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Thomas Dehaeze 2020-10-29 10:42:00 +01:00
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-10-29 jeu. 10:06 --> <!-- 2020-10-29 jeu. 10:41 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Attocube - Test Bench</title> <title>Attocube - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -15,6 +15,14 @@
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -27,46 +35,132 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgb69bc8c">1. First Measurements</a> <li><a href="#org28fc04b">1. Estimation of the Spectral Density of the Attocube Noise</a>
<ul> <ul>
<li><a href="#org170c3a9">1.1. Load Data</a></li> <li><a href="#org8f7a999">1.1. Long and Slow measurement</a></li>
<li><a href="#orgf4f16a8">1.2. Short and Fast measurement</a></li>
<li><a href="#org7bd25e6">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgb69bc8c" class="outline-2"> <div id="outline-container-org28fc04b" class="outline-2">
<h2 id="orgb69bc8c"><span class="section-number-2">1</span> First Measurements</h2> <h2 id="org28fc04b"><span class="section-number-2">1</span> Estimation of the Spectral Density of the Attocube Noise</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-org170c3a9" class="outline-3"> <div id="outline-container-org8f7a999" class="outline-3">
<h3 id="org170c3a9"><span class="section-number-3">1.1</span> Load Data</h3> <h3 id="org8f7a999"><span class="section-number-3">1.1</span> Long and Slow measurement</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<div class="org-src-container"> <p>
<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>) The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).
Ts = 1; <span class="org-comment">% [s]</span> </p>
win = hann(ceil(length(x)<span class="org-type">/</span>10)); <div class="org-src-container">
<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>)
Ts = 0.1; <span class="org-comment">% [s]</span>
</pre>
</div>
<div id="org7f956e7" class="figure">
<p><img src="figs/long_meas_time_domain_full.png" alt="long_meas_time_domain_full.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Long measurement time domain data</p>
</div>
<p>
We can see in Figure <a href="#org7f956e7">1</a> that there is a transient period where the measured displacement experiences some drifts.
This is probably due to thermal effects.
We only select the data between <code>t1</code> and <code>t2</code>.
The obtained displacement is shown in Figure <a href="#orgab24552">2</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">t1 = 11; t2 = 17; <span class="org-comment">% [h]</span>
x = x(t <span class="org-type">&gt;</span> t1<span class="org-type">*</span>60<span class="org-type">*</span>60 <span class="org-type">&amp;</span> t <span class="org-type">&lt;</span> t2<span class="org-type">*</span>60<span class="org-type">*</span>60);
x = x <span class="org-type">-</span> mean(x);
t = t(t <span class="org-type">&gt;</span> t1<span class="org-type">*</span>60<span class="org-type">*</span>60 <span class="org-type">&amp;</span> t <span class="org-type">&lt;</span> t2<span class="org-type">*</span>60<span class="org-type">*</span>60);
t = t <span class="org-type">-</span> t(1);
</pre>
</div>
<div id="orgab24552" class="figure">
<p><img src="figs/long_meas_time_domain_zoom.png" alt="long_meas_time_domain_zoom.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Kept data (removed slow drifts during the first hours)</p>
</div>
<p>
The Power Spectral Density of the measured displacement is computed
</p>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>20));
[p_1, f_1] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts); [p_1, f_1] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
</pre> </pre>
</div> </div>
</div>
</div>
<div id="outline-container-orgf4f16a8" class="outline-3">
<h3 id="orgf4f16a8"><span class="section-number-3">1.2</span> Short and Fast measurement</h3>
<div class="outline-text-3" id="text-1-2">
<p>
An second measurement is done in order to estimate the high frequency noise of the interferometer.
The measurement is done with a sampling time of \(T_s = 0.1\,ms\) and a duration of ~100s.
</p>
<div class="org-src-container"> <div class="org-src-container">
<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>) <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>)
Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span> Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
</pre>
</div>
win = hann(ceil(length(x)<span class="org-type">/</span>50)); <p>
The time domain measurement is shown in Figure <a href="#orge8034c6">3</a>.
</p>
<div id="orge8034c6" class="figure">
<p><img src="figs/short_meas_time_domain.png" alt="short_meas_time_domain.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Time domain measurement with the high sampling rate</p>
</div>
<p>
The Power Spectral Density of the measured displacement is computed
</p>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>20));
[p_2, f_2] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts); [p_2, f_2] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org7bd25e6" class="outline-3">
<h3 id="org7bd25e6"><span class="section-number-3">1.3</span> Obtained Amplitude Spectral Density of the measured displacement</h3>
<div class="outline-text-3" id="text-1-3">
<p>
The computed ASD of the two measurements are combined in Figure <a href="#org060925e">4</a>.
</p>
<div id="org060925e" class="figure">
<p><img src="figs/psd_combined.png" alt="psd_combined.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Obtained Amplitude Spectral Density of the measured displacement</p>
</div>
</div>
</div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-10-29 jeu. 10:06</p> <p class="date">Created: 2020-10-29 jeu. 10:41</p>
</div> </div>
</body> </body>
</html> </html>

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@ -37,7 +37,7 @@
#+PROPERTY: header-args:matlab+ :output-dir figs #+PROPERTY: header-args:matlab+ :output-dir figs
:END: :END:
* First Measurements * Estimation of the Spectral Density of the Attocube Noise
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
@ -47,29 +47,116 @@
<<matlab-init>> <<matlab-init>>
#+end_src #+end_src
** Load Data ** Long and Slow measurement
#+begin_src matlab The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$.
load('./mat/long_test.mat', 'x', 't')
Ts = 1; % [s]
win = hann(ceil(length(x)/10));
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
#+end_src
#+begin_src matlab #+begin_src matlab
load('./mat/test.mat', 'x', 't') load('./mat/long_test2.mat', 'x', 't')
Ts = 1e-4; % [s] Ts = 0.1; % [s]
win = hann(ceil(length(x)/50));
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
#+end_src #+end_src
#+begin_src matlab :exports none
figure;
plot(t/60/60, 1e9*x)
xlabel('Time [h]'); ylabel('Displacement [nm]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/long_meas_time_domain_full.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:long_meas_time_domain_full
#+caption: Long measurement time domain data
#+RESULTS:
[[file:figs/long_meas_time_domain_full.png]]
We can see in Figure [[fig:long_meas_time_domain_full]] that there is a transient period where the measured displacement experiences some drifts.
This is probably due to thermal effects.
We only select the data between =t1= and =t2=.
The obtained displacement is shown in Figure [[fig:long_meas_time_domain_zoom]].
#+begin_src matlab
t1 = 11; t2 = 17; % [h]
x = x(t > t1*60*60 & t < t2*60*60);
x = x - mean(x);
t = t(t > t1*60*60 & t < t2*60*60);
t = t - t(1);
#+end_src
#+begin_src matlab :exports none
figure;
plot(t/60/60, 1e9*x);
xlabel('Time [h]'); ylabel('Measured Displacement [nm]')
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/long_meas_time_domain_zoom.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:long_meas_time_domain_zoom
#+caption: Kept data (removed slow drifts during the first hours)
#+RESULTS:
[[file:figs/long_meas_time_domain_zoom.png]]
The Power Spectral Density of the measured displacement is computed
#+begin_src matlab
win = hann(ceil(length(x)/20));
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
#+end_src
** Short and Fast measurement
An second measurement is done in order to estimate the high frequency noise of the interferometer.
The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s.
#+begin_src matlab
load('./mat/test.mat', 'x', 't')
Ts = 1e-4; % [s]
#+end_src
The time domain measurement is shown in Figure [[fig:short_meas_time_domain]].
#+begin_src matlab :exports none
figure;
plot(t, 1e9*x)
xlabel('Time [s]'); ylabel('Displacement [nm]');
xlim([0, 100]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/short_meas_time_domain.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:short_meas_time_domain
#+caption: Time domain measurement with the high sampling rate
#+RESULTS:
[[file:figs/short_meas_time_domain.png]]
The Power Spectral Density of the measured displacement is computed
#+begin_src matlab
win = hann(ceil(length(x)/20));
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
#+end_src
** Obtained Amplitude Spectral Density of the measured displacement
The computed ASD of the two measurements are combined in Figure [[fig:psd_combined]].
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(f_1(8:end), sqrt(p_1(8:end))); plot(f_1(8:end), sqrt(p_1(8:end)), 'k-');
plot(f_2(8:end), sqrt(p_2(8:end))); plot(f_2(8:end), sqrt(p_2(8:end)), 'k-');
hold off; hold off;
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log'); set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
#+end_src #+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/psd_combined.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:psd_combined
#+caption: Obtained Amplitude Spectral Density of the measured displacement
#+RESULTS:
[[file:figs/psd_combined.png]]

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