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Abstract
A soft highly sensitive tactile sensor based on an in-fiber interferometer embedded in polydimethylsiloxane (PDMS) structure is studied. Theoretical simulation obtains that the high order sensing modes and PDMS can improve the sensitivity. Experiments show that different order sensing modes, derived by fast Fourier transform (FFT) and inverse FFT methods, present different sensing performance. Corresponding to high order mode, 1.3593 nm/kPa sensitivity and 37 Pa (0.015 N) detection limit is obtained. Meanwhile, it also shows very good stability, reproducibility, and response time. This study not only demonstrates a tactile sensor with high sensitivity but also provides a novel sensing modes analysis method.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Tactile sensors have attracted increasing attention with the development of modern intelligent robots, which can be applied in robot grasp feeling [1], smart skin [2], minimally invasive robotic surgery [3], etc;. Sensors usually employ structures for embedding or pasting various sensing elements to elastic materials, such as polydimethylsiloxane (PDMS), silicone gel, natural rubber, and polyurethane [4–7]. Normally, tactile force is very small, the sensor needs high sensitivity [2,3]. Furthermore, as many sensors function simultaneously, the sensors need a high networking capability [1]. Further, the tactile sensor should be lightweight and have small size and anti-electromagnetic interference properties. Therefore, many optical fiber soft tactile sensors have appeared in recent years [8–10]. Fiber Bragg gratings (FBG) are generally chosen as sensing elements in tactile sensors [11]. Typically, in 2021, a dual-range tactile sensor integrated in a three-layer skin with a wide range of 0–50 N and maximum sensitivity of 0.03 nm/N, was proposed [12]. Compared to FBGs, the sensitivities of micro-nanofiber-based tactile sensors were significantly improved [13]. For example, a highly sensitive sensor based on a PDMS-enveloped optical fiber taper was studied, in which the maximum sensitivity was obtained -29.03 nm/N [14]. However, since FBG tactile sensors are based on fiber core mode working, it is essentially insensitive to bending, therefore, this kind of sensors are different to achieve high sensitivity. Compared with FBG, although the micro-nano fiber can effectively improve the sensing sensitivity by leaking the core mode to outside and become high order cladding modes to participate in sensing, its diameter is generally a few microns, which will bring many disadvantages include low mechanical strength, high optical power loss, and poor spectral stability to the sensors, which will limit its further practical applicability.
In this study, a highly sensitive tactile sensor based on PDMS-embedded all in-fiber Match-Zehnder interferometer, consisting of single mode-thinned core-single mode (STS) optical fiber cascade structure is proposed, and the theoretical principle of STS axial tension sensing is established. The simulation results not only indicate that the axial strain sensitivity can be improved by excitation of high order cladding modes but also verify the strain sensitivity improving contribution of PDMS packaging material. In the experiment, by tracking the sensing dips of the transmission spectrum of the sensor change with the pressure from 0 to 2.5 kPa, the sensing sensitivities are 1.259 nm/kPa at 1549.57 nm dip wavelength with 89.04% linearity, 1.432 nm/kPa at 1574.92 nm with 95.52% linearity, and 1.328 nm/kPa at 1587.02 nm with 99.39% linearity, respectively. With the traditional analysis methods of the in-fiber interferometer sensors [15,16], different dips correspond to different sensitivities, mainly due to the large number of cladding modes that are involved in sensing, which makes the sensitivity of this kind of sensors difficult to be determined, and therefore limits its further practical applications. To achieve a uniform high sensitivity corresponding to the main working sensing modes of the sensor, low order modes must be removed. In this study, the fast Fourier transform (FFT) and inverse FFT methods are used for sensing spectral processing. Furthermore, all the dips present the same sensitivity and linearity of 1.3593 nm/kPa and 98.66%, respectively. Furthermore, the pressure (force) detection limit of the sensor can get 37 Pa (0.015 N). Meanwhile, the stability, repeatability and response time of the sensor is also experimentally investigated and analyzed.
2. Theory
2.1. Theoretical analysis of the relationship between strain sensitivity and cladding mode orders of the sensor
In this tactile pressure sensor, an STS optical fiber cascade structure is adopted as the sensing element, and its schematic diagram is shown in Fig. 1. It can be observed that the light that is injected into the input-SMF (single mode fiber) is divided into two parts at the first splicing point due to the core-core mismatch, between SMF with 8.2 µm and TCF (thin core fiber) with 5.0 µm core diameter, respectively. One part of the light propagates along the TCF core and another part enters the TCF cladding, which stimulates numerous cladding modes. At the second splicing point, these two parts of light of partly cladding modes and core mode intersect again and cause interference in the core of the output SMF. Thus, this structure can be considered an in-fiber Mach-Zehnder (M-Z) interferometer (MZI) and its output spectrum expression can be written as [15]:
From Eq. (1), the output spectrum of this structure is modulated by its phase, and the intensity dip wavelength of the mth-order can be written as follows [15]:
Force can cause axial strain, force-induced elastic-optic effect [17,18], and waveguide dispersion of the optical fiber, in which waveguide dispersion is usually negligible compared to the other two effects [19]. Thus, according to the Eq. (2), the relative wavelength change caused by the force can be expressed as:
Considering that TCF is an isotropic and homogeneous material, it conforms to the generalized Hooke’s law equations and can be written as [20]:
To further understand the relationship between the cladding mode and the ${K_{a}}$ of the sensor, the ERI of the 1st to 15th-order cladding modes at 1570 nm wavelength is obtained by solving the Eigen equation of the in-fiber MZI, which is shown in Fig. 2. The relationship between the cladding mode-order and ${K_{a}}$ is also obtained and shown in Fig. 2. It can be observed that ${K_{a}}$ is positively correlated with the order of the cladding modes, which means that the sensitivity of the sensor can be improved by exciting the high-order cladding modes to participate in the sensing process.
Fig. 2. Scatter plot of the ERI and the cladding mode order of MZI, and the relationship between the cladding mode order and the axial strain sensitivity (${K_{a}}$), respectively.
2.2. Theoretical analysis of the function of the PDMS packaging material
In this sensor, the MZI is embedded into the PDMS, which is a soft and elastic substance. To reveal the contribution of the PDMS in tactile pressure sensing process, the sensing response of the substance is simulated by COMSOL Multiphysics. The structure model diagram of the sensor is shown in Fig. 3(a). The sensor is a cuboid structure with a size of 20 × 20 × 5 mm, and the STS optical fiber with 20 mm length thinned core fiber is embedded along the diagonal in the cross-section at a depth of 1.5 mm. Assuming that a force of 1 N is applied on the upper surface of PDMS along the y-axis, simulations of the pressure distribution and deformation directions of the PDMS along the optical fiber are performed and shown in Fig. 3(a), in which the red arrow indicates the deformation direction of the optical fiber, and the color table represents the pressure distribution on the surface of PDMS and STS. From Fig. 3(a), it can be observed that the stress concentrates on the surface of the sensor, as the magnitude of the Young's modulus of PDMS is five orders smaller than that of the silica optical fiber. Thus, the PDMS in the sensing process enables pressure sensitization. Due to the Poisson's ratio of the PDMS, the optical fiber expands along the z-axis and bends along the y-axis, respectively. The displacement diagrams of the STS in the z- and y-axes are shown in Fig. 3(b) and Fig. 3(c), respectively. From Fig. 3(b), it can be deduced that the elongation of the optical fiber along the z-axis is 0.528 µm. From Fig. 3(c), it can be deduced that the displacement difference between the optical fiber center position and the splicing point of the optical fiber is approximately 3 µm along the y-axis.
Fig. 3. (a) Simulated pressure distribution and deformation trend of PDMS-coated STS under 1N pressure. One-dimensional displacement diagrams of STS structure in (b) z-axis and (c) y-axis.
The light field and output spectral characteristics of the sensing process are also simulated. Light field simulation of the sensor under 1 N pressure is performed by finite difference beam propagation method and is shown in Fig. 4(a). From this figure, it can be observed that the TCF simultaneously excites the core and high-order cladding modes at the first splicing point, and the light interferes at the second splicing point. The output spectrum drifts with the force change from 0 to 1 N with steps of 0.2 N, and the sensing process simulations are shown in Fig. 4(b), from which it can be deduced that the output spectrum dip wavelength exhibits a red-shift with sensitivities of 2.7143 nm/N (1.08572 nm/kPa), 2.1571 nm/N (0.86284 nm/kPa), and 2.2143 nm/N (0.88572 nm/kPa) at different dip wavelengths, respectively.
Fig. 4. Simulation results of (a) light propagation under 1 N pressure, and (b) transmission interference spectrum of the sensor under 0 to 1 N (steps of 0.2 N) pressure.
3. Experiments and discussions
3.1 Sensor fabrication
The fabrication process of STS-embedded PDMS includes: preparation of the STS structure, preparation of the PDMS solution, and encapsulation of the sensor. First, the STS is fabricated by splicing a 20 mm long TCF with 5/125 µm core/cladding diameter ratio between two standard SMFs with 8.2/125 µm core/cladding diameter ratio, respectively [22]. Subsequently, the PDMS solution is prepared by mixing the main agent and curing agent (SYLGARDTM 184 Silicone Elastomer) in a ratio of 10:1 [23]. A cube titanium groove (20 × 20 × 5 mm) is prepared as a mold, and then the STS is put into the mold, as shown in Fig. 5(a). Moreover, the STS section at the slotted location is protected by plastic sealing pipe to prevent breakage during demolding. Next, the prepared PDMS solution is decanted into the mold, which is then inserted into the thermostat and heated at 100°C for 30 min. Finally, the STS-embedded PDMS is obtained after removing the mold, as shown in Fig. 5(b). The image of the sensor is shown in Fig. 5(c).
Fig. 5. (a) Preparation of the sensor. (b) Schematic diagram of the sensor. (c) Image of the sensor.
3.2. Tactile pressure-sensing experiment of the sensor
The schematic diagram of the experimental setup is shown in Fig. 6, in which one-end of the sensor is connected to a broad band source (BBS) with 1520–1620 nm wavelength range and the other end is connected to an optical spectrum analyzer (OSA, YOKOGAWA, AQ6370 with 0.05 nm resolution). The weights of 10 to 100 g (step value 10 g) are used to apply force. A piece of glass slide is placed on the top of the sensor to ensure that a uniform pressure can be applied on the sensor surface.
Figure 7(a) shows the measurement transmission spectral overlap of the sensor at different pressures from 0 to 2.5 kPa with steps of 0.25 kPa. From Fig. 7(a), it can be observed that all the intensity dips of the sensor exhibit a red-shift with the increase of the pressure. By tracing the sensing dip1, dip2, and dip3, the linear fittings of dips changing with the pressure, are obtained, as shown in Fig. 7(b). It can be observed that the sensing sensitivities are 1.259 nm/kPa at 1549.57 nm dip wavelength with 89.04% linearity, 1.432 nm/kPa at 1574.92 nm with 95.52% linearity, and 1.328 nm/kPa at 1587.02 nm with 99.39% linearity, respectively. Different dips correspond to different sensing sensitivities, due to the inclusion of many cladding modes in each dip in the interference spectrum of this kind of sensor.
Fig. 7. (a) Transmission spectrum overlap of the sensor under different pressures, and (b) linear fitting of the dips change with the pressure.
Comparing Fig. 7(b) and Fig. 4(b), it can be inferred that the experimental result is consistent with the simulation except that the sensitivity of the experiment is high than that of the simulation, which is mainly because the core mismatch is exacerbated with the pressure increase in the experiment. As a result, the order and number of the cladding modes involved in the interference increase, thus improving the sensing sensitivity of the sensor [24].
3.3 Repeatability and response time
In this paper, repeatability of the sensor is tested and the dip2 is tracked. By repeating increasing/decreasing pressure tests four times, the resulting wavelength drifts of the dip2 and its linear fitting are obtained, which is shown in Fig. 8(a). From Fig. 8(a), it can be observed that sensing sensitivities are 1.408 nm/kPa, 1.416 nm/kPa, 1.435 nm/kPa, and 1.431 nm/kPa, respectively. By calculation, the absolute error of the sensitivity is less than or equal to 1%.
Pressure response rate of the sensor is also investigated. The transmission spectrum with a span from1573.4 nm to 1574.4 nm (with 0.01 nm sampling interval and a total of 101 sampling points, about 0.4 s sampling time) are recorded continuedly. Adding a weight of 10 g on the sensor suddenly, and the transmission spectrum changes suddenly. The same experiments are repeated ten times. The transmission spectrum of 0 N and 0.1 N force is shown in Fig. 8(b), respectively. The response time from loading to stabilization is about 0.4 s.
3.4 Stability test
Considering that PDMS is a temperature-sensitive material with a large thermos-optic coefficient (TOC) of −4.5 × 10−4/°C [25], its RI is easily disturbed by changes in environmental temperature. To avoid the impact of changes in temperature, all experiments are conducted in a constant temperature environment. Then, to investigate the stability of sensors in constant temperature environment, the sensing dip2 is tracked, which is shown in Fig. 9. The transmission spectrum is recorded every 6 min for 1 h. From Fig. 9, it can be observed that the dip wavelength is kept stable at 1573.85 nm, and the dip intensity fluctuation of dip2 is lower than ±0.0026.
3.5 Cladding modes affecting the sensing sensitivity experiment
Through above discussion, it can be seen that different dips corresponding to different sensing sensitivity and linearity are present of the multi-mode interferometer. It is due to each dip contains numerous interference modes which will lead to the inability to accurately analyze the sensing properties of such sensors. To clarity the effects of different cladding modes on the pressure sensitivity of the sensor, the cladding modes that are mainly involved in the sensing process are investigated though FFT method [26,27]. The spatial frequencies of the sensing process (shown in Fig. 10(a)) are obtained through FFT of the transmission spectrum of the sensor at different pressures, in which core mode and two main groups of cladding modes are obtained and represented as LP01 mode(core-mode), 10th-order, and 13th-order cladding modes, respectively. From Fig. 10(a), it can be observed that the amplitude of the 10th-order cladding modes experiences a small increase, while the amplitude of the 13th-order cladding modes increases significantly. To reveal the effect of different cladding modes on pressure sensitivity, the spatial spectrum of two cladding modes is transformed by inverse FFT, which is shown in Fig. 10(b), and Fig. 10(c), respectively. For the low-order cladding modes, it can be observed that the dips are kept relative stable and exhibit a small red-drift. For the high order cladding modes, it can be observed that all the dips show obvious red-drift, which means that, with the pressure increase, the high order cladding modes play a more significant role. By tracking the sensing dip1’, and dip2’, the corresponding pressure sensitivities are obtained, as shown in Fig. 10(d). The sensitivity of 10th-order cladding modes is 0.1302 nm/kPa with 98.89% linearity, which is much smaller than that of 13th-order cladding modes with a sensitivity of 1.3593 nm/kPa and a linearity of 98.66%. According to the result shown as above, the major high order cladding mode can be adopted to analyze the sensing properties the sensor, and low-order cladding modes can be ignored, thus avoiding interference with sensor performance from multi-mode sensing. From the obtained sensitivity, the detection limit can be deduced as 37 Pa (0.015 N).
Fig. 10. (a) Spatial spectrum and modes distribution after FFT calculation. (b) Superposition of the interference spectrum of the (b) 10th-order cladding modes and the (c) 13th-order cladding modes after inverse FFT calculation. (d) Linear fittings of dip1’ and dip2’ with the pressure.
The sensitivity is an important index to evaluate the performance of the tactile sensor. A high sensitivity means that a tiny force/pressure can be recognized. Table 1 lists the performance of the sensors in this work. For the sake of comparison, we convert the units of sensitivity to (nm/N). Table 2 shows the comparison of the sensing performance between the sensor in this research and other representative existing tactile sensors and interferometric force sensors. It can be observed that force sensing can be realized by various sensing structure. For the proposed sensor in our work, typical sensitivity is higher than FBGs [11,28,29] and most interferometric sensor [30,31,33–35]. With regard to taper fiber [14,32], typical sensing sensitivity is high and shows a value higher than 10 nm/N. This is due to its thin tapered diameter, expanding the evanescent field effect. However, its high optical power loss resulting in poor spectral stability, which will limit its further practical applicability especially in tactile sensing fields. Compared to the existing sensors, the proposed PDMS-embedded STS sensor can reach a high and stable sensitivity of 3.398 nm/N, and it also shows the advantages of easy fabrication, simple structure and good mechanical properties, making the proposed sensor a potential tactile sensor.
Table 1. Sensing performance of proposed sensor
Table 2. Comparison of sensing performance of different tactile sensor or interferometric force sensor developed to date
4. Conclusion
In conclusion, a highly sensitive soft optical fiber tactile pressure sensor based on the STS optical fiber structure embedded in PDMS, is theoretically and experimentally demonstrated. Theoretically, the working principle of the sensor is derived and the sensitivity coefficient is simulated. Simulation results show that the higher the order of cladding modes involved in the sensing, the greater the sensitivity of the sensor. In addition, the simulation of the tactile force-sensing properties of the STS-embedded PDMS structural sensors show that the PDMS can improve the sensing sensitivity. Experimentally, a type of STS-embedded PDMS structural tactile pressure sensor is fabricated and its sensing characteristics, with the tactile pressure from 0 to 2.5 kPa, is investigated. The relationship between intensity dips at different wavelengths and varying tactile pressure is obtained by which different sensitivities and linearities are recorded. The experimental results show the same law as the theoretical simulation, except that the experimental sensitivity is significantly higher than the theoretical value, which is mainly because the core mismatch increases with the increasing pressure in the experiment, thus resulting in an increase in the order and number of the cladding modes. Through FFT of these spectra of the sensor in sensing process, all the modes including high order and low order modes involved in the sensing process are obtained. Through the inverse FFT of the spatial frequency spectrum, its sensing spectrum of these two order modes can be obtained. Based on this, its sensing performance of different modes can be deduced, which shows that high order mode exhibits a high sensitivity, and all the dips present same sensitivity and linearity as 1.3593 nm/kPa and 98.66%, respectively. It can be seen that this method can effectively remove the disturbance of low order modes and improve sensing performance of the sensor. Moreover, at a constant temperature, this sensor exhibits excellent wavelength stability. The sensitivity repeatability obtained from multiple measurements is less than or equal to 1%. And the pressure respond time is about 0.4 s by suddenly load force from 0 N to 0.1 N. In a word, the proposed sensor not only presents high sensitivity, high stability, high repeatability and fast respond rate advantageous, but also possess a compact, small size, and low-cost structure, which increases its applicability in the intelligent robot sensing field.
Funding
State Key Laboratory of Mining Disaster Prevention and Control, Shandong University of Science and Technology (MDPC201602, MDPC2022ZR04); Department of Education of Shandong Province (J06P14); The Qingdao Feibo Technology Co., Ltd (02040102401); Postdoctoral Research Foundation of China (20080441150, 200902574).
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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