2020-10-29 10:07:20 +01:00
<?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 >
2020-11-02 16:03:55 +01:00
<!-- 2020 - 11 - 02 lun. 16:03 -->
2020-10-29 10:07:20 +01:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< title > Attocube - Test Bench< / title >
< meta name = "generator" content = "Org mode" / >
< meta name = "author" content = "Dehaeze Thomas" / >
< 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 >
2020-10-29 10:42:00 +01:00
< script > M a t h J a x = {
tex: {
tags: 'ams',
macros: {bm: ["\\boldsymbol{#1}",1],}
}
};
< / script >
< script type = "text/javascript" src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
2020-10-29 10:07:20 +01:00
< / 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" > Attocube - Test Bench< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2020-11-02 16:03:55 +01:00
< li > < a href = "#org301870a" > 1. Estimation of the Spectral Density of the Attocube Noise< / a >
2020-10-29 10:07:20 +01:00
< ul >
2020-11-02 16:03:55 +01:00
< 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 “ bubble sheet” 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 >
2020-10-29 10:07:20 +01:00
< / ul >
< / li >
< / ul >
< / div >
< / div >
2020-11-02 16:03:55 +01:00
< 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 >
2020-10-29 10:07:20 +01:00
< div class = "outline-text-2" id = "text-1" >
2020-10-29 11:20:34 +01:00
2020-11-02 16:03:55 +01:00
< div id = "org90d970d" class = "figure" >
2020-10-29 11:20:34 +01:00
< 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 >
2020-10-29 10:07:20 +01:00
< / div >
2020-11-02 16:03:55 +01:00
< 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 “ bubble sheet” < / p >
< / div >
2020-10-29 11:20:34 +01:00
< / div >
2020-11-02 16:03:55 +01:00
< div id = "outline-container-orga74fad8" class = "outline-3" >
< h3 id = "orga74fad8" > < span class = "section-number-3" > 1.1< / span > Long and Slow measurement< / h3 >
2020-10-29 10:07:20 +01:00
< div class = "outline-text-3" id = "text-1-1" >
2020-10-29 10:42:00 +01:00
< p >
The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).
< / p >
< 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 >
2020-11-02 16:03:55 +01:00
< div id = "org64c5513" class = "figure" >
2020-10-29 10:42:00 +01:00
< p > < img src = "figs/long_meas_time_domain_full.png" alt = "long_meas_time_domain_full.png" / >
< / p >
2020-11-02 16:03:55 +01:00
< p > < span class = "figure-number" > Figure 3: < / span > Long measurement time domain data< / p >
2020-10-29 10:42:00 +01:00
< / div >
< p >
2020-11-02 16:03:55 +01:00
Let’ s fit the data with a step response to a first order low pass filter (Figure < a href = "#orgc356556" > 4< / a > ).
2020-10-29 11:05:45 +01:00
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > f = @(b,x) b(1)< span class = "org-type" > *< / span > (1 < span class = "org-type" > -< / span > exp(< span class = "org-type" > -< / span > x< span class = "org-type" > /< / span > b(2)));
y_cur = x(t < span class = "org-type" > < < / span > 17< span class = "org-type" > *< / span > 60< span class = "org-type" > *< / span > 60);
t_cur = t(t < span class = "org-type" > < < / span > 17< span class = "org-type" > *< / span > 60< span class = "org-type" > *< / span > 60);
nrmrsd = @(b) norm(y_cur < span class = "org-type" > -< / span > f(b,t_cur)); < span class = "org-comment" > % Residual Norm Cost Function< / span >
B0 = [400e< span class = "org-type" > -< / span > 9, 2< span class = "org-type" > *< / span > 60< span class = "org-type" > *< / span > 60]; < span class = "org-comment" > % Choose Appropriate Initial Estimates< / span >
[B,rnrm] = fminsearch(nrmrsd, B0); < span class = "org-comment" > % Estimate Parameters ‘ B’ < / span >
< / pre >
< / div >
< p >
The corresponding time constant is (in [h]):
< / p >
< pre class = "example" >
2.0576
< / pre >
2020-10-29 11:07:35 +01:00
2020-11-02 16:03:55 +01:00
< div id = "orgc356556" class = "figure" >
2020-10-29 11:07:35 +01:00
< p > < img src = "figs/long_meas_time_domain_fit.png" alt = "long_meas_time_domain_fit.png" / >
2020-10-29 11:05:45 +01:00
< / p >
2020-11-02 16:03:55 +01:00
< 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 >
2020-10-29 11:07:35 +01:00
< / div >
2020-10-29 11:05:45 +01:00
< p >
2020-11-02 16:03:55 +01:00
We can see in Figure < a href = "#org64c5513" > 3< / a > that there is a transient period where the measured displacement experiences some drifts.
2020-10-29 10:42:00 +01:00
This is probably due to thermal effects.
We only select the data between < code > t1< / code > and < code > t2< / code > .
2020-11-02 16:03:55 +01:00
The obtained displacement is shown in Figure < a href = "#orgb851634" > 5< / a > .
2020-10-29 10:42:00 +01:00
< / p >
2020-10-29 10:07:20 +01:00
< div class = "org-src-container" >
2020-10-29 10:42:00 +01:00
< pre class = "src src-matlab" > t1 = 11; t2 = 17; < span class = "org-comment" > % [h]< / span >
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);
x = x < span class = "org-type" > -< / span > mean(x);
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);
t = t < span class = "org-type" > -< / span > t(1);
< / pre >
< / div >
2020-10-29 10:07:20 +01:00
2020-10-29 10:42:00 +01:00
2020-11-02 16:03:55 +01:00
< div id = "orgb851634" class = "figure" >
2020-10-29 10:42:00 +01:00
< p > < img src = "figs/long_meas_time_domain_zoom.png" alt = "long_meas_time_domain_zoom.png" / >
< / p >
2020-11-02 16:03:55 +01:00
< p > < span class = "figure-number" > Figure 5: < / span > Kept data (removed slow drifts during the first hours)< / p >
2020-10-29 10:42:00 +01:00
< / 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));
2020-10-29 10:07:20 +01:00
[p_1, f_1] = pwelch(x, win, [], [], 1< span class = "org-type" > /< / span > Ts);
< / pre >
< / div >
2020-11-02 16:03:55 +01:00
< 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’ 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" > < < / span > 2);
f_1 = f_1(f_1 < span class = "org-type" > < < / span > 2);
< / pre >
< / div >
2020-10-29 10:42:00 +01:00
< / div >
< / div >
2020-11-02 16:03:55 +01:00
< div id = "outline-container-org594bfe8" class = "outline-3" >
< h3 id = "org594bfe8" > < span class = "section-number-3" > 1.2< / span > Short and Fast measurement< / h3 >
2020-10-29 10:42:00 +01:00
< 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 >
2020-10-29 10:07:20 +01:00
< div class = "org-src-container" >
2020-11-02 16:03:55 +01:00
< pre class = "src src-matlab" > load(< span class = "org-string" > './mat/short_test_plastic.mat'< / span > )
2020-10-29 10:07:20 +01:00
Ts = 1e< span class = "org-type" > -< / span > 4; < span class = "org-comment" > % [s]< / span >
2020-10-29 10:42:00 +01:00
< / pre >
< / div >
2020-11-02 16:03:55 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > x = detrend(x, 0);
< / pre >
< / div >
2020-10-29 10:42:00 +01:00
< p >
2020-11-02 16:03:55 +01:00
The time domain measurement is shown in Figure < a href = "#orged82baf" > 6< / a > .
2020-10-29 10:42:00 +01:00
< / p >
2020-11-02 16:03:55 +01:00
< div id = "orged82baf" class = "figure" >
2020-10-29 10:42:00 +01:00
< p > < img src = "figs/short_meas_time_domain.png" alt = "short_meas_time_domain.png" / >
< / p >
2020-11-02 16:03:55 +01:00
< p > < span class = "figure-number" > Figure 6: < / span > Time domain measurement with the high sampling rate< / p >
2020-10-29 10:42:00 +01:00
< / div >
2020-10-29 10:07:20 +01:00
2020-10-29 10:42:00 +01:00
< p >
The Power Spectral Density of the measured displacement is computed
< / p >
< div class = "org-src-container" >
2020-11-02 16:03:55 +01:00
< pre class = "src src-matlab" > win = hann(ceil(length(x)< span class = "org-type" > /< / span > 10));
2020-10-29 10:07:20 +01:00
[p_2, f_2] = pwelch(x, win, [], [], 1< span class = "org-type" > /< / span > Ts);
< / pre >
< / div >
< / div >
< / div >
2020-10-29 10:42:00 +01:00
2020-11-02 16:03:55 +01:00
< 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 >
2020-10-29 10:42:00 +01:00
< div class = "outline-text-3" id = "text-1-3" >
< p >
2020-11-02 16:03:55 +01:00
The computed ASD of the two measurements are combined in Figure < a href = "#org5032549" > 7< / a > .
2020-10-29 10:42:00 +01:00
< / p >
2020-11-02 16:03:55 +01:00
< div id = "org5032549" class = "figure" >
2020-10-29 10:42:00 +01:00
< p > < img src = "figs/psd_combined.png" alt = "psd_combined.png" / >
< / p >
2020-11-02 16:03:55 +01:00
< 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 “ bubble sheet” 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 >
2020-10-29 10:42:00 +01:00
< / div >
< / div >
< / div >
2020-10-29 10:07:20 +01:00
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2020-11-02 16:03:55 +01:00
< p class = "date" > Created: 2020-11-02 lun. 16:03< / p >
2020-10-29 10:07:20 +01:00
< / div >
< / body >
< / html >
