172 lines
6.3 KiB
Org Mode
172 lines
6.3 KiB
Org Mode
#+TITLE: NASS - Short Stroke Metrology
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:DRAWER:
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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#+BIND: org-latex-image-default-option "scale=1"
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#+BIND: org-latex-image-default-width ""
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#+LaTeX_CLASS: scrreprt
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#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
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#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :noweb yes
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
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#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
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#+PROPERTY: header-args:latex+ :results file raw replace
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#+PROPERTY: header-args:latex+ :buffer no
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#+PROPERTY: header-args:latex+ :tangle no
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#+PROPERTY: header-args:latex+ :eval no-export
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#+PROPERTY: header-args:latex+ :exports results
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#+PROPERTY: header-args:latex+ :mkdirp yes
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#+PROPERTY: header-args:latex+ :output-dir figs
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
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:END:
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#+begin_export html
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<hr>
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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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<hr>
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#+end_export
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* Introduction :ignore:
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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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- Section [[sec:meas_principle]]: the meaurement principle is described.
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- Section [[sec:translation_interferometers]]: the requirements for the interferometers measuring translations are described
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- Section [[sec:rotation_interferometers]]: the same is done for the rotations
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* Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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* Measurement Principle
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<<sec:meas_principle>>
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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 [[fig:short_stroke_metrology_concept]].
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#+begin_src matlab
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d_x = 0; % Wanted translation of the reflector in the x direction [m]
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d_y = 1e-3; % Wanted translation of the reflector in the y direction [m]
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d_z = 1e-3; % Wanted translation of the reflector in the z direction [m]
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R_x = 10e-3; % Wanted rotation of the reflector along the x axis [rad]
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R_y = 0; % Wanted rotation of the reflector along the y axis [rad]
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#+end_src
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#+name: fig:short_stroke_metrology_concept
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#+caption: 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.
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#+attr_latex: :width \linewidth
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[[file:figs/short_stroke_metrology_concept.png]]
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Here are the approximate dimensions shown in Figure [[fig:short_stroke_metrology_concept]]:
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- $d_0 \approx 10\,[mm]$
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- $L \approx 150\,[mm]$
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- $R \approx 250\,[mm]$
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#+begin_src matlab
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d0 = 10e-3; % [m]
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L = 150e-3; % [m]
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R = 250e-3; % [m]
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#+end_src
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* X-Y-Z measurement
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<<sec:translation_interferometers>>
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The geometry for the interferometers measuring translations is shown in Figure [[fig:translation_interferometers]]:
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- $R = 250\,[mm]$
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- $d_0 > 10\,[mm]$
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- $d_x = \pm 1\,[mm]$
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- $d_y = \pm 1\,[mm]$
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#+name: fig:translation_interferometers
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#+caption: Interferometers that are measuring translation
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[[file:figs/translation_interferometers.png]]
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The angle of the reflected beam is approximately equal to:
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\begin{equation}
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\theta \approx 2 \frac{d_y}{R}
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\end{equation}
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And we obtain:
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#+begin_src matlab :results raw replace :exports results :tangle no
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sprintf('\\[ \\theta \\approx %.1f\\,[mrad] \\]', 1e3*(2*d_y/R))
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#+end_src
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#+RESULTS:
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\[ \theta \approx 8.0\,[mrad] \]
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#+name: tab:spec_translation
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#+caption: Specifications for the translation interferometers
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#+attr_latex: :environment tabularx :width 0.6\linewidth :align Xc
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#+attr_latex: :center t :booktabs t :float t
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| *Specification* | *Value* |
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|--------------------+-----------------------------|
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| Axial Acceptance | $\pm 1\,[mm]$ |
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| Angular Acceptance | $\pm 8\,[mrad]$ |
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| Distance to target | $10\,[mm]$ |
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| Target | Convex with $R = 250\,[mm]$ |
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* Tilt measurement
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<<sec:rotation_interferometers>>
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The tilt $\theta$ of the flat mirror is directly equal to the tilt of the reflector.
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However, the $z$ displacement on the flat part is equal to:
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\begin{equation}
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z \approx d_z + L \theta_y
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\end{equation}
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And we obtain:
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#+begin_src matlab :results raw replace :exports results :tangle no
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sprintf('\\[ z \\approx %.1f\\,[mm] \\]', 1e3*(d_z + R_x*L))
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#+end_src
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#+RESULTS:
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\[ z \approx 2.5\,[mm] \]
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The geometry for the interferometers measuring rotations is shown in Figure [[fig:rotation_interferometers]]:
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- $d_0 > 10\,[mm]$
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- $\theta = \pm 10\,[mrad]$
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- $z = \pm 2.5\, [mm]$
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#+name: fig:rotation_interferometers
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#+caption: Interferometers that are measuring tilt
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[[file:figs/rotation_interferometers.png]]
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#+name: tab:spec_rotation
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#+caption: Specifications for the rotation interferometers
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#+attr_latex: :environment tabularx :width 0.4\linewidth :align Xc
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#+attr_latex: :center t :booktabs t :float t
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| *Specification* | *Value* |
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|--------------------+------------------|
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| Axial Acceptance | $\pm 2.5\,[mm]$ |
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| Angular Acceptance | $\pm 10\,[mrad]$ |
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| Distance to target | $10\,[mm]$ |
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| Target | Flat mirror |
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* Conclusion
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