Aug 15, 2002 - Received February 20, 2002. A novel concept for an intrinsic relative humidity (RH) sensor that uses polyimide-recoated fiber Bragg gratings.
August 15, 2002 / Vol. 27, No. 16 / OPTICS LETTERS
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Relative humidity sensor with optical fiber Bragg gratings Pascal Kronenberg and Pramod K. Rastogi Institute of Structural Engineering and Mechanics, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland
Philippe Giaccari and Hans G. Limberger Institute of Applied Optics, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland Received February 20, 2002 A novel concept for an intrinsic relative humidity (RH) sensor that uses polyimide-recoated fiber Bragg gratings is presented. Tests in a controlled environment indicate that the sensor has a linear, reversible, and accurate response behavior at 10 – 90% RH and at 13– 60 ±C. The RH and temperature sensitivities were measured as a function of coating thickness, and the thermal and hygroscopic expansion coefficients of the polyimide coating were determined. © 2002 Optical Society of America OCIS codes: 060.2370, 060.2400, 160.5470.
Numerous applications such as chemical processing, air conditioning, agriculture, food storage, and civil engineering require humidity sensing. Several researchers have reported on the measurement of relative humidity (RH) in air by use of optical fiber sensors, which are particularly valued for their performance in harsh environments. Optical sensing techniques proposed so far include extrinsic interferometric1 and spectroscopic2 point sensors as well as intrinsic evanescent-field3 and microbend-loss4 based distributed sensors. Recently Giaccari et al.5 presented a study of the inf luence of RH and temperature on a commercial polyimide-recoated f iber Bragg grating. Here we explore a novel concept for an intrinsic RH point sensor that uses polyimide-recoated fiber Bragg gratings. We describe the steady-state RH and temperature response of the sensor as a function of the fiber coating thickness, which also allows us to determine the thermal and hygroscopic expansion coeff icients of the polyimide. Fiber Bragg grating sensors have been topic of sizable research efforts in recent years.6 A fiber Bragg grating is a permanent, periodically index-changing structure written into the core of an optical fiber. Fiber Bragg gratings are attractive sensing elements because they exhibit a response that is reversible, accurate, and stable over long time periods, can be used for absolute measurements, and can be readily applied to in-line multiplexed sensor chains. Their use in such sensor chains makes it possible to set up multipoint and multiparameter (e.g., strain, temperature) single-f iber sensors. Bare silica fibers are not sensitive to humidity. Polyimide polymers, however, are hygroscopic and swell in aqueous media as the water molecules migrate into them. As with the hair in a mechanical absorption hygrometer, the swelling of the polyimide coating strains the fiber, which modif ies the Bragg condition of the f iber Bragg grating and thus serves as the basis of the proposed sensor. It has already been shown that the response behavior of a polyimide-recoated f iber Bragg grating is a linear superposition of RH and temperature (T) effects.5 In the presence of variations in relative humidity, DRH, and temperature, DT, the relative Bragg wavelength shift Dl兾l is therefore given by 0146-9592/02/161385-03$15.00/0
Dl兾l 苷 SRH DRH 1 ST DT ,
(1)
where SRH and ST are the sensor sensitivities to relative humidity and temperature, respectively. To relate the sensitivities to material properties, one may express SRH as the sum of a mechanical, a strain-optic, and, for ST only, a thermo-optic contribution: ˆ e 共bcf 2 bf 兲 关%RH21 兴 , SRH 苷 bcf 2 p ˆ e 共acf 2 af 兲 1 j 关K21 兴 , ST 苷 acf 2 p
(2) (3)
where bi is the hygroscopic longitudinal expansion coefficient, which is zero for bare f iber, and ai is the thermal longitudinal expansion coeff icient. The subscript stands for bare f iber 共i 苷 f 兲, coating 共i 苷 c兲, and coated 2 关p12 1 ef , r 兾ef , z 共p11 1 p12 兲兴兾2 fiber 共i 苷 cf 兲. pˆ e 苷 neff is the effective photoelastic coefficient of the coated fiber, where neff is the effective refractive index of the mode, pij are the coefficients of the strain-optic tensor, and ef , r and ef , z are the radial and axial elastic fiber strains, respectively. j is the thermo-optic coeff icient of the fiber core. The mechanical behavior of the coated fiber is modeled with an infinitely long, bimaterial composite rod wherein the two materials cohere perfectly. The RH- or T-induced differential expansion of the f iber and coating materials introduces strain in the f iber. For a one-dimensional (1-D), purely axial model, the equilibrium and compatibility conditions are sf Af 1 sc Ac 苷 0 and DLf 兾L 苷 DLc 兾L 苷 bcf DRH 1 acf DT, respectively, where si is the normal stress, Ai is the cross-section area, and DLi 兾L 苷 ei, z 1 bi DRH 1 ai DT is the relative deformation. Assuming that silica and polyimide are isotropic and behave linearly elastically, we can use Hooke’s constitutive law to express the elastic strain, ei, z 苷 si 兾Ei , where Ei is Young’s modulus. Based on these relations the longitudinal expansion coefficients of the coated fiber are the sums of the stiffness-weighted expansion coefficients of the bare f iber and of the coating, i.e., bcf 苷 kf bf 1 kc bc and acf 苷 kf af 1 kc ac , where © 2002 Optical Society of America
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P ki 苷 Ei Ai 兾 Ej Aj is the stiffness proportion. Regarding pˆ e we note that, with the 1-D model, ´f, r is set to zero (no radial strain). For a more realistic simulation of the mechanical behavior of the coated fiber that also takes into account both radial and tangential effects, a three-dimensional (3-D) f inite element model was employed. The sensor’s responses to RH and T were measured experimentally in a computer-controlled climatic chamber. A linear array of eight f iber Bragg gratings written in SMF 28–type fiber with several Bragg wavelengths in the 1550-nm band was spliced together and integrated into a fiber Bragg grating measurement setup (Fig. 1). The ref lected spectra were demodulated with a f iber Bragg grating interrogation system (FBG-IS) based on a fiber Fabry – Perot tunable filter with a wavelength resolution of 1 pm. For reference monitoring, an industry-standardscompliant, combined resistive T and capacitive RH gauge from Rotronic was placed next to the gratings. To quantify the inf luence of the coating thickness on the sensor sensitivity, we installed one bare grating (FBG 1) and seven gratings with average coating thicknesses of 3.6 (FBG 2), 6.6 (FBG 3), 11.8 (FBG 4), 18.7 (FBG 5), 21.3 (FBG 6), 27.3 (FBG 7), and 29.3 (FBG 8) mm, respectively, in the measurement system. The coating thickness, measured by microscope, exhibited an uncertainty of 61 mm that was due to nonhomogeneity. All gratings were fabricated in house and, with the exception of FBG 1, mold coated in a Vytran UV recoater. The polyimide used for coating was obtained from HD MicroSystems (Pyralin) and contains a UV-curable component, which we employed to transform the liquid polymer into a soft gel before proceeding with the heat cure. The coating procedure had to be repeated several times to yield thicker coatings. For tests related to sensor characterization and calibration, the climatic chamber was set to maintain a constant temperature during RH cycles. The RH was raised incrementally from 10% to 90% and then lowered back to 10% for f ive different temperatures that ranged from 13 to 60 ±C. The highest temperature achievable is limited by the maximum operating range of the electrical gauge. Yet additional tests showed that the sensor was not damaged by being exposed to temperatures ranging from 220 to 160 ±C. For each RH and T combination, we made measurements at 1-min intervals for 2 h to make sure that the water content within the polyimide reached an equilibrium state. As a rule, the Bragg wavelength shift saturates after a few minutes.5 Figure 2 shows the relative Bragg wavelength shift of FBG 8 as a function of RH (steady-state average values) for f ive temperatures. The sensor response, and hence the polyimide swelling, is reversible.5 An increase in RH or T will shift the Bragg wavelength to higher values. Experimental data were found to vary linearly with changes in RH and T, as assumed in the model described in Eq. (1), conf irming a linear relationship between RH and polyimide expansion. A two-dimensional linear regression of the T and RH data led to T and RH sensitivities ST 苷 共7.79 6 0.08兲 3 1026 K21 and
SRH 苷 共2.21 6 0.10兲 3 1026 % RH21 , respectively. The errors resulted from measurement uncertainties. With the application of a quadratic regression, the quadratic and mixed terms were smaller than the uncertainties, a result that demonstrates that the material properties were not signif icantly inf luenced over the tested temperature range, by T or by RH. Figure 3 shows the RH and T sensitivities with respect to the cross-section area of the polyimide coating, Ac , for all f iber Bragg gratings. For low ratios of coating to fiber cross-section area, the fitted curves, which correspond to the sensitivity models [Eqs. (2) and (3)], show an almost linear dependence of SRH and ST on Ac . The deviation from linearity was less than 4% for the coating thicknesses used in this research. For thicker coatings the sensitivities eventually saturate asymptotically. As for the bare grating, SRH 苷 0 K21 , whereas ST 苷 共6.31 6 0.05兲 3 1026 K21 , which matches the temperature sensitivity obtained
Fig. 1.
Experimental setup.
Fig. 2. Relative Bragg wavelength shift of FBG 8 as a function of RH for several values of T.
Fig. 3. T and RH sensitivities of f iber Bragg gratings with several polyimide coating thicknesses.
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August 15, 2002 / Vol. 27, No. 16 / OPTICS LETTERS Table 1. Properties of Fiber and Coating Materials This Work Parameter Fiber (silica) Young’s modulus, Ef 共GPa兲 Thermal expansion coeff icient, af 共1025 K21 兲 Hygroscopic expansion coefficient, bf 共%RH21 兲 Thermo-optic coeff icient, j 共1025 K21 兲 Effective refractive index of the mode, neff Strain-optic coeff icient, p11 Strain-optic coeff icient, p12 Coating (polyimide) Young’s modulus, Ec 共GPa兲 Thermal expansion coeff icient, ac 共1025 K21 兲 Hygroscopic expansion coeff icient, bc 共1025 %RH21 兲
1-D
3-D
0 0.581a
5.5 8.3
4.9 7.4
Other Work
(Reference)
72 0.05 0 0.617b 1.446a 0.121 0.270
(7) (8)
2.45 4
(9) (9)
(6) (8) (8)
a Wavelength, b
1550 nm. Wavelength, 1310 nm.
by means of an independent calibration measurement made with a thermostatic water bath. Using the known thermal expansion coeff icient of the f iber, af , we obtained the thermo-optic coefficient j (Table 1). Our value is different from the values found in the literature,6 which might be due to the dependence of j on wavelength, temperature, and core doping. Given the typical mechanical properties of a silica fiber, Ef 苷 72 GPa,7 and af 苷 0.05 3 1025 K21 ,8 the bare-fiber diameter of 127 mm and the modulus of the polyimide, Ec 苷 2.45 GPa,9 we may determine the thermal and hygroscopic expansion coeff icients of the polyimide. By f itting Eqs. (2) and (3) based on the 1-D model to the experimental SRH and ST data we obtained expansion coefficients bc1-D 苷 8.3 3 1025 %RH21 and ac1-D 苷 5.5 3 1025 K21 , respectively. Although the value of ac1-D was higher than the value given by the supplier 共4 3 1025 K21 兲,9 we could not trace any other value of bc in the literature. With ac1-D and bc1-D used in the 3-D model, we calculated as much as 16% higher sensitivities for the sensor geometries exploited in this research. Fitting the 3-D model to the experimental sensitivities yielded estimations of bc3-D 苷 7.4 3 1025 %RH21 and ac3-D 苷 4.9 3 1025 K21 . Table 1 lists the material properties determined in this research as well as reference values. We can note that bc is bigger than ac ; therefore SRH is more sensitive to changes in coating thickness than is ST . In summary, we have presented a new f iber-optic relative humidity sensor that uses polyimide-coated fiber Bragg gratings. Tests in a controlled climatic chamber showed a linear, reversible, and accurate sensor response for temperature and relative humidity ranges from 13 to 60±C and from 10 to 90% RH, respectively. We may easily compensate for the T cross sensitivity by using an additional bare fiber Bragg grating that is not RH sensitive.
The T and RH sensitivities depend on the coating thickness, with the sensor becoming more sensitive with increasing coating thickness. Using this interrelation, we were able to determine the hygroscopic and thermal expansion coeff icients of the polyimide coating. From a practical point of view, the sensor proposed here is easy to implement and may be readily integrated into a multipoint and multiparameter optical fiber Bragg grating sensor network because of its multiplexing capabilities. The authors thank G. Tirabassi of Rotronic AG, Switzerland, who kindly lent us a calibrated T and RH gauge. Ph. Giaccari acknowledges the support of the Swiss National Science Foundation. P. Kronenberg’s e-mail address is pascal.kronenberg@epf l.ch. References 1. F. Mitschke, Opt. Lett. 14, 967 (1989). 2. Q. Zhou, M. R. Shahriari, D. Kritz, and G. H. Sigel, Anal. Chem. 60, 2317 (1988). 3. A. Kharaz and B. E. Jones, Sensors Actuators A 46 – 47, 491 (1995). 4. W. C. Michie, B. Culshaw, A. McLean, M. Konstantaki, and S. Hadjiloucas, Cement Concrete Composites 19, 35 (1997). 5. Ph. Giaccari, H. G. Limberger, and P. Kronenberg, in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Vol. 61 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper BFB2. 6. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, J. Lightwave Technol. 15, 1442 (1997). 7. F. P. Mallinder and B. A. Proctor, Phys. Chem. Glasses 5, 91 (1964). 8. G. B. Hocker, Appl. Opt. 18, 1445 (1979). 9. Pyralin Product Information, HD MicroSystems (2001).
