cuves of powe tansfe coefficient vesus vaiation. The cuve showed in Fig. 4 indicates that small vaiations in membane angle,, can cause lage vaiations in. Fo a vaiation fom 10% to 90% it is necessay a tilt angle vaiation of appoximately 0.85 mad. Regading the positive slope of cuve and the expeimental data, the calibation facto obtained was appoximately 98 ad/v, which means that a 1 V incease at the photodetecto output coesponds to a incease of 98 ad in tilt angle Longitudinal displacement Secondly, it is evaluated how longitudinal vaiation in distance between membane and lens, d 1, can cause vaiations on powe tansfe coefficient. Now the vaiable in (1) is d 1 and to each value of it, one can detemine y, d, 1, and. The computational simulation was done to a fixed, appoximately equals to 8.3 mad. This angle is the one which gives the maximum output to the initial value of d 1. n this case, d 1 anges fom 60 to 00 mm. The esult was nomalized and is shown in the black solid line in Fig. 5. The membane suppot was fixed in a tanslation stage with a micomete to povide longitudinal displacement, o d 1 vaiation. Then to each position d 1 was measued the optical intensity with the photodetecto. The measuement was done fo d 1 fom 60 to 83 mm due to tanslation stage limitation. This cuve is shown in ed makes in Fig. 5 and it was nomalized to compae with simulation. n Fig. 5 one can ealize that a lage displacement d 1 is necessay to have optical amplitude modulation. Note

7 J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco / Physics Pocedia 00 (010) that a vaiation fom 10% to 90% needs a displacement of appoximately 80 mm. n othe wods, egading that membane movement is a longitudinal displacement, the micophone would have a vey low sensitivity. The calibation facto obtained to this cuve was -8.9 mm/v, which means that a 1 V decease in output voltage coesponds to an incease of appoximately 8.9 mm in distance between membane and lens. Fig.5 Expeimental and simulation cuves of powe tansfe coefficient vesus d 1 vaiation. 4. Conclusion Accoding esults obtained by computational simulation and cooboated by expeiment, to obtain a modulation of light coespondent to an output voltage of 1 V, though longitudinal displacement, it is necessay an unealistic movement of membane aound 8.9 mm. On the othe hand, to obtain the same amount of light modulation, though membane tilt angle vaiation, it is necessay only 98 ad. As can be concluded, the esults indicated that the main modulation paamete of this micophone is the membane tilt angle vaiation instead the membane longitudinal displacement. This occus as a consequence of the collimating and focusing lens effect. t is impotant to point out that the pesented esult claifies the misundestanding of the two lens micophone [7], in which the authos use the back and fowad displacement of membane to explain the light intensity modulation. Physically, the tilt angle vaiation is due to actual membane movement, which is fee on cente to displace and it is fixed at the bode. This cente displacement causes a membane cuvatue. Such cuvatue coesponds to a tilt angle, especially if the light beam povided by tansmitting fibe is positioned off cente of membane. Also, since membane has a small diamete, about 19.4 mm, the actual longitudinal membane movement is less than 1 mm, which cannot poduce a detectable modulation of light. Analyzing the chaacteistic cuve of powe tansfe coefficient vesus tilt angle one can ealize that it pesents linea egions appopiated to choose a suitable static opeation point, in which membane tilt angle is conveted in optical powe vaiation. To obtain high sensitivity and maximum dynamic ange, the static opeation point must be achieved setting the angle to dop to half of its maximum value. At this point, the micophone can be used to detect the dynamic vibation of membane, o the acoustic waves. This use was shown befoe by the authos in [8]. Acknowledgements Wok suppoted by the National Counsel of Technological and Scientific Development, CNPq. The authos wish to thank the Electonic Wafae Laboatoy, LABGE, of TA by some optical components help.

8 658 J.M. Salvi Sakamoto, G.M. Pacheco / Physics Pocedia 3 (010) João M.S. Sakamoto, Gefeson M. Pacheco/ Physics Pocedia 00 (010) Refeences [1] J.P.F. Woole, B. Hodde and R.. Cickmoe, Acoustic popeties of a fibe-lase micophone, Meas. Sci. Technol., vol. 18, pp , Feb [] P. McDowell, B. Bougeois, P. J. McDowell, S. S. yenga, J. Chen, Relative positioning fo team obot navigation, Autonomous Robots., vol., nº.5, pp , Feb [3] C. M. Taweek, T. A. Wettegen, Efficient Senso Chaacteistic Selection fo Cost-Effective Distibuted Senso Netwoks, EEE Jounal of Oceanic Engineeing, vol. 31, nº., pp , Ap [4] M. S. NessAive, M. Stone, V. Pathasaathy, Y. Kahana, A. Paistky Recoding High Quality Speech Duing Tagged Cine-MR Studies Using a Fibe Optic Micophone, Jounal of Magnetic Resonance maging 3:9-97, 006. [5] J.A. Bucao, N. Lagakos, Lightweight fibe optic micophones and acceleometes, Rev. Sci. nstum., vol. 7, n o 6, pp , Jun [6] J. A. Bucao, N. Lagakos, B. H. Houston, Miniatue, high pefomance, low-cost fibe optic micophone, J. Acoust. Soc. Am., vol. 118, pp , Sep [7] M. Feldmann and S. Büttgenbach, Micooptical Distance Senso with ntegated Micooptics applied to an Optical Micophone, EEE Sensos 005, vine, CA, USA, pp , Nov [8] J. M. S. Sakamoto, E. C. Pimenta J., G. M. Pacheco, Analysis of a single lens fibe optical micophone configuation, MOMAG 008, pp , 008.