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Preliminary Investigation of Air-Included Polymer Coatings for Enhanced Sensitivity of Fiber-optic Acoustic Sensors James H. Cole*, Christopher Sundermad, Alan B. Tveten*, Clay Kirkendall* and Anthony Dandridge* *Optical Techniques Branch, Code 5670, Naval Research Laboratory, 4555 Overlook Ave. SW, Washington, DC 20375-5320,202: 404-4203, Fax 202: 767-5792, e-mail:
[email protected], tveten@,nrl.navv.mil, kirkendall@,nrl.navy.mil,
dandridcre(dnrl.navv.mil 0 SFA Inc., 93 15 Largo Drive West Suite 200, Largo, MD 20774, Phone: 202 404-5434, Fax 202: 767-5792, e-mail: sunderc(dnrl.navv.mil
Introduction Since the first fiber-optic acoustic sensors were reported the desire for a coated fiber that could provide adequate acoustic sensitivity for nominal lengths of fiber has yet to be realized. If achieved, this would simplify multi-sensor array fabrication resulting in appreciable system cost reduction. Isotropic polymer coatings that enhance the acoustic sensitivity of optical fibers have been studied extensively 3,4. A conclusion of Ref. 4 is that lowering the bulk modulus of the coating material increases the sensitivity. For isotropic polymer materials the bulk modulus is greater than 1 GigaPascal (GPa), which limits the acoustic sensitivity. Inclusion of air within the polymer coating dramatically increases the compliance and therefore the acoustic sensitivity. Previously, static measurements have been taken on such polymers’. We report here, the acoustically induced normalized phase sensitivity for polyurethane and uv-curable acrylate airincluded polymers (AIP) measured dynamically over the frequency range of 0.1 to 1 kHz. The measured sensitivity is compared with a simple model. ,$ ’’
Analysis The phase sensitivity of an optical fiber normalized to the total static phase is given by6 --=E, A(P
(P
--n 2 [(&I + & ) E r + &E, 1 2
(1)
where A$ is the change in phase induced by a change in the strain on the fiber, is the static phase, n is the index of refraction, Pij are the elasto-optic constants for hsed silica and ez and E, are the axial and radial strains respectively. Reference 4 describes the solution of Eq. (1) using the exact composition and geometry of multi-layer fibers. We are interested here in the case of thick-jacketed fibers where the phase change is dominated by the axial strain of the coating. The plane strain approximation’ has been shown to be in ood agreement with an exact calculation of the axial strain for multilayer structuresf. The plane strain approximation assumes that all layers of a composite, multi-layer fiber move together in a single plane when under stress. In thick-jacketed fiber sensing geometry, the axial strain dominates the radial strain and the second term in
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Eq. 1 can be ignored. This greatly simplifies the analysis since calculation of the radial strain requires a multi-layer analysis4.
Now we must calculate the axial strain in the coating, E ~for , a pressure change, AP7 E = - A1 - (1-20) -----
E
1 0
dp
(3)
where 1 is the length of the fiber, a i s Poisson’s ratio and E is the composite Young’s modulus of the fiber given by
E=
EJiber
*
AJiber
’Jib
+ Ecoating
*
Acoating
(4)
+ Acoating
where E and A are the Young’s moduli and the areas respectively of the fiber and coating as denoted by the subscripts. Figure 1 contains a plot of the normalized acoustic phase sensitivity versus the fiber coating diameter as a h c t i o n of Young’s modulus, E, with a fixed Bulk modulus, K=4.0 GPa as calculated by combining equations 2 through 4.
0
2
4
6
8
10
Coating Diameter in mm
The plot of Fig. 1 illustrates that the agreement of this simple model with the exact model of Ref. 4 is excellent near the sensitivity saturation limit. This model tends to nominally underestimate the sensitivity for low Young’s moduli and thin coatings. At the present time we are using this surrogate model and assuming that the elastic properties of the AIP can be represented by a single bulk and a single Young’s modulus. Measurements of the elastic moduli for the polymer materials both with and without air inclusion are ongoing and all results are not presently available.
318
Copting Diameter in mm
Figure 2 is a plot of the calculated and measured normalized phase sensitivities versus coating thickness for the polyurethane and uv-curable acrylate polymers under investigation. The dashed curves in Fig. 2 are for polyurethane. The lower curve is calculated for the base polymer and the upper curve for the AIP. The square data point represents the measured sensitivity of the AIP polyurethane. For the polyurethane, all elastic moduli have been measured. The upper and lower solid curves are calculated for a UV-curable acrylate and represent the AIP and the base polymer sensitivities respectively. The diamond is data measured for a fiber coated with the base polymer and the circles are for coatings with the AIP. Both base polymer and AIP data were measured over a frequency range of 0.1 to 1 kHz in a G40 acoustic calibrator. The shape of the curve for the base uv-curable acrylate is steeper at low coating thickness due a higher Young's modulus. In the uv-acrylate AIP case, neither the bulk nor the Young's modulus has been measured. The bulk modulus used in the calculation, was the geometric mean of the volume normalized bulk moduli of the polymer and of air at 1 atmosphere. The Young's moduli used to calculate the curve for the AIP was determined by iterative adjustment to obtain an eyeball fit to the data points. It should be noted that the geometric mean of the volume normalized bulk moduli for the case of polyurethane agrees exactly with the measured bulk modulus for the AIP polyurethane.
L
Figure 3
0 0
4
0
a
0
20 40 60 80 Percent Air- Encapsulation
31 9
100
Comparison of the AIP sensitivitiesto the base polymers sensitivities contained in Fig. 2 shows that a 40 times improvement in the acoustic sensitivity of polymer coated optical fiber has been achieved by air-inclusion.The calculated sensitivities indicate that it may be possible to achieve a 100 times improvement in acoustic sensitivity over isotropic polymers. Figure 3 plots the measured normalized phase response of a coated optical fiber versus the percent of air-inclusion by volume. In this case the response has been normalized by the coating diameter, d (mm), as well as the static phase. The data point at 0% represents the fiber response with a base polymer coating only, while the data point at 100% represents the response of the bare (uncoated) glass fiber. To avoid the singularity at 100% air, a coating of air lmm thick was assumed. The acoustic sensitivity of the coated fiber initially rises as the percentage of air is increased. Although not observed with the limited data presented here, as the percentage of air continues to increase, the coupling of the axial strain from the coating to glass fiber will degrade as the Young’s modulus (which controls this coupling) decreases. Thus, a maximum in acoustic sensitivity will be found for some optimum amount of air inclusion.
Conclusions In conclusion, a surrogate model to predict the normalized acoustic phase sensitivity for the case of thick polymer coatings has been presented. We have demonstrated a 40 times improvement in the normalized acoustic sensitivity of an airincluded polymer optical fiber coating over a similar fiber coating without air inclusion. Analysis indicates that air-included polymer optical fiber coatings may provide a factor of 100 times improvement over isotropic polymers. For a given polymer, a maximum sensitivity exists for an optimum percentage of air inclusion.
References 1. J. H. Cole, R. L. Johnson and P. G. Bhuta, “ Fiber Optic Detection of Sound”, J. Acoust. SOC. Amer. v62, p. 11361138,1977 2. J. A. Bucaro, H. D. Dardy and E. F. Carome, “Fiber Optic Hydrophone”, J. Acoust. SOC.Amer. ~ 6 2p., 1302-1304, 1977 3. R. Hughes and J. Jarzynski, “Static pressure sensitivity amplification in interferometric fiber-optic hydrophones”, Appl. Opt. v19; p. 98-107, 1980 4. Nicholas Lagakos, Edward U. Schnaus, James H. Cole, Jacek Jarzynski and Joseph A. Bucaro, “Optimizing Fiber Coatings for InterferometricAcoustic Sensors”, IEEE JQE. vQEr 18, p. 683689, 1982 5 . S. T. Vohra, A. Dandridge, C. C. Chang, G. A. Johnson, A. B. Tveten and G. M. Nau, “High Sensitivity Pressure Sensors Utilizing Advanced Polymer Coating”, Proc. of OFS- 13,p.557-560, 1998 6. Thomas G. Giallorenzi, Joseph A. Bucaro, Anthony Dandridge, G.H. Sigel, Jr., James H. Cole, Scott C. Rashleigh and Richard G. Priest, “Optical Fiber Sensor Technology”, IEEE JQE. vQE- 18, p. 626-665, 1982 7. B. Budiansky, D.C. Drucker, G.S. Kino, and J.R. Rice, “Pressure sensitivity of a clad optical fiber”, Appl. Opt. v18, pp 4085-4088, 1979 8. G. B. Hocker, “Fiber-optic acoustic sensors with composite structure: An analysis”, Appl. Opt. ~ 1 8p., 3679-3683,1979
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