From 7a174b630f3f841a5541eb88c0df456c1d1c325a Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 10 Nov 2020 12:51:54 +0100 Subject: [PATCH] Move to matlab folder / tangle / list of sections --- index.html | 181 ++++++++++-------- index.org | 56 +++++- matlab/analyse_data.m | 7 - matlab/attocube_asd_noise.m | 152 +++++++++++++++ matlab/attocube_non_linearity.m | 131 +++++++++++++ matlab/effect_air_protection.m | 73 +++++++ {mat => matlab/mat}/int_enc_comp.mat | Bin {mat => matlab/mat}/long_test_plastic.mat | Bin {mat => matlab/mat}/short_test_alu_tube.mat | Bin {mat => matlab/mat}/short_test_plastic.mat | Bin .../mat}/short_test_without_material.mat | Bin matlab/test_attocube.slx.r2018a | Bin 44399 -> 0 bytes 12 files changed, 503 insertions(+), 97 deletions(-) delete mode 100644 matlab/analyse_data.m create mode 100644 matlab/attocube_asd_noise.m create mode 100644 matlab/attocube_non_linearity.m create mode 100644 matlab/effect_air_protection.m rename {mat => matlab/mat}/int_enc_comp.mat (100%) rename {mat => matlab/mat}/long_test_plastic.mat (100%) rename {mat => matlab/mat}/short_test_alu_tube.mat (100%) rename {mat => matlab/mat}/short_test_plastic.mat (100%) rename {mat => matlab/mat}/short_test_without_material.mat (100%) delete mode 100644 matlab/test_attocube.slx.r2018a diff --git a/index.html b/index.html index 66558ea..13bd718 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Attocube - Test Bench @@ -34,73 +34,84 @@

Table of Contents

-
-

1 Estimation of the Spectral Density of the Attocube Noise

+

+In this document, few caracteristics of the Attocube Displacement Measuring Interferometer IDS3010 (link) are studied: +

+ + +
+

1 Estimation of the Spectral Density of the Attocube Noise

+

+ +

-
+

test-bench-schematic.png

Figure 1: Test Bench Schematic

-
+

IMG-7865.JPG

Figure 2: Picture of the test bench. The Attocube and mirror are covered by a “bubble sheet”

- -
-

1.1 Long and Slow measurement

+
+

1.1 Long and Slow measurement

The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).

-
load('./mat/long_test_plastic.mat', 'x', 't')
+
load('long_test_plastic.mat', 'x', 't')
 Ts = 0.1; % [s]
-
+

long_meas_time_domain_full.png

Figure 3: Long measurement time domain data

-Let’s fit the data with a step response to a first order low pass filter (Figure 4). +Let’s fit the data with a step response to a first order low pass filter (Figure 4).

@@ -124,17 +135,17 @@ The corresponding time constant is (in [h]): -
+

long_meas_time_domain_fit.png

Figure 4: Fit of the measurement data with a step response of a first order low pass filter

-We can see in Figure 3 that there is a transient period where the measured displacement experiences some drifts. +We can see in Figure 3 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 5. +The obtained displacement is shown in Figure 5.

@@ -148,7 +159,7 @@ t = t - t(1);
-
+

long_meas_time_domain_zoom.png

Figure 5: Kept data (removed slow drifts during the first hours)

@@ -183,8 +194,8 @@ f_1 = f_1(f_1 < 2);
-
-

1.2 Short and Fast measurement

+
+

1.2 Short and Fast measurement

An second measurement is done in order to estimate the high frequency noise of the interferometer. @@ -192,7 +203,7 @@ The measurement is done with a sampling time of \(T_s = 0.1\,ms\) and a duration

-
load('./mat/short_test_plastic.mat')
+
load('short_test_plastic.mat')
 Ts = 1e-4; % [s]
@@ -203,11 +214,11 @@ Ts = 1e-4; % [s]

-The time domain measurement is shown in Figure 6. +The time domain measurement is shown in Figure 6.

-
+

short_meas_time_domain.png

Figure 6: Time domain measurement with the high sampling rate

@@ -224,15 +235,15 @@ The Power Spectral Density of the measured displacement is computed
-
-

1.3 Obtained Amplitude Spectral Density of the measured displacement

+
+

1.3 Obtained Amplitude Spectral Density of the measured displacement

-The computed ASD of the two measurements are combined in Figure 7. +The computed ASD of the two measurements are combined in Figure 7.

-
+

psd_combined.png

Figure 7: Obtained Amplitude Spectral Density of the measured displacement

@@ -241,22 +252,24 @@ The computed ASD of the two measurements are combined in Figure -

2 Effect of the “bubble sheet” and “Aluminium tube”

+
+

2 Effect of the “bubble sheet” and “Aluminium tube”

+

+ +

-
+

IMG-7864.JPG

Figure 8: Aluminium tube used to protect the beam path from disturbances

- -
-

2.1 Aluminium Tube and Bubble Sheet

+
+

2.1 Aluminium Tube and Bubble Sheet

-
load('./mat/short_test_plastic.mat');
+
load('short_test_plastic.mat');
 Ts = 1e-4; % [s]
@@ -274,11 +287,11 @@ Ts = 1e-4; % [s]
-
-

2.2 Only Aluminium Tube

+
+

2.2 Only Aluminium Tube

-
load('./mat/short_test_alu_tube.mat');
+
load('short_test_alu_tube.mat');
 Ts = 1e-4; % [s]
@@ -289,7 +302,7 @@ Ts = 1e-4; % [s]

-The time domain measurement is shown in Figure 6. +The time domain measurement is shown in Figure 6. 

win = hann(ceil(length(x)/10));
@@ -299,11 +312,11 @@ The time domain measurement is shown in Figure 6.
-
-

2.3 Nothing

+
+

2.3 Nothing

-
load('./mat/short_test_without_material.mat');
+
load('short_test_without_material.mat');
 Ts = 1e-4; % [s]
@@ -314,7 +327,7 @@ Ts = 1e-4; % [s]

-The time domain measurement is shown in Figure 6. +The time domain measurement is shown in Figure 6. 

win = hann(ceil(length(x)/10));
@@ -324,11 +337,11 @@ The time domain measurement is shown in Figure 6.
-
-

2.4 Comparison

+
+

2.4 Comparison

-
+

asd_noise_comp_bubble_aluminium.png

Figure 9: Comparison of the noise ASD with and without bubble sheet

@@ -337,14 +350,17 @@ The time domain measurement is shown in Figure 6.
-
-

3 Measurement of the Attocube’s non-linearity

+
+

3 Measurement of the Attocube’s non-linearity

-The measurement setup is shown in Figure 10. + +

+

+The measurement setup is shown in Figure 10.

-
+

Here are the equipment used in the test bench:

@@ -359,7 +375,7 @@ Here are the equipment used in the test bench:
-
+

exp_setup_schematic.png

Figure 10: Schematic of the Experiment

@@ -374,16 +390,15 @@ The encoder and the attocube are measure ring the same motion. As will be shown shortly, this measurement permitted to measure the period non-linearity of the Attocube.

- -
-

3.1 Load Data

+
+

3.1 Load Data

The measurement data are loaded and the offset are removed using the detrend command.

-
load('mat/int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't');
+
load('int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't');
 Ts = 1e-4; % Sampling Time [s]
@@ -397,11 +412,11 @@ u = detrend(u, 0);
-
-

3.2 Time Domain Results

+
+

3.2 Time Domain Results

-One period of the displacement of the mass as measured by the encoder and interferometer are shown in Figure 11. +One period of the displacement of the mass as measured by the encoder and interferometer are shown in Figure 11. It consist of the sinusoidal motion at 0.5Hz with an amplitude of approximately \(70\mu m\).

@@ -411,18 +426,18 @@ This should improve the coherence between the measurements made by the encoder a

-
+

int_enc_one_cycle.png

Figure 11: One cycle measurement

-The difference between the two measurements during the same period is shown in Figure 12. +The difference between the two measurements during the same period is shown in Figure 12.

-
+

int_enc_one_cycle_error.png

Figure 12: Difference between the Encoder and the interferometer during one cycle

@@ -430,8 +445,8 @@ The difference between the two measurements during the same period is shown in F
-
-

3.3 Difference between Encoder and Interferometer as a function of time

+
+

3.3 Difference between Encoder and Interferometer as a function of time

The data is filtered using a second order low pass filter with a cut-off frequency \(\omega_0\) as defined below. @@ -446,7 +461,7 @@ G_lpf = 1/(1 + 2

-After filtering, the data is “re-shaped” such that we can superimpose all the measured periods as shown in Figure 13. +After filtering, the data is “re-shaped” such that we can superimpose all the measured periods as shown in Figure 13. This gives an idea of the measurement error as given by the Attocube during a \(70 \mu m\) motion.

@@ -456,7 +471,7 @@ d_err_mean = d_err_mean - mean(d_err_mean);
-
+

int_enc_error_mean_time.png

Figure 13: Difference between the two measurement in the time domain, averaged for all the cycles

@@ -464,17 +479,17 @@ d_err_mean = d_err_mean - mean(d_err_mean);
-
-

3.4 Difference between Encoder and Interferometer as a function of position

+
+

3.4 Difference between Encoder and Interferometer as a function of position

-Figure 13 gives the measurement error as a function of time. +Figure 13 gives the measurement error as a function of time. We here wish the compute this measurement error as a function of the position (as measured by the encoer).

To do so, all the attocube measurements corresponding to each position measured by the Encoder (resolution of \(1nm\)) are averaged. -Figure 14 is obtained where we clearly see an error with a period comparable to the motion range and a much smaller period corresponding to the non-linear period errors that we wish the estimate. +Figure 14 is obtained where we clearly see an error with a period comparable to the motion range and a much smaller period corresponding to the non-linear period errors that we wish the estimate. 

[e_sorted, ~, e_ind] = unique(encoder);
@@ -489,7 +504,7 @@ i_mean_error = (i_mean - e_sorted);
-
+

int_enc_error_mean_position.png

Figure 14: Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles

@@ -511,11 +526,11 @@ e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init15. +The obtained periodic non-linearity is shown in Figure 15.

-
+

int_non_linearity_period_wavelength.png

Figure 15: Non-Linearity of the Interferometer over the period of the wavelength

@@ -526,7 +541,7 @@ The obtained periodic non-linearity is shown in Figure 15<

Author: Dehaeze Thomas

-

Created: 2020-11-10 mar. 10:21

+

Created: 2020-11-10 mar. 12:50

diff --git a/index.org b/index.org index 0a1df84..ebff8b8 100644 --- a/index.org +++ b/index.org @@ -15,7 +15,6 @@ #+HTML_HEAD: #+PROPERTY: header-args:matlab :session *MATLAB* -#+PROPERTY: header-args:matlab+ :tangle no #+PROPERTY: header-args:matlab+ :comments org #+PROPERTY: header-args:matlab+ :exports both #+PROPERTY: header-args:matlab+ :results none @@ -25,7 +24,18 @@ #+PROPERTY: header-args:matlab+ :output-dir figs :END: +* Introduction :ignore: + +In this document, few caracteristics of the Attocube Displacement Measuring Interferometer IDS3010 ([[https://www.attocube.com/en/products/laser-displacement-sensor/displacement-measuring-interferometer][link]]) are studied: +- Section [[sec:attocube_asd_noise]]: the ASD noise of the measured displacement is estimated +- Section [[sec:effect_air_protection]]: the effect of two air protections on the stability of the measurement is studied +- Section [[sec:attocube_non_linearity]]: the cyclic non-linearity of the attocube is estimated using a encoder + * Estimation of the Spectral Density of the Attocube Noise +:PROPERTIES: +:header-args:matlab+: :tangle matlab/attocube_asd_noise.m +:END: +<> ** Introduction :ignore: #+name: fig:test-bench-schematic @@ -46,11 +56,19 @@ <> #+end_src +#+begin_src matlab :tangle no + addpath('./matlab/mat/'); +#+end_src + +#+begin_src matlab :eval no + addpath('./mat/'); +#+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_test_plastic.mat', 'x', 't') + load('long_test_plastic.mat', 'x', 't') Ts = 0.1; % [s] #+end_src @@ -162,7 +180,7 @@ An second measurement is done in order to estimate the high frequency noise of t The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s. #+begin_src matlab - load('./mat/short_test_plastic.mat') + load('short_test_plastic.mat') Ts = 1e-4; % [s] #+end_src @@ -217,6 +235,10 @@ The computed ASD of the two measurements are combined in Figure [[fig:psd_combin [[file:figs/psd_combined.png]] * Effect of the "bubble sheet" and "Aluminium tube" +:PROPERTIES: +:header-args:matlab+: :tangle matlab/effect_air_protection.m +:END: +<> ** Introduction :ignore: #+name: fig:picture-test-bench-aluminium-tube @@ -233,9 +255,17 @@ The computed ASD of the two measurements are combined in Figure [[fig:psd_combin <> #+end_src +#+begin_src matlab :tangle no + addpath('./matlab/mat/'); +#+end_src + +#+begin_src matlab :eval no + addpath('./mat/'); +#+end_src + ** Aluminium Tube and Bubble Sheet #+begin_src matlab - load('./mat/short_test_plastic.mat'); + load('short_test_plastic.mat'); Ts = 1e-4; % [s] #+end_src @@ -256,7 +286,7 @@ The computed ASD of the two measurements are combined in Figure [[fig:psd_combin ** Only Aluminium Tube #+begin_src matlab - load('./mat/short_test_alu_tube.mat'); + load('short_test_alu_tube.mat'); Ts = 1e-4; % [s] #+end_src @@ -278,7 +308,7 @@ The time domain measurement is shown in Figure [[fig:short_meas_time_domain]]. ** Nothing #+begin_src matlab - load('./mat/short_test_without_material.mat'); + load('short_test_without_material.mat'); Ts = 1e-4; % [s] #+end_src @@ -325,6 +355,10 @@ The time domain measurement is shown in Figure [[fig:short_meas_time_domain]]. [[file:figs/asd_noise_comp_bubble_aluminium.png]] * Measurement of the Attocube's non-linearity +:PROPERTIES: +:header-args:matlab+: :tangle matlab/attocube_non_linearity.m +:END: +<> ** Introduction :ignore: The measurement setup is shown in Figure [[fig:exp_setup_schematic]]. @@ -355,11 +389,19 @@ As will be shown shortly, this measurement permitted to measure the period non-l <> #+end_src +#+begin_src matlab :tangle no + addpath('./matlab/mat/'); +#+end_src + +#+begin_src matlab :eval no + addpath('./mat/'); +#+end_src + ** Load Data The measurement data are loaded and the offset are removed using the =detrend= command. #+begin_src matlab - load('mat/int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't'); + load('int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't'); Ts = 1e-4; % Sampling Time [s] #+end_src diff --git a/matlab/analyse_data.m b/matlab/analyse_data.m deleted file mode 100644 index 0a0e838..0000000 --- a/matlab/analyse_data.m +++ /dev/null @@ -1,7 +0,0 @@ -load('./mat/test.mat', 't', 'x'); - -figure; plot(t, x) - -load('./mat/long_test.mat', 't', 'x'); - -figure; plot(t/60/60, 1e9*x) \ No newline at end of file diff --git a/matlab/attocube_asd_noise.m b/matlab/attocube_asd_noise.m new file mode 100644 index 0000000..0e4cbbd --- /dev/null +++ b/matlab/attocube_asd_noise.m @@ -0,0 +1,152 @@ +%% Clear Workspace and Close figures +clear; close all; clc; + +%% Intialize Laplace variable +s = zpk('s'); + +addpath('./mat/'); + +% Long and Slow measurement +% The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$. + + +load('long_test_plastic.mat', 'x', 't') +Ts = 0.1; % [s] + +figure; +plot(t/60/60, 1e9*x) +xlim([0, 17.5]); +xlabel('Time [h]'); ylabel('Displacement [nm]'); + + + +% #+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]]). + + +f = @(b,x) b(1)*(1 - exp(-x/b(2))); + +y_cur = x(t < 17.5*60*60); +t_cur = t(t < 17.5*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’ + + + +% The corresponding time constant is (in [h]): + +B(2)/60/60 + + + +% #+RESULTS: +% : 2.0658 + + +figure; +hold on; +plot(t_cur/60/60, 1e9*y_cur); +plot(t_cur/60/60, 1e9*f(B, t_cur)); +hold off; +xlim([0, 17.5]) +xlabel('Time [h]'); ylabel('Displacement [nm]'); + + + +% #+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]]. + + +t1 = 10.5; t2 = 17.5; % [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; +plot(t/60/60, 1e9*x); +xlabel('Time [h]'); ylabel('Measured Displacement [nm]') + + + +% #+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 + +win = hann(ceil(length(x)/20)); +[p_1, f_1] = pwelch(x, win, [], [], 1/Ts); + + + +% As a low pass filter was used in the measurement process, we multiply the PSD by the square of the inverse of the filter's norm. + +G_lpf = 1/(1 + s/2/pi); +p_1 = p_1./abs(squeeze(freqresp(G_lpf, f_1, 'Hz'))).^2; + + + +% Only frequencies below 2Hz are taken into account (high frequency noise will be measured afterwards). + +p_1 = p_1(f_1 < 2); +f_1 = f_1(f_1 < 2); + +% 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. + + +load('short_test_plastic.mat') +Ts = 1e-4; % [s] + +x = detrend(x, 0); + + + +% The time domain measurement is shown in Figure [[fig:short_meas_time_domain]]. + + +figure; +plot(t, 1e9*x) +xlabel('Time [s]'); ylabel('Displacement [nm]'); + + + +% #+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 + +win = hann(ceil(length(x)/20)); +[p_2, f_2] = pwelch(x, win, [], [], 1/Ts); + +% Obtained Amplitude Spectral Density of the measured displacement + +% The computed ASD of the two measurements are combined in Figure [[fig:psd_combined]]. + + +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]'); diff --git a/matlab/attocube_non_linearity.m b/matlab/attocube_non_linearity.m new file mode 100644 index 0000000..7943149 --- /dev/null +++ b/matlab/attocube_non_linearity.m @@ -0,0 +1,131 @@ +%% Clear Workspace and Close figures +clear; close all; clc; + +%% Intialize Laplace variable +s = zpk('s'); + +addpath('./mat/'); + +% Load Data +% The measurement data are loaded and the offset are removed using the =detrend= command. + + +load('int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't'); +Ts = 1e-4; % Sampling Time [s] + +interferometer = detrend(interferometer, 0); +encoder = detrend(encoder, 0); +u = detrend(u, 0); + +% Time Domain Results +% One period of the displacement of the mass as measured by the encoder and interferometer are shown in Figure [[fig:int_enc_one_cycle]]. +% It consist of the sinusoidal motion at 0.5Hz with an amplitude of approximately $70\mu m$. + +% The frequency of the motion is chosen such that no resonance in the system is excited. +% This should improve the coherence between the measurements made by the encoder and interferometer. + + +figure; +hold on; +plot(t, encoder, '-', 'DisplayName', 'Encoder') +plot(t, interferometer, '--', 'DisplayName', 'Interferometer') +hold off; +xlabel('Time [s]'); ylabel('Displacement [m]'); +legend('location', 'southeast'); +xlim([50, 52]) + + + +% #+name: fig:int_enc_one_cycle +% #+caption: One cycle measurement +% #+RESULTS: +% [[file:figs/int_enc_one_cycle.png]] + +% The difference between the two measurements during the same period is shown in Figure [[fig:int_enc_one_cycle_error]]. + + +figure; +hold on; +plot(t, encoder - interferometer, 'DisplayName', 'Difference') +hold off; +xlabel('Time [s]'); ylabel('Displacement [m]'); +legend('location', 'northeast'); +xlim([50, 52]) + +% Difference between Encoder and Interferometer as a function of time +% The data is filtered using a second order low pass filter with a cut-off frequency $\omega_0$ as defined below. + + +w0 = 2*pi*5; % [rad/s] +xi = 0.7; + +G_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2); + + + +% After filtering, the data is "re-shaped" such that we can superimpose all the measured periods as shown in Figure [[fig:int_enc_error_mean_time]]. +% This gives an idea of the measurement error as given by the Attocube during a $70 \mu m$ motion. + +d_err_mean = reshape(lsim(G_lpf, encoder - interferometer, t), [2/Ts floor(Ts/2*length(encoder))]); +d_err_mean = d_err_mean - mean(d_err_mean); + +figure; +hold on; +for i_i = 1:size(d_err_mean, 2) + plot(t(1:size(d_err_mean, 1)), d_err_mean(:, i_i), 'k-') +end +plot(t(1:size(d_err_mean, 1)), mean(d_err_mean, 2), 'r-') +hold off; +xlabel('Time [s]'); ylabel('Displacement [m]'); + +% Difference between Encoder and Interferometer as a function of position +% Figure [[fig:int_enc_error_mean_time]] gives the measurement error as a function of time. +% We here wish the compute this measurement error as a function of the position (as measured by the encoer). + +% To do so, all the attocube measurements corresponding to each position measured by the Encoder (resolution of $1nm$) are averaged. +% Figure [[fig:int_enc_error_mean_position]] is obtained where we clearly see an error with a period comparable to the motion range and a much smaller period corresponding to the non-linear period errors that we wish the estimate. + +[e_sorted, ~, e_ind] = unique(encoder); + +i_mean = zeros(length(e_sorted), 1); +for i = 1:length(e_sorted) + i_mean(i) = mean(interferometer(e_ind == i)); +end + +i_mean_error = (i_mean - e_sorted); + +figure; +hold on; +% plot(encoder, interferometer - encoder, 'k.', 'DisplayName', 'Difference') +plot(1e6*(e_sorted), 1e9*(i_mean_error)) +hold off; +xlabel('Encoder Measurement [$\mu m$]'); ylabel('Measrement Error [nm]'); + + + +% #+name: fig:int_enc_error_mean_position +% #+caption: Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles +% #+RESULTS: +% [[file:figs/int_enc_error_mean_position.png]] + +% The period of the non-linearity seems to be equal to $765 nm$ which corresponds to half the wavelength of the Laser ($1.53 \mu m$). +% For the motion range done here, the non-linearity is measured over ~18 periods which permits to do some averaging. + + +win_length = 1530/2; % length of the windows (corresponds to 765 nm) +num_avg = floor(length(e_sorted)/win_length); % number of averaging + +i_init = ceil((length(e_sorted) - win_length*num_avg)/2); % does not start at the extremity + +e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init:i_init+win_length*num_avg-1), [win_length num_avg]), 2); + + + +% The obtained periodic non-linearity is shown in Figure [[fig:int_non_linearity_period_wavelength]]. + + +figure; +hold on; +plot(1e-3*(0:win_length-1), 1e9*(e_sorted_mean_over_period)) +hold off; +xlabel('Displacement [$\mu m$]'); ylabel('Measurement Non-Linearity [nm]'); diff --git a/matlab/effect_air_protection.m b/matlab/effect_air_protection.m new file mode 100644 index 0000000..08f965f --- /dev/null +++ b/matlab/effect_air_protection.m @@ -0,0 +1,73 @@ +%% Clear Workspace and Close figures +clear; close all; clc; + +%% Intialize Laplace variable +s = zpk('s'); + +addpath('./mat/'); + +% Aluminium Tube and Bubble Sheet + +load('short_test_plastic.mat'); +Ts = 1e-4; % [s] + +x = detrend(x, 0); + +figure; +plot(t, 1e9*x) +xlabel('Time [s]'); ylabel('Displacement [nm]'); + +win = hann(ceil(length(x)/10)); +[p_1, f_1] = pwelch(x, win, [], [], 1/Ts); + +% Only Aluminium Tube + +load('short_test_alu_tube.mat'); +Ts = 1e-4; % [s] + +x = detrend(x, 0); + + + +% The time domain measurement is shown in Figure [[fig:short_meas_time_domain]]. + +figure; +plot(t, 1e9*x) +xlabel('Time [s]'); ylabel('Displacement [nm]'); + +win = hann(ceil(length(x)/10)); +[p_2, f_2] = pwelch(x, win, [], [], 1/Ts); + +% Nothing + +load('short_test_without_material.mat'); +Ts = 1e-4; % [s] + +x = detrend(x, 0); + + + +% The time domain measurement is shown in Figure [[fig:short_meas_time_domain]]. + +figure; +plot(t, 1e9*x) +xlabel('Time [s]'); ylabel('Displacement [nm]'); + +win = hann(ceil(length(x)/10)); +[p_3, f_3] = pwelch(x, win, [], [], 1/Ts); + +% Comparison + +figure; +hold on; +plot(f_1(8:end), sqrt(p_1(8:end)), '-', ... + 'DisplayName', 'Alunimium + Bubble'); +plot(f_2(8:end), sqrt(p_2(8:end)), '-', ... + 'DisplayName', 'Aluminium'); +plot(f_3(8:end), sqrt(p_3(8:end)), '-', ... + 'DisplayName', 'nothing'); +hold off; +set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log'); +ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]'); +xlim([1e-1, 5e3]); +legend('location', 'northeast'); diff --git a/mat/int_enc_comp.mat b/matlab/mat/int_enc_comp.mat similarity index 100% rename from mat/int_enc_comp.mat rename to matlab/mat/int_enc_comp.mat diff --git a/mat/long_test_plastic.mat b/matlab/mat/long_test_plastic.mat similarity index 100% rename from mat/long_test_plastic.mat rename to matlab/mat/long_test_plastic.mat diff --git a/mat/short_test_alu_tube.mat b/matlab/mat/short_test_alu_tube.mat similarity index 100% rename from mat/short_test_alu_tube.mat rename to matlab/mat/short_test_alu_tube.mat diff --git a/mat/short_test_plastic.mat b/matlab/mat/short_test_plastic.mat similarity index 100% rename from mat/short_test_plastic.mat rename to matlab/mat/short_test_plastic.mat diff --git a/mat/short_test_without_material.mat b/matlab/mat/short_test_without_material.mat similarity index 100% rename from mat/short_test_without_material.mat rename to matlab/mat/short_test_without_material.mat diff --git a/matlab/test_attocube.slx.r2018a b/matlab/test_attocube.slx.r2018a deleted file mode 100644 index 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