2021-02-19 11:10:48 +01:00
<?xml version="1.0" encoding="utf-8"?>
< !DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
< html xmlns = "http://www.w3.org/1999/xhtml" lang = "en" xml:lang = "en" >
< head >
2021-02-19 11:13:39 +01:00
<!-- 2021 - 02 - 19 ven. 11:13 -->
2021-02-19 11:10:48 +01:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< title > NASS - Short Stroke Metrology< / 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,
fontCache: "global"
},
tex: {
tags: "ams",
multlineWidth: "%MULTLINEWIDTH",
tagSide: "right",
macros: {bm: ["\\boldsymbol{#1}",1],},
tagIndent: ".8em"
}
};
< / script >
< 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" > NASS - Short Stroke Metrology< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2021-02-19 11:13:39 +01:00
< li > < a href = "#orgbab5500" > 1. Measurement Principle< / a > < / li >
< li > < a href = "#org8f0a94b" > 2. X-Y-Z measurement< / a > < / li >
< li > < a href = "#orgda8f2a5" > 3. Tilt measurement< / a > < / li >
< li > < a href = "#org6ff8891" > 4. Conclusion< / a > < / li >
2021-02-19 11:10:48 +01:00
< / ul >
< / div >
< / div >
2021-02-19 11:13:39 +01:00
< hr >
< p > This report is also available as a < a href = "./short-stroke-metrology.pdf" > pdf< / a > .< / p >
< hr >
2021-02-19 11:10:48 +01:00
< p >
The goal of this document is to analyze the feasibility of a short stroke metrology system for the NASS using fixed interferemoter and the same reflector as for the long stroke metrology system.
< / p >
< p >
It is structured as follow:
< / p >
< ul class = "org-ul" >
2021-02-19 11:13:39 +01:00
< li > Section < a href = "#org81efe49" > 1< / a > : the meaurement principle is described.< / li >
< li > Section < a href = "#orga41b53c" > 2< / a > : the requirements for the interferometers measuring translations are described< / li >
< li > Section < a href = "#org8b209d1" > 3< / a > : the same is done for the rotations< / li >
2021-02-19 11:10:48 +01:00
< / ul >
2021-02-19 11:13:39 +01:00
< div id = "outline-container-orgbab5500" class = "outline-2" >
< h2 id = "orgbab5500" > < span class = "section-number-2" > 1< / span > Measurement Principle< / h2 >
2021-02-19 11:10:48 +01:00
< div class = "outline-text-2" id = "text-1" >
< p >
2021-02-19 11:13:39 +01:00
< a id = "org81efe49" > < / a >
2021-02-19 11:10:48 +01:00
< / p >
< p >
Here are the defined wanted displacement of the reflector that should be inside the measurement stroke of the metrology system.
2021-02-19 11:13:39 +01:00
The defined translations and rotations are defined with respect to the frame shown in Figure < a href = "#org25ba32a" > 1< / a > .
2021-02-19 11:10:48 +01:00
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > d_x = 0; < span class = "org-comment" > % Wanted translation of the reflector in the x direction [m]< / span >
d_y = 1e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Wanted translation of the reflector in the y direction [m]< / span >
d_z = 1e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Wanted translation of the reflector in the z direction [m]< / span >
R_x = 10e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Wanted rotation of the reflector along the x axis [rad]< / span >
R_y = 0; < span class = "org-comment" > % Wanted rotation of the reflector along the y axis [rad]< / span >
< / pre >
< / div >
2021-02-19 11:13:39 +01:00
< div id = "org25ba32a" class = "figure" >
2021-02-19 11:10:48 +01:00
< p > < img src = "figs/short_stroke_metrology_concept.png" alt = "short_stroke_metrology_concept.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Short Stroke Metrology - Concept. Blue interferometers are used to measure the X-Y-Z motion of the reflector. Red interferometers are used to measure tilt motion of the reflector.< / p >
< / div >
< p >
2021-02-19 11:13:39 +01:00
Here are the approximate dimensions shown in Figure < a href = "#org25ba32a" > 1< / a > :
2021-02-19 11:10:48 +01:00
< / p >
< ul class = "org-ul" >
< li > \(d_0 \approx 10\,[mm]\)< / li >
< li > \(L \approx 150\,[mm]\)< / li >
< li > \(R \approx 250\,[mm]\)< / li >
< / ul >
< div class = "org-src-container" >
< pre class = "src src-matlab" > d0 = 10e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % [m]< / span >
L = 150e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % [m]< / span >
R = 250e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % [m]< / span >
< / pre >
< / div >
< / div >
< / div >
2021-02-19 11:13:39 +01:00
< div id = "outline-container-org8f0a94b" class = "outline-2" >
< h2 id = "org8f0a94b" > < span class = "section-number-2" > 2< / span > X-Y-Z measurement< / h2 >
2021-02-19 11:10:48 +01:00
< div class = "outline-text-2" id = "text-2" >
< p >
2021-02-19 11:13:39 +01:00
< a id = "orga41b53c" > < / a >
2021-02-19 11:10:48 +01:00
< / p >
< p >
2021-02-19 11:13:39 +01:00
The geometry for the interferometers measuring translations is shown in Figure < a href = "#org0718921" > 2< / a > :
2021-02-19 11:10:48 +01:00
< / p >
< ul class = "org-ul" >
< li > \(R = 250\,[mm]\)< / li >
< li > \(d_0 > 10\,[mm]\)< / li >
< li > \(d_x = \pm 1\,[mm]\)< / li >
< li > \(d_y = \pm 1\,[mm]\)< / li >
< / ul >
2021-02-19 11:13:39 +01:00
< div id = "org0718921" class = "figure" >
2021-02-19 11:10:48 +01:00
< p > < img src = "figs/translation_interferometers.png" alt = "translation_interferometers.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Interferometers that are measuring translation< / p >
< / div >
< p >
The angle of the reflected beam is approximately equal to:
< / p >
\begin{equation}
\theta \approx 2 \frac{d_y}{R}
\end{equation}
< p >
And we obtain:
< / p >
< p >
\[ \theta \approx 8.0\,[mrad] \]
< / p >
2021-02-19 11:13:39 +01:00
< table id = "org27e7f4b" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
2021-02-19 11:10:48 +01:00
< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Specifications for the translation interferometers< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Specification< / th >
< th scope = "col" class = "org-left" > Value< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Axial Acceptance< / td >
< td class = "org-left" > \(\pm 1\,[mm]\)< / td >
< / tr >
< tr >
< td class = "org-left" > Angular Acceptance< / td >
< td class = "org-left" > \(\pm 8\,[mrad]\)< / td >
< / tr >
< tr >
< td class = "org-left" > Distance to target< / td >
< td class = "org-left" > \(10\,[mm]\)< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
2021-02-19 11:13:39 +01:00
< div id = "outline-container-orgda8f2a5" class = "outline-2" >
< h2 id = "orgda8f2a5" > < span class = "section-number-2" > 3< / span > Tilt measurement< / h2 >
2021-02-19 11:10:48 +01:00
< div class = "outline-text-2" id = "text-3" >
< p >
2021-02-19 11:13:39 +01:00
< a id = "org8b209d1" > < / a >
2021-02-19 11:10:48 +01:00
< / p >
< p >
The tilt \(\theta\) of the flat mirror is directly equal to the tilt of the reflector.
However, the \(z\) displacement on the flat part is equal to:
< / p >
\begin{equation}
z \approx d_z + L \theta_y
\end{equation}
< p >
And we obtain:
< / p >
< p >
\[ z \approx 2.5\,[mm] \]
< / p >
< p >
2021-02-19 11:13:39 +01:00
The geometry for the interferometers measuring rotations is shown in Figure < a href = "#org5e4c6eb" > 3< / a > :
2021-02-19 11:10:48 +01:00
< / p >
< ul class = "org-ul" >
< li > \(d_0 > 10\,[mm]\)< / li >
< li > \(\theta = \pm 10\,[mrad]\)< / li >
< li > \(z = \pm 2.5\, [mm]\)< / li >
< / ul >
2021-02-19 11:13:39 +01:00
< div id = "org5e4c6eb" class = "figure" >
2021-02-19 11:10:48 +01:00
< p > < img src = "figs/rotation_interferometers.png" alt = "rotation_interferometers.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Interferometers that are measuring tilt< / p >
< / div >
2021-02-19 11:13:39 +01:00
< table id = "org0d63b1d" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
2021-02-19 11:10:48 +01:00
< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Specifications for the rotation interferometers< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Specification< / th >
< th scope = "col" class = "org-left" > Value< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Axial Acceptance< / td >
< td class = "org-left" > \(\pm 2.5\,[mm]\)< / td >
< / tr >
< tr >
< td class = "org-left" > Angular Acceptance< / td >
< td class = "org-left" > \(\pm 10\,[mrad]\)< / td >
< / tr >
< tr >
< td class = "org-left" > Distance to target< / td >
< td class = "org-left" > \(10\,[mm]\)< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
2021-02-19 11:13:39 +01:00
< div id = "outline-container-org6ff8891" class = "outline-2" >
< h2 id = "org6ff8891" > < span class = "section-number-2" > 4< / span > Conclusion< / h2 >
2021-02-19 11:10:48 +01:00
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2021-02-19 11:13:39 +01:00
< p class = "date" > Created: 2021-02-19 ven. 11:13< / p >
2021-02-19 11:10:48 +01:00
< / div >
< / body >
< / html >
