202 lines
6.7 KiB
Org Mode
202 lines
6.7 KiB
Org Mode
#+TITLE: Attocube - Test Bench
|
||
:DRAWER:
|
||
#+LANGUAGE: en
|
||
#+EMAIL: dehaeze.thomas@gmail.com
|
||
#+AUTHOR: Dehaeze Thomas
|
||
|
||
#+HTML_LINK_HOME: ../index.html
|
||
#+HTML_LINK_UP: ../index.html
|
||
|
||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
|
||
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
|
||
#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
|
||
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
|
||
#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
|
||
|
||
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
|
||
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
||
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
||
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
|
||
#+PROPERTY: header-args:latex+ :eval no-export
|
||
#+PROPERTY: header-args:latex+ :exports both
|
||
#+PROPERTY: header-args:latex+ :mkdirp yes
|
||
#+PROPERTY: header-args:latex+ :output-dir figs
|
||
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
|
||
|
||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||
#+PROPERTY: header-args:matlab+ :tangle script.m
|
||
#+PROPERTY: header-args:matlab+ :comments org
|
||
#+PROPERTY: header-args:matlab+ :exports both
|
||
#+PROPERTY: header-args:matlab+ :results none
|
||
#+PROPERTY: header-args:matlab+ :eval no-export
|
||
#+PROPERTY: header-args:matlab+ :noweb yes
|
||
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||
:END:
|
||
|
||
* Estimation of the Spectral Density of the Attocube Noise
|
||
** Matlab Init :noexport:ignore:
|
||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||
<<matlab-dir>>
|
||
#+end_src
|
||
|
||
#+begin_src matlab :exports none :results silent :noweb yes
|
||
<<matlab-init>>
|
||
#+end_src
|
||
|
||
** Long and Slow measurement
|
||
The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$.
|
||
|
||
#+begin_src matlab
|
||
load('./mat/long_test2.mat', 'x', 't')
|
||
Ts = 0.1; % [s]
|
||
#+end_src
|
||
|
||
#+begin_src matlab :exports none
|
||
figure;
|
||
plot(t/60/60, 1e9*x)
|
||
xlabel('Time [h]'); ylabel('Displacement [nm]');
|
||
#+end_src
|
||
|
||
#+begin_src matlab :tangle no :exports results :results file replace
|
||
exportFig('figs/long_meas_time_domain_full.pdf', 'width', 'wide', 'height', 'normal');
|
||
#+end_src
|
||
|
||
#+name: fig:long_meas_time_domain_full
|
||
#+caption: Long measurement time domain data
|
||
#+RESULTS:
|
||
[[file:figs/long_meas_time_domain_full.png]]
|
||
|
||
Let's fit the data with a step response to a first order low pass filter (Figure [[fig:long_meas_time_domain_fit]]).
|
||
|
||
#+begin_src matlab
|
||
f = @(b,x) b(1)*(1 - exp(-x/b(2)));
|
||
|
||
y_cur = x(t < 17*60*60);
|
||
t_cur = t(t < 17*60*60);
|
||
|
||
nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
|
||
B0 = [400e-9, 2*60*60]; % Choose Appropriate Initial Estimates
|
||
[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
|
||
#+end_src
|
||
|
||
The corresponding time constant is (in [h]):
|
||
#+begin_src matlab :results value replace :exports results
|
||
B(2)/60/60
|
||
#+end_src
|
||
|
||
#+RESULTS:
|
||
: 2.0576
|
||
|
||
#+begin_src matlab :exports none
|
||
figure;
|
||
hold on;
|
||
plot(t_cur/60/60, 1e9*y_cur);
|
||
plot(t_cur/60/60, 1e9*f(B, t_cur));
|
||
hold off;
|
||
xlabel('Time [h]'); ylabel('Displacement [nm]');
|
||
#+end_src
|
||
|
||
#+begin_src matlab :tangle no :exports results :results file replace
|
||
exportFig('figs/long_meas_time_domain_fit.pdf', 'width', 'wide', 'height', 'normal');
|
||
#+end_src
|
||
|
||
#+name: fig:long_meas_time_domain_fit
|
||
#+caption: Fit of the measurement data with a step response of a first order low pass filter
|
||
#+RESULTS:
|
||
[[file:figs/long_meas_time_domain_fit.png]]
|
||
|
||
We can see in Figure [[fig:long_meas_time_domain_full]] that there is a transient period where the measured displacement experiences some drifts.
|
||
This is probably due to thermal effects.
|
||
We only select the data between =t1= and =t2=.
|
||
The obtained displacement is shown in Figure [[fig:long_meas_time_domain_zoom]].
|
||
|
||
#+begin_src matlab
|
||
t1 = 11; t2 = 17; % [h]
|
||
|
||
x = x(t > t1*60*60 & t < t2*60*60);
|
||
x = x - mean(x);
|
||
t = t(t > t1*60*60 & t < t2*60*60);
|
||
t = t - t(1);
|
||
#+end_src
|
||
|
||
#+begin_src matlab :exports none
|
||
figure;
|
||
plot(t/60/60, 1e9*x);
|
||
xlabel('Time [h]'); ylabel('Measured Displacement [nm]')
|
||
#+end_src
|
||
|
||
#+begin_src matlab :tangle no :exports results :results file replace
|
||
exportFig('figs/long_meas_time_domain_zoom.pdf', 'width', 'wide', 'height', 'normal');
|
||
#+end_src
|
||
|
||
#+name: fig:long_meas_time_domain_zoom
|
||
#+caption: Kept data (removed slow drifts during the first hours)
|
||
#+RESULTS:
|
||
[[file:figs/long_meas_time_domain_zoom.png]]
|
||
|
||
The Power Spectral Density of the measured displacement is computed
|
||
#+begin_src matlab
|
||
win = hann(ceil(length(x)/20));
|
||
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
|
||
#+end_src
|
||
|
||
** Short and Fast measurement
|
||
An second measurement is done in order to estimate the high frequency noise of the interferometer.
|
||
The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s.
|
||
|
||
#+begin_src matlab
|
||
load('./mat/test.mat', 'x', 't')
|
||
Ts = 1e-4; % [s]
|
||
#+end_src
|
||
|
||
The time domain measurement is shown in Figure [[fig:short_meas_time_domain]].
|
||
|
||
#+begin_src matlab :exports none
|
||
figure;
|
||
plot(t, 1e9*x)
|
||
xlabel('Time [s]'); ylabel('Displacement [nm]');
|
||
xlim([0, 100]);
|
||
#+end_src
|
||
|
||
#+begin_src matlab :tangle no :exports results :results file replace
|
||
exportFig('figs/short_meas_time_domain.pdf', 'width', 'wide', 'height', 'normal');
|
||
#+end_src
|
||
|
||
#+name: fig:short_meas_time_domain
|
||
#+caption: Time domain measurement with the high sampling rate
|
||
#+RESULTS:
|
||
[[file:figs/short_meas_time_domain.png]]
|
||
|
||
The Power Spectral Density of the measured displacement is computed
|
||
#+begin_src matlab
|
||
win = hann(ceil(length(x)/20));
|
||
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
|
||
#+end_src
|
||
|
||
** Obtained Amplitude Spectral Density of the measured displacement
|
||
|
||
The computed ASD of the two measurements are combined in Figure [[fig:psd_combined]].
|
||
|
||
#+begin_src matlab :exports none
|
||
figure;
|
||
hold on;
|
||
plot(f_1(8:end), sqrt(p_1(8:end)), 'k-');
|
||
plot(f_2(8:end), sqrt(p_2(8:end)), 'k-');
|
||
hold off;
|
||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
|
||
#+end_src
|
||
|
||
#+begin_src matlab :tangle no :exports results :results file replace
|
||
exportFig('figs/psd_combined.pdf', 'width', 'wide', 'height', 'tall');
|
||
#+end_src
|
||
|
||
#+name: fig:psd_combined
|
||
#+caption: Obtained Amplitude Spectral Density of the measured displacement
|
||
#+RESULTS:
|
||
[[file:figs/psd_combined.png]]
|