208 lines
6.9 KiB
Org Mode
208 lines
6.9 KiB
Org Mode
#+TITLE: Attocube - Test Bench
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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="./css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
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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 raw replace :buffer no
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#+PROPERTY: header-args:latex+ :eval no-export
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#+PROPERTY: header-args:latex+ :exports both
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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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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :tangle script.m
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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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:END:
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* Estimation of the Spectral Density of the Attocube Noise
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** Introduction :ignore:
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#+name: fig:test-bench-shematic
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#+caption: Test Bench Schematic
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[[file:figs/test-bench-shematic.png]]
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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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** Long and Slow measurement
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The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$.
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#+begin_src matlab
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load('./mat/long_test2.mat', 'x', 't')
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Ts = 0.1; % [s]
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#+end_src
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#+begin_src matlab :exports none
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figure;
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plot(t/60/60, 1e9*x)
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xlabel('Time [h]'); ylabel('Displacement [nm]');
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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/long_meas_time_domain_full.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:long_meas_time_domain_full
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#+caption: Long measurement time domain data
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#+RESULTS:
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[[file:figs/long_meas_time_domain_full.png]]
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Let's fit the data with a step response to a first order low pass filter (Figure [[fig:long_meas_time_domain_fit]]).
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#+begin_src matlab
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f = @(b,x) b(1)*(1 - exp(-x/b(2)));
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y_cur = x(t < 17*60*60);
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t_cur = t(t < 17*60*60);
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nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
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B0 = [400e-9, 2*60*60]; % Choose Appropriate Initial Estimates
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[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
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#+end_src
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The corresponding time constant is (in [h]):
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#+begin_src matlab :results value replace :exports results
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B(2)/60/60
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#+end_src
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#+RESULTS:
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: 2.0576
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(t_cur/60/60, 1e9*y_cur);
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plot(t_cur/60/60, 1e9*f(B, t_cur));
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hold off;
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xlabel('Time [h]'); ylabel('Displacement [nm]');
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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/long_meas_time_domain_fit.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:long_meas_time_domain_fit
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#+caption: Fit of the measurement data with a step response of a first order low pass filter
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#+RESULTS:
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[[file:figs/long_meas_time_domain_fit.png]]
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We can see in Figure [[fig:long_meas_time_domain_full]] that there is a transient period where the measured displacement experiences some drifts.
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This is probably due to thermal effects.
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We only select the data between =t1= and =t2=.
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The obtained displacement is shown in Figure [[fig:long_meas_time_domain_zoom]].
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#+begin_src matlab
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t1 = 11; t2 = 17; % [h]
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x = x(t > t1*60*60 & t < t2*60*60);
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x = x - mean(x);
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t = t(t > t1*60*60 & t < t2*60*60);
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t = t - t(1);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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plot(t/60/60, 1e9*x);
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xlabel('Time [h]'); ylabel('Measured Displacement [nm]')
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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/long_meas_time_domain_zoom.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:long_meas_time_domain_zoom
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#+caption: Kept data (removed slow drifts during the first hours)
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#+RESULTS:
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[[file:figs/long_meas_time_domain_zoom.png]]
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The Power Spectral Density of the measured displacement is computed
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#+begin_src matlab
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win = hann(ceil(length(x)/20));
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[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
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#+end_src
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** Short and Fast measurement
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An second measurement is done in order to estimate the high frequency noise of the interferometer.
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The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s.
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#+begin_src matlab
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load('./mat/test.mat', 'x', 't')
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Ts = 1e-4; % [s]
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#+end_src
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The time domain measurement is shown in Figure [[fig:short_meas_time_domain]].
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#+begin_src matlab :exports none
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figure;
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plot(t, 1e9*x)
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xlabel('Time [s]'); ylabel('Displacement [nm]');
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xlim([0, 100]);
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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/short_meas_time_domain.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:short_meas_time_domain
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#+caption: Time domain measurement with the high sampling rate
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#+RESULTS:
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[[file:figs/short_meas_time_domain.png]]
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The Power Spectral Density of the measured displacement is computed
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#+begin_src matlab
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win = hann(ceil(length(x)/20));
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[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
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#+end_src
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** Obtained Amplitude Spectral Density of the measured displacement
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The computed ASD of the two measurements are combined in Figure [[fig:psd_combined]].
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(f_1(8:end), sqrt(p_1(8:end)), 'k-');
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plot(f_2(8:end), sqrt(p_2(8:end)), 'k-');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
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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/psd_combined.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:psd_combined
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#+caption: Obtained Amplitude Spectral Density of the measured displacement
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#+RESULTS:
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[[file:figs/psd_combined.png]]
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