Add links to sections + tangle matlab files
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@ -52,6 +52,10 @@
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* Introduction
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Several Lookup Tables (LUT) are used for the DCM in order to compensate for *repeatable* errors.
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- Section [[sec:dcm_stepper_lut]]: the stepper motors are calibrated using interferometers.
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- Section [[sec:dcm_attocube_lut]]: the Attocube periodic non-linearities are calibrated using piezoelectric actuators.
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* Stepper Motors Calibration
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/dcm_stepper_lut.m
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@ -270,6 +274,9 @@ for i = 1:length(icepap_steps_output_new)
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end
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#+end_src
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The output motion with both LUT are shown in Figure [[fig:compare_old_new_lut_motion]].
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It is confirmed that the new LUT is the correct one.
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Also, it is interesting to note that the old LUT gives an output motion that is above the ideal one, as was seen during the experiments.
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#+begin_src matlab :exports none
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%% Measured Motion and Idealized Motion
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% Use only middle motion where the LUT is working
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@ -296,7 +303,34 @@ exportFig('figs/compare_old_new_lut_motion.pdf', 'width', 'wide', 'height', 'nor
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#+RESULTS:
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[[file:figs/compare_old_new_lut_motion.png]]
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* Attocube Calibration :noexport:
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* Attocube Calibration
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/dcm_attocube_lut.m
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:END:
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<<sec:dcm_attocube_lut>>
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** Introduction :ignore:
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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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#+begin_src matlab :tangle no :noweb yes
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<<m-init-path>>
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#+end_src
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#+begin_src matlab :eval no :noweb yes
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<<m-init-path-tangle>>
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#+end_src
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#+begin_src matlab :noweb yes
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<<m-init-other>>
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#+end_src
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* Helping Functions :noexport:
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Binary file not shown.
14
matlab/dcm_attocube_lut.m
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14
matlab/dcm_attocube_lut.m
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@ -0,0 +1,14 @@
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(1, 3, 1000);
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202
matlab/dcm_stepper_lut.m
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202
matlab/dcm_stepper_lut.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(1, 3, 1000);
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% Simulation
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% In this section, we suppose that we are in the frame of one fast jack (all transformations are already done), and we wish to create a LUT for one fast jack.
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% Let's say with make a Bragg angle scan between 10deg and 60deg during 100s.
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Fs = 10e3; % Sample Frequency [Hz]
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t = 0:1/Fs:10; % Time vector [s]
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theta = linspace(10, 40, length(t)); % Bragg Angle [deg]
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% The IcePAP steps are following the theoretical formula:
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% \begin{equation}
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% d_z = \frac{d_{\text{off}}}{2 \cos \theta}
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% \end{equation}
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% with $\theta$ the bragg angle and $d_{\text{off}} = 10\,mm$.
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% The motion to follow is then:
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perfect_motion = 10e-3./(2*cos(theta*pi/180)); % Perfect motion [m]
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% And the IcePAP is generated those steps:
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icepap_steps = perfect_motion; % IcePAP steps measured by Speedgoat [m]
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%% Steps as a function of the bragg angle
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figure;
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plot(theta, icepap_steps);
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xlabel('Bragg Angle [deg]'); ylabel('IcePAP Steps [m]');
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% #+name: fig:bragg_angle_icepap_steps_idealized
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% #+caption: IcePAP Steps as a function of the Bragg Angle
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% #+RESULTS:
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% [[file:figs/bragg_angle_icepap_steps_idealized.png]]
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% Then, we are measuring the motion of the Fast Jack using the Interferometer.
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% The motion error is larger than in reality to be angle to see it more easily.
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motion_error = 100e-6*sin(2*pi*perfect_motion/1e-3); % Error motion [m]
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measured_motion = perfect_motion + motion_error; % Measured motion of the Fast Jack [m]
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%% Measured Motion and Idealized Motion
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figure;
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hold on;
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plot(icepap_steps, measured_motion, ...
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'DisplayName', 'Measured Motion');
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plot(icepap_steps, perfect_motion, 'k--', ...
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'DisplayName', 'Ideal Motion');
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hold off;
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xlabel('IcePAP Steps [m]'); ylabel('Measured Motion [m]');
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legend('location', 'southeast');
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% #+name: fig:measured_and_ideal_motion_fast_jacks
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% #+caption: Measured motion as a function of the IcePAP Steps
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% #+RESULTS:
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% [[file:figs/measured_and_ideal_motion_fast_jacks.png]]
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% Let's now compute the lookup table.
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% For each micrometer of the IcePAP step, another step is associated that correspond to a position closer to the wanted position.
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%% Get range for the LUT
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% We correct only in the range of tested/measured motion
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lut_range = round(1e6*min(icepap_steps)):round(1e6*max(icepap_steps)); % IcePAP steps [um]
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%% Initialize the LUT
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lut = zeros(size(lut_range));
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%% For each um in this range
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for i = 1:length(lut_range)
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% Get points indices where the measured motion is closed to the wanted one
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close_points = measured_motion > 1e-6*lut_range(i) - 500e-9 & measured_motion < 1e-6*lut_range(i) + 500e-9;
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% Get the corresponding closest IcePAP step
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lut(i) = round(1e6*mean(icepap_steps(close_points))); % [um]
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end
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%% Generated Lookup Table
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figure;
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plot(lut_range, lut);
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xlabel('IcePAP input step [um]'); ylabel('Lookup Table output [um]');
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% #+name: fig:generated_lut_icepap
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% #+caption: Generated Lookup Table
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% #+RESULTS:
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% [[file:figs/generated_lut_icepap.png]]
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% The current LUT implementation is the following:
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motion_error_lut = zeros(size(lut_range));
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for i = 1:length(lut_range)
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% Get points indices where the icepap step is close to the wanted one
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close_points = icepap_steps > 1e-6*lut_range(i) - 500e-9 & icepap_steps < 1e-6*lut_range(i) + 500e-9;
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% Get the corresponding motion error
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motion_error_lut(i) = lut_range(i) + (lut_range(i) - round(1e6*mean(measured_motion(close_points)))); % [um]
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end
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% Let's compare the two Lookup Table in Figure [[fig:lut_comparison_two_methods]].
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%% Comparison of the two Generated Lookup Table
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figure;
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hold on;
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plot(lut_range, lut, ...
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'DisplayName', 'New LUT');
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plot(lut_range, motion_error_lut, ...
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'DisplayName', 'Old LUT');
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hold off;
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xlabel('IcePAP input step [um]'); ylabel('Lookup Table output [um]');
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legend('location', 'southeast');
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% #+name: fig:lut_comparison_two_methods
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% #+caption: Comparison of the two lookup tables
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% #+RESULTS:
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% [[file:figs/lut_comparison_two_methods.png]]
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% If we plot the "corrected steps" for all steps for both methods, we clearly see the difference (Figure [[fig:lut_correct_and_motion_error]]).
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%% Corrected motion and motion error at each step position
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figure;
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hold on;
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plot(lut_range, lut-lut_range, ...
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'DisplayName', 'New LUT');
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plot(lut_range, motion_error_lut-lut_range, ...
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'DisplayName', 'Old LUT');
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hold off;
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xlabel('IcePAP Steps [um]'); ylabel('Corrected motion [um]');
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ylim([-110, 110])
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legend('location', 'southeast');
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% #+name: fig:lut_correct_and_motion_error
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% #+caption: LUT correction and motion error as a function of the IcePAP steps
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% #+RESULTS:
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% [[file:figs/lut_correct_and_motion_error.png]]
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% Let's now implement both LUT to see which implementation is correct.
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icepap_steps_output_new = lut(round(1e6*icepap_steps)-lut_range(1)+1);
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i = round(1e6*icepap_steps)-motion_error_lut(1)+1;
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i(i>length(motion_error_lut)) = length(motion_error_lut);
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icepap_steps_output_old = motion_error_lut(i);
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motion_new = zeros(size(icepap_steps_output_new));
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motion_old = zeros(size(icepap_steps_output_old));
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for i = 1:length(icepap_steps_output_new)
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[~, i_step] = min(abs(icepap_steps_output_new(i) - 1e6*icepap_steps));
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motion_new(i) = measured_motion(i_step);
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[~, i_step] = min(abs(icepap_steps_output_old(i) - 1e6*icepap_steps));
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motion_old(i) = measured_motion(i_step);
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end
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% The output motion with both LUT are shown in Figure [[fig:compare_old_new_lut_motion]].
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% It is confirmed that the new LUT is the correct one.
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% Also, it is interesting to note that the old LUT gives an output motion that is above the ideal one, as was seen during the experiments.
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%% Measured Motion and Idealized Motion
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% Use only middle motion where the LUT is working
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i = round(0.1*length(icepap_steps)):round(0.9*length(icepap_steps));
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figure;
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hold on;
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plot(icepap_steps(i), motion_new(i), ...
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'DisplayName', 'Motion (new LUT)');
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plot(icepap_steps(i), motion_old(i), ...
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'DisplayName', 'Motion (old LUT)');
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plot(icepap_steps(i), perfect_motion(i), 'k--', ...
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'DisplayName', 'Ideal Motion');
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hold off;
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xlabel('IcePAP Steps [m]'); ylabel('Measured Motion [m]');
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legend('location', 'southeast');
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