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Thomas Dehaeze
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<title>Attocube - Test Bench</title>
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<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org31551fe">1. Estimation of the Spectral Density of the Attocube Noise</a>
<li><a href="#org904a034">1. Estimation of the Spectral Density of the Attocube Noise</a>
<ul>
<li><a href="#org2ca70e8">1.1. Long and Slow measurement</a></li>
<li><a href="#org4dffcb8">1.2. Short and Fast measurement</a></li>
<li><a href="#org83ac827">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
<li><a href="#org82d6608">1.1. Long and Slow measurement</a></li>
<li><a href="#org3c3c1f8">1.2. Short and Fast measurement</a></li>
<li><a href="#orgcaa0ccd">1.3. Obtained Amplitude Spectral Density of the measured displacement</a></li>
</ul>
</li>
<li><a href="#orgf63ae3e">2. Effect of the &ldquo;bubble sheet&rdquo; and &ldquo;Aluminium tube&rdquo;</a>
<li><a href="#org1b2ca10">2. Effect of the &ldquo;bubble sheet&rdquo; and &ldquo;Aluminium tube&rdquo;</a>
<ul>
<li><a href="#org1f1ce7f">2.1. Aluminium Tube and Bubble Sheet</a></li>
<li><a href="#orgb26f1e7">2.2. Only Aluminium Tube</a></li>
<li><a href="#org38d2ea6">2.3. Nothing</a></li>
<li><a href="#orgc931b82">2.4. Comparison</a></li>
<li><a href="#orgecd70c2">2.1. Aluminium Tube and Bubble Sheet</a></li>
<li><a href="#orgc9ed213">2.2. Only Aluminium Tube</a></li>
<li><a href="#org8e5170d">2.3. Nothing</a></li>
<li><a href="#org38a78d3">2.4. Comparison</a></li>
</ul>
</li>
<li><a href="#org8ec3157">3. Measurement of the Attocube&rsquo;s non-linearity</a>
<li><a href="#org2ece93a">3. Measurement of the Attocube&rsquo;s non-linearity</a>
<ul>
<li><a href="#orgd049784">3.1. Load Data</a></li>
<li><a href="#orga29027e">3.2. Time Domain Results</a></li>
<li><a href="#orgce6e0ff">3.3. Difference between Encoder and Interferometer as a function of time</a></li>
<li><a href="#org2008a1e">3.4. Difference between Encoder and Interferometer as a function of position</a></li>
<li><a href="#org224e296">3.1. Load Data</a></li>
<li><a href="#org587ad8c">3.2. Time Domain Results</a></li>
<li><a href="#orgbc1a5af">3.3. Difference between Encoder and Interferometer as a function of time</a></li>
<li><a href="#org50e2719">3.4. Difference between Encoder and Interferometer as a function of position</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org31551fe" class="outline-2">
<h2 id="org31551fe"><span class="section-number-2">1</span> Estimation of the Spectral Density of the Attocube Noise</h2>
<div id="outline-container-org904a034" class="outline-2">
<h2 id="org904a034"><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="org5b9ba48" class="figure">
<div id="org95807e5" class="figure">
<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Test Bench Schematic</p>
</div>
<div id="org9ef7a86" class="figure">
<div id="org7768f2f" 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-org2ca70e8" class="outline-3">
<h3 id="org2ca70e8"><span class="section-number-3">1.1</span> Long and Slow measurement</h3>
<div id="outline-container-org82d6608" class="outline-3">
<h3 id="org82d6608"><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 \(T_s = 0.1\,s\).
@@ -94,14 +93,14 @@ Ts = 0.1; <span class="org-comment">% [s]</span>
</div>
<div id="org4b6374b" class="figure">
<div id="orgcfab522" 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 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="#org36afa1e">4</a>).
Let&rsquo;s fit the data with a step response to a first order low pass filter (Figure <a href="#org3c0ac65">4</a>).
</p>
<div class="org-src-container">
@@ -125,17 +124,17 @@ The corresponding time constant is (in [h]):
<div id="org36afa1e" class="figure">
<div id="org3c0ac65" 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 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="#org4b6374b">3</a> that there is a transient period where the measured displacement experiences some drifts.
We can see in Figure <a href="#orgcfab522">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="#orgf2cfa94">5</a>.
The obtained displacement is shown in Figure <a href="#orgfb35792">5</a>.
</p>
<div class="org-src-container">
@@ -149,7 +148,7 @@ t = t <span class="org-type">-</span> t(1);
</div>
<div id="orgf2cfa94" class="figure">
<div id="orgfb35792" 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 5: </span>Kept data (removed slow drifts during the first hours)</p>
@@ -184,8 +183,8 @@ f_1 = f_1(f_1 <span class="org-type">&lt;</span> 2);
</div>
</div>
<div id="outline-container-org4dffcb8" class="outline-3">
<h3 id="org4dffcb8"><span class="section-number-3">1.2</span> Short and Fast measurement</h3>
<div id="outline-container-org3c3c1f8" class="outline-3">
<h3 id="org3c3c1f8"><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.
@@ -204,11 +203,11 @@ 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="#org0f2f571">6</a>.
The time domain measurement is shown in Figure <a href="#org526dbb8">6</a>.
</p>
<div id="org0f2f571" class="figure">
<div id="org526dbb8" class="figure">
<p><img src="figs/short_meas_time_domain.png" alt="short_meas_time_domain.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Time domain measurement with the high sampling rate</p>
@@ -225,15 +224,15 @@ The Power Spectral Density of the measured displacement is computed
</div>
</div>
<div id="outline-container-org83ac827" class="outline-3">
<h3 id="org83ac827"><span class="section-number-3">1.3</span> Obtained Amplitude Spectral Density of the measured displacement</h3>
<div id="outline-container-orgcaa0ccd" class="outline-3">
<h3 id="orgcaa0ccd"><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="#orga897ad9">7</a>.
The computed ASD of the two measurements are combined in Figure <a href="#orgcd7a108">7</a>.
</p>
<div id="orga897ad9" class="figure">
<div id="orgcd7a108" class="figure">
<p><img src="figs/psd_combined.png" alt="psd_combined.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Obtained Amplitude Spectral Density of the measured displacement</p>
@@ -242,19 +241,19 @@ The computed ASD of the two measurements are combined in Figure <a href="#orga89
</div>
</div>
<div id="outline-container-orgf63ae3e" class="outline-2">
<h2 id="orgf63ae3e"><span class="section-number-2">2</span> Effect of the &ldquo;bubble sheet&rdquo; and &ldquo;Aluminium tube&rdquo;</h2>
<div id="outline-container-org1b2ca10" class="outline-2">
<h2 id="org1b2ca10"><span class="section-number-2">2</span> Effect of the &ldquo;bubble sheet&rdquo; and &ldquo;Aluminium tube&rdquo;</h2>
<div class="outline-text-2" id="text-2">
<div id="orgff246fc" class="figure">
<div id="orgcda5fc5" 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-org1f1ce7f" class="outline-3">
<h3 id="org1f1ce7f"><span class="section-number-3">2.1</span> Aluminium Tube and Bubble Sheet</h3>
<div id="outline-container-orgecd70c2" class="outline-3">
<h3 id="orgecd70c2"><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/short_test_plastic.mat'</span>);
@@ -275,8 +274,8 @@ Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% [s]</span>
</div>
</div>
<div id="outline-container-orgb26f1e7" class="outline-3">
<h3 id="orgb26f1e7"><span class="section-number-3">2.2</span> Only Aluminium Tube</h3>
<div id="outline-container-orgc9ed213" class="outline-3">
<h3 id="orgc9ed213"><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/short_test_alu_tube.mat'</span>);
@@ -290,7 +289,7 @@ 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="#org0f2f571">6</a>.
The time domain measurement is shown in Figure <a href="#org526dbb8">6</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>10));
@@ -300,8 +299,8 @@ The time domain measurement is shown in Figure <a href="#org0f2f571">6</a>.
</div>
</div>
<div id="outline-container-org38d2ea6" class="outline-3">
<h3 id="org38d2ea6"><span class="section-number-3">2.3</span> Nothing</h3>
<div id="outline-container-org8e5170d" class="outline-3">
<h3 id="org8e5170d"><span class="section-number-3">2.3</span> Nothing</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/short_test_without_material.mat'</span>);
@@ -315,7 +314,7 @@ 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="#org0f2f571">6</a>.
The time domain measurement is shown in Figure <a href="#org526dbb8">6</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(length(x)<span class="org-type">/</span>10));
@@ -325,11 +324,11 @@ The time domain measurement is shown in Figure <a href="#org0f2f571">6</a>.
</div>
</div>
<div id="outline-container-orgc931b82" class="outline-3">
<h3 id="orgc931b82"><span class="section-number-3">2.4</span> Comparison</h3>
<div id="outline-container-org38a78d3" class="outline-3">
<h3 id="org38a78d3"><span class="section-number-3">2.4</span> Comparison</h3>
<div class="outline-text-3" id="text-2-4">
<div id="org0e0ae0d" class="figure">
<div id="orgda221c2" 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>
@@ -338,15 +337,29 @@ The time domain measurement is shown in Figure <a href="#org0f2f571">6</a>.
</div>
</div>
<div id="outline-container-org8ec3157" class="outline-2">
<h2 id="org8ec3157"><span class="section-number-2">3</span> Measurement of the Attocube&rsquo;s non-linearity</h2>
<div id="outline-container-org2ece93a" class="outline-2">
<h2 id="org2ece93a"><span class="section-number-2">3</span> Measurement of the Attocube&rsquo;s non-linearity</h2>
<div class="outline-text-2" id="text-3">
<p>
The measurement setup is shown in Figure <a href="#org30833d7">10</a>.
The measurement setup is shown in Figure <a href="#org7db5634">10</a>.
</p>
<div class="note" id="org292fd7d">
<p>
Here are the equipment used in the test bench:
</p>
<ul class="org-ul">
<li>Renishaw Resolution Encoder with 1nm resolution (<a href="doc/L-9517-9448-05-B_Data_sheet_RESOLUTE_BiSS_en.pdf">doc</a>)</li>
<li>Attocube interferometer (<a href="doc/IDS3010.pdf">doc</a>)</li>
<li>Cedrat Amplified Piezoelectric Actuator APA95ML (<a href="doc/APA95ML.pdf">doc</a>)</li>
<li>Voltage Amplifier LA75B (<a href="doc/LA75B.pdf">doc</a>)</li>
<li>Speedgoat IO131 with 16bits ADC and DAC (<a href="doc/IO130 IO131 OEM Datasheet.pdf">doc</a>)</li>
</ul>
<div id="org30833d7" class="figure">
</div>
<div id="org7db5634" class="figure">
<p><img src="figs/exp_setup_schematic.png" alt="exp_setup_schematic.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Schematic of the Experiment</p>
@@ -362,8 +375,8 @@ As will be shown shortly, this measurement permitted to measure the period non-l
</p>
</div>
<div id="outline-container-orgd049784" class="outline-3">
<h3 id="orgd049784"><span class="section-number-3">3.1</span> Load Data</h3>
<div id="outline-container-org224e296" class="outline-3">
<h3 id="org224e296"><span class="section-number-3">3.1</span> Load Data</h3>
<div class="outline-text-3" id="text-3-1">
<p>
The measurement data are loaded and the offset are removed using the <code>detrend</code> command.
@@ -384,11 +397,11 @@ u = detrend(u, 0);
</div>
</div>
<div id="outline-container-orga29027e" class="outline-3">
<h3 id="orga29027e"><span class="section-number-3">3.2</span> Time Domain Results</h3>
<div id="outline-container-org587ad8c" class="outline-3">
<h3 id="org587ad8c"><span class="section-number-3">3.2</span> Time Domain Results</h3>
<div class="outline-text-3" id="text-3-2">
<p>
One period of the displacement of the mass as measured by the encoder and interferometer are shown in Figure <a href="#orgeb04850">11</a>.
One period of the displacement of the mass as measured by the encoder and interferometer are shown in Figure <a href="#org5cfca4b">11</a>.
It consist of the sinusoidal motion at 0.5Hz with an amplitude of approximately \(70\mu m\).
</p>
@@ -398,18 +411,18 @@ This should improve the coherence between the measurements made by the encoder a
</p>
<div id="orgeb04850" class="figure">
<div id="org5cfca4b" class="figure">
<p><img src="figs/int_enc_one_cycle.png" alt="int_enc_one_cycle.png" />
</p>
<p><span class="figure-number">Figure 11: </span>One cycle measurement</p>
</div>
<p>
The difference between the two measurements during the same period is shown in Figure <a href="#org3ddfc88">12</a>.
The difference between the two measurements during the same period is shown in Figure <a href="#org58e59b1">12</a>.
</p>
<div id="org3ddfc88" class="figure">
<div id="org58e59b1" class="figure">
<p><img src="figs/int_enc_one_cycle_error.png" alt="int_enc_one_cycle_error.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Difference between the Encoder and the interferometer during one cycle</p>
@@ -417,8 +430,8 @@ The difference between the two measurements during the same period is shown in F
</div>
</div>
<div id="outline-container-orgce6e0ff" class="outline-3">
<h3 id="orgce6e0ff"><span class="section-number-3">3.3</span> Difference between Encoder and Interferometer as a function of time</h3>
<div id="outline-container-orgbc1a5af" class="outline-3">
<h3 id="orgbc1a5af"><span class="section-number-3">3.3</span> Difference between Encoder and Interferometer as a function of time</h3>
<div class="outline-text-3" id="text-3-3">
<p>
The data is filtered using a second order low pass filter with a cut-off frequency \(\omega_0\) as defined below.
@@ -433,7 +446,7 @@ G_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> 2<spa
</div>
<p>
After filtering, the data is &ldquo;re-shaped&rdquo; such that we can superimpose all the measured periods as shown in Figure <a href="#org18b1b55">13</a>.
After filtering, the data is &ldquo;re-shaped&rdquo; such that we can superimpose all the measured periods as shown in Figure <a href="#orgef18651">13</a>.
This gives an idea of the measurement error as given by the Attocube during a \(70 \mu m\) motion.
</p>
<div class="org-src-container">
@@ -443,7 +456,7 @@ d_err_mean = d_err_mean <span class="org-type">-</span> mean(d_err_mean);
</div>
<div id="org18b1b55" class="figure">
<div id="orgef18651" class="figure">
<p><img src="figs/int_enc_error_mean_time.png" alt="int_enc_error_mean_time.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Difference between the two measurement in the time domain, averaged for all the cycles</p>
@@ -451,17 +464,17 @@ d_err_mean = d_err_mean <span class="org-type">-</span> mean(d_err_mean);
</div>
</div>
<div id="outline-container-org2008a1e" class="outline-3">
<h3 id="org2008a1e"><span class="section-number-3">3.4</span> Difference between Encoder and Interferometer as a function of position</h3>
<div id="outline-container-org50e2719" class="outline-3">
<h3 id="org50e2719"><span class="section-number-3">3.4</span> Difference between Encoder and Interferometer as a function of position</h3>
<div class="outline-text-3" id="text-3-4">
<p>
Figure <a href="#org18b1b55">13</a> gives the measurement error as a function of time.
Figure <a href="#orgef18651">13</a> gives the measurement error as a function of time.
We here wish the compute this measurement error as a function of the position (as measured by the encoer).
</p>
<p>
To do so, all the attocube measurements corresponding to each position measured by the Encoder (resolution of \(1nm\)) are averaged.
Figure <a href="#orgdfccfb5">14</a> is obtained where we clearly see an error with a period comparable to the motion range and a much smaller period corresponding to the non-linear period errors that we wish the estimate.
Figure <a href="#orgfbf0bc5">14</a> is obtained where we clearly see an error with a period comparable to the motion range and a much smaller period corresponding to the non-linear period errors that we wish the estimate.
</p>
<div class="org-src-container">
<pre class="src src-matlab">[e_sorted, <span class="org-type">~</span>, e_ind] = unique(encoder);
@@ -476,7 +489,7 @@ i_mean_error = (i_mean <span class="org-type">-</span> e_sorted);
</div>
<div id="orgdfccfb5" class="figure">
<div id="orgfbf0bc5" class="figure">
<p><img src="figs/int_enc_error_mean_position.png" alt="int_enc_error_mean_position.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles</p>
@@ -498,11 +511,11 @@ e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init<span class="org-typ
</div>
<p>
The obtained periodic non-linearity is shown in Figure <a href="#orgcfbb9a2">15</a>.
The obtained periodic non-linearity is shown in Figure <a href="#org9e948e3">15</a>.
</p>
<div id="orgcfbb9a2" class="figure">
<div id="org9e948e3" class="figure">
<p><img src="figs/int_non_linearity_period_wavelength.png" alt="int_non_linearity_period_wavelength.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Non-Linearity of the Interferometer over the period of the wavelength</p>
@@ -513,7 +526,7 @@ The obtained periodic non-linearity is shown in Figure <a href="#orgcfbb9a2">15<
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-10 mar. 09:53</p>
<p class="date">Created: 2020-11-10 mar. 10:21</p>
</div>
</body>
</html>