1. Introduction

Three-dimensional micro-displacement precision measurement is widely used in geological monitoring, equipment control, dental correction, etc. And fiber micro-displacement sensor occupies an important position in the field of micro-displacement measurement because of its high sensitivity, miniaturization, anti-interference and other advantages. At present, most of the fiber micro displacement sensors are one-dimensional micro displacement sensors [1,2]. When sensing the 3D micro displacement, three one-dimensional micro displacement sensors should be used in three directions of X, Y and Z [3–5]. If the fiber grating micro displacement sensing system is combined to measure the 3D micro displacement [6], multiple FBGs and optical filters are required to process the signal. The micro displacement sensing system is complex and the measurement is difficult to achieve.

Fiber SPR micro displacement sensor [7–10] has realized two-dimensional micro displacement sensing of single sensor [11], but 3D micro displacement sensing has not been realized yet. The principle of fiber SPR micro displacement sensing is: making SPR sensing area on the graded multimode fiber to form the sensing optical fiber. Because of the self-focusing effect of the graded multimode fiber on the transmission beam [12,13], its internal beam is transmitted in the cosine path. Displacement fiber usually employs single-mode fiber to inject light into the end face of graded multimode sensing fiber. When the displacement fiber and sensing fiber generate micro displacement, the injection position of the graded multimode fiber changes, the amplitude of the cosine path of the beam changes, and in the SPR sensing area, the SPR resonance angle changes, and the SPR resonance wavelength also changes [14,15]. The relationship between the micro displacement of the fiber and the SPR resonance wavelength can be established to achieve micro displacement sensing.

At present, the proposed fiber SPR micro displacement sensor has only one sensing area and is usually circumferential symmetric. When the displacement fiber is shifted in the Y (up and down) or Z (front and back) directions, the amplitude of the transmission light cosine path in the graded multimode fiber is the same. When the transmission beam enters the SPR sensing area with the same circumference symmetry, the change trend and size of the SPR resonance angle are consistent, and it is impossible to distinguish whether the displacement is from the Y or Z direction. If two asymmetric sensing areas can be constructed on the graded multimode sensing fiber, one is used to sense the micro displacement in the Y axis direction, and the other is used to sense the micro displacement in the Z axis direction, and make the resonance wavelength of the two sensing areas move in opposite directions, it is expected to solve the separate sensing of the micro displacement in the Y axis and Z axis direction through a single fiber SPR sensor.

When the displacement fiber emits a straight beam and moves in the X-axis (left and right) direction relative to the sensing fiber, the light injection position of the graded multimode sensing fiber cannot be changed, and the SPR resonance wavelength will not move. When the displacement fiber emits an oblique beam and moves in the X-axis direction relative to the sensing fiber, the light injection position of the sensing fiber changes, the cosine path amplitude of the transmission light in the graded multimode fiber changes, and the SPR resonance wavelength changes, which can establish the relationship between the X-axis micro displacement offset of the displacement fiber and the SPR resonance wavelength, and realize the micro displacement sensing in the X-axis direction.

Based on the above analysis, we designed and demonstrated a displacement fiber by cascading an eccentric dual-core fiber and a T/4 length graded multimode fiber to achieve two different forms of outgoing light fields, which are the oblique beam from the eccentric core and the straight beam from the middle core of the eccentric dual-core fiber. 3D micro displacement sensing of single fiber SPR sensor was realized by fabricating two V-groove SPR sensing areas in the vertical (Y axis) direction and horizontal (Z axis) direction on the graded multimode fiber.

2. Sensor principle and fabrication

2.1. Sensor structure

The structure diagram of the fiber SPR 3D micro displacement sensor is shown in Fig. 1. The left displacement fiber which was coaxially spliced by the eccentric dual-core fiber and graded multimode fiber with a core diameter of 100 µm. It can move along the X axis, Y axis or Z axis to generate micro displacement relative to the right sensing fiber and realize 3D micro displacement sensing. The right side is the sensing fiber, which is fabricated by a CO2 laser processing V-groove in the vertical and horizontal directions on graded multimode fiber with a core diameter of 105µm, and making a SPR sensing area on the slope of the V-groove. The two V-grooves were perpendicular to each other, and the inclined surface was coated with 50 nm gold film which was covered with low refractive index UV curing adhesive. Figure 1(a) and (b) are the top and front view micrographs of the dual V-groove graded multimode sensing fiber, respectively.

 

Fig. 1. Structure diagram of fiber SPR 3D micro displacement sensor. (a) Top view micrograph of double V-groove sensing fiber, (b) front view micrograph of double V-groove sensing fiber.

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2.2. Analysis of sensing principle

For the fiber SPR 3D micro displacement sensor with double V-grooves, the schematic diagram of X axis and Y axis sensing principle is shown in Fig. 2. The viewing angle is that the V1 groove in the vertical direction of the sensor is upward. Figure 2(a) is the schematic diagram of the micro displacement sensing principle in X-axis direction. The wide spectrum light source was injected into the eccentric core of the eccentric dual-core fiber. The beam in the eccentric core is modulated by the self-focusing effect of the graded multimode fiber section of the displacement fiber, and the oblique beam emerges from the middle of the right graded multimode fiber, the included angle with the fiber axis is α. When the lateral offset x_i between the right end face of the displacement fiber and the left end face of the sensing fiber increases gradually, the amplitude of the transmitted cosine beam injected into the sensing graded multimode fiber increases gradually after being modulated by the self-focusing effect of the graded multimode fiber on the left side of V1 groove. When the beam enters the inclined plane of V1 groove, the slope is positive (the front slope of the cosine peak), and the total reflection angle θ_i decreases gradually. The transmitted light beam contacts the gold film on the surface of the V1 groove, and SPR effect occurs. The offset x_i between the two fibers increases, which will lead to the decrease of the total reflection angle θ_i (SPR resonance angle) and the increase of evanescent field, and then lead to the shift of SPR resonance wavelength to longer wavelength and the deepening of resonance valley depth, which realize the position sensing of X axis by SPR resonance wavelength and resonant valley depth.

 

Fig. 2. View angle diagram of fiber SPR 3D micro displacement sensor with double V-grooves when V1 groove upward. (a) Schematic diagram of X axis micro displacement sensing principle, (b) schematic diagram of Y axis micro displacement sensing principle.

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Figure 2(b) shows the principle of micro displacement sensing in the Y-axis direction. A wide spectrum light source was injected into the middle core of the eccentric dual-core fiber, and a horizontal beam was emitted from the center of the right end face of the displacement graded multimode fiber. When the longitudinal offset y_i of the displacement fiber increases gradually. The amplitude is gradually increased after being modulated by the graded multimode fiber. When the beam hits the inclined plane of the V1 groove, the slope is negative (the north slope of the cosine peak), and the total reflection angle θ_i^’ gradually increases, which leads to the shift of SPR resonance wavelength to the short wavelength direction and the deepening of resonance valley depth, so as to realize the position sensing of Y-axis by SPR resonance wavelength and resonance valley depth.

For the fiber SPR 3D micro displacement sensor with double V-grooves, the schematic diagram of Z-axis sensing principle is shown in Fig. 3. The viewing angle is that the V2 groove in the horizontal direction of the sensor is upward. As shown in Fig. 3(a), the wide spectrum light source was injected into the middle core of the eccentric dual-core fiber, and the horizontal beam was injected into the left end face of the sensing fiber. After being modulated by the graded multimode optical fiber, it did not contact the sensing area of the vertical V1 groove but entered the sensing area of the horizontal V2 groove, with a positive slope (the front slope of the cosine peak). When the Z-axis offset of the displacement fiber increases gradually, and the total reflection angle of the beam on the V2 groove slope decreases, that is, the SPR incidence angle θ_i^” decreases, and the evanescent field strength increases, which will cause the SPR resonance wavelength to move towards the long wavelength direction and the depth of the resonance valley to deepen, so that the sensing of the Z-axis position by the SPR resonance wavelength and the depth of the resonance valley can be realized.

 

Fig. 3. View angle diagram of fiber SPR 3D micro displacement sensor with double V-grooves when V2 groove upward. (a) Schematic diagram of Z axis micro displacement sensing principle.

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The V-groove opening angle of the sensing fiber and the two core distance of the displacement fiber will affect the displacement sensitivity of the micro-displacement sensor with the V-groove structure. When the opening angle of the V-groove is smaller, the SPR resonance angle of the beam incident on the V groove slope is smaller, and the SPR resonance wavelength shift trend is more obvious. That is, the smaller the V-groove opening angle of the sensing fiber, the greater the displacement sensitivity of the sensor. The maximum V-groove opening angle that can be prepared by CO2 laser is 116 °, and the minimum V-groove opening angle is 100 °. To prepare the V-groove structure micro-displacement sensor with high sensitivity, we selected the sensor with V-groove angle 100 ° to carry out the three-dimensional sensing research. In addition, the two core distance of the displacement fiber will also affect the displacement sensitivity of the sensor, which is verified in subsequent experiments.

2.3. Transmission light field simulation of sensor

In order to further verify the change of the beam in the sensing fiber when the displacement fiber has different micro displacement in the X, Y, and Z directions relative to the sensing fiber, the beam transmission path in the sensing area is simulated and calculated by the Rsoft software, as shown in Fig. 4. The core and cladding diameter of the eccentric dual-core fiber was set to be 8.4µm and 125µm, the refractive index of the fiber core and cladding was set to be 1.4645 and 1.4613. The core and cladding diameter of the graded multimode fiber on the right side of the eccentric dual-core fiber was 100 µm and 125 µm. The maximum refractive index of the fiber core was 1.4807, the refractive index type of the fiber core was Diffused, the refractive index of the cladding was 1.4613. The light source type was set as Gaussian light source. The core diameter and cladding diameter of the graded multimode fiber as sensing fiber are 105µm and 125µm respectively. The maximum refractive index of the core was 1.4207, the refractive index type of the core was Diffused, and the refractive index of the cladding was 1.3642.

 

Fig. 4. When the micro displacement of the sensor is different in the 3D direction, the simulation diagram of the beam transmission path in (a) X axis, (b) Y axis, (c) Z axis direction.

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Figure 4(a) shows the simulation diagram of the micro displacement sensing optical path in the X-axis direction (V1 groove in the vertical direction of the sensor is upward). It can be seen that the light is injected into the eccentric core of the eccentric dual-core fiber. After being modulated by graded multimode fiber with the core diameter of 100 µm, the displacement fiber exits as an oblique beam. The beam in the sensing fiber core contacts V1 groove, and when it contacts the slope of V1 groove, the slope of the beam is positive value. As the distance between the displacement fiber and the sensing fiber X gradually increases, the amplitude of the cosine path of the beam in the modulation area on the left side of V1 groove increases, and the reflection angle of the beam transmitted to the inclined plane of V1 groove θ_i (SPR incidence angle) decreases gradually. When the injection offset X is 0 µm, 30 µm, 60 µm, 90 µm and 120 µm, its corresponding SPR incidence angle θ_i is 83.4°, 81.4°, 80.1°, 78.7° and 77.2° respectively (when the incident angle of SPR decreases, the resonance wavelength of SPR will red shift).

Figure 4(b) is the simulation diagram of the micro displacement sensing optical path in the Y-axis direction (the V1 groove in the vertical direction of the sensor is upward). It can be seen that the light is injected into the middle core of the eccentric dual-core fiber. After being modulated by graded multimode fiber, the displacement fiber exits with a horizontal beam. The beam in the sensing fiber core contacts V1 groove, and when it contacts the slope of V1 groove, the beam slope is negative value. As the offset between the displacement fiber and the sensing fiber increases along the Y axis, the amplitude of the cosine path of the beam in the modulation area on the left side of V1 groove increases, and the reflection angle of the beam transmitted to the slope of V1 groove θ_i^’ (SPR incidence angle) increases gradually. When the injection light offset Y is 5 µm, 8 µm, 11 µm, 14 µm and 17 µm, its corresponding SPR incidence angle θ_i^’ is 74 °, 75.8 °, 77.5 °, 82.4 ° and 87.5 ° respectively (the wavelength of SPR resonance valley will shift blue when the incident angle of SPR increases).

Figure 4(c) is the simulation diagram of the micro displacement sensing optical path in the Z-axis direction (V2 groove in the horizontal direction of the sensor is upward). It can be seen that the light is injected into the middle core of the eccentric dual-core fiber, the displacement fiber exits with a horizontal beam, the beam in the sensing fiber core contacts the V2 groove, and the beam slope is positive value when it contacts the inclined plane of V2 groove. As the offset between the displacement fiber and the sensing fiber increases along the Z-axis, the amplitude of the cosine path of the beam in the modulation area on the left side of V2 groove increases, and the reflection angle of the beam transmitted to the inclined plane of V2 groove θ_i^” (SPR incidence angle) decreases gradually. When offset Z is 5 µm, 8 µm, 11 µm,14 µm and 17 µm, its corresponding SPR incidence angle θ_i^” is 86.6 °, 84.2 °, 82.9 °, 81.2 ° and 79.1 ° respectively (when the incident angle of SPR decreases, the wavelength of SPR resonant valley will red shift).

2.4. Simulation of 3D displacement sensing SPR resonance spectrum

According to the simulation calculation results of the beam transmission path in the X, Y and Z directions in Fig. 4, the X direction offset of the displacement fiber and the sensing fiber increases, and the SPR incidence angle θ_i decreases. The Y-axis offset of displacement fiber and sensing fiber increases, the SPR incidence angle θ_i^’ increases. The Z-axis offset of displacement fiber and sensing fiber increases, and the SPR incidence angle θ_i^” decreases. In order to further verify the influence of SPR incidence angle change on the resonance wavelength of SPR sensing spectrum, Matlab software was used to calculate the P-light reflectivity spectrum at different SPR incidence angles, the thickness of sensing gold film was set to be 50 nm and the environmental refractive index was set to be 1.35, and the SPR incidence angle corresponding to different offsets in the X-axis, Y-axis and Z-axis direction θ_i, θ_i^’ and θ_i^’’ were brought into the calculation. The results are shown in Fig. 5(a), Fig. 5(b) and Fig. 5(c) respectively, with the increase of X axis offset, the SPR resonance wavelength moves to the long wavelength direction. With the increase of the offset in the Y-axis direction, the SPR resonance wavelength moves to the short wavelength direction. With the increase of the offset in the Z-axis direction, the SPR resonance wavelength moves to the long wavelength direction. According to the above simulation calculation, the fiber SPR 3D sensor based on double V-groove structure proposed in this paper can realize the sensing of micro displacement in X, Y and Z directions by SPR resonance wavelength parameters.

 

Fig. 5. SPR spectrum simulation diagram of fiber V-groove micro displacement sensor with different micro displacement (a) in X-axis direction, (b) in Y-axis direction, (c) in Z-axis direction.

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2.5. Fabrication of displacement probe and sensing probe

Firstly, a displacement fiber was fabricated by splicing an eccentric dual-core fiber and a graded multimode fiber. A 100 cm long eccentric dual-core fiber (both core diameters are 8.4 µm. The distance between eccentric core and intermediate core is 37 µm. Cladding diameter is 125 µm. The fiber was drawn by Beijing Xingyuan Aote Technology Co., Ltd.) and a 20 cm long graded index multimode fiber (GI100/125-14/250, YOFC) was coaxially spliced as shown in Fig. 6(a). By the fixed length cutting system, the right end of the graded multimode fiber was cut and kept the length of graded multimode fiber at 800 µm (T1/4), as shown in Fig. 6(b). The fabricated displacement optical fiber is shown in Fig. 6(c). When the single-mode fiber was employed to align the eccentric core of the left eccentric dual-core fiber and the light was injected into. The outgoing light field of the right end face of the displacement fiber is observed under the microscope, which is consistent with the simulation analysis. It is an oblique outgoing light field, and the angle of the oblique beam is about 4 °. When the single-mode fiber was employed to inject light from the middle core of the eccentric dual-core fiber. The output light field of the right end face of the displacement fiber was observed under a microscope. The output beam is a horizontal straight beam, as shown in Fig. 6(d).

 

Fig. 6. Schematic diagram of displacement fiber.

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Subsequently, the sensing fiber was fabricated. Taking a section of graded multimode fiber with core diameter of 105µm (GI105/125-30/250, YOFC), peeling off the coating layer 5 cm in the middle of the fiber with Miller pliers, and wiping it with alcohol, as shown in Fig. 7(a). The two ends of the fiber were clamped on two 3D micro motion table clamps under the CO₂ laser (MC-E-B, Yueming Laser), and the coating removal area was directly below the laser beam. The right inching table was moved slightly to the right, so that the fiber was in a straight and horizontal state under axial stress. At the same time, the left and right inching tables were adjusted to make the fiber coincide with the focal spot of the laser beam. The processing speed was set to 800 mm/s, the power was 50%, the frequency was 5 kHz, and the machining depth was 55µm (It can not only prevent the beam from incident to the V1 and V2 sensing areas at the same time, but also minimize the empty range of the displacement sensor and increase the displacement detection range). The laser output by the CO₂ laser was focused by the cylindrical mirror and acted on the fiber surface, and the fiber was deformed to form V1 groove (V groove angle is 100°) when heated, as shown in Fig. 7(b). The rotary fixture on the inching table on both sides counterclockwise were turned, the rotation angle was 90 °, and the left and right inching tables were simultaneously moved 1400 µm(7T2/8) to the right. By the laser processing with the same parameters, the fiber was deformed to form V2 groove when heated, as shown in Fig. 7(c). The left and right ends of the fabricated double V groove fiber were threaded into the quartz sleeve to cover the bare fiber on the left side of V1 groove and the right side of V2 groove. Then the double V groove fiber was put into the magnetron sputtering instrument (ETD-650 MS, YLBT), and the V1 and V2 grooves were coated with 50 nm gold film respectively, as shown in Fig. 7(d). The double V groove sensing fiber coated with gold film was took out and cut at 1000 µm (5T2/8) of the left end of V1 groove under the microscope of the fiber fixed length cutting system, as shown in Fig. 7(e). The surfaces of the two V-groove sensing areas were covered with low refractive index UV curing adhesive (NOA135, Norland) with a refractive index of 1.35, as shown in Fig. 7(f). After the UV curing adhesive was cured, the sensing probe was fabricated completely.

 

Fig. 7. Manufacturing process schematic diagram of the sensing probe.

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2.6. Establishment of 3D micro displacement testing device

The fiber 3D micro displacement sensing test device was built as shown in Fig. 8. Wide spectrum light source (HL-2000, Ocean Optics) light was injected into single-mode fiber. Under the electron microscope, the single-mode fiber core was aligned with the eccentric core or middle core of the eccentric dual-core fiber by the fiber coupling micro motion platform (1) in Fig 8, so that the displacement fiber can emit oblique beam or straight beam. The displacement fiber end and the sensing fiber end were respectively clamped on the left and right sides of the 3D precision micro displacement adjustment platform 2 (MP-225, Sutter). Under the electron microscope, the center of the displacement probe and the sensing probe was aligned by the 3D precision displacement platform, and then the displacement along the X axis, Y axis or Z axis was generated by moving the precision micro displacement adjustment platform with the displacement fiber on the left side. The outgoing light from the displacement probe entered the left ensd face of the sensing fiber, the beam entered the graded multimode fiber and transmitted as a cosine path, entered the sensing area. of V1 groove or V2 groove. The transmitted light evanescent field contacted the 50 nm gold film coated on the surface of the V groove, causing SPR effect. The sensing light signal continued to transmit to the right, and sent to the spectrometer (USB2000+, Ocean Optics). The spectrometer connected the computer to collect data for processing of the SPR attenuation spectrum.

 

Fig. 8. Experimental test device of fiber 3D micro displacement sensor.

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3. Testing results

3.1. Experimental results of 3D micro displacement sensing

The X axis (left and right) micro displacement sensing performance of the double V-groove fiber SPR 3D micro displacement sensor was tested. Under the electron microscope, by the fiber coupling micro platform (1) in Fig 8, the single-mode fiber core was controlled to align with the core of the eccentric dual-core fiber, so as to achieve the output oblique beam of the displacement fiber. The 3D precision displacement adjustment platform (2) in Fig 8 was adjusted to first make the displacement fiber and the sensing fiber coaxial, and then control the displacement fiber to move along the X-axis direction. Each time the displacement was 30 µm, the micro displacement sensing spectrum of the probe was collected as shown in Fig. 9(a). When the micro displacement of the displacement fiber increases in the X direction, the depth of the SPR resonant valley continues to deepen. In order to better observe the shift of SPR resonance wavelength, the data in Fig. 9(a) was normalized to get Fig. 9(b). It can be seen that when the micro displacement of the displacement fiber increases along the X-axis direction, the SPR resonance wavelength moves to the long wavelength. By the eccentric injection light for the eccentric dual-core fiber, the sensing of micro displacement in the X-axis direction with resonance wavelength was realized.

 

Fig. 9. Testing results of the fiber SPR 3D micro displacement sensor in (a) x-axis, (c) y-axis, (e) z-axis. (b) Normalization results of (a), (d) normalization results of (c), (f) normalization results of (e).

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The Y axis (up and down) direction micro displacement sensing performance of the double V-groove fiber SPR 3D micro displacement sensor was tested. Under the electron microscope, the single-mode fiber core was controlled to align with the middle core of the eccentric dual-core fiber through the fiber coupling micro motion Table 1, so that the displacement fiber can emit a straight beam. The 3D precision displacement Table 2 was adjusted to first align the center of the displacement probe and the sensing probe, and then control the displacement fiber to move along the Y-axis direction (when the micro displacement reached 5 µm, SPR resonance spectrum occurred well, and Y-axis micro displacement spectrum acquisition was started). The displacement range is 1-14 µm with a step of 1µm. The micro displacement sensing spectrum of the probe was collected as shown in Fig. 9(c). When the micro displacement of the displacement fiber increases in the Y-axis direction, the depth of the SPR resonance valley continues to deepen. The data in Fig. 9(c) was normalized to get Fig. 9(d). It can be seen that when the micro displacement of the displacement fiber increases along the Y-axis direction, the SPR resonance wavelength moves to the short wavelength direction, which indicates that the light injection in the middle core of the eccentric dual-core fiber can realize the sensing (blue shift) of the resonance wavelength to the micro displacement in the Y-axis direction.

Table 1. Performance comparison of double V-groove fiber SPR 3D micro displacement sensor with other sensors

View Table

Similarly, the Z-axis (front and back) micro displacement sensing performance of the double V-groove fiber SPR 3D micro displacement sensor was tested. As shown in Fig. 9(e), when the micro displacement of the displacement fiber in the Z-axis direction increases, the depth of the SPR resonance valley increases. The data in Fig. 9(e) was normalized to get Fig. 9(f). It can be seen that when the micro displacement of the displacement fiber increases along the Z-axis direction, the SPR resonance wavelength moves to the long wavelength direction. The testing results indicate that the light injection in the middle core of the eccentric dual-core fiber can realize the sensing (red shift) of the resonance wavelength to the micro displacement in the Z-axis direction.

According to the data in Fig. 9(a) and (b), the micro displacement in the X-axis direction was taken as the abscissa, the depth of SPR resonance valley corresponding to different micro displacements in the X-axis direction was taken as the left ordinate, and the wavelength of SPR resonance valley corresponding to different micro displacements in the X-axis direction was taken as the right ordinate. A graph and perform linear fitting according to the data trend were plotted to obtain Fig. 10(a). The SPR resonance valley depth sensitivity and wavelength sensitivity of the 3D micro displacement sensor for micro displacement in the X-axis direction are -0.0014a.u/µm and 0.148 nm/µm, the measuring range of X-axis displacement can reach 0-240 µm. Similarly, according to Fig. 9(c) and (d), the relationship curves between resonance wavelength, the depth of SPR resonance valley and micro displacements in the Y-axis direction were obtained as shown in Fig. 10(b). The SPR resonance valley depth sensitivity and wavelength sensitivity of the 3D micro displacement sensor for micro displacement in the Y-axis direction are -0.0458a.u/µm and -3.724 nm/µm, the measuring range of X-axis displacement can reach 5-14 µm. According to Fig. 9(e) and (f), the Fig. 10(c) was obtained. In which, the SPR resonance valley depth sensitivity and wavelength sensitivity of the 3D micro displacement sensor for micro displacement in the Z-axis direction are -0.0494a.u/µm and 3.543 nm/µm, the measuring range of X-axis displacement can reach 5-11 µm.

 

Fig. 10. Relationship curves between relationship curves between micro displacement and resonance wavelength, resonance valley depth in (a) x-axis direction, (b) y-axis direction, (c) z-axis direction.

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3.2. Effect of the eccentric dual-core fiber parameters on the sensing performance

Aim at the two bottleneck problems that fiber SPR micro displacement sensor has not yet realized 3D micro displacement sensing, and it is difficult to adjust the sensitivity. In this paper, a fiber SPR 3D micro displacement sensor based on double V- groove structure has been constructed. which can detect the micro displacement in the X, Y and Z directions. For the problem that sensitivity adjustment is difficult, we find that when the distance between two cores of the eccentric dual-core fiber is different and the light is injected into the eccentric core, the tilt angle of the inclined beam changes, the cosine path amplitude of the transmitted beam in the sensing fiber core changes, and the total reflection angle incident to the sensing area changes, as shown in Fig. 11, which plays a role in adjusting the micro displacement sensing sensitivity.

 

Fig. 11. Sensing principle diagram of oblique beams at different angles.

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The displacement sensing performance of the sensor in the X-axis direction was tested by directly fusing the eccentric dual-core fiber with the core distance of 37µm and 45 µm and the GI-100 fiber with the length of T1/4, respectively, as the displacement fiber. The experimental results of the displacement fiber SPR sensor with a core distance of 37 µm are shown in Fig. 12(a). It can be seen that the depth of SPR resonance valley increases with the increase of displacement in the X-axis direction, and the detection range can reach 0-240 µm. The data in Fig. 12(a) was normalized to get Fig. 12(b). It can be seen that the SPR resonance wavelength moves to the longer wavelength direction with the increase of the displacement in the X-axis direction. The experimental results of the displacement fiber SPR sensor with a core distance of 45 µm are shown in Fig. 12(c) and (d), the detection range is 0-200 µm. It can be seen from Fig. 12 that with the increase of the distance between the two cores of the displacement fiber, the displacement detection range decreases and the sensitivity increases.

 

Fig. 12. Testing results of X-axis micro displacement sensing experiment with the eccentric dual-core fiber core distance of (a) 37 µm, (c) 45 µm. (b) and (d) Normalized results of (a) and (c).

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The data was extracted from Fig. 12(a) and (c), and the relation curve between micro displacement and SPR resonance vally depth was draw,as shown in Fig. 13(a). Where, the resonance valley depth sensitivity of the sensor with core distance of 37 µm and 45 µm are -0.00118a.u./µm and -0.00168a.u./µm, respectively. Similarly, the data was extracted from Fig. 12(b) and (d), and the relation curve between micro displacement and SPR resonance wavelength was draw,as shown in Fig. 13(b). Where, the resonance wavelength sensitivity of the sensor with core distance of 37 µm and 45 µm are 0.146 nm/µm and 0.251 nm/µm, respectively. That is, the sensitivity of SPR resonance vally depth and the sensitivity of resonance wavelength increases with the increase of the distance between the two cores of the displacement fiber.

 

Fig. 13. Relationship curves between micro displacement in X-axis and (a) resonance valley depth, (b) resonance wavelength of the sensor with different core distance of the displacement fiber.

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4. Discussion

Table1 compared the performance of fiber interference type, grating type and fiber SPR type multi-dimensional micro displacement sensors, including sensitivity, resolution, detection range and number of sensors required. It can be seen that the sensitivity of the 3D micro displacement sensor based on the fiber double V-groove structure is 12 times that of the fiber SPR two-dimensional micro displacement sensor, and the number of sensors is only one compared with the fiber interference type and grating type micro displacement sensors. This sensor has the advantage that a single sensor can realize 3D micro displacement sensing, and the sensing system is simple. As far as we know, there is no report on the use of fiber SPR technology to realize 3D micro displacement sensing, the proposed sensor in this paper will promote the new development of SPR technology in the field of micro displacement measurement.

5. Conclusion

In conclusion, this paper proposed a fiber SPR 3D micro displacement sensor with adjustable sensitivity, which realized the 3D micro displacement sensing by a single fiber sensor and can selectively adjust the displacement sensitivity and detection range in the X-axis direction. When the sensor is slightly displaced in the X-axis direction, the average sensitivities of the resonance wavelength and the resonance valley depth are 0.148 nm/µm and -0.0014a.u/µm, respectively, the detection range can reach 0-240 µm. The resonance wavelength and valley depth sensitivity in Y-axis and Z-axis direction are -3.724 nm/µm, 3.543 nm/µm and -0.0458a.u./µm, -0.0494a.u./µm, respectively. The testing results indicate that the performance of the sensor for micro displacement in X-axis direction will be affected if the eccentric dual-core fiber with different core spacing is selected as the displacement fiber. The larger the dual core distance is, the larger the angle of oblique beam of displacement fiber is, and the greater the displacement wavelength sensitivity and valley depth sensitivity are, but the displacement detection range is reduced. According to the sensitivity and detection range requirements, the appropriate dual core spacing of eccentric dual-core fiber can be selected. The fiber SPR 3D micro displacement sensor with adjustable sensitivity proposed in this paper can be used for precise 3D displacement measurement and spatial 3D positioning in narrow areas.