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Abstract
This study investigates the utilization of an in-fiber interferometer embedded in polydimethylsiloxane (PDMS) to develop a highly sensitive tactile sensor. The tapered mode-field mismatch structure is more conducive to stimulating strong high order modes to promote the sensitivity of the sensor. Experimental investigations are conducted to study the sensing performance of the sensor, resulting in a sensitivity of 23.636 nm/N and a detection limit of 0.746 mN. The experiments demonstrate that employing fast Fourier transform (FFT) and inverse FFT (IFFT) methods to filter weak high order modes significantly improves the repeatability of the sensor, resulting in a repeatability error of less than 1%.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Touch is considered to be one of the fundamental senses of the human body, enabling the acquisition of external information pertaining to temperature and pressure. With the prompting of robot technology, combining the feedback of the instrument with human perception is more conducive to improving human-machine interaction technology. In recent times, the utilization of tactile sensors embedded in flexible materials has emerged as a viable approach, enabling robots to effectively detect applied force and monitor carrier deformation, thus serving as intelligent skins [1,2]. Haptic detection can be achieved through the utilization of tactile sensors employing various detection principles, including capacitance-based [3], piezoelectric-based [4], resistance-based [5], and optical-based technologies [6]. However, it is important to note that sensors composed of electronic components are vulnerable to electromagnetic interference. Conversely, the tactile sensor based on optical technology possesses advantageous characteristics such as lightweight, compact size, immunity to electromagnetic interference, and easy integration into flexible materials. Consequently, it can serve as a sensing unit for distributed sensor networks, which find applications in wearable devices and intelligent robots [7,8]. In the past decade, numerous optical tactile sensors based on optical fiber have been reported. Fiber Bragg grating (FBG) has been widely used in the field of tactile sensing due to its favorable linearity and uncomplicated structure [8–10]. In 2023, Guan et al. introduced a tactile force sensor employing a square hole structure based on FBG for detecting touch in robotic fingers, with a detection sensitivity of 8.85 pm/N and a detection limit of 0.2 N [10]. It is evident that the tactile sensor based on FBG possesses a relatively low sensitivity, measuring below 10 nm/N, which may restrict their application in high-precision detection [8–10]. Furthermore, extensive research has been conducted on tactile sensors utilizing various specialized optical fibers. For instance, photonic crystal fiber (PCF) in the tactile sensor for weight detection of small objects has been proposed, exhibiting a detection sensitivity of 16.32 nm/N [11]. However, it is worth noting that despite the enhanced sensitivity, this particular structure is more costly to fabricate compared to standard optical fibers due to its intricate manufacturing process. Additionally, tactile detection can also be accomplished through structures based on distinctive fabrication techniques, such as air bubbles [12] and S-taper [13]. The tactile sensors utilized in these structures exhibit a notable sensitivity of up to 29 nm/N (S-taper structure [13]). However, their abilities for prolonged and consistent work are hindered due to their low mechanical strength and high optical power loss resulting from the intricate micromachining techniques employed.
In this paper, a flexible tactile sensor employing a Mach-Zehnder (M-Z) interferometer embedded in polydimethylsiloxane (PDMS) is proposed, capitalizing on the exceptional photoelastic effect of PDMS. Compared with tapered SMF, the mode-field mismatch structure is conducive to exciting stronger high order modes. To quantitatively assess the sensor's sensitivity to force response, the impact of strain on the effective refractive index (ERI) of the mode is examined through calculation. The corresponding sensitivities for force and temperature can be determined through the experimental process of monitoring the dips in the transmission spectra. The maximum sensitivity values are 26.818 nm/N for forces ranging from 0 N to 0.1 N, and -1.06 nm/°C for temperatures ranging from 24°C to 30°C. The matrix decoupling method is employed to mitigate the impact of temperature cross-sensitivity on force response. Three random experiments are conducted to validate the accuracy and feasibility of this approach in measuring force. The findings indicate that our measurement outcomes are basically consistent with those obtained from the balance. To verify the stability of the sensor, the dip wavelength is continuously monitored at room temperature. The results indicate that subsequent to the elimination of temperature cross-sensitivity, the dip wavelength of the sensor fluctuations decreases within ±0.02 nm. Additionally, to comprehensively assess the sensor's performance, its response time and repeatability are also studied. The practical application of the sensor is constrained by the random deviation caused by the loading/unloading force, which adversely affects its repeatability. To mitigate the influence of minor deviations leading to weak high order modes, the utilization of fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) methods are employed to filter out these modes. The findings demonstrate a significant reduction in the repeatability error, decreasing it from 5% to below 1%. Furthermore, this analytical approach holds promise for enhancing the consistency of interferometers by extending its applicability to different sensors with the same structures.
2. Design and fabrication
It is challenging to achieve high sensitivity in conventional M-Z Interferometers based on core mismatch, as they rely on mode field mismatch to induce interference between the fundamental mode and high order modes. Numerous studies have demonstrated that tapered fiber can effectively stimulate the high order modes to enhance its detection sensitivity. Combined with the tapering method, a sensing structure embedded in PDMS has been devised, as depicted in Fig. 1. The light is injected into the input single-mode fiber (SMF), which subsequently splits into two beams at the initial splicing point between the SMF and thin-core fiber (TCF) due to a mismatch of the mode field. One of these beams enters the cladding of the TCF, while the other propagates through the core of the TCF. An improvement in the effect of the evanescent field will lead to stimulating high order modes in the taper-down region and enhancing energy exchange with the fiber tapering. Due to the change in extinction ratio, part cladding order modes enter the core in the taper-up region of TCF and interfere with the core mode. Subsequently, the individual lights propagate independently along the core and cladding of the TCF, leading to re-interference with each other in the core of the output SMF, and its output light intensity can be expressed as
The transmission modes in the sensing process are determined by the diameter of the sensor, which subsequently impacts the sensor's sensing performance. In order to quantitatively assess this performance, numerically examine the correlation between the diameter of the tapered TCF and the transmission mode, as shown in Fig. 2(a). It is evident from Fig. 2(a) that an increase in the taper waist diameter results in a higher number of modes present in the TCF. In comparison to the low order mode, the high order mode exhibits a higher proportion of evanescent field in microfiber, thereby rendering it more susceptible to alterations in the surrounding environment [14]. Nonetheless, the thinner diameter is associated with increased optical power loss and decreased mechanical strength, thus constraining the applications of the sensor. The proposed sensor adopts a taper waist diameter of 19.8 µm, which exists modes of LP01, LP02, LP03, LP04, and LP05.
Fig. 2. (a) Calculated ERI of LP01∼ LP05 modes in the tapered TCF under different waist diameters at surrounding RI of 1.406, (b) the power evolution process of exciting modes in StTS and (c) in tapered SMF with the typical wavelength of 1550 nm.
To elucidate the mode excitation and evolution process, the calculation of the relationship between the relative power of each mode and transmission position is conducted, as shown in Fig. 2(b). In the simulation, SMFs with a core refractive index (RI) of 1.4544 and a core/cladding diameter ratio of 8.2/125 µm are utilized, while a tapered TCF with a core RI of 1.4581 and a core/cladding diameter ratio of 4.2/125 µm is employed. The simulation entails an input SMF with a length of 2000µm, a tapered TCF with a length of 32000µm (including a 2000µm intermediate taper), and an output SMF with a length of 2000µm. The surrounding RI of the sensing structure is 1.406. Light with 1550 nm is launched into the sensor from input SMF. The surrounding RI of the sensing structure is 1.406. Light with 1550 nm is launched into the sensor from input SMF. In Fig. 2(b), the blue line depicts the energy variation of LP01 mode within the fiber core, while the remaining colored lines represent the energy variation of LP02-LP05 modes within the cladding. Upon reaching the first splicing point, partly guide mode within the core transitions into the cladding and stimulates the high order mode as a result of mode field mismatch. Within the taper region of the TCF, the power of the LP01 mode experiences a further decrease within the core due to the reduction in core diameter, while the power of other high order modes increases, which indicates that a higher extinction ratio of the spectrum can be obtained. To assess the impact of mode-field mismatch on mode excitation, the simulation replaces the TCF with a SMF, while keeping all other parameters constant. Through a comparison of Fig. 2(b) and (c), it can be seen that the mode field mismatch between SMF and tapered TCF facilitates the stimulation of high order modes with increased power, aligning with the literature reported [15]. Consequently, the proposed sensor is expected to exhibit higher sensitivity in comparison to a tapered SMF structure possessing the same taper waist diameter. Furthermore, compared to the microfiber fabricated by SMF with a similar sensitivity, the proposed sensor with a large diameter offers superior mechanical strength, rendering it more suitable for integration into wearable devices.
The fabrication process of the sensor begins with the preparation of StTS. Firstly, a 3 cm long TCF is spliced between two standard SMFs to form an STS structure. And then tapering the prepared STS through a two-step tapering process, involving checking the arc discharge of the fusion splicer before tapering. The prepared STS is placed in a fusion splicer, and the arc discharges towards the center of the TCF, resulting in a slightly tapered TCF with a diameter of 90 µm. The first tapering process and micrograph of the tapered TCF after the first tapering step are shown in Fig. 3(a) and (b), respectively. Subsequently, the length of the TCF with the intermediate taper is marked to ensure that the intermediate taper can be aligned with the center of the hydrogen flame torch. Then, the intermediate taper TCF is fixed on the displacement platform of the optical fiber melt-drawn tapering system (AFBT-7000) to taper into a microfiber tapered TCF. It is noticed that the hydrogen flame torch of the melt-drawn tapering system needs to be preheated before tapering. Under heating of the flame at the marked position as shown in Fig. 3(c), drawing back of the displacement platform, the intermediate taper is turned into a long microfiber taper (∼2000µm in length) with two abrupt taper regions (∼450 µm in length) and a uniform waist region (∼1100 µm in length). The micrograph of the fabricated microfiber TCF is shown in Fig. 3(d).
Fig. 3. (a) Schematic diagram of the first tapering process using a fusion splicer, (b) micrograph of the fabricated taper TCF after the first tapering step, (c) schematic diagram of the second tapering process using an optical fiber melt-drawn tapering system, (d) micrograph of the fabricated microfiber TCF, (e) fabrication process of the sensor, (f) image of the sensor.
To prepare the flexible sensor, the sensing structure needs to be embedded in the PDMS using a two-step procedure. Initially, the PDMS liquid is prepared by combining the main agent and curing agent in a 10:1 ratio. Then, a small quantity of the prepared PDMS liquid is dispensed into a cube titanium groove with dimensions of 50 × 50 × 4 mm using a dropper and evenly distributed to cover the entire surface. The steel groove is placed on a heating platform equipped with temperature control capabilities. The steel groove is heated to a temperature of 100 °C for 20 minutes, resulting in the liquid PDMS solidified. Subsequently, the prepared bare StTS is placed onto the solidified PDMS, which serves as a substrate to provide support for the fiber structure. To fully encase the fiber structure with PDMS, a small amount of PDMS is once again dropped into the steel groove, as shown in Fig. 3(e), until the fiber is completely immersed in the liquid PDMS. The newly added PDMS through the same curing method undergoes solidification upon heating at 100 °C for 20 minutes. The schematic diagram of the final fabricated sensor is shown in Fig. 3(f).
3. Theoretical simulation
Theoretical research is performed to analyze the sensing characteristics of the proposed sensor which is fabricated by StTS embedded in PDMS. According to the interference principle, the dip wavelength of the mth order in the output spectrum can be written as
When a small force is applied to the surface of the sensor, the ERI of the mode and the coupling length will change, resulting in a shift in the dip wavelength. In this case, the change in dip wavelength can be deduced as
To analyze the impact of force on the PDMS and optical fiber structure, a force response is simulated by using the commercial software “COMSOL”. In the simulation, PDMS is a solid square with a size of 50 × 50 × 4 mm, and the fiber structure is embedded along the y-axis at a depth of 1.5 mm from the top surface of the sensor. A force of 0.1 N with a size of 5 × 5 mm along the z-axis is exerted on the top surface of the PDMS. The schematic diagram of the force application is shown in Fig. 4(a). The PDMS serves as a medium for transmitting the applied force to the fiber structure, resulting in deformation, as illustrated in the inset of Fig. 4(b). In Fig. 4(b), the red arrows above and below indicate the direction of deformation for the PDMS and fiber structure, respectively. Additionally, the color table illustrates the stress distribution of the PDMS and fiber structure. The observation from Fig. 4(b) reveals that the PDMS experiences displacement in the direction of the arrow when subjected to a force, indicating compression of the PDMS. Large deformation will lead to a change in the density of the polymer which affects the refractive index (RI) change. Simultaneously, the fiber structure moves along the below arrow with PDMS, which induces lateral and longitudinal displacement, while the fiber is not compressed longitudinally. The lateral displacement induces a change in the RI of the fiber material due to the photoelastic effect. The alterations in both the RI of PDMS and the RI of the optical fiber material will lead to the change in ERIs of modes, leading to a shift in the dip wavelength. Besides, the longitudinal displacement of the fiber will result in its elongation along its length. Considering the aforementioned impact on the sensor caused by force, the sensitivity of a small force can be expressed as [16]
Fig. 4. (a) Schematic diagrams of force imposed on the sensor, (b) inset of the sensor highlighting the effect of the applied force on it (sectional view perpendicular to the x-axis), (c) scatter plot of changes in RI differences of PDMS with different forces applied on the sensor and the relationship between applied force and RI of PDMS, (d) scatter plot of changes in ERIs differences of modes with different RI of PDMS, and (e) dependence of force sensitivities for different modes on wavelengths
The application of force on the sensor induces both transverse and longitudinal stress in PDMS. The application of force-induced compression results in an increase in the density of the material, consequently causing a variation in the RI of PDMS. This change in RI can be written as [17]
The simulation results of ${\varepsilon _z}$ and ${\varepsilon _x}$ are substituted into Eq. (5) to obtain the RI of PDMS. The resulting calculations of the force-induced RI changes in PDMS and the ERIs changes in modes under different RI of PDMS are shown in Fig. 4. As illustrated in Fig. 4(c), the RI of PDMS increases as the applied force increases, resulting in the increase of the RI difference of PDMS. By combining the calculated RI of PDMS by using Eq. (5) at various pressures, the ERI of transmission modes and the ERI differences between different modes and the fundamental mode are determined, as shown in Fig. 4(d). Based on previous analysis, the tapered TCF with a diameter of 19.8 µm exhibits five transmission modes, which are LP01, LP02, LP03, LP04, and LP05. Figure 4(d) illustrates that the rate of change in the ERI difference between LP05 and LP01 is the most significant when the RI of PDMS increases, reaching a value of 0.295. Conversely, the rate of change in the difference of ERI between LP02 and LP01 is the least significant, which is 0.015. Combined with Eq. (4), a large $[\partial (\Delta {n_{eff}})/\partial {n_P}] \cdot (d{n_P}/dF)$ corresponds to a high force sensitivity. It means that the increase in high order modes is conducive to improving the sensitivity of the sensor. Therefore, we hope that the sensor can excite high order modes to improve the sensing sensitivity, the sensor proposed in this paper conforms to this characteristic, so that high sensitivity detection with small forces can be achieved.
Additionally, the sensitivity of the sensor will be influenced by the force-induced photoelastic effect of the fiber material, resulting in a modification of the RI of the fiber. According to the photoelastic effect, the RI of silica-based fiber subjected to external force can be represented as [19]
Based on Eq. (4), it can be inferred that the longitudinal strain induced by the fiber structure is also one of the factors influencing the sensitivity of the sensor subjected to a force. The calculated result of $(\Delta {n_{eff}}/L) \cdot (\partial L/\partial F)$, approximately on the order of 10−11, is consistent with the impact of fiber materials on the difference in ERIs of modes as the applied forces increase from 0 N to 0.1 N. Therefore, the impact of longitudinal strain on the ERI of the transmission mode is disregarded in this analysis.
Based on the aforementioned analysis, the calculation of force sensitivity for various modes can be determined by employing Eq. (4), and the results are shown in Fig. 4(e). It demonstrates that as the force varies from 0 N to 0.1 N, the sensitivity for different modes exhibits an increase as wavelength increases, while remaining positive within the wavelength range of 1525 nm to 1565 nm. This implies that the dip wavelength in the interference spectrum shifts towards longer wavelengths, with longer wavelengths exhibiting greater sensitivity compared to shorter wavelengths. Different colors indicate the dependence of the calculated force sensitivities of the sensor for different modes interfere with the fundamental mode (LP01) on the wavelengths in Fig. 4(e). As can be seen from the figure, the high order mode (LP05) has great sensitivity with a maximum sensitivity of 28.26 nm/N at a wavelength of 1565 nm.
4. Experiments
4.1 Force response experiments
The force response of the proposed sensor is investigated through experimental analysis. The broadband light source (BBS) with a wavelength range from 1525 to 1565 nm, the sensor, the optical spectrum analyzer (OSA, Yokogawa-AQ6370) with a resolution of 0.02 nm are sequentially connected by SMF. To ensure uniformity in the applied force, a square glass slide measuring 5 × 5 mm is positioned at the center of the sensor's top surface. Different weights ranging from 0 g to 10 g at 1 g a step is sequentially applied as forces on the glass slide. The experiments are conducted in a constant temperature environment.
Figure 5(a) shows the transmission spectra overlap within the wavelength range from 1525 nm to 1565 nm at different forces from 0 N to 0.1 N at 0.01 N a step. The figure reveals a gradual increase in applied force, accompanied by red shifts in the dip wavelength of the transmission spectra. By tracking and performing linear fitting on the wavelength of the five dips with force sensitivities of 5.682 nm/N, 7.891 nm/N, 14.155 nm/N, 23.636 nm/N, and 26.818 nm/N are determined, corresponding to different dip wavelengths as illustrated in Fig. 5(b). The sensor exhibits a maximum sensitivity of 26.818 nm/N for force response which is 300 times higher than FBG structure [20–22], and the minimum detection limit is 0.746 mN. The obtained experimental results indicate that the long wavelength corresponds to a higher sensitivity, which is consistent with the theoretical simulation results. The experimental sensitivity exhibits a slight decrease compared to the simulation results, which can be attributed to the collaborative operation of the five modes during the sensing process.
Fig. 5. (a) The transmission spectra overlaps with different applied forces and (b) linear fittings of dip wavelengths.
4.2 Temperature response experiments
Because the PDMS and tapered structure are sensitive to temperature, the temperature response is experimentally investigated. The same sensor used in the force experiments is placed into an adjustable temperature control box and connected to an OSA and a BBS, respectively. Figure 6(a) displays the transmission spectra overlap of the sensor as the temperature rises from 24°C to 30°C at 1°C a step. Blue shifts of the dip wavelengths can be observed in Fig. 6(a) as the temperature increases. The linear fittings of the dip wavelengths are plotted in Fig. 6(b), exhibiting temperature sensitivities of −0.453 nm/°C, −0.544 nm/°C, −0.93 nm/°C, and −1.06 nm/°C, respectively.
Fig. 6. (a) The transmission spectra overlap with different temperatures and (b) the linear fittings of dip wavelengths.
5. Discussion
5.1 Cross-sensitivity with temperature
Since the RI of PDMS is impacted on the applied force and temperature, cross-sensitivity with temperature should be considered for the sensor operating at room temperature. The sensitivities of the four dips exhibit dissimilar responses to force and temperature, a sensitivity matrix can be built by tracking sensitivities under two different dip wavelengths to eliminate this problem, which can be written as [23]
The decoupling of the matrix allows for the acquisition of the force that effectively eliminates cross-sensitivity with temperature when both the temperature and the applied force change.
In order to validate the feasibility and accuracy of the aforementioned calibration approach, the sensor is subjected to three random temperature and pressure tests. A thermocouple thermometer (TCT) to monitor the ambient temperature in the three tests. By tracking the dip3 and dip4 in the transmission spectra, the temperature and force are determined for various conditions using Eq. (8). The obtained results are presented in Table 1. Table 1 presents a comparative analysis of the outcomes obtained through our measurements and those obtained through balance. The results show that our measurements are basically consistent with balance, with an average error of 2.4%.
Table 1. Comparisons of our tests with other instrument
5.2 Stability
The aforementioned experimental research demonstrates that the variability in room temperature has a detrimental impact on the stability of the sensor, as it is highly sensitive to temperature. Consequently, an investigation into the sensor's stability during continuous operation is conducted. λdip3 and λdip4 in the transmission spectrum are recorded every 10 min over a period of 100 min, as shown in Fig. 7(a). In this figure, the blue and red points represent the dip wavelengths obtained from the output spectra and the dip wavelengths with temperature correction by using calculations from Eq. (8), respectively. The dip wavelengths exhibit substantial fluctuations at room temperature, approximately ±0.2 nm. However, the dip wavelengths demonstrate a great improvement in stability by applying temperature correction, with fluctuations below ±0.02 nm.
5.3 Response time
The force response rate of the sensor is experimentally tested. Upon the sudden application of a force of 0.01 N on the sensor's surface, a significant decrease in dip intensity is observed. The dip intensity of dip5 is recorded continuously for 4 s with 0.2 s sample time which is shown in Fig. 8(a). The response time for the force of the sensor can be determined by the dip intensity of dip5 transitioning from 90% to 10% of its steady value, thus the response time of 0.34 s can be estimated.
Fig. 8. (a) The force response time of the sensor, and (b) the dynamic response of the sensor to finger movements of tapping and pressing.
A series of dynamic response tests are performed due to the short response time of the sensor to the force as different amounts of force applied vertically to the sensor. Figure 8(b) demonstrates the sensor's response to finger tapping and continuous pressing on its surface by tracking dip5 to illustrate its potential application as a human-machine interface device. The analysis of Fig. 8(b) reveals that the independent response with different wavelength shifts represents finger tapping and the continuous response with uniform wavelength shifts represents finger pressing. This implies that the distinction between these two action modes can be made based on the duration of the action and the magnitude of wavelength drifts.
5.4 Repeatability
To solve the problem of inconsistent sensitivity at different dip wavelengths, an analytical method has been introduced to examine the primary interference modes and their sensitivities during the sensing process of optical fiber interferometers in our previous research [24]. The spatial frequencies can be derived through the implementation of the FFT on the transmission spectra under different applied forces, which also reveal the main interference modes in the sensing process. The sensitivity of the dominant mode is determined by employing the IFFT to transform the spatial spectrum of the dominant interference mode for the purpose of analyzing the sensing characteristics. This approach effectively solves the issue of inconsistent sensitivity across different dip wavelengths. By utilizing the aforementioned approach, the spatial spectra of transmission spectra through FFT and the interference spectra of the dominant mode through IFFT can be obtained, as shown in Fig. 9. It can be seen from Fig. 9(a) that the low order mode displays the greatest amplitude. The sensing procedure demonstrates a single amplitude peak with noticeable variations and multiple weaker high order modes. The mode with the highest amplitude is LP05 mode by calculated [25]. Figure 9(b) presents the interference spectra of the LP05 mode obtained through IFFT. The figure reveals that the sensitivities of various dip wavelengths remain consistent by employing the IFFT method, with a force sensitivity of 24.127 nm/N. Furthermore, although the transmission mode has been determined by determining the diameter of the tapered TCF, an increase in diameter in taper-down region results in the excitation of multiple weakly high order modes. Confinement of a significant portion of energy within the core due to the enlarged diameter leads to a diminished evanescent field, thus the weak high order modes contribute less to the sensing performance of the sensor. In order to mitigate the impact of multimode sensing on the performance of the sensor, it is possible to eliminate the weak high mode and use the dominant mode LP05 to evaluate the sensing performance of the sensor.
Fig. 9. (a) Spatial spectrum and modes distribution by using FFT, and (b) superposition of the interference spectrum of dominant mode and its linear fitting.
Due to the high sensitivity of the proposed sensor, any tiny difference in experimental operation will exhibit different sensing performances, including slight deviations in the load/unload force process. In order to investigate the impact of these random deviations on the sensor's performance, an experimental study is conducted to assess its repeatability. The force response experiment shown in Fig. 5 is denoted as T1, while two additional repetitions of the experiment are carried out, which are labeled as T2 and T3, respectively. Each test involved a gradual increase in the applied force, starting from 0 N and reaching 0.1 N at 0.01 N a step. All experiments are conducted in a constant temperature environment. The transmission spectra overlaps of these tests are presented in Fig. 10(a) and (b), respectively. By tracking the dip wavelength of dip5, linear fittings are obtained for each test, as shown in Fig. 10(g). The force sensitivity values for the three tests are found to be 26.818 nm/N, 25.482 nm/N, and 26.455 nm/N, with corresponding linear fittings of 98.7%, 97.4%, and 99.0%, respectively. The calculated maximum repeatability error is 4.98%. In order to examine the distribution of modes in the three tests, the spatial spectra overlaps of the three tests can be obtained by using the FFT, as shown in Fig. 9(a), Fig. 10(c), and (d), respectively. By considering the spatial spectra of the three tests, it indicates that the spatial spectra of T3 exhibit a lower proportion of weak high order modes compared to T1, resulting in a reduced experimental sensitivity of T3. While the weak high order mode in the spatial spectrum of T2 is the least, leading to the lowest experimental sensitivity among the three tests. It reveals that tiny deviations hardly impact on the dominant mode LP05, but can significantly affect the weak high order modes. To eliminate this influence, the method of filtering out the weak mode is used to calculate the sensitivities of the dominant mode LP05, enabling analysis of the sensor's sensing performance. The IFFT transformations of LP05 for T1, T2, and T3 are shown in Fig. 9(b), Fig. 10(e), and (f), respectively, while their linear fittings are illustrated in Fig. 10(h). The force sensitivities of the LP05 mode, as determined through the mode filtering method, are measured to be 24.127 nm/N, 23.973 nm/N, and 23.945 nm/N, exhibiting a repeatability error of less than 1%. Additionally, the application of the mode filtering method in analyzing the sensor performance proves to be highly effective in enhancing the sensor linearity, resulting in linearities of 99.9% of the three tests. The sensitivity of the dominant mode, as demonstrated by the aforementioned results, can be employed as a means of examining the sensing characteristics of the sensor. This approach serves to alleviate disruptions to sensor performance arising from multiple modes, while concurrently enhancing the repeatability of the sensor. Furthermore, this analytical methodology can be extended to different sensors with the same structure, which is expected to improve the consistency among sensors and solve the low consistency problem of the interferometer.
Fig. 10. The transmission spectra overlaps of (a) T2 and (b) T3, the spatial spectra overlaps of (c) T2 and (d) T3 obtained by FFT, the spectra overlaps of LP05 in (e) T2 and (f) T3 calculated by IFFT, the linear fittings of (g) dip5 and (h) LP05 in the three tests with applied forces.
Table 2. Comparison results of other force and load sensors
The sensitivity of the sensor is a crucial parameter that needs to be considered. Table 2 shows the comparison results between the proposed sensor in this paper and other representative existing force and load sensors. The table clearly indicates that force detection can be accomplished using various optical fiber sensing structures. Notably, the sensitivity of the sensor proposed in this study is hundreds of times higher than the FBG structure [20–22] and higher than that of the majority of fiber sensors [11–12,24,26–27]. PDMS-coated S-tapered fiber has a higher sensitivity, because of the increasing coupling ratio and exciting higher modes by asymmetric structure [13]. However, an asymmetric structure leads to significant optical power loss and reduced mechanical strength, which is susceptible to spectral instability and unsuitable for prolonged monitoring. In contrast, the proposed sensor with PDMS-embedded StTS has a simple structure and easy fabrication, while also demonstrating exceptional detection sensitivity and repeatable spectra. Consequently, this sensor has the potential to be utilized in flexible wearable devices.
6. Conclusion
In conclusion, this study proposes a tactile sensor that utilizes the StTS structure embedded in PDMS for the detection of millinewton force, and its sensing performance is theoretical and experimental research. The sensing principle of the sensor is deduced theoretically, and the factors affecting the sensitivity of the force response are analyzed. In comparison to tapered SMF, tapered TCF has the ability to stimulate stronger high order modes, thus facilitating an improvement in the sensitivity of the sensor. Additionally, the results demonstrate that the flexible packaging of PDMS also can enhance the force response sensitivity of the sensor. The tactile sensor based on PDMS-embedded StTS is prepared and its force and temperature sensing performance are investigated. The trend in the experimental results aligns with that of the theoretical simulation, although the experimental values are lower than those of the simulation. This difference can be attributed to the multi-mode interference during the experimental sensing process. Furthermore, the temperature cross-sensitivity, response time, stability, and repeatability of the sensor are also investigated experimentally. Through the elimination of temperature cross-sensitivity, our measurements exhibit a fundamental alignment with the other instrument (balance) and demonstrate notable wavelength stability when conducted at ambient room temperature. A sudden load force changing from 0 N to 0.01 N is subjected to the sensor with a response time of 0.34 s, and a prompt reaction in dynamic testing. Moreover, the weak high order modes of the sensor are affected by tiny deviations in the experiment. The dominant mode is acquired by eliminating the less influential high order modes, which can be used to analyze the sensing performance of the sensor. In contrast to the traditional method of evaluating sensor performance via dip wavelength tracking, the analysis of the dominant mode significantly enhances the sensor's repeatability, with a repeatability error of less than 1%. In summary, the presented sensor exhibits notable benefits such as easy fabrication, high sensitivity, good repeatability, and consistency, thereby the sensor will find application in human-machine interface devices and the field of flexible robotics.
Funding
Postdoctoral Research Foundation of China (20080441150, 200902574); The Qingdao Feibo Technology Co., Ltd. (02040102401); Department of Education of Shandong Province (J06P14); State Key Laboratory of Mining Disaster Prevention and Control (MDPC201602, MDPC2022ZR04).
Disclosures
The authors declare no conflict of interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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