Add bubble/aluminium effect plots

This commit is contained in:
Thomas Dehaeze 2020-11-02 16:03:55 +01:00
parent 88dd1ac88b
commit 40cb3408d7
11 changed files with 594 additions and 559 deletions

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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. 11:20 -->
<!-- 2020-11-02 lun. 16:03 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Attocube - Test Bench</title>
<meta name="generator" content="Org mode" />
@ -35,30 +35,45 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org8d030f4">1. Estimation of the Spectral Density of the Attocube Noise</a>
<li><a href="#org301870a">1. Estimation of the Spectral Density of the Attocube Noise</a>
<ul>
<li><a href="#org50a760f">1.1. Long and Slow measurement</a></li>
<li><a href="#org70295ba">1.2. Short and Fast measurement</a></li>
<li><a href="#org17d3959">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
<li><a href="#orga74fad8">1.1. Long and Slow measurement</a></li>
<li><a href="#org594bfe8">1.2. Short and Fast measurement</a></li>
<li><a href="#orgd9ca1ad">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
</ul>
</li>
<li><a href="#orgacf938d">2. Effect of the &ldquo;bubble sheet&rdquo; and <b>Aluminium tube</b></a>
<ul>
<li><a href="#org30a0a1b">2.1. Aluminium Tube and Bubble Sheet</a></li>
<li><a href="#orgfe4b4f1">2.2. Only Aluminium Tube</a></li>
<li><a href="#org5d943ee">2.3. Nothing</a></li>
<li><a href="#org6b21819">2.4. Comparison</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org8d030f4" class="outline-2">
<h2 id="org8d030f4"><span class="section-number-2">1</span> Estimation of the Spectral Density of the Attocube Noise</h2>
<div id="outline-container-org301870a" class="outline-2">
<h2 id="org301870a"><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 id="orge0e29bf" class="figure">
<div id="org90d970d" class="figure">
<p><img src="figs/test-bench-shematic.png" alt="test-bench-shematic.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Test Bench Schematic</p>
</div>
<div id="org2b65a6c" class="figure">
<p><img src="figs/IMG-7865.JPG" alt="IMG-7865.JPG" />
</p>
<p><span class="figure-number">Figure 2: </span>Picture of the test bench. The Attocube and mirror are covered by a &ldquo;bubble sheet&rdquo;</p>
</div>
</div>
<div id="outline-container-org50a760f" class="outline-3">
<h3 id="org50a760f"><span class="section-number-3">1.1</span> Long and Slow measurement</h3>
<div id="outline-container-orga74fad8" class="outline-3">
<h3 id="orga74fad8"><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 \(T_s = 0.1\,s\).
@ -71,14 +86,14 @@ Ts = 0.1; <span class="org-comment">% [s]</span>
</div>
<div id="org4beccfe" class="figure">
<div id="org64c5513" 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 2: </span>Long measurement time domain data</p>
<p><span class="figure-number">Figure 3: </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="#org02547b0">3</a>).
Let&rsquo;s fit the data with a step response to a first order low pass filter (Figure <a href="#orgc356556">4</a>).
</p>
<div class="org-src-container">
@ -102,17 +117,17 @@ The corresponding time constant is (in [h]):
<div id="org02547b0" class="figure">
<div id="orgc356556" 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 3: </span>Fit of the measurement data with a step response of a first order low pass filter</p>
<p><span class="figure-number">Figure 4: </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="#org4beccfe">2</a> that there is a transient period where the measured displacement experiences some drifts.
We can see in Figure <a href="#org64c5513">3</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="#orgad8d3f9">4</a>.
The obtained displacement is shown in Figure <a href="#orgb851634">5</a>.
</p>
<div class="org-src-container">
@ -126,10 +141,10 @@ t = t <span class="org-type">-</span> t(1);
</div>
<div id="orgad8d3f9" class="figure">
<div id="orgb851634" 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 4: </span>Kept data (removed slow drifts during the first hours)</p>
<p><span class="figure-number">Figure 5: </span>Kept data (removed slow drifts during the first hours)</p>
</div>
<p>
@ -140,11 +155,29 @@ The Power Spectral Density of the measured displacement is computed
[p_1, f_1] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
<p>
As a low pass filter was used in the measurement process, we multiply the PSD by the square of the inverse of the filter&rsquo;s norm.
</p>
<div class="org-src-container">
<pre class="src src-matlab">G_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>);
p_1 = p_1<span class="org-type">./</span>abs(squeeze(freqresp(G_lpf, f_1, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
</pre>
</div>
<p>
Only frequencies below 2Hz are taken into account (high frequency noise will be measured afterwards).
</p>
<div class="org-src-container">
<pre class="src src-matlab">p_1 = p_1(f_1 <span class="org-type">&lt;</span> 2);
f_1 = f_1(f_1 <span class="org-type">&lt;</span> 2);
</pre>
</div>
</div>
</div>
<div id="outline-container-org70295ba" class="outline-3">
<h3 id="org70295ba"><span class="section-number-3">1.2</span> Short and Fast measurement</h3>
<div id="outline-container-org594bfe8" class="outline-3">
<h3 id="org594bfe8"><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.
@ -152,45 +185,125 @@ The measurement is done with a sampling time of \(T_s = 0.1\,ms\) and a duration
</p>
<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/short_test_plastic.mat'</span>)
Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">x = detrend(x, 0);
</pre>
</div>
<p>
The time domain measurement is shown in Figure <a href="#org8d7915d">5</a>.
The time domain measurement is shown in Figure <a href="#orged82baf">6</a>.
</p>
<div id="org8d7915d" class="figure">
<div id="orged82baf" class="figure">
<p><img src="figs/short_meas_time_domain.png" alt="short_meas_time_domain.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Time domain measurement with the high sampling rate</p>
<p><span class="figure-number">Figure 6: </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));
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>10));
[p_2, f_2] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
</div>
</div>
<div id="outline-container-org17d3959" class="outline-3">
<h3 id="org17d3959"><span class="section-number-3">1.3</span> Obtained Amplitude Spectral Density of the measured displacement</h3>
<div id="outline-container-orgd9ca1ad" class="outline-3">
<h3 id="orgd9ca1ad"><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="#org68a3367">6</a>.
The computed ASD of the two measurements are combined in Figure <a href="#org5032549">7</a>.
</p>
<div id="org68a3367" class="figure">
<div id="org5032549" class="figure">
<p><img src="figs/psd_combined.png" alt="psd_combined.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Obtained Amplitude Spectral Density of the measured displacement</p>
<p><span class="figure-number">Figure 7: </span>Obtained Amplitude Spectral Density of the measured displacement</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgacf938d" class="outline-2">
<h2 id="orgacf938d"><span class="section-number-2">2</span> Effect of the &ldquo;bubble sheet&rdquo; and <b>Aluminium tube</b></h2>
<div class="outline-text-2" id="text-2">
<div id="orgd503177" class="figure">
<p><img src="figs/IMG-7864.JPG" alt="IMG-7864.JPG" />
</p>
<p><span class="figure-number">Figure 8: </span>Aluminium tube used to protect the beam path from disturbances</p>
</div>
</div>
<div id="outline-container-org30a0a1b" class="outline-3">
<h3 id="org30a0a1b"><span class="section-number-3">2.1</span> Aluminium Tube and Bubble Sheet</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/long_test_plastic.mat'</span>);
Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">x = detrend(x, 0);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>10));
[p_1, f_1] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgfe4b4f1" class="outline-3">
<h3 id="orgfe4b4f1"><span class="section-number-3">2.2</span> Only Aluminium Tube</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/long_test_alu_tube.mat'</span>);
Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">x = detrend(x, 0);
</pre>
</div>
<p>
The time domain measurement is shown in Figure <a href="#orged82baf">6</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>10));
[p_2, f_2] = pwelch(x, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
</div>
</div>
<div id="outline-container-org5d943ee" class="outline-3">
<h3 id="org5d943ee"><span class="section-number-3">2.3</span> Nothing</h3>
</div>
<div id="outline-container-org6b21819" class="outline-3">
<h3 id="org6b21819"><span class="section-number-3">2.4</span> Comparison</h3>
<div class="outline-text-3" id="text-2-4">
<div id="org2d3dd04" class="figure">
<p><img src="figs/asd_noise_comp_bubble_aluminium.png" alt="asd_noise_comp_bubble_aluminium.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Comparison of the noise ASD with and without bubble sheet</p>
</div>
</div>
</div>
@ -198,7 +311,7 @@ The computed ASD of the two measurements are combined in Figure <a href="#org68a
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-10-29 jeu. 11:20</p>
<p class="date">Created: 2020-11-02 lun. 16:03</p>
</div>
</body>
</html>

100
index.org
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@ -44,6 +44,10 @@
#+caption: Test Bench Schematic
[[file:figs/test-bench-shematic.png]]
#+name: fig:test-bench-picture
#+caption: Picture of the test bench. The Attocube and mirror are covered by a "bubble sheet"
[[file:figs/IMG-7865.JPG]]
** 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>>
@ -150,22 +154,37 @@ The Power Spectral Density of the measured displacement is computed
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
#+end_src
As a low pass filter was used in the measurement process, we multiply the PSD by the square of the inverse of the filter's norm.
#+begin_src matlab
G_lpf = 1/(1 + s/2/pi);
p_1 = p_1./abs(squeeze(freqresp(G_lpf, f_1, 'Hz'))).^2;
#+end_src
Only frequencies below 2Hz are taken into account (high frequency noise will be measured afterwards).
#+begin_src matlab
p_1 = p_1(f_1 < 2);
f_1 = f_1(f_1 < 2);
#+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')
load('./mat/short_test_plastic.mat')
Ts = 1e-4; % [s]
#+end_src
#+begin_src matlab
x = detrend(x, 0);
#+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
@ -179,7 +198,7 @@ The time domain measurement is shown in Figure [[fig:short_meas_time_domain]].
The Power Spectral Density of the measured displacement is computed
#+begin_src matlab
win = hann(ceil(length(x)/20));
win = hann(ceil(length(x)/10));
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
#+end_src
@ -205,3 +224,78 @@ The computed ASD of the two measurements are combined in Figure [[fig:psd_combin
#+caption: Obtained Amplitude Spectral Density of the measured displacement
#+RESULTS:
[[file:figs/psd_combined.png]]
* Effect of the "bubble sheet" and *Aluminium tube*
** Introduction :ignore:
#+name: fig:picture-test-bench-aluminium-tube
#+caption: Aluminium tube used to protect the beam path from disturbances
[[file:figs/IMG-7864.JPG]]
** Aluminium Tube and Bubble Sheet
#+begin_src matlab
load('./mat/long_test_plastic.mat');
Ts = 1e-4; % [s]
#+end_src
#+begin_src matlab
x = detrend(x, 0);
#+end_src
#+begin_src matlab :exports none
figure;
plot(t, 1e9*x)
xlabel('Time [s]'); ylabel('Displacement [nm]');
#+end_src
#+begin_src matlab
win = hann(ceil(length(x)/10));
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
#+end_src
** Only Aluminium Tube
#+begin_src matlab
load('./mat/long_test_alu_tube.mat');
Ts = 1e-4; % [s]
#+end_src
#+begin_src matlab
x = detrend(x, 0);
#+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]');
#+end_src
#+begin_src matlab
win = hann(ceil(length(x)/10));
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
#+end_src
** Nothing
** Comparison
#+begin_src matlab :exports none
figure;
hold on;
plot(f_1(8:end), sqrt(p_1(8:end)), '-', ...
'DisplayName', 'Alunimium + Bubble');
plot(f_2(8:end), sqrt(p_2(8:end)), '-', ...
'DisplayName', 'Aluminium');
hold off;
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
legend('location', 'northeast');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/asd_noise_comp_bubble_aluminium.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:asd_noise_comp_bubble_aluminium
#+caption: Comparison of the noise ASD with and without bubble sheet
#+RESULTS:
[[file:figs/asd_noise_comp_bubble_aluminium.png]]