Parametric study of a polymer-coated fibre-optic humidity sensor

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Meas. Sci. Technol. 23 (2012) 035103 (8pp) doi:10.1088/0957-0233/23/3/035103

Parametric study of a polymer-coatedfibre-optic humidity sensorNigel A David, Peter M Wild and Ned Djilali

Department of Mechanical Engineering and Institute for Integrated Energy Systems, University ofVictoria, Victoria, Canada

E-mail: nadavid@uvic.ca

Received 24 August 2011, in final form 4 January 2012Published 1 February 2012Online at stacks.iop.org/MST/23/035103

AbstractA relative humidity sensor based on polymer-coated optical fibre Bragg gratings is presented.This fully functional sensor has response time and resolution comparable to the currentcapacitive relative humidity (RH) sensors, but with greater applicability. Numerical andexperimental methods are used to determine the effects of coating thickness and fibre diameteron the response time and sensitivity of Bragg gratings coated with Pyralin. Transient resultsindicate that coating thicknesses of less than 4 μm are needed to achieve a response time of5 s, competitive with commercial capacitive RH sensors. Using thin coatings of ∼2 μm, for ashort response time, sensors with reduced fibre diameter were fabricated and tested understeady-state, transient and saturated conditions. By chemical etching from 125 to 20 μm, thesensitivity increased by a factor of 7. Such an increase in sensitivity allows for the resolutionand response time of the Pyralin-coated sensor to be comparable to commercial capacitive RHsensors. These characteristics, in addition to the sensor’s rapid recovery from saturation inliquid water, indicate good potential for use of this sensor design in applications whereelectronic RH sensors are not suitable.

Keywords: Bragg grating, humidity, polymer

(Some figures may appear in colour only in the online journal)

Nomenclature

λB Bragg wavelengthεi principal strainsn0 effective index of refractionξ thermo-optic coefficientPe effective strain-optic coefficientα coefficient of thermal expansionST sensitivity to temperatureSRH sensitivity to RHk stiffness weighting factorβ coefficient of hygroscopic expansionE Young’s modulusA cross-sectional areaη moisture concentrationD diffusion coefficientτ63 1/e response time

1. Introduction

Relative humidity (RH) is a parameter that must be measuredand controlled in many environments and industrial processes.Many of the miniature RH sensors on the market today arecapacitive and based on MEMS technology [1]. These types ofsensors offer low-cost, accurate, fast response measurementsover a large humidity range, satisfying the demands of mostapplications. In some instances, however, the sensor sizeand inability to recover quickly from saturation are limitingfactors in their usage. Further limitations are typical ofelectronic sensors, such as the need to isolate the leads fromelectromagnetic interference and the restricted ability of multi-channel multiplexing.

An application where the limitations of miniaturecapacitive RH sensors have become evident is in polymerelectrolyte membrane fuel cells (PEMFCs). Humidity levelsin the gas streams of commercial PEMFCs often need tobe controlled to achieve optimal performance [2, 3]. Recent

0957-0233/12/035103+08$33.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

in situ measurements across the active area of a single cellhave indicated significant gradients in RH arising duringcell operation [4, 5]. These gradients, if extending over therelatively large active area of commercial fuel cell stacks,could be a source of performance loss and degradation.Further understanding of this phenomenon requires non-invasive distributed measurements of RH in commercialPEMFC stacks.

The current commercially available miniature RH sensorsare not particularly well suited for use in fuel cells. The sensorsize is too large for the confined flow channels, the sensorsare slow to recover from condensation, which is commonin a PEMFC, the sensor leads need to be carefully isolatedsince a fuel cell is electrically active and there is limited spaceinside the PEMFC for multiple leads that would be requiredfor distributed measurements.

Fibre-optic sensors, unlike the current capacitive RHsensors, have the advantages of being intrinsically small andimmune to electromagnetic interference. Among the fibre-optic sensor technologies for humidity measurement discussedin a recent review by Yeo [6], the polymer-coated fibreBragg grating (FBG) RH sensor stands out for having awide measurement range combined with the capability ofmultiplexing several sensors on a single fibre. Multiple studieshave shown these sensors to have a linear, reversible andaccurate response over the range of 10–100% RH [7–9].

FBGs have found myriad sensing applications [10],particularly for the measurement of strain and temperature,to which an FBG is inherently sensitive. The sensing principleof the polymer-coated FBG is based on the hygroscopicexpansion of the polymer coating, which induces strain inthe fibre core. The strain is detected as a wavelength shift inthe FBG signal. The FBG-based RH sensor was first reportedby Giaccari et al after researchers found that commerciallyavailable FGBs that had been recoated with polyimide weresensitive to changes in humidity [11]. Polyimide is oftenused for coating optical fibre and FBGs to provide increasedtensile strength and durability. In addition to its favourablethermomechanical properties, polyimide exhibits fast andreversible moisture absorption, making it ideal as the sensinglayer in capacitive RH sensors [1], and since the work ofGiacarri, in fibre-optic RH sensors.

Sensitivity and response time of polyimide-coated FBGRH sensors have been shown to increase with increasingcoating thickness. In studies by Kronenberg et al [8] and Yeoet al [7], FBGs were coated with the polyimide Pyralin R©

(HD Microsystems) and tested for steady-state sensitivityand response time, respectively. The shortest response timereported by Yeo et al [7] was approximately τ63 = 5 minfor a coating thickness of 10 μm. Thinner coatings, down to3.6 μm, were tested by Kronenberg et al, but only for steady-state sensitivity. The sensitivity of their thinnest coating sensor,which had the shortest response time, was 0.3 pm %RH−1.Optical interrogators for FBGs typically have a wavelengthresolution of ∼1 pm. This implies a minimum detectablechange in RH of no less than 3% RH for the fast FBGRH sensor. Operating characteristics of commercial miniaturecapacitive RH sensors, such as the HIH-4000 from Honeywell,

Inc. [12], with τ63 = 5 s and a resolution of 0.5% RH indicatea need for design improvements on the polyimide-coated FBGsensors for them to be competitive.

Following our recent work in which the use of FBG RHsensors was demonstrated in situ in an operating fuel cell,the focus of this paper is the realization of fully functionalFBG sensors with response time and resolution comparableto the current capacitive RH sensors, but with greaterapplicability. A numerical analysis is presented allowing asystematic investigation of the effect of coating thickness andfibre diameter on the steady-state and transient response ofthe coated FBG sensor. The fabrication process to realizesensors with varying coating thickness and fibre diametersis described, and experimental results obtained under a rangeof environmental conditions are presented.

2. Methodology

2.1. Theoretical background

An FBG typically consists of a short segment of a single-modeoptical fibre with a photo-induced periodically modulatedindex of refraction in the core of the fibre. When the grating isilluminated with broadband light, the reflected spectrum hasa peak at the Bragg wavelength, λB = 2n0, where n0 is theeffective index of refraction of the silica fibre core and isthe grating pitch. The dependences of both n0 and on strainand temperature allow the use of FBGs for sensing these andother parameters. Many of the growing number of sensingapplications for FBGs have been reviewed by Rao [10].

The influence of strain and temperature changes on theBragg wavelength of an FBG sensor can be obtained bythe Taylor series expansion of the expression for the Braggwavelength about a reference state of strain and temperature.Assuming zero reference strain and keeping only first-orderterms in the expansion, a general expression for the relativeBragg wavelength shift for unpolarized light is given by [13]

λB

λB= εz − n2

0

2(εz p12 + εr(p11 + p12)) + ξT . (1)

The first term, εz, is the thermally and mechanically inducedaxial strain in the grating, which changes the grating pitch.The second term represents the strain-optic effect, where p11

and p12 are the principal components of the strain-optic tensorand εz and εr are the corresponding axial and radial strains.The third term represents the thermo-optic effect, where ξ isthe thermo-optic coefficient.

For a Bragg grating written in the single-mode opticalfibre subjected only to axial strain, the following simplifiedversion is often used [7]:

λB

λB= (1 − Pe)εz + ((1 − Pe)α + ξ )T , (2)

where

Pe = p12 − ν(p11 + p12) (3)

represents the effective strain-optic coefficient, in whichthe radial strain is accounted for by the Poisson effect.Equation (2) is a superposition of the mechanical and thermalresponse of the FBG, α is the coefficient of thermal expansion(CTE) of the fibre and ξ is the thermo-optic coefficient.

2

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

Figure 1. Schematic of the Pyralin R©-coated FBG sensor.

For a polymer-coated FBG humidity sensor isolated fromexternal forces, as shown in figure 1, the response to RH andtemperature is given by

λB

λB= (1 − Pe)εRH + (1 − Pe)εT + ξT, (4)

where the axial strain in the fibre is separated into RH-inducedstrain, εRH, and temperature-induced strain, εT . These strainsarise from the hygroscopic and thermal expansions of thematerials comprising the sensor and can be determined using aone-dimensional (1D) model of the sensor in which the radialstrain is neglected.

The coated FBG is modelled as an infinitely long bi-material rod in which the two materials adhere perfectly. Atequilibrium, the axial stresses in the materials must balance:

σ f A f + σcAc = 0, (5)

where A f and Ac are the cross-sectional areas of the fibre andcoating, respectively. Furthermore, the axial deformations ofthe materials are equal:

L f = Lc. (6)

Assuming linear, elastic and isotropic behaviour for thesilica and Pyralin R©, the stress and strain in the respectivematerials are related by

εz = σ c/Ec (7)

and

εz = σ f /E f , (8)

where E is Young’s modulus.Based on the above conditions and assumptions, the strain

induced in the fibre from a change in relative humidity, RH,is given by

εRH = EcAc

EcAc + E f A fβcRH, (9)

where βc is the constant coefficient of hygroscopic expansionof the polymer. As expected, equation (9) indicates that the RH-induced strain in the fibre increases with increasing coatingcross section and reaches zero when there is no coating.

The strain induced by a change in temperature, T, isgiven by

εT = α f T + EcAc

EcAc + E f A f(αc − α f )T, (10)

where α f is the CTE of the fibre and αc is the CTE ofthe Pyralin coating. The first term in equation (10) is thethermal strain of a bare fibre and the second term ariseswhen there is a polymer coating. The CTE of Pyralin is twoorders of magnitude larger than that of glass [8]. For theapplication of a Pyralin coating to the fibre to achieve RHsensitivity, the thermal strain in the fibre is increased whichleads to an increase in temperature sensitivity. This increasein temperature sensitivity for increased coating thickness wasexperimentally verified in the work of Kronenberg et al [8].The results of their work showed that the temperature responseof a Pyralin-coated FBG RH sensor was linear and repeatablefor a broad range of constant humidity levels. This suggeststhat the sensors’ co-sensitivity to temperature can easily becompensated for by using an additional bare fibre Bragggrating that is not RH sensitive.

As reported by Kronenberg et al, the relative Braggwavelength shift of the coated FBG sensor can be written as alinear superposition of RH and temperature sensitivity [8]:

λB

λB= SRHRH + ST T, (11)

where SRH and ST are the RH and temperature sensitivitycoefficients. Substituting equation (9) into equation (4), thesecoefficients are given by

SRH = (1 − Pe)EcAc

EcAc + E f A fβc (12)

ST = (1 − Pe)

[α f + EcAc

EcAc + E f A f(αc − α f )

]+ ξ . (13)

In Kronenberg et al and Yeo et al [8, 7], known values of Eand Pe were used in equation (12). By varying βc, equation (12)was fitted to experimental sensitivity results for sensors withincreasing coating thickness. Values for the 1D coefficient ofhygroscopic expansion, β1−D

c , determined in both studies werein good agreement with each other. Kronenberg et al also useda three-dimensional (3D) finite element model to determineβc; however, there was a discrepancy between β1−D

c and β3−Dc ,

indicating a dependence on the radial strain.

2.2. Transient model

In the current study, for a more complete representation ofthe coated fibre that includes radial strain and diffusion, thesensor is modelled in three dimension using the commercialfinite element software Comsol R©. In this model, the diffusionof moisture into the Pyralin R© is assumed to be Fickian and,therefore, governed by equation (14), where η is the moistureconcentration and D is the diffusion coefficient. The diffusion-driven moisture concentration in the polymer is coupled to themechanical behaviour of the sensor by prescribing an isotropic3D coefficient of hygroscopic expansion, β3−D

c , a Poisson ratio,ν, and a Young’s modulus, Ec, to the polymer-coating silicafibre and the silica fibre, where, of course, the hygroscopiccoefficient of the glass fiber is set to zero:

∂η

∂t= D∇2η. (14)

3

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

Given the axial symmetry of the sensor and negligibleazimuthal changes under the surface conditions, only radial (r)and axial (z) dependences were considered in the simulation,and the computational domain was restricted to the half-plane.The length of the coated fibre domain was set to 800 μm, whichensured that edge effects were avoided. A mesh of about 30 000triangular elements was used, with a higher density of pointsnear the interface of the two materials.

Transient simulations of the sensor response to a stepchange in humidity were run by prescribing initial andboundary conditions on the moisture concentration. Time-dependent radial and axial strains along the fibre axis wereobtained and then converted to a Bragg wavelength shiftusing equation (1). By comparing simulation results to thoseobtained from transient experiments for different coatingthicknesses, an estimate of the diffusion coefficient for thePyralin coating was made and the Fickian diffusion modelvalidated.

Steady-state strains induced by RH changes wereconverted to Bragg wavelength shifts using equation (1).Sensitivity to RH for different coating thicknesses and reducedfibre diameters was obtained and compared to experiment. Thecoefficient of hygroscopic expansion, β3−D

c , was varied in the3D model to fit the model results to the data.

2.3. Experimental details

Several Pyralin R©-coated FBG sensors with varying coatingthickness and fibre diameter were fabricated in-house andtested for static sensitivity and transient response. Methods forfabrication and testing are described in the following sections.

2.3.1. Sensor fabrication. 10 mm long Bragg gratings fromMicron Optics, Inc. (Atlanta, GA) were used for the full-diameter fibre sensors and 2 mm long gratings from TechnicaSA (Zug, Switzerland) were used for the etched fibre sensors.The shorter gratings were used to facilitate fabrication andto miniaturize the design, but otherwise behave in the samemanner as the longer gratings. The gratings were written in thestandard SMF 28 optical fibre with nominal Bragg wavelengthsof 1550 nm. The moisture sensitive Pyralin coating was appliedto the FBG using the procedure outlined in Yeo et al [7].The stock polyimide recoat was first removed by immersionin 98% sulphuric acid for approximately 10 min. The fibrewas then rinsed in de-ionized water and wiped with isopropylalcohol. The FBG was then dipped in Pyralin and withdrawn ata speed slow enough to produce a uniform coating without beadformation. Speeds of 10–20 mm min−1 were used dependingon the fibre diameter. Each coat was pre-cured in an oven for5 min at 150 ◦C. Subsequent coats were applied to obtain thedesired thickness. The final baking of the fibre was done at180 ◦C for 1 h.

To reduce the fibre diameter for increased sensorsensitivity, the fibre was etched with hydrofluoric acid (HF)prior to coating with the Pyralin. The section of bare fibrewith a 2 mm Bragg grating was immersed in 48% HF forsufficient time, using a predetermined etching rate, to producethe desired diameter. The etched fibre was then neutralized

Table 1. Unetched and etched FBG sensors fabricated and tested inthis work.

Diameter Coating thickness SRH

Sensor (±0.5 μm) (±1.0 μm) (±0.01(10−6%RH−1))

FBG 1 125.0 2.7 0.16FBG 2 125.0 9.5 0.74FBG 3 125.0 17.0 1.54FBG 4 125.0 18.1 2.22FBG A 75.0 2.0 0.23FBG B 50.0 2.5 0.41FBG C 40.0 2.5 0.55FBG D 31.5 2.3 0.83FBG E 20.0 2.0 1.42

in a saturated CaOH solution to stop the etching. The sameprocedure as described above was then used to coat the etchedfibre with Pyralin.

The fibre diameters and coating thicknesses of the sensorswere measured with an optical microscope and are shown intable 1. The uncertainty in the coating thickness was estimatedto be 1.0 μm based on measurement precision and slight non-uniformity in coating thickness.

2.3.2. Sensor testing. The sensors’ steady-state responseto RH was measured at constant temperature in aprogrammable environmental chamber. The individual FBGsensors were protected with perforated hypodermic tubing.During calibration the sensors were placed next to a referencehumidity probe, the HX80 from Omega with specifiedaccuracy of ±1% over a range of 10–95% RH. The Braggwavelength shift of the FBG was detected using an opticalinterrogation unit (SM130, Micron Optics, Inc., Atlanta,GA), with a specified wavelength resolution of 0.1 pm at10 Hz sampling rate. The temperature was held constant at24.0 ± 0.2 ◦C while the RH in the chamber was cycled from30% to 90% in increments of ∼10%, allowing the chamberand sensors to reach equilibrium at each step.

For the transient testing that was performed on bothetched and unetched sensors, a two-compartment chamberwas constructed, with which a step change in RH could beapplied to the sensor. See figure 2. The upper compartmentis exposed to ambient RH, while the lower compartment issealed with a pierceable Teflon diaphragm and held at 85%RH achieved using a saturated KCl salt solution. During testingthe chamber was placed in the environmental chamber set to45% RH and 24 ◦C. Beginning in the upper compartment, theFBG sensor gets pushed through the diaphragm such that itis immediately exposed to the high humidity level. From theBragg wavelength data acquired during this procedure, it ispossible to characterize the response time of the sensor. Thesensor response to saturation with liquid water was tested byusing water in the lower chamber.

3. Results and discussion

3.1. Unetched sensors

3.1.1. Steady state. RH calibration data for FBG 2 is plottedin figure 3(a) and shows linearity that is representative of

4

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

Figure 2. Schematic of the two-part chamber used for transienttesting of the sensors.

the other sensors. A linear fit to the data yields a slope ofm = 1.00 ± 0.02 pm %RH−1, which, for a nominal Braggwavelength of 1550 nm, gives RH sensitivity SRH = (0.64 ±0.01) × 10−6%RH−1. See equation (11). Upon cycling thechamber three times there was no apparent hysteresis nor wasthere a change in sensitivity. Temperature calibration of FBG2 was carried out in the environmental chamber at constanthumidity. The calibration curve, shown in figure 3, is linearand has a slightly higher slope than an FBG without polymercoating. This behaviour is consistent with equation (13) and theprevious work of Kronenberg et al [8]. The RH sensitivities forall of the unetched sensors are given in table 1. The calibrationresults for the unetched Pyralin-coated sensors confirmed the

0.00 0.25 0.50 0.75 1.00 1.25 1.500.0

0.5

1.0

1.5

2.0

2.5

FB

G4

FB

G3

FB

G2

FB

G1

Present workKronenberg et al.1D model (β=7.7[10-5%RH])3D model (β=7.5)3D model (β=7.0)

RH

sens

itivi

ty,S

RH

(10-6

%R

H- 1)

Coating cross section area (104μm2)

Figure 4. RH sensitivity for sensors of different coating thicknessincluding results from the 1D and 3D models and results fromKronenberg et al.

linear and reversible behaviour of this sensor design reportedin previous studies.

Shown in figure 4 is a plot of SRH of the four unetchedsensors versus the coating cross-sectional area. Also plottedare curves obtained using the 1D and 3D models as well as datapoints from the work of Kronenberg et al, which are shownfor comparison. In the models, the mechanical properties ofE f = 72 GPa [8] and Ec = 2.45 GPa [14] were used alongwith a bare fibre diameter of 125 μm.

In the case of the 1D model, a value of β1−Dc = 7.7 ×

10−5%RH−1 gives the best-fit equation (12) to our data. Thisvalue is 7% lower than that of Kronenberg et al who usedthe same model. This difference is attributed to our use ofstrain-optic coefficients, p1i, that are specific to SMF 28 fibrecore [15] and 7% lower than the bulk silica values used byKronenberg et al [8].

With the use of β3−Dc = 7.3 × 10−5%RH−1 in the 3D

model, the steady-state sensitivities obtained were in good

20 30 40 50 60 70 80 90 100-10

0

10

20

30

40

50

60

70

FBG 2 calibration dataLinear fit

slope= 1.00 pm/%RHr2= 0.9994

Bra

ggw

avel

engt

hsh

ift(p

m)

Relative humidity (% RH)15 20 30 40 50 60 70 80 90

-50

0

100

200

300

400

500

600

650

Bra

ggw

avel

engt

hsh

ift(p

m)

Temperature (°C)

Slope = 10.62 pm/°Cr2 = 0.999

(a) (b)

Figure 3. RH and temperature calibration data for unetched FBG with 9.5 μm Pyralin coating.

5

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

0 100 200 300 400 500 600 700 800 900 1000 11000.0

0.2

0.4

0.6

0.8

1.0

1.2

145.0 s35.0 s3.2 s

FBG 4FBG 2FBG 1

Response time, τ63

(FBG4)

(FBG2)

t = 18.1 μm

t = 9.5 μm

Nor

mal

ized

Br a

ggw

avel

engt

hsh

ift

Time (s)

Coating thickness: t = 2.7 μm (FBG1)

Sensor

Figure 5. Transient response of three unetched fibre sensors ofincreasing coating thickness to a step change in RH from 45% to85%. The wavelength shift was normalized relative to the sensorvalue reached at equilibrium at 85% RH.

-25 0 50 100 150 200 250 300 3500.0

0.2

0.4

0.6

0.8

1.0

1.1

Nor

mal

ized

Bra

ggw

avel

engt

hsh

ift

Time (s)

9.5 μm coating sensor dataD=7.5 [10-13m2s-1]D=8.5D=9.5

Figure 6. Transient response of FBG 2 (9.5 μm coating) after a stepchange from 45%–85% RH. Data are shown in comparison withsimulation results obtained using Comsol.

agreement with the data from both groups. This value of β3−Dc

is only 1% lower than that of Kronenberg et al.

3.1.2. Transient. Results from the transient tests forthree sensors of increasing coating thickness are shown infigure 5. It is clear from these results that the response time ofthe sensor increases significantly with coating thickness andthat a thin coating is desirable for applications where transientRH conditions are to be investigated.

Transient simulation results for FBG 2 (9.5 μm coating)using three different diffusion coefficients are shown incomparison to an experimental response curve in figure 6. Thestrains in the fibre core for each time step in the simulationwere used to compute the wavelength shift as a function oftime. Agreement between the shape of the simulation curve

54 56 58 60 62 64 66 68 70 72 74-2

0

2

4

6

8

10

12

14

16

18

20

22

t = 0s 5s 20s 60s 100s 250s

Polyimide coating

Moi

stur

e co

ncen

trat

ion,

η (g

/m3 )

Radius (μm)

Silica fiber

Figure 7. Radial moisture concentration profiles for FBG 2 acquiredwith Comsol transient simulation.

0 2 4 6 8 10 12 14 16 18 20

0102030405060708090

100110120130140150160

FB

G 4

FB

G 2

FB

G 1

τ63

data

D=7.5 [10-13m2s-1] D=8.5 D=9.5

63%

res

pons

e tim

e, τ

63 (s

)

Coating thickness (μm)

Figure 8. Experimental and model results for τ63 as a function ofcoating thickness.

and the actual response curve validates the assumption thatFickian diffusion governs the transient behaviour of the sensor.

Figure 7 shows radial concentration profiles for FBG 2obtained with the 3D transient model. It is more appropriate torefer the moisture concentration rather than relative humidity,since water diffuses in the material as liquid rather than gas.To simulate the experiment, the moisture concentration, η,throughout the polymer was initially set to 9.79 g m−3, whichis equivalent to the water vapour concentration in air at 45%RH and 24 ◦C. The boundary conditions for t > 0 of thesimulation were η = 18.5 g m−3 at the outer surface of thecoating and zero flux, or ∂η/∂r = 0, at the glass–polymerinterface.

Transient simulations were carried out for coatingthicknesses from 1 to 20 μm. It was found that by usingD = 8.5 ± 1.0 × 10−13 m2 s−1, τ63 of the tested FBGscould be predicted within experimental uncertainty. Seefigure 8. This value for the diffusion coefficient is within 10%

6

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

5 10 20 30 40 50 60 70 80 90 100-10

0

20

40

60

80

100

120

31.5 μm ∅ FBG calibration data Linear fit

Bra

gg w

avel

engt

h sh

ift (

pm)

Relative humidity (%RH)

slope = 1.28 pm/%RHr2 = 0.9995

15 20 30 40 50 60 70 80 90-100

0

100

200

300

400

500

600

700

Bra

gg w

ave l

e ng t

h sh

ift (

pm)

Temperature (°C)

Slope = 10.86 pm/°Cr2 = 0.9997

(a) (b)

Figure 9. RH and temperature calibration data for a 31.5 μm etched fibre sensor with 2.3 μm Pyralin coating.

of literature values for polyimide that have been measuredusing two different techniques [16].

For the response time of the Pyralin-coated FBG sensordesign to be competitive with the Honeywell HIH-4000mini capacitive sensor (τ63 = 5 s), the coating thicknessmust be less than ∼4 μm. The FBG sensor should also becompetitive in terms of RH resolution, which is 0.5% RH forthe HIH-4000 mini. FBG 1, for example, with τ63 = 3 s andSRH = (0.16 ± 0.01)× 10−6%RH−1, would carry a minimumdetectable change in RH, or resolution, of ∼4% RH using acommon FBG interrogator. Improved sensitivity is, therefore,necessary for the FBG sensor resolution to rival capacitivesensors. The 1D model for the FBG sensor (equation (12)),however, suggests that a reduced fibre diameter can lead toincreased sensitivity and therefore improved resolution.

3.2. Etched sensors

3.2.1. Steady state. Five 2 mm long FBGs were etchedwith HF to reduce the diameter for increased sensitivity.See table 1. A coating thickness of ∼2.5 μm was chosenbecause, as shown in the preceding section, it yielded a shortresponse time of τ63 ∼ 3 s for the unetched sensor. Thesensors were calibrated in the environmental chamber usingthe same procedure as for the unetched FBGs. Shown infigure 9(a) are the calibration data for the 31.5 μm sensor overthe range of ∼15%–95% RH. It was seen that in addition to anincrease in sensitivity, the linearity and repeatable behaviourwas preserved with the reduction in diameter. Temperaturecalibration data for the 31.5 μm etched sensor taken at constantRH are shown in figure 9(b). The sensor exhibited a linear andrepeatable response to changes in temperature with sensitivity∼6% higher than a bare fibre. This is consistent with the1D model predictions of equation (13) and suggests thattemperature compensation of this etched FBG RH sensor canbe easily carried out using a co-located uncoated FBG. Thiswas the method used by David et al for the RH measurementsin an operating PEMFC [5].

0 10 20 30 40 50 60 70 80 90 100 110 120 1300.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

E

D

CB

FB

G 1

FBG sensors

3D model (β=7.5 [10-5%RH-1], t = 2.5 μm)

1D model (β=7.7 [10-5%RH-1])

RH

sen

sitiv

ity, S

RH (

10-6

%R

H-1)

Fibre diameter (μm)

A

Figure 10. Sensitivity (SRH) versus fibre diameter for etched FBGsensors from table 1. Solid and dashed lines indicate 3D and 1Dmodel results, respectively, using a coating thickness of 2.5 andβ3−D

c and β1−Dc from the unetched analysis.

Sensitivities of the five etched sensors versus fibrediameter are shown in figure 10. Also shown are 1D and 3Dmodel results, obtained by using β1−D

c and β3−Dc from the

unetched fibre analysis. These results show that the 1D modelpredicts a significantly higher RH sensitivities for the etchedfibre sensors.

Results from the 3D model shown in figure 10 can beused to establish a limit on the possible increase in sensitivitythat can be achieved by etching the FBG. The sensitivity of ashort-response time sensor, i.e. FBG 1, can be increased by anorder of magnitude if the fibre diameter is etched to 10 μm,the diameter of the fibre core. In practice, however, etching tothe core is not feasible with this sensor design, as evanescentfield interaction would likely comprise the measurements. Afactor of 7 increase in sensitivity over FBG 1 was achievedwith FBG E, having a diameter of 20 μm. Such an increase insensitivity brings the resolution of the polyimide-coated RHsensor to less than 1% RH, and into the range of commercialcapacitive RH sensors.

3.2.2. Transient. The response curves shown in figure 11indicate consistent response times of τ63 ∼ 3 s despite the

7

Meas. Sci. Technol. 23 (2012) 035103 N A David et al

-5 0 5 10 15 20 25 30 35 40 45-0.1

0.0

0.2

0.4

0.6

0.8

1.0

1.1

FBG 1 FBG B FBG C FBG D

Nor

mal

ized

Bra

gg w

avel

engt

h sh

ift

Time (s)

Figure 11. Transient response of Pyralin-coated FBG sensors ofvarying fibre diameter with similar coating thicknesses (∼ 2.5 μm).

-20 0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

110Sensor out of water

Rel

ativ

e hu

mid

ity (

%R

H)

Time (s)

Sensor into water

Figure 12. Response to liquid water of a 31.5 μm etched fibresensor with 2.3 μm Pyralin coating.

reduction in fibre diameter, which is to be expected since thecoating thickness are all similar.

Tests for effects of liquid water by sensor immersion wereperformed on FBG D, with a diameter of 31.5 μm and coatingthickness 2.3 μm. Results from this test are shown in figure 12.It is seen that upon immersion in water, the sensor measuresnear 100% RH with a response time comparable to the RHtransient tests. Full recovery from saturation takes place in20 s, at which point the sensor again measures the 39% RH ofthe room.

4. Conclusions

Etched fibre Pyralin-coated FBG humidity sensors werefabricated with varying coating thicknesses and fibre diametersto test the effect these parameters have on response time andsensitivity. Transient results indicated that coating thicknessesof less than 4 μm are needed to achieve a response time of5 s, competitive with commercial capacitive RH sensors. Forthin-coating (∼2.5 μm), and hence fast response sensors, it

was found that by etching the fibre diameter from 125 to20 μm, the sensitivity increased by a factor of 7. Suchan increase in sensitivity allows for the resolution andresponse time of the Pyralin-coated sensor to be comparableto commercial capacitive RH sensors. These characteristics, inaddition to the sensors rapid recovery from saturation in liquidwater, indicate good potential for the use of this sensor designin applications where electronic RH sensors are not suitable.

Acknowledgments

This work was funded through a Strategic Research grant fromthe Natural Sciences and Engineering Council of Canada.

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