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figs/long_meas_time_domain_full.pdf
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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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<!-- 2020-10-29 jeu. 10:06 -->
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<!-- 2020-10-29 jeu. 10:41 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Attocube - Test Bench</title>
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<script type="text/javascript" src="./js/bootstrap.min.js"></script>
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<script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
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<script>MathJax = {
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</head>
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<body>
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<div id="org-div-home-and-up">
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@ -27,46 +35,132 @@
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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="#orgb69bc8c">1. First Measurements</a>
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<li><a href="#org28fc04b">1. Estimation of the Spectral Density of the Attocube Noise</a>
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<ul>
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<li><a href="#org170c3a9">1.1. Load Data</a></li>
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<li><a href="#org8f7a999">1.1. Long and Slow measurement</a></li>
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<li><a href="#orgf4f16a8">1.2. Short and Fast measurement</a></li>
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<li><a href="#org7bd25e6">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgb69bc8c" class="outline-2">
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<h2 id="orgb69bc8c"><span class="section-number-2">1</span> First Measurements</h2>
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<div id="outline-container-org28fc04b" class="outline-2">
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<h2 id="org28fc04b"><span class="section-number-2">1</span> Estimation of the Spectral Density of the Attocube Noise</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org170c3a9" class="outline-3">
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<h3 id="org170c3a9"><span class="section-number-3">1.1</span> Load Data</h3>
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<div id="outline-container-org8f7a999" class="outline-3">
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<h3 id="org8f7a999"><span class="section-number-3">1.1</span> Long and Slow measurement</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'./mat/long_test.mat'</span>, <span class="org-string">'x'</span>, <span class="org-string">'t'</span>)
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Ts = 1; <span class="org-comment">% [s]</span>
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<p>
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The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).
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</p>
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win = hann(ceil(length(x)<span class="org-type">/</span>10));
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'./mat/long_test2.mat'</span>, <span class="org-string">'x'</span>, <span class="org-string">'t'</span>)
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Ts = 0.1; <span class="org-comment">% [s]</span>
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</pre>
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</div>
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<div id="org7f956e7" class="figure">
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<p><img src="figs/long_meas_time_domain_full.png" alt="long_meas_time_domain_full.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Long measurement time domain data</p>
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</div>
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<p>
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We can see in Figure <a href="#org7f956e7">1</a> that there is a transient period where the measured displacement experiences some drifts.
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This is probably due to thermal effects.
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We only select the data between <code>t1</code> and <code>t2</code>.
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The obtained displacement is shown in Figure <a href="#orgab24552">2</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">t1 = 11; t2 = 17; <span class="org-comment">% [h]</span>
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x = x(t <span class="org-type">></span> t1<span class="org-type">*</span>60<span class="org-type">*</span>60 <span class="org-type">&</span> t <span class="org-type"><</span> t2<span class="org-type">*</span>60<span class="org-type">*</span>60);
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x = x <span class="org-type">-</span> mean(x);
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t = t(t <span class="org-type">></span> t1<span class="org-type">*</span>60<span class="org-type">*</span>60 <span class="org-type">&</span> t <span class="org-type"><</span> t2<span class="org-type">*</span>60<span class="org-type">*</span>60);
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t = t <span class="org-type">-</span> t(1);
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</pre>
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</div>
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<div id="orgab24552" class="figure">
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<p><img src="figs/long_meas_time_domain_zoom.png" alt="long_meas_time_domain_zoom.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Kept data (removed slow drifts during the first hours)</p>
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</div>
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<p>
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The Power Spectral Density of the measured displacement is computed
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>20));
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[p_1, f_1] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
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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-orgf4f16a8" class="outline-3">
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<h3 id="orgf4f16a8"><span class="section-number-3">1.2</span> Short and Fast measurement</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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An second measurement is done in order to estimate the high frequency noise of the interferometer.
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The measurement is done with a sampling time of \(T_s = 0.1\,ms\) and a duration of ~100s.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'./mat/test.mat'</span>, <span class="org-string">'x'</span>, <span class="org-string">'t'</span>)
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Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
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</pre>
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</div>
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win = hann(ceil(length(x)<span class="org-type">/</span>50));
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<p>
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The time domain measurement is shown in Figure <a href="#orge8034c6">3</a>.
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</p>
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<div id="orge8034c6" class="figure">
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<p><img src="figs/short_meas_time_domain.png" alt="short_meas_time_domain.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Time domain measurement with the high sampling rate</p>
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</div>
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<p>
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The Power Spectral Density of the measured displacement is computed
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>20));
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[p_2, f_2] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
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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-org7bd25e6" class="outline-3">
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<h3 id="org7bd25e6"><span class="section-number-3">1.3</span> Obtained Amplitude Spectral Density of the measured displacement</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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The computed ASD of the two measurements are combined in Figure <a href="#org060925e">4</a>.
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</p>
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<div id="org060925e" class="figure">
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<p><img src="figs/psd_combined.png" alt="psd_combined.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Obtained Amplitude Spectral Density of the measured displacement</p>
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</div>
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</div>
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</div>
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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: 2020-10-29 jeu. 10:06</p>
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<p class="date">Created: 2020-10-29 jeu. 10:41</p>
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</div>
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</body>
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</html>
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119
index.org
119
index.org
@ -37,7 +37,7 @@
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#+PROPERTY: header-args:matlab+ :output-dir figs
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:END:
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* First Measurements
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* Estimation of the Spectral Density of the Attocube Noise
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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@ -47,29 +47,116 @@
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<<matlab-init>>
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#+end_src
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** Load Data
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#+begin_src matlab
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load('./mat/long_test.mat', 'x', 't')
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Ts = 1; % [s]
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win = hann(ceil(length(x)/10));
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[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
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#+end_src
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** Long and Slow measurement
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The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$.
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#+begin_src matlab
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load('./mat/test.mat', 'x', 't')
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Ts = 1e-4; % [s]
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win = hann(ceil(length(x)/50));
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[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
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load('./mat/long_test2.mat', 'x', 't')
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Ts = 0.1; % [s]
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#+end_src
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#+begin_src matlab :exports none
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figure;
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plot(t/60/60, 1e9*x)
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xlabel('Time [h]'); ylabel('Displacement [nm]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/long_meas_time_domain_full.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:long_meas_time_domain_full
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#+caption: Long measurement time domain data
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#+RESULTS:
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[[file:figs/long_meas_time_domain_full.png]]
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We can see in Figure [[fig:long_meas_time_domain_full]] that there is a transient period where the measured displacement experiences some drifts.
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This is probably due to thermal effects.
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We only select the data between =t1= and =t2=.
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The obtained displacement is shown in Figure [[fig:long_meas_time_domain_zoom]].
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#+begin_src matlab
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t1 = 11; t2 = 17; % [h]
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x = x(t > t1*60*60 & t < t2*60*60);
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x = x - mean(x);
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t = t(t > t1*60*60 & t < t2*60*60);
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t = t - t(1);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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plot(t/60/60, 1e9*x);
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xlabel('Time [h]'); ylabel('Measured Displacement [nm]')
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/long_meas_time_domain_zoom.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:long_meas_time_domain_zoom
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#+caption: Kept data (removed slow drifts during the first hours)
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#+RESULTS:
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[[file:figs/long_meas_time_domain_zoom.png]]
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The Power Spectral Density of the measured displacement is computed
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#+begin_src matlab
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win = hann(ceil(length(x)/20));
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[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
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#+end_src
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** Short and Fast measurement
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An second measurement is done in order to estimate the high frequency noise of the interferometer.
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The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s.
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#+begin_src matlab
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load('./mat/test.mat', 'x', 't')
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Ts = 1e-4; % [s]
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#+end_src
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The time domain measurement is shown in Figure [[fig:short_meas_time_domain]].
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#+begin_src matlab :exports none
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figure;
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plot(t, 1e9*x)
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xlabel('Time [s]'); ylabel('Displacement [nm]');
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xlim([0, 100]);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/short_meas_time_domain.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:short_meas_time_domain
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#+caption: Time domain measurement with the high sampling rate
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#+RESULTS:
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[[file:figs/short_meas_time_domain.png]]
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The Power Spectral Density of the measured displacement is computed
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#+begin_src matlab
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win = hann(ceil(length(x)/20));
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[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
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#+end_src
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** Obtained Amplitude Spectral Density of the measured displacement
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The computed ASD of the two measurements are combined in Figure [[fig:psd_combined]].
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(f_1(8:end), sqrt(p_1(8:end)));
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plot(f_2(8:end), sqrt(p_2(8:end)));
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plot(f_1(8:end), sqrt(p_1(8:end)), 'k-');
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plot(f_2(8:end), sqrt(p_2(8:end)), 'k-');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/psd_combined.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:psd_combined
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#+caption: Obtained Amplitude Spectral Density of the measured displacement
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#+RESULTS:
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[[file:figs/psd_combined.png]]
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mat/long_test2.mat
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mat/long_test2.mat
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