1st Internatinal Sympsium n Laser Ultrasnics: Science, echnlgy and Applicatins July 16-18 008, Mntreal, Canada Displacement and Deflectin Sensitivity f Gas-cupled Laser Acustic Detectin James N. CARON 1, 1 Research Supprt Instruments Lanham, Maryland, USA; Phne: 301-306-0010, Fax 301-306-095; carn@rsimd.cm Quarktet Silver Spring, Maryland, USA; carn@quarktet.cm Abstract Ultrasund radiated frm a surface can change the path f an ptical beam, directed thrugh the acustic field and parallel t the surface, thrugh acust-ptic interactin. Sensing f the beam mtin with a psitin-sensitive detectr prduces a simple but effective nn-cntact ultrasund detectr, designated Gas-cupled Laser Acustic Detectin, r GCLAD. Recent research has shwn that the received signal is a cmbinatin f the deflectin and displacement f beam. he technique prved capable f detecting displacements f the beam, created by a transducer-generated airbrne ultrasund wave, f less than a micrmeter. Deflectins were recrded that measured less than a micrradian. he presented wrk estimates the sensitivity f GCLAD t an ultrasnic surface displacement. he results are cmpared t the sensitivities f mre standard ultrasund detectin methds. Keywrds: Laser ultrasund, ultrasund detectin, nn-cntact inspectin, ptical beam deflectin, ultrasund transducer. 1. Intrductin Airbrne ultrasund can be sensed by directing a laser beam thrugh the acustic disturbance. he disturbance causes a change in the ptical path f the beam that can be detected with a psitin-sensitive phtdetectr; a technique designated gas-cupled laser acustic detectin (GCLAD). [1-3] One such disturbance is the radiatin f an ultrasund wave frm the surface f a sample, generated with either a pulsed laser r ultrasund transducer. As shwn in Figure 1, the prbe beam passes parallel t the surface with a standff distance that has ranged between 1 mm and 3 cm. his enables laser-based ultrasund sensing that is nt dependent upn the ptical qualities f the sample surface. he methd prvides wideband sensing up t 8 MHz and cnsists f cmparatively simple ptics and electrnics. Cntinuuswave Laser z1 z Detectr θ r r 1 Surce Lens z3 z4 Figure 1. Arrangement fr bservatin f laser-generated ultrasnic wavefrms with GCLAD. Ultrasnic wavefrms, upn transmissin thrugh the material, radiate an airbrne wave, which mdulates the index f refractin transverse t the prbe beam and alters the path f the laser beam. he mvement is detected by a psitin-sensitive phtdetectr.
w imprtant achievements were prduced frm reference [4]. he first achievement was the verificatin that an airbrne ultrasund wave prduces a displacement as well as a deflectin f the laser beam, as illustrated in Figure. first rder, signal sensitivity t the deflectin f the beam is prprtinal t the distance between the interactin pint and the detectr. hus higher sensitivity cmes at the expense f a larger system. In previus wrk, [5] the sensitivity f the deflectin cmpnent has been cmpared t the sensitivity f ther NDE methds. In cntrast, the displacement cmpnent enables the system t be independent n the length f the ptical path, prducing a much smaller system. θ x Figure. he received signal was fund t be a cmbinatin f a deflectin (lef, r a cmbinatin f deflectins that give rise t a displacement (righ. he secnd achievement was the develpment f a quantitative measure f the angle f deflectin and the displacement amunt culd be calculated. In this wrk, these results are discussed and cmpared t the theretical sensitivity f the system.. hery he derivatin f the detectin f the deflectin and displacement cmpnents was presented in reference [4], but is summarized here. A split-cell, r bi-cell, phtdetectr is used t sense the psitin f the laser beam. he received signal at the detectr is 8GRκP 0 d c x d / 4 D c / 4 D ( ) ( ) [ c ω t ω Vtt x erf e e ] (1) 3 π ω D ωd where G is the gain f the amplifier, R is the resistance value that cnverts the current t a vltage, κ is the sensitivity f the phtcell, P 0 is the average pwer f the laser, d c is the width f the phtcell, ω D is the beam width at the detectr and t c is the separatin distance between the tw phtcells. his relatinship shws that fr small deviatins, the received signal is prprtinal t the beam displacement n the phtdetectr. he beam width at the detectr, with n lens in the ptical path, is calculated frm λz ω D ( = ω 1+ ( ) () πω n where ω is the riginal waist f the beam, z is the distance alng the ptical path, λ is the wavelength f light, and n is the index f refractin. he beam widthω D at the detectr, with a single cnvex lens f fcal length f in the ptical path, is
where s λ /πω n and A + B / s ω D ( = ω (3) A D B C A B 1 z4 / f z1 + z3 + z4 z4( z1 + z3 ) / f = C D 1/ f 1 ( z1 + z3) / f where z 1 + z3 is the distance frm the minimum beam waist (the laser) t the lens. (4) With n lens in the set-up, the relatinship between a deflectin f angle θ at the interactin pint and the beam displacement n the detectr is x = z θ. he displacement cmpnent is recrded with a cnvex lens inserted in t the ptical path. he displacement at the interactin pint x prduces a displacement at the detectr f x( x (1- z 4/f). (5) he received signal V(z, frm the phtdetectr was shwn t be a cmbinatin f the tw wavefrms V ( z, = A( x( + B( θ( (6) where A( describes hw the amplitude f the displaced wavefrm changes with distance, and B( describes hw the deflected wavefrm changes. estimate x(, we assume that clse t the interactin, as clse as the detectr can be placed, Vθ ( 0, << V x (0, such that x V x ( 0, / A(0). he beam deflectin θ( can be calculated frm V ( z, A( x( θ (. (7) B( 3. Experiment Figure 3. (Lef A displacement wavefrm measured very clse t the interactin pint and scaled using x V x ( 0, / A(0). (Righ A series f deflectin wavefrms calculated frm equatin (7) fr varius values f z.
Figure 3 (lef shws a displacement wavefrm created by a 1 MHz cntact transducer placed abut 1.3 cm frm the laser beam. his wavefrm shws that the laser beam was displaced by ttal amplitude f 1 µm. Wavefrms were captured as z 4 was increased frm.9 cm t 97 cm. Inserting the captured wavefrms int Equatin (7) prduced the family f curves in Figure 3 (righ. Since θ( is independent f z, these curves having similar amplitudes. he angle f deflectin has values that range frm 3 t 3 micrradians. 4. Analysis We can use the results abve t estimate the minimum detectin values fr a frequency f 1 MHz. he detectin limit ccurs when the signal-t-nise rati is unity. he nise level frm the displacement wavefrm that has been averaged ver 64 shts is 0.019 µm. hus, fr a single sht, the nise level is 0.15 µm. Frm the analysis in reference [5], the signal can be imprved 8% by inserting a lens int the system. (his has the added benefit f mving the detectr a cmfrtable distance frm the interactin pint.) hus, the minimal detectable beam displacement is abut 0.14 µm. Fr an average f 64 shts, the nise level fr beam deflectin where z 4 = 1 meter is 0.054 micrradians, prducing a single sht value f 0.44 µrad. Accrding t reference [5], a system with z 4 = 5.5 meters wuld increase sensitivity by 78%, prducing a minimum detectable beam deflectin f 0.5 µrad. Accrding t reference [5], the minimal detectable surface displacement (MDSD) [6,7] fr the deflectin cmpnent f GCLAD can be expressed as δ min α ' ν d g e nu = 4π b( n θ min 1) ν where n 0 is the ambient index f refractin, ν is the frequency f surface scillatins, u g is the speed f sund in air, b is the width f the interactin, d is the distance frm the surce t the ptical beam, and α is the attenuatin cefficient in air fr frequencies abve 00 khz. [8] his relatinship assumes the ultrasnic surce prduces a plane wave with insignificant transverse spreading f the wave frnt. Althugh this simplifies the calculatin, we nte that actual acustic envirnment is mre cmplicated. Using θ min = 0.5 µrad, n 0 = 1.0009, u g = 343 m/s, b = 0.8 cm, ν = 1 MHz, α = 10 11 m 1 Hz, and d = 1.3 cm, the MDSD is 0.4 nanmeters. Fr ν =1 MHz, the MDSD is 4. 10 13 mhz 1/. see hw this cmpares t theretical predictins, Figure 4 shws a graph with the MSDS pltted as a functin f frequency fr GCLAD (d = 1.3 cm and d = 0.4 cm) and a cnfcal Fabry-Pert (CFP) in transmissin and reflectin mde. [9] he lwer the line n the graph, the higher the sensitivity t a surface displacement.
Figure 4. Minimum detectable surface displacements fr GCLAD and Cnfcal Fabry-Pert Interfermeters. he 'X' shws the measured value fr a GCLAD system with d = 1.3 cm. he sensitivities were calculated with an average laser pwer f 0.13 Watts. he sensitivity f GCLAD cmpares well with a CFP interfermeter in the range f 1-3 MHz. his assumes that the surface under test has ideal ptical prperties. If the surface is less-than-ideal, the CFP sensitivity will decrease whereas the GCLAD curve remains cnstant. he X n the graph shws the measured value frm the analysis abve. he value ccurs mre than an rder f magnitude abve the theretical MDSD. We suspect the disagreement is partly due t the assumptin that the radiated wavefrm was mdelled as a plane wave. A mre cmplicated wavefrm wuld reduce the verall deflectin f the laser beam thrugh multiple interir deflectins. In additin, the wavelength f the radiated ultrasund is 0.34 mm, which is cmparable t the riginal width f the prbe laser beam. As the wavefrm passes thrugh the beam, prtins f the beam can deflect by different and ppsite angles. his wuld als reduce the amplitude f the received signal. Ideally, the laser prbe beam width shuld be significantly smaller than the ultrasund wavelength. he plane wave mdel als des nt give rise t a displacement wavefrm. A spherical wavefrm radiating frm the surface wuld result in a displacement cmpnent. Hwever, the additinal dimensin cmplicates the calculatin. Since the beam traverses the near-field f the acustic surce, even a spherical wavefrm may nt accurately describe the situatin. hus, future wrk will develp an imprved mdel f the radiated wavefrm in hpe f imprving the accuracy fr the deflectin cmpnent, and adequately describing the frequency dependence f the displacement cmpnent.
5. Cmments his wrk discussed the sensitivity f GCLAD fr the detectin f radiated ultrasund resulting frm a surface vibratin. he received GCLAD signal results frm the cmbinatin f a deflectin and a displacement f the ptical beam resulting frm an acustic disturbance in the beam path. he amunt f deflectin and displacement was measured and minimum detectin levels were estimated. his prduced a value fr the minimal detectable surface displacement that can be acquired using the deflectin cmpnent f GCLAD. he MDSD value was mre than an rder f magnitude higher than the theretical value. Hwever, we feel that narrwing the laser beam width, and using a mre sphisticated mdel can mitigate the difference between thery and experiment. References 1. J.N. Carn, Y. Yang, J.B. Mehl, and K.V. Steiner, Gas cupled laser acustic detectin fr ultrasund inspectin f cmpsite materials, Materials Evaluatin, Vl. 58, N. 5, pp. 667-671, 001.. J.N Carn, Y. Yang, J.B. Mehl and K.V. Steiner, Gas-cupled Laser Acustic Detectin at Ultrasnic and Audible Frequencies, Review f Scientific Instruments, Vl. 69(8), pp. 91-917, 1998. 3. J.N Carn, Y. Yang, J.B. Mehl and K.V. Steiner, Gas-cupled Laser Acustic Detectin, US Patent N. 6 041 00, March 1, 000. 4. J.N. Carn, Displacement and Deflectin f an Optical Beam by Airbrne Ultrasund, Review f Prgress in Quantitative Nndestructive Evaluatin, ed. by D.O. hmpsn and D.E. Chimenti, AIP, Vl. 7, 008. 5. J.N. Carn, Y. Yang, J.B. Mehl and K.V. Steiner, Prgress in Gas-cupled Laser Acustic Detectin, Review f Prgress in Quantitative Nndestructive Evaluatin, ed. by D.O. hmpsn and D.E. Chimenti, Vl. 18, p. 317, 1998. 6. J.W. Wagner and J.B. Spicer, heretical Nise-Limited Sensitivity f Classical Interfermetry, Jurnal f the Optical Sciety f America B, Vl. 4, n. 8, p. 1316, 1987. 7. E.S. Bltz, C.M. Frtunk, M.A. Hamstad, and M.C. Renken, Abslute Sensitivity f Air, Light, and Direct-Cupled Wideband Acustic Emissin ransducers, Review f Prgress in Quantitative Nndestructive Evaluatin, ed. by D.O. hmpsn and D.E. Chimenti, Vl. 14, p. 967, 1995. 8. R. Hickling and S.P. Marin, "he Use f Ultrasnics fr Gauging and Prximity Sensing in Air," Jurnal f the Acustical Sciety f America, Vl. 79, n. 4, p. 1151, 1986. 9. J.-P. Mnchalin and R. Hén, Laser Generatin and Optical Detectin with a Cnfcal Fabry-Pert Interfermeter, Materials Evaluatin, Vl. 44, 1986, p. 13.