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.gitignore
vendored
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.gitignore
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auto/
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*.tex
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*.bbl
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*.synctex.gz
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.auctex-auto/
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_minted*
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# Emacs
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auto/
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||||||
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# Simulink Real Time
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*bio.m
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*pt.m
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*ref.m
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*ri.m
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*xcp.m
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*.mldatx
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*.slxc
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*.xml
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*_slrt_rtw/
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# data
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data/
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# Windows default autosave extension
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*.asv
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# OSX / *nix default autosave extension
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*.m~
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# Compiled MEX binaries (all platforms)
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*.mex*
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||||||
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||||||
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# Packaged app and toolbox files
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||||||
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*.mlappinstall
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*.mltbx
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||||||
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# Generated helpsearch folders
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helpsearch*/
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||||||
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# Simulink code generation folders
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||||||
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slprj/
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||||||
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sccprj/
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||||||
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||||||
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# Matlab code generation folders
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||||||
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codegen/
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||||||
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||||||
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# Simulink autosave extension
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||||||
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*.autosave
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# Octave session info
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||||||
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octave-workspace
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figs/rotation_interferometers.pdf
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figs/rotation_interferometers.pdf
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figs/rotation_interferometers.png
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figs/rotation_interferometers.png
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figs/rotation_interferometers.svg
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figs/rotation_interferometers.svg
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<title>NASS - Short Stroke Metrology</title>
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|
<a accesskey="h" href="../index.html"> UP </a>
|
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|
|
|
||||||
|
<a accesskey="H" href="../index.html"> HOME </a>
|
||||||
|
</div><div id="content">
|
||||||
|
<h1 class="title">NASS - Short Stroke Metrology</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orge8c6134">1. Measurement Principle</a></li>
|
||||||
|
<li><a href="#org4742c55">2. X-Y-Z measurement</a></li>
|
||||||
|
<li><a href="#org0ca496a">3. Tilt measurement</a></li>
|
||||||
|
<li><a href="#org4a349c9">4. Conclusion</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
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.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
It is structured as follow:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>Section <a href="#orgcce215b">1</a>: the meaurement principle is described.</li>
|
||||||
|
<li>Section <a href="#org7f61293">2</a>: the requirements for the interferometers measuring translations are described</li>
|
||||||
|
<li>Section <a href="#orgd21778d">3</a>: the same is done for the rotations</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="outline-container-orge8c6134" class="outline-2">
|
||||||
|
<h2 id="orge8c6134"><span class="section-number-2">1</span> Measurement Principle</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<p>
|
||||||
|
<a id="orgcce215b"></a>
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Here are the defined wanted displacement of the reflector that should be inside the measurement stroke of the metrology system.
|
||||||
|
The defined translations and rotations are defined with respect to the frame shown in Figure <a href="#org26e55bb">1</a>.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">d_x = 0; <span class="org-comment">% Wanted translation of the reflector in the x direction [m]</span>
|
||||||
|
d_y = 1e<span class="org-type">-</span>3; <span class="org-comment">% Wanted translation of the reflector in the y direction [m]</span>
|
||||||
|
d_z = 1e<span class="org-type">-</span>3; <span class="org-comment">% Wanted translation of the reflector in the z direction [m]</span>
|
||||||
|
R_x = 10e<span class="org-type">-</span>3; <span class="org-comment">% Wanted rotation of the reflector along the x axis [rad]</span>
|
||||||
|
R_y = 0; <span class="org-comment">% Wanted rotation of the reflector along the y axis [rad]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org26e55bb" class="figure">
|
||||||
|
<p><img src="figs/short_stroke_metrology_concept.png" alt="short_stroke_metrology_concept.png" />
|
||||||
|
</p>
|
||||||
|
<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>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Here are the approximate dimensions shown in Figure <a href="#org26e55bb">1</a>:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>\(d_0 \approx 10\,[mm]\)</li>
|
||||||
|
<li>\(L \approx 150\,[mm]\)</li>
|
||||||
|
<li>\(R \approx 250\,[mm]\)</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">d0 = 10e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
|
||||||
|
L = 150e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
|
||||||
|
R = 250e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4742c55" class="outline-2">
|
||||||
|
<h2 id="org4742c55"><span class="section-number-2">2</span> X-Y-Z measurement</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<p>
|
||||||
|
<a id="org7f61293"></a>
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The geometry for the interferometers measuring translations is shown in Figure <a href="#org98aebff">2</a>:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>\(R = 250\,[mm]\)</li>
|
||||||
|
<li>\(d_0 > 10\,[mm]\)</li>
|
||||||
|
<li>\(d_x = \pm 1\,[mm]\)</li>
|
||||||
|
<li>\(d_y = \pm 1\,[mm]\)</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org98aebff" class="figure">
|
||||||
|
<p><img src="figs/translation_interferometers.png" alt="translation_interferometers.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 2: </span>Interferometers that are measuring translation</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The angle of the reflected beam is approximately equal to:
|
||||||
|
</p>
|
||||||
|
\begin{equation}
|
||||||
|
\theta \approx 2 \frac{d_y}{R}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we obtain:
|
||||||
|
</p>
|
||||||
|
<p>
|
||||||
|
\[ \theta \approx 8.0\,[mrad] \]
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<table id="org7dbf661" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||||
|
<caption class="t-above"><span class="table-number">Table 1:</span> Specifications for the translation interferometers</caption>
|
||||||
|
|
||||||
|
<colgroup>
|
||||||
|
<col class="org-left" />
|
||||||
|
|
||||||
|
<col class="org-left" />
|
||||||
|
</colgroup>
|
||||||
|
<thead>
|
||||||
|
<tr>
|
||||||
|
<th scope="col" class="org-left">Specification</th>
|
||||||
|
<th scope="col" class="org-left">Value</th>
|
||||||
|
</tr>
|
||||||
|
</thead>
|
||||||
|
<tbody>
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Axial Acceptance</td>
|
||||||
|
<td class="org-left">\(\pm 1\,[mm]\)</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Angular Acceptance</td>
|
||||||
|
<td class="org-left">\(\pm 8\,[mrad]\)</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Distance to target</td>
|
||||||
|
<td class="org-left">\(10\,[mm]\)</td>
|
||||||
|
</tr>
|
||||||
|
</tbody>
|
||||||
|
</table>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org0ca496a" class="outline-2">
|
||||||
|
<h2 id="org0ca496a"><span class="section-number-2">3</span> Tilt measurement</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<p>
|
||||||
|
<a id="orgd21778d"></a>
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The tilt \(\theta\) of the flat mirror is directly equal to the tilt of the reflector.
|
||||||
|
However, the \(z\) displacement on the flat part is equal to:
|
||||||
|
</p>
|
||||||
|
\begin{equation}
|
||||||
|
z \approx d_z + L \theta_y
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we obtain:
|
||||||
|
</p>
|
||||||
|
<p>
|
||||||
|
\[ z \approx 2.5\,[mm] \]
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The geometry for the interferometers measuring rotations is shown in Figure <a href="#orgb2621f2">3</a>:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>\(d_0 > 10\,[mm]\)</li>
|
||||||
|
<li>\(\theta = \pm 10\,[mrad]\)</li>
|
||||||
|
<li>\(z = \pm 2.5\, [mm]\)</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgb2621f2" class="figure">
|
||||||
|
<p><img src="figs/rotation_interferometers.png" alt="rotation_interferometers.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 3: </span>Interferometers that are measuring tilt</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<table id="org53ac3fe" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||||
|
<caption class="t-above"><span class="table-number">Table 2:</span> Specifications for the rotation interferometers</caption>
|
||||||
|
|
||||||
|
<colgroup>
|
||||||
|
<col class="org-left" />
|
||||||
|
|
||||||
|
<col class="org-left" />
|
||||||
|
</colgroup>
|
||||||
|
<thead>
|
||||||
|
<tr>
|
||||||
|
<th scope="col" class="org-left">Specification</th>
|
||||||
|
<th scope="col" class="org-left">Value</th>
|
||||||
|
</tr>
|
||||||
|
</thead>
|
||||||
|
<tbody>
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Axial Acceptance</td>
|
||||||
|
<td class="org-left">\(\pm 2.5\,[mm]\)</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Angular Acceptance</td>
|
||||||
|
<td class="org-left">\(\pm 10\,[mrad]\)</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Distance to target</td>
|
||||||
|
<td class="org-left">\(10\,[mm]\)</td>
|
||||||
|
</tr>
|
||||||
|
</tbody>
|
||||||
|
</table>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4a349c9" class="outline-2">
|
||||||
|
<h2 id="org4a349c9"><span class="section-number-2">4</span> Conclusion</h2>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
|
<p class="date">Created: 2021-02-19 ven. 11:10</p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
163
short-stroke-metrology.org
Normal file
163
short-stroke-metrology.org
Normal file
@ -0,0 +1,163 @@
|
|||||||
|
#+TITLE: NASS - Short Stroke Metrology
|
||||||
|
:DRAWER:
|
||||||
|
#+LANGUAGE: en
|
||||||
|
#+EMAIL: dehaeze.thomas@gmail.com
|
||||||
|
#+AUTHOR: Dehaeze Thomas
|
||||||
|
|
||||||
|
#+HTML_LINK_HOME: ../index.html
|
||||||
|
#+HTML_LINK_UP: ../index.html
|
||||||
|
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||||||
|
|
||||||
|
#+BIND: org-latex-image-default-option "scale=1"
|
||||||
|
#+BIND: org-latex-image-default-width ""
|
||||||
|
|
||||||
|
#+LaTeX_CLASS: scrreprt
|
||||||
|
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
|
||||||
|
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
|
||||||
|
|
||||||
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||||
|
#+PROPERTY: header-args:matlab+ :comments org
|
||||||
|
#+PROPERTY: header-args:matlab+ :exports both
|
||||||
|
#+PROPERTY: header-args:matlab+ :results none
|
||||||
|
#+PROPERTY: header-args:matlab+ :eval no-export
|
||||||
|
#+PROPERTY: header-args:matlab+ :noweb yes
|
||||||
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||||||
|
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||||
|
|
||||||
|
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
|
||||||
|
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||||||
|
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
||||||
|
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
||||||
|
#+PROPERTY: header-args:latex+ :results file raw replace
|
||||||
|
#+PROPERTY: header-args:latex+ :buffer no
|
||||||
|
#+PROPERTY: header-args:latex+ :tangle no
|
||||||
|
#+PROPERTY: header-args:latex+ :eval no-export
|
||||||
|
#+PROPERTY: header-args:latex+ :exports results
|
||||||
|
#+PROPERTY: header-args:latex+ :mkdirp yes
|
||||||
|
#+PROPERTY: header-args:latex+ :output-dir figs
|
||||||
|
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
|
||||||
|
:END:
|
||||||
|
|
||||||
|
* Introduction :ignore:
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
It is structured as follow:
|
||||||
|
- Section [[sec:meas_principle]]: the meaurement principle is described.
|
||||||
|
- Section [[sec:translation_interferometers]]: the requirements for the interferometers measuring translations are described
|
||||||
|
- Section [[sec:rotation_interferometers]]: the same is done for the rotations
|
||||||
|
|
||||||
|
|
||||||
|
* Matlab Init :noexport:ignore:
|
||||||
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
|
<<matlab-dir>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
|
<<matlab-init>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Measurement Principle
|
||||||
|
<<sec:meas_principle>>
|
||||||
|
|
||||||
|
Here are the defined wanted displacement of the reflector that should be inside the measurement stroke of the metrology system.
|
||||||
|
The defined translations and rotations are defined with respect to the frame shown in Figure [[fig:short_stroke_metrology_concept]].
|
||||||
|
#+begin_src matlab
|
||||||
|
d_x = 0; % Wanted translation of the reflector in the x direction [m]
|
||||||
|
d_y = 1e-3; % Wanted translation of the reflector in the y direction [m]
|
||||||
|
d_z = 1e-3; % Wanted translation of the reflector in the z direction [m]
|
||||||
|
R_x = 10e-3; % Wanted rotation of the reflector along the x axis [rad]
|
||||||
|
R_y = 0; % Wanted rotation of the reflector along the y axis [rad]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:short_stroke_metrology_concept
|
||||||
|
#+caption: 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.
|
||||||
|
#+attr_latex: :width \linewidth
|
||||||
|
[[file:figs/short_stroke_metrology_concept.png]]
|
||||||
|
|
||||||
|
Here are the approximate dimensions shown in Figure [[fig:short_stroke_metrology_concept]]:
|
||||||
|
- $d_0 \approx 10\,[mm]$
|
||||||
|
- $L \approx 150\,[mm]$
|
||||||
|
- $R \approx 250\,[mm]$
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
d0 = 10e-3; % [m]
|
||||||
|
L = 150e-3; % [m]
|
||||||
|
R = 250e-3; % [m]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* X-Y-Z measurement
|
||||||
|
<<sec:translation_interferometers>>
|
||||||
|
|
||||||
|
The geometry for the interferometers measuring translations is shown in Figure [[fig:translation_interferometers]]:
|
||||||
|
- $R = 250\,[mm]$
|
||||||
|
- $d_0 > 10\,[mm]$
|
||||||
|
- $d_x = \pm 1\,[mm]$
|
||||||
|
- $d_y = \pm 1\,[mm]$
|
||||||
|
|
||||||
|
#+name: fig:translation_interferometers
|
||||||
|
#+caption: Interferometers that are measuring translation
|
||||||
|
[[file:figs/translation_interferometers.png]]
|
||||||
|
|
||||||
|
The angle of the reflected beam is approximately equal to:
|
||||||
|
\begin{equation}
|
||||||
|
\theta \approx 2 \frac{d_y}{R}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
And we obtain:
|
||||||
|
#+begin_src matlab :results raw replace :exports results :tangle no
|
||||||
|
sprintf('\\[ \\theta \\approx %.1f\\,[mrad] \\]', 1e3*(2*d_y/R))
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
\[ \theta \approx 8.0\,[mrad] \]
|
||||||
|
|
||||||
|
#+name: tab:spec_translation
|
||||||
|
#+caption: Specifications for the translation interferometers
|
||||||
|
#+attr_latex: :environment tabularx :width 0.4\linewidth :align lc
|
||||||
|
#+attr_latex: :center t :booktabs t :float t
|
||||||
|
| Specification | Value |
|
||||||
|
|--------------------+-----------------|
|
||||||
|
| Axial Acceptance | $\pm 1\,[mm]$ |
|
||||||
|
| Angular Acceptance | $\pm 8\,[mrad]$ |
|
||||||
|
| Distance to target | $10\,[mm]$ |
|
||||||
|
|
||||||
|
* Tilt measurement
|
||||||
|
<<sec:rotation_interferometers>>
|
||||||
|
|
||||||
|
The tilt $\theta$ of the flat mirror is directly equal to the tilt of the reflector.
|
||||||
|
However, the $z$ displacement on the flat part is equal to:
|
||||||
|
\begin{equation}
|
||||||
|
z \approx d_z + L \theta_y
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
And we obtain:
|
||||||
|
#+begin_src matlab :results raw replace :exports results :tangle no
|
||||||
|
sprintf('\\[ z \\approx %.1f\\,[mm] \\]', 1e3*(d_z + R_x*L))
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
\[ z \approx 2.5\,[mm] \]
|
||||||
|
|
||||||
|
The geometry for the interferometers measuring rotations is shown in Figure [[fig:rotation_interferometers]]:
|
||||||
|
- $d_0 > 10\,[mm]$
|
||||||
|
- $\theta = \pm 10\,[mrad]$
|
||||||
|
- $z = \pm 2.5\, [mm]$
|
||||||
|
|
||||||
|
#+name: fig:rotation_interferometers
|
||||||
|
#+caption: Interferometers that are measuring tilt
|
||||||
|
[[file:figs/rotation_interferometers.png]]
|
||||||
|
|
||||||
|
#+name: tab:spec_rotation
|
||||||
|
#+caption: Specifications for the rotation interferometers
|
||||||
|
#+attr_latex: :environment tabularx :width 0.4\linewidth :align lc
|
||||||
|
#+attr_latex: :center t :booktabs t :float t
|
||||||
|
| Specification | Value |
|
||||||
|
|--------------------+------------------|
|
||||||
|
| Axial Acceptance | $\pm 2.5\,[mm]$ |
|
||||||
|
| Angular Acceptance | $\pm 10\,[mrad]$ |
|
||||||
|
| Distance to target | $10\,[mm]$ |
|
||||||
|
|
||||||
|
* Conclusion
|
BIN
short-stroke-metrology.pdf
Normal file
BIN
short-stroke-metrology.pdf
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user