@@ -27,46 +35,132 @@
-Table of Contents
-
1 First Measurements
+
+
->
@@ -47,29 +47,116 @@
<>
#+end_src
-** Load Data
-#+begin_src matlab
- load('./mat/long_test.mat', 'x', 't')
- Ts = 1; % [s]
-
- win = hann(ceil(length(x)/10));
- [p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
-#+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/test.mat', 'x', 't')
- Ts = 1e-4; % [s]
-
- win = hann(ceil(length(x)/50));
- [p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
+ 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]]
+
+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)));
- plot(f_2(8:end), sqrt(p_2(8:end)));
+ 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]]
diff --git a/mat/long_test2.mat b/mat/long_test2.mat
new file mode 100755
index 0000000..dd64cd7
Binary files /dev/null and b/mat/long_test2.mat differ
1 Estimation of the Spectral Density of the Attocube Noise
-
1.1 Load Data
+
+
1.1 Long and Slow measurement
-
+
+
-
+load('./mat/long_test.mat', 'x', 't') -Ts = 1; % [s] ++The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\). +
-win = hann(ceil(length(x)/10)); +++ + +load('./mat/long_test2.mat', 'x', 't') +Ts = 0.1; % [s] ++++ ++
+
Figure 1: Long measurement time domain data
++We can see in Figure 1 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
+ +t1andt2. +The obtained displacement is shown in Figure 2. +++ + +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); ++++ ++
+
Figure 2: Kept data (removed slow drifts during the first hours)
++The Power Spectral Density of the measured displacement is computed +
+++win = hann(ceil(length(x)/20)); [p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
+
+
+1.2 Short and Fast measurement
+
+
-win = hann(ceil(length(x)/50));
+
+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. +
load('./mat/test.mat', 'x', 't') Ts = 1e-4; % [s] ++
+The time domain measurement is shown in Figure 3. +
+ + +
+
+
+
+
Figure 3: Time domain measurement with the high sampling rate
++The Power Spectral Density of the measured displacement is computed +
+
+
win = hann(ceil(length(x)/20)); [p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
+
1.3 Obtained Amplitude Spectral Density of the measured displacement
+
+
++The computed ASD of the two measurements are combined in Figure 4. +
+ + +
+
+
+
Figure 4: Obtained Amplitude Spectral Density of the measured displacement
+
-
diff --git a/index.org b/index.org
index ee5af7a..93a3434 100644
--- a/index.org
+++ b/index.org
@@ -37,7 +37,7 @@
#+PROPERTY: header-args:matlab+ :output-dir figs
:END:
-* First Measurements
+* 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)
<Created: 2020-10-29 jeu. 10:06
+Created: 2020-10-29 jeu. 10:41