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Thomas Dehaeze 2020-10-29 11:07:35 +01:00
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-10-29 jeu. 11:06 -->
<!-- 2020-10-29 jeu. 11:07 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Attocube - Test Bench</title>
<meta name="generator" content="Org mode" />
@ -35,23 +35,23 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org04fd555">1. Estimation of the Spectral Density of the Attocube Noise</a>
<li><a href="#orgfaed8bc">1. Estimation of the Spectral Density of the Attocube Noise</a>
<ul>
<li><a href="#orgb5c08b7">1.1. Long and Slow measurement</a></li>
<li><a href="#org16781eb">1.2. Short and Fast measurement</a></li>
<li><a href="#org05880ea">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
<li><a href="#org42d8bf8">1.1. Long and Slow measurement</a></li>
<li><a href="#orgc5a3450">1.2. Short and Fast measurement</a></li>
<li><a href="#orgc18a5a3">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org04fd555" class="outline-2">
<h2 id="org04fd555"><span class="section-number-2">1</span> Estimation of the Spectral Density of the Attocube Noise</h2>
<div id="outline-container-orgfaed8bc" class="outline-2">
<h2 id="orgfaed8bc"><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>
<div id="outline-container-orgb5c08b7" class="outline-3">
<h3 id="orgb5c08b7"><span class="section-number-3">1.1</span> Long and Slow measurement</h3>
<div id="outline-container-org42d8bf8" class="outline-3">
<h3 id="org42d8bf8"><span class="section-number-3">1.1</span> Long and Slow measurement</h3>
<div class="outline-text-3" id="text-1-1">
<p>
The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).
@ -64,14 +64,14 @@ Ts = 0.1; <span class="org-comment">% [s]</span>
</div>
<div id="org988c594" class="figure">
<div id="orgd7563fe" 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>
Let&rsquo;s fit the data with a step response to a first order low pass filter (Figure <a href="#org9fca17b">2</a>).
Let&rsquo;s fit the data with a step response to a first order low pass filter (Figure <a href="#org5d8ea16">2</a>).
</p>
<div class="org-src-container">
@ -94,15 +94,18 @@ The corresponding time constant is (in [h]):
</pre>
<p>
<a href="figs/long_meas_time_domain_fit.pdf">figs/long_meas_time_domain_fit.pdf</a>
<div id="org5d8ea16" class="figure">
<p><img src="figs/long_meas_time_domain_fit.png" alt="long_meas_time_domain_fit.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Fit of the measurement data with a step response of a first order low pass filter</p>
</div>
<p>
We can see in Figure <a href="#org988c594">1</a> that there is a transient period where the measured displacement experiences some drifts.
We can see in Figure <a href="#orgd7563fe">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="#orgfaaa772">2</a>.
The obtained displacement is shown in Figure <a href="#org9806b5d">3</a>.
</p>
<div class="org-src-container">
@ -116,10 +119,10 @@ t = t <span class="org-type">-</span> t(1);
</div>
<div id="orgfaaa772" class="figure">
<div id="org9806b5d" 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>
<p><span class="figure-number">Figure 3: </span>Kept data (removed slow drifts during the first hours)</p>
</div>
<p>
@ -133,8 +136,8 @@ The Power Spectral Density of the measured displacement is computed
</div>
</div>
<div id="outline-container-org16781eb" class="outline-3">
<h3 id="org16781eb"><span class="section-number-3">1.2</span> Short and Fast measurement</h3>
<div id="outline-container-orgc5a3450" class="outline-3">
<h3 id="orgc5a3450"><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.
@ -148,14 +151,14 @@ Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
</div>
<p>
The time domain measurement is shown in Figure <a href="#org09490dd">3</a>.
The time domain measurement is shown in Figure <a href="#org658d16a">4</a>.
</p>
<div id="org09490dd" class="figure">
<div id="org658d16a" 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>
<p><span class="figure-number">Figure 4: </span>Time domain measurement with the high sampling rate</p>
</div>
<p>
@ -169,18 +172,18 @@ The Power Spectral Density of the measured displacement is computed
</div>
</div>
<div id="outline-container-org05880ea" class="outline-3">
<h3 id="org05880ea"><span class="section-number-3">1.3</span> Obtained Amplitude Spectral Density of the measured displacement</h3>
<div id="outline-container-orgc18a5a3" class="outline-3">
<h3 id="orgc18a5a3"><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="#org5a319f0">4</a>.
The computed ASD of the two measurements are combined in Figure <a href="#orgfdb6fa9">5</a>.
</p>
<div id="org5a319f0" class="figure">
<div id="orgfdb6fa9" 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>
<p><span class="figure-number">Figure 5: </span>Obtained Amplitude Spectral Density of the measured displacement</p>
</div>
</div>
</div>
@ -188,7 +191,7 @@ The computed ASD of the two measurements are combined in Figure <a href="#org5a3
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-10-29 jeu. 11:06</p>
<p class="date">Created: 2020-10-29 jeu. 11:07</p>
</div>
</body>
</html>

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@ -107,7 +107,7 @@ The corresponding time constant is (in [h]):
#+name: fig:long_meas_time_domain_fit
#+caption: Fit of the measurement data with a step response of a first order low pass filter
#+RESULTS:
[[file:figs/long_meas_time_domain_fit.pdf]]
[[file:figs/long_meas_time_domain_fit.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.