The field of temperature sensors covers a high percentage of today's World sensors market due to the large number of application in which it is necessary to measure temperature, for instance: the automotive industry, air-conditioning control and the chemical industry, among others. Nevertheless, traditional temperature sensors such as thermocouples and thermistors are not well suited for use whenever specific needs are required. This is the case of temperature measurement in many low-cost industrial processes in the presence of electromagnetic disturbances. To solve these problems, innovative solutions based on amplitude or phase fiber-optic techniques have been developed [1]. Temperature phase sensors are based on phase changes of an electromagnetic wave traveling along an optical fiber caused by temperature changes. Different interferometric configurations have been proposed as temperature sensor such as Mach-Zehnder [2] and Fabry-Perot one [3]. Although they usually have larger sensitivities, they require more complex reception circuits. Temperature amplitude modulation sensors are based on optical power variations. Some proposed sensors are based on light attenuation [4], frustration of total internal reflection [5–8], controlled mode coupling [9], light generation [10], Fiber Bragg Grating wavelength shifts [11,12], and fluorescence [13,14]. These sensors have different degrees of complexity that depend on their configuration. All intensity sensors need a reference technique [9,15–17] to avoid false readings caused by fluctuations of the light source, optical fiber attenuation coefficient or other undesired losses.

In this paper, the authors propose and characterize a low-cost intensity macro-bend temperature sensor based on polymer optical fiber (POF). The sensor system used a dummy fiber-optic sensor for reference purposes. Other techniques to measure the temperature with a macro-bend sensor have been developed using either single mode [5] or multimode [7,18] silica optical fiber. The main advantages of using POF instead of glass fiber to build the sensor are the large core diameter and smaller Young modulus, making them less fragile and easier to handle; reducing development and maintenance costs. Although polymer based sensors have a smaller temperature range. The highly multimode nature of POF sensors implies especial features as the influence of external surrounding media that have to be considered in practical implementations.

In this context, the purpose of this work is to design and implement a POF [8] temperature sensor in a self-reference configuration and including a comprehensive experimental analysis to provide insight into the effect of different surrounding media and bend radii on the sensor response. Experimental results are also compared with mathematical models based on geometric approaches [18].

Figure 1 shows a schematic of a curved multimode step index optical fiber [19]. The radius of curvature is R and the core diameter is 2ρ_Core. The refractive indices of the core and cladding are n_Core and n_Cladding, respectively. Optical power is launched at the beginning of the rectilinear region of the fiber. The geometrical description of the core rays in a step-index optical fiber is more complex than in a planar waveguide [20], due to the presence of the skew rays. The guidance of the core rays is achieved by ensuring that the propagation angle, α, satisfies the condition: 0 ≤ α ≤ α_c, where the critical angle (α_c) is given by: α_c = sin⁻¹ (n_Cladding/n_Core) The expression of the numerical aperture (NA) for the rectilinear region is given by: (1) N A = n Core ⋅ sin α ≤ ( n Core 2 − n Cladding 2 ) 1 / 2

However, in the bend optical fiber, the guidance of the core rays can follow two ways. Only the rays entering the bent part of the fiber in the meridional plane remain with the same angle of incidence along a given ray path. On the other hand, the skew rays entering this plane, after the successive reflections within the core, do not follow a simple repeatable pattern because of the asymmetry introduced by bending the fiber. So when the optical fiber is bent, the local numerical aperture changes at a given location of the bent optical fiber. The dependence of the numerical aperture with the bend is given by [19]: (2) N A ( R , ρ , ϕ ) = n Core [ 1 − n Cladding 2 n Core 2 ( R + ρ Core R − ρ ⋅ cos ϕ ) 2 ] 1 / 2where ϕ is the ray angle at the beginning of the bend, which varies from 0° to 180°, ρ_Core is the fiber core radius and ρ is the radial position in the core satisfying the relation 0≤ ρ≤ ρ_Core.

The optical fiber sensor proposed in this paper is based on a macro-bend POF. In this intensity sensor, the losses induced by the bending effect depend on the numerical aperture, that change with temperature. The refractive index of the core and cladding POF depend on the temperature. The POF used in the experiments is a Rayon^® Eska^® SH-4001 (Mitsubishi, Tokyo, Japan) with core and cladding manufactured using polymethyl methacrylate (PMMA) and fluorinated polymer, respectively. The temperature dependence of the core refractive index can be expressed as [21]: (3) n Core ( T ) = K 2 ⋅ T 2 + K 1 ⋅ T + n 0where K₁= −1.15·10⁻⁴(°C)⁻¹ is the thermo-optic (TO) coefficient of the core, K₂= −5.173·10⁻⁷(°C)⁻² is the second order temperature dependence term of the core and n₀=1.49538 is the core refractive index at 0 °C. On the other hand, the temperature dependence of the cladding refractive index is given by [22]: (4) n Cladding ( T ) = n Cladding ( T 0 ) + K 3 ⋅ ( T − T 0 )where K₃= −3.5·10⁻⁴ (°C)⁻¹ is the TO coefficient of the cladding and n_Cladding(T₀)=1.403 is the cladding refractive index at the reference temperature (T₀ = +25 °C).

It can be seen that |K₃| > |K₁|. Finally, from Equation (2), the local numerical aperture in the bent section of the fiber versus the temperature can be expressed as: (5) N A ( T , R , ρ , ϕ ) = n Core ( T ) [ 1 − n Cladding 2 ( T ) n Core 2 ( T ) ( R + ρ Core R − ρ ⋅ cos ϕ ) 2 ] 1 / 2

Using Equations (3) to (5), the temperature dependence of the numerical aperture for different ray radial positions in the core has been plotted in Figure 2.

Analyzing the positive slope of the curves for each radial position, it can be seen that the local numerical aperture increases when the applied temperature increases. This increment happens because an optical ray that is unguided at the reference temperature becomes guided at temperatures greater than the reference temperature. Figure 3 shows the local numerical aperture as a function of the bend radius at T = 25 °C. The local numerical aperture increases as the bend radius increases up to the local numerical aperture for a straight fiber (R = ∞) with a value around 0.5.

The insertion losses of the sensor at a specific temperature increase as the bend radius decreases. The POF used in the experiments has a critical radius of curvature of 25 mm, so the manufactured sensor is always operating at a lower R value as it is shown below.

In this section, the sensor manufacturing process, the experimental set-up and the measurements of the sensor calibration curves are reported. In Figure 4, a photograph of the manufactured fiber-optic temperature sensor can be seen. A commercial step index POF fiber with a good tensile strength and flexing is used. These characteristics provide good mechanical properties at the time of manufacturing the sensor. From the middle section of the fiber length, the buffer coating is partially stripped. The length of this stripped section is about 30 mm. The fiber sensor is formed by creating a single 180° loop (½ turn) with a concrete bend radius, as shown in Figure 4. To fix the radius, a cylinder is used to facilitate and give more precision to the bending process. Then, the buffer coating in the junction of the two branches is fixed by cyanoacrylate adhesive. With this simple method, a stable macro-bend fiber temperature sensor can be manufactured.

The schematic of the experimental set-up is shown in Figure 5a. The light source is a 660 nm Light-Emitting Diode (LED). The fiber-optic sensor was fixed close to the rectangular highly conductive metal base plate of a heating unit (LTS350, Linkam, Surrey, United Kingdom). The temperature of the hot plate was controlled with a controller unit (Linkam TP94). For measuring the real temperature of the optical fiber sensor, an independent electronic temperature sensor LM35 was used in the measurements. Temperature measurements are taken on the hot plate and at a 1 mm distance from the hot plate. A thermal isolated stage has been performed for supporting the fiber sensor when it is placed at a 1 mm distance from the plate. A caliper has been used to measure the position.

An additional macrobend fiber loop, identical to the proposed fiber-optic sensor is used for reference purposes, as shown in Figure 5. This fiber-optic reference or dummy sensor, placed outside of the heating unit, monitors the optical power fluctuations not related to the sensing magnitude. The output voltage at the reference (V_Reference) and sensing (V_Sensor) branch can be expressed as: (6) V Re ference = β Re ference ⋅ ℜ λ ⋅ δ ⋅ G Re ference ⋅ F ' ( T 0 ) ⋅ P Light Source (7) V Sensor = β Sensor ⋅ ℜ λ ⋅ δ ⋅ G Sensor ⋅ F ( T ) ⋅ P Light Sourcewhere β_Sensor and β_Reference are factors including the attenuation of the fiber leads, coupler insertion losses and connectors losses, of the sensing and reference branch respectively. 𝕽_λ is the photodiode responsivity at the operating wavelength (λ = 660 nm), considering identical photodiodes. δ is the scale factor of the receivers for a specific output impedance. G_Reference and G_Sensor are the transimpedance amplifier gains for the reference and sensor branch, respectively. F(T) is the optical power modulation function versus temperature at the fiber-optic sensor and F'(T₀) is the insertion losse at the reference temperature (T₀) of the dummy sensor. Finally, P_{Light Source} is the optical power of the light source.

In order to compare the calibration curve with mathematical models and other intensity fiber optic sensors, the output voltage at the reference and sensing branch has been expressed in optical power units. The output optical power at the reference (P_Reference) and sensing (P_Sensor) branch can be expressed as: (8) P Re ference = β Re ference ⋅ F ' ( T 0 ) ⋅ P Light Source (9) P Sensor = β Sensor ⋅ F ( T ) ⋅ P Light Source

From both equations, the self-reference output power ratio γ_SR is defined as: (10) γ S R = P Sensor P Re ference = β Sensor ⋅ F ( T ) ⋅ P Light Source β Re ference ⋅ F ' ( T 0 ) ⋅ P Light Source = β Sensor β Re ference ⋅ F ' ( T 0 ) ⋅ F ( T )

Therefore the ratio of the output optical powers depends on the power sensor variations with temperature and on a constant ratio between the insertion losses of the sensing and reference branch.

As previously stated, the conditioning circuit is made of a photodiode and a transimpedance amplifier, see Figure 5a. The amplifier gain was fixed at 10dB for all measurements.

In the experiments, the self-reference output power ratio (γ_SR) has been measured from +29 to +70°C at 2 °C intervals. The minimum temperature has been limited by the cooling capabilities of the heating unit and the maximum temperature was limited by the capabilities of the POF. A time interval of 2 min has been set, between each temperature measurement, to ensure the stabilization of the voltage values. The sample rate and the number of samples of the output power ratio at each temperature have been fixed at 5 Hz and 10 samples, respectively. A total of six sets of measurements of the calibration curve have been carried out to perform a complete statistical analysis of the sensor parameters. Software based on National Instrument Labview^® code has been developed to acquire the voltage from the receivers, to calculate the optical power of each branch and to post-process the data.

In this article, the authors have shown a temperature sensor based on a POF macro-bend loop. Different experiments have been carried out for measuring the calibration curves at different conditions. To ensure the stability of the sensor over time, six sets of measurements were carried out with a time interval between them of about 2 h. For a bend radius of 2.0 mm, the temperature sensor system has a calibration curve whose sensitivity is 1.92·10⁻³(°C)⁻¹. A statistical analysis of the calibration curve shows that the sensor has a linear response with a non-linearity full scale error of 3.9%. The designed system allows a resolution of 0.3 °C from +27.2 to +50.2 °C.

The most limiting component in the system resolution is the data acquisition card. The acquisition card in this experiment is a USB 6009 (National Instruments^®, Austin, TX, United States of America) with a noise value of 0.5 mV_RMS at a voltage range of ±1.0 V. Using another acquisition card, the resolution of the system can be reduced to obtain a value of 0.1 °C being limited by the noise generated by the transimpedance amplifier gain.

The optical input and output power measured at the sensor curve are compared with the simulations. Those values are obtained from measuring the optical power at the input and output of the sensor and estimating the connector, adaptor and straight section fiber losses. In the measurements, two types of connectors have been used from different manufacturers and with different losses. For a bend radius of 1.5 mm and 2.0 mm, the connector losses are measured to be 1.2 and 2.2 dB, respectively. These values are below the maximum limits (≤2.5 dB) set by the two manufacturers. The self-reference topology proposed avoid the sensor response dependence of these connector losses and of other losses that can be present under the sensor operation.

The intensity sensors are usually used at non-critical and low-cost systems when high precision and resolution are not required. A comparative analysis has been developed between the proposed sensor and other intensity temperature sensors reported on the literature (see Table 1).

From Table 1, it can be seen that the different sensor parameters are similar, apart from the sensitivity. The sensitivity of the proposed sensor is similar to that obtained with silica fibers [5,7,13], but they are also more fragile and usually needs more expensive equipment. The other sensors based on fluorescence techniques, measure the attenuation of the luminescence signal caused by the presence of a convenient indicator, such as glue or ink [13,14]; they can obtain a higher sensitivity but making them also more complex approaches.

In terms of reproducibility, as in any intensity sensor it is essential to have a self-reference configuration to avoid the influence of external loss variations of the whole set-up. Special care should be taken with connector losses, and with the manufacturing process of the fiber-optic sensor.

On the other hand, the experimental results show the effect of the external environment on the temperature measurement. As described previously, changes in the refractive index of the surrounding media in contact with the cladding, especially metals, produce a reduction in a factor of more than two in the sensor sensitivity. For the proper operation of the proposed temperature sensor, it is very important to carry out a characterization of the sensor under real working conditions. This property can also be used to improve the system but at the expense of increasing its complexity. As shown in Table 1, different sensors use absorbed coatings that modify the refractive index of the fiber to increase the sensitivity of the sensor and thereby improving the sensor parameters. Finally, this behavior can also be used to develop other type of sensors, as for example a detector of different metal materials in industrial processes.

In conclusion, macrobending loss, caused by the different thermo-optic coefficients of the cladding and core of a step-index Polymer Optical Fibers (POFs) has shown to be a usable technique for temperature sensing. The sensor has been tested in the temperature range from +27.2 to +50.2 °C. The sensor sensitivity for a bend radius of 2.0 mm is 1.29·10⁻³(°C⁻¹). The sensitivity increases as the radius of curvature increases. In addition, sensor sensitivity measurements are in good agreement with simulations. The automated self-reference sensor system shows a resolution below 0.3 °C and a 3.9% non-linearity full scale error. The proposed sensor requires only a few and relative low-cost components. The influence of external media in contact with the sensor has been analyzed. The sensor can be used in a large range of applications, for instance: instrumentation process, automotive industry, air-conditioning control, chemical industry, biomedical sector and detection of metal particles in contaminated fluids.