**3. Experimental Results and Discussion**

In the experiment, the proposed PT/PFFI device is placed inside the THCC, a closed space in which the tilt angle is operated from φ = –10◦~+10◦ with a step of 1◦ under fixed T and fixed relative humidity of 50%. Figure 5 shows the results. For the sensor with d = 46 μm, Figure 5a,b show the spectral responses to positive φ and negative φ, respectively. These experimental results are almost similar due to the central symmetry of the PT structure. Figure 5c displays variations of FV of reflection for sensors A and B as the φ changes from −10◦~+10◦. When the φ of the sensor increases, the FV has high attenuation. Moreover, at high angles, the FV gradually weakens and then vanishes because the optical light almost leaks out in the great bending of PT. When different sensing structures of sensors A and B are used (as shown in Figure 1), the responses and sensitivities of φ

variation from −10◦ ~ +10◦ are obtained and shown in Figure 5c,d, respectively. Sensor A (d = 23 μm) with thinner PT seems to be more sensitive than sensor B (d = 46 μm). However, the tilt measurement range is relatively small for sensor A. The tilt sensitivity S is defined as:

$$\mathbf{S} = \frac{\mathbf{d}(\mathbf{F} \mathbf{V})}{\mathbf{d}\boldsymbol{\Phi}} \tag{1}$$

**Figure 5.** Optical responses for the variations of tilt angle (φ) by (**a**) positive φ and (**b**) negative φ; (**c**) Responses of FV to tilt angles by sensor A with d = 23 μm and sensor B with d = 46 μm; (**d**) φ-related sensitivities of the tapered polymer sensors for sensors A and B.

Figure 5d shows that high responses are achieved from tilt angles of φ = −10◦ ~ +10◦ and sensors A and B obtain the highest sensitivities of 0.72 dB/◦ at φ of ±2◦ and 0.6 dB/◦ at φ of ±2.7◦, respectively. It is worth mentioning that in the tilt sensing, the interference power and FV highly vary but the wavelength peaks of optical interferences are nearly unshifted, as shown in Figure 6a. The inset of Figure 6a displays the detailed optical interference spectra for the variations of corresponding parameters φ at T = 25 ◦C. On the other hand, when the sensor is heating and cooling with T, the range is 20 ~ 45 ◦C at a fixed φ = 0◦. The interference is red-shifted as T increases and vice versa. Figure 6b plots the T-sensitivity of the proposed PT/PFFI sensor. The detailed optical interference spectra for heating and cooling are shown in the Figure 6c,d, respectively. The results indicate that the optical responses have high repeatability, and the sensitivity is linearly proportional to T with 0.17 nm/◦C. The obtained results of the T sensitivity may not be high; however, the optical power of the spectral responses almost does not

decay that can easily distinguish non-tilt variations. Based on the above sensing results, the proposed PT/PFFI can demonstrate the superiority of sensing characteristics to avoid the cross-sensitivity of the measured parameters.

**Figure 6.** Wavelength shift responses for the variations of (**a**) tilt angle, φ at fixed T = 25 ◦C and (**b**) temperature, T by (**c**) heating and (**d**) cooling with fixed φ = 0◦.

The effectiveness for the developed sensing configuration is examined by simultaneously varying φ and T from their reference values of ambient (set as φ<sup>0</sup> = 0◦ and T0 = 20 ◦C) to various conditions, as shown in Figures 7 and 8, respectively. The optical spectra of the initial condition of φ<sup>0</sup> = 0◦ and T0 = 20 ◦C as the reference for the test sensor B are recorded at the beginning of the experimental investigations (as blue-dashed lines of Figures 7 and 8). Figure 7 presents the simultaneous measurement of the arbitrarily chosen φ and T for many cases. Clearly, the variation of the FV is only due to changes of φ and the wavelength shift (Δλ) is merely affected by T variation. The parameters of φ and T can be respectively estimated by using the experimental relations of FV = 2.66·exp(−0.0715·φ2) and Δλ = 0.17·T − 3.565 when these two factors are measured.

Figure 8 shows the individual interference spectra of every case to compare with that of the initial φ<sup>0</sup> and T0. The arbitrary conditions are: (a) T = 20 ◦C, φ = 4◦; (b) T = 25 ◦C, φ = 1◦; (c) T = 30 ◦C, φ = 2◦; (d) T = 35 ◦C, φ = 0◦; (e) T = 40 ◦C, φ = 2◦; and (f) T = 45 ◦C, φ = 5◦. The measured values of the φ and T can be estimated by the measured FV and Δλ in the optical interference spectra by using the experimental

relations of FV = 2.66·exp(−0.0715·φ2) and Δλ = 0.17·T − 3.56. The measured FV and Δλ of each case are: (a) Δλ = −0.1 nm, FV = 0.847 dB (b) Δλ = 0.73 nm, FV = 2.399 dB, (c) Δλ = 1.48 nm, FV = 1.488 dB, (d) Δλ = 2.42 nm, FV = 2.654 dB, (e) Δλ = 3.28 nm, FV = 2.094 dB, and (f) Δλ = 4.11 nm, FV = 0.471 dB for determining every case of the measured T and φ, as shown in Figure 8 and also listed in the following Table 1. Here, the second decimal point for the measured Δλ is an artificial estimation value, so that the accuracy of the measured Δλ as well as the obtained T is one decimal point.

**Table 1.** Evaluating the simultaneous measurement of φ and T in different conditions by measuring the Δλ and FV.


**Figure 7.** Interference spectra of the sensor when φ and T simultaneously change at different conditions.

**Figure 8.** Interference spectra individually compared with the reference spectrum for (**a**) T = 20 ◦C, φ = 4◦; (**b**) T = 25 ◦C, φ = 1◦; (**c**) T = 30 ◦C, φ = 2◦; (**d**) T = 35 ◦C, φ = 0◦; (**e**) T = 40 ◦C, φ = 2◦; and (**f**) T = 45 ◦C, φ = 5◦.

The results in Figures 7 and 8 and Table 1 show that the simultaneous sensing of φ and T is accomplished. The simultaneously measured values of φ and T are very close

to the setting values displayed in the THCC and tilt stages. The six setting conditions of (a) T = 20 ◦C, φ = 4◦; (b) T = 25 ◦C, φ = 1◦; (c) T = 30 ◦C, φ = 2◦; (d) T = 35 ◦C, φ = 0◦; (e) T = 40 ◦C, φ = 2◦; and (f) T = 45 ◦C, φ = 5◦ can achieve the measured T and φ with (a) T = 20.38 ◦C, φ = 4◦; (b) T = 25.26 ◦C, φ = 1.2◦; (c) T = 29.68 ◦C, φ = 2.85◦; (d) T = 35.21 ◦C, φ = 0.18◦; (e) T = 40.26 ◦C, φ = 1.83◦; and (f) T = 45.09 ◦C, φ = 4.92◦, respectively. The measured errors in T and φ are also shown in Figure 9 with (a) Terror = 0.38 ◦C, φerror = 0◦; (b) Terror = 0.26 ◦C, φerror = 0.2◦; (c) Terror = −0.32 ◦C, φerror = −0.15◦; (d) Terror = 0.21 ◦C, φerror = 0.18◦; (e) Terror = 0.26 ◦C, φerror = −0.17◦; and (f) Terror = 0.09 ◦C, φerror = −0.08◦, respectively. Based on the above data, the average errors of the measured φ and T of the six simultaneous measurements are approximately 0.253 ◦C and 0.13◦, respectively. The above results demonstrate the effectiveness of the proposed PT/PFFI sensor for simultaneous measurement of φ and T. The small errors of the measurements are attributable to the deviations of operating the instruments. Moreover, non-flat endface of the fibers caus20ed by the mechanical fiber cleaver is another reason. The flat surface would be effectively cleaved by using a femtosecond laser to improve the measured accuracy [21]. ° °° °

**Figure 9.** (**a**) Sample data for measurement comparison; (**b**) Error analysis of the sample measurement.
