552 lines
17 KiB
HTML
552 lines
17 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="en">
|
||
<head>
|
||
<meta charset="utf-8">
|
||
<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
|
||
<title>Position Sensors - My digital brain</title>
|
||
<meta name="renderer" content="webkit" />
|
||
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"/>
|
||
|
||
<meta http-equiv="Cache-Control" content="no-transform" />
|
||
<meta http-equiv="Cache-Control" content="no-siteapp" />
|
||
|
||
<meta name="theme-color" content="#f8f5ec" />
|
||
<meta name="msapplication-navbutton-color" content="#f8f5ec">
|
||
<meta name="apple-mobile-web-app-capable" content="yes">
|
||
<meta name="apple-mobile-web-app-status-bar-style" content="#f8f5ec">
|
||
|
||
|
||
<meta name="author" content="
|
||
|
||
|
||
—
|
||
|
||
Thomas Dehaeze
|
||
|
||
|
||
|
||
" /><meta name="description" content="Tags Inertial Sensors Reviews of position sensors (Collette {\it et al.}, 2012) Fleming, A. J., A review of nanometer resolution position sensors: operation and performance (Andrew Fleming, 2013) (Notes) Relative Position Sensors
|
||
Table 1: Characteristics of relative measurement sensors collette11_review Technology Frequency Resolution Range T Range LVDT DC-200 Hz 10 nm rms 1-10 mm -50,100 °C Eddy current 5 kHz 0." />
|
||
<link rel="canonical" href="/zettels/position_sensors/" />
|
||
<link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png">
|
||
<link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png">
|
||
|
||
|
||
|
||
<link href="/sass/main.min.47a894bd6354cc46903f62433747958dc936e1c95c28a76ac80319bca9708ed1.css" rel="stylesheet">
|
||
|
||
|
||
|
||
|
||
</head>
|
||
<body>
|
||
<div id="mobile-navbar" class="mobile-navbar">
|
||
<div class="mobile-header-logo">
|
||
<a href="/" class="logo">Digital Brain</a>
|
||
</div>
|
||
<div class="mobile-navbar-icon">
|
||
<span></span>
|
||
<span></span>
|
||
<span></span>
|
||
</div>
|
||
</div>
|
||
<nav id="mobile-menu" class="mobile-menu slideout-menu">
|
||
<ul class="mobile-menu-list">
|
||
<a href="/">
|
||
<li class="mobile-menu-item">Home</li>
|
||
</a><a href="/zettels/">
|
||
<li class="mobile-menu-item">Zettels</li>
|
||
</a><a href="/book/">
|
||
<li class="mobile-menu-item">Books</li>
|
||
</a><a href="/paper/">
|
||
<li class="mobile-menu-item">Papers</li>
|
||
</a><a href="/search/">
|
||
<li class="mobile-menu-item">Search</li>
|
||
</a>
|
||
</ul>
|
||
</nav>
|
||
<div class="container" id="mobile-panel">
|
||
<header id="header" class="header">
|
||
<div class="logo-wrapper">
|
||
<a href="/" class="logo">Digital Brain</a>
|
||
</div>
|
||
|
||
<nav class="site-navbar">
|
||
<ul id="menu" class="menu">
|
||
<li class="menu-item">
|
||
<a class="menu-item-link" href="/">Home</a>
|
||
</li><li class="menu-item">
|
||
<a class="menu-item-link" href="/zettels/">Zettels</a>
|
||
</li><li class="menu-item">
|
||
<a class="menu-item-link" href="/book/">Books</a>
|
||
</li><li class="menu-item">
|
||
<a class="menu-item-link" href="/paper/">Papers</a>
|
||
</li><li class="menu-item">
|
||
<a class="menu-item-link" href="/search/">Search</a>
|
||
</li>
|
||
</ul>
|
||
</nav>
|
||
|
||
</header>
|
||
|
||
<main id="main" class="main">
|
||
<div class="content-wrapper">
|
||
<div id="content" class="content">
|
||
<article class="post">
|
||
|
||
<header class="post-header">
|
||
<h1 class="post-title">Position Sensors</h1>
|
||
</header>
|
||
|
||
<div class="post-toc" id="post-toc">
|
||
<h2 class="post-toc-title">Contents</h2>
|
||
<div class="post-toc-content">
|
||
<nav id="TableOfContents">
|
||
<ul>
|
||
<li><a href="#reviews-of-position-sensors">Reviews of position sensors</a></li>
|
||
<li><a href="#relative-position-sensors">Relative Position Sensors</a>
|
||
<ul>
|
||
<li><a href="#strain-gauge">Strain Gauge</a></li>
|
||
<li><a href="#capacitive-sensor">Capacitive Sensor</a></li>
|
||
<li><a href="#inductive-sensor--eddy-current">Inductive Sensor (Eddy Current)</a></li>
|
||
<li><a href="#inductive-sensor--lvdt">Inductive Sensor (LVDT)</a></li>
|
||
<li><a href="#interferometers">Interferometers</a></li>
|
||
<li><a href="#fiber-optic-displacement-sensor">Fiber Optic Displacement Sensor</a></li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
|
||
<ul>
|
||
<li><a href="#backlinks">Backlinks</a></li>
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
<div class="post-content">
|
||
<dl>
|
||
<dt>Tags</dt>
|
||
<dd><a href="/zettels/inertial_sensors/">Inertial Sensors</a></dd>
|
||
</dl>
|
||
<h2 id="reviews-of-position-sensors">Reviews of position sensors</h2>
|
||
<ul>
|
||
<li><sup id="0b0b67de6dddc4d28031ab2d3b28cd3d"><a href="#collette12_compar" title="Collette, Janssens, Mokrani, Fueyo-Roza, L, Artoos, Esposito, Fernandez-Carmona, , Guinchard \& Leuxe, Comparison of new absolute displacement sensors, in in: {International Conference on Noise and Vibration Engineering
|
||
(ISMA)}, edited by (2012)">(Collette {\it et al.}, 2012)</a></sup></li>
|
||
<li>Fleming, A. J., A review of nanometer resolution position sensors: operation and performance <sup id="3fb5b61524290e36d639a4fac65703d0"><a href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors: Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup> (<a href="/paper/fleming13_review_nanom_resol_posit_sensor/">Notes</a>)</li>
|
||
</ul>
|
||
<h2 id="relative-position-sensors">Relative Position Sensors</h2>
|
||
<p><a id="table--tab:characteristics-relative-sensor"></a></p>
|
||
<div class="table-caption">
|
||
<span class="table-number"><a href="#table--tab:characteristics-relative-sensor">Table 1</a></span>:
|
||
Characteristics of relative measurement sensors <a class='org-ref-reference' href="#collette11_review">collette11_review</a>
|
||
</div>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Technology</th>
|
||
<th>Frequency</th>
|
||
<th>Resolution</th>
|
||
<th>Range</th>
|
||
<th>T Range</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>LVDT</td>
|
||
<td>DC-200 Hz</td>
|
||
<td>10 nm rms</td>
|
||
<td>1-10 mm</td>
|
||
<td>-50,100 °C</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Eddy current</td>
|
||
<td>5 kHz</td>
|
||
<td>0.1-100 nm rms</td>
|
||
<td>0.5-55 mm</td>
|
||
<td>-50,100 °C</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Capacitive</td>
|
||
<td>DC-100 kHz</td>
|
||
<td>0.05-50 nm rms</td>
|
||
<td>50 nm - 1 cm</td>
|
||
<td>-40,100 °C</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Interferometer</td>
|
||
<td>300 kHz</td>
|
||
<td>0.1 nm rms</td>
|
||
<td>10 cm</td>
|
||
<td>-250,100 °C</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Encoder</td>
|
||
<td>DC-1 MHz</td>
|
||
<td>1 nm rms</td>
|
||
<td>7-27 mm</td>
|
||
<td>0,40 °C</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Bragg Fibers</td>
|
||
<td>DC-150 Hz</td>
|
||
<td>0.3 nm rms</td>
|
||
<td>3.5 cm</td>
|
||
<td>-30,80 °C</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><a id="table--tab:summary-position-sensors"></a></p>
|
||
<div class="table-caption">
|
||
<span class="table-number"><a href="#table--tab:summary-position-sensors">Table 2</a></span>:
|
||
Summary of position sensor characteristics. The dynamic range (DNR) and resolution are approximations based on a full-scale range of \(100 \mu m\) and a first order bandwidth of \(1 kHz\) <a class='org-ref-reference' href="#fleming13_review_nanom_resol_posit_sensor">fleming13_review_nanom_resol_posit_sensor</a>
|
||
</div>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Sensor Type</th>
|
||
<th>Range</th>
|
||
<th>DNR</th>
|
||
<th>Resolution</th>
|
||
<th>Max. BW</th>
|
||
<th>Accuracy</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Metal foil</td>
|
||
<td>\(10-500 \mu m\)</td>
|
||
<td>230 ppm</td>
|
||
<td>23 nm</td>
|
||
<td>1-10 kHz</td>
|
||
<td>1% FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Piezoresistive</td>
|
||
<td>\(1-500 \mu m\)</td>
|
||
<td>5 ppm</td>
|
||
<td>0.5 nm</td>
|
||
<td>>100 kHz</td>
|
||
<td>1% FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Capacitive</td>
|
||
<td>\(10 \mu m\) to \(10 mm\)</td>
|
||
<td>24 ppm</td>
|
||
<td>2.4 nm</td>
|
||
<td>100 kHz</td>
|
||
<td>0.1% FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Electrothermal</td>
|
||
<td>\(10 \mu m\) to \(1 mm\)</td>
|
||
<td>100 ppm</td>
|
||
<td>10 nm</td>
|
||
<td>10 kHz</td>
|
||
<td>1% FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Eddy current</td>
|
||
<td>\(100 \mu m\) to \(80 mm\)</td>
|
||
<td>10 ppm</td>
|
||
<td>1 nm</td>
|
||
<td>40 kHz</td>
|
||
<td>0.1% FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>LVDT</td>
|
||
<td>\(0.5-500 mm\)</td>
|
||
<td>10 ppm</td>
|
||
<td>5 nm</td>
|
||
<td>1 kHz</td>
|
||
<td>0.25% FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Interferometer</td>
|
||
<td>Meters</td>
|
||
<td></td>
|
||
<td>0.5 nm</td>
|
||
<td>>100kHz</td>
|
||
<td>1 ppm FSR</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Encoder</td>
|
||
<td>Meters</td>
|
||
<td></td>
|
||
<td>6 nm</td>
|
||
<td>>100kHz</td>
|
||
<td>5 ppm FSR</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h3 id="strain-gauge">Strain Gauge</h3>
|
||
<h3 id="capacitive-sensor">Capacitive Sensor</h3>
|
||
<p>Description:</p>
|
||
<ul>
|
||
<li><a href="http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html">http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html</a></li>
|
||
<li><a href="https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors">https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors</a></li>
|
||
</ul>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Micro Sense</td>
|
||
<td><a href="http://www.microsense.net/products-position-sensors.htm">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Micro-Epsilon</td>
|
||
<td><a href="https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>PI</td>
|
||
<td><a href="https://www.physikinstrumente.com/en/technology/sensor-technologies/capacitive-sensors/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Unipulse</td>
|
||
<td><a href="https://www.unipulse.com/product/ps-ia/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Lion-Precision</td>
|
||
<td><a href="https://www.lionprecision.com/products/capacitive-sensors">link</a></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h3 id="inductive-sensor--eddy-current">Inductive Sensor (Eddy Current)</h3>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Micro-Epsilon</td>
|
||
<td><a href="https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Lion Precision</td>
|
||
<td><a href="https://www.lionprecision.com/products/eddy-current-sensors">link</a></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h3 id="inductive-sensor--lvdt">Inductive Sensor (LVDT)</h3>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Micro-Epsilon</td>
|
||
<td><a href="https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Keyence</td>
|
||
<td><a href="https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp">link</a></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h3 id="interferometers">Interferometers</h3>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Attocube</td>
|
||
<td><a href="http://www.attocube.com/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Zygo</td>
|
||
<td><a href="https://www.zygo.com/?/met/markets/stageposition/zmi/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Smaract</td>
|
||
<td><a href="https://www.smaract.com/interferometry">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Qutools</td>
|
||
<td><a href="https://www.qutools.com/qudis/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Renishaw</td>
|
||
<td><a href="https://www.renishaw.com/en/fibre-optic-laser-encoder-products--6594">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Sios</td>
|
||
<td><a href="https://sios-de.com/products/length-measurement/laser-interferometer/">link</a></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Keysight</td>
|
||
<td><a href="https://www.keysight.com/en/pc-1000000393%3Aepsg%3Apgr/laser-heads?nid=-536900395.0&cc=FR&lc=fre">link</a></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<div class="table-caption">
|
||
<span class="table-number">Table 3</span>:
|
||
Characteristics of Environmental Units
|
||
</div>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th>Temperature (\(\pm\ ^oC\))</th>
|
||
<th>Pressure (\(\pm\ hPa\))</th>
|
||
<th>Humidity \(\pm\% RH\)</th>
|
||
<th>Wavelength Accuracy (\(\pm\ \text{ppm}\))</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Attocube</td>
|
||
<td>0.1</td>
|
||
<td>1</td>
|
||
<td>2</td>
|
||
<td>0.5</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Renishaw</td>
|
||
<td>0.2</td>
|
||
<td>1</td>
|
||
<td>6</td>
|
||
<td>1</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Picoscale</td>
|
||
<td>0.2</td>
|
||
<td>2</td>
|
||
<td>2</td>
|
||
<td>1</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><sup id="7658b1219a4458a62ae8c6f51b767542"><a href="#jang17_compen_refrac_index_air_laser" title="Yoon-Soo Jang \& Seung-Woo Kim, Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: a Review, {International Journal of Precision Engineering and
|
||
Manufacturing}, v(12), 1881-1890 (2017).">(Yoon-Soo Jang & Seung-Woo Kim, 2017)</a></sup></p>
|
||
<p><a id="orge1e204f"></a></p>
|
||
<figure>
|
||
<img src="/ox-hugo/position_sensor_interferometer_precision.png"
|
||
alt="Figure 1: Expected precision of interferometer as a function of measured distance"/> <figcaption>
|
||
<p>Figure 1: Expected precision of interferometer as a function of measured distance</p>
|
||
</figcaption>
|
||
</figure>
|
||
|
||
<h3 id="fiber-optic-displacement-sensor">Fiber Optic Displacement Sensor</h3>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>Unipulse</td>
|
||
<td><a href="https://www.unipulse.com/product/atw200-2/">link</a></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h1 id="bibliography">Bibliography</h1>
|
||
<p><a id="collette12_compar"></a>Collette, C., Janssens, S., Mokrani, B., Fueyo-Roza, L., Artoos, K., Esposito, M., Fernandez-Carmona, P., …, <em>Comparison of new absolute displacement sensors</em>, In , International Conference on Noise and Vibration Engineering (ISMA) (pp. ) (2012). : . <a href="#0b0b67de6dddc4d28031ab2d3b28cd3d">↩</a></p>
|
||
<p><a id="fleming13_review_nanom_resol_posit_sensor"></a>Fleming, A. J., <em>A review of nanometer resolution position sensors: operation and performance</em>, Sensors and Actuators A: Physical, <em>190(nil)</em>, 106–126 (2013). <a href="http://dx.doi.org/10.1016/j.sna.2012.10.016">http://dx.doi.org/10.1016/j.sna.2012.10.016</a> <a href="#3fb5b61524290e36d639a4fac65703d0">↩</a></p>
|
||
<p><a id="collette11_review"></a>Collette, C., Artoos, K., Guinchard, M., Janssens, S., Carmona Fernandez, P., & Hauviller, C., <em>Review of sensors for low frequency seismic vibration measurement</em> (2011). <a href="#642a18d86de4e062c6afb0f5f20501c4">↩</a></p>
|
||
<p><a id="jang17_compen_refrac_index_air_laser"></a>Jang, Y., & Kim, S., <em>Compensation of the refractive index of air in laser interferometer for distance measurement: a review</em>, International Journal of Precision Engineering and Manufacturing, <em>18(12)</em>, 1881–1890 (2017). <a href="http://dx.doi.org/10.1007/s12541-017-0217-y">http://dx.doi.org/10.1007/s12541-017-0217-y</a> <a href="#7658b1219a4458a62ae8c6f51b767542">↩</a></p>
|
||
<h2 id="backlinks">Backlinks</h2>
|
||
<ul>
|
||
<li><a href="/paper/gao15_measur_techn_precis_posit/">Measurement technologies for precision positioning</a></li>
|
||
<li><a href="/paper/fleming13_review_nanom_resol_posit_sensor/">A review of nanometer resolution position sensors: operation and performance</a></li>
|
||
</ul>
|
||
|
||
</div>
|
||
|
||
<footer class="post-footer">
|
||
|
||
<nav class="post-nav">
|
||
<a class="prev" href="/zettels/nano_active_stabilization_system/">
|
||
<i class="iconfont icon-left"></i>
|
||
<span class="prev-text nav-default">Nano Active Stabilization System</span>
|
||
<span class="prev-text nav-mobile">Prev</span>
|
||
</a>
|
||
<a class="next" href="/zettels/positioning_stations/">
|
||
<span class="next-text nav-default">Positioning Stations</span>
|
||
<span class="next-text nav-mobile">Next</span>
|
||
<i class="iconfont icon-right"></i>
|
||
</a>
|
||
</nav>
|
||
</footer>
|
||
</article>
|
||
</div>
|
||
</div>
|
||
</main>
|
||
|
||
<footer id="footer" class="footer">
|
||
<div class="social-links">
|
||
<a href="mailto:dehaeze.thomas@gmail.com" class="iconfont icon-email" title="email"></a>
|
||
<a href="https://github.com/tdehaeze/" class="iconfont icon-github" title="github"></a>
|
||
<a href="/index.xml" type="application/rss+xml" class="iconfont icon-rss" title="rss"></a>
|
||
</div>
|
||
|
||
<div class="copyright">
|
||
<span class="power-by">
|
||
Powered by <a class="hexo-link" href="https://gohugo.io">Hugo</a>
|
||
</span>
|
||
|
||
<span class="copyright-year">
|
||
©
|
||
2020
|
||
<span class="heart">
|
||
<i class="iconfont icon-heart"></i>
|
||
</span>
|
||
<span class="author">Thomas Dehaeze</span>
|
||
</span>
|
||
</div>
|
||
|
||
</footer>
|
||
|
||
<div class="back-to-top" id="back-to-top">
|
||
<i class="iconfont icon-up"></i>
|
||
</div>
|
||
</div>
|
||
|
||
<script src="https://cdn.jsdelivr.net/npm/jquery@3.2.1/dist/jquery.min.js" integrity="sha256-hwg4gsxgFZhOsEEamdOYGBf13FyQuiTwlAQgxVSNgt4=" crossorigin="anonymous"></script>
|
||
<script src="https://cdn.jsdelivr.net/npm/slideout@1.0.1/dist/slideout.min.js" integrity="sha256-t+zJ/g8/KXIJMjSVQdnibt4dlaDxc9zXr/9oNPeWqdg=" crossorigin="anonymous"></script>
|
||
|
||
|
||
<script type="text/javascript" src="/js/main.4bada4f824623eea2eb7cfd5cf8c1d99c3dd797297e7e8cbc59a41da450bb334.js"></script>
|
||
|
||
|
||
<script type="text/javascript">
|
||
window.MathJax = {
|
||
loader: {
|
||
load: ['[tex]/ams']
|
||
},
|
||
tex: {
|
||
inlineMath: [
|
||
['$','$'], ['\\(','\\)']
|
||
],
|
||
tags: 'ams',
|
||
packages: {'[+]': ['ams']},
|
||
}
|
||
};
|
||
</script>
|
||
|
||
<script async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" crossorigin="anonymous"></script>
|
||
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/3.2.0/fuse.min.js"></script>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/jquery.mark.min.js"></script>
|
||
<script type="text/javascript" src="/lib/search/search.js"></script>
|
||
|
||
|
||
|
||
|
||
</body>
|
||
</html>
|