Add biblatex
This commit is contained in:
parent
f2d67886b4
commit
985cac5865
@ -11,7 +11,7 @@
|
||||
# PDF Generation/Building/Compilation
|
||||
# ======================================================================================
|
||||
|
||||
@default_files=('dcm_metrology.tex');
|
||||
@default_files=('dcm-metrology.tex');
|
||||
|
||||
# PDF-generating modes are:
|
||||
# 1: pdflatex, as specified by $pdflatex variable (still largely in use)
|
||||
|
||||
@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2022-06-02 Thu 22:25 -->
|
||||
<!-- 2022-06-07 Tue 10:58 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>ESRF Double Crystal Monochromator - Metrology</title>
|
||||
<meta name="author" content="Dehaeze Thomas" />
|
||||
@ -39,51 +39,52 @@
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents" role="doc-toc">
|
||||
<ul>
|
||||
<li><a href="#org5b4a8ea">1. Metrology Concept</a>
|
||||
<li><a href="#org2c2c62b">1. Metrology Concept</a>
|
||||
<ul>
|
||||
<li><a href="#orgee0936b">1.1. Sensor Topology</a></li>
|
||||
<li><a href="#orgcc7ab6e">1.2. Computation of the relative pose between first and second crystals</a></li>
|
||||
<li><a href="#org3fa59ba">1.1. Sensor Topology</a></li>
|
||||
<li><a href="#orgc5b3b8f">1.2. Computation of the relative pose between first and second crystals</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgd1e6cf8">2. Relation Between Crystal position and X-ray measured displacement</a>
|
||||
<li><a href="#orgcf5cfb5">2. Relation Between Crystal position and X-ray measured displacement</a>
|
||||
<ul>
|
||||
<li><a href="#orgf98dcda">2.1. Definition of frame</a></li>
|
||||
<li><a href="#orgcc56e18">2.2. Effect of an error in crystal’s distance</a></li>
|
||||
<li><a href="#org4f10916">2.3. Effect of an error in crystal’s x parallelism</a></li>
|
||||
<li><a href="#org214d2fb">2.4. Effect of an error in crystal’s y parallelism</a></li>
|
||||
<li><a href="#orga01ea08">2.5. Summary</a></li>
|
||||
<li><a href="#orgbe05a5f">2.6. “Channel cut” Scan</a></li>
|
||||
<li><a href="#org06f9ee5">2.1. Definition of frame</a></li>
|
||||
<li><a href="#org4f17ec2">2.2. Effect of an error in crystal’s distance</a></li>
|
||||
<li><a href="#orgc5a82df">2.3. Effect of an error in crystal’s x parallelism</a></li>
|
||||
<li><a href="#org7a64dc0">2.4. Effect of an error in crystal’s y parallelism</a></li>
|
||||
<li><a href="#org60c73bc">2.5. Summary</a></li>
|
||||
<li><a href="#orgd3145d9">2.6. “Channel cut” Scan</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgd1c9f1e">3. Determining relative pose between the crystals using the X-ray</a>
|
||||
<li><a href="#org11191b2">3. Determining relative pose between the crystals using the X-ray</a>
|
||||
<ul>
|
||||
<li><a href="#orgb9a7cbf">3.1. Determine the \(y\) parallelism - “Rocking Curve”</a></li>
|
||||
<li><a href="#orgf1f155c">3.2. Determine the \(x\) parallelism - Bragg Scan</a></li>
|
||||
<li><a href="#org340a305">3.3. Determine the \(z\) distance - Bragg Scan</a></li>
|
||||
<li><a href="#org550643d">3.4. Use Channel cut scan to determine crystal <code>dry</code> parallelism</a></li>
|
||||
<li><a href="#org3f02fcd">3.5. Effect of an error on Bragg angle</a></li>
|
||||
<li><a href="#org0854b62">3.1. Determine the \(y\) parallelism - “Rocking Curve”</a></li>
|
||||
<li><a href="#org79c2679">3.2. Determine the \(x\) parallelism - Bragg Scan</a></li>
|
||||
<li><a href="#org15cd655">3.3. Determine the \(z\) distance - Bragg Scan</a></li>
|
||||
<li><a href="#orgb9628d9">3.4. Use Channel cut scan to determine crystal <code>dry</code> parallelism</a></li>
|
||||
<li><a href="#orgf6270d8">3.5. Effect of an error on Bragg angle</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org4eedaad">4. Deformations of the Metrology Frame</a>
|
||||
<li><a href="#orgb8e523b">4. Deformations of the Metrology Frame</a>
|
||||
<ul>
|
||||
<li><a href="#orge197959">4.1. Measurement Setup</a></li>
|
||||
<li><a href="#org7cfa17e">4.2. Simulations</a></li>
|
||||
<li><a href="#org0c10c30">4.3. Comparison</a></li>
|
||||
<li><a href="#org25a32fa">4.4. Test</a></li>
|
||||
<li><a href="#orgb7db314">4.5. Measured frame deformation</a></li>
|
||||
<li><a href="#org5494ab9">4.6. Test</a></li>
|
||||
<li><a href="#org218f95f">4.7. Repeatability of frame deformation</a></li>
|
||||
<li><a href="#org8391240">4.1. Measurement Setup</a></li>
|
||||
<li><a href="#org0a584b6">4.2. Simulations</a></li>
|
||||
<li><a href="#org0820684">4.3. Comparison</a></li>
|
||||
<li><a href="#org91e6317">4.4. Test</a></li>
|
||||
<li><a href="#org5ca0ac8">4.5. Measured frame deformation</a></li>
|
||||
<li><a href="#orgb94c7fb">4.6. Test</a></li>
|
||||
<li><a href="#org1c4abff">4.7. Repeatability of frame deformation</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org5b8904d">5. Attocube - Periodic Non-Linearity</a>
|
||||
<li><a href="#orgcf35007">5. Attocube - Periodic Non-Linearity</a>
|
||||
<ul>
|
||||
<li><a href="#org9f6a57f">5.1. Measurement Setup</a></li>
|
||||
<li><a href="#orgc06acba">5.2. Choice of the reference signal</a></li>
|
||||
<li><a href="#org26743c0">5.3. Repeatability of the non-linearity</a></li>
|
||||
<li><a href="#org15014d3">5.4. Simulation</a></li>
|
||||
<li><a href="#orga71d790">5.5. Measurements</a></li>
|
||||
<li><a href="#org91573e9">5.1. Measurement Setup</a></li>
|
||||
<li><a href="#orgdd79356">5.2. Choice of the reference signal</a></li>
|
||||
<li><a href="#org2268c53">5.3. Repeatability of the non-linearity</a></li>
|
||||
<li><a href="#orgadef69b">5.4. Simulation</a></li>
|
||||
<li><a href="#org8ddf260">5.5. Measurements</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org515d8fb">Bibliography</a></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
@ -93,26 +94,26 @@
|
||||
|
||||
<p>
|
||||
In this document, the metrology system is studied.
|
||||
First, in Section <a href="#orga8ac352">1</a> the goal of the metrology system is stated and the proposed concept is described.
|
||||
First, in Section <a href="#orga1bc36b">1</a> the goal of the metrology system is stated and the proposed concept is described.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
How the relative crystal pose is affecting the pose of the output beam is studied in Section <a href="#org4b9a066">2</a>.
|
||||
How the relative crystal pose is affecting the pose of the output beam is studied in Section <a href="#org2865464">2</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In order to increase the accuracy of the metrology system, two problems are to be dealt with:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>The deformation of the metrology frame under the action of gravity (Section <a href="#orgf31717e">4</a>)</li>
|
||||
<li>The periodic non-linearity of the interferometers (Section <a href="#org44bdb6d">5</a>)</li>
|
||||
<li>The deformation of the metrology frame under the action of gravity (Section <a href="#org45af7a1">4</a>)</li>
|
||||
<li>The periodic non-linearity of the interferometers (Section <a href="#org455a211">5</a>)</li>
|
||||
</ul>
|
||||
|
||||
<div id="outline-container-org5b4a8ea" class="outline-2">
|
||||
<h2 id="org5b4a8ea"><span class="section-number-2">1.</span> Metrology Concept</h2>
|
||||
<div id="outline-container-org2c2c62b" class="outline-2">
|
||||
<h2 id="org2c2c62b"><span class="section-number-2">1.</span> Metrology Concept</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
<a id="orga8ac352"></a>
|
||||
<a id="orga1bc36b"></a>
|
||||
</p>
|
||||
<p>
|
||||
The goal of the metrology system is to measure the distance and default of parallelism between the first and second crystals.
|
||||
@ -127,8 +128,8 @@ Only 3 degrees of freedom are of interest:
|
||||
<li>\(r_x\)</li>
|
||||
</ul>
|
||||
</div>
|
||||
<div id="outline-container-orgee0936b" class="outline-3">
|
||||
<h3 id="orgee0936b"><span class="section-number-3">1.1.</span> Sensor Topology</h3>
|
||||
<div id="outline-container-org3fa59ba" class="outline-3">
|
||||
<h3 id="org3fa59ba"><span class="section-number-3">1.1.</span> Sensor Topology</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
In order to measure the relative pose of the two crystals, instead of performing a direct measurement which is complicated, the pose of the two crystals are measured from a metrology frame.
|
||||
@ -138,11 +139,11 @@ Three additional interferometers are used to measured the relative motion of the
|
||||
|
||||
|
||||
<p>
|
||||
In total, there are 15 interferometers represented in Figure <a href="#orgce5aaa3">1</a>.
|
||||
The measurements are summarized in Table <a href="#org943c065">2</a>.
|
||||
In total, there are 15 interferometers represented in Figure <a href="#org0ba932c">1</a>.
|
||||
The measurements are summarized in Table <a href="#org9256fe4">2</a>.
|
||||
</p>
|
||||
|
||||
<table id="org5dd8abe" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orgf3e6978" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Notations for the metrology frame</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -194,7 +195,7 @@ The measurements are summarized in Table <a href="#org943c065">2</a>.
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<table id="org943c065" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org9256fe4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 2:</span> List of Interferometer measurements</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -305,7 +306,7 @@ The measurements are summarized in Table <a href="#org943c065">2</a>.
|
||||
</table>
|
||||
|
||||
|
||||
<div id="orgce5aaa3" class="figure">
|
||||
<div id="org0ba932c" class="figure">
|
||||
<p><img src="figs/metrology_schematic.png" alt="metrology_schematic.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Schematic of the Metrology System</p>
|
||||
@ -313,8 +314,8 @@ The measurements are summarized in Table <a href="#org943c065">2</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcc7ab6e" class="outline-3">
|
||||
<h3 id="orgcc7ab6e"><span class="section-number-3">1.2.</span> Computation of the relative pose between first and second crystals</h3>
|
||||
<div id="outline-container-orgc5b3b8f" class="outline-3">
|
||||
<h3 id="orgc5b3b8f"><span class="section-number-3">1.2.</span> Computation of the relative pose between first and second crystals</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<p>
|
||||
To understand how the relative pose between the crystals is computed from the interferometer signals, have a look at <a href="https://gitlab.esrf.fr/dehaeze/dcm-kinematics">this repository</a> (<code>https://gitlab.esrf.fr/dehaeze/dcm-kinematics</code>).
|
||||
@ -324,7 +325,7 @@ To understand how the relative pose between the crystals is computed from the in
|
||||
Basically, Jacobian matrices are derived from the geometry and are used to convert the 15 interferometer signals to the <b>relative pose</b> of the primary and secondary crystals \([d_{h,z},\ r_{h,y},\ r_{h,x}]\) or \([d_{r,z},\ r_{r,y},\ r_{r,x}]\).
|
||||
</p>
|
||||
|
||||
<div class="note" id="org5a06b04">
|
||||
<div class="note" id="orgc0eb804">
|
||||
<p>
|
||||
The sign conventions for the relative crystal pose are:
|
||||
</p>
|
||||
@ -379,11 +380,11 @@ Values of the matrices can be found in the document describing the kinematics of
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd1e6cf8" class="outline-2">
|
||||
<h2 id="orgd1e6cf8"><span class="section-number-2">2.</span> Relation Between Crystal position and X-ray measured displacement</h2>
|
||||
<div id="outline-container-orgcf5cfb5" class="outline-2">
|
||||
<h2 id="orgcf5cfb5"><span class="section-number-2">2.</span> Relation Between Crystal position and X-ray measured displacement</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org4b9a066"></a>
|
||||
<a id="org2865464"></a>
|
||||
</p>
|
||||
<p>
|
||||
In this section, the impact of an error in the relative pose between the first and second crystals on the output X-ray beam is studied.
|
||||
@ -406,8 +407,8 @@ In order to simplify the problem, the first crystal is supposed to be fixed (i.e
|
||||
In order to easily study that, “ray tracing” techniques are used.
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgf98dcda" class="outline-3">
|
||||
<h3 id="orgf98dcda"><span class="section-number-3">2.1.</span> Definition of frame</h3>
|
||||
<div id="outline-container-org06f9ee5" class="outline-3">
|
||||
<h3 id="org06f9ee5"><span class="section-number-3">2.1.</span> Definition of frame</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
@ -483,15 +484,15 @@ The xy position of the beam is taken in the \(x=0\) plane.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcc56e18" class="outline-3">
|
||||
<h3 id="orgcc56e18"><span class="section-number-3">2.2.</span> Effect of an error in crystal’s distance</h3>
|
||||
<div id="outline-container-org4f17ec2" class="outline-3">
|
||||
<h3 id="org4f17ec2"><span class="section-number-3">2.2.</span> Effect of an error in crystal’s distance</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
<a id="orgfce54e9"></a>
|
||||
<a id="orgc160166"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In Figure <a href="#orga24d92a">2</a> is shown the light path for three bragg angles (5, 55 and 85 degrees) when there is an error in the <code>dz</code> position of 1mm.
|
||||
In Figure <a href="#org56aadc9">2</a> is shown the light path for three bragg angles (5, 55 and 85 degrees) when there is an error in the <code>dz</code> position of 1mm.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -499,14 +500,14 @@ Visually, it is clear that this induce a <code>z</code> offset of the output bea
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga24d92a" class="figure">
|
||||
<div id="org56aadc9" class="figure">
|
||||
<p><img src="figs/ray_tracing_error_dz_overview.png" alt="ray_tracing_error_dz_overview.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Visual Effect of an error in <code>dz</code> (1mm). Side view.</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The motion of the output beam is displayed as a function of the Bragg angle in Figure <a href="#orgf3acc2d">3</a>.
|
||||
The motion of the output beam is displayed as a function of the Bragg angle in Figure <a href="#org72617ff">3</a>.
|
||||
It is clear that an error in the distance <code>dz</code> between the crystals only induce a <code>z</code> offset of the output beam.
|
||||
This offset decreases with the Bragg angle.
|
||||
</p>
|
||||
@ -519,7 +520,7 @@ This is indeed equal to:
|
||||
\end{equation}
|
||||
|
||||
|
||||
<div id="orgf3acc2d" class="figure">
|
||||
<div id="org72617ff" class="figure">
|
||||
<p><img src="figs/motion_beam_dz_error.png" alt="motion_beam_dz_error.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Motion of the output beam with dZ error</p>
|
||||
@ -527,29 +528,29 @@ This is indeed equal to:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4f10916" class="outline-3">
|
||||
<h3 id="org4f10916"><span class="section-number-3">2.3.</span> Effect of an error in crystal’s x parallelism</h3>
|
||||
<div id="outline-container-orgc5a82df" class="outline-3">
|
||||
<h3 id="orgc5a82df"><span class="section-number-3">2.3.</span> Effect of an error in crystal’s x parallelism</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
<a id="org10b6b9d"></a>
|
||||
<a id="org08f1e7c"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The effect of an error in <code>rx</code> crystal parallelism on the output beam is visually shown in Figure <a href="#orgf3fcd25">4</a> for three bragg angles (5, 55 and 85 degrees).
|
||||
The effect of an error in <code>rx</code> crystal parallelism on the output beam is visually shown in Figure <a href="#org64e88a1">4</a> for three bragg angles (5, 55 and 85 degrees).
|
||||
The error is set to one degree, and the top view is shown.
|
||||
It is clear that the output beam experiences some rotation around a vertical axis.
|
||||
The amount of rotation depends on the bragg angle.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgf3fcd25" class="figure">
|
||||
<div id="org64e88a1" class="figure">
|
||||
<p><img src="figs/ray_tracing_error_drx_overview.png" alt="ray_tracing_error_drx_overview.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Visual Effect of an error in <code>drx</code> (1 degree). Top View.</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The effect of <code>drx</code> as a function of the Bragg angle on the output beam pose is computed and shown in Figure <a href="#org3ce23f8">5</a>.
|
||||
The effect of <code>drx</code> as a function of the Bragg angle on the output beam pose is computed and shown in Figure <a href="#orgca99abd">5</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -568,7 +569,7 @@ We can note that the \(y\) shift is equal to zero for a bragg angle of 45 degree
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org3ce23f8" class="figure">
|
||||
<div id="orgca99abd" class="figure">
|
||||
<p><img src="figs/motion_beam_drx_error.png" alt="motion_beam_drx_error.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Motion of the output beam with drx error</p>
|
||||
@ -576,26 +577,26 @@ We can note that the \(y\) shift is equal to zero for a bragg angle of 45 degree
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org214d2fb" class="outline-3">
|
||||
<h3 id="org214d2fb"><span class="section-number-3">2.4.</span> Effect of an error in crystal’s y parallelism</h3>
|
||||
<div id="outline-container-org7a64dc0" class="outline-3">
|
||||
<h3 id="org7a64dc0"><span class="section-number-3">2.4.</span> Effect of an error in crystal’s y parallelism</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<p>
|
||||
<a id="orged8dba0"></a>
|
||||
<a id="org4e5ab76"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The effect of an error in <code>ry</code> crystal parallelism on the output beam is visually shown in Figure <a href="#orgb3ea9d4">6</a> for three bragg angles (5, 55 and 85 degrees).
|
||||
The effect of an error in <code>ry</code> crystal parallelism on the output beam is visually shown in Figure <a href="#org2cd7448">6</a> for three bragg angles (5, 55 and 85 degrees).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgb3ea9d4" class="figure">
|
||||
<div id="org2cd7448" class="figure">
|
||||
<p><img src="figs/ray_tracing_error_dry_overview.png" alt="ray_tracing_error_dry_overview.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Visual Effect of an error in <code>dry</code> (1 degree). Side view.</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The effect of <code>dry</code> as a function of the Bragg angle on the output beam pose is computed and shown in Figure <a href="#org28da5fb">7</a>.
|
||||
The effect of <code>dry</code> as a function of the Bragg angle on the output beam pose is computed and shown in Figure <a href="#org53f9e3e">7</a>.
|
||||
It is clear that this induces a rotation of the output beam in the <code>y</code> direction equals to 2 times <code>dry</code>:
|
||||
</p>
|
||||
\begin{equation}
|
||||
@ -607,7 +608,7 @@ It also induces a small vertical motion of the beam (at the \(x=0\) location) wh
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org28da5fb" class="figure">
|
||||
<div id="org53f9e3e" class="figure">
|
||||
<p><img src="figs/motion_beam_dry_error.png" alt="motion_beam_dry_error.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Motion of the output beam with dry error</p>
|
||||
@ -615,16 +616,16 @@ It also induces a small vertical motion of the beam (at the \(x=0\) location) wh
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga01ea08" class="outline-3">
|
||||
<h3 id="orga01ea08"><span class="section-number-3">2.5.</span> Summary</h3>
|
||||
<div id="outline-container-org60c73bc" class="outline-3">
|
||||
<h3 id="org60c73bc"><span class="section-number-3">2.5.</span> Summary</h3>
|
||||
<div class="outline-text-3" id="text-2-5">
|
||||
<p>
|
||||
Effects of crystal’s pose errors on the output beam are summarized in Table <a href="#org01cc930">3</a>.
|
||||
Effects of crystal’s pose errors on the output beam are summarized in Table <a href="#orga8d650f">3</a>.
|
||||
Note that the three pose errors are well decoupled regarding their effects on the output beam.
|
||||
Also note that the effect of an error in crystal’s distance does not depend on the Bragg angle.
|
||||
</p>
|
||||
|
||||
<table id="org01cc930" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orga8d650f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 3:</span> Summary of the effects of the errors in second crystal’s pose on the output beam</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -677,30 +678,30 @@ Also note that the effect of an error in crystal’s distance does not depen
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbe05a5f" class="outline-3">
|
||||
<h3 id="orgbe05a5f"><span class="section-number-3">2.6.</span> “Channel cut” Scan</h3>
|
||||
<div id="outline-container-orgd3145d9" class="outline-3">
|
||||
<h3 id="orgd3145d9"><span class="section-number-3">2.6.</span> “Channel cut” Scan</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<p>
|
||||
A “channel cut” scan is a Bragg scan where the distance between the crystals is fixed.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
This is visually shown in Figure <a href="#org278d240">8</a> where it is clear that the output beam experiences some vertical motion.
|
||||
This is visually shown in Figure <a href="#org3e8b9c1">8</a> where it is clear that the output beam experiences some vertical motion.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org278d240" class="figure">
|
||||
<div id="org3e8b9c1" class="figure">
|
||||
<p><img src="figs/ray_tracing_channel_cut.png" alt="ray_tracing_channel_cut.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Visual Effect of a channel cut scan</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The \(z\) offset of the beam for several channel cut scans are shown in Figure <a href="#org588c503">9</a>.
|
||||
The \(z\) offset of the beam for several channel cut scans are shown in Figure <a href="#orgfe14da2">9</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org588c503" class="figure">
|
||||
<div id="orgfe14da2" class="figure">
|
||||
<p><img src="figs/channel_cut_scan.png" alt="channel_cut_scan.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Z motion of the beam during “channel cut” scans</p>
|
||||
@ -709,8 +710,8 @@ The \(z\) offset of the beam for several channel cut scans are shown in Figure <
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd1c9f1e" class="outline-2">
|
||||
<h2 id="orgd1c9f1e"><span class="section-number-2">3.</span> Determining relative pose between the crystals using the X-ray</h2>
|
||||
<div id="outline-container-org11191b2" class="outline-2">
|
||||
<h2 id="org11191b2"><span class="section-number-2">3.</span> Determining relative pose between the crystals using the X-ray</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
As Interferometers are only measuring <i>relative</i> displacement, it is mandatory to initialize them correctly.
|
||||
@ -729,21 +730,21 @@ In order to do that, an external metrology using the x-ray is used.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb9a7cbf" class="outline-3">
|
||||
<h3 id="orgb9a7cbf"><span class="section-number-3">3.1.</span> Determine the \(y\) parallelism - “Rocking Curve”</h3>
|
||||
<div id="outline-container-org0854b62" class="outline-3">
|
||||
<h3 id="org0854b62"><span class="section-number-3">3.1.</span> Determine the \(y\) parallelism - “Rocking Curve”</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf1f155c" class="outline-3">
|
||||
<h3 id="orgf1f155c"><span class="section-number-3">3.2.</span> Determine the \(x\) parallelism - Bragg Scan</h3>
|
||||
<div id="outline-container-org79c2679" class="outline-3">
|
||||
<h3 id="org79c2679"><span class="section-number-3">3.2.</span> Determine the \(x\) parallelism - Bragg Scan</h3>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org340a305" class="outline-3">
|
||||
<h3 id="org340a305"><span class="section-number-3">3.3.</span> Determine the \(z\) distance - Bragg Scan</h3>
|
||||
<div id="outline-container-org15cd655" class="outline-3">
|
||||
<h3 id="org15cd655"><span class="section-number-3">3.3.</span> Determine the \(z\) distance - Bragg Scan</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org550643d" class="outline-3">
|
||||
<h3 id="org550643d"><span class="section-number-3">3.4.</span> Use Channel cut scan to determine crystal <code>dry</code> parallelism</h3>
|
||||
<div id="outline-container-orgb9628d9" class="outline-3">
|
||||
<h3 id="orgb9628d9"><span class="section-number-3">3.4.</span> Use Channel cut scan to determine crystal <code>dry</code> parallelism</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
Now, let’s suppose we want to determine the <code>dry</code> angle between the crystals.
|
||||
@ -763,16 +764,16 @@ The error is
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3f02fcd" class="outline-3">
|
||||
<h3 id="org3f02fcd"><span class="section-number-3">3.5.</span> Effect of an error on Bragg angle</h3>
|
||||
<div id="outline-container-orgf6270d8" class="outline-3">
|
||||
<h3 id="orgf6270d8"><span class="section-number-3">3.5.</span> Effect of an error on Bragg angle</h3>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4eedaad" class="outline-2">
|
||||
<h2 id="org4eedaad"><span class="section-number-2">4.</span> Deformations of the Metrology Frame</h2>
|
||||
<div id="outline-container-orgb8e523b" class="outline-2">
|
||||
<h2 id="orgb8e523b"><span class="section-number-2">4.</span> Deformations of the Metrology Frame</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orgf31717e"></a>
|
||||
<a id="org45af7a1"></a>
|
||||
</p>
|
||||
<p>
|
||||
The transformation matrices are valid only if the metrology frames are solid bodies.
|
||||
@ -787,8 +788,8 @@ When the bragg axis is scanned, the effect of gravity on the metrology frame is
|
||||
This can be calibrated.
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orge197959" class="outline-3">
|
||||
<h3 id="orge197959"><span class="section-number-3">4.1.</span> Measurement Setup</h3>
|
||||
<div id="outline-container-org8391240" class="outline-3">
|
||||
<h3 id="org8391240"><span class="section-number-3">4.1.</span> Measurement Setup</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
Two beam viewers:
|
||||
@ -805,7 +806,7 @@ This position is the wanted position for a given Bragg angle.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgec71cad" class="figure">
|
||||
<div id="org4769d08" class="figure">
|
||||
<p><img src="figs/calibration_setup.png" alt="calibration_setup.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Schematic of the setup</p>
|
||||
@ -835,8 +836,8 @@ Frame rate is: 42 fps
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org7cfa17e" class="outline-3">
|
||||
<h3 id="org7cfa17e"><span class="section-number-3">4.2.</span> Simulations</h3>
|
||||
<div id="outline-container-org0a584b6" class="outline-3">
|
||||
<h3 id="org0a584b6"><span class="section-number-3">4.2.</span> Simulations</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
The deformations of the metrology frame and therefore the expected interferometric measurements can be computed as a function of the Bragg angle.
|
||||
@ -845,12 +846,12 @@ This may be done using FE software.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0c10c30" class="outline-3">
|
||||
<h3 id="org0c10c30"><span class="section-number-3">4.3.</span> Comparison</h3>
|
||||
<div id="outline-container-org0820684" class="outline-3">
|
||||
<h3 id="org0820684"><span class="section-number-3">4.3.</span> Comparison</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org25a32fa" class="outline-3">
|
||||
<h3 id="org25a32fa"><span class="section-number-3">4.4.</span> Test</h3>
|
||||
<div id="outline-container-org91e6317" class="outline-3">
|
||||
<h3 id="org91e6317"><span class="section-number-3">4.4.</span> Test</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">aa = importdata(<span class="org-string">"correctInterf-vlm-220201.dat"</span>);
|
||||
@ -865,8 +866,8 @@ This may be done using FE software.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb7db314" class="outline-3">
|
||||
<h3 id="orgb7db314"><span class="section-number-3">4.5.</span> Measured frame deformation</h3>
|
||||
<div id="outline-container-org5ca0ac8" class="outline-3">
|
||||
<h3 id="org5ca0ac8"><span class="section-number-3">4.5.</span> Measured frame deformation</h3>
|
||||
<div class="outline-text-3" id="text-4-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">data = table2array(readtable(<span class="org-string">'itf_polynom.csv'</span>,<span class="org-string">'NumHeaderLines'</span>,1));
|
||||
@ -894,7 +895,7 @@ ry1 = 1e<span class="org-builtin">-</span>9<span class="org-builtin">*</span>dat
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6aebdab" class="figure">
|
||||
<div id="org96336ed" class="figure">
|
||||
<p><img src="figs/calibration_drx_pres.png" alt="calibration_drx_pres.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>description</p>
|
||||
@ -967,8 +968,8 @@ f_ry1 = fit(180<span class="org-builtin">/</span><span class="org-matlab-math">p
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5494ab9" class="outline-3">
|
||||
<h3 id="org5494ab9"><span class="section-number-3">4.6.</span> Test</h3>
|
||||
<div id="outline-container-orgb94c7fb" class="outline-3">
|
||||
<h3 id="orgb94c7fb"><span class="section-number-3">4.6.</span> Test</h3>
|
||||
<div class="outline-text-3" id="text-4-6">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">filename = <span class="org-string">"/home/thomas/mnt/data_id21/22Jan/blc13550/id21/test_xtal1_interf/test_xtal1_interf_0001/test_xtal1_interf_0001.h5"</span>;
|
||||
@ -1000,7 +1001,7 @@ data.xtal2_111_d = double(h5read(filename, <span class="org-string">'/7.1/instru
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org85bdc09" class="figure">
|
||||
<div id="orgb431cdd" class="figure">
|
||||
<p><img src="figs/drifts_xtal2_detrend.png" alt="drifts_xtal2_detrend.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Drifts of the second crystal as a function of Bragg Angle</p>
|
||||
@ -1017,8 +1018,8 @@ data.xtal2_111_d = double(h5read(filename, <span class="org-string">'/7.1/instru
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org218f95f" class="outline-3">
|
||||
<h3 id="org218f95f"><span class="section-number-3">4.7.</span> Repeatability of frame deformation</h3>
|
||||
<div id="outline-container-org1c4abff" class="outline-3">
|
||||
<h3 id="org1c4abff"><span class="section-number-3">4.7.</span> Repeatability of frame deformation</h3>
|
||||
<div class="outline-text-3" id="text-4-7">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">filename = <span class="org-string">"/home/thomas/mnt/data_id21/22Jan/blc13550/id21/test_xtal1_interf/test_xtal1_interf_0001/test_xtal1_interf_0001.h5"</span>;
|
||||
@ -1068,15 +1069,15 @@ data_2.dz = 1e<span class="org-builtin">-</span>9<span class="org-builtin">*<
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5b8904d" class="outline-2">
|
||||
<h2 id="org5b8904d"><span class="section-number-2">5.</span> Attocube - Periodic Non-Linearity</h2>
|
||||
<div id="outline-container-orgcf35007" class="outline-2">
|
||||
<h2 id="orgcf35007"><span class="section-number-2">5.</span> Attocube - Periodic Non-Linearity</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<p>
|
||||
<a id="org44bdb6d"></a>
|
||||
<a id="org455a211"></a>
|
||||
</p>
|
||||
<p>
|
||||
Interferometers have some periodic nonlinearity (NO_ITEM_DATA:thurner15_fiber_based_distan_sensin_inter).
|
||||
The period is a fraction of the wavelength (usually \(\lambda/2\)) and can be due to polarization mixing, non perfect alignment of the optical components and unwanted reflected beams (See NO_ITEM_DATA:ducourtieux18_towar_high_precis_posit_contr, NO_ITEM_DATA:thurner15_fiber_based_distan_sensin_inter).
|
||||
The period is a fraction of the wavelength (usually \(\lambda/2\)) and can be due to polarization mixing, non perfect alignment of the optical components and unwanted reflected beams (<a href="#citeproc_bib_item_1">Ducourtieux 2018</a>; <a href="#citeproc_bib_item_2">Thurner et al. 2015</a>).
|
||||
The amplitude of the nonlinearity can vary from a fraction of a nanometer to tens of nanometers.
|
||||
</p>
|
||||
|
||||
@ -1093,8 +1094,8 @@ This process is performed over several periods in order to characterize the erro
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9f6a57f" class="outline-3">
|
||||
<h3 id="org9f6a57f"><span class="section-number-3">5.1.</span> Measurement Setup</h3>
|
||||
<div id="outline-container-org91573e9" class="outline-3">
|
||||
<h3 id="org91573e9"><span class="section-number-3">5.1.</span> Measurement Setup</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<p>
|
||||
The metrology that will be compared with the interferometers are the strain gauges incorporated in the PI piezoelectric stacks.
|
||||
@ -1105,7 +1106,7 @@ It is here supposed that the measured displacement by the strain gauges are conv
|
||||
It is also supposed that we are at a certain Bragg angle, and that the stepper motors are not moving: only the piezoelectric actuators are used.
|
||||
</p>
|
||||
|
||||
<div class="note" id="org3574ce6">
|
||||
<div class="note" id="org38e45ca">
|
||||
<p>
|
||||
Note that the strain gauges are measuring the relative displacement of the piezoelectric stacks while the interferometers are measuring the relative motion between the second crystals and the metrology frame.
|
||||
</p>
|
||||
@ -1121,7 +1122,7 @@ As any deformations of the metrology frame of deformation of the crystal’s
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The setup is schematically with the block diagram in Figure <a href="#orgf2d914c">13</a>.
|
||||
The setup is schematically with the block diagram in Figure <a href="#org5df73e7">13</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -1137,7 +1138,7 @@ The PI controller takes care or controlling to position as measured by the strai
|
||||
</ul>
|
||||
|
||||
|
||||
<div id="orgf2d914c" class="figure">
|
||||
<div id="org5df73e7" class="figure">
|
||||
<p><img src="figs/block_diagram_lut_attocube.png" alt="block_diagram_lut_attocube.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Block Diagram schematic of the setup used to measure the periodic non-linearity of the Attocube</p>
|
||||
@ -1149,8 +1150,8 @@ The problem is to estimate the periodic non-linearity of the Attocube from the i
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc06acba" class="outline-3">
|
||||
<h3 id="orgc06acba"><span class="section-number-3">5.2.</span> Choice of the reference signal</h3>
|
||||
<div id="outline-container-orgdd79356" class="outline-3">
|
||||
<h3 id="orgdd79356"><span class="section-number-3">5.2.</span> Choice of the reference signal</h3>
|
||||
<div class="outline-text-3" id="text-5-2">
|
||||
<p>
|
||||
The main specifications for the reference signal are;
|
||||
@ -1174,8 +1175,8 @@ Based on the above discussion, one suitable excitation signal is a sinusoidal sw
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org26743c0" class="outline-3">
|
||||
<h3 id="org26743c0"><span class="section-number-3">5.3.</span> Repeatability of the non-linearity</h3>
|
||||
<div id="outline-container-org2268c53" class="outline-3">
|
||||
<h3 id="org2268c53"><span class="section-number-3">5.3.</span> Repeatability of the non-linearity</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
<p>
|
||||
Instead of calibrating the non-linear errors of the interferometers over the full fast jack stroke (25mm), one can only calibrate the errors of one period.
|
||||
@ -1195,8 +1196,8 @@ One way to precisely estimate the laser wavelength is to estimate the non linear
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org15014d3" class="outline-3">
|
||||
<h3 id="org15014d3"><span class="section-number-3">5.4.</span> Simulation</h3>
|
||||
<div id="outline-container-orgadef69b" class="outline-3">
|
||||
<h3 id="orgadef69b"><span class="section-number-3">5.4.</span> Simulation</h3>
|
||||
<div class="outline-text-3" id="text-5-4">
|
||||
<p>
|
||||
Suppose we have a first approximation of the non-linear period.
|
||||
@ -1216,10 +1217,10 @@ period_nl = period_est <span class="org-builtin">+</span> period_err; <span clas
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The non-linear errors are first estimated at the beginning of the stroke (Figure <a href="#org94b9790">14</a>).
|
||||
The non-linear errors are first estimated at the beginning of the stroke (Figure <a href="#org4cf8064">14</a>).
|
||||
</p>
|
||||
|
||||
<div id="org94b9790" class="figure">
|
||||
<div id="org4cf8064" class="figure">
|
||||
<p><img src="figs/non_linear_errors_start_stroke.png" alt="non_linear_errors_start_stroke.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Estimation of the non-linear errors at the beginning of the stroke</p>
|
||||
@ -1227,7 +1228,7 @@ The non-linear errors are first estimated at the beginning of the stroke (Figure
|
||||
|
||||
<p>
|
||||
From this only measurement, it is not possible to estimate with great accuracy the period of the error.
|
||||
To do so, the same measurement is performed with a stroke of several millimeters (Figure <a href="#org8301473">15</a>).
|
||||
To do so, the same measurement is performed with a stroke of several millimeters (Figure <a href="#orgb57a43c">15</a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -1236,7 +1237,7 @@ This is due to a mismatch between the estimated period and the true period of th
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org8301473" class="figure">
|
||||
<div id="orgb57a43c" class="figure">
|
||||
<p><img src="figs/non_linear_errors_middle_stroke.png" alt="non_linear_errors_middle_stroke.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Estimated non-linear errors at a latter position</p>
|
||||
@ -1269,7 +1270,7 @@ with \(\lambda_{\text{est}}\) the estimated error’s period.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
From Figure <a href="#org8301473">15</a>, we can see that there is an offset between the two curves.
|
||||
From Figure <a href="#orgb57a43c">15</a>, we can see that there is an offset between the two curves.
|
||||
Let’s call this offset \(\epsilon_x\), we then have:
|
||||
</p>
|
||||
\begin{equation}
|
||||
@ -1349,8 +1350,8 @@ The maximum stroke is 2.9 [mm]
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga71d790" class="outline-3">
|
||||
<h3 id="orga71d790"><span class="section-number-3">5.5.</span> Measurements</h3>
|
||||
<div id="outline-container-org8ddf260" class="outline-3">
|
||||
<h3 id="org8ddf260"><span class="section-number-3">5.5.</span> Measurements</h3>
|
||||
<div class="outline-text-3" id="text-5-5">
|
||||
<p>
|
||||
We have some constrains on the way the motion is imposed and measured:
|
||||
@ -1376,10 +1377,20 @@ Suppose we have the power spectral density (PSD) of both \(n_a\) and \(n_g\).
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org515d8fb" class="outline-2">
|
||||
<h2 id="org515d8fb">Bibliography</h2>
|
||||
<div class="outline-text-2" id="text-org515d8fb">
|
||||
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
|
||||
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” doi:<a href="https://doi.org/10.13140/rg.2.2.21044.35205">10.13140/rg.2.2.21044.35205</a>.</div>
|
||||
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” <i>Applied Optics</i> 54 (10). Optical Society of America: 3051–63.</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2022-06-02 Thu 22:25</p>
|
||||
<p class="date">Created: 2022-06-07 Tue 10:58</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -16,7 +16,7 @@
|
||||
#+LaTeX_CLASS: scrreprt
|
||||
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
|
||||
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
|
||||
#+LATEX_HEADER_EXTRA: \bibliography{ref}
|
||||
#+LATEX_HEADER_EXTRA: \addbibresource{dcm-metrology.bib}
|
||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||
#+PROPERTY: header-args:matlab+ :comments org
|
||||
@ -1069,7 +1069,7 @@ plot(data_2.bragg, data_2.mframe_u)
|
||||
** Introduction :ignore:
|
||||
|
||||
Interferometers have some periodic nonlinearity [cite:@thurner15_fiber_based_distan_sensin_inter].
|
||||
The period is a fraction of the wavelength (usually $\lambda/2$) and can be due to polarization mixing, non perfect alignment of the optical components and unwanted reflected beams [cite:See @ducourtieux18_towar_high_precis_posit_contr page 67 to 69;@thurner15_fiber_based_distan_sensin_inter;].
|
||||
The period is a fraction of the wavelength (usually $\lambda/2$) and can be due to polarization mixing, non perfect alignment of the optical components and unwanted reflected beams cite:ducourtieux18_towar_high_precis_posit_contr,thurner15_fiber_based_distan_sensin_inter.
|
||||
The amplitude of the nonlinearity can vary from a fraction of a nanometer to tens of nanometers.
|
||||
|
||||
In the DCM case, when using Attocube interferometers, the period non-linearity are in the order of several nanometers with a period of $765\,nm$.
|
||||
@ -1584,3 +1584,10 @@ xtal2_rectangle = [results.ps + 0.02/2*y + 0.07/2*x;
|
||||
#+begin_src matlab
|
||||
patch(100*xtal2_rectangle(:,1), 100*xtal2_rectangle(:,2), 100*xtal2_rectangle(:,3), 'k-')
|
||||
#+end_src
|
||||
|
||||
* Bibliography
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
#+latex: \printbibliography[heading=none]
|
||||
[[bibliography:dcm-metrology.bib]]
|
||||
|
||||
Binary file not shown.
Loading…
Reference in New Issue
Block a user