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short-stroke-metrology.html
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short-stroke-metrology.html
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-02-19 ven. 11:10 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>NASS - Short Stroke Metrology</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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tex: {
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">NASS - Short Stroke Metrology</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orge8c6134">1. Measurement Principle</a></li>
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<li><a href="#org4742c55">2. X-Y-Z measurement</a></li>
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<li><a href="#org0ca496a">3. Tilt measurement</a></li>
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<li><a href="#org4a349c9">4. Conclusion</a></li>
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</ul>
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</div>
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</div>
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<p>
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The goal of this document is to analyze the feasibility of a short stroke metrology system for the NASS using fixed interferemoter and the same reflector as for the long stroke metrology system.
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</p>
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<p>
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It is structured as follow:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#orgcce215b">1</a>: the meaurement principle is described.</li>
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<li>Section <a href="#org7f61293">2</a>: the requirements for the interferometers measuring translations are described</li>
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<li>Section <a href="#orgd21778d">3</a>: the same is done for the rotations</li>
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</ul>
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<div id="outline-container-orge8c6134" class="outline-2">
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<h2 id="orge8c6134"><span class="section-number-2">1</span> Measurement Principle</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orgcce215b"></a>
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</p>
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<p>
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Here are the defined wanted displacement of the reflector that should be inside the measurement stroke of the metrology system.
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The defined translations and rotations are defined with respect to the frame shown in Figure <a href="#org26e55bb">1</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">d_x = 0; <span class="org-comment">% Wanted translation of the reflector in the x direction [m]</span>
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d_y = 1e<span class="org-type">-</span>3; <span class="org-comment">% Wanted translation of the reflector in the y direction [m]</span>
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d_z = 1e<span class="org-type">-</span>3; <span class="org-comment">% Wanted translation of the reflector in the z direction [m]</span>
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R_x = 10e<span class="org-type">-</span>3; <span class="org-comment">% Wanted rotation of the reflector along the x axis [rad]</span>
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R_y = 0; <span class="org-comment">% Wanted rotation of the reflector along the y axis [rad]</span>
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</pre>
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</div>
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<div id="org26e55bb" class="figure">
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<p><img src="figs/short_stroke_metrology_concept.png" alt="short_stroke_metrology_concept.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Short Stroke Metrology - Concept. Blue interferometers are used to measure the X-Y-Z motion of the reflector. Red interferometers are used to measure tilt motion of the reflector.</p>
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</div>
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<p>
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Here are the approximate dimensions shown in Figure <a href="#org26e55bb">1</a>:
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</p>
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<ul class="org-ul">
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<li>\(d_0 \approx 10\,[mm]\)</li>
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<li>\(L \approx 150\,[mm]\)</li>
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<li>\(R \approx 250\,[mm]\)</li>
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</ul>
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<div class="org-src-container">
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<pre class="src src-matlab">d0 = 10e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
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L = 150e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
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R = 250e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org4742c55" class="outline-2">
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<h2 id="org4742c55"><span class="section-number-2">2</span> X-Y-Z measurement</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org7f61293"></a>
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</p>
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<p>
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The geometry for the interferometers measuring translations is shown in Figure <a href="#org98aebff">2</a>:
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</p>
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<ul class="org-ul">
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<li>\(R = 250\,[mm]\)</li>
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<li>\(d_0 > 10\,[mm]\)</li>
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<li>\(d_x = \pm 1\,[mm]\)</li>
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<li>\(d_y = \pm 1\,[mm]\)</li>
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</ul>
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<div id="org98aebff" class="figure">
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<p><img src="figs/translation_interferometers.png" alt="translation_interferometers.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Interferometers that are measuring translation</p>
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</div>
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<p>
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The angle of the reflected beam is approximately equal to:
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</p>
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\begin{equation}
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\theta \approx 2 \frac{d_y}{R}
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\end{equation}
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<p>
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And we obtain:
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</p>
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<p>
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\[ \theta \approx 8.0\,[mrad] \]
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</p>
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<table id="org7dbf661" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Specifications for the translation interferometers</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left">Specification</th>
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<th scope="col" class="org-left">Value</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Axial Acceptance</td>
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<td class="org-left">\(\pm 1\,[mm]\)</td>
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</tr>
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<tr>
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<td class="org-left">Angular Acceptance</td>
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<td class="org-left">\(\pm 8\,[mrad]\)</td>
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</tr>
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<tr>
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<td class="org-left">Distance to target</td>
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<td class="org-left">\(10\,[mm]\)</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org0ca496a" class="outline-2">
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<h2 id="org0ca496a"><span class="section-number-2">3</span> Tilt measurement</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="orgd21778d"></a>
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</p>
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<p>
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The tilt \(\theta\) of the flat mirror is directly equal to the tilt of the reflector.
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However, the \(z\) displacement on the flat part is equal to:
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</p>
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\begin{equation}
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z \approx d_z + L \theta_y
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\end{equation}
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<p>
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And we obtain:
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</p>
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<p>
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\[ z \approx 2.5\,[mm] \]
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</p>
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<p>
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The geometry for the interferometers measuring rotations is shown in Figure <a href="#orgb2621f2">3</a>:
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</p>
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<ul class="org-ul">
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<li>\(d_0 > 10\,[mm]\)</li>
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<li>\(\theta = \pm 10\,[mrad]\)</li>
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<li>\(z = \pm 2.5\, [mm]\)</li>
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</ul>
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<div id="orgb2621f2" class="figure">
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<p><img src="figs/rotation_interferometers.png" alt="rotation_interferometers.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Interferometers that are measuring tilt</p>
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</div>
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<table id="org53ac3fe" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Specifications for the rotation interferometers</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left">Specification</th>
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<th scope="col" class="org-left">Value</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Axial Acceptance</td>
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<td class="org-left">\(\pm 2.5\,[mm]\)</td>
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</tr>
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<tr>
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<td class="org-left">Angular Acceptance</td>
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<td class="org-left">\(\pm 10\,[mrad]\)</td>
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</tr>
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<tr>
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<td class="org-left">Distance to target</td>
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<td class="org-left">\(10\,[mm]\)</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org4a349c9" class="outline-2">
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<h2 id="org4a349c9"><span class="section-number-2">4</span> Conclusion</h2>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2021-02-19 ven. 11:10</p>
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</div>
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</body>
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