<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-05-14 mar. 09:52 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Static Measurements</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Dehaeze Thomas" />
<style type="text/css">
<!--/*--><![CDATA[/*><!--*/
.title { text-align: center;
margin-bottom: .2em; }
.subtitle { text-align: center;
font-size: medium;
font-weight: bold;
margin-top:0; }
.todo { font-family: monospace; color: red; }
.done { font-family: monospace; color: green; }
.priority { font-family: monospace; color: orange; }
.tag { background-color: #eee; font-family: monospace;
padding: 2px; font-size: 80%; font-weight: normal; }
.timestamp { color: #bebebe; }
.timestamp-kwd { color: #5f9ea0; }
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
.underline { text-decoration: underline; }
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
p.verse { margin-left: 3%; }
pre {
border: 1px solid #ccc;
box-shadow: 3px 3px 3px #eee;
padding: 8pt;
font-family: monospace;
overflow: auto;
margin: 1.2em;
}
pre.src {
position: relative;
overflow: visible;
padding-top: 1.2em;
}
pre.src:before {
display: none;
position: absolute;
background-color: white;
top: -10px;
right: 10px;
padding: 3px;
border: 1px solid black;
}
pre.src:hover:before { display: inline;}
/* Languages per Org manual */
pre.src-asymptote:before { content: 'Asymptote'; }
pre.src-awk:before { content: 'Awk'; }
pre.src-C:before { content: 'C'; }
/* pre.src-C++ doesn't work in CSS */
pre.src-clojure:before { content: 'Clojure'; }
pre.src-css:before { content: 'CSS'; }
pre.src-D:before { content: 'D'; }
pre.src-ditaa:before { content: 'ditaa'; }
pre.src-dot:before { content: 'Graphviz'; }
pre.src-calc:before { content: 'Emacs Calc'; }
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
pre.src-fortran:before { content: 'Fortran'; }
pre.src-gnuplot:before { content: 'gnuplot'; }
pre.src-haskell:before { content: 'Haskell'; }
pre.src-hledger:before { content: 'hledger'; }
pre.src-java:before { content: 'Java'; }
pre.src-js:before { content: 'Javascript'; }
pre.src-latex:before { content: 'LaTeX'; }
pre.src-ledger:before { content: 'Ledger'; }
pre.src-lisp:before { content: 'Lisp'; }
pre.src-lilypond:before { content: 'Lilypond'; }
pre.src-lua:before { content: 'Lua'; }
pre.src-matlab:before { content: 'MATLAB'; }
pre.src-mscgen:before { content: 'Mscgen'; }
pre.src-ocaml:before { content: 'Objective Caml'; }
pre.src-octave:before { content: 'Octave'; }
pre.src-org:before { content: 'Org mode'; }
pre.src-oz:before { content: 'OZ'; }
pre.src-plantuml:before { content: 'Plantuml'; }
pre.src-processing:before { content: 'Processing.js'; }
pre.src-python:before { content: 'Python'; }
pre.src-R:before { content: 'R'; }
pre.src-ruby:before { content: 'Ruby'; }
pre.src-sass:before { content: 'Sass'; }
pre.src-scheme:before { content: 'Scheme'; }
pre.src-screen:before { content: 'Gnu Screen'; }
pre.src-sed:before { content: 'Sed'; }
pre.src-sh:before { content: 'shell'; }
pre.src-sql:before { content: 'SQL'; }
pre.src-sqlite:before { content: 'SQLite'; }
/* additional languages in org.el's org-babel-load-languages alist */
pre.src-forth:before { content: 'Forth'; }
pre.src-io:before { content: 'IO'; }
pre.src-J:before { content: 'J'; }
pre.src-makefile:before { content: 'Makefile'; }
pre.src-maxima:before { content: 'Maxima'; }
pre.src-perl:before { content: 'Perl'; }
pre.src-picolisp:before { content: 'Pico Lisp'; }
pre.src-scala:before { content: 'Scala'; }
pre.src-shell:before { content: 'Shell Script'; }
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
/* additional language identifiers per "defun org-babel-execute"
in ob-*.el */
pre.src-cpp:before { content: 'C++'; }
pre.src-abc:before { content: 'ABC'; }
pre.src-coq:before { content: 'Coq'; }
pre.src-groovy:before { content: 'Groovy'; }
/* additional language identifiers from org-babel-shell-names in
ob-shell.el: ob-shell is the only babel language using a lambda to put
the execution function name together. */
pre.src-bash:before { content: 'bash'; }
pre.src-csh:before { content: 'csh'; }
pre.src-ash:before { content: 'ash'; }
pre.src-dash:before { content: 'dash'; }
pre.src-ksh:before { content: 'ksh'; }
pre.src-mksh:before { content: 'mksh'; }
pre.src-posh:before { content: 'posh'; }
/* Additional Emacs modes also supported by the LaTeX listings package */
pre.src-ada:before { content: 'Ada'; }
pre.src-asm:before { content: 'Assembler'; }
pre.src-caml:before { content: 'Caml'; }
pre.src-delphi:before { content: 'Delphi'; }
pre.src-html:before { content: 'HTML'; }
pre.src-idl:before { content: 'IDL'; }
pre.src-mercury:before { content: 'Mercury'; }
pre.src-metapost:before { content: 'MetaPost'; }
pre.src-modula-2:before { content: 'Modula-2'; }
pre.src-pascal:before { content: 'Pascal'; }
pre.src-ps:before { content: 'PostScript'; }
pre.src-prolog:before { content: 'Prolog'; }
pre.src-simula:before { content: 'Simula'; }
pre.src-tcl:before { content: 'tcl'; }
pre.src-tex:before { content: 'TeX'; }
pre.src-plain-tex:before { content: 'Plain TeX'; }
pre.src-verilog:before { content: 'Verilog'; }
pre.src-vhdl:before { content: 'VHDL'; }
pre.src-xml:before { content: 'XML'; }
pre.src-nxml:before { content: 'XML'; }
/* add a generic configuration mode; LaTeX export needs an additional
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
pre.src-conf:before { content: 'Configuration File'; }
table { border-collapse:collapse; }
caption.t-above { caption-side: top; }
caption.t-bottom { caption-side: bottom; }
td, th { vertical-align:top; }
th.org-right { text-align: center; }
th.org-left { text-align: center; }
th.org-center { text-align: center; }
td.org-right { text-align: right; }
td.org-left { text-align: left; }
td.org-center { text-align: center; }
dt { font-weight: bold; }
.footpara { display: inline; }
.footdef { margin-bottom: 1em; }
.figure { padding: 1em; }
.figure p { text-align: center; }
.equation-container {
display: table;
text-align: center;
width: 100%;
}
.equation {
vertical-align: middle;
}
.equation-label {
display: table-cell;
text-align: right;
vertical-align: middle;
}
.inlinetask {
padding: 10px;
border: 2px solid gray;
margin: 10px;
background: #ffffcc;
}
#org-div-home-and-up
{ text-align: right; font-size: 70%; white-space: nowrap; }
textarea { overflow-x: auto; }
.linenr { font-size: smaller }
.code-highlighted { background-color: #ffff00; }
.org-info-js_info-navigation { border-style: none; }
#org-info-js_console-label
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
.org-info-js_search-highlight
{ background-color: #ffff00; color: #000000; font-weight: bold; }
.org-svg { width: 90%; }
/*]]>*/-->
</style>
<link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
<link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
<link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
<script type="text/javascript" src="../js/jquery.min.js"></script>
<script type="text/javascript" src="../js/bootstrap.min.js"></script>
<script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
<script type="text/javascript" src="../js/readtheorg.js"></script>
<script type="text/javascript">
/*
@licstart The following is the entire license notice for the
JavaScript code in this tag.
Copyright (C) 2012-2019 Free Software Foundation, Inc.
The JavaScript code in this tag is free software: you can
redistribute it and/or modify it under the terms of the GNU
General Public License (GNU GPL) as published by the Free Software
Foundation, either version 3 of the License, or (at your option)
any later version. The code is distributed WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
As additional permission under GNU GPL version 3 section 7, you
may distribute non-source (e.g., minimized or compacted) forms of
that code without the copy of the GNU GPL normally required by
section 4, provided you include this license notice and a URL
through which recipients can access the Corresponding Source.
@licend The above is the entire license notice
for the JavaScript code in this tag.
*/
<!--/*--><![CDATA[/*><!--*/
function CodeHighlightOn(elem, id)
{
var target = document.getElementById(id);
if(null != target) {
elem.cacheClassElem = elem.className;
elem.cacheClassTarget = target.className;
target.className = "code-highlighted";
elem.className = "code-highlighted";
}
}
function CodeHighlightOff(elem, id)
{
var target = document.getElementById(id);
if(elem.cacheClassElem)
elem.className = elem.cacheClassElem;
if(elem.cacheClassTarget)
target.className = elem.cacheClassTarget;
}
/*]]>*///-->
</script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
displayAlign: "center",
displayIndent: "0em",
"HTML-CSS": { scale: 100,
linebreaks: { automatic: "false" },
webFont: "TeX"
},
SVG: {scale: 100,
linebreaks: { automatic: "false" },
font: "TeX"},
NativeMML: {scale: 100},
TeX: { equationNumbers: {autoNumber: "AMS"},
MultLineWidth: "85%",
TagSide: "right",
TagIndent: ".8em"
}
});
</script>
<script type="text/javascript"
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
</head>
<body>
<div id="org-div-home-and-up">
<a accesskey="h" href="../index.html"> UP </a>
|
<a accesskey="H" href="../index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Static Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org9dbeefe">1. Ty Stage</a>
<ul>
<li><a href="#org98becb2">1.1. Notes</a></li>
<li><a href="#orgbab4f4e">1.2. Data Pre-processing</a></li>
<li><a href="#orgbb084a6">1.3. Matlab - Data Import</a></li>
<li><a href="#orgb7b2129">1.4. Data - Plot</a></li>
<li><a href="#org01e23ef">1.5. Translate to time domain</a></li>
<li><a href="#org13bc3d4">1.6. Compute the PSD</a></li>
</ul>
</li>
<li><a href="#orgc7af6bd">2. <span class="todo TODO">TODO</span> Spindle</a></li>
</ul>
</div>
</div>
<div id="outline-container-org9dbeefe" class="outline-2">
<h2 id="org9dbeefe"><span class="section-number-2">1</span> Ty Stage</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org0ab6482"></a>
</p>
<div class="note">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/static_ty.zip">here</a>.
</p>
</div>
</div>
<div id="outline-container-org98becb2" class="outline-3">
<h3 id="org98becb2"><span class="section-number-3">1.1</span> Notes</h3>
<div class="outline-text-3" id="text-1-1">
<ul class="org-ul">
<li><b>5530</b>: Straightness Plot: Yz</li>
<li><b>Filename</b>: <code>r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt</code></li>
<li><b>Acquisition date</b>: 09/01/2019 13:49:42</li>
<li><b>Current date</b>: 08/03/2019 08:46:35</li>
<li><b>Measurement Type</b>: STRAIGHTNESS vertical</li>
<li><b>Travel Mode</b>: Bidirectional</li>
<li><b>Number of Target Positions</b>: 401</li>
<li><b>Number of total data pairs</b>: 2406</li>
<li><b>Number of total data runs</b>:6</li>
<li><b>Position Value Units</b>: millimeters</li>
<li><b>Error Value Units</b>: micrometers</li>
</ul>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Environmental Data</th>
<th scope="col" class="org-left">Min</th>
<th scope="col" class="org-left">Max</th>
<th scope="col" class="org-left">Avg</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Air Temp (C)</td>
<td class="org-left">024,57</td>
<td class="org-left">024,61</td>
<td class="org-left">024,59</td>
</tr>
<tr>
<td class="org-left">Air Prs (mm)</td>
<td class="org-left">742,56</td>
<td class="org-left">743,29</td>
<td class="org-left">742,83</td>
</tr>
<tr>
<td class="org-left">Air Hmd (%)</td>
<td class="org-left">024,00</td>
<td class="org-left">024,00</td>
<td class="org-left">024,00</td>
</tr>
<tr>
<td class="org-left">MT1 Temp (C)</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">020,00</td>
</tr>
<tr>
<td class="org-left">MT2 Temp (C)</td>
<td class="org-left">024,40</td>
<td class="org-left">024,44</td>
<td class="org-left">024,42</td>
</tr>
<tr>
<td class="org-left">MT3 Temp (C)</td>
<td class="org-left">024,32</td>
<td class="org-left">024,36</td>
<td class="org-left">024,34</td>
</tr>
</tbody>
</table>
<p>
In a very schematic way, the measurement is explained on figure <a href="#orgb91392e">1</a>.
The positioning error \(d\) is measure as a function of \(x\).
Because the measurement is done in a static way, the dynamics of the station (represented by the mass-spring-damper system on the schematic) does not play a role in the measure.
</p>
<p>
The obtained data corresponds to the guiding errors.
</p>
<div id="orgb91392e" class="figure">
<p><img src="./figs/guiding_errors.png" alt="guiding_errors.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Schematic of the measurement</p>
</div>
</div>
</div>
<div id="outline-container-orgbab4f4e" class="outline-3">
<h3 id="orgbab4f4e"><span class="section-number-3">1.2</span> Data Pre-processing</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-shell">sed <span class="org-string">'s/\t/ /g;s/\,/./g'</span> <span class="org-string">"mat/linear_deviation_tyz_401_points.txt"</span> > data/data_tyz.txt
</pre>
</div>
<div class="org-src-container">
<pre class="src src-shell">head <span class="org-string">"mat/data_tyz.txt"</span>
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Run</th>
<th scope="col" class="org-right">Pos</th>
<th scope="col" class="org-right">TargetValue</th>
<th scope="col" class="org-right">ErrorValue</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-right">1</td>
<td class="org-right">-4.5E+00</td>
<td class="org-right">7.5377892E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">2</td>
<td class="org-right">-4.4775E+00</td>
<td class="org-right">7.5422246E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">3</td>
<td class="org-right">-4.455E+00</td>
<td class="org-right">7.5655617E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">4</td>
<td class="org-right">-4.4325E+00</td>
<td class="org-right">7.5149518E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">5</td>
<td class="org-right">-4.41E+00</td>
<td class="org-right">7.4886377E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">6</td>
<td class="org-right">-4.3875E+00</td>
<td class="org-right">7.437007E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">7</td>
<td class="org-right">-4.365E+00</td>
<td class="org-right">7.4449354E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">8</td>
<td class="org-right">-4.3425E+00</td>
<td class="org-right">7.3937387E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">9</td>
<td class="org-right">-4.32E+00</td>
<td class="org-right">7.3287468E+00</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgbb084a6" class="outline-3">
<h3 id="orgbb084a6"><span class="section-number-3">1.3</span> Matlab - Data Import</h3>
<div class="outline-text-3" id="text-1-3">
<div class="org-src-container">
<pre class="src src-matlab">filename = <span class="org-string">'mat/data_tyz.txt'</span>;
fileID = fopen<span class="org-rainbow-delimiters-depth-1">(</span>filename<span class="org-rainbow-delimiters-depth-1">)</span>;
data = cell2mat<span class="org-rainbow-delimiters-depth-1">(</span>textscan<span class="org-rainbow-delimiters-depth-2">(</span>fileID,'<span class="org-comment">%f %f %f </span>%f', 'collectoutput', <span class="org-highlight-numbers-number">1</span>,'headerlines',<span class="org-highlight-numbers-number">1</span>));
fclose<span class="org-rainbow-delimiters-depth-3">(</span>fileID<span class="org-rainbow-delimiters-depth-3">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb7b2129" class="outline-3">
<h3 id="orgb7b2129"><span class="section-number-3">1.4</span> Data - Plot</h3>
<div class="outline-text-3" id="text-1-4">
<p>
First, we plot the straightness error as a function of the position (figure <a href="#orge60d823">2</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">end, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-k'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Target Value </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Error Value <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orge60d823" class="figure">
<p><img src="figs/raw_data_tyz.png" alt="raw_data_tyz.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Time domain Data</p>
</div>
<p>
Then, we compute mean value of each position, and we remove this mean value from the data.
The results are shown on figure <a href="#org6b6ea44">3</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">mean_pos = zeros<span class="org-rainbow-delimiters-depth-1">(</span>sum<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">==</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:sum</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-constant">:, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-constant">==</span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
mean_pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = mean<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">==</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">end, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
filt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span>filt, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span>filt, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> mean_pos, <span class="org-string">'-k'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Target Value </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Error Value <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org6b6ea44" class="figure">
<p><img src="figs/processed_data_tyz.png" alt="processed_data_tyz.png" />
</p>
<p><span class="figure-number">Figure 3: </span>caption</p>
</div>
</div>
</div>
<div id="outline-container-org01e23ef" class="outline-3">
<h3 id="org01e23ef"><span class="section-number-3">1.5</span> Translate to time domain</h3>
<div class="outline-text-3" id="text-1-5">
<p>
We here make the assumptions that, during a scan with the translation stage, the Z motion of the translation stage will follow the guiding error measured.
</p>
<p>
We then create a time vector \(t\) from 0 to 1 second that corresponds to a typical scan, and we plot the guiding error as a function of the time on figure <a href="#orgb3c2727">4</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">t = linspace<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, length<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span>data<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">==</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>t, data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> mean_pos, <span class="org-string">'-k'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Error Value </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">um</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgb3c2727" class="figure">
<p><img src="figs/time_domain_tyz.png" alt="time_domain_tyz.png" />
</p>
<p><span class="figure-number">Figure 4: </span>caption</p>
</div>
</div>
</div>
<div id="outline-container-org13bc3d4" class="outline-3">
<h3 id="org13bc3d4"><span class="section-number-3">1.6</span> Compute the PSD</h3>
<div class="outline-text-3" id="text-1-6">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
We remove the mean position from the data.
</p>
<div class="org-src-container">
<pre class="src src-matlab">x = data<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> mean_pos;
</pre>
</div>
<p>
And finally, we compute the power spectral density of the displacement obtained in the time domain.
</p>
<p>
The result is shown on figure <a href="#org7446cbb">5</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
pxx_t = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>pxx<span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span>end, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">end, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
x = data<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> mean_pos;
<span class="org-rainbow-delimiters-depth-1">[</span>pxx, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
pxx_t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = pxx;
<span class="org-keyword">end</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>pxx_t, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org7446cbb" class="figure">
<p><img src="figs/psd_tyz.png" alt="psd_tyz.png" />
</p>
<p><span class="figure-number">Figure 5: </span>PSD of the Z motion when scanning with Ty at 1Hz</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgc7af6bd" class="outline-2">
<h2 id="orgc7af6bd"><span class="section-number-2">2</span> <span class="todo TODO">TODO</span> Spindle</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 09:52</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>