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< title > Attocube - Test Bench< / title >
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< h1 class = "title" > Attocube - Test Bench< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
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< li > < a href = "#orga021312" > 1. Estimation of the Spectral Density of the Attocube Noise< / a >
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< ul >
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< li > < a href = "#orgb20f98b" > 1.1. Long and Slow measurement< / a > < / li >
< li > < a href = "#org8254ac0" > 1.2. Short and Fast measurement< / a > < / li >
< li > < a href = "#orgaf51073" > 1.3. Obtained Amplitude Spectral Density of the measured displacement< / a > < / li >
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< li > < a href = "#orgf208589" > 2. Effect of the “ bubble sheet” and < b > Aluminium tube< / b > < / a >
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< ul >
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< li > < a href = "#org90b8461" > 2.1. Aluminium Tube and Bubble Sheet< / a > < / li >
< li > < a href = "#org1034139" > 2.2. Only Aluminium Tube< / a > < / li >
< li > < a href = "#orgdc4cc8b" > 2.3. Nothing< / a > < / li >
< li > < a href = "#org9dbca5a" > 2.4. Comparison< / a > < / li >
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< h2 id = "orga021312" > < span class = "section-number-2" > 1< / span > Estimation of the Spectral Density of the Attocube Noise< / h2 >
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< p > < img src = "figs/test-bench-shematic.png" alt = "test-bench-shematic.png" / >
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< p > < span class = "figure-number" > Figure 1: < / span > Test Bench Schematic< / p >
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< p > < img src = "figs/IMG-7865.JPG" alt = "IMG-7865.JPG" / >
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< p > < span class = "figure-number" > Figure 2: < / span > Picture of the test bench. The Attocube and mirror are covered by a “ bubble sheet” < / p >
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< h3 id = "orgb20f98b" > < 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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< p >
The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).
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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 > )
Ts = 0.1; < span class = "org-comment" > % [s]< / span >
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< div id = "org5b16cc1" 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 > < span class = "figure-number" > Figure 3: < / span > Long measurement time domain data< / p >
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< p >
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Let’ s fit the data with a step response to a first order low pass filter (Figure < a href = "#orgf3ec0e8" > 4< / a > ).
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< 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 >
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The corresponding time constant is (in [h]):
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2.0576
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< div id = "orgf3ec0e8" class = "figure" >
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< p > < img src = "figs/long_meas_time_domain_fit.png" alt = "long_meas_time_domain_fit.png" / >
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< / p >
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< 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 >
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< p >
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We can see in Figure < a href = "#org5b16cc1" > 3< / 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.
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 = "#org7a26e27" > 5< / a > .
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< 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);
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< div id = "org7a26e27" 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 > < span class = "figure-number" > Figure 5: < / span > Kept data (removed slow drifts during the first hours)< / p >
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The Power Spectral Density of the measured displacement is computed
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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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< 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.
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< 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;
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Only frequencies below 2Hz are taken into account (high frequency noise will be measured afterwards).
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< 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);
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< h3 id = "org8254ac0" > < span class = "section-number-3" > 1.2< / span > Short and Fast measurement< / h3 >
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< 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 >
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< pre class = "src src-matlab" > load(< span class = "org-string" > './mat/short_test_plastic.mat'< / span > )
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Ts = 1e< span class = "org-type" > -< / span > 4; < span class = "org-comment" > % [s]< / span >
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< pre class = "src src-matlab" > x = detrend(x, 0);
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< p >
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The time domain measurement is shown in Figure < a href = "#orgcde3d83" > 6< / a > .
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< p > < img src = "figs/short_meas_time_domain.png" alt = "short_meas_time_domain.png" / >
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< p > < span class = "figure-number" > Figure 6: < / span > Time domain measurement with the high sampling rate< / p >
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The Power Spectral Density of the measured displacement is computed
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< pre class = "src src-matlab" > win = hann(ceil(length(x)< span class = "org-type" > /< / span > 10));
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[p_2, f_2] = pwelch(x, win, [], [], 1< span class = "org-type" > /< / span > Ts);
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< h3 id = "orgaf51073" > < span class = "section-number-3" > 1.3< / span > Obtained Amplitude Spectral Density of the measured displacement< / h3 >
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< p >
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The computed ASD of the two measurements are combined in Figure < a href = "#org9da7f60" > 7< / a > .
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< p > < img src = "figs/psd_combined.png" alt = "psd_combined.png" / >
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< p > < span class = "figure-number" > Figure 7: < / span > Obtained Amplitude Spectral Density of the measured displacement< / p >
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< h2 id = "orgf208589" > < span class = "section-number-2" > 2< / span > Effect of the “ bubble sheet” and < b > Aluminium tube< / b > < / h2 >
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< p > < img src = "figs/IMG-7864.JPG" alt = "IMG-7864.JPG" / >
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< p > < span class = "figure-number" > Figure 8: < / span > Aluminium tube used to protect the beam path from disturbances< / p >
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< h3 id = "org90b8461" > < span class = "section-number-3" > 2.1< / span > Aluminium Tube and Bubble Sheet< / h3 >
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< 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 >
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< pre class = "src src-matlab" > x = detrend(x, 0);
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< 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);
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< h3 id = "org1034139" > < span class = "section-number-3" > 2.2< / span > Only Aluminium Tube< / h3 >
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< 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 >
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< pre class = "src src-matlab" > x = detrend(x, 0);
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The time domain measurement is shown in Figure < a href = "#orgcde3d83" > 6< / a > .
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< / p >
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< 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);
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< h3 id = "orgdc4cc8b" > < span class = "section-number-3" > 2.3< / span > Nothing< / h3 >
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< h3 id = "org9dbca5a" > < span class = "section-number-3" > 2.4< / span > Comparison< / h3 >
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< div id = "org3fc64bb" class = "figure" >
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< p > < img src = "figs/asd_noise_comp_bubble_aluminium.png" alt = "asd_noise_comp_bubble_aluminium.png" / >
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< p > < span class = "figure-number" > Figure 9: < / span > Comparison of the noise ASD with and without bubble sheet< / p >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-11-02 lun. 16:06< / p >
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