The authors thank the Optics Laboratory for their equipment and are thankful for financial support through the Program for Changjiang Scholars and Innovative Research Team in University and the Ministry of Education of China.

1. Fabrication of the fiber Bragg grating
<ol>
	<li>To enhance the photosensitivity of fiber core, put a standard single-mode fiber into a hydrogen-loaded airtight canister for 1 week.</li>
	<li>Fabricate the fiber Bragg grating using the scanning phase-mask technique and a frequency-doubled, continuous wave argon-ion laser at a wavelength of 244 nm.
	<ol>
		<li>Focus on the optical fiber with a cylindrical lens and an ultraviolet (UV) laser beam. Imprint the grating (periodic modulation of refractive index) in the photosensitive core by using a phase mask (parallel with the fiber axis) placed in front of the fiber. The light output by the laser is shaped and perpendicular to the phase mask. Place the fiber at the position of the &#177;1 order diffracted light for UV exposure.</li>
	</ol>
	</li>
	<li>After UV inscription, place the two fiber Bragg gratings in a 100 &#176;C oven for 48 h to remove any residual hydrogen, until the reflectivity of the fiber grating is reduced by 10%, the 3 dB bandwidth is reduced by 0.1 nm, and the center wavelength is shifted by 0.8 nm. This step is called the annealing processing. The parameters of FBG will not change after the annealing processing. 
	NOTE: The central wavelengths of these two FBGs are 1,555.12 nm (1#FBG) and 1,557.29 nm (2#FBG) with grating lengths of 5 mm.</li>
</ol>
2. Preparation of the magnetic scale and the matching clamp
<ol>
	<li>Determine the size of the permanent magnet according to the previously described design8. The description of the permanent magnet is shown in Table 1.</li>
	<li>Design the slot of the magnetic scale, whose dimension matches the permanent magnet, as shown in Figure 1.
	<ol>
		<li>Confirm the dimension of the matching clamp and set a distance of 22.5 mm between the two slots in the clamp. In order to remove magnetic field interference, the clamp is made of stainless steel.</li>
		<li>Set a distance of 10 mm of the pitch in the magnetic scale (&#964;) to distinguish the direction of movement, and set a distance of 22.5 mm ((2+1/4)&#183;&#964;) between the two detectors. Two detectors can obtain the displacement characteristic according to the following formulas, which can achieve sinusoidal function variations by a phase difference of 90&#176;, where x is the displacement, F1#FBG and F2#FBG are the magnetic force of the two detectors, and B is a constant. The structure of the magnetic scale and its matching clamp are shown in Figure 1. 
		<img alt="Equation 1" src="/files/ftp_upload/58182/58182eq1.jpg" /></li>
	</ol>
	</li>
	<li>Put permanent magnets into the slots of the clamp, with the magnetic N/S alternately arranged. Cylindrical permanent magnets are only magnetized in the axial direction, and its magnetic vector is 750 kA/m.</li>
</ol>
3. Fabrication of the displacement sensor
<ol>
	<li>Prepare a mixture of heat-curable fiber optic epoxy (glue) by adding 100 mg of hardener (Component A) to 200 mg of resin (Component B), as shown in Figure 2.</li>
	<li>Measure the distance of fiber pigtail, approximately 10 mm between the end face of fiber pigtail and the grating region, and then, score it with a fine-point marker.</li>
	<li>Use a fiber optic stripper to peel the fiber coating and strip it from the marker position of the previous step.</li>
	<li>Clean the surface of any remaining polymer with dust-free paper. Position the blade of a high-precision fiber cleaver perpendicular to the fiber optic cable and cut it.</li>
	<li>Put a permanent magnet on the hot plate and place a spring with a length of 15 mm above the permanent magnet. 
	NOTE: The length of the spring is the main element of the preloaded force in the next step.</li>
	<li>Glue the fiber obtained from step 3.3. Place the pigtail of the fiber inside of the spring, as shown in Figure 2, and cure the adhesive (Epoxy #1) for 30 min at 150 &#176;C. 
	NOTE: These three combined parts are called 1#P.</li>
	<li>Put 1#P into the tapered pipe and use adhesive tape to fix the permanent magnet. as shown in Figure 3. Place adhesive exactly above the permanent magnet, and cure the adhesive (Epoxy #2 is the same as Epoxy #1) for 30 min at a temperature of 150 &#176;C. Then, apply the preloaded force by hand to the fiber Bragg grating; the pretightening force allows the fiber to be in a nonbending state. 
	NOTE: These combined parts are called the FBG detector. The FBG detector is responsible for converting the signal of the magnetic force into the signal of the displacement parameters.</li>
	<li>Remove the adhesive tape; the production of this step is called 2#P.</li>
	<li>Splice an APC-type single-mode connector to the end of the 2#P fiber using a fusion splicer, following manufacturer&#8217;s instructions.</li>
	<li>Fix two FBG detectors into the slot of the clamp, and then, fix the clamp to the displacement platform.</li>
</ol>
4. Building the testing system
<ol>
	<li>Power the high-speed wavelength interrogator with the built-in optical switch.</li>
	<li>Turn on the amplified spontaneous emission (ASE). Guide the light into the input-output fiber and propagate it to the FBG-based displacement sensor. Then, the reflection spectra modulated by the sensor reflects it to the interrogator via the input-output fiber again.</li>
	<li>Connect the interrogator to the computer with an ethernet cable, based on the UDP protocol.</li>
	<li>Connect the optical circulator to the optical spectrum analyzer (OSA) with a minimum resolution of 0.02 nm, for monitoring the Bragg wavelength shift.</li>
	<li>Power the stepper motor with 24 V.</li>
	<li>Change the speed of the motor by adjusting the DIP switch of the stepper motor controller. With the external control port, the stepper motor controller can be driven in half-step, normal, and other drive modes, as shown in Table 2, and on-chip PWM chopper circuits permit switch-mode control of the current in the windings based on an MCU.</li>
	<li>Adjust the distance between the two detectors and the magnetic scale.
	<ol>
		<li>Adjust until there is a better sinusoidal curve between the displacement and the magnetic field.</li>
		<li>Adjust until there are well-described methods to stimulate the best distance11 because cylindrical permanent magnets with opposite magnetic fields are arranged adjacent to each other. 
		NOTE: There is a sinusoidal relationship between the displacement and the magnetic field when there is a suitable distance between the magnetic scale and the detector. The magnetic force has a linear relationship with the magnetic field. According to Hooke&#8217;s law, force has a linear relationship with strain, and the center wavelength shift of FBG is linear with strain applied on the FBG; thus, a sinusoidal curve can be obtained.</li>
		<li>Separate the two detectors from each other for 22.5 mm. 
		NOTE: (m &#177; 1/4)&#964; equals 22.5 mm (m is a positive integer, m = 2), &#964; is the pitch of the magnetic scale, and (m &#177; 1/4)&#964; &#8804; the total length of the magnetic scale, where &#964; equals 10.</li>
	</ol>
	</li>
</ol>
5. Evaluation of the designed displacement sensor
<ol>
	<li>Adjust the distance between the detector and the magnetic scale to be 1.5 mm and, then, fix the clamp.</li>
	<li>Plug the APC-type connector end of the sensor into the interrogator port and start the configuration software. Set the sampling frequency of the interrogator to 5 kHz for a real-time recording of the FBG center wavelength change over time. Push the button to control the motor by an increment of 40 &#956;m each time (type F, as shown in Table 2). Different types represent different steps. If the motor works with type F, the motor can have the smallest step interval and the highest displacement accuracy.</li>
	<li>Plug the APC-type connector end of the sensor into the OSA port and start the configuration software. An OSA and interrogator monitor the central wavelengths shift of FBGs. Save the data from the static state calibration.</li>
	<li>Alternate the clockwise and anticlockwise rotation of the motor in a dynamic state. Save the data as above.</li>
	<li>Put the sensor on the hot plate and conduct a temperature calibration experiment. Change the temperature of the hot plate from 25 &#176;C to 90 &#176;C.</li>
	<li>Perform data analysis.
	<ol>
		<li>Import the data in a .csv format from the static calibration experiment into MATLAB. Employ the findpeaks function to extract the center wavelength of the fiber Bragg grating. Use the sinusoidal function from the curve fitting tool to fit the relationship between the center wavelength and the displacement, as shown in Figure 5a. The fitting residual errors between sample points and the fitting curve also are depicted in Figure 5b. The two Fourier fitting curves between the center wavelength shifts and the linear displacement despite the original phase are here: 
		<img alt="Equation 2" src="/files/ftp_upload/58182/58182eq2.jpg" /></li>
		<li>Import the data into the processing software. Using the curve fitting tool, process the data obtained from a dynamic clockwise rotation (forward movement) and an anticlockwise rotation (backward movement) of the motor (Figure 6).</li>
		<li>Process the data obtained from the temperature calibration experiment as above (Figure 7).</li>
	</ol>
	</li>
</ol>

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Technology. 22 (2), 025203 (2011).</li><li>Lin, G., Adhami, R., Dong, X., Zou, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Wide+range+FBG+displacement+sensor+based+on+twin-core+fiber+filter.">Wide range FBG displacement sensor based on twin-core fiber filter.</a> Journal of Lightwave Technology. 30 (3), 337-343 (2012).</li><li>Li, M., Guo, J., Tong, B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+double-fiber+F-P+displacement+sensor+based+on+direct+phase+demodulation.">A double-fiber F-P displacement sensor based on direct phase demodulation.</a> The International Conference on Optical Fibre Sensors. 8421, 84212R (2012).</li><li>Zhou, X., Yu, Q. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Wide-range+displacement+sensor+based+on+fiber-Optic+Fabry-Perot+Interferometer+for+Subnanometer+Measurement.">Wide-range displacement sensor based on fiber-Optic Fabry-Perot Interferometer for Subnanometer Measurement.</a> IEEE Sensors Journal. 11, 1602-1606 (2011).</li><li>Shen, W., Wu, X., Meng, H., Huang, X. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Long+distance+fiber-optic+displacement+sensor+based+on+fiber+collimator.">Long distance fiber-optic displacement sensor based on fiber collimator.</a> Review of Scientific Instruments. 81 (12), (2010).</li><li>Zhu, L., Lu, L., Zhuang, W., Zeng, Z., Dong, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Non-contact+temperature-independent+random-displacement+sensor+using+two+fiber+bragg+gratings.">Non-contact temperature-independent random-displacement sensor using two fiber bragg gratings.</a> Applied Optics. 57 (3), 447 (2018).</li><li>Yu, H., Yang, X., Tong, Z., Cao, Y., Zhang, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Temperature-independent+rotational+angle+sensor+based+on+fiber+Bragg+grating.">Temperature-independent rotational angle sensor based on fiber Bragg grating.</a> IEEE Sensors Journal. 11 (5), 1233-1235 (2011).</li><li>Liu, J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+Wide-Range+Displacement+Sensor+Based+on+Plastic+Fiber+Macro-Bend+Coupling.">A Wide-Range Displacement Sensor Based on Plastic Fiber Macro-Bend Coupling.</a> Sensors. 17 (1), 196 (2017).</li></ol>

The authors have nothing to disclose.

We have demonstrated a new method for random linear displacement measurements by combining a magnetic scale and two fiber Bragg gratings. The main advantage of these sensors is random displacement without limitation. The magnetic scale used here generated a periodicity of the magnetic field at 10 mm, far beyond the practical limits of conventional optical fiber displacement sensors, such as the displacement mentioned by Lin et al.7 and Li et al.8. The temperature-dependent displacement sensor is also suitable for experiments involved in remote monitoring.
The preloaded force on the FBG is the critical step in the packaging protocol of the FBG-based magnetic detector. When the spring is stretched or compressed, a uniform axis stress distribution of the FBG is obtained. A distance of (m &#177; 1/4)&#964; between two detectors is essential to ensure that the entire system recognizes the direction of movement.
This new displacement measurement technology requires a reduced susceptibility to vibration. The sensors may also be improved by reducing their sensitivity to humidity changes, which are affected by the spring in the detector. Future work could focus on the development of software algorithms to eliminate vibration affection. This displacement sensor system can become commercially available if the pitch of the magnetic scale can be decreased as the commercial electronic magnetic scale.
This sensor can be used to measure random displacement without range limitation with respect to existing methods. Although the protocol here has been proven to be effective as a displacement sensor, it can also be used to measure other parameters, such as velocity and acceleration.

Optical fiber-based sensors have great advantages, such as flexibility, wavelength division multiplexing, remote monitoring, corrosion resistance, and other characteristics. Thus, the optical fiber displacement sensor has broad applications.
To realize targeted linear displacement measurements in complex environments, various structures of the optical fiber (e.g., the Michelson interferometer1, the Fabry-Perot cavity interferometer2, the fiber Bragg grating3, the bending loss4)&#160;have been developed over recent years. The bending loss requires the light source in a stable station and is unsuitable for environmental vibration. Qu et al. have designed an interferometric fiber-optic nanodisplacement sensor based on a plastic dual-core fiber with one end coated with a silver mirror; it has a resolution of 70 nm5. A simple displacement sensor based on a bent single-mode-multimode-single-mode (SMS) fiber structure was proposed to overcome the limitations on the measurement of the displacement range; it increased the displacement sensitivity threefold with a range from 0 to 520 &#181;m6. Lin et al.&#160;presented a displacement sensor system that combines the FBG together with a spring; the output power is approximately linear with the displacement of 110-140 mm7. A fiber Fabry-Perot displacement sensor has a measurement range of 0-0.5 mm with a linearity of 1.1% and a resolution of 3 &#181;m8. Zhou et al. reported a wide-range displacement sensor based on a fiber-optic Fabry-Perot interferometer for subnanometer measurements, up to 0.084 nm over a dynamic range of 3 mm9. A fiber-optic displacement sensor based on reflective intensity modulated technology was demonstrated using a fiber collimator; this had a sensing range over 30 cm10. Although optical fibers can be fabricated into many kinds of displacement sensors, these fiber-based sensors generally make use of the tensile limit of the material itself, which limits their application in wide-range measurements. Thus, compromises are usually made between the measurement range and sensitivity. Moreover, it is difficult to determine the displacement as various variables occur simultaneously; especially, cross-sensitivity of the strain and temperature could damage the experimental precision. There are many discrimination techniques reported in the literature, such as using two different sensing structures, using a single FBG half-bonded by different glues, or using special optical fibers. Thus, the further development of optical fiber displacement sensors requires high sensitivity, a small size, great stability, full range, and temperature independence.
Here, the periodic structure of the magnetic scale makes a full-range measurement possible. A random displacement without a limited measurement range with a magnetic scale is achieved. Combined with two FBGs, both temperaturecross-sensitivity and the identification for the direction of movement could be solved. Various steps within this method require precision and attention to detail. The protocol of the sensor fabrication is described in detail as following.

<table><tbody><tr><td>ASE</td><td>OPtoElectronics Technology Co., Ltd.</td><td></td><td>1525nm-1610nm</td></tr><tr><td>computer</td><td>Thinkpad</td><td></td><td>win10</td></tr><tr><td>fiber cleaver/ CT-32</td><td>Fujikura</td><td></td><td>the diameter of 125</td></tr><tr><td>fiber optic epoxy /DP420</td><td>henkel-loctite</td><td></td><td>Ratio 2:1</td></tr><tr><td>interrogator</td><td>BISTU</td><td></td><td>sample rate:17kHz</td></tr><tr><td>motor driver</td><td>Zolix</td><td></td><td>PSMX25</td></tr><tr><td>optical circulator</td><td>Thorlab</td><td></td><td>three ports</td></tr><tr><td>optical couple</td><td>Thorlab</td><td></td><td>50:50</td></tr><tr><td>optical spectrum analyzer/OSA</td><td>Fujikura</td><td></td><td>AQ6370D</td></tr><tr><td>permanent magnet</td><td>Shanghai Sichi Magnetic Industry Co., Ltd.</td><td></td><td>D5x4mm</td></tr><tr><td>plastic shaped pipe</td><td>Topphotonics</td><td></td><td></td></tr><tr><td>power source</td><td>RIGOL</td><td></td><td>adjustable power</td></tr><tr><td>single mode fiber</td><td>Corning</td><td></td><td>9/125um</td></tr><tr><td>Spring</td><td>tengluowujin</td><td></td><td>D3x15mm</td></tr><tr><td>stepper motor controller</td><td></td><td></td><td>JF24D03M</td></tr></tbody></table>

a random-displacement measurement by combining a magnetic scale and two fiber bragg gratings

Long-distance displacement measurements using optical fibers have always been a challenge in both basic research and industrial production. We developed and characterized a temperature-independent fiber Bragg grating (FBG)-based random-displacement sensor that adopts a magnetic scale as a novel transferring mechanism. By detecting shifts of two FBG center wavelengths, a full-range measurement can be obtained with a magnetic scale. For identification of the clockwise and counterclockwise rotation direction of the motor (in fact, the direction of movement of the object to be tested), there is a sinusoidal relationship between the displacement and the center wavelength shift of the FBG; as the anticlockwise rotation alternates, the center wavelength shift of the second FBG detector shows a leading phase difference of around 90&#176; (+90&#176;). As the clockwise rotation alternates, the center wavelength shift of the second FBG displays a lagging phase difference of around 90&#176; (-90&#176;). At the same time, the two FBG-based sensors are temperature independent. If there is some need for a remote monitor without any electromagnetic interference, this striking approach makes them a useful tool for determining the random displacement. This methodology is appropriate for industrial production. As the structure of the whole system is relatively simple, this displacement sensor can be used in commercial production. In addition to it being a displacement sensor, it can be used to measure other parameters, such as velocity and acceleration.

The distance, ranging from 1 mm to 3 mm11, between the magnetic scale and the detector enabled the detection of the linear displacement with a sinusoidal function. A distance of 22.5 mm between two detectors enabled this approach to realize detection of the direction of an object&#39;s movement with a phase difference of 90&#176;. The two detectors were separated from each other for (m &#177; 1/4)&#964; (m is a positive integer) and (m &#177; 1/4)&#964; &#8804; the total length of the magnetic scale, where &#964; = 10 mm and m = 2 are used in the experiment described here (Figure 1). The composition and structure of the displacement detector are shown in Figure 2. The key of the packaging process is to apply a preloaded force to the FBG; when there was a movement, the magnetic force between the magnetic scale and the detector would change (Figure 3), and the axis stress distribution of the FBG would be uniform as the spring stretched or compressed. The measurement system is based on the ASE, the interrogator, and the OSA, which characterizes the sensor&#39;s center wavelength signature (Figure 4). The OSA, with a minimum resolution of 0.02 nm, was more accurate than the interrogator when measuring the spectrum statically. OSA has a high resolution; it is more suitable than the interrogator in static calibration experiments.
The results of static calibration (Figure 5a) and corresponding residual errors (Figure 5b) revealed that the designed detector allows the exploration of the random-displacement position at its best. For the identification of the forward and inverse movement direction of the motor, as the forward movementalternates, the center wavelength shift of the 2#FBG detector has a leading phase difference of around 90&#176; (+90&#176;). As the inverse displacement alternates , the center wavelength shift of the 2#FBG displayed the sinusoidal function variations by a lagging phase difference of around 90&#176; (-90&#176;) (Figure 6). The temperature cross-sensitivity on the proposed sensor could be eliminated by a differential sine function. A positive or negative change in the phase angle could be obtained. The direction of the displacement could easily be solved, as mentioned previously12. In brief, the data collected from the temperature calibration experiment is shown in Figure 7. It can be known that the temperature sensitivity (KT) of both FBG detectors is the same when the temperature interference is not ignored in this system. The relationship between the displacement and the wavelength shifts can be expressed as follows; thus, temperature compensation is the merit of this system. 
<img alt="Equation 3" src="/files/ftp_upload/58182/58182eq3.jpg" />
The uncertainty from the data fitting shows that the maximum uncertainty is almost parallel with the maximum amplitude of the sinusoidal fitting curve. There can be some improvement to make uncertainty smaller so that the uncertainty represents the property of the sensor. We took the balanced point (5 mm, a position in which the detector is opposite in polarity to the magnetic scale) and the maximum amplitude (2.5 mm, a position in which the detector has polarity to the magnetic scale) of 1#FBG as an example (depicted in Figure 5b), and the repeatability of the measurement (10 counts) is shown in Figure 8. It is clear that the balanced point (5 mm) was more stable than the maximum amplitude (2.5 mm), and the maximum residual error (7.5 pm) occurred on the maximum amplitude (2.5 mm) of 1#FBG. The accuracy of the displacement measurement is 0.69 &#181;m.
<img alt="Equation 4" src="/files/ftp_upload/58182/58182eq4.jpg" />
<img alt="Equation 5" src="/files/ftp_upload/58182/58182eq5.jpg" />
<img alt="Equation 6" src="/files/ftp_upload/58182/58182eq6.jpg" />
Automatic control and production, especially for machine monitoring in serious oil-contaminated circumstances, need optical fiber-based long displacement. Thus, the designed optical fiber sensor can be used in steel and iron process.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/58182/58182fig1.jpg" /> 
Figure 1: The magnetic scale and matching clamp. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/58182/58182fig2.jpg" /> 
Figure 2: Composition and structure of the displacement detector. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/58182/58182fig3.jpg" /> 
Figure 3: Method of applied preloaded force during packaging. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/58182/58182fig4.jpg" /> 
Figure 4: Experiment setup for displacement measurements. The system is based on the ASE, the interrogator, and the OSA, which characterize the sensor&#39;s center wavelength signature. This figure is reprinted with permission from Zhu et al.11. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/58182/58182fig5.jpg" /> 
Figure 5: Static calibration and residual errors. (a) The relationship between the displacement and the two FBGs wavelength shift. (b) The fitting curve residual error between the original data and the sinusoidal curve. This figure is reprinted with permission from Zhu et al.11. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/58182/58182fig6.jpg" /> 
Figure 6: Identification of the clockwise and counterclockwise rotation direction of the motor. This figure is reprinted with permission from Zhu et al.11. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 7" class="xfigimg" src="/files/ftp_upload/58182/58182fig7.jpg" /> 
Figure 7: The relationship between the center wavelength and temperature. This figure is reprinted with permission from Zhu et al.11. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig7large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 8" class="xfigimg" src="/files/ftp_upload/58182/58182fig8.jpg" /> 
Figure 8: The repeatability of the measurement. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/58182/58182fig8large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Name</td>
			<td>Parameters</td>
		</tr>
		<tr>
			<td>Magnetic Grade</td>
			<td>N35</td>
		</tr>
		<tr>
			<td>Magnet Material</td>
			<td>NdFeB</td>
		</tr>
		<tr>
			<td>Surface &#38; Coating</td>
			<td>Nickel</td>
		</tr>
		<tr>
			<td>Magnetizing direction</td>
			<td>N/S pole on both sides of the plane</td>
		</tr>
		<tr>
			<td>Size</td>
			<td>D5 x 4 mm</td>
		</tr>
		<tr>
			<td>M(magnetization)</td>
			<td>750 [kA/m]</td>
		</tr>
	</tbody>
</table>
Table 1:Description of the permanent magnet. This table is reprinted with permission from Zhu et al.11.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Type</td>
			<td>Steps</td>
			<td>Displacement/step (&#956;m)</td>
		</tr>
		<tr>
			<td>A</td>
			<td>1,600</td>
			<td>312</td>
		</tr>
		<tr>
			<td>B</td>
			<td>2,000</td>
			<td>250</td>
		</tr>
		<tr>
			<td>C</td>
			<td>3,200</td>
			<td>156</td>
		</tr>
		<tr>
			<td>D</td>
			<td>4,000</td>
			<td>125</td>
		</tr>
		<tr>
			<td>E</td>
			<td>6,400</td>
			<td>78</td>
		</tr>
		<tr>
			<td>F</td>
			<td>12,800</td>
			<td>40</td>
		</tr>
	</tbody>
</table>
Table 2: Description of the microstep driver.

Watch this Scientific Journal Video about A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings at JoVE.com

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

A protocol to create a full-range linear displacement sensor, combining two packaged fiber Bragg grating detectors with a magnetic scale, is presented.

Long-distance displacement measurements using optical fibers have always been a challenge in both basic research and industrial production. We developed ...

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6.2K Views.  Beijing Information Science and Technology University. We hebben de uitdaging van lange afstandsverplaatsingsmetingen aangepakt. Je dan, optische vezels. De technische kan worden gebruikt in zowel fundamenteel onderzoek als industriële productie.Met de juiste opstelling kan de verplaatsing worden gemeten. Andere gemeten van de optische vezel. Deze metrologie is geschikt voor gebruik in industriële omgevingen.De gebruiker hoeft alleen maar de magnetische weegschaal op de vangrail te trekken. Deze methode kan inzicht geven in het on...

Video: A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

Writing Bragg Gratings in Multicore Fibers

Fiber Bragg gratings in multicore fibers can be used as compact and robust filters in astronomical and other research and commercial applications. Strong suppression at a single wavelength requires that all cores have matching transmission profiles. These gratings cannot be inscribed using the same method as for single-core fibers because the curved surface of the cladding acts as a lens, focusing the incoming UV laser beam and causing variations in exposure between cores. Therefore we use an additional optical element to ensure that the beam shape does not change while passing through the cross-section of the multicore fiber. This consists of a glass capillary tube which has been polished flat on one side, which is then placed over the section of the fiber to be inscribed. The laser beam enters the fiber through the flat surface of the capillary tube and hence maintains its original dimensions. This paper demonstrates the improvements in core-to-core uniformity for a 7-core fiber using this method. The technique can be generalized to larger multicore fibers.

We describe a technique for inscribing identical fiber Bragg gratings into each core of a multicore fiber. This is achieved by introducing an additional surface into the optical path to mitigate lensing by the curved surface of the fiber cladding.

Fiber Bragg gratings in multicore fibers can be used as compact and robust filters in astronomical and other research and commercial applications. Strong ...

Frequency Mixing Magnetic Detection Scanner for Imaging Magnetic Particles in Planar Samples

The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. It consists of two magnetic measurement heads on both sides of the sample mounted on the legs of a u-shaped support. The sample is locally exposed to a magnetic excitation field consisting of two distinct frequencies, a stronger component at about 77 kHz and a weaker field at 61 Hz. The nonlinear magnetization characteristics of superparamagnetic particles give rise to the generation of intermodulation products. A selected sum-frequency component of the high and low frequency magnetic field incident on the magnetically nonlinear particles is recorded by a demodulation electronics. In contrast to a conventional MPI scanner, p-FMMD does not require the application of a strong magnetic field to the whole sample because mixing of the two frequencies occurs locally. Thus, the lateral dimensions of the sample are just limited by the scanning range and the supports. However, the sample height determines the spatial resolution. In the current setup it is limited to 2 mm. As examples, we present two 20 mm &#215; 25 mm p-FMMD images acquired from samples with 1 &#181;m diameter maghemite particles in silanol matrix and with 50 nm magnetite particles in aminosilane matrix. The results show that the novel MPI scanner can be applied for analysis of thin biological samples and for medical diagnostic purposes.

A scanner for imaging magnetic particles in planar samples was developed using the planar frequency mixing magnetic detection technique. The magnetic intermodulation product response from the nonlinear nonhysteretic magnetization of the particles is recorded upon a two-frequency excitation. It can be used to take 2D images of thin biological samples.

The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. ...

Fiber Optic Distributed Sensors for High-resolution Temperature Field Mapping

The reliability of computational fluid dynamics (CFD) codes is checked by comparing simulations with experimental data. A typical data set consists chiefly of velocity and temperature readings, both ideally having high spatial and temporal resolution to facilitate rigorous code validation. While high resolution velocity data is readily obtained through optical measurement techniques such as particle image velocimetry, it has proven difficult to obtain temperature data with similar resolution. Traditional sensors such as thermocouples cannot fill this role, but the recent development of distributed sensing based on Rayleigh scattering and swept-wave interferometry offers resolution suitable for CFD code validation work. Thousands of temperature measurements can be generated along a single thin optical fiber at hundreds of Hertz. Sensors function over large temperature ranges and within opaque fluids where optical techniques are unsuitable. But this type of sensor is sensitive to strain and humidity as well as temperature and so accuracy is affected by handling, vibration, and shifts in relative humidity. Such behavior is quite unlike traditional sensors and so unconventional installation and operating procedures are necessary to ensure accurate measurements. This paper demonstrates implementation of a Rayleigh scattering-type distributed temperature sensor in a thermal mixing experiment involving two air jets at 25 and 45 &#176;C. We present criteria to guide selection of optical fiber for the sensor and describe installation setup for a jet mixing experiment. We illustrate sensor baselining, which links readings to an absolute temperature standard, and discuss practical issues such as errors due to flow-induced vibration. This material can aid those interested in temperature measurements having high data density and bandwidth for fluid dynamics experiments and similar applications. We highlight pitfalls specific to these sensors for consideration in experiment design and operation.

We demonstrate use of a fiber optic distributed sensor for mapping the temperature field of mixing air jets. The Rayleigh scattering-based sensor generates thousands of data points along a single fiber to provide exceptional spatial resolution that is unattainable with traditional sensors such as thermocouples.

The reliability of computational fluid dynamics (CFD) codes is checked by comparing simulations with experimental data. A typical data set consists ...

Remote Magnetic Actuation of Micrometric Probes for in situ 3D Mapping of Bacterial Biofilm Physical Properties

Bacterial adhesion and growth on interfaces lead to the formation of three-dimensional heterogeneous structures so-called biofilms. The cells dwelling in these structures are held together by physical interactions mediated by a network of extracellular polymeric substances. Bacterial biofilms impact many human activities and the understanding of their properties is crucial for a better control of their development &#8212; maintenance or eradication &#8212; depending on their adverse or beneficial outcome. This paper describes a novel methodology aiming to measure in situ the local physical properties of the biofilm that had been, until now, examined only from a macroscopic and homogeneous material perspective. The experiment described here&#160;involves introducing magnetic particles into a growing biofilm to seed local probes that can be remotely actuated without disturbing the structural properties of the biofilm. Dedicated magnetic tweezers were developed to exert a defined force on each particle embedded in the biofilm. The setup is mounted on the stage of a microscope to enable the&#160;recording of time-lapse images of the particle-pulling period. The particle trajectories are then extracted from the pulling sequence and the local viscoelastic parameters are derived from each particle displacement curve, thereby providing the 3D-spatial distribution of the parameters. Gaining insights into the biofilm mechanical profile is essential from an engineer&#39;s point of view for biofilm control purposes but also from a fundamental perspective to clarify the relationship between the architectural properties and the specific biology of these structures.

Remote Magnetic Actuation of Micrometric Probes for in situ 3D Mapping of Bacterial Biofilm Physical Properties

This paper shows an original methodology based on the remote actuation of magnetic particles seeded in a bacterial biofilm and the development of dedicated magnetic tweezers to measure in situ the local mechanical properties of the complex living material built by micro-organisms at interfaces.

Bacterial adhesion and growth on interfaces lead to the formation of three-dimensional heterogeneous structures so-called biofilms. The cells dwelling in ...

Bioengineering

Micro/Nano-scale Strain Distribution Measurement from Sampling Moir&#233; Fringes

This work describes the measurement procedure and principles of a sampling moir&#233; technique for full-field micro/nano-scale deformation measurements. The developed technique can be performed in two ways: using the reconstructed multiplication moir&#233; method or the spatial phase-shifting sampling moir&#233; method. When the specimen grid pitch is around 2 pixels, 2-pixel sampling moir&#233; fringes are generated to reconstruct a multiplication moir&#233; pattern for a deformation measurement. Both the displacement and strain sensitivities are twice as high as in the traditional scanning moir&#233; method in the same wide field of view. When the specimen grid pitch is around or greater than 3 pixels, multi-pixel sampling moir&#233; fringes are generated, and a spatial phase-shifting technique is combined for a full-field deformation measurement. The strain measurement accuracy is significantly improved, and automatic batch measurement is easily achievable. Both methods can measure the two-dimensional (2D) strain distributions from a single-shot grid image without rotating the specimen or scanning lines, as in traditional moir&#233; techniques. As examples, the 2D displacement and strain distributions, including the shear strains of two carbon fiber-reinforced plastic specimens, were measured in three-point bending tests. The proposed technique is expected to play an important role in the non-destructive quantitative evaluations of mechanical properties, crack occurrences, and residual stresses of a variety of materials.

A sampling moir&#233; technique featuring 2-pixel and multi-pixel sampling methods for high-accuracy strain distribution measurements at the micro/nano-scale is presented here.

This work describes the measurement procedure and principles of a sampling moir&#233; technique for full-field micro/nano-scale deformation measurements. ...

Design, Instrumentation and Usage Protocols for Distributed In Situ Thermal Hot Spots Monitoring in Electric Coils using FBG Sensor Multiplexing

Random wound coils are a key operational element of most electric apparatus in modern industrial systems, including low voltage electric machines. One of the major current bottlenecks in improved exploitation of electrical devices is the high sensitivity of their wound components to in-service thermal stress. The application of conventional thermal sensing methods (e.g., thermocouples, resistance temperature detectors) for thermal condition monitoring of current carrying random wound coils can impose considerable operational limitations due to sensor size, EMI sensitivity and the existence of electrically conductive material in their construction. Another substantial limitation exists in distributed sensing applications and is caused by what is often a considerable length and volume of conventional sensor wiring leads.
This paper reports the design of a fiber optic FBG&#160;sensing system&#160;intended for enabling real-time distributed internal thermal&#160;condition monitoring within random wound coils. The procedure of random wound coil instrumentation with the FBG sensing system is reported in a case study on an IEEE standard wound coil representative of those utilized in electrical machines. The reported work also presents and discusses important practical and technical aspects of FBG sensing system implementation and application, including the FBG array geometry design, sensing head and fiber packaging, the sensor array installation and calibration procedure and the use of a commercial interrogation system for obtaining thermal measurements. Finally, the in situ multiplexed FBG sensing system thermal monitoring performance is demonstrated in representative static and dynamic thermal conditions.&#160;

This paper presents a protocol that enables instrumentation of random wound electric coils with fiber Bragg grating (FBG) thermal sensors for the purpose of distributed condition monitoring of internal thermal hot spots.

Random wound coils are a key operational element of most electric apparatus in modern industrial systems, including low voltage electric machines. One of ...

Optimized Sealing Process and Real-Time Monitoring of Glass-to-Metal Seal Structures

Residual stress is an essential factor to keeping the hermeticity and robustness of a glass-to-metal seal structure. The purpose of this report is to demonstrate a novel protocol to characterize and measure residual stress in a glass-to-metal seal structure without destroying the insulation and hermeticity of sealing materials. In this research, a femto-laser inscribed fiber Bragg grating sensor is used. The glass-to-metal seal structure that is measured consists of a metal shell, sealing glass, and Kovar conductor. To make the measurements worthwhile, the specific heat treatment of metal-to-glass seal (MTGS) structure is explored to obtain the model with best hermeticity. Then, the FBG sensor is embedded into the path of sealing glass and becomes well-fused with the glass as the temperature cools to RT. The Bragg wavelength of FBG shifts with the residual stress generated in sealing the glass. To calculate the residual stress, the relationship between Bragg wavelength shift and strain is applied, and the finite element method is also used to make the results reliable. The online monitoring experiments of residual stress in sealing glass are carried out at different loads, such as high temperature and high pressure, to broaden functions of this protocol in harsh environments.

Key procedures to optimize the sealing process and achieve real-time monitoring of the metal-to-glass seal (MTGS) structure are described in detail. The embedded fiber Bragg grating (FBG) sensor is designed to achieve online monitoring of temperature and high-level residual stress in the MTGS with simultaneous environmental pressure monitoring.

Residual stress is an essential factor to keeping the hermeticity and robustness of a glass-to-metal seal structure. The purpose of this report is to ...

Production of a Strain-Measuring Device with an Improved 3D Printer

A traditional strain measurement sensor needs to be electrified and is susceptible to electromagnetic interference. In order to solve the fluctuations in the analog electrical signal in a traditional strain gauge operation, a new strain measurement method is presented here. It uses a photographic technique to display the strain change by amplifying the change of the pointer displacement of the mechanism. A visual polydimethylsiloxane (PDMS) lens with a focal length of 7.16 mm was added to a smartphone camera to generate a lens group acting as a microscope to capture images. It had an equivalent focal length of 5.74 mm. Acrylonitrile butadiene styrene (ABS) and nylon amplifiers were used to test the influence of different materials on the sensor performance. The production of the amplifiers and PDMS lens is based on improved 3D printing technology. The data obtained were compared with the results from finite element analysis (FEA) to verify their validity. The sensitivity of the ABS amplifier was 36.03 &plusmn; 1.34 &#181;&epsilon;/&#181;m, and the sensitivity of the nylon amplifier was 36.55 &plusmn; 0.53 &#181;&epsilon;/&#181;m.

This work presents a strain measurement sensor consisting of an amplification mechanism and a polydimethylsiloxane microscope manufactured using an improved 3D printer.

A traditional strain measurement sensor needs to be electrified and is susceptible to electromagnetic interference. In order to solve the fluctuations in ...

Optimizing Brillouin Optical Time-Domain Analyzers Based on Gain Spectrum Engineering

Demonstrated is a unique method for sensing performance enhancement in Brillouin optical time-domain analyzers (BOTDA). A Brillouin gain spectrum (BGS) is superimposed with two symmetric Brillouin loss spectra (BLS). This leads to a complex engineered spectrum shape that is more resistant to the sensing system noise. Instead of only one pump and probe interaction as in the conventional BOTDA setup, three optical probe waves are exploited, with one probe located in the BGS and the other two symmetrically in the BLS. Due to the resistance and insensitivity of the engineered spectrum shape to the noise, the sensing performance is enhanced by 60% and the measurand resolution is doubled.

A protocol for Brillouin optical time-domain analyzers based on gain spectrum engineering is presented. Enhancements in the sensing performance, including sensing range and measurand resolution are achieved and the excess Brillouin intensity noise is studied. The protocol introduces a new way to enhance distributed Brillouin sensing performance.

Demonstrated is a unique method for sensing performance enhancement in Brillouin optical time-domain analyzers (BOTDA). A Brillouin gain spectrum (BGS) is ...

A Micro-Displacement Measurement Based on the Shadow Technique

The precision measurement of micro displacement is important in scientific and industrial fields. However, it is a tough challenge due to the complex design and the high cost of measuring instruments. Inspired by the shadow formed from water striders walking on a water surface under sunlight, a micro-displacement measurement method was proposed. Water strider legs with superhydrophobic properties bend the water surface. The curved surface of the water refracts sunlight, creating a shadow with a bright edge at the bottom of the pond. The shadow size is generally larger than the indentation depth of the legs from the water surface. In the micro-displacement measurement system, the applied displacement is proportional to the change in the diameter of the shadow. The presented study proposes a micro-displacement measurement procedure based on this shadow technique. The displacement sensitivity can reach 10.0 nm/pixel in the range of 5 &#181;m. This system is simple to construct, low cost, and has high precision with good linear performance. The method provides a convenient additional option to measure micro-displacement.

High-precision micro-displacement measurement is significant in the field of aerospace engineering, ultra-precision machining, and micro-assembly. The present protocol describes measuring micro displacements based on the shadow technique.

The precision measurement of micro displacement is important in scientific and industrial fields. However, it is a tough challenge due to the complex ...

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

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