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Smart textile plasmonic fiber dew sensors

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Abstract

We propose a novel Surface Plasmon Resonance (SPR)-based sensor that detects dew formation in optical fiber-based smart textiles. The proposed SPR sensor facilitates the observation of two phenomena: condensation of moisture and evaporation of water molecules in air. This sensor detects dew formation in less than 0.25 s, and determines dew point temperature with an accuracy of 4%. It can be used to monitor water layer depth changes during dew formation and evaporation in the range of a plasmon depth probe, i.e., 250 nm, with a resolution of 7 nm. Further, it facilitates estimation of the relative humidity of a medium over a dynamic range of 30% to 70% by measuring the evaporation time via the plasmon depth probe.

© 2015 Optical Society of America

1. Introduction

The dew point is the temperature to which water vapor in the air has to be cooled in order to condense into water on a solid surface at constant pressure. Dew point monitoring to prevent catastrophic effects is very critical, especially in advanced industries dealing with electronic devices and pharmaceuticals. Further, dew point is measured in various drying and heat-treatment processes such as in plastic molding and metal treatment. It is also monitored in compressed air pipelines, where excess moisture results in poor end-product quality, ice formation, and equipment corrosion. Other typical dew monitoring applications include dry environments for lithium battery manufacturing and gas-insulated high-voltage equipment for use in the power industry [1–3].

A dew sensor can detect dew formation on a surface and determine the dew point temperature of a medium. Various types of hygrometers and humidity sensors can operate as dew sensors. These include mechanical hygrometers, wet and dry bulb psychrometers, Infrared (IR) optical absorption hygrometers, electronic humid sensors, and optical waveguide humid sensors [4,5]. However, none of these hygrometers and humidity sensors can satisfy the majority of dew sensor requirements in terms of precision, cost, ease of operation, maintenance, and remote operation.

In contrast to electrical humidity sensors, optical fiber humidity sensors can offer features such as small size, immunity to electromagnetic interference, multiplexing, and remote sensing capabilities. In fact, to date, numerous investigations have been conducted on the use of optical fiber sensors for humidity and moisture measurement since the beginning of this millennium [6,7]. In general, these sensors use direct spectroscopic [8,9], evanescent wave [10,11], in-fiber grating [12,13], interferometry, or hybrid methods [14–16] to measure humidity. Among these optical fiber humidity sensors, only a few can be used for dew point detection, and those that do often have working principles based on interferometry in optical fibers [16–19]. For example, Mathew et al. presented a sensor for dew detection that is based on a photonic crystal fiber interferometer (PCFI) operated in reflection mode. Their proposed sensor has good dew point measurement accuracy, estimated at ± 0.1 °C [16]. Further, Bao et al. [19] recently introduced a reflection-based fiber optic phase sensing method to quantify the dew point of CO2 in an industrially relevant post-capture CO2 mixture stream. Their method, which employs thin film interference on the tip of an optical fiber, has an accuracy of 5%.

In this paper, we propose the first SPR-based optical fiber dew sensor. The SPR effect results in high sensitivity to refractive index changes in a dielectric adjacent to its metal layer and has numerous applications, from biochemical sensing to environmental monitoring [20–23]. Rivero et al. previously used localized SPR in optical fiber to sense humidity [24]. Iwamia et al. [25] were the first to introduce a working dew sensor based on localized SPR for dew forming on a nonporous ceramic in an optical free-space setup. However, despite its high sensitivity, their optical free-space setup is not suitable for remote or inline detection outside of the laboratory. In our method, we use optical fiber instead of a free-space setup and, consequently, we propose a novel approach based on the plasmonic effect to detect dew formation as well as humidity.

We also investigate the integration of plasmonic optical fiber dew sensors in an ordinary textile as part of a smart textile for future distributed dew sensing. Smart textiles are active materials formed by the incorporation of electronic or optical sensing elements into fabrics or garments, resulting in such materials having sensing and actuation properties. Although, to date, most smart textiles are only based on microelectronic devices, nevertheless the idea of making smart textiles using optical fiber is still very interesting because the flexibility of optical fibers could result in textiles supporting many fibers to form a distributed sensor. Recently, polymer optical fiber sensors have been used in the body of smart textiles (operating based on grating or micro-bend principles) for stress and pressure sensing [26,27], biomedical and medical cases [28,29], geotextile and environmental engineering [30], and also decorative purposes [31].

Figure 1 shows the integration of our SPR sensor (the polished one in the middle) with two other fibers (covered with red cladding jackets) in the body of a smart textile. (The two other fibers in the figure are not sensors, they were simply embedded in the textile to demonstrate our idea of having several distributed sensors in the body of a smart textile.) Although, we here propose to have several dew sensors in textiles to form a distributed smart textile dew sensor, the other fibers can actually be other types of sensors; for example, Bragg grating fiber sensors to detect the temperature or pressure simultaneously. In this paper, our focus is on smart textiles dew sensors that detect dew points using only one plasmonic optical fiber dew sensor.

 figure: Fig. 1

Fig. 1 Sample of our proposed distributed smart textile SPR dew sensor.

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The remainder of this paper is organized as follows. Section 2 gives an overview of the theory underlying plasmon waves and their sensitivity to water layer formation on top of the gold layer. This is followed by a look at dew formation and evaporation. Section 3 discusses how dew formation and humidity are sensed using our proposed SPR sensor and presents our SPR measurement results.

2. Theory

2.1 SPR and depth probe

SPR is excited by an electromagnetic (EM) field perpendicular to a metal surface at the phase-matching point between an electron and an optical wave. In a gold layer coated on the polished surface of an optical fiber, this phase-matching occurs when the propagation constant of a guided mode of the optical fiber is equal to that of the SPR [20]. Each plasmon wave has a depth probe indicating how far the plasmon field penetrates to the dielectric adjacent to the metal surface. We briefly explain the general formulation for surface plasmon and depth probe in a plasmonic sensor to give a better understanding of our dew sensing method and its relation to plasmonic depth probe. Surface plasmon waves are surface electromagnetic waves that propagate parallel to a metal/dielectric interface, represented as

E=e(x)exp(i(βzωt))
where β is propagation constant in the z direction and e(x) is the electrical field component, represented by
ez(x)=Aexp(γd,mx) , and  γd,m=ikεdεd+εm          
where εm and εd are metal and dielectric permittivity, respectively, and k=2π/λ. Figure 2(a) shows an SPR electric field at λ = 800 nm inside both metal and dielectric. This figure illustrates the depth probe where the tail of the plasmonic field diminishes gradually in the dielectric. This means that the SPR can sense the dielectric index change very close to the metal/dielectric boundary.

 figure: Fig. 2

Fig. 2 (a) Electric field distribution for surface plasmons on the metal/dielectric boundary. (b) Depth probe of surface plasmon versus operating wavelength at the metal/dielectric boundary.

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Mathematically, the penetration depth of SPR can be calculated using Eq. (3). Figure 2(b) shows the linear relation between penetration or probe depth and plasmonic excitation wavelength:

Lpd=1Re{γd}                              
In Fig. 2(b), the penetration depth is a few hundred nanometers; thus, surface plasmon depth probes are extremely sensitive to changes in the refractive index (or ε) of dielectrics that are very close to the metal/dielectric boundary. This characteristic enables us to design a very sensitive dew sensor based on SPR, especially when the dielectric index varies from the index of air (~1) to the index of water (~1.33), which are huge variations compared to the sensitivity of surface plasmon sensors, thus enabling us to immediately measure very tiny changes in the thickness of the water layer due to dew condensation on the surface of the metal.

2.2 Dew formation and evaporation

Relative humidity (RH) is one of the most important parameters in dew formation theory. It is defined as the ratio of water partial pressure (H2O), e, to saturated water vapor pressure es(T), at a given temperature (T), and can be defined as

RH(%)=ees(T)×100
where T(°C) is the temperature of air and es(T) is calculated using a Buck formula [32]:
es(T)=(1.0007+3.46×106P)×(6.1121)e17.502T240.97+T
where P is pressure in hectopascal.

Figure 3 depicts the correlation between RH and T in the temperature range 10 °C to 50 °C. The dashed-line black curve shows that RH decreases as the air temperature increases. Equation (6) is a Magnus formula to calculate the dew point temperature (TD) using the known temperature (T) and RH of an air parcel in the medium adjacent to the surface [33]:

TD=243.04[ln(RH100)+17.625T243.04+T] 17.625ln(RH100)17.625T243.04+T
In the dew process, we study the condensation of water vapor. However, the inverse process, evaporation, is also interesting for us here. In the evaporation phenomenon, water evaporates from the surface where the water vapor in the air is not saturated (RH ˂ 100%), which implies that the evaporation rate (E) is related to RH. Introduced by Brutsaert’s theoretical model [34], Eq. (7) can be used to estimate the evaporation rate, which in turn can be compared to direct measurements:
λE=ΔΔ+γ*(RnG)+γ*Δ+γ*EA    
where, λE (W/m2) is the latent heat flux, in which λ (kJ/kg) is the latent heat of vaporization and E(kg/m2.s) is evaporation rate; ∆ (Pa/°K) is the rate of saturation pressure, which depends on the temperature; Rn (W/ m2) is the net radiation; G (W/ m2) is the sum of ground and water heat fluxes; and γ* = 0.93γ, where γ is the psychometric constant. EA= ρCp[es(T)e]/0.93 raγ is an atmosphere drying function that represents the capacity of the atmosphere to transport water vapor [35], in which ra (s.m−1) is aerodynamic constant, ρ(kg/m3) is air density. cp (J kg−1 K−1) is air specific heat, γ is the psychometric constant, T (K) is the air temperature, and e (pa) is vapor pressure—with subscript s indicating saturation.

 figure: Fig. 3

Fig. 3 (Left) Relative Humidity (RH) versus temperature, dashed-line curve. (Right) Evaporation rate of a wet surface (Ev) versus temperature, solid blue line.

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If the net radiation and heat fluxes are negligible, and ∆ is relatively constant, the first term of Eq. (7) becomes negligible; thus, the evaporation rate can be simplified as in Eq. (8):

E=ρCpλra(Δ+γ*)[es(T)e]=eρCpλra(Δ+γ*)[100RH1]
The right hand side of Fig. 3, blue solid curve, depicts the evaporation rate vs temperature plotted using Eq. (8). The evaporation rate increases with the temperature of the air in the medium adjacent to a wet surface.

In our sensor, condensation and evaporation will happen in the environment adjacent to a metal surface, where the plasmon waves are excited by the optical power. Thus, to give an illustration of the dew point and evaporation rate at our SPR sensor, we start with a simulation showing excited plasmons and a depth probe. Figure 4(a) shows a cross section of our fiber optic SPR dew sensor with the plasmon waves excited on top of the gold layer, coated on the side-polished surface. In this simulation, the fundamental core mode excites surface plasmons at 632 nm, while we consider 250 nm of dew (water) formed on top of the 45 nm gold layer. Because surface plasmon sensors are very sensitive to any tiny change in the thickness of the water layer (~10 nm), it is possible to measure any tiny condensation or evaporation in the sensing area by measuring the plasmonic loss.

 figure: Fig. 4

Fig. 4 (a) Cross section of the side-polished SPR fiber sensor showing the power distribution and plasmonic waves; plasmons are excited on the top of the gold layer to form a sensing area for dew measurements. (b) Schematics of temperature and humidity gradients adjacent to gold surface layer with tiny water layers forming.

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Figure 4(b) depicts schematics of the sensing area and its adjacent air environment. Because of the temperature difference between the surface and the air, a temperature gradient exists between adjacent environment (T) and the gold surface (TS), as well as a humidity gradient in air between the environment (RH ˂ 100%) and the gold layer (RH = 100%), where dew can be formed. No dew forms on the gold surface as long as the temperature of the gold surface (TS) is greater than that of the dew point of the adjacent environment (TD). We assume that dew forms in consecutive layers on the gold surface while Ts becomes equal or less than TD. In the next section, we experimentally demonstrate and discuss how the SPR method is used to sense the dew formation and evaporation phenomena on the gold layer.

3. Measurement

3.1 Dew sensing experimental environment

To demonstrate dew formation using SPR, we used the smart textile sample in Fig. 1, in which plasmonic side-polished optical fibers are woven into a white fabric along with two other optical fibers. As stated above, we used two red fibers in our smart textiles to demonstrate the potential to have distributed sensing smart textiles. Our SPR optical fiber dew sensor was a standard SM fiber (8/125 μm) polished using the Controllable hybrid side-polishing method (CHPM) which had been introduced in our previous work [36]. The CHPM method enhances the surface smoothness by 34%, which improves the sensitivity of our plasmonic sensor. Figure 5 shows an optical microscope image of two parallel side-polished fibers, fixed in an aluminum mount, with a polished length of approximately 8 mm and a residual cladding thickness of approximately 0.5 μm. The two bottom images in Fig. 5 show the cross section of the side-polished fiber, in the waist area, bottom left, and the top view of one of the polished fibers taken by a scanning electron microscope, bottom right.

 figure: Fig. 5

Fig. 5 Optical microscope image of the side-polished SM fiber, fixed in Al mount, under light reflection. The bottom images show the cross section (left) and the top view (right).

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Figure 6 shows our experimental setup in the laboratory, which includes a supercontinuum (SC) light source, smart textile sensor, and a spectrometer. The SC light source, which is used in the measurement setup only for research purposes, enables us to study the response of our sensor for a wide range spectrum [37], but it is quite feasible to use a low-price white light LED with lower power as well. To generate the SC beam, we used a Ti: Sapphire pulsed laser, 40X coupling objective, photonic crystal fiber tube (SKT-800 Newport) and other optical components, as schematically depicted in Fig. 6.

 figure: Fig. 6

Fig. 6 Schematic of the optical setup used to test the SPR dew sensor in the laboratory: (Top image) a picture of the supercontinuum beam; (middle image) layout of the environmental chamber, including the sensor, thermoelectric cooler, and other required equipment; (bottom image) the side-polished fiber sensor woven into the textile.

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To study the dew response of the smart textile sensor, it was affixed to a thermoelectric cooler (TEC), connected to the probe of a surface thermometer, as illustrated in Fig. 6. The setup was accommodated inside an environmental chamber equipped with a digital thermo-hygrometer and an ultrasonic humidifier. The dew sensing experiment was carried out at room temperature and normal atmospheric pressure. In addition, the temperature and humidity of our laboratory and the chamber were the same here. The measured temperature and relative humidity of the environment were T = 21°C and RH = 45%, respectively. To determine the dew point of the environment, TD, the temperature of the sensor was reduced using a TEC from ambient temperature to the dew point temperature at the fixed ambient RH, i.e., RH = 45%. Thus, we reduced the temperature in our smart textile sensor to reach the saturated condition for the water vapor in the air adjacent to the gold layer, leading to dew formation on the gold surface. While the temperature of the dew sensor was being reduced from T = 21 °C to T = 9 °C, there was no change in the transmission spectra of the sensor (black narrow solid curve in Fig. 7) implying that the gold surface was still dry, or TS ˃ TD. However, at T = 9 °C, the transmitted spectra gradually changed from black narrow solid curve (dry) to red thick solid curve (wet) in Fig. 7 in 9 s because of dew formation on the surface of the gold layer.

 figure: Fig. 7

Fig. 7 Left, variation of the transmitted spectrum during dew formation in the sensor; Right, normalized plasmonic loss spectrum.

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During this process, a thin layer of water formed on top of the gold layer, changing the refractive index on the top of the layer from one to approximately 1.33, which caused SPR excitation on different wavelengths to be observed in the transmission spectrum. The black and red curves show the minimum and maximum loss range of the sensor, which means that the SPR sensor can sense any tiny change in water layer thickness from zero to the SPR depth probe. Thus, our sensor can detect any layer formation from zero to around 250 nm, which is very sensitive for consolidation on and evaporation from the gold surface. Subsequently, we used Eq. (6) to calculate the dew point and compared it with the results measured using our SPR sensor. By substituting T = 21°C and RH = 45% into Eq. (6), we calculated the dew point temperature to be TD = 9.4 °C, which is very close to the temperature that we observed from maximum loss in our SPR sensor.

The right side of Fig. 7 shows the normalized plasmonic loss spectrum, defined as relative loss change (∆P/P), for an index difference of 0.33, implying that the SPR sensor has the best sensitivity around 600 nm. Thus, a simple red light LED can be used as a source here.

Figure 8 shows the real-time loss response at 632 nm when the temperature reached 9 °C, with a helium-neon laser source. This is the point at which the dew formed on the top of the gold layer in our experiment and the output power in the SPR sensor decayed in 9 s. We calculated the depth probe to be 250 nm at 632 nm, which means that the loss starting from the minimum reached to its maximum while the 250 nm water layer was forming on top of the gold layer in 9 s, at an average rate of approximately 27 nm/s. This dew formation rate is meaningful compared with typical values of condensation rates, such as those introduced by Garratt et al. [38]. For any water layer thicker than 250 nm no loss or transmission change can be observed.

 figure: Fig. 8

Fig. 8 Real-time loss response at λ = 632 nm when the temperature reaches 9 °C. The SPR output power decreases from its maximum to its minimum in 9 s.

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Our detector can detect loss changes of 2%, which means we can monitor the water layer formation on the top of the gold layer. Our sensor is thus suitable for in situ measurement of the thickness of the dew layer. Hassani and Skorobogatiy previously reported that they used an SPR sensor to monitor the thickness of bio layers [39]. Hence, we believe that we can use the same formulation in [39] to calculate the thickness of the dew layer forming on the surface of the gold layer. Equation (9) gives the definition of the sensitivity of SPR sensors:

S[nm1]=limdDew0|P(dDew)P(0)|/P(0)dDew 
where P(0) is the output power at a dew thickness of zero and P(dDew) is a function of the dew layer thickness at a specific operating wavelength of λ, which is 632 nm here. Using Eq. (9) and taking dDew = 250 nm at 632 nm, we measure P(dDew) = 0.18 and P(0) = 0.98, normalized values, leading to a sensitivity of approximately 0.0032 nm−1 and a signal-to-noise ratio (SNR) of 16 dB—by definition, SNR = 10 Log[(P(0)-P(dDew))/noise] and the noise here is 0.02 (or 2%). With the detection of the 2% change in the transmitted power, the sensor can easily detect the formation of 7 nm water layer thickness. Considering 9 s for loss saturation, the response time of the sensor is then 0.25 s for the formation of each 7 nm dew layer. This is much faster than commercial electronic dew meters, which have response times of several seconds to one minute.

Further, in order to assess the reliability of the measurements, we repeated the experiment four times in sequence with identical conditions. The condensation times were measured as 9.5 s, 9 s, 8.5 s, and 8.5 s, respectively, leading to a variation of 5% and good repeatability.

3.2 Evaporation rate measurements

In the inverse process to our activities in the previous section, the SPR sensor can be exploited to measure the evaporation rate for a wet layer. This means that in the range of 250 nm we can detect the evaporation of each 7 nm layer by monitoring the loss, so that, the 2% loss change leads to 7 nm water layer decrease on the top of the gold layer. Figure 9 shows the real-time measurement for a total 250 nm water layer evaporation, τ = 7.2 s and τ = 9.3 s when the RH of the adjacent air is 38% and 47%, respectively. Based on this measurement, evaporation rates of ~41 nm/s and ~32 nm/s are obtained, respectively.

 figure: Fig. 9

Fig. 9 Real-time measurement of optical output intensity versus total evaporation time of the layer of water with 250 nm probe depth thickness.

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3.3 Dependence of humidity and evaporation rate

According to the laws of thermodynamics, water evaporation rate slows as the surrounding environment becomes more humid or cooler, and vice versa. This also applies to the evaporation rate of the tiny water layer on the gold surface in our sensor. In this section, we estimate RH using the measured evaporation rate in Eq. (8).

Another useful term that can be used instead of evaporation rate is evaporating time (τ), which is the time that the water layer with depth probe thickness 250 nm takes to evaporate from the surface of the gold layer. Eav.τ=A shows the relation between the average evaporation rate (Eav) and (τ), where A = 0.25 g/m2. By substitutingEav=A/τin Eq. (8), we obtain the relationship between RH and τ as

RH(%)=100ατA+ατ
The blue dashed curve in Fig. 10 shows the RH and τ dependency in our experiment obtained using Eq. (10), where α = 0.023 g/m2.s was obtained based on parameters in the laboratory,α=eρCp/λra(Δ+γ*).

 figure: Fig. 10

Fig. 10 Comparison between RH obtained by Eq. (10) (the blue dashed curve) and those measured using our SPR sensor (red circular points).

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The red circular points in Fig. 10 are the measured evaporation times of the 250 nm water layer for RHs from 30% to 70% by our SPR sensor. The horizontal error bars in Fig. 10 show approximately 5% error in our evaporation time measurements. The vertical error bars are calculated considering the intrinsic errors of all employed measurement modules such as resolution of photo wattmeter and instability of light source. It is also a safe assumption to consider approximately 10% error based on equipment that people use in the laboratory. It is not too wonderful if the theoretical results fit perfectly with the experimental results because the SPR senor is very sensitive to the water layer thickness in its probe depth range. Thus, the sensor can sense the evaporation rate of the water layer, which implies a better resolution for humidity change in the laboratory environment. Thus it is safe to propose to calculate the RH in the environment using evaporation time as measured by our SPR sensor.

4. Conclusion

In this paper, we proposed the first smart textile dew sensor using plasmonic optical fiber, in which we utilize a surface plasmon depth probe to detect dew formation and evaporation with higher response times and sensitivities than conventional sensors. In addition, the proposed smart textile plasmonic dew sensor offers electrical immunity and distributed sensing, which are not possible or not sufficiently achievable with electrical dew point sensors.

In introducing our smart textile plasmonic dew sensor, we demonstrated the high sensitivity of surface plasmon resonance in relation to condensation and evaporation. This is the core sensing mechanism of our sensor. Two approaches were used to show the utilization of this core sensing mechanism. In the first approach, the focus was on using the condensation phenomenon to make a dew sensor, where the plasmonic fiber sensor was able to accurately detect dew formation on the surface of the sensor. In the second approach, the focus was on water evaporation rate, and the smart textile operated as a humidity sensor in an RH dynamic range of 30% to 70%. This case is worth further study using flammable gases instead of water and steam.

Acknowledgments

We would like to thank Robert Johnston, Mathieu Laliberte, and Morteza Mozafari for technical assistance rendered in their respective laboratories throughout this project. This research was funded by INRS-EMT and the NSERC CREATE Training Program in Integrated Sensor Systems (ISS), grant number 371305-2010.

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Figures (10)

Fig. 1
Fig. 1 Sample of our proposed distributed smart textile SPR dew sensor.
Fig. 2
Fig. 2 (a) Electric field distribution for surface plasmons on the metal/dielectric boundary. (b) Depth probe of surface plasmon versus operating wavelength at the metal/dielectric boundary.
Fig. 3
Fig. 3 (Left) Relative Humidity (RH) versus temperature, dashed-line curve. (Right) Evaporation rate of a wet surface (Ev) versus temperature, solid blue line.
Fig. 4
Fig. 4 (a) Cross section of the side-polished SPR fiber sensor showing the power distribution and plasmonic waves; plasmons are excited on the top of the gold layer to form a sensing area for dew measurements. (b) Schematics of temperature and humidity gradients adjacent to gold surface layer with tiny water layers forming.
Fig. 5
Fig. 5 Optical microscope image of the side-polished SM fiber, fixed in Al mount, under light reflection. The bottom images show the cross section (left) and the top view (right).
Fig. 6
Fig. 6 Schematic of the optical setup used to test the SPR dew sensor in the laboratory: (Top image) a picture of the supercontinuum beam; (middle image) layout of the environmental chamber, including the sensor, thermoelectric cooler, and other required equipment; (bottom image) the side-polished fiber sensor woven into the textile.
Fig. 7
Fig. 7 Left, variation of the transmitted spectrum during dew formation in the sensor; Right, normalized plasmonic loss spectrum.
Fig. 8
Fig. 8 Real-time loss response at λ = 632 nm when the temperature reaches 9 °C. The SPR output power decreases from its maximum to its minimum in 9 s.
Fig. 9
Fig. 9 Real-time measurement of optical output intensity versus total evaporation time of the layer of water with 250 nm probe depth thickness.
Fig. 10
Fig. 10 Comparison between RH obtained by Eq. (10) (the blue dashed curve) and those measured using our SPR sensor (red circular points).

Equations (10)

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E=e( x )exp( i( βzωt ) )
e z ( x )=Aexp( γ d,m x ) , and   γ d,m =ik ε d ε d + ε m           
L pd = 1 Re{ γ d }                               
RH( % )= e e s ( T ) ×100
e s (T)=(1.0007+3.46× 10 6 P)×(6.1121) e 17.502T 240.97+T
T D = 243.04[ ln( RH 100 )+ 17.625T 243.04+T ]  17.625ln( RH 100 ) 17.625T 243.04+T
λE= Δ Δ+ γ * ( R n G )+ γ * Δ+ γ * E A     
E= ρ C p λ r a ( Δ+ γ * ) [ e s ( T )e ]= eρ C p λ r a ( Δ+ γ * ) [ 100 RH 1 ]
S[ n m 1 ]= lim d Dew 0 | P( d Dew )P( 0 ) |/P( 0 ) d Dew  
RH( % )= 100ατ A+ατ
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