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< title > NASS - Short Stroke Metrology< / title >
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< h1 class = "title" > NASS - Short Stroke Metrology< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
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< li > < a href = "#org59912f6" > 1. Measurement Principle< / a > < / li >
< li > < a href = "#orge0aedba" > 2. X-Y-Z measurement< / a > < / li >
< li > < a href = "#orgdd43e82" > 3. Tilt measurement< / a > < / li >
< li > < a href = "#orgbaaa145" > 4. Conclusion< / a > < / li >
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< p > This report is also available as a < a href = "./short-stroke-metrology.pdf" > pdf< / a > .< / p >
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< 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.
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It is structured as follow:
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< ul class = "org-ul" >
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< li > Section < a href = "#orgc196cb4" > 1< / a > : the meaurement principle is described.< / li >
< li > Section < a href = "#org54a9efd" > 2< / a > : the requirements for the interferometers measuring translations are described< / li >
< li > Section < a href = "#org55ec5cf" > 3< / a > : the same is done for the rotations< / li >
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< h2 id = "org59912f6" > < span class = "section-number-2" > 1< / span > Measurement Principle< / h2 >
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< a id = "orgc196cb4" > < / a >
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Here are the defined wanted displacement of the reflector that should be inside the measurement stroke of the metrology system.
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The defined translations and rotations are defined with respect to the frame shown in Figure < a href = "#orgbada069" > 1< / a > .
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< 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 >
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< div id = "orgbada069" class = "figure" >
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< p > < img src = "figs/short_stroke_metrology_concept.png" alt = "short_stroke_metrology_concept.png" / >
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< 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 >
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< p >
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Here are the approximate dimensions shown in Figure < a href = "#orgbada069" > 1< / a > :
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< li > \(d_0 \approx 10\,[mm]\)< / li >
< li > \(L \approx 150\,[mm]\)< / li >
< li > \(R \approx 250\,[mm]\)< / li >
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< 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 >
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< h2 id = "orge0aedba" > < span class = "section-number-2" > 2< / span > X-Y-Z measurement< / h2 >
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< a id = "org54a9efd" > < / a >
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< p >
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The geometry for the interferometers measuring translations is shown in Figure < a href = "#orgda75e82" > 2< / a > :
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< 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 >
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< div id = "orgda75e82" class = "figure" >
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< p > < img src = "figs/translation_interferometers.png" alt = "translation_interferometers.png" / >
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< p > < span class = "figure-number" > Figure 2: < / span > Interferometers that are measuring translation< / p >
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< 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:
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< p >
\[ \theta \approx 8.0\,[mrad] \]
< / p >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Specifications for the translation interferometers< / caption >
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< th scope = "col" class = "org-left" > < b > Specification< / b > < / th >
< th scope = "col" class = "org-left" > < b > Value< / b > < / th >
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< td class = "org-left" > Axial Acceptance< / td >
< td class = "org-left" > \(\pm 1\,[mm]\)< / td >
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< td class = "org-left" > Angular Acceptance< / td >
< td class = "org-left" > \(\pm 8\,[mrad]\)< / td >
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< td class = "org-left" > Distance to target< / td >
< td class = "org-left" > \(10\,[mm]\)< / td >
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< td class = "org-left" > Target< / td >
< td class = "org-left" > Convex with \(R = 250\,[mm]\)< / td >
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< h2 id = "orgdd43e82" > < span class = "section-number-2" > 3< / span > Tilt measurement< / h2 >
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< a id = "org55ec5cf" > < / a >
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< 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:
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< p >
\[ z \approx 2.5\,[mm] \]
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< p >
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The geometry for the interferometers measuring rotations is shown in Figure < a href = "#org8855462" > 3< / a > :
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< / p >
< ul class = "org-ul" >
< li > \(d_0 > 10\,[mm]\)< / li >
< li > \(\theta = \pm 10\,[mrad]\)< / li >
< li > \(z = \pm 2.5\, [mm]\)< / li >
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< div id = "org8855462" class = "figure" >
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< p > < img src = "figs/rotation_interferometers.png" alt = "rotation_interferometers.png" / >
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< p > < span class = "figure-number" > Figure 3: < / span > Interferometers that are measuring tilt< / p >
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< table id = "orgb2b4f70" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Specifications for the rotation interferometers< / caption >
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< th scope = "col" class = "org-left" > < b > Specification< / b > < / th >
< th scope = "col" class = "org-left" > < b > Value< / b > < / th >
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< td class = "org-left" > Axial Acceptance< / td >
< td class = "org-left" > \(\pm 2.5\,[mm]\)< / td >
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< td class = "org-left" > Angular Acceptance< / td >
< td class = "org-left" > \(\pm 10\,[mrad]\)< / td >
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< td class = "org-left" > Distance to target< / td >
< td class = "org-left" > \(10\,[mm]\)< / td >
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< td class = "org-left" > Target< / td >
< td class = "org-left" > Flat mirror< / td >
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< h2 id = "orgbaaa145" > < span class = "section-number-2" > 4< / span > Conclusion< / h2 >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2021-02-19 ven. 11:20< / p >
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