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Figure 1 presents a schematic diagram of the micro-force sensor microprinted on the single mode fiber (SMF) end face using TPP. A pair of polymer bases, with lengths of 20 μm, widths of 20 um, and heights of 30 um, were designed to support and connect the clamped beam. The clamped beam, 100 um in length, 20 um in width, and 3 um in height, was parallel to the fiber-end surface. In addition, a cylindrical probe, with a diameter of 5 um and a length of 35 um, was printed on the upper surface center of the clamped beam, and the tip of the probe was hemispherical. The lead-in fiber-end surface and the two surfaces of the clamped beam define FPIs. Firstly, the light propagating in the SMF is partially reflected at the end face of the fiber, and then the rest of the light transmitted to the lower and upper surfaces of the clamped beam will also be partially reflected into the optical fiber. These three light beams will interfere in SMF and form a reflection spectrum. Actually, three FPIs are formed, i.e., an air cavity (FPI1) formed by the fiber end face and the lower surface of the clamped beam, a polymer cavity (FPI2) formed by the two surfaces of the clamped beam, and a mixed cavity (PFI3) formed by the fiber end face and the upper surface of the clamped beam. However, in this work, the optical intensity of FPI3 is much lower than those of FPI1 and FPI2, and FPI2 has a fixed cavity length once the sensor was fabricated. Thus, the air cavity was chosen for demodulation. When the force of a small object is applied to the probe, the clamped beam will be deformed and the cavity length of FPI1 will be changed, leading to a change of dip wavelength in the reflection spectrum of SMF. The relationship between the dip-wavelength shift (Δλr) and the cavity length reduction (ΔD) is Δλr/λr = ΔD/D, where, λr is the dip wavelength, and D is the cavity length, so the force on the probe can be calculated by tracing the dip wavelength shift of the reflection spectrum. The polymer has a low Young's modulus and stiffness39, 40, which enables the clamped beam to deform enough under the action of small force, resulting in high sensitivity and a small force-detection limit of the sensor.
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The reflection spectra of three clamped-beam probes with different bases heights (15, 30, and 50 µm) were measured using a broadband light source (BBS, 600–1700 nm) and an optical spectrum analyzer (OSA) to optimize the structural parameters. The expression of free spectral range (FSR) is shown in Eq. 1 (ref. 35). The optical microscopy images of a clamped-beam probe with different heights and their corresponding reflection spectra are presented in Fig. 2a. The clamped-beam probe and the end face of the optical fiber remain parallel as the base height increases. Besides, this kind of polymer clamped-beam probe has achieved a relatively high reflection spectrum contrast (> 15 dB) compared with other polymer fiber sensors based on microcantilever (< 7 dB)35. All these characteristics show that the device microprinted by TPP has superior functions34. The FSRs of these three structures were measured to be 71.6, 32.7, and 19.5 nm, corresponding to the λr of 1441.5, 1418.9, and 1415.4 nm, respectively. Combining these measured values, the heights of the bases for these three structures were calculated to be 14.5, 30.8, and 51.4 um, respectively, according to Eq. 1.
$$ {FSR} = \frac{{\lambda _r^2}}{{2nD}} $$ (1) Fig. 2 Micro-force sensor structural characterization and static performance.
a Optical microscopy images of the clamped-beam probe with different heights and their corresponding reflection spectra. b–d are the bending deformation simulation results of the sensor under the same micro force (1 μN) acting on the probe with different diameters (10, 5, and 3 μm). e Relationship between the probe diameter and flexure deformation under the same micro force (1 μN)Where n is the refractive index of the medium in the cavity. These heights are consistent with the designed heights, indicating the high accuracy of TPP. In the experiment, it is found that the increase in base height can reduce the structural stability of the sensor, and it is easier to topple under the action of an external force. In contrast, a shorter base can increase the shift range of the sensor while maintaining structural stability35. However, if the base height is too small, i.e., the length of the air cavity is too small, the polymer structure will easily fall off when the washing solution volatilizes due to the solution surface tension between the clamped-beam and the fiber end face, reducing the development success rate of sensors. Therefore, in the sensor design, to achieve a good balance between structural stability and development success rate, we have chosen a base height of 30 μm.
To investigate the static performance of the proposed structure, models of the force sensor with different probe diameters (10, 5, and 3 μm) were established using COMSOL Multiphysics®, and the simulation results are presented in Figs. 2b, 2c, and 2d, respectively. The other values of the established simulation model were set to match the corresponding values used in the sensor-fabrication process. The measured parameters, i.e., the polymer material density of 1499 kg (m3)−1, Young's modulus of 2.34 GPa, Poisson ratio of 0.33, and the standard parameters, i.e., silica density of 2700 kg (m3)−1, Young's modulus of 73 GPa, and the Poisson ratio of 0.17, were employed in the simulations41. The same microforce of 1 μN was exerted on the probe, and the deformation distribution results are presented in Figs. 2b, 2c, and 2d, respectively. The sensor-cavity length decreases as the displacement of the probe increases. The sensor-cavity length decreased more when the probe diameter was smaller, indicating that reducing the probe diameter can effectively improve the force sensitivity of the sensor. Moreover, the relationship between the probe diameter and flexure deformation under the same microforce (1 μN) was evaluated, as shown in Fig. 2(e). The results also suggest that decreasing the probe diameter can increase the bending deformation of the sensor. The reason may be that the effective surface area of the clamped beam is the difference between the surface area of the clamped beam and the probe-lower-end area, thus the sensitivity of the sensor will be higher as the effective surface area becomes larger11. Therefore, a diameter of 5 μm was selected to ensure that the probe has both high mechanical strength and high sensitivity. In addition, the sensitivity of the sensor is defined as the ratio of the shift of the dip wavelength to the force, and reducing the thickness of the clamped beam can also improve its sensitivity significantly. Since the polymer material has low stiffness, the thickness of the clamped beam cannot be too small. Therefore, a thickness of 3 μm was selected to ensure the support and high sensitivity of the probe.
Figure 3a presents the scanning electron microscope (SEM) images of the polymer clamped-beam probe. The three main parts, i.e. the bases, clamped beam, and probe, can be clearly distinguished. The structure of the pair of bases with a cross-sectional area of 20 × 20 μm2 can be seen at the bottom of the figure, and a large cross-sectional area of the bases can increase the adhesion force between the polymer structure and the end face of the fiber, which makes the structure more robust. In the middle, the clamped beam attached to the bases can be seen. At the top, a cylindrical probe is located directly above the clamped beam. The SEM images show that the printed cylindrical probe has good perpendicularity with the surface of the clamped-beam, the clamped-beam has good parallelism with the end face of fiber, and the surface of the polymer structure is smooth. All these characteristics can improve both the contrast of the reflection spectrum and the sensitivity to external force, indicating the reliability of using TPP to print the microstructure on the end face of the fiber. Furthermore, the elastic properties of the prepared clamped beam probe structure were investigated by simply pressing the structure on another fiber end face. Optical microscopy images of pressing and releasing the fiber end face are presented in Figs. 3b and 3c, respectively. As observed in Fig. 3c, the probe recovered to its original state after testing.
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Before the microforce sensing test, the force was calibrated carefully in order to ensure measurement precision. Thus, the relationship between the applied force and the output of the sensor was quantified. The static characteristics and force sensitivity of the proposed sensor were measured using the experimental setup shown in Fig. 4a. The setup consisted of a 3D translation stage (3D stage) for micro-manipulation of the sensor, a BBS, an OSA, a 3-dB coupler, a sample holder, and a CCD camera. A section of SMF with a fixed length was mounted perpendicularly to the micro-force sensor through the sample holder. The sensor probe was pushed against the SMF to deflect it from its initial position, and the observed CCD image is shown in the inset of Fig. 4a. As observed in Fig. 4b, the diameter of the probe was much smaller than that of SMF. Thus, this process can be regarded as the deformation of a cantilever beam under a point load, which satisfies the following deflection equation (ref. 42):
$$ {\Delta}L = \frac{{FL^3}}{{3EI}} $$ (2) Fig. 4 Experimental setup.
a Measurement system setup. The inset shows a CCD image of pushing against the SMF of the clamped-beam probe sensor. b Schematic diagram of cantilever-beam deflection under point loadHere, ΔL (mm) is the deflection of the cantilever beam. L (mm) is the length of the cantilever beam. F (kN) is the point load on the end of the cantilever beam. E (GPa) is Young's modulus of the cantilever beam, and I is the second moment of area of the cantilever beam.
The vertical downward displacement of the probe, i.e., the deflection ΔL, can be accurately controlled by the 3D stage. We employed standard parameters in the calculations for SMF, including a diameter of 125 um, a length of 55.9 mm, an SMF deflection ΔL (obtained from the motor controller), and Young's modulus of 73 GPa. The formula for the circular second moment of area is as follows (ref. 43):
$$ I = \frac{{\pi d^4}}{{64}} $$ (3) where d, in units of mm, is the diameter of the cantilever beam.
The forces exerted on the sensor were calculated by combining Eqs. 2 and 3. During the application of gradual force, the reflection spectrum was monitored in real time. Figure 5a shows the reflection spectral evolution of the clamped-beam probe as the force was gradually increased from 0 to 2700 nN in increments of 300 nN. A blue-shift in the dip wavelength was clearly observed, as marked by arrows. The fringe visibility of the reflection spectrum has a slight decrease as the force increases, due to the bending of the clamped-beam. The dip wavelength vs. the magnitude of the force is plotted in Fig. 5b. The dip wavelength shifted linearly toward a shorter wavelength as the applied force increases, the force sensitivity of the force sensor was calculated to be −1.51 nm μN−1 by using a linear fit of the dip wavelength change, which are two orders of magnitude higher than that of the previously reported fiber-optic force sensor based on a balloon-like interferometer15. R-square (R2), which describes how well the data matches the fit function, is 0.98378. It is worth noting that in our microforce sensing measurements, the clamped-beam is working within the framework of the linearly elastic range, and there is no hysteresis between the force and the cavity change. Furthermore, FEM simulation was performed; the 3D modeling of the SMF was pushed against by the clamped beam probe, and the pushing displacement was 20 um. The SMF was fixed at one end and free at the other end with a length of 55.9 mm. Figure 5c presents the simulated deformation distribution result. When a 20-um displacement occurred at the free end of the SMF, the bending deformation of the clamped beam and the cavity length decreased due to the action of reaction (in the insets of Fig. 5c), and the reaction force was 301 nN, which is well consistent with the experimental increment step. In addition, the external force not perpendicular in the practical application can also be measured (see Fig. S3 in supporting information). The force sensitivity of the proposed sensor can be further improved by reducing the polymerization thickness of the clamped-beam when the stiffness is allowed, for the force sensitivity of the sensor is inversely proportional to the third power of the thickness of the clamped-beam44. Although the robustness and mechanical durability to other loads, such as lateral forces, were not tested systematically, none of the sensors failed in a wide range of experiments in this study. This might be attributed to the excellent surface quality (obtained by TPP processes) and the inherent high elasticity of polymer structure45. The experimental results show that the maximum force measurement of the sensor is 2.9 mN.
Fig. 5 Microforce measurements and simulation.
a Evolution of reflection spectra of the sensor as the force increased from 0 to 2700 nN, as indicated by the arrows. b Dip wavelength versus force. The line is the linear fitting of measured data points and the error bar is obtained by critically repeating the experiment of force measurement three times. c Simulation results of deformation distribution based on FEMI. M. White et al. introduced the concept of sensor detection limit (DLs), in which the spectral resolution and correlated noise parameters of the system were fully considered46. Herein, the detection limit of the micro-force sensor is the definition of the smallest applied-force variation that can be accurately measured. The DLs is expressed as
$$ {DL}_{{{\mathrm{s}}}} = \frac{{R_s}}{{S_s}} $$ (4) where, Ss and Rs represent the sensitivity and resolution of the sensor, respectively, and the resolution of the sensor can be approximately solved by individual noise variances (namely, Rs = 3σ), i.e.,
$$ \sigma \approx \frac{{{\Delta}\lambda _{{{\mathrm{F}}}}}}{{4.5({SNR}^{0.25})}} $$ (5) Here, ΔλF is the full-width at half-maximum (FWHM) of the fringe. SNR is the signal-noise ratio.
In our micro-force sensing experiment, the main restriction of the detection limit is the FWHM. The measured value of FWHM is 2.21 nm, and the SNR expressed in linear units is 50 dB. The DLs of the device was calculated to be 54.9 nN. Such an ultra-small DLs value can help the proposed sensor detect tiny force variations. With its ability to measure forces from the nN to mN level, this probe sensor has a force measurement range spanning of more than five orders of magnitude, which is expected to facilitate cross-scale force sensing.
Table 1 compares the performance of optical-fiber sensors with different configurations for micro-force measurement. In terms of force sensitivity, the proposed micro-force sensor is much higher than other fiber-optical force sensors types. In addition, the device has the advantages of flexible fabrication, high mechanical strength, an ultra-small detection limit, and ultra-compactness.
Sensor structure Size of sensor Force sensitivity (pm μN -1) Reference Photonic crystal fiber 125 μm × 3 cm 0.016 × 10 −3 54 Microfiber Bragg grating 2.4 mm × 2.4 mm 0.73 × 10 −3 55 FP cuboid cavity 18 μm × 60 μm 0.026 56 Microfiber asymmetrical FP interferometer 20 mm × 7.3 um 0.221 57 FP micro-cavity plugged by cantilever taper 1.36 mm × 125 μm 0.842 58 Balloon-like interferometer 24 mm × 14 μm 24.9 15 Clamped beam probe 68 μm × 100 μm 1510 This work Table 1. Comparison of performance of fiber sensors with different configurations for micro-force measurements
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The proposed sensor was applied in a few typical applications, including the measurement of Young's modulus of PDMS, a butterfly feeler, and human hair. To obtain the required PDMS sample, the elastomer and cross-linking agent were mixed with a ratio of 10:1, degassed for 30 min, and then cured in an oven at 100 ℃ for 60 min. The PDMS sample was first cut into pieces with a size of 17.7 mm × 1.27 mm and a thickness of 1.03 mm. Then, one end was fixed into the sample holder and the other end was deflected by a 3D stage with an attached micro-force sensor, as shown in the inset in Fig. 6. Figure 6 presents the reflection spectra of the sensor when the PDMS was in the initial state (ΔL = 0 μm) and deflected by 20 μm. When the PDMS was pushed down with a distance of 20 μm, the reflection spectrum blue-shifted, and the dip wavelength was 1409.03 nm. According to the linear fitting function between dip wavelength and force applied, the tested force was calculated to be 5999.397 nN. However, the calculation for the rectangular second moment of area differs from that of the circular second moment (ref. 43):
$$ I = \frac{{bh^3}}{{12}} $$ (6) Fig. 6 Evolution of reflection spectrum of the sensor as PDMS deflects from 0 to 20 μm.
As shown in the inset, one end of the PDMS sample is fixed while the other end is deflected by the proposed sensorHere, b (mm) is the width of the cantilever beam and h (mm) is the thickness of the cantilever beam. Thus, Young's modulus of PDMS was calculated to be 4.8 MPa by combining Eqs. 2 and 6, using the geometry of PDMS, i.e., L = 17.7 mm, b = 1.27 mm, h = 1.03 mm, and point load F = 5999.397 nN on the end of the PDMS. Our value (4.8 MPa) of Young's modulus are comparable to those obtained on the PDMS in both Seghir et al. that ranged from 0.8 to 10 MPa47 and Chaudhury et al. that ranged from 0.2 to 9.4 MPa48, which certifies the reliability of the proposed sensor.
To verify the calculated results of Young's modulus of PDMS, an AFM (Bruker) was used to perform mechanical measurements on the same PDMS sample. In AFM measurement, a 20 × 20 μm area of the PDMS sample is selected for depth-sensing indentation experiment, and the total length of the vertical ramp is kept at 5 μm. We used a standard sharp indenter model RTESPA with an average semi-angle aperture θ = 20° (measured by SEM). The elastic spring constant, i.e., k = 18.7 Nm−1 was calibrated in the air using the thermal tune method49. The AFM tip was indented vertically on the surface of PDMS to obtain the force indentation curve, so that the morphology and mechanical properties of the samples were obtained. In order to improve the reliability of experimental data statistics, the indentation experiments were repeated three times at room temperature (T = 23 ℃).
The Young's modulus of PDMS was obtained by fitting the force indentation curve obtained from AFM depth-sensing indentation experiment in Matlab50. According to the shape of the AFM probe used, the Sneddon model is used to fit, and the expression is as follows51, 52.
$$ F = 0.7453\frac{{E\tan \theta }}{{\left( {1 - \nu ^2} \right)}}\delta ^2 $$ (7) Here, E represents the local Young's modulus of the sample, ν is the Poisson ratio, and θ represents the average half-opening angle of the AFM probe.
The AFM results measured are shown in Fig. 7. Figure 7a shows the morphology of the PDMS obtained by AFM. The surface topography of the PDMS film was uniform, and the root mean square roughness was determined to be 87.4 nm. Figure 7b presents Young's modulus mechanical map of the PDMS thin film. The vertical color bar is in the form of logarithmic coordinates. The Young's modulus distribution of PDMS was relatively uniform, with an average level of 5.11 ± 0.01 MPa. Force indentation curves of the sample are presented in Fig. 7c. The black dotted line represents the measurement data, and the red line represents the Sneddon fit curve. The histogram of Young's modulus is shown in Fig. 7d and the red curve is Gaussian fitting. The Young's modulus of PDMS was mainly concentrated around 5.11 MPa. The measurement results of the proposed micro-force sensor are mostly consistent with the AFM results, and the error is within 10%, which certifies the accuracy of the measured results of the proposed sensor.
Fig. 7 Graphical results of mechanical analysis by AFM.
a Force volume morphology map of PDMS thin film, the color bar indicates height value. b Young's modulus mechanical diagram on a logarithmic scale. c The Young's modulus of the sample was estimated by Sneddon model fitting based on the force indentation experimental data. d Histograms of Young's modulus values, the red curve is Gaussian fittingSimilarly, one feeler of a butterfly (Danaidae) was fixed into the sample holder, similar to the PDMS measurement process. The free end of the butterfly feeler was pushed by the micro-force sensor probe, as shown in Fig. 8a, thus the feeler was deflected from its initial position. Figure 8b presents the reflection spectrum of the sensor when the butterfly feeler was in the initial state (ΔL = 0 um) and when it was deflected 150 um from the initial state. When the butterfly feeler was pushed down at a distance of 150 μm, the dip wavelength became 1407.87 nm. The Young's modulus of the butterfly feeler can be calculated according to the asserted forces measured by the sensor and the geometric (butterfly feeler, L = 8.2 mm, d = 165 μm), similar to the aforementioned calibration process. The Young's modulus was calculated to be 227.8 MPa for the butterfly feeler and ~5.65 GPa for the human hair (black hair from Chinese adult women), which agrees well with the findings reported in biological literature53.