6.2        Relative Humidity Sensor Using Optical Fiber Bragg Gratings

This section presents the paper that has been published in Optics Letters, 27 (16), p. 1385-7. The authors are :

-         Pascal Kronenberg, Pramod K. Rastogi : Institute of Structural Engineering and Mechanics, Swiss Federal Institute of Technology

-         Philippe Giaccari, Hans G. Limberger : Institute of Applied Optics, Swiss Federal Institute of Technology

This paper presents a novel concept for an intrinsic relative humidity sensor using polyimide-recoated fiber Bragg gratings. Tests in a controlled environment indicate that the sensor has a linear, reversible and accurate response behavior between 10 and 90 %RH and between 13 and 60 °C. The relative humidity and temperature sensitivities were measured as a function of the coating thickness and the thermal and hygroscopic expansion coefficients of the polyimide coating were determined.

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 in air using optical fiber sensors, which are particularly valued for their performance in harsh environments [1]. Optical sensing techniques proposed so far include extrinsic interferometric [2, 3] and spectroscopic [4] point sensors, as well as intrinsic evanescent-field [5] and microbend loss based [6] distributed sensors. Recently we presented a study on the influence of relative humidity and temperature on a commercial polyimide-recoated fiber Bragg grating [7]. Here we explore a novel concept for an intrinsic relative humidity point sensor using polyimide-recoated fiber Bragg gratings. We describe the steady state relative humidity 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 coefficients of the polyimide.

Fiber Bragg grating sensors have been a topic of sizeable research efforts in recent years [8]. 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 since they feature 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. The latter makes it possible to set up multi-point and multi-parameter (e.g. strain, temperature) single-fiber 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. Analogous to the hair in a mechanical hair hygrometer, the swelling of the polyimide coating induces strain in the fiber, which modifies the Bragg condition of the fiber Bragg grating and thus serves as the basis of the proposed sensor.

We have already shown that the response behavior of a polyimide-recoated fiber Bragg grating is a linear superposition of relative humidity and temperature effects [7]. In the presence of a variation in humidity and temperature, the relative Bragg wavelength shift, Δλ/λ, for relative humidity, ΔRH, and temperature changes, ΔT, is therefore given by

where S_RH and S_T are the sensor sensitivities to relative humidity and temperature, respectively.

To relate the sensitivities to material properties, S_RH and S_T may be expressed as the sum of a mechanical, a strain- and, for S_T only, a thermo-optic contribution:

and

where, β_cf and β_f are the hygroscopic expansion coefficients of the coated and the bare fiber - which is zero -, respectively; α_cf and α_f are the thermal expansion coefficients of the coated and the bare fiber, respectively. = n_eff² (p₁₂ + e_el,r / e_el,z (p₁₁ + p₁₂)) / 2 is the effective photo-elastic constant of the coated fiber, where n_eff is the effective refractive index of the fiber, p_ij are the Pockel's (piezo) coefficients of the strain-optic tensor, and e_el,r and e_el,z are the radial and axial elastic strains of the coated fiber, respectively. ξ is the thermo-optic coefficient of the fiber core.

The mechanical behavior of the coated fiber is modeled with an infinitely long, bi-material composite rod wherein the two materials cohere perfectly. As both materials exhibit different relative humidity and temperature sensitivities, the humidity- and temperature-induced constrained expansion exerts strain on the fiber. Assuming a one-dimensional (1-D), purely axial model, the equilibrium and compatibility conditions are s_fA_f + s_cA_c = 0 and e_f = e_c, respectively, where, s_i is the axial stress; A_i is the cross-section area; and e_i is the total, i.e. elastic and thermal / hygroscopic, axial strain of the fiber (i = f) and of the coating (i = c). With the deformation obeying an elastic, Hookean law, the hygroscopic and thermal expansion coefficients of the coated fiber are the sums of the stiffness weighted expansion coefficients of the bare fiber and of the coating, β_cf = k_fβ_f + k_cβ_c and α_cf = k_fα_f + k_cα_c, respectively. β_c and α_c are the hygroscopic and thermal expansion coefficients of the coating, k_i = E_iA_i / SE_jA_j is the stiffness proportion of the silica fiber and of the polyimide coating (i, j = f, c) with E_f and E_c being the moduli of silica and polyimide, respectively. Regarding , we notice that, using the 1-D model, e_el,r is set to zero (no radial strain). For a more realistic simulation of the mechanical behavior of the fiber, which also takes into account both radial and tangential effects, a 3-D finite element model was employed.

Fig. 1. Experimental setup.

The sensor response to relative humidity and temperature was experimentally measured in a computer controlled climatic chamber. An array of eight fiber Bragg gratings written in SMF 28 type fiber with different Bragg wavelengths in the 1550 nm band were spliced together and integrated into a fiber Bragg grating measurement setup (Fig. 1). The reflected spectrum was demodulated using a fiber Fabry-Perot tunable filter. For reference monitoring, an industry standards-compliant, combined resistive temperature (RTD) and capacitive relative humidity gauge from Rotronic was placed next to the gratings. A computer acquired the read out from the fiber Bragg grating interrogation system (FBG-IS) and from the reference gauge.

In order to quantify the influence of the coating thickness on the sensor sensitivity, one bare grating (FBG 1) and seven gratings with different 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 mm (FBG 8), respectively, were installed into the measurement system. The coating thickness, measured by microscope, exhibits an uncertainty of ± 1 mm due to non-homogeneity. All gratings were fabricated in-house and, with 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 is employed to transform the liquid polymer into a soft gel state before proceeding with the heat cure. The coating procedure had to be repeated several times to obtain thicker coatings.

For tests related to sensor characterization and calibration, the climatic chamber was set to maintain a constant temperature during relative humidity cycles. The relative humidity was incrementally raised from 10 to 90 %RH, and then lowered back down to 10 %RH, for five different temperatures between 13 and 60 °C. The highest temperature is limited by the maximum operating range of the electrical gauge. Yet additional tests have shown that the sensor is not damaged by being exposed to temperatures ranging from -20 up to 160 °C. For each relative humidity and temperature combination, measurements were taken in 1-minute intervals for two hours to make sure that the water content within the polyimide reaches an equilibrium state. As a rule, the Bragg wavelength shift saturates after a few minutes [7]. The changes in environmental conditions in the climatic chamber were monitored using the gauge, simultaneously with the recording of signals returned from each fiber Bragg grating.

Figure 2 shows the relative Bragg wavelength shift of FBG 8 as a function of relative humidity (steady state average values) for different temperatures. An increase in relative humidity or temperature shifts the Bragg wavelength to higher values. Experimental data are found to vary linearly with relative humidity and temperature changes, as assumed in the model described in eq. (1), confirming a linear relationship between relative humidity and polyimide expansion. A two-dimensional linear regression of the temperature and relative humidity data leads to temperature and relative humidity sensitivities of S_T = (7.79 ± 0.08)·10^-6 K^-1 and S_RH = (2.21 ± 0.10)·10^-6 %RH^-1, respectively. The errors result from measurement uncertainties. Applying a quadratic regression, the quadratic and mixed terms are smaller than the uncertainties, which demonstrates that the material properties are not significantly influenced over the tested temperature range, neither by temperature nor by relative humidity.

Fig. 2. Relative Bragg wavelength shift of FBG 8 as a function of relative humidity for different temperatures (zero relative Bragg wavelength shift arbitrary chosen).

The influence of relative humidity on the swelling of the polyimide is reversible, as the Bragg wavelength is the same at the beginning and at the end of a relative humidity cycle at constant temperature. Experiments have also shown a non-reversible component for temperatures exceeding values previously experienced. This may be due to a final thermal curing process needed for the polyimide to stabilize, and can be by-passed with an initial burn-in cycle.

Figure 3 shows the plots of the relative humidity, S_RH, and temperature sensitivities, S_T, with respect to cross-section areas of the polyimide coating, A_c, for all fiber Bragg gratings. For low coating to fiber cross-section area ratios, the fitted curves, which correspond to the sensitivity models (eqs. (2) and (3)), show an almost linear dependence of S_RH and S_T on A_c. The deviation from linearity is less than 4% for the coating thicknesses used in this work. For thicker coatings, the sensitivities eventually tend to saturate at values similar to those for bulk polyimide. As for the bare grating, S_RH = 0 K^-1, whereas S_T = (6.31 ± 0.05)·10^-6 K^-1, which matches the temperature sensitivity obtained via an independent calibration measurement using a thermostatic water bath. Using the known thermal expansion coefficient of the fiber, α_f, we obtain the thermo-optic coefficient ξ (table 1). Our value is different from the values found in literature, e.g. [8], which might be due to the dependence of ξ on wavelength, temperature and core doping. Given the typical mechanical properties of a silica fiber, E_f = 72 GPa [10] and α_f = 0.05·10^-5 K^-1 [9], the bare fiber diameter of 127 mm and the modulus of the polyimide, E_c = 2.45 GPa [11], we may determine the thermal and hygroscopic expansion coefficients of the polyimide. By fitting eqs. (2) and (3) based on the 1-D model to the corresponding S_RH and S_T data, the expansion coefficients become = 8.3·10^-5 %RH^-1 and = 5.5·10^-5 K^-1, respectively. While is higher than the value given by the supplier (4·10^-5 K^-1) [11], we could not trace any other value of β_c in the literature. With and used in the 3-D model, we calculated up to 16% higher sensitivities for the sensor geometries exploited in this work. Fitting the 3-D model to the experimental sensitivities gives estimations of = 7.4·10^-5 %RH^-1 and = 4.9·10^-5 K^-1. Table 1 shows the material properties determined in this work as well as reference values. We notice that the mechanical contribution is higher for S_RH than for S_T; therefore, S_RH is more sensitive to coating thickness changes than S_T.

Fig. 3. Temperature and relative humidity sensitivities of fiber Bragg gratings with different polyimide coating thicknesses.

In summary, we presented a new fiber optic relative humidity sensor using polyimide coated fiber Bragg gratings. Tests in a controlled climatic chamber show a linear, reversible and accurate sensor response for temperature and relative humidity ranges from 13 to 60 °C, and 10 to 90 %RH, respectively. We may easily compensate for the temperature cross-sensitivity using an additional bare fiber Bragg grating, which is not humidity sensitive. The temperature and relative humidity 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 coefficients of the polyimide coating. From a practical point of view, the sensor proposed here is easy to implement, and may be readily integrated within a multipoint and -parameter optical fiber Bragg grating sensor network thanks to its multiplexing capabilities.

The authors would like to thank G. Tirabassi from Rotronic AG, Switzerland, who kindly agreed to lend us a calibrated temperature and relative humidity gauge.

^(a) wavelength: 1550 nm; ^(b) wavelength: 1310 nm

Table 1. Fiber and coating material properties