long measurements

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Analyse long measurement
2021-02-17 11:14:29 +01:00 · 2021-02-12 18:26:24 +01:00 · 2021-02-11 15:22:02 +01:00 · 2021-02-11 13:48:19 +01:00 · 2021-02-11 10:17:38 +01:00 · 2021-02-11 10:16:58 +01:00
42 changed files with 2522 additions and 338 deletions
--- a/encoder-model-schematic.pdf
+++ b/encoder-model-schematic.pdf
--- a/figs/IMG_20210211_170551.jpg
+++ b/figs/IMG_20210211_170551.jpg
--- a/figs/IMG_20210211_170554.jpg
+++ b/figs/IMG_20210211_170554.jpg
--- a/figs/IMG_20210211_170607.jpg
+++ b/figs/IMG_20210211_170607.jpg
--- a/figs/encoder-model-schematic-with-asd.pdf
+++ b/figs/encoder-model-schematic-with-asd.pdf
--- a/figs/encoder-model-schematic-with-asd.png
+++ b/figs/encoder-model-schematic-with-asd.png
--- a/figs/encoder-model-schematic-with-asd.svg
+++ b/figs/encoder-model-schematic-with-asd.svg
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--- a/figs/encoder_vionic.pdf
+++ b/figs/encoder_vionic.pdf
--- a/figs/vionic_drifts_linear_fit.pdf
+++ b/figs/vionic_drifts_linear_fit.pdf
--- a/figs/vionic_drifts_linear_fit.png
+++ b/figs/vionic_drifts_linear_fit.png
--- a/figs/vionic_drifts_time.pdf
+++ b/figs/vionic_drifts_time.pdf
--- a/figs/vionic_drifts_time.png
+++ b/figs/vionic_drifts_time.png
--- a/figs/vionic_noise_asd.pdf
+++ b/figs/vionic_noise_asd.pdf
--- a/figs/vionic_noise_asd.png
+++ b/figs/vionic_noise_asd.png
--- a/figs/vionic_noise_asd_combined.pdf
+++ b/figs/vionic_noise_asd_combined.pdf
--- a/figs/vionic_noise_asd_combined.png
+++ b/figs/vionic_noise_asd_combined.png
--- a/figs/vionic_noise_asd_low_freq.pdf
+++ b/figs/vionic_noise_asd_low_freq.pdf
--- a/figs/vionic_noise_asd_low_freq.png
+++ b/figs/vionic_noise_asd_low_freq.png
--- a/figs/vionic_noise_asd_model.pdf
+++ b/figs/vionic_noise_asd_model.pdf
--- a/figs/vionic_noise_asd_model.png
+++ b/figs/vionic_noise_asd_model.png
--- a/figs/vionic_noise_cas_model.pdf
+++ b/figs/vionic_noise_cas_model.pdf
--- a/figs/vionic_noise_cas_model.png
+++ b/figs/vionic_noise_cas_model.png
--- a/figs/vionic_noise_raw_lpf.pdf
+++ b/figs/vionic_noise_raw_lpf.pdf
--- a/figs/vionic_noise_raw_lpf.png
+++ b/figs/vionic_noise_raw_lpf.png
--- a/figs/vionic_noise_time.pdf
+++ b/figs/vionic_noise_time.pdf
--- a/figs/vionic_noise_time.png
+++ b/figs/vionic_noise_time.png
--- a/index.html
+++ b/index.html
@@ -1,200 +0,0 @@
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-<head>
-<!-- 2021-01-04 lun. 11:44 -->
-<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
-<title>Encoder Renishaw Vionic - Test Bench</title>
-<meta name="generator" content="Org mode" />
-<meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
-<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
-<script>MathJax = {
-          tex: {
-            tags: 'ams',
-            macros: {bm: ["\\boldsymbol{#1}",1],}
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-          </script>
-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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-<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">Encoder Renishaw Vionic - Test Bench</h1>
-<div id="table-of-contents">
-<h2>Table of Contents</h2>
-<div id="text-table-of-contents">
-<ul>
-<li><a href="#org55157ef">1. Encoder Model</a></li>
-<li><a href="#org8ef40ec">2. Test-Bench Description</a></li>
-<li><a href="#orgce223ed">3. Measurement procedure</a></li>
-<li><a href="#org51852cb">4. Measurement Results</a></li>
-</ul>
-</div>
-</div>
-
-<div class="note" id="org4436bab">
-<p>
-You can find below the document of:
-</p>
-<ul class="org-ul">
-<li><a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Vionic Encoder</a></li>
-<li><a href="doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf">Linear Scale</a></li>
-</ul>
-
-</div>
-
-<p>
-We would like to characterize the encoder measurement system.
-</p>
-
-<p>
-In particular, we would like to measure:
-</p>
-<ul class="org-ul">
-<li>Power Spectral Density of the measurement noise</li>
-<li>Bandwidth of the sensor</li>
-<li>Linearity of the sensor</li>
-</ul>
-
-
-<div id="orgeb4726b" class="figure">
-<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
-</p>
-<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
-</div>
-
-<div id="outline-container-org55157ef" class="outline-2">
-<h2 id="org55157ef"><span class="section-number-2">1</span> Encoder Model</h2>
-<div class="outline-text-2" id="text-1">
-<p>
-The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; displacement \(y\) to measured displacement \(y_m\).
-Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
-</p>
-
-<p>
-It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD).
-</p>
-
-<p>
-The model of the encoder is shown in Figure <a href="#org2d59f14">2</a>.
-</p>
-
-
-<div id="org2d59f14" class="figure">
-<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
-</p>
-<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
-</div>
-
-
-<table id="org476b3d6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
-<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption>
-
-<colgroup>
-<col  class="org-left" />
-
-<col  class="org-left" />
-</colgroup>
-<thead>
-<tr>
-<th scope="col" class="org-left"><b>Characteristics</b></th>
-<th scope="col" class="org-left"><b>Manual</b></th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td class="org-left">Resolution</td>
-<td class="org-left">2.5nm</td>
-</tr>
-
-<tr>
-<td class="org-left">Sub-Divisional Error</td>
-<td class="org-left">\(< \pm 15\,nm\)</td>
-</tr>
-
-<tr>
-<td class="org-left">Bandwidth</td>
-<td class="org-left">&gt; 50 kHz</td>
-</tr>
-</tbody>
-</table>
-
-
-
-<div id="orgb8bf3d5" class="figure">
-<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
-</p>
-<p><span class="figure-number">Figure 3: </span>Expected interpolation errors for the Vionic Encoder</p>
-</div>
-</div>
-</div>
-
-
-<div id="outline-container-org8ef40ec" class="outline-2">
-<h2 id="org8ef40ec"><span class="section-number-2">2</span> Test-Bench Description</h2>
-<div class="outline-text-2" id="text-2">
-<p>
-To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
-Then, the measured signal \(y_m\) corresponds to the noise \(n\).
-</p>
-
-<p>
-In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
-An interferometer or capacitive sensor should work fine.
-An actuator should also be there so impose a displacement.
-</p>
-
-<p>
-One idea is to use the test-bench shown in Figure <a href="#org1fd5a94">4</a>.
-</p>
-
-<p>
-The APA300ML is used to excite the mass in a broad bandwidth.
-The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
-</p>
-
-<p>
-As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder is it is less than the Nyquist frequency (~ 5kHz).
-</p>
-
-
-<div id="org1fd5a94" class="figure">
-<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
-</p>
-<p><span class="figure-number">Figure 4: </span>Schematic of the test bench</p>
-</div>
-
-<p>
-To measure the noise of the sensor, we can also simply measure the output signal when the relative motion between the encoder and the ruler is null.
-This can be done by clamping the two as done in the mounting strut tool (Figure <a href="#orgab0ed8d">5</a>).
-</p>
-
-
-<div id="orgab0ed8d" class="figure">
-<p><img src="figs/test_bench_measure_noise.png" alt="test_bench_measure_noise.png" />
-</p>
-<p><span class="figure-number">Figure 5: </span>Mounting Strut test bench as a clamping method to measure the encoder noise.</p>
-</div>
-</div>
-</div>
-
-<div id="outline-container-orgce223ed" class="outline-2">
-<h2 id="orgce223ed"><span class="section-number-2">3</span> Measurement procedure</h2>
-</div>
-
-<div id="outline-container-org51852cb" class="outline-2">
-<h2 id="org51852cb"><span class="section-number-2">4</span> Measurement Results</h2>
-</div>
-</div>
-<div id="postamble" class="status">
-<p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2021-01-04 lun. 11:44</p>
-</div>
-</body>
-</html>
--- a/index.html
+++ b/index.html
@@ -0,0 +1 @@
+test-bench-vionic.html
--- a/index.org
+++ b/index.org
@@ -1,138 +0,0 @@
-#+TITLE: Encoder Renishaw Vionic - Test Bench
-:DRAWER:
-#+LANGUAGE: en
-#+EMAIL: dehaeze.thomas@gmail.com
-#+AUTHOR: Dehaeze Thomas
-
-#+HTML_LINK_HOME: ../index.html
-#+HTML_LINK_UP:   ../index.html
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-
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-#+PROPERTY: header-args:latex+ :mkdirp yes
-#+PROPERTY: header-args:latex+ :output-dir figs
-#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
-:END:
-
-* Introduction                                                        :ignore:
-
-#+begin_note
-You can find below the document of:
- [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic Encoder]]
- [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Linear Scale]]
-#+end_note
-
-We would like to characterize the encoder measurement system.
-
-In particular, we would like to measure:
- Power Spectral Density of the measurement noise
- Bandwidth of the sensor
- Linearity of the sensor
-
-#+name: fig:encoder_vionic
-#+caption: Picture of the Vionic Encoder
-[[file:figs/encoder_vionic.png]]
-
-* Encoder Model
-The Encoder is characterized by its dynamics $G_m(s)$ from the "true" displacement $y$ to measured displacement $y_m$.
-Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
-
-It is also characterized by its measurement noise $n$ that can be described by its Power Spectral Density (PSD).
-
-The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
-
-#+begin_src latex :file encoder-model-schematic.pdf
-  \begin{tikzpicture}
-    \node[block] (G) at (0,0){$G_m(s)$};
-    \node[addb, left=0.8 of G] (add){};
-
-    \draw[<-] (add.west) -- ++(-1.0, 0) node[above right]{$y$};
-    \draw[->] (add.east) -- (G.west);
-    \draw[->] (G.east) -- ++(1.0, 0) node[above left]{$y_m$};
-    \draw[<-] (add.north) -- ++(0, 0.6) node[below right](n){$n$};
-
-    \begin{scope}[on background layer]
-      \node[fit={(add.west|-G.south) (n.north-|G.east)}, inner sep=8pt, draw, dashed, fill=black!20!white] (P) {};
-      \node[below left] at (P.north east) {Encoder};
-    \end{scope}
-  \end{tikzpicture}
-#+end_src
-
-#+name: fig:encoder-model-schematic
-#+caption: Model of the Encoder
-#+RESULTS:
-[[file:figs/encoder-model-schematic.png]]
-
-
-#+name: tab:vionic_characteristics_manual
-#+caption: Characteristics of the Vionic Encoder
-#+attr_latex: :environment tabularx :width \linewidth :align lXX
-#+attr_latex: :center t :booktabs t :float t
-| *Characteristics*    | *Manual*       |
-|----------------------+----------------|
-| Resolution           | 2.5nm          |
-| Sub-Divisional Error | $< \pm 15\,nm$ |
-| Bandwidth            | > 50 kHz       |
-
-
-#+name: fig:vionic_expected_noise
-#+caption: Expected interpolation errors for the Vionic Encoder
-[[file:./figs/vionic_expected_noise.png]]
-
-
-* Test-Bench Description
-
-To measure the noise $n$ of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
-Then, the measured signal $y_m$ corresponds to the noise $n$.
-
-In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
-An interferometer or capacitive sensor should work fine.
-An actuator should also be there so impose a displacement.
-
-One idea is to use the test-bench shown in Figure [[fig:test_bench_encoder_calibration]].
-
-The APA300ML is used to excite the mass in a broad bandwidth.
-The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
-
-As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder is it is less than the Nyquist frequency (~ 5kHz).
-
-#+name: fig:test_bench_encoder_calibration
-#+caption: Schematic of the test bench
-[[file:figs/test_bench_encoder_calibration.png]]
-
-To measure the noise of the sensor, we can also simply measure the output signal when the relative motion between the encoder and the ruler is null.
-This can be done by clamping the two as done in the mounting strut tool (Figure [[fig:test_bench_measure_noise]]).
-
-#+name: fig:test_bench_measure_noise
-#+caption: Mounting Strut test bench as a clamping method to measure the encoder noise.
-[[file:figs/test_bench_measure_noise.png]]
-
-* Measurement procedure
-
-* Measurement Results
--- a/matlab/mat/noise_meas_100Hz_without_AGC.mat
+++ b/matlab/mat/noise_meas_100Hz_without_AGC.mat
--- a/matlab/mat/noise_meas_100s_20kHz_1.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_1.mat
--- a/matlab/mat/noise_meas_100s_20kHz_2.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_2.mat
--- a/matlab/mat/noise_meas_100s_20kHz_3.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_3.mat
--- a/matlab/mat/noise_meas_100s_20kHz_4.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_4.mat
--- a/matlab/mat/noise_meas_100s_20kHz_5.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_5.mat
--- a/matlab/mat/noise_meas_100s_20kHz_6.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_6.mat
--- a/matlab/mat/noise_meas_100s_20kHz_7.mat
+++ b/matlab/mat/noise_meas_100s_20kHz_7.mat
--- a/matlab/mat/noise_meas_17h_200Hz_1.mat
+++ b/matlab/mat/noise_meas_17h_200Hz_1.mat
--- a/matlab/mat/noise_meas_40h_100Hz_1.mat
+++ b/matlab/mat/noise_meas_40h_100Hz_1.mat
--- a/matlab/mat/noise_meas_80h_100Hz_1.mat
+++ b/matlab/mat/noise_meas_80h_100Hz_1.mat
--- a/test-bench-vionic.html
+++ b/test-bench-vionic.html
@@ -0,0 +1,510 @@
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+"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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+<head>
+<!-- 2021-02-12 ven. 18:26 -->
+<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
+<title>Encoder Renishaw Vionic - Test Bench</title>
+<meta name="generator" content="Org mode" />
+<meta name="author" content="Dehaeze Thomas" />
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+<script>
+           MathJax = {
+             svg: {
+               scale: 1,
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+               tags: "ams",
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+                       macros: {bm: ["\\boldsymbol{#1}",1],},
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+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
+</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">Encoder Renishaw Vionic - Test Bench</h1>
+<div id="table-of-contents">
+<h2>Table of Contents</h2>
+<div id="text-table-of-contents">
+<ul>
+<li><a href="#orgfa3d11e">1. Expected Performances</a></li>
+<li><a href="#orgf23b21b">2. Encoder Model</a></li>
+<li><a href="#org9c17913">3. Noise Measurement</a>
+<ul>
+<li><a href="#orgb9429ef">3.1. Test Bench</a></li>
+<li><a href="#orgd9c9c77">3.2. Thermal drifts</a></li>
+<li><a href="#org8ec1ba2">3.3. Time Domain signals</a></li>
+<li><a href="#org833451c">3.4. Noise Spectral Density</a></li>
+<li><a href="#org71a7d07">3.5. Noise Model</a></li>
+</ul>
+</li>
+<li><a href="#org61522ff">4. Linearity Measurement</a>
+<ul>
+<li><a href="#orge455e25">4.1. Test Bench</a></li>
+<li><a href="#orgc6e5044">4.2. Results</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</div>
+<hr>
+<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
+<hr>
+
+<div class="note" id="orge01a92a">
+<p>
+You can find below the documentation of:
+</p>
+<ul class="org-ul">
+<li><a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Vionic Encoder</a></li>
+<li><a href="doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf">Linear Scale</a></li>
+</ul>
+
+</div>
+
+<p>
+In this document, we wish to characterize the performances of the encoder measurement system.
+In particular, we would like to measure:
+</p>
+<ul class="org-ul">
+<li>the measurement noise</li>
+<li>the linearity of the sensor</li>
+<li>the bandwidth of the sensor</li>
+</ul>
+
+<p>
+This document is structured as follow:
+</p>
+<ul class="org-ul">
+<li>Section <a href="#org5ddac7d">1</a>: the expected performance of the Vionic encoder system are described</li>
+<li>Section <a href="#org55cdc69">2</a>: a simple model of the encoder is developed</li>
+<li>Section <a href="#orgb828c8d">3</a>: the noise of the encoder is measured and a model of the noise is identified</li>
+<li>Section <a href="#org49975c3">4</a>: the linearity of the sensor is estimated</li>
+</ul>
+
+<div id="outline-container-orgfa3d11e" class="outline-2">
+<h2 id="orgfa3d11e"><span class="section-number-2">1</span> Expected Performances</h2>
+<div class="outline-text-2" id="text-1">
+<p>
+<a id="org5ddac7d"></a>
+</p>
+
+<p>
+The Vionic encoder is shown in Figure <a href="#orga0ecb6c">1</a>.
+</p>
+
+
+<div id="orga0ecb6c" class="figure">
+<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
+</p>
+<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
+</div>
+
+<p>
+From the Renishaw <a href="https://www.renishaw.com/en/how-optical-encoders-work--36979">website</a>:
+</p>
+<blockquote>
+<p>
+The VIONiC encoder features the third generation of Renishaw&rsquo;s unique filtering optics that average the contributions from many scale periods and effectively filter out non-periodic features such as dirt.
+The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector.
+Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals.
+These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining <b>bandwidth to beyond 500 kHz</b>.
+</p>
+
+<p>
+Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure <b>ultra-low Sub-Divisional Error (SDE) of typically</b> \(<\pm 15\, nm\).
+</p>
+
+<p>
+This evolution of filtering optics, combined with carefully-selected electronics, provide incremental signals with wide bandwidth achieving a maximum speed of 12 m/s with the lowest positional jitter (noise) of any encoder in its class.
+Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve <b>jitter of just 1.6 nm RMS</b>.
+</p>
+</blockquote>
+
+<p>
+The expected interpolation errors (non-linearity) is shown in Figure <a href="#orgc38e53f">2</a>.
+</p>
+
+
+<div id="orgc38e53f" class="figure">
+<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
+</p>
+<p><span class="figure-number">Figure 2: </span>Expected interpolation errors for the Vionic Encoder</p>
+</div>
+
+<p>
+The characteristics as advertise in the manual as well as our specifications are shown in Table <a href="#org091f419">1</a>.
+</p>
+
+<table id="org091f419" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic compared with the specifications</caption>
+
+<colgroup>
+<col  class="org-left" />
+
+<col  class="org-center" />
+
+<col  class="org-center" />
+</colgroup>
+<thead>
+<tr>
+<th scope="col" class="org-left"><b>Characteristics</b></th>
+<th scope="col" class="org-center"><b>Manual</b></th>
+<th scope="col" class="org-center"><b>Specification</b></th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="org-left">Time Delay</td>
+<td class="org-center">&lt; 10 ns</td>
+<td class="org-center">&lt; 0.5 ms</td>
+</tr>
+
+<tr>
+<td class="org-left">Bandwidth</td>
+<td class="org-center">&gt; 500 kHz</td>
+<td class="org-center">&gt; 5 kHz</td>
+</tr>
+
+<tr>
+<td class="org-left">Noise</td>
+<td class="org-center">&lt; 1.6 nm rms</td>
+<td class="org-center">&lt; 50 nm rms</td>
+</tr>
+
+<tr>
+<td class="org-left">Linearity</td>
+<td class="org-center">&lt; +/- 15 nm</td>
+<td class="org-center">&#xa0;</td>
+</tr>
+
+<tr>
+<td class="org-left">Range</td>
+<td class="org-center">Ruler length</td>
+<td class="org-center">&gt; 200 um</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+
+<div id="outline-container-orgf23b21b" class="outline-2">
+<h2 id="orgf23b21b"><span class="section-number-2">2</span> Encoder Model</h2>
+<div class="outline-text-2" id="text-2">
+<p>
+<a id="org55cdc69"></a>
+</p>
+
+<p>
+The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; displacement \(y\) to measured displacement \(y_m\).
+Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
+</p>
+
+<p>
+It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD) \(\Gamma_n(\omega)\).
+</p>
+
+<p>
+The model of the encoder is shown in Figure <a href="#org4fdb73a">3</a>.
+</p>
+
+
+<div id="org4fdb73a" class="figure">
+<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
+</p>
+<p><span class="figure-number">Figure 3: </span>Model of the Encoder</p>
+</div>
+
+<p>
+We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure <a href="#orgc38e53f">2</a>.
+</p>
+
+
+<div id="org793433f" class="figure">
+<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
+</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org9c17913" class="outline-2">
+<h2 id="org9c17913"><span class="section-number-2">3</span> Noise Measurement</h2>
+<div class="outline-text-2" id="text-3">
+<p>
+<a id="orgb828c8d"></a>
+</p>
+<p>
+This part is structured as follow:
+</p>
+<ul class="org-ul">
+<li>Section <a href="#org8cfb922">3.1</a>: the measurement bench is described</li>
+<li>Section <a href="#orgfd5ce06">3.2</a>: long measurement is performed to estimate the low frequency drifts in the measurement</li>
+<li>Section <a href="#org4df45c5">3.3</a>: high frequency measurements are performed to estimate the high frequency noise</li>
+<li>Section <a href="#orgd464562">3.4</a>: the Spectral density of the measurement noise is estimated</li>
+<li>Section <a href="#orgd6ec52a">3.5</a>: finally, the measured noise is modeled</li>
+</ul>
+</div>
+
+<div id="outline-container-orgb9429ef" class="outline-3">
+<h3 id="orgb9429ef"><span class="section-number-3">3.1</span> Test Bench</h3>
+<div class="outline-text-3" id="text-3-1">
+<p>
+<a id="org8cfb922"></a>
+</p>
+
+<p>
+To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
+Then, the measured signal \(y_m\) corresponds to the noise \(n\).
+</p>
+
+<p>
+The measurement bench is shown in Figures <a href="#org4037996">5</a> and <a href="#org06e2754">6</a>.
+Note that the bench is then covered with a &ldquo;plastic bubble sheet&rdquo; in order to keep disturbances as small as possible.
+</p>
+
+
+<div id="org4037996" class="figure">
+<p><img src="figs/IMG_20210211_170554.jpg" alt="IMG_20210211_170554.jpg" />
+</p>
+<p><span class="figure-number">Figure 5: </span>Top view picture of the measurement bench</p>
+</div>
+
+
+<div id="org06e2754" class="figure">
+<p><img src="figs/IMG_20210211_170607.jpg" alt="IMG_20210211_170607.jpg" />
+</p>
+<p><span class="figure-number">Figure 6: </span>Side view picture of the measurement bench</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-orgd9c9c77" class="outline-3">
+<h3 id="orgd9c9c77"><span class="section-number-3">3.2</span> Thermal drifts</h3>
+<div class="outline-text-3" id="text-3-2">
+<p>
+<a id="orgfd5ce06"></a>
+Measured displacement were recording during approximately 40 hours with a sample frequency of 100Hz.
+A first order low pass filter with a corner frequency of 1Hz
+</p>
+
+<div class="org-src-container">
+<pre class="src src-matlab">enc_l = load(<span class="org-string">'mat/noise_meas_40h_100Hz_1.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
+</pre>
+</div>
+
+<p>
+The measured time domain data are shown in Figure <a href="#org1454db4">7</a>.
+</p>
+
+<div id="org1454db4" class="figure">
+<p><img src="figs/vionic_drifts_time.png" alt="vionic_drifts_time.png" />
+</p>
+<p><span class="figure-number">Figure 7: </span>Measured thermal drifts</p>
+</div>
+
+<p>
+The measured data seems to experience a constant drift after approximately 20 hour.
+Let&rsquo;s estimate this drift.
+</p>
+
+<pre class="example">
+The mean drift is approximately 60.9 [nm/hour] or 1.0 [nm/min]
+</pre>
+
+
+<p>
+Comparison between the data and the linear fit is shown in Figure <a href="#orgfbe5f53">8</a>.
+</p>
+
+<div id="orgfbe5f53" class="figure">
+<p><img src="figs/vionic_drifts_linear_fit.png" alt="vionic_drifts_linear_fit.png" />
+</p>
+<p><span class="figure-number">Figure 8: </span>Measured drift and linear fit</p>
+</div>
+
+<p>
+Let&rsquo;s now estimate the Power Spectral Density of the measured displacement.
+The obtained low frequency ASD is shown in Figure <a href="#org42f3fad">9</a>.
+</p>
+
+<div id="org42f3fad" class="figure">
+<p><img src="figs/vionic_noise_asd_low_freq.png" alt="vionic_noise_asd_low_freq.png" />
+</p>
+<p><span class="figure-number">Figure 9: </span>Amplitude Spectral density of the measured displacement</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org8ec1ba2" class="outline-3">
+<h3 id="org8ec1ba2"><span class="section-number-3">3.3</span> Time Domain signals</h3>
+<div class="outline-text-3" id="text-3-3">
+<p>
+<a id="org4df45c5"></a>
+</p>
+
+<p>
+Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz.
+</p>
+
+<p>
+The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure <a href="#org28ad5da">10</a>.
+</p>
+
+<div id="org28ad5da" class="figure">
+<p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" />
+</p>
+<p><span class="figure-number">Figure 10: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</p>
+</div>
+
+<p>
+The time domain data for all the encoders are compared in Figure <a href="#org1656541">11</a>.
+</p>
+
+<p>
+We can see some drifts that are in the order of few nm to 20nm per minute.
+As shown in Section <a href="#orgfd5ce06">3.2</a>, these drifts should diminish over time down to 1nm/min.
+</p>
+
+<div id="org1656541" class="figure">
+<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
+</p>
+<p><span class="figure-number">Figure 11: </span>Comparison of the time domain measurement</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org833451c" class="outline-3">
+<h3 id="org833451c"><span class="section-number-3">3.4</span> Noise Spectral Density</h3>
+<div class="outline-text-3" id="text-3-4">
+<p>
+<a id="orgd464562"></a>
+</p>
+
+<p>
+The amplitude spectral densities for all the encoder are computed and shown in Figure <a href="#org7e93bb1">12</a>.
+</p>
+
+<div id="org7e93bb1" class="figure">
+<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
+</p>
+<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the measured signal</p>
+</div>
+
+<p>
+We can combine these measurements with the low frequency noise computed in Section <a href="#orgfd5ce06">3.2</a>.
+The obtained ASD is shown in Figure <a href="#org7e54160">13</a>.
+</p>
+
+<div id="org7e54160" class="figure">
+<p><img src="figs/vionic_noise_asd_combined.png" alt="vionic_noise_asd_combined.png" />
+</p>
+<p><span class="figure-number">Figure 13: </span>Combined low frequency and high frequency noise measurements</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org71a7d07" class="outline-3">
+<h3 id="org71a7d07"><span class="section-number-3">3.5</span> Noise Model</h3>
+<div class="outline-text-3" id="text-3-5">
+<p>
+<a id="orgd6ec52a"></a>
+</p>
+
+<p>
+Let&rsquo;s create a transfer function that approximate the measured noise of the encoder.
+</p>
+<div class="org-src-container">
+<pre class="src src-matlab">Gn_e = 1.8e<span class="org-type">-</span>11<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><span class="org-type">/</span>1e4);
+</pre>
+</div>
+
+<p>
+The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org5d39757">14</a>.
+</p>
+
+
+<div id="org5d39757" class="figure">
+<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
+</p>
+<p><span class="figure-number">Figure 14: </span>Measured ASD of the noise and modeled one</p>
+</div>
+
+<p>
+The cumulative amplitude spectrum is now computed and shown in Figure <a href="#org05b258c">15</a>.
+</p>
+
+<p>
+We can see that the Root Mean Square value of the measurement noise is \(\approx 1.6 \, nm\) as advertise in the datasheet.
+</p>
+
+
+<div id="org05b258c" class="figure">
+<p><img src="figs/vionic_noise_cas_model.png" alt="vionic_noise_cas_model.png" />
+</p>
+<p><span class="figure-number">Figure 15: </span>Meassured CAS of the noise and modeled one</p>
+</div>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org61522ff" class="outline-2">
+<h2 id="org61522ff"><span class="section-number-2">4</span> Linearity Measurement</h2>
+<div class="outline-text-2" id="text-4">
+<p>
+<a id="org49975c3"></a>
+</p>
+</div>
+<div id="outline-container-orge455e25" class="outline-3">
+<h3 id="orge455e25"><span class="section-number-3">4.1</span> Test Bench</h3>
+<div class="outline-text-3" id="text-4-1">
+<p>
+In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
+An interferometer or capacitive sensor should work fine.
+An actuator should also be there so impose a displacement.
+</p>
+
+<p>
+One idea is to use the test-bench shown in Figure <a href="#org177aa2c">16</a>.
+</p>
+
+<p>
+The APA300ML is used to excite the mass in a broad bandwidth.
+The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
+</p>
+
+<p>
+As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder if it is less than the Nyquist frequency that can be around 10kHz.
+</p>
+
+
+<div id="org177aa2c" class="figure">
+<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
+</p>
+<p><span class="figure-number">Figure 16: </span>Schematic of the test bench</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-orgc6e5044" class="outline-3">
+<h3 id="orgc6e5044"><span class="section-number-3">4.2</span> Results</h3>
+</div>
+</div>
+</div>
+<div id="postamble" class="status">
+<p class="author">Author: Dehaeze Thomas</p>
+<p class="date">Created: 2021-02-12 ven. 18:26</p>
+</div>
+</body>
+</html>
--- a/test-bench-vionic.org
+++ b/test-bench-vionic.org
@@ -0,0 +1,572 @@
+#+TITLE: Encoder Renishaw Vionic - Test Bench
+:DRAWER:
+#+LANGUAGE: en
+#+EMAIL: dehaeze.thomas@gmail.com
+#+AUTHOR: Dehaeze Thomas
+
+#+HTML_LINK_HOME: ../index.html
+#+HTML_LINK_UP:   ../index.html
+
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+
+#+BIND: org-latex-image-default-option "scale=1"
+#+BIND: org-latex-image-default-width ""
+
+#+LaTeX_CLASS: scrreprt
+#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
+#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
+
+#+PROPERTY: header-args:matlab  :session *MATLAB*
+#+PROPERTY: header-args:matlab+ :comments org
+#+PROPERTY: header-args:matlab+ :exports both
+#+PROPERTY: header-args:matlab+ :results none
+#+PROPERTY: header-args:matlab+ :eval no-export
+#+PROPERTY: header-args:matlab+ :noweb yes
+#+PROPERTY: header-args:matlab+ :mkdirp yes
+#+PROPERTY: header-args:matlab+ :output-dir figs
+
+#+PROPERTY: header-args:latex  :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
+#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
+#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
+#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
+#+PROPERTY: header-args:latex+ :results file raw replace
+#+PROPERTY: header-args:latex+ :buffer no
+#+PROPERTY: header-args:latex+ :tangle no
+#+PROPERTY: header-args:latex+ :eval no-export
+#+PROPERTY: header-args:latex+ :exports results
+#+PROPERTY: header-args:latex+ :mkdirp yes
+#+PROPERTY: header-args:latex+ :output-dir figs
+#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
+:END:
+
+#+begin_export html
+  <hr>
+  <p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
+  <hr>
+#+end_export
+
+* Introduction                                                        :ignore:
+
+#+begin_note
+You can find below the documentation of:
+- [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic Encoder]]
+- [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Linear Scale]]
+#+end_note
+
+In this document, we wish to characterize the performances of the encoder measurement system.
+In particular, we would like to measure:
+- the measurement noise
+- the linearity of the sensor
+- the bandwidth of the sensor
+
+This document is structured as follow:
+- Section [[sec:vionic_expected_performances]]: the expected performance of the Vionic encoder system are described
+- Section [[sec:encoder_model]]: a simple model of the encoder is developed
+- Section [[sec:noise_measurement]]: the noise of the encoder is measured and a model of the noise is identified
+- Section [[sec:linearity_measurement]]: the linearity of the sensor is estimated
+
+* Expected Performances
+<<sec:vionic_expected_performances>>
+
+The Vionic encoder is shown in Figure [[fig:encoder_vionic]].
+
+#+name: fig:encoder_vionic
+#+caption: Picture of the Vionic Encoder
+#+attr_latex: :width 0.6\linewidth
+[[file:figs/encoder_vionic.png]]
+
+From the Renishaw [[https://www.renishaw.com/en/how-optical-encoders-work--36979][website]]:
+#+begin_quote
+The VIONiC encoder features the third generation of Renishaw's unique filtering optics that average the contributions from many scale periods and effectively filter out non-periodic features such as dirt.
+The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector.
+Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals.
+These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining *bandwidth to beyond 500 kHz*.
+
+Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure *ultra-low Sub-Divisional Error (SDE) of typically* $<\pm 15\, nm$.
+
+This evolution of filtering optics, combined with carefully-selected electronics, provide incremental signals with wide bandwidth achieving a maximum speed of 12 m/s with the lowest positional jitter (noise) of any encoder in its class.
+Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve *jitter of just 1.6 nm RMS*.
+#+end_quote
+
+The expected interpolation errors (non-linearity) is shown in Figure [[fig:vionic_expected_noise]].
+
+#+name: fig:vionic_expected_noise
+#+attr_latex: :width \linewidth
+#+caption: Expected interpolation errors for the Vionic Encoder
+[[file:./figs/vionic_expected_noise.png]]
+
+The characteristics as advertise in the manual as well as our specifications are shown in Table [[tab:vionic_characteristics]].
+
+#+name: tab:vionic_characteristics
+#+caption: Characteristics of the Vionic compared with the specifications
+#+attr_latex: :environment tabularx :width 0.6\linewidth :align lcc
+#+attr_latex: :center t :booktabs t :float t
+| <l>               |     <c>      |       <c>       |
+| *Characteristics* |   *Manual*   | *Specification* |
+|-------------------+--------------+-----------------|
+| Time Delay        |   < 10 ns    |    < 0.5 ms     |
+| Bandwidth         |  > 500 kHz   |     > 5 kHz     |
+| Noise             | < 1.6 nm rms |   < 50 nm rms   |
+| Linearity         | < +/- 15 nm  |                 |
+| Range             | Ruler length |    > 200 um     |
+
+* Encoder Model
+<<sec:encoder_model>>
+
+The Encoder is characterized by its dynamics $G_m(s)$ from the "true" displacement $y$ to measured displacement $y_m$.
+Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
+
+It is also characterized by its measurement noise $n$ that can be described by its Power Spectral Density (PSD) $\Gamma_n(\omega)$.
+
+The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
+
+#+begin_src latex :file encoder-model-schematic.pdf
+  \begin{tikzpicture}
+    \node[block] (G) at (0,0){$G_m(s)$};
+    \node[addb, left=0.8 of G] (add){};
+
+    \draw[<-] (add.west) -- ++(-1.0, 0) node[above right]{$y$};
+    \draw[->] (add.east) -- (G.west);
+    \draw[->] (G.east) -- ++(1.0, 0) node[above left]{$y_m$};
+    \draw[<-] (add.north) -- ++(0, 0.6) node[below right](n){$n$};
+
+    \begin{scope}[on background layer]
+      \node[fit={(add.west|-G.south) (n.north-|G.east)}, inner sep=8pt, draw, dashed, fill=black!20!white] (P) {};
+      \node[below left] at (P.north east) {Encoder};
+    \end{scope}
+  \end{tikzpicture}
+#+end_src
+
+#+name: fig:encoder-model-schematic
+#+caption: Model of the Encoder
+#+RESULTS:
+[[file:figs/encoder-model-schematic.png]]
+
+We can also use a transfer function $G_n(s)$ to shape a noise $\tilde{n}$ with unity ASD as shown in Figure [[fig:vionic_expected_noise]].
+
+#+begin_src latex :file encoder-model-schematic-with-asd.pdf
+  \begin{tikzpicture}
+    \node[block] (G) at (0,0){$G_m(s)$};
+    \node[addb, left=0.8 of G] (add){};
+    \node[block, above=0.5 of add] (Gn) {$G_n(s)$};
+
+    \draw[<-] (add.west) -- ++(-1.0, 0) node[above right]{$y$};
+    \draw[->] (add.east) -- (G.west);
+    \draw[->] (G.east) -- ++(1.0, 0) node[above left]{$y_m$};
+    \draw[->] (Gn.south) -- (add.north) node[above right]{$n$};
+    \draw[<-] (Gn.north) -- ++(0, 0.6) node[below right](n){$\tilde{n}$};
+
+    \begin{scope}[on background layer]
+      \node[fit={(Gn.west|-G.south) (n.north-|G.east)}, inner sep=8pt, draw, dashed, fill=black!20!white] (P) {};
+      \node[below left] at (P.north east) {Encoder};
+    \end{scope}
+  \end{tikzpicture}
+#+end_src
+
+#+RESULTS:
+[[file:figs/encoder-model-schematic-with-asd.png]]
+
+* Noise Measurement
+<<sec:noise_measurement>>
+
+** Introduction                                                      :ignore:
+
+This part is structured as follow:
+- Section [[sec:noise_bench]]: the measurement bench is described
+- Section [[sec:thermal_drifts]]: long measurement is performed to estimate the low frequency drifts in the measurement
+- Section [[sec:vionic_noise_time]]: high frequency measurements are performed to estimate the high frequency noise
+- Section [[sec:noise_asd]]: the Spectral density of the measurement noise is estimated
+- Section [[sec:vionic_noise_model]]: finally, the measured noise is modeled
+
+** Test Bench
+<<sec:noise_bench>>
+
+To measure the noise $n$ of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
+Then, the measured signal $y_m$ corresponds to the noise $n$.
+
+The measurement bench is shown in Figures [[fig:meas_bench_top_view]] and [[fig:meas_bench_side_view]].
+Note that the bench is then covered with a "plastic bubble sheet" in order to keep disturbances as small as possible.
+
+#+name: fig:meas_bench_top_view
+#+caption: Top view picture of the measurement bench
+#+attr_latex: :width 0.8\linewidth
+[[file:figs/IMG_20210211_170554.jpg]]
+
+#+name: fig:meas_bench_side_view
+#+caption: Side view picture of the measurement bench
+#+attr_latex: :width 0.8\linewidth
+[[file:figs/IMG_20210211_170607.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>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+<<matlab-init>>
+#+end_src
+
+#+begin_src matlab :tangle no
+addpath('./matlab/mat/');
+addpath('./matlab/');
+#+end_src
+
+#+begin_src matlab :eval no
+addpath('./mat/');
+#+end_src
+
+** Thermal drifts
+<<sec:thermal_drifts>>
+Measured displacement were recording during approximately 40 hours with a sample frequency of 100Hz.
+A first order low pass filter with a corner frequency of 1Hz
+
+#+begin_src matlab
+enc_l = load('mat/noise_meas_40h_100Hz_1.mat', 't', 'x');
+#+end_src
+
+The measured time domain data are shown in Figure [[fig:vionic_drifts_time]].
+#+begin_src matlab :exports none
+enc_l.x = enc_l.x(enc_l.t > 5); % Remove first 5 seconds
+enc_l.t = enc_l.t(enc_l.t > 5); % Remove first 5 seconds
+enc_l.t = enc_l.t - enc_l.t(1); % Start at 0
+
+enc_l.x = enc_l.x - mean(enc_l.x(enc_l.t < 1)); % Start at zero displacement
+#+end_src
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(enc_l.t/3600, 1e9*enc_l.x, '-');
+hold off;
+xlabel('Time [h]');
+ylabel('Displacement [nm]');
+xlim([0, 40]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_drifts_time.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_drifts_time
+#+caption: Measured thermal drifts
+#+RESULTS:
+[[file:figs/vionic_drifts_time.png]]
+
+The measured data seems to experience a constant drift after approximately 20 hour.
+Let's estimate this drift.
+
+#+begin_src matlab :exports none
+t0 = 20*3600; % Start time [s]
+x_stab = enc_l.x(enc_l.t > t0);
+x_stab = x_stab - x_stab(1);
+t_stab = enc_l.t(enc_l.t > t0);
+t_stab = t_stab - t_stab(1);
+#+end_src
+
+#+begin_src matlab :results value replace :exports results
+sprintf('The mean drift is approximately %.1f [nm/hour] or %.1f [nm/min]', 3600*1e9*(t_stab\x_stab), 60*1e9*(t_stab\x_stab))
+#+end_src
+
+#+RESULTS:
+: The mean drift is approximately 60.9 [nm/hour] or 1.0 [nm/min]
+
+Comparison between the data and the linear fit is shown in Figure [[fig:vionic_drifts_linear_fit]].
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(t_stab/3600, 1e9*x_stab, '-');
+plot(t_stab/3600, 1e9*t_stab*(t_stab\x_stab), 'k--');
+hold off;
+xlabel('Time [h]');
+ylabel('Displacement [nm]');
+xlim([0, 20]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_drifts_linear_fit.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_drifts_linear_fit
+#+caption: Measured drift and linear fit
+#+RESULTS:
+[[file:figs/vionic_drifts_linear_fit.png]]
+
+Let's now estimate the Power Spectral Density of the measured displacement.
+The obtained low frequency ASD is shown in Figure [[fig:vionic_noise_asd_low_freq]].
+#+begin_src matlab :exports none
+% Compute sampling Frequency
+Ts = (enc_l.t(end) - enc_l.t(1))/(length(enc_l.t)-1);
+Fs = 1/Ts;
+
+% Hannning Windows
+win = hanning(ceil(60*10/Ts));
+
+[pxx_l, f_l] = pwelch(x_stab, win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(f_l, sqrt(pxx_l))
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+xlim([1e-2, 1e0]);
+ylim([1e-11, 1e-8]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_asd_low_freq.pdf', 'width', 'side', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_asd_low_freq
+#+caption: Amplitude Spectral density of the measured displacement
+#+RESULTS:
+[[file:figs/vionic_noise_asd_low_freq.png]]
+
+** Time Domain signals
+<<sec:vionic_noise_time>>
+
+Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz.
+
+#+begin_src matlab :exports none
+%% Load all the measurements
+enc = {};
+for i = 1:7
+    enc(i) = {load(['mat/noise_meas_100s_20kHz_' num2str(i) '.mat'], 't', 'x')};
+end
+#+end_src
+
+#+begin_src matlab :exports none
+%% Remove initial offset
+for i = 1:7
+    enc{i}.x = enc{i}.x - mean(enc{i}.x(1:1000));
+end
+#+end_src
+
+The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure [[fig:vionic_noise_raw_lpf]].
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(enc{1}.t, 1e9*enc{1}.x, '.', 'DisplayName', 'Enc 1 - Raw');
+plot(enc{1}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{1}.x, enc{1}.t), '-', 'DisplayName', 'Enc 1 - LPF');
+hold off;
+xlabel('Time [s]');
+ylabel('Displacement [nm]');
+legend('location', 'northwest');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_raw_lpf.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_raw_lpf
+#+caption: Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)
+#+RESULTS:
+[[file:figs/vionic_noise_raw_lpf.png]]
+
+The time domain data for all the encoders are compared in Figure [[fig:vionic_noise_time]].
+
+We can see some drifts that are in the order of few nm to 20nm per minute.
+As shown in Section [[sec:thermal_drifts]], these drifts should diminish over time down to 1nm/min.
+#+begin_src matlab :exports none
+figure;
+hold on;
+for i=1:7
+    plot(enc{i}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{i}.x, enc{i}.t), '.', ...
+         'DisplayName', sprintf('Enc %i', i));
+end
+hold off;
+xlabel('Time [s]');
+ylabel('Displacement [nm]');
+legend('location', 'northwest');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_time.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_time
+#+caption: Comparison of the time domain measurement
+#+RESULTS:
+[[file:figs/vionic_noise_time.png]]
+
+** Noise Spectral Density
+<<sec:noise_asd>>
+
+The amplitude spectral densities for all the encoder are computed and shown in Figure [[fig:vionic_noise_asd]].
+#+begin_src matlab :exports none
+% Compute sampling Frequency
+Ts = (enc{1}.t(end) - enc{1}.t(1))/(length(enc{1}.t)-1);
+Fs = 1/Ts;
+
+% Hannning Windows
+win = hanning(ceil(0.5/Ts));
+
+[pxx, f] = pwelch(enc{1}.x, win, [], [], Fs);
+enc{1}.pxx = pxx;
+
+for i=2:7
+    [pxx, ~] = pwelch(enc{i}.x, win, [], [], Fs);
+    enc{i}.pxx = pxx;
+end
+#+end_src
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+for i=1:7
+    plot(f, sqrt(enc{i}.pxx), ...
+         'DisplayName', sprintf('Enc %i', i));
+end
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+xlim([10, Fs/2]);
+ylim([1e-11, 1e-9]);
+legend('location', 'northeast');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_asd.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_asd
+#+caption: Amplitude Spectral Density of the measured signal
+#+RESULTS:
+[[file:figs/vionic_noise_asd.png]]
+
+We can combine these measurements with the low frequency noise computed in Section [[sec:thermal_drifts]].
+The obtained ASD is shown in Figure [[fig:vionic_noise_asd_combined]].
+#+begin_src matlab :exports none
+[pxx_h, f_h] = pwelch(enc{2}.x, hanning(ceil(10/Ts)), [], [], Fs);
+
+figure;
+hold on;
+plot(f_h(f_h>0.6), sqrt(pxx_h(f_h>0.6)), 'k-');
+plot(f_l(f_l<1), sqrt(pxx_l(f_l<1)), 'k-')
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+xlim([1e-2, Fs/2]);
+ylim([1e-12, 1e-8]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_asd_combined.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_asd_combined
+#+caption: Combined low frequency and high frequency noise measurements
+#+RESULTS:
+[[file:figs/vionic_noise_asd_combined.png]]
+
+** Noise Model
+<<sec:vionic_noise_model>>
+
+Let's create a transfer function that approximate the measured noise of the encoder.
+#+begin_src matlab
+Gn_e = 1.8e-11/(1 + s/2/pi/1e4);
+#+end_src
+
+The amplitude of the transfer function and the measured ASD are shown in Figure [[fig:vionic_noise_asd_model]].
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(f, sqrt(enc{1}.pxx), 'color', [0, 0, 0, 0.5], 'DisplayName', '$\Gamma_n(\omega)$');
+for i=2:7
+    plot(f, sqrt(enc{i}.pxx), 'color', [0, 0, 0, 0.5], ...
+         'HandleVisibility', 'off');
+end
+plot(f, abs(squeeze(freqresp(Gn_e, f, 'Hz'))), 'r-', 'DisplayName', '$|G_n(j\omega)|$');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+xlim([10, Fs/2]);
+ylim([1e-11, 1e-10]);
+legend('location', 'northeast');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_asd_model.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_asd_model
+#+caption: Measured ASD of the noise and modeled one
+#+RESULTS:
+[[file:figs/vionic_noise_asd_model.png]]
+
+The cumulative amplitude spectrum is now computed and shown in Figure [[fig:vionic_noise_cas_model]].
+
+We can see that the Root Mean Square value of the measurement noise is $\approx 1.6 \, nm$ as advertise in the datasheet.
+
+#+begin_src matlab :exports none
+for i = 1:7
+    enc{i}.CPS = flip(-cumtrapz(flip(f), flip(enc{i}.pxx)));
+end
+
+CAS_Gn = flip(-cumtrapz(flip(f), flip(abs(squeeze(freqresp(Gn_e, f, 'Hz'))).^2)));
+#+end_src
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(f, sqrt(enc{1}.CPS), 'color', [0, 0, 0, 0.5], 'DisplayName', '$CAS_n(\omega)$');
+for i=2:7
+    plot(f, sqrt(enc{i}.CPS), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off');
+end
+plot(f, sqrt(CAS_Gn), 'r-', 'DisplayName', 'model');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('CPS [$m$]');
+xlim([10, Fs/2]);
+ylim([1e-10, 1e-8]);
+legend('location', 'northeast');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/vionic_noise_cas_model.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:vionic_noise_cas_model
+#+caption: Meassured CAS of the noise and modeled one
+#+RESULTS:
+[[file:figs/vionic_noise_cas_model.png]]
+
+* Linearity Measurement
+<<sec:linearity_measurement>>
+** Test Bench
+In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
+An interferometer or capacitive sensor should work fine.
+An actuator should also be there so impose a displacement.
+
+One idea is to use the test-bench shown in Figure [[fig:test_bench_encoder_calibration]].
+
+The APA300ML is used to excite the mass in a broad bandwidth.
+The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
+
+As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder if it is less than the Nyquist frequency that can be around 10kHz.
+
+#+name: fig:test_bench_encoder_calibration
+#+caption: Schematic of the test bench
+[[file:figs/test_bench_encoder_calibration.png]]
+
+** 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>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+<<matlab-init>>
+#+end_src
+
+#+begin_src matlab :tangle no
+addpath('./matlab/mat/');
+addpath('./matlab/');
+#+end_src
+
+#+begin_src matlab :eval no
+addpath('./mat/');
+#+end_src
+
+** Results
+
--- a/test-bench-vionic.pdf
+++ b/test-bench-vionic.pdf
Author	SHA1	Message	Date
Thomas Dehaeze	4776c89343	long measurements	2021-02-17 11:14:29 +01:00
Thomas Dehaeze	195c5b5598	Add pictures	2021-02-12 18:26:24 +01:00
Thomas Dehaeze	9a06c0995f	Analyse long measurement	2021-02-11 15:22:02 +01:00
Thomas Dehaeze	73dc280ab3	Prepare files for long measurement	2021-02-11 13:48:19 +01:00
Thomas Dehaeze	15d8508bf0	Merge branch 'master' of https://git.tdehaeze.xyz/tdehaeze/test-bench-vionic	2021-02-11 10:17:38 +01:00
Thomas Dehaeze	bc5876f32f	long measurement	2021-02-11 10:16:58 +01:00
Thomas Dehaeze	080b788768	Add some details	2021-02-10 15:14:14 +01:00
Thomas Dehaeze	30177e4809	Update with last measured encoder	2021-02-04 20:23:22 +01:00
Thomas Dehaeze	006cb20df1	measure last encoder	2021-02-04 14:57:10 +01:00
Thomas Dehaeze	53ffaaa793	Analyze the measured noise of all encoders	2021-02-03 11:20:22 +01:00
Thomas Dehaeze	0296f80900	measure encoder noise	2021-02-03 10:38:27 +01:00
Thomas Dehaeze	d924339f63	add serial numbers	2021-02-03 10:16:49 +01:00
Thomas Dehaeze	983b300650	rename mat files with encoder number	2021-02-03 09:56:49 +01:00
Thomas Dehaeze	78e8097ca6	long meas	2021-02-03 09:37:38 +01:00
Thomas Dehaeze	8fa4975b41	Rename index.org	2021-02-02 18:49:54 +01:00
Thomas Dehaeze	bed36ce9d0	Simlink index.html to test-bench-vionic.html	2021-02-02 18:48:30 +01:00
Thomas Dehaeze	9e38f0bd14	Export to pdf	2021-02-02 18:46:58 +01:00
Thomas Dehaeze	99e3c94d59	First analysis of the sensor noise	2021-02-02 18:25:28 +01:00
Thomas Dehaeze	fa4b391336	Rename file with correct sampling rate	2021-02-02 18:10:47 +01:00