334 lines
11 KiB
Org Mode
334 lines
11 KiB
Org Mode
#+TITLE: ESRF Double Crystal Monochromator - Lookup Tables
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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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#+LATEX_HEADER_EXTRA: \bibliography{ref}
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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+ :tangle no
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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="./dcm_lookup_tables.pdf">pdf</a>.</p>
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<hr>
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#+end_export
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#+latex: \clearpage
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* Introduction
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* Stepper Motors Calibration
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/dcm_stepper_lut.m
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:END:
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<<sec:dcm_stepper_lut>>
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** Introduction :ignore:
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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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#+begin_src matlab :tangle no :noweb yes
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<<m-init-path>>
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#+end_src
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#+begin_src matlab :eval no :noweb yes
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<<m-init-path-tangle>>
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#+end_src
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#+begin_src matlab :noweb yes
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<<m-init-other>>
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#+end_src
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** Schematic
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** Simulation
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In this section, we suppose that we are in the frame of one fast jack (all transformations are already done), and we wish to create a LUT for one fast jack.
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Let's say with make a Bragg angle scan between 10deg and 60deg during 100s.
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#+begin_src matlab
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Fs = 10e3; % Sample Frequency [Hz]
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t = 0:1/Fs:10; % Time vector [s]
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theta = linspace(10, 40, length(t)); % Bragg Angle [deg]
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#+end_src
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The IcePAP steps are following the theoretical formula:
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\begin{equation}
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d_z = \frac{d_{\text{off}}}{2 \cos \theta}
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\end{equation}
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with $\theta$ the bragg angle and $d_{\text{off}} = 10\,mm$.
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The motion to follow is then:
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#+begin_src matlab
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perfect_motion = 10e-3./(2*cos(theta*pi/180)); % Perfect motion [m]
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#+end_src
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And the IcePAP is generated those steps:
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#+begin_src matlab
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icepap_steps = perfect_motion; % IcePAP steps measured by Speedgoat [m]
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#+end_src
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#+begin_src matlab :exports none
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%% Steps as a function of the bragg angle
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figure;
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plot(theta, icepap_steps);
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xlabel('Bragg Angle [deg]'); ylabel('IcePAP Steps [m]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/bragg_angle_icepap_steps_idealized.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:bragg_angle_icepap_steps_idealized
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#+caption: IcePAP Steps as a function of the Bragg Angle
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#+RESULTS:
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[[file:figs/bragg_angle_icepap_steps_idealized.png]]
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Then, we are measuring the motion of the Fast Jack using the Interferometer.
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The motion error is larger than in reality to be angle to see it more easily.
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#+begin_src matlab
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motion_error = 100e-6*sin(2*pi*perfect_motion/1e-3); % Error motion [m]
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measured_motion = perfect_motion + motion_error; % Measured motion of the Fast Jack [m]
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#+end_src
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#+begin_src matlab :exports none
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%% Measured Motion and Idealized Motion
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figure;
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hold on;
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plot(icepap_steps, measured_motion, ...
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'DisplayName', 'Measured Motion');
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plot(icepap_steps, perfect_motion, 'k--', ...
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'DisplayName', 'Ideal Motion');
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hold off;
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xlabel('IcePAP Steps [m]'); ylabel('Measured Motion [m]');
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/measured_and_ideal_motion_fast_jacks.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:measured_and_ideal_motion_fast_jacks
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#+caption: Measured motion as a function of the IcePAP Steps
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#+RESULTS:
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[[file:figs/measured_and_ideal_motion_fast_jacks.png]]
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Let's now compute the lookup table.
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For each micrometer of the IcePAP step, another step is associated that correspond to a position closer to the wanted position.
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#+begin_src matlab
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%% Get range for the LUT
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% We correct only in the range of tested/measured motion
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lut_range = round(1e6*min(icepap_steps)):round(1e6*max(icepap_steps)); % IcePAP steps [um]
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%% Initialize the LUT
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lut = zeros(size(lut_range));
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%% For each um in this range
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for i = 1:length(lut_range)
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% Get points indices where the measured motion is closed to the wanted one
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close_points = measured_motion > 1e-6*lut_range(i) - 500e-9 & measured_motion < 1e-6*lut_range(i) + 500e-9;
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% Get the corresponding closest IcePAP step
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lut(i) = round(1e6*mean(icepap_steps(close_points))); % [um]
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end
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#+end_src
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#+begin_src matlab :exports none
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%% Generated Lookup Table
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figure;
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plot(lut_range, lut);
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xlabel('IcePAP input step [um]'); ylabel('Lookup Table output [um]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/generated_lut_icepap.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:generated_lut_icepap
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#+caption: Generated Lookup Table
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#+RESULTS:
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[[file:figs/generated_lut_icepap.png]]
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The current LUT implementation is the following:
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#+begin_src matlab
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motion_error_lut = zeros(size(lut_range));
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for i = 1:length(lut_range)
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% Get points indices where the icepap step is close to the wanted one
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close_points = icepap_steps > 1e-6*lut_range(i) - 500e-9 & icepap_steps < 1e-6*lut_range(i) + 500e-9;
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% Get the corresponding motion error
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motion_error_lut(i) = lut_range(i) + (lut_range(i) - round(1e6*mean(measured_motion(close_points)))); % [um]
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end
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#+end_src
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Let's compare the two Lookup Table in Figure [[fig:lut_comparison_two_methods]].
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#+begin_src matlab :exports none
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%% Comparison of the two Generated Lookup Table
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figure;
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hold on;
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plot(lut_range, lut, ...
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'DisplayName', 'New LUT');
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plot(lut_range, motion_error_lut, ...
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'DisplayName', 'Old LUT');
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hold off;
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xlabel('IcePAP input step [um]'); ylabel('Lookup Table output [um]');
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/lut_comparison_two_methods.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:lut_comparison_two_methods
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#+caption: Comparison of the two lookup tables
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#+RESULTS:
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[[file:figs/lut_comparison_two_methods.png]]
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If we plot the "corrected steps" for all steps for both methods, we clearly see the difference (Figure [[fig:lut_correct_and_motion_error]]).
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#+begin_src matlab :exports none
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%% Corrected motion and motion error at each step position
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figure;
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hold on;
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plot(lut_range, lut-lut_range, ...
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'DisplayName', 'New LUT');
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plot(lut_range, motion_error_lut-lut_range, ...
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'DisplayName', 'Old LUT');
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hold off;
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xlabel('IcePAP Steps [um]'); ylabel('Corrected motion [um]');
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ylim([-110, 110])
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/lut_correct_and_motion_error.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:lut_correct_and_motion_error
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#+caption: LUT correction and motion error as a function of the IcePAP steps
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#+RESULTS:
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[[file:figs/lut_correct_and_motion_error.png]]
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Let's now implement both LUT to see which implementation is correct.
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#+begin_src matlab :exports none
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icepap_steps_output_new = lut(round(1e6*icepap_steps)-lut_range(1)+1);
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i = round(1e6*icepap_steps)-motion_error_lut(1)+1;
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i(i>length(motion_error_lut)) = length(motion_error_lut);
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icepap_steps_output_old = motion_error_lut(i);
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#+end_src
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#+begin_src matlab
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motion_new = zeros(size(icepap_steps_output_new));
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motion_old = zeros(size(icepap_steps_output_old));
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for i = 1:length(icepap_steps_output_new)
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[~, i_step] = min(abs(icepap_steps_output_new(i) - 1e6*icepap_steps));
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motion_new(i) = measured_motion(i_step);
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[~, i_step] = min(abs(icepap_steps_output_old(i) - 1e6*icepap_steps));
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motion_old(i) = measured_motion(i_step);
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end
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#+end_src
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#+begin_src matlab :exports none
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%% Measured Motion and Idealized Motion
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% Use only middle motion where the LUT is working
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i = round(0.1*length(icepap_steps)):round(0.9*length(icepap_steps));
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figure;
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hold on;
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plot(icepap_steps(i), motion_new(i), ...
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'DisplayName', 'Motion (new LUT)');
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plot(icepap_steps(i), motion_old(i), ...
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'DisplayName', 'Motion (old LUT)');
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plot(icepap_steps(i), perfect_motion(i), 'k--', ...
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'DisplayName', 'Ideal Motion');
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hold off;
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xlabel('IcePAP Steps [m]'); ylabel('Measured Motion [m]');
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/compare_old_new_lut_motion.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:compare_old_new_lut_motion
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#+caption: Comparison of the obtained motion with new and old LUT
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#+RESULTS:
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[[file:figs/compare_old_new_lut_motion.png]]
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* Attocube Calibration :noexport:
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* Helping Functions :noexport:
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** Initialize Path
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#+NAME: m-init-path
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#+BEGIN_SRC matlab
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%% Path for functions, data and scripts
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addpath('./matlab/mat/'); % Path for data
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addpath('./matlab/'); % Path for scripts
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#+END_SRC
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#+NAME: m-init-path-tangle
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#+BEGIN_SRC matlab
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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#+END_SRC
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** Initialize Simscape Model
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#+NAME: m-init-simscape
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#+begin_src matlab
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#+end_src
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** Initialize other elements
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#+NAME: m-init-other
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#+BEGIN_SRC matlab
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(1, 3, 1000);
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#+END_SRC
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* Bibliography :ignore:
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#+latex: \printbibliography
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