Add analysis on the effect of LUT on the errors

dcm_lookup_tables.org

@@ -56,7 +56,7 @@ Several Lookup Tables (LUT) are used for the DCM in order to compensate for *rep
 - Section [[sec:dcm_stepper_lut]]: the stepper motors are calibrated using interferometers.
 - Section [[sec:dcm_attocube_lut]]: the Attocube periodic non-linearities are calibrated using piezoelectric actuators.
 
-* Stepper Motors Calibration
+* Stepper Motors
 :PROPERTIES:
 :header-args:matlab+: :tangle matlab/dcm_stepper_lut.m
 :END:
@@ -171,7 +171,7 @@ The measured motion of the fast jacks $[d_{u_r},\ r_{u_h},\ r_d]$ can be compare
 #+RESULTS:
 [[file:figs/block_diagram_lut_stepper.png]]
 
-** TODO Repeatability of the motion                                :noexport:
+** TODO [#A] Repeatability of the motion                           :noexport:
 
 ** Patterns in the Fast Jack motion errors
 In order to understand what should be the "sampling distance" for the lookup table of the stepper motor, we have to analyze the displacement errors induced by the stepper motor.
@@ -188,7 +188,7 @@ ol_drx   = 1e-9*double(h5read('Qutools_test_0001.h5','/33.1/instrument/xtal_111_
 
 ol_t = 1e-6*double(h5read('Qutools_test_0001.h5','/33.1/instrument/time/data')); % Time [s]
 
-ol_ddz   = ol_fj-ol_dz; % Distance Error between crystals [m]
+ol_ddz   = ol_dzw-ol_dz; % Distance Error between crystals [m]
 #+end_src
 
 #+begin_src matlab :exports none
@@ -732,8 +732,159 @@ exportFig('figs/lut_comp_old_new_experiment_zoom.pdf', 'width', 'wide', 'height'
 #+RESULTS:
 [[file:figs/lut_comp_old_new_experiment_zoom.png]]
 
+** Comparison of the errors in the reciprocal length space
+#+begin_src matlab
+%% Load Data of the new LUT method
+ol_bragg = (pi/180)*1e-5*double(h5read('Qutools_test_0001.h5','/33.1/instrument/trajmot/data'));
+ol_dz    = 1e-9*double(h5read('Qutools_test_0001.h5','/33.1/instrument/xtal_111_dz_filter/data'));
+ol_dry   = 1e-9*double(h5read('Qutools_test_0001.h5','/33.1/instrument/xtal_111_dry_filter/data'));
+ol_drx   = 1e-9*double(h5read('Qutools_test_0001.h5','/33.1/instrument/xtal_111_drx_filter/data'));
+ol_dzw   = 10.5e-3./(2*cos(ol_bragg)); % Wanted distance between crystals [m]
+ol_t     = 1e-6*double(h5read('Qutools_test_0001.h5','/33.1/instrument/time/data')); % Time [s]
+ol_ddz   = ol_dzw-ol_dz; % Distance Error between crystals [m]
 
-* Attocube Calibration
+lut_bragg = (pi/180)*1e-5*double(h5read('Qutools_test_0001.h5','/34.1/instrument/trajmot/data'));
+lut_dz    = 1e-9*double(h5read('Qutools_test_0001.h5','/34.1/instrument/xtal_111_dz_filter/data'));
+lut_dry   = 1e-9*double(h5read('Qutools_test_0001.h5','/34.1/instrument/xtal_111_dry_filter/data'));
+lut_drx   = 1e-9*double(h5read('Qutools_test_0001.h5','/34.1/instrument/xtal_111_drx_filter/data'));
+lut_dzw   = 10.5e-3./(2*cos(lut_bragg)); % Wanted distance between crystals [m]
+lut_t     = 1e-6*double(h5read('Qutools_test_0001.h5','/34.1/instrument/time/data')); % Time [s]
+lut_ddz   = lut_dzw-lut_dz; % Distance Error between crystals [m]
+#+end_src
+
+#+begin_src matlab
+%% Compute Fast Jack position errors
+% Jacobian matrix for Fast Jacks and 111 crystal
+J_a_111 = [1,  0.14, -0.1525
+           1,  0.14,  0.0675
+           1, -0.14,  0.0425];
+
+ol_de_111 = [ol_ddz'; ol_dry'; ol_drx'];
+
+% Fast Jack position errors
+ol_de_fj = J_a_111*ol_de_111;
+
+ol_fj_ur = ol_de_fj(1,:);
+ol_fj_uh = ol_de_fj(2,:);
+ol_fj_d  = ol_de_fj(3,:);
+
+lut_de_111 = [lut_ddz'; lut_dry'; lut_drx'];
+
+% Fast Jack position errors
+lut_de_fj = J_a_111*lut_de_111;
+
+lut_fj_ur = lut_de_fj(1,:);
+lut_fj_uh = lut_de_fj(2,:);
+lut_fj_d  = lut_de_fj(3,:);
+#+end_src
+
+#+begin_src matlab
+Xs = 0.1e-6; % Sampling Distance [m]
+
+%% Re-sampled data with uniform spacing [m]
+ol_fj_ur_u = resample(ol_fj_ur, ol_dzw, 1/Xs);
+ol_fj_uh_u = resample(ol_fj_uh, ol_dzw, 1/Xs);
+ol_fj_d_u  = resample(ol_fj_d,  ol_dzw, 1/Xs);
+
+ol_fj_u = Xs*[1:length(ol_fj_ur_u)]; % Sampled Jack Position
+
+% Only take first 500um
+ol_fj_ur_u = ol_fj_ur_u(ol_fj_u<0.5e-3);
+ol_fj_uh_u = ol_fj_uh_u(ol_fj_u<0.5e-3);
+ol_fj_d_u  = ol_fj_d_u (ol_fj_u<0.5e-3);
+ol_fj_u    = ol_fj_u   (ol_fj_u<0.5e-3);
+#+end_src
+
+#+begin_src matlab
+%% Re-sampled data with uniform spacing [m]
+lut_fj_ur_u = resample(lut_fj_ur, lut_dzw, 1/Xs);
+lut_fj_uh_u = resample(lut_fj_uh, lut_dzw, 1/Xs);
+lut_fj_d_u  = resample(lut_fj_d,  lut_dzw, 1/Xs);
+
+lut_fj_u = Xs*[1:length(lut_fj_ur_u)]; % Sampled Jack Position
+
+% Only take first 500um
+lut_fj_ur_u = lut_fj_ur_u(lut_fj_u<0.5e-3);
+lut_fj_uh_u = lut_fj_uh_u(lut_fj_u<0.5e-3);
+lut_fj_d_u  = lut_fj_d_u (lut_fj_u<0.5e-3);
+lut_fj_u    = lut_fj_u   (lut_fj_u<0.5e-3);
+#+end_src
+
+#+begin_src matlab
+% Hanning Windows with 250um width
+win = hanning(floor(400e-6/Xs));
+
+% Power Spectral Density [m2/(1/m)]
+[S_ol_ur, f] = pwelch(ol_fj_ur_u-mean(ol_fj_ur_u), win, 0, [], 1/Xs);
+[S_ol_uh, ~] = pwelch(ol_fj_uh_u-mean(ol_fj_uh_u), win, 0, [], 1/Xs);
+[S_ol_d,  ~] = pwelch(ol_fj_d_u -mean(ol_fj_d_u ), win, 0, [], 1/Xs);
+
+[S_lut_ur, ~] = pwelch(lut_fj_ur_u-mean(lut_fj_ur_u), win, 0, [], 1/Xs);
+[S_lut_uh, ~] = pwelch(lut_fj_uh_u-mean(lut_fj_uh_u), win, 0, [], 1/Xs);
+[S_lut_d,  ~] = pwelch(lut_fj_d_u -mean(lut_fj_d_u ), win, 0, [], 1/Xs);
+#+end_src
+
+As seen in Figure [[fig:effect_lut_on_psd_error_spatial]], the LUT as an effect only on spatial errors with a period of at least few $\mu m$.
+This is very logical considering the $1\,\mu m$ sampling of the LUT in the IcePAP.
+
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(1e6./f, sqrt(S_ol_d) , 'DisplayName', '$u_r$ - OL');
+plot(1e6./f, sqrt(S_lut_d), 'DisplayName', '$u_r$ - LUT');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Spectral Distance [$\mu$m]');
+ylabel('Spectral Content [$\frac{m}{1/\sqrt{m}}$]')
+legend('location', 'northwest');
+xlim([0.5, 200]); ylim([1e-13, 1e-8]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/effect_lut_on_psd_error_spatial.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:effect_lut_on_psd_error_spatial
+#+caption: Effect of the LUT on the spectral content of the positioning errors
+#+RESULTS:
+[[file:figs/effect_lut_on_psd_error_spatial.png]]
+
+Let's now look at it in a cumulative way.
+
+#+begin_src matlab
+CPS_ol_ur = flip(-cumtrapz(flip(f), flip(S_ol_ur)));
+CPS_ol_uh = flip(-cumtrapz(flip(f), flip(S_ol_uh)));
+CPS_ol_d  = flip(-cumtrapz(flip(f), flip(S_ol_d)));
+
+CPS_lut_ur = flip(-cumtrapz(flip(f), flip(S_lut_ur)));
+CPS_lut_uh = flip(-cumtrapz(flip(f), flip(S_lut_uh)));
+CPS_lut_d  = flip(-cumtrapz(flip(f), flip(S_lut_d)));
+#+end_src
+
+#+begin_src matlab :results none
+%% Cumulative Spectrum
+figure;
+hold on;
+plot(1e6./f, sqrt(CPS_ol_ur) , 'DisplayName', '$u_r$ - OL');
+plot(1e6./f, sqrt(CPS_lut_ur), 'DisplayName', '$u_r$ - LUT');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Spectral Distance [$\mu m$]'); ylabel('Cumulative Spectrum [$m$]')
+xlim([1, 500]); ylim([1e-9, 1e-5]);
+legend('location', 'northwest');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/effect_lut_on_cps_error_spatial.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:effect_lut_on_cps_error_spatial
+#+caption: Cumulative Spectrum with and without the LUT
+#+RESULTS:
+[[file:figs/effect_lut_on_cps_error_spatial.png]]
+
+* Metrology Frame Deformations
+* Attocube Periodic Non-Linearity
 :PROPERTIES:
 :header-args:matlab+: :tangle matlab/dcm_attocube_lut.m
 :END: