Add non-repeatability plots

index.org

@@ -2022,7 +2022,7 @@ Multiple measurements are done with different experimental configuration as foll
   hold off;
   set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
   xlabel('Frequency [Hz]');
-  ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$');
+  ylabel('ASD $\left[\frac{1}{\sqrt{Hz}}\right]$');
   legend('location', 'northeast');
   xlim([1, 1000]);
 #+end_src
@@ -3011,7 +3011,9 @@ The controllers can be downloaded [[./mat/K_newport.mat][here]].
 * Measurement of the non-repeatability
 <<sec:non_rep_meas>>
 ** Introduction                                                     :ignore:
-- Explanation of the procedure
+The goal here is the measure the non-repeatability of the setup.
+
+All sources of error (detailed in the budget error in Section [[sec:budget_error]]) will contribute to the non-repeatability of the system.
 
 ** Matlab Init                                              :noexport:ignore:
 #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@@ -3026,7 +3028,7 @@ The controllers can be downloaded [[./mat/K_newport.mat][here]].
   fs = 1e4;
 #+end_src
 
-** Data Load
+** Data Load and pre-processing
 #+begin_src matlab
   uh = load('mat/data_rep_h.mat', ...
        't', 'Uch', 'Ucv', ...
@@ -3083,6 +3085,53 @@ The controllers can be downloaded [[./mat/K_newport.mat][here]].
   uv.t = uv.t - uv.t(1);
 #+end_src
 
+** Some Time domain plots
+#+begin_src matlab :exports none
+  tend = 5; % [s]
+
+  figure;
+  ax1 = subplot(2, 2, 1);
+  hold on;
+  plot(uh.t(1:tend*fs), uh.Unh(1:tend*fs));
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  title('Newport Tilt - Horizontal Direction');
+
+  ax3 = subplot(2, 2, 3);
+  hold on;
+  plot(uh.t(1:tend*fs), 1e9*uh.Va(1:tend*fs));
+  hold off;
+  xlabel('Time [s]'); ylabel('Distance [nm]');
+  title('Attocube - Horizontal Direction');
+
+  ax2 = subplot(2, 2, 2);
+  hold on;
+  plot(uv.t(1:tend*fs), uv.Unv(1:tend*fs));
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  title('Newport Tilt - Vertical Direction');
+
+  ax4 = subplot(2, 2, 4);
+  hold on;
+  plot(uv.t(1:tend*fs), 1e9*uv.Va(1:tend*fs));
+  hold off;
+  xlabel('Time [s]'); ylabel('Distance [nm]');
+  title('Attocube - Vertical Direction');
+
+  linkaxes([ax1,ax2,ax3,ax4],'x');
+  linkaxes([ax1,ax2],'xy');
+  linkaxes([ax3,ax4],'xy');
+#+end_src
+
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/repeat_time_signals.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:repeat_time_signals
+#+CAPTION: Time domain Signals for the repeatability measurement ([[./figs/repeat_time_signals.png][png]], [[./figs/repeat_time_signals.pdf][pdf]])
+[[file:figs/repeat_time_signals.png]]
+
 ** Verify Tracking Angle Error
 Let's verify that the positioning error of the beam is small and what could be the effect on the distance measured by the intereferometer.
 
@@ -3090,7 +3139,7 @@ Let's verify that the positioning error of the beam is small and what could be t
   load('./mat/plant.mat', 'Gd');
 #+end_src
 
-#+begin_src matlab
+#+begin_src matlab :exports none
   figure;
   ax1 = subplot(1, 2, 1);
   hold on;
@@ -3113,6 +3162,15 @@ Let's verify that the positioning error of the beam is small and what could be t
   linkaxes([ax1,ax2],'xy');
 #+end_src
 
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/repeat_tracking_errors.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:repeat_tracking_errors
+#+CAPTION: Tracking errors during the repeatability measurement ([[./figs/repeat_tracking_errors.png][png]], [[./figs/repeat_tracking_errors.pdf][pdf]])
+[[file:figs/repeat_tracking_errors.png]]
+
 Let's compute the PSD of the error to see the frequency content.
 
 #+begin_src matlab
@@ -3148,6 +3206,16 @@ Let's compute the PSD of the error to see the frequency content.
   xlim([1, 1000]);
 #+end_src
 
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/psd_tracking_error_rad.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_tracking_error_rad
+#+CAPTION: Power Spectral Density of the tracking errors ([[./figs/psd_tracking_error_rad.png][png]], [[./figs/psd_tracking_error_rad.pdf][pdf]])
+[[file:figs/psd_tracking_error_rad.png]]
+
+
 Let's convert that to errors in distance
 
 \[ \Delta L = L^\prime - L = \frac{L}{\cos(\alpha)} - L \approx \frac{L \alpha^2}{2} \]
@@ -3167,33 +3235,7 @@ with
   [psd_UvLv, ~] = pwelch(0.5*L*(uv.Vpv/freqresp(Gd(2,2), 0)).^2, hanning(ceil(1*fs)), [], [], fs);
 #+end_src
 
-#+begin_src matlab :exports none
-  figure;
-  ax1 = subplot(1, 2, 1);
-  hold on;
-  plot(f, sqrt(psd_UhLh), 'DisplayName', '$\Gamma_{L_h}$');
-  plot(f, sqrt(psd_UhLv), 'DisplayName', '$\Gamma_{L_v}$');
-  hold off;
-  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$')
-  legend('Location', 'southwest');
-  title('Newport Tilt - Horizontal Direction');
-
-  ax2 = subplot(1, 2, 2);
-  hold on;
-  plot(f, sqrt(psd_UvLh), 'DisplayName', '$\Gamma_{L_h}$');
-  plot(f, sqrt(psd_UvLv), 'DisplayName', '$\Gamma_{L_v}$');
-  hold off;
-  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$')
-  legend('Location', 'southwest');
-  title('Newport Tilt - Vertical Direction');
-
-  linkaxes([ax1,ax2],'xy');
-  xlim([1, 1000]);
-#+end_src
-
-Now, compare that with the PSD of the measured distance by the interferometer.
+Now, compare that with the PSD of the measured distance by the interferometer (Fig. [[fig:compare_tracking_error_attocube_meas]]).
 #+begin_src matlab
   [psd_Lh, f] = pwelch(uh.Va, hanning(ceil(1*fs)), [], [], fs);
   [psd_Lv, ~] = pwelch(uv.Va, hanning(ceil(1*fs)), [], [], fs);
@@ -3227,6 +3269,19 @@ Now, compare that with the PSD of the measured distance by the interferometer.
   xlim([1, 1000]);
 #+end_src
 
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/compare_tracking_error_attocube_meas.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:compare_tracking_error_attocube_meas
+#+CAPTION: Comparison of the effect of tracking error on the measured distance and the measured distance by the Attocube ([[./figs/compare_tracking_error_attocube_meas.png][png]], [[./figs/compare_tracking_error_attocube_meas.pdf][pdf]])
+[[file:figs/compare_tracking_error_attocube_meas.png]]
+
+#+begin_important
+The tracking errors are a limiting factor.
+#+end_important
+
 ** Processing
 First, we get the mean value as measured by the interferometer for each value of the Newport angle.
 #+begin_src matlab
@@ -3252,8 +3307,20 @@ First, we get the mean value as measured by the interferometer for each value of
   plot(Unvm, Vavm)
   hold off;
   xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
+
+  linkaxes([ax1,ax2],'xy');
 #+end_src
 
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/repeat_plot_raw.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:repeat_plot_raw
+#+CAPTION: Repeatability of the measurement ([[./figs/repeat_plot_raw.png][png]], [[./figs/repeat_plot_raw.pdf][pdf]])
+[[file:figs/repeat_plot_raw.png]]
+
+
 #+begin_src matlab :exports none
   figure;
   ax1 = subplot(1, 2, 1);
@@ -3272,93 +3339,11 @@ First, we get the mean value as measured by the interferometer for each value of
   ylim([-100 100]);
 #+end_src
 
-We then subtract
-#+begin_src matlab
-  figure;
-  hold on;
-  plot(uh.Unh, 1e9*(uh.Va - repmat(Vam, length(uh.t)/length(Vam),1)))
-  hold off;
-  xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [nm]');
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/repeat_plot_subtract_mean.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
 #+end_src
 
-** Some Plots
-#+begin_src matlab
-  figure;
-  hold on;
-  plot(uh.Unh, uh.Va);
-  plot(Unhm, Vam)
-  hold off;
-  xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
-#+end_src
-
-#+begin_src matlab :exports none
-  figure;
-  ax1 = subplot(1, 2, 1);
-  hold on;
-  plot(uh.Vnh(1:fs/2), uh.Va(1:fs/2));
-  hold off;
-  xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
-
-  ax2 = subplot(1, 2, 2);
-  hold on;
-  plot(uv.Vnv, uv.Va);
-  hold off;
-  xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
-#+end_src
-
-
-#+begin_src matlab :exports none
-  figure;
-  ax1 = subplot(1, 2, 1);
-  hold on;
-  plot(uh.Vnh, uh.Va);
-  hold off;
-  xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
-
-  ax2 = subplot(1, 2, 2);
-  hold on;
-  plot(uv.Vnv, uv.Va);
-  hold off;
-  xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
-#+end_src
-
-** Repeatability
-#+begin_src matlab :exports none
-  figure;
-  ax1 = subplot(1, 2, 1);
-  hold on;
-  plot(Vnh, Va);
-  hold off;
-  xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
-
-  ax2 = subplot(1, 2, 2);
-  hold on;
-  plot(Vnv, Va);
-  hold off;
-  xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
-#+end_src
-
-
-#+begin_src matlab
-  bh = [ones(size(Vnh)) Vnh]\Vph;
-  bv = [ones(size(Vnv)) Vnv]\Vpv;
-#+end_src
-
-#+begin_src matlab :exports none
-  figure;
-  ax1 = subplot(1, 2, 1);
-  hold on;
-  plot(2*gn0*uh.Vnh, uh.Vph, 'o', 'DisplayName', 'Exp. data');
-  plot(2*gn0*[min(uh.Vnh) max(uh.Vnh)], 2*gn0*[min(uh.Vnh) max(uh.Vnh)].*bh(2) + bh(1), 'k--', 'DisplayName', sprintf('%.1e x + %.1e', bh(2), bh(1)))
-  hold off;
-  xlabel('$\alpha_{0,h}$ [rad]'); ylabel('$Vp_h$ [V]');
-  legend();
-
-  ax2 = subplot(1, 2, 2);
-  hold on;
-  plot(2*gn0*uv.Vnv, uv.Vpv, 'o', 'DisplayName', 'Exp. data');
-  plot(2*gn0*[min(uv.Vnv) max(uv.Vnv)], 2*gn0*[min(uv.Vnv) max(uv.Vnv)].*bv(2) + bv(1), 'k--', 'DisplayName', sprintf('%.1e x + %.1e', bv(2), bv(1)))
-  hold off;
-  xlabel('$\alpha_{0,v}$ [rad]'); ylabel('$Vp_v$ [V]');
-  legend();
-#+end_src
+#+NAME: fig:repeat_plot_subtract_mean
+#+CAPTION: Repeatability of the measurement after subtracting the mean value ([[./figs/repeat_plot_subtract_mean.png][png]], [[./figs/repeat_plot_subtract_mean.pdf][pdf]])
+[[file:figs/repeat_plot_subtract_mean.png]]